(* ::Package:: *)

<|"group.exists_list_of_mem_closure" -> "algebra", "lt_add_one" -> "algebra", "differentiable_at.smul_const" -> "analysis", "tangent_bundle_proj_open" -> "geometry", "tactic.ring_exp.mul_pp_pf_overlap" -> "tactic", "eq_ff_of_not_eq_tt" -> "init", "equiv.of_injective_apply" -> "data", "times_cont_diff.differentiable" -> "analysis", "nat.elim_zero" -> "computability", "simple_graph.adj_iff_exists_edge" -> "combinatorics", "int.lt_of_le_sub_one" -> "init", "multiset.card_eq_zero" -> "data", "filter.eventually_bot" -> "order", "pow_eq_zero" -> "algebra", "valuation.self_le_supp_comap" -> "algebra", "map_cluster_pt_iff" -> "topology", "hyperreal.is_st_st'" -> "data", "list.append_inj'" -> "data", "set.mem_diff_of_mem" -> "data", "matrix.dot_product_assoc" -> "data", "is_scalar_tower.algebra.ext" -> "algebra", "int.neg_le_sub_left_of_le_add" -> "init", "finset.filter_inter" -> "data", "list.lookup_all_cons_eq" -> "data", "linear_equiv.of_injective_apply" -> "algebra", "continuous_linear_map.extend_zero" -> "analysis", "norm_sub_square_eq_norm_square_add_norm_square_iff_inner_eq_zero" -> "analysis", "turing.partrec_to_TM2.tr_pos_num_nat_end" -> "computability", "algebra.adjoin_singleton_eq_range" -> "algebra", "primrec.nat_elim\:2081" -> "computability", "function.sometimes_spec" -> "logic", "mem_image_univ_iff_mem_range" -> "data", "inf_eq_min" -> "order", "category_theory.comonad.coalgebra.hom.comp_f" -> "category_theory", "list.not_mem_of_count_eq_zero" -> "data", "list.chain'.cons" -> "data", "pnat.xgcd_type.reduce_reduced'" -> "data", "tensor_product.tmul_sum" -> "algebra", "polynomial.monic.next_coeff_mul" -> "data", "algebra.tensor_product.comm_tmul" -> "algebra", "zmod.exists_pow_two_eq_two_iff" -> "number_theory", "free_add_semigroup.add_bind" -> "algebra", "list.nil_bag_inter" -> "data", "has_fderiv_within_at.union" -> "analysis", "computation.get_think" -> "data", "category_theory.limits.limit.pre_pre" -> "category_theory", "finset.sum_range_eq_sum_fin" -> "data", "set.union_inter_cancel_right" -> "data", "turing.tape.move_right_mk'" -> "computability", "polynomial.mul_div_by_monic_eq_iff_is_root" -> "data", "category_theory.limits.biproduct.total" -> "category_theory", "lie_algebra.equiv.coe_to_linear_equiv" -> "algebra", "heq_of_eq_rec_left" -> "init", "int.sub_lt_sub_of_lt_of_le" -> "init", "ideal.comap_bot_le_of_injective" -> "algebra", "sesq_form.zero_right" -> "algebra", "filter.singleton_mem_pure_sets" -> "order", "is_glb.cInf_eq" -> "order", "multiplicity.multiplicity_lt_iff_neg_dvd" -> "algebra", "category_theory.over.over_morphism.ext" -> "category_theory", "real.sqrt_div" -> "data", "polynomial.coe_C" -> "algebra", "computation.eq_empty_of_not_terminates" -> "data", "bnot_eq_true_eq_eq_ff" -> "init", "subsemiring.coe_nat_mem" -> "algebra", "bilin_form.mem_skew_adjoint_submodule" -> "algebra", "inner_sub_sub_self" -> "analysis", "monoid_hom.mclosure_preimage_le" -> "algebra", "with_zero.div_coe" -> "algebra", "category_theory.coyoneda_obj_obj" -> "category_theory", "structure_groupoid.local_invariant_prop.lift_prop_on_congr" -> "geometry", "euclidean_geometry.angle_comm" -> "geometry", "list.pairwise_of_forall" -> "data", "formal_multilinear_series.change_origin_eval" -> "analysis", "filter.frequently_at_bot'" -> "order", "continuous_multiset_prod" -> "topology", "is_integral_zero" -> "algebra", "norm_num.inv_one_div" -> "tactic", "set.sep_univ" -> "data", "monoid_hom.eq_on_mclosure" -> "algebra", "times_cont_diff_at.times_cont_diff_within_at" -> "analysis", "ne_of_mem_of_not_mem" -> "logic", "erased.out_proof" -> "data", "set.compl_compl" -> "data", "polynomial.coeff_single" -> "data", "measure_theory.lintegral_indicator" -> "analysis", "int.mod_two_eq_zero_or_one" -> "data", "vector.to_list_nil" -> "data", "nat.partrec.code.curry_prim" -> "computability", "is_invariant_subring.coe_subtype_hom" -> "algebra", "category_theory.graded_object.comap_eq_symm" -> "category_theory", "nat.odd_of_mod_four_eq_three" -> "data", "discrete_valuation_ring.associated_pow_irreducible" -> "algebra", "measure_theory.measure.haar_outer_measure_self_pos" -> "analysis", "category_theory.limits.kernel_not_epi_of_nonzero" -> "category_theory", "add_submonoid.sup_eq_range" -> "algebra", "is_local_max.add" -> "topology", "bounded_continuous_function.const_apply" -> "topology", "bitvec.to_fin_val" -> "data", "min_add_max" -> "algebra", "edist_lt_top" -> "topology", "eq_or_eq_neg_of_pow_two_eq_pow_two" -> "algebra", "is_lub.Sup_eq" -> "order", "onote.repr_scale" -> "set_theory", "mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset" -> "topology", "local_homeomorph.eq_of_local_equiv_eq" -> "topology", "rel.image_comp" -> "data", "list.range_eq_range'" -> "data", "linear_map.map_injective" -> "algebra", "of_set_mem_times_cont_diff_groupoid" -> "geometry", "set.mem_add" -> "algebra", "convex_cone.mem_inf" -> "analysis", "nat.add_right_cancel" -> "init", "quadratic_form.polar_add_right" -> "algebra", "turing.TM1.step_supports" -> "computability", "unique_diff_within_at.mono_nhds" -> "analysis", "equiv.perm.same_cycle.trans" -> "algebra", "equiv.to_fun_as_coe" -> "data", "bilin_form.ortho_zero" -> "algebra", "nat.one_le_two_pow" -> "data", "emetric.diam_pair" -> "topology", "polynomial.splits_mul" -> "algebra", "with_bot.coe_bit0" -> "algebra", "nat.shiftl_eq_mul_pow" -> "init", "pfun.core_inter" -> "data", "local_homeomorph.mdifferentiable.range_mfderiv_eq_univ" -> "geometry", "set.maps_to_Union_Union" -> "data", "norm_num.nat_succ_eq" -> "tactic", "pgame.zero_left_moves" -> "set_theory", "computation.eq_thinkN'" -> "data", "filter.map_at_top_finset_prod_le_of_prod_eq" -> "order", "lcm_dvd_lcm_mul_left" -> "algebra", "local_homeomorph.mk_coe_symm" -> "topology", "nnreal.rpow_lt_rpow_of_exponent_gt" -> "analysis", "is_R_or_C.sub_conj" -> "data", "composition.length_gather" -> "analysis", "eqv_gen.is_equivalence" -> "init", "filter.has_basis.cauchy_seq_iff'" -> "topology", "cau_seq.equiv_def\:2083" -> "data", "measure_theory.l1.of_fun_add" -> "analysis", "set.eq_empty_iff_forall_not_mem" -> "data", "encodable.mem_sorted_univ" -> "data", "set.interval_subset_interval_iff_mem" -> "data", "comp_rel_assoc" -> "topology", "computation.results.length" -> "data", "quotient_ring.quotient_map_coe_coe" -> "topology", "cardinal.pos_iff_ne_zero" -> "set_theory", "is_noetherian_ring.exists_factors" -> "algebra", "list.perm.foldl_eq'" -> "data", "is_bounded_bilinear_map.continuous" -> "analysis", "computable.vector_tail" -> "computability", "right_eq_sup" -> "order", "Top.sheaf_condition.fork_\[Iota]" -> "topology", "model_with_corners.mk_coe" -> "geometry", "measurable_space.comap_id" -> "analysis", "set.preimage_mul_const_Ioi_of_neg" -> "data", "is_connected.Ioo_cInf_cSup_subset" -> "topology", "complex.exp_zero" -> "data", "or_and_distrib_left" -> "logic", "finset.card_lt_card" -> "data", "primrec.nat_min" -> "computability", "free_monoid.closure_range_of" -> "algebra", "local_homeomorph.subtype_restr_def" -> "topology", "option.ext" -> "data", "finsupp.zero_not_mem_frange" -> "data", "padic_seq.norm_eq_of_add_equiv_zero" -> "data", "mul_le_mul_left" -> "algebra", "real.sin_sub_pi_div_two" -> "analysis", "is_group_hom.mem_ker" -> "algebra", "ordinal.nfp_eq_self" -> "set_theory", "category_theory.abelian.pseudoelement.zero_apply" -> "category_theory", "wseq.join_ret" -> "data", "con.coe_one" -> "algebra", "differentiable.differentiable_on" -> "analysis", "decidable.iff_iff_not_or_and_or_not" -> "logic", "add_monoid_hom.iterate_map_add" -> "algebra", "nnreal.div_pos" -> "data", "continuous_right_of_strict_mono_surjective" -> "topology", "metric.bounded_closed_ball" -> "topology", "list.count_nil" -> "data", "filter.tendsto_at_top_of_add_bdd_above_right'" -> "order", "cauchy_seq_finset_iff_vanishing_norm" -> "analysis", "computation.has_map_eq_map" -> "data", "complex.sin_add_two_pi" -> "analysis", "set.diff_diff" -> "data", "matrix.vec_mul_vec_mul" -> "data", "is_basis.to_dual_swap_eq_to_dual" -> "algebra", "turing.list_blank.cons_mk" -> "computability", "asymptotics.is_O.exists_pos" -> "analysis", "nat.succ_sub_sub_succ" -> "init", "Inf_insert" -> "order", "sym2.mk_has_mem_right" -> "data", "filter.of_sets_filter_eq_generate" -> "order", "alg_equiv.symm_symm" -> "algebra", "equiv.subset_image" -> "data", "set.diff_eq_self" -> "data", "list.chain'_reverse" -> "data", "local_equiv.trans_refl" -> "data", "wseq.dropn_congr" -> "data", "equiv.perm.sign_aux3_mul_and_swap" -> "algebra", "quotient.hrec_on\:2082'_mk'" -> "data", "equiv.set.of_eq_apply" -> "data", "isometric.to_homeomorph_to_equiv" -> "topology", "rel.image_union" -> "data", "Module.monoidal_category.right_unitor_hom_apply" -> "algebra", "measure_theory.ae_eq_fun.neg_to_germ" -> "analysis", "closure_inter_open" -> "topology", "polynomial.splitting_field.adjoin_roots" -> "algebra", "equiv_of_is_basis_trans_symm" -> "algebra", "nat.shiftl'_tt_ne_zero" -> "data", "equiv.coe_vadd_const" -> "algebra", "function.embedding.injective" -> "logic", "is_local_max.has_deriv_at_eq_zero" -> "analysis", "local_homeomorph.prod_target" -> "topology", "is_local_min.add" -> "topology", "submodule.restrict_scalars'_inj" -> "algebra", "has_fderiv_at_filter.mono" -> "analysis", "submodule.mul_sup" -> "algebra", "computable.encode" -> "computability", "quadratic_form.associated_lin_mul_lin" -> "algebra", "category_theory.monoidal_category.associator_nat_iso_inv_app" -> "category_theory", "category_theory.limits.cone.category_to_category_struct_comp_hom" -> "category_theory", "nat.mul_div_assoc" -> "init", "cau_seq.const_sub" -> "data", "set.nonempty_Icc" -> "data", "finite_dimensional.finite_dimensional_iff_dim_lt_omega" -> "algebra", "is_noetherian_ring_of_fg" -> "algebra", "many_one_degree.add_le" -> "computability", "add_submonoid.localization_map.mk'_self'" -> "algebra", "function.has_left_inverse.injective" -> "init", "int.cast_sub_nat_nat" -> "data", "list.length_take_le" -> "init", "normalize_idem" -> "algebra", "le_inv_mul_of_mul_le" -> "algebra", "add_gsmul" -> "algebra", "multiset.ext'" -> "data", "norm_num.sub_pos" -> "tactic", "circle_deg1_lift.monotone" -> "dynamics", "free_abelian_group.sub_seq" -> "algebra", "set.mem_sInter" -> "data", "finset.union_idempotent" -> "data", "list.exists_or_eq_self_of_erasep" -> "data", "vector.continuous_insert_nth" -> "topology", "pSet.subset.congr_right" -> "set_theory", "filter.germ.coe_comp_tendsto'" -> "order", "sub_le_sub_iff_right" -> "algebra", "strict_mono.iterate" -> "order", "matrix.findim_matrix" -> "algebra", "asymptotics.is_O.join" -> "analysis", "tensor_product.mk_apply" -> "algebra", "nat.decreasing_induction_succ'" -> "data", "mdifferentiable_within_at.mfderiv_within_congr_mono" -> "geometry", "category_theory.limits.biprod.braid_natural_assoc" -> "category_theory", "multiset.sup_erase_dup" -> "data", "multiset.sort_sorted" -> "data", "open_embedding.to_local_homeomorph_coe" -> "topology", "vector.continuous_insert_nth'" -> "topology", "pmf.bind.summable" -> "analysis", "ordinal.add_omega" -> "set_theory", "differentiable.sub" -> "analysis", "set.Union_lt_succ" -> "data", "lt_add_of_le_of_pos" -> "algebra", "denumerable.raise'_sorted" -> "data", "filter.eventually_eq_set" -> "order", "nat.sub_eq_zero_of_le" -> "init", "ordinal.sup_lt" -> "set_theory", "isometric.point_reflection_midpoint_right" -> "analysis", "alg_equiv.symm_apply_apply" -> "algebra", "differentiable_at.const_mul" -> "analysis", "embedding_open" -> "topology", "lucas_lehmer.X.one_fst" -> "number_theory", "continuous_Inf_dom" -> "topology", "list.sum_hom" -> "data", "convex_on_id" -> "analysis", "category_theory.abelian.pseudoelement.comp_comp" -> "category_theory", "set.eq_univ_of_univ_subset" -> "data", "category_theory.functor.left_unitor_inv_app" -> "category_theory", "typevec.comp_assoc" -> "data", "int.lt_add_of_neg_add_lt" -> "init", "nat.choose_symm_add" -> "data", "fin.tail_update_zero" -> "data", "set.maps_to_Inter" -> "data", "finset.prod_Ico_reflect" -> "algebra", "filter.tendsto_neg_at_top_at_bot" -> "order", "cardinal.mk_image_le" -> "set_theory", "submodule.quotient.eq" -> "algebra", "associates.sup_mul_inf" -> "algebra", "initial_seg.eq_or_principal" -> "set_theory", "nat.primrec.add" -> "computability", "turing.TM2to1.step_run" -> "computability", "convex_on.exists_ge_of_mem_convex_hull" -> "analysis", "ennreal.Icc_mem_nhds" -> "topology", "continuous_multilinear_map.map_sum_finset" -> "topology", "pfun.image_def" -> "data", "pgame.not_first_wins_of_first_loses" -> "set_theory", "list.sublist.erasep" -> "data", "filter.eventually_eq.times_cont_diff_within_at_iff" -> "analysis", "polynomial.coeff_X" -> "data", "wseq.eq_or_mem_iff_mem" -> "data", "measurable_bsupr" -> "analysis", "nhds_induced" -> "topology", "stream.tails_eq_iterate" -> "data", "all_mem_nhds_filter" -> "topology", "add_equiv.map_zero" -> "data", "typevec.last_fun_prod" -> "data", "is_add_group_hom.map_neg" -> "algebra", "upper_bounds_mono_mem" -> "order", "complex.has_deriv_at_cos" -> "analysis", "list.erase_dup_cons_of_not_mem'" -> "data", "mv_polynomial.total_degree_X" -> "data", "floor_add_fract" -> "algebra", "mvpfunctor.W_path_dest_left_W_path_cases_on" -> "data", "list.perm.sizeof_eq_sizeof" -> "data", "nodup_perms_of_list" -> "data", "has_deriv_at.cosh" -> "analysis", "is_preirreducible_empty" -> "topology", "equiv.conj_symm" -> "data", "add_monoid_hom.to_range_ker" -> "algebra", "linear_map.ker_smul" -> "algebra", "unique_factorization_domain.exists_reduced_factors" -> "algebra", "emetric.Hausdorff_edist_closure\:2081" -> "topology", "set.singleton_inter_eq_empty" -> "data", "computation.exists_results_of_mem" -> "data", "finset.sum_mul_boole" -> "algebra", "hyperreal.st_of_is_st" -> "data", "set.Icc_union_Ici_eq_Ici" -> "data", "mul_smul" -> "algebra", "complex.im_le_abs" -> "data", "filter.lift'_ne_bot_iff" -> "order", "turing.to_partrec.code_is_ok" -> "computability", "nat.add_le_add_iff_le_right" -> "init", "cardinal.mul_lt_omega_iff" -> "set_theory", "geom_series\:2082_one" -> "algebra", "finsupp.is_basis_single" -> "algebra", "cardinal.one_le_iff_ne_zero" -> "set_theory", "nat.prime.irrational_sqrt" -> "data", "ideal.mem_pi" -> "algebra", "has_sum.neg" -> "topology", "commutative_ring_iff_abelian_lie_ring" -> "algebra", "real.exp_nat_mul" -> "data", "set.Ioi_inter_Iio" -> "data", "set.Ici_subset_Ioi" -> "data", "finset.insert_eq" -> "data", "is_basis.comp" -> "algebra", "euclidean_domain.gcd_eq_zero_iff" -> "algebra", "rel.core_inter" -> "data", "infi_congr_Prop" -> "order", "stream.composition" -> "data", "list.foldr_eta" -> "data", "primrec.of_equiv_iff" -> "computability", "canonically_ordered_semiring.mul_le_mul_right'" -> "algebra", "computation.mem_unique" -> "data", "computation.results.val_unique" -> "data", "add_subgroup.coe_map" -> "algebra", "filter.comap_mono" -> "order", "polynomial.card_roots_sub_C'" -> "data", "hyperreal.epsilon_pos" -> "data", "finmap.to_finmap_cons" -> "data", "vector.head'_to_list" -> "data", "nat.zero_le" -> "init", "hyperreal.not_infinite_real" -> "data", "multiplicity.pow" -> "algebra", "set.subset_insert_diff_singleton" -> "data", "polynomial.differentiable" -> "analysis", "computation.parallel_empty" -> "data", "finset.disjoint_sdiff" -> "data", "seq.head_nil" -> "data", "erased.bind_def" -> "data", "measure_theory.simple_func.pos_part_sub_neg_part" -> "analysis", "pgame.equiv_congr_left" -> "set_theory", "list.perm.rec_heq" -> "data", "with_zero.one_div" -> "algebra", "padic_val_nat_primes" -> "data", "topological_fiber_bundle_core.local_triv_fst" -> "topology", "ring_hom.coe_pow" -> "algebra", "semidirect_product.right_hom_inr" -> "algebra", "irrational_sub_rat_iff" -> "data", "mul_right_inj" -> "algebra", "list.cons_inj" -> "data", "vector.nth_eq_nth_le" -> "data", "roption.get_or_else_none" -> "data", "char_p.int_cast_eq_zero_iff" -> "algebra", "list.sum_nil" -> "data", "ne_top_of_le_ne_top" -> "order", "setoid.eqv_class_mem" -> "data", "le_of_forall_lt'" -> "algebra", "category_theory.is_iso.inv_id" -> "category_theory", "gcd_dvd_gcd_mul_right_right" -> "algebra", "norm_zero" -> "analysis", "function.injective.map_at_top_finset_sum_eq" -> "order", "times_cont_mdiff_on_const" -> "geometry", "of_digits_one" -> "data", "bounded_continuous_function.dist_le_two_norm'" -> "topology", "filter.prod_at_top_at_top_eq" -> "order", "int.add_zero" -> "init", "deriv_const" -> "analysis", "polynomial.derivative_expand" -> "algebra", "polynomial.splits_X_sub_C" -> "algebra", "set.Ioi_union_left" -> "data", "direct_sum.to_module.unique" -> "algebra", "differentiable_within_at.ccosh" -> "analysis", "filter.tendsto.uniformity_trans" -> "topology", "nat.exists_infinite_primes" -> "data", "units.coe_mk_of_mul_eq_one" -> "algebra", "filter.infi_ne_bot_of_directed" -> "order", "category_theory.non_preadditive_abelian.neg_sub" -> "category_theory", "measure_theory.ae_eq_fun.edist_smul" -> "analysis", "local_equiv.symm_maps_to" -> "data", "exists_between_of_forall_le" -> "order", "real.cos_pi_div_two_sub" -> "analysis", "char_dvd_card_solutions" -> "algebra", "zsqrtd.coe_int_re" -> "data", "is_max_filter.add" -> "order", "compact_space.tendsto_subseq" -> "topology", "circle_deg1_lift.translate_gpow" -> "dynamics", "set.countable.union" -> "data", "ring.direct_limit.of.zero_exact_aux2" -> "algebra", "fpow_ne_zero_of_ne_zero" -> "algebra", "uniform_space.has_basis_symmetric" -> "topology", "is_R_or_C.bit1_re" -> "data", "continuous_linear_map.coe_add'" -> "topology", "sup_right_idem" -> "order", "finset.union_subset" -> "data", "power_series.coeff_trunc" -> "algebra", "uniform_space.has_basis_nhds" -> "topology", "equiv.symm_symm" -> "data", "finsupp.to_multiset_to_finsupp" -> "data", "filter.eventually_eq.has_deriv_at_filter_iff" -> "analysis", "continuous_at_of_locally_lipschitz" -> "topology", "category_theory.monoidal_of_has_finite_products.tensor_hom" -> "category_theory", "finsupp.filter_pos_add_filter_neg" -> "data", "is_absolute_value.abv_sub_le" -> "data", "prime_spectrum.ext" -> "algebraic_geometry", "nat.sub_add_min" -> "data", "tsum_sub" -> "topology", "has_mfderiv_within_at.continuous_within_at" -> "geometry", "is_compact.is_seq_compact" -> "topology", "ideal.maximal_of_no_maximal" -> "algebra", "monotonicity.false" -> "meta", "category_theory.nat_iso.op_inv" -> "category_theory", "sub_pow_char_of_commute" -> "algebra", "mv_polynomial.rename_monomial" -> "data", "equiv.coe_subtype_equiv_codomain" -> "data", "matrix.dot_product_zero'" -> "data", "category_theory.split_epi.id" -> "category_theory", "int.neg_add_neg" -> "data", "smodeq.smul" -> "algebra", "pnat.coprime.factor_eq_gcd_right" -> "data", "with_one.one_ne_coe" -> "algebra", "has_deriv_within_at_inv" -> "analysis", "wseq.append_assoc" -> "data", "filter.lift_mono" -> "order", "tendsto_extend_from" -> "topology", "linear_map.to_continuous_linear_map\:2081_apply" -> "analysis", "is_R_or_C.div_I" -> "data", "primrec.encdec" -> "computability", "finset.union_inter_cancel_left" -> "data", "subsemiring.mem_bot" -> "algebra", "finset.prod_erase" -> "algebra", "ennreal.continuous_inv" -> "topology", "ne_top_of_lt" -> "order", "nnreal.div_rpow" -> "analysis", "mv_polynomial.aeval_X" -> "data", "char_p.false_of_nonzero_of_char_one" -> "algebra", "has_fderiv_at_filter.is_O_sub_rev" -> "analysis", "quotient_add_group.lift_mk" -> "algebra", "fin.coe_val_eq_self" -> "data", "quadratic_form.equivalent.symm" -> "algebra", "alg_equiv.to_lie_equiv_apply" -> "algebra", "supr_le_supr" -> "order", "semiquot.eq_pure" -> "data", "computable.option_some_iff" -> "computability", "bounded_continuous_function.coe_smul" -> "topology", "set.insert_comm" -> "data", "affine_map.const_linear" -> "algebra", "basic_smooth_bundle_core.smooth_within_at_proj" -> "geometry", "submodule.restrict_scalars'_top" -> "algebra", "map_cinfi_of_continuous_at_of_monotone" -> "topology", "submodule.span_insert_eq_span" -> "algebra", "is_integral_one" -> "algebra", "category_theory.limits.is_limit.unique_up_to_iso_hom" -> "category_theory", "classical.cases_true_false" -> "init", "linear_map.exists_left_inverse_of_injective" -> "algebra", "matrix.transpose_empty_cols" -> "data", "has_sum_subtype_support" -> "topology", "finset.mul_sum" -> "algebra", "category_theory.functor.sum_obj_inr" -> "category_theory", "set.interval_of_ge" -> "data", "uniform_space.eq_of_separated_of_uniform_continuous" -> "topology", "finset.bUnion_singleton" -> "data", "rel_iso.coe_fn_to_equiv" -> "order", "local_homeomorph.coe_coe_symm" -> "topology", "linear_map.inj_of_disjoint_ker" -> "algebra", "ordinal.mul_omega_dvd" -> "set_theory", "nat.eq_zero_of_le_div" -> "data", "ring_hom.eq_int_cast" -> "data", "pnat.coe_bit0" -> "data", "rel_embedding.trans_apply" -> "order", "nat.one_add_le_iff" -> "data", "tendsto_norm_at_top_at_top" -> "analysis", "Kuratowski_embedding.embedding_of_subset_dist_le" -> "topology", "mv_polynomial.pderivative_monomial_single" -> "data", "filter.sequence_mono" -> "order", "add_submonoid.coe_top" -> "algebra", "finset.subset_empty" -> "data", "nat.gcd_eq_right_iff_dvd" -> "data", "matrix.row_cons" -> "data", "set.bUnion_image" -> "data", "has_sum_zero" -> "topology", "commute.units_coe_iff" -> "algebra", "category_theory.limits.coprod.inl_map_assoc" -> "category_theory", "add_submonoid.mem_Sup_of_directed_on" -> "algebra", "zmod.ring_hom_surjective" -> "data", "with_top.zero_eq_coe" -> "algebra", "finset.inter_univ" -> "data", "not_and_self" -> "init", "ball.imp_right" -> "logic", "finite_dimensional.findim_pos_iff" -> "algebra", "vector_span_def" -> "algebra", "continuous_on_iff'" -> "topology", "ball_congr" -> "logic", "vsub_mem_vector_span_of_mem_span_points_of_mem_span_points" -> "algebra", "formal_multilinear_series.comp_change_of_variables_length" -> "analysis", "turing.TM1to1.supports_stmt_move" -> "computability", "polynomial.exists_root_of_splits" -> "algebra", "nat.eq_of_dvd_of_div_eq_one" -> "data", "continuous_map.image_coev" -> "topology", "set.compl_comp_compl" -> "data", "sylow.mem_vectors_prod_eq_one_iff" -> "algebra", "function.embedding.total" -> "set_theory", "is_glb_pair" -> "order", "ctop.of_equiv_val" -> "data", "measure_theory.meas_ge_le_lintegral_div" -> "analysis", "category_theory.limits.colimit.is_colimit_desc" -> "category_theory", "function.surjective.preimage_subset_preimage_iff" -> "data", "pow_ite" -> "algebra", "real.arcsin_eq_zero_iff" -> "analysis", "is_R_or_C.abs_mul" -> "data", "linear_map.fun_left_apply" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_at_congr_of_eventually_eq" -> "geometry", "inv_mul_eq_one" -> "algebra", "free_comm_ring.lift_of" -> "algebra", "supr_sup_eq" -> "order", "pgame.impartial.good_right_move_iff_first_wins" -> "set_theory", "subalgebra.nsmul_mem" -> "algebra", "state_t.run_monad_map" -> "init", "rat.cast_pow" -> "data", "tactic.ring2.horner_expr.cseval_add_const" -> "tactic", "list.nth_le_of_eq" -> "data", "iff_false_intro" -> "init", "multiset.pi.cons_ne" -> "data", "nnreal.inv_le" -> "data", "group.mem_conjugates_self" -> "algebra", "Kuratowski_embedding.embedding_of_subset_coe" -> "topology", "hyperreal.exists_st_of_not_infinite" -> "data", "irrational_inv_iff" -> "data", "unit_associated_one" -> "algebra", "localization_map.mem_map_to_map_iff" -> "algebra", "list.sublists_reverse" -> "data", "bifunctor.snd_id" -> "control", "submodule.quotient.quot_mk_eq_mk" -> "algebra", "int.coe_nat_ne_zero_iff_pos" -> "data", "is_compact.is_measurable" -> "analysis", "nat.le_trans" -> "init", "is_local_max.deriv_eq_zero" -> "analysis", "sup_ind" -> "order", "nat.mod_mul_right_mod" -> "data", "bundle_trivialization.coe_mk" -> "topology", "mul_action.bijective" -> "algebra", "is_add_subgroup.gsmul_coe" -> "algebra", "int.lt_add_of_pos_left" -> "init", "approximates_linear_on.to_local_homeomorph_source" -> "analysis", "semiconj_by.inv_symm_left_iff'" -> "algebra", "associates.forall_associated" -> "algebra", "category_theory.over.post_map_right" -> "category_theory", "eq_or_lt_of_not_lt" -> "init", "nat.prime.coprime_iff_not_dvd" -> "data", "multiset.map_singleton" -> "data", "gcd_eq_left_iff" -> "algebra", "matrix.mul_empty" -> "data", "contracting_with.aposteriori_dist_iterate_fixed_point_le" -> "topology", "continuous_linear_equiv.is_O_comp_rev" -> "analysis", "nat.land_zero" -> "data", "quotient_add_group.ker_mk" -> "algebra", "subtype.coe_image_subset" -> "data", "category_theory.limits.kernel.condition_assoc" -> "category_theory", "pell.eq_of_xn_modeq_lem2" -> "number_theory", "polynomial.eisenstein_criterion_aux.le_nat_degree_of_map_eq_mul_X_pow" -> "algebra", "linear_independent.restrict_of_comp_subtype" -> "algebra", "commute.one_left" -> "algebra", "initial_seg.antisymm_to_fun" -> "set_theory", "bitvec.of_fin_val" -> "data", "uniform_extend_subtype" -> "topology", "list_all.imp" -> "number_theory", "bounded_continuous_function.ext_iff" -> "topology", "with_top.coe_eq_zero" -> "algebra", "finset.center_mass_ite_eq" -> "analysis", "neg_sub_neg" -> "algebra", "polynomial.expand_eq_zero" -> "algebra", "is_greatest_Iic" -> "order", "filter.mem_lift" -> "order", "int.exists_sum_two_squares_add_one_eq_k" -> "number_theory", "primrec.list_nth\:2081" -> "computability", "measure_theory.measure.restrict_apply" -> "analysis", "typevec.append_fun_aux" -> "data", "finsupp.is_basis.tensor_product" -> "algebra", "is_add_subgroup.of_sub" -> "algebra", "nhds_discrete" -> "topology", "equiv.add_def" -> "data", "measure_theory.mul_meas_ge_le_lintegral" -> "analysis", "enorm.coe_fn_injective" -> "analysis", "preimage_neg" -> "topology", "conj_injective" -> "algebra", "emetric.complete_of_convergent_controlled_sequences" -> "topology", "polynomial.eval\:2082_smul" -> "data", "lie_algebra.equiv.coe_to_lie_equiv" -> "algebra", "complex.sin_of_real_re" -> "data", "eckmann_hilton.group.is_unital" -> "algebra", "formal_multilinear_series.change_origin_has_sum" -> "analysis", "continuous_linear_equiv.coe_refl'" -> "topology", "smooth_within_at_snd" -> "geometry", "ring_hom.iterate_map_pow" -> "algebra", "int.sub_nat_nat_add_neg_succ_of_nat" -> "init", "primrec\:2082.pair" -> "computability", "nnreal.of_real_eq_zero" -> "data", "set.image_eq_Union" -> "data", "sum_geometric_two_le" -> "analysis", "submodule.bot_ne_top" -> "algebra", "alist.mem_lookup_union" -> "data", "category_theory.iso.conj_Aut_pow" -> "category_theory", "zmod.neg_eq_self_mod_two" -> "data", "omega.nat.valid_of_unsat_not" -> "tactic", "encodable.decode2_is_partial_inv" -> "data", "differentiable_within_at.differentiable_at" -> "analysis", "state_t.run_adapt" -> "init", "ff_eq_tt_eq_false" -> "init", "filter.tendsto_at_top_add_nonneg_right'" -> "order", "add_con.lift_range" -> "algebra", "ideal.span_zero" -> "algebra", "bool.bxor_iff_ne" -> "data", "sdiff_eq" -> "order", "is_closed.mem_of_nhds_within_ne_bot" -> "topology", "set.Union_eq_comp_Inter_comp" -> "data", "ordinal.lift_univ" -> "set_theory", "dense_range.induction_on" -> "topology", "model_with_corners.right_inv" -> "geometry", "polynomial.coeff_mul_X_zero" -> "data", "if_ctx_congr" -> "init", "is_measurable_eq" -> "analysis", "continuous_map.ext" -> "topology", "filter.eventually_or_distrib_right" -> "order", "lipschitz_with.mul_edist_le" -> "topology", "add_submonoid.localization_map.neg_inj" -> "algebra", "add_submonoid.bot_sum_bot" -> "algebra", "holor.slice_zero" -> "data", "extend_from_eq" -> "topology", "euclidean_geometry.orthogonal_projection_vsub_mem_direction_orthogonal" -> "geometry", "nat.Inf_mem" -> "order", "cardinal.mk_empty" -> "set_theory", "uniform_space.completion.map\:2082_coe_coe" -> "topology", "algebra.tensor_product.assoc_aux_2" -> "algebra", "dfinsupp.sum_zero" -> "data", "bitvec.to_nat_lt" -> "data", "matrix.ker_diagonal_to_lin" -> "algebra", "perfect_closure.eq_pth_root" -> "algebra", "list.mem_sublists_len" -> "data", "bilin_form.is_adjoint_pair.add" -> "algebra", "set.sUnion_eq_Union" -> "data", "category_theory.non_preadditive_abelian.\[CapitalDelta]_map" -> "category_theory", "has_deriv_at.inv" -> "analysis", "dist_comm" -> "topology", "filter.ne_bot.comap_of_surj" -> "order", "equiv.coe_neg" -> "data", "add_monoid_hom.injective_iff" -> "algebra", "add_submonoid.map_id" -> "algebra", "topological_space.opens.map_obj" -> "topology", "int.mul_one" -> "init", "list.singleton_disjoint" -> "data", "prod.mk_vadd_mk" -> "algebra", "add_submonoid.add_mem" -> "algebra", "ring_hom.prod_comp_prod_map" -> "algebra", "nhds_contain_boxes.symm" -> "topology", "cardinal.lift_mk" -> "set_theory", "pos_num.cast_pos" -> "data", "add_monoid_hom.eq_of_eq_on_top" -> "algebra", "tactic.ring2.horner_expr.cseval_mul" -> "tactic", "padic_int.mk_coe" -> "data", "fin.succ_above_ne" -> "data", "dvd_gcd_iff" -> "algebra", "vector_span_image_eq_span_vsub_set_right_ne" -> "algebra", "set.compl_subset_iff_union" -> "data", "ite_add" -> "algebra", "continuous_multilinear_map.curry_left_norm" -> "analysis", "add_submonoid.top_prod_top" -> "algebra", "multiset.disjoint_union_left" -> "data", "category_theory.yoneda_pairing_map" -> "category_theory", "circle_deg1_lift.translation_number_le_ceil_sub" -> "dynamics", "multiset.eq_of_le_of_card_le" -> "data", "sum_add_tsum_nat_add" -> "topology", "alist.union_comm_of_disjoint" -> "data", "partrec.merge'" -> "computability", "set.prod_eq_seq" -> "data", "is_refl.swap" -> "order", "is_R_or_C.mul_re" -> "data", "set.image_neg_Ico" -> "data", "turing.reaches_total" -> "computability", "finset.choose_mem" -> "data", "category_theory.preadditive.mono_of_cancel_zero" -> "category_theory", "nhds_within_eq_of_open" -> "topology", "category_theory.mono_comp" -> "category_theory", "inducing_id" -> "topology", "int.div_of_neg_of_pos" -> "data", "nnreal.of_real_lt_of_real_iff" -> "data", "homological_complex.graded_homology_obj" -> "algebra", "filter.germ.const_sup" -> "order", "topological_space.compacts.map_val" -> "topology", "traversable.traverse_map'" -> "control", "has_fderiv_at_inverse" -> "analysis", "mv_polynomial.eval\:2082_mul" -> "data", "tangent_map_within_eq_tangent_map" -> "geometry", "interval_integral.integral_has_deriv_within_at_right" -> "analysis", "function.commute.iterate_right" -> "logic", "finmap.mem_replace" -> "data", "set.Ici_diff_left" -> "data", "set.eq_on_refl" -> "data", "algebraic_geometry.structure_sheaf_stalk_to_fiber_injective" -> "algebraic_geometry", "category_theory.over.iterated_slice_equiv_inverse" -> "category_theory", "measure_theory.measure_union" -> "analysis", "directed.le_sequence" -> "data", "category_theory.Monad.of_Mon_str_\[Mu]" -> "category_theory", "cardinal.one_le_iff_pos" -> "set_theory", "subring.mul_mem" -> "algebra", "matrix.vec_mul_neg" -> "data", "norm_prod_le_iff" -> "analysis", "generalized_continued_fraction.int_fract_pair.stream_eq_none_of_fr_eq_zero" -> "algebra", "local_homeomorph.eventually_right_inverse" -> "topology", "nat.dvd_lcm_right" -> "data", "hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg" -> "data", "pgame.nim.nim_wf_lemma" -> "set_theory", "continuous_on_iff_continuous_restrict" -> "topology", "if_simp_congr_prop" -> "init", "wseq.flatten_equiv" -> "data", "option_t.run_monad_map" -> "init", "linear_map.mul_eq_one_of_mul_eq_one" -> "algebra", "formal_multilinear_series.id_comp" -> "analysis", "mv_polynomial.eval\:2082_sub" -> "data", "measure_theory.lintegral_add_measure" -> "analysis", "measurable_space.dynkin_system.generate_le" -> "analysis", "dioph.mod_dioph" -> "number_theory", "list.nodup_append" -> "data", "asymptotics.is_O_with.join'" -> "analysis", "polynomial.eval_prod" -> "data", "list.nth_le_take'" -> "data", "lt_of_mul_lt_mul_right" -> "algebra", "nnreal.mul_ne_zero'" -> "data", "equiv.point_reflection_midpoint_right" -> "algebra", "function.embedding.trans_apply" -> "logic", "free_abelian_group.lift.map_hom" -> "algebra", "measure_theory.simple_func.fin_meas_supp.of_map" -> "analysis", "of_digits_one_cons" -> "data", "set.diff_subset" -> "data", "nnreal.inv_eq_zero" -> "data", "category_theory.monoidal_category.unitors_equal.cells_9_13" -> "category_theory", "category_theory.hom_of_element_eq_iff" -> "category_theory", "continuous_at_snd" -> "topology", "pnat.add_sub_of_lt" -> "data", "compact_iff_finite_subfamily_closed" -> "topology", "nat.primrec.sub" -> "computability", "measure_theory.integrable.mono_measure" -> "analysis", "category_theory.limits.image_mono_iso_source_inv_\[Iota]_assoc" -> "category_theory", "canonically_ordered_semiring.one_le_pow_of_one_le" -> "algebra", "summable_of_nonneg_of_le" -> "topology", "finset.mono_of_fin_bij_on" -> "data", "submonoid.localization_map.mul_equiv_of_localizations_left_inv" -> "algebra", "convex_halfspace_re_gt" -> "analysis", "nat.partrec.prec'" -> "computability", "is_bounded_bilinear_map.differentiable_at" -> "analysis", "affine_subspace.direction_of_nonempty_eq_direction" -> "algebra", "polynomial.map_monomial" -> "data", "list.subperm_cons_erase" -> "data", "category_theory.pi.sum_map_app" -> "category_theory", "ordinal.typein_surj" -> "set_theory", "ennreal.inv_eq_inv" -> "data", "list.perm_split" -> "data", "quadratic_ne_zero_of_discrim_ne_square" -> "algebra", "algebraic_closure.exists_root" -> "algebra", "left_add_coset_mem_left_add_coset" -> "algebra", "int.coe_nat_div" -> "data", "dfinsupp.mk_injective" -> "data", "local_equiv.of_set_source" -> "data", "category_theory.currying_unit_iso_hom_app_app_app" -> "category_theory", "has_fpower_series_on_ball.change_origin" -> "analysis", "emetric.inf_edist_image" -> "topology", "int.mul_sub" -> "init", "cardinal.cantor_function_succ" -> "data", "deriv_within_fderiv_within" -> "analysis", "filter.ultrafilter_bind" -> "order", "category_theory.abelian.pseudoelement.epi_of_pseudo_surjective" -> "category_theory", "filter.tendsto.Ico" -> "order", "uniq_inv_of_is_field" -> "algebra", "closed_nhds_basis" -> "topology", "add_monoid_hom.id_comp" -> "algebra", "continuous_map.continuous_induced" -> "topology", "is_path_connected.preimage_coe" -> "topology", "list.length_enum_from" -> "data", "add_self_iff_eq_zero" -> "algebra", "floor_le" -> "algebra", "ideal.mul_mem_mul_rev" -> "algebra", "category_theory.limits.image.iso_strong_epi_mono_hom_comp_\[Iota]" -> "category_theory", "nat.totient_zero" -> "data", "category_theory.coe_comp" -> "category_theory", "bounded_continuous_function.norm_const_eq" -> "topology", "stream.nil_append_stream" -> "data", "finset.bUnion_insert_update" -> "data", "is_R_or_C.rat_cast_re" -> "data", "deriv_within_const_add" -> "analysis", "primrec.subtype_val" -> "computability", "affine_map.id_comp" -> "algebra", "iterated_deriv_within_succ'" -> "analysis", "lucas_lehmer.X.\[Omega]b_mul_\[Omega]" -> "number_theory", "add_submonoid.localization_map.comp_eq_of_eq" -> "algebra", "category_theory.limits.equalizer.iso_source_of_self_hom" -> "category_theory", "polynomial.coeff_mul_monomial" -> "data", "mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset" -> "topology", "polynomial.degree_derivative_le" -> "data", "alg_equiv.to_linear_equiv_apply" -> "algebra", "add_submonoid.comap_comap" -> "algebra", "norm_add_le_of_le" -> "analysis", "list.eq_or_mem_of_mem_insert" -> "data", "lucas_lehmer.X.one_snd" -> "number_theory", "mv_polynomial.eval_eq'" -> "data", "int.mod_mul_left_mod" -> "data", "ennreal.top_mem_upper_bounds" -> "data", "set.diff_self" -> "data", "zmod.cast_mod_int" -> "data", "bounded_continuous_function.norm_smul_le" -> "topology", "multiset.countp_filter" -> "data", "congr_arg" -> "init", "joined.symm" -> "topology", "measure_theory.simple_func.lintegral_smul" -> "analysis", "list.prod_range_succ" -> "data", "set.image_neg_Ioi" -> "data", "and_iff_right_iff_imp" -> "logic", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_comp_is_iso_inv" -> "category_theory", "pfunctor.M.iselect_nil" -> "data", "set.Icc_self" -> "data", "set.maps_to'" -> "data", "set.Union_of_singleton" -> "data", "onote.zero_lt_one" -> "set_theory", "set.Ici_subset_Ico_union_Ici" -> "data", "category_theory.limits.limit_uncurry_iso_limit_comp_lim_inv_\[Pi]" -> "category_theory", "ring_hom.restrict_apply" -> "algebra", "list.range_subset" -> "data", "quotient.induction_on\:2082'" -> "data", "list.nil_product" -> "data", "asymptotics.is_O.trans_tendsto_nhds" -> "analysis", "divp_eq_div" -> "algebra", "topological_fiber_bundle_core.continuous_proj" -> "topology", "nat.min_fac_pos" -> "data", "list.alternating_sum_cons_cons'" -> "data", "metric.closed_ball_zero" -> "topology", "alist.lookup_union_left" -> "data", "category_theory.abelian.images.image.fac_assoc" -> "category_theory", "is_open_map_add_right" -> "topology", "list.argmax_concat" -> "data", "nat.mul_div_cancel'" -> "init", "nat.sqrt_aux_0" -> "data", "nhds_one_symm" -> "topology", "is_preconnected.Ioi_cInf_subset" -> "topology", "mem_right_coset_right_coset" -> "algebra", "of_mul_injective" -> "algebra", "iterated_fderiv_one_apply" -> "analysis", "vector.insert_nth_comm" -> "data", "set.Ioc_subset_Ioc_right" -> "data", "category_theory.limits.biproduct.inl_map" -> "category_theory", "computable_pred.computable_of_many_one_reducible" -> "computability", "normalize_zero" -> "algebra", "ennreal.inv_lt_one" -> "data", "hyperreal.infinite_pos_iff_infinite_of_nonneg" -> "data", "summable.prod_factor" -> "topology", "polynomial.eval_monomial" -> "data", "mul_right_comm" -> "algebra", "multiset.map_hcongr" -> "data", "submodule.prod_equiv_of_is_compl_symm_apply_left" -> "algebra", "left_ne_zero_of_mul" -> "algebra", "apply_ite" -> "logic", "metric.compact_space_iff_seq_compact_space" -> "topology", "fintype.prod_extend_by_one" -> "data", "enat.coe_lt_coe" -> "data", "ennreal.continuous_at_mul_const" -> "topology", "normed_field.norm_mul" -> "analysis", "algebra.algebra_map_eq_smul_one" -> "algebra", "add_commute.symm" -> "algebra", "category_theory.iso.trans_symm" -> "category_theory", "measure_theory.outer_measure.le_smul_caratheodory" -> "analysis", "nat.prime.dvd_iff_not_coprime" -> "data", "rat.lt_def" -> "data", "is_preconnected_Ico" -> "topology", "set.union_empty_iff" -> "data", "con.comp_mk'_apply" -> "algebra", "turing.list_blank.map_modify_nth" -> "computability", "list.perm_option_to_list" -> "data", "intermediate_value_univ" -> "topology", "mul_aut.coe_mul" -> "data", "monoid_hom.map_exists_right_inv" -> "algebra", "turing.blank_rel.refl" -> "computability", "alg_equiv.comp_symm" -> "algebra", "ideal.mem_span_pair" -> "algebra", "omega.sat_eq_elim" -> "tactic", "is_add_group_hom.comp" -> "algebra", "measure_theory.lintegral_finset_sum" -> "analysis", "is_totally_separated_singleton" -> "topology", "computation.destruct_eq_think" -> "data", "lower_bounds_le_upper_bounds" -> "order", "infi_lt_iff" -> "order", "complex.arg_real_mul" -> "analysis", "asymptotics.is_o.trans" -> "analysis", "list.countp_eq_length_filter" -> "data", "finset.mem_sort" -> "data", "submodule.smul_mem_span_smul'" -> "algebra", "frontier_closed_ball'" -> "analysis", "list.map_filter_map" -> "data", "set.preimage_const_sub_Ici" -> "data", "uniform_space.ball_mem_nhds" -> "topology", "list.merge_sort_eq_self" -> "data", "set.preimage_mono" -> "data", "continuous_linear_equiv.surjective" -> "topology", "int.mul_div_assoc" -> "data", "list.nodup_pmap" -> "data", "matrix.matrix_eq_sum_std_basis" -> "data", "ennreal.bit1_eq_one_iff" -> "data", "power_series.nat_le_order" -> "algebra", "measure_theory.measure.dirac_apply_of_mem" -> "analysis", "pgame.le_of_relabelling" -> "set_theory", "finset.mem_preimage" -> "data", "is_preirreducible_iff_closed_union_closed" -> "topology", "rtendsto'_nhds" -> "topology", "norm_num.pow_bit0" -> "tactic", "open_embedding.is_open_map" -> "topology", "unique_diff_within_at_univ" -> "analysis", "category_theory.monoidal_of_has_finite_coproducts.left_unitor_inv" -> "category_theory", "pell.xn_zero" -> "number_theory", "localization_map.mk'_mem_iff" -> "algebra", "set.Ioc_subset_Ioc_union_Icc" -> "data", "equiv.conj_trans" -> "data", "pgame.not_le" -> "set_theory", "tactic.ring.pow_add_rev_right" -> "tactic", "mv_polynomial.is_basis_monomials" -> "algebra", "cardinal.lt_univ'" -> "set_theory", "filter.eventually_imp_distrib_left" -> "order", "is_clopen_union" -> "topology", "multiset.to_finset_cons" -> "data", "nat.sub_lt_of_pos_le" -> "init", "real.cos_two_mul" -> "data", "finsupp.filter_single_of_neg" -> "data", "convex.convex_hull_eq" -> "analysis", "add_le_of_le_sub_right" -> "algebra", "filter.frequently.forall_exists_of_at_top" -> "order", "submodule.map_mkq_eq_top" -> "algebra", "filter.has_basis_generate" -> "order", "with_top.is_lub_Sup'" -> "order", "filter.join_mono" -> "order", "tendsto_sub_comap_self" -> "topology", "submodule.is_open_mono" -> "topology", "zmod.nat_abs_val_min_abs_neg" -> "data", "set.neg_neg" -> "algebra", "set.Ioi_inter_Iic" -> "data", "roption.mem_bind_iff" -> "data", "ff_bor" -> "init", "bdd_below.inter_of_left" -> "order", "poly.sumsq_eq_zero" -> "number_theory", "is_bounded_bilinear_map_deriv_coe" -> "analysis", "real.arctan_zero" -> "analysis", "is_R_or_C.abs_im_le_abs" -> "data", "filter.ext" -> "order", "irrational_nrt_of_notint_nrt" -> "data", "category_theory.symmetric_of_has_finite_coproducts_to_braided_category_braiding" -> "category_theory", "add_units.add_lift_right_neg" -> "algebra", "turing.partrec_to_TM2.tr_nat_zero" -> "computability", "conjugate_i" -> "algebra", "linear_map.lipschitz_of_bound" -> "analysis", "list.count_tail" -> "data", "mul_eq_one_iff_eq_one_of_one_le" -> "algebra", "is_compact.integrable_on_of_nhds_within" -> "analysis", "int.test_bit_ldiff" -> "data", "cardinal.out_embedding" -> "set_theory", "composition.card_boundaries_eq_succ_length" -> "combinatorics", "smodeq.def" -> "algebra", "set.eq_on.eventually_eq" -> "order", "multiset.inf_erase_dup" -> "data", "category_theory.monoidal_category.left_unitor_product_aux_perimeter" -> "category_theory", "int.le_sub_one_of_lt" -> "init", "finset.piecewise_insert_self" -> "data", "nat_ceil_le" -> "algebra", "list.length_insert_of_not_mem" -> "data", "Inf_lt_iff" -> "order", "tactic.abel.const_add_termg" -> "tactic", "set.image_eq_empty" -> "data", "category_theory.limits.types.sigma_map" -> "category_theory", "is_extr_filter.comp_tendsto" -> "order", "measure_theory.simple_func.add_lintegral" -> "analysis", "mul_lt_of_lt_one_of_lt" -> "algebra", "inv_sub_inv" -> "algebra", "tactic.ring_exp.add_pf_sum_gt" -> "tactic", "continuous_multiset_sum" -> "topology", "enorm.coe_max" -> "analysis", "finset.affine_combination_linear" -> "algebra", "measure_theory.simple_func.integral_eq_lintegral'" -> "analysis", "category_theory.graded_object.shift_functor_map_apply" -> "category_theory", "euclidean_geometry.angle_add_angle_add_angle_eq_pi" -> "geometry", "list.cons_subset_of_subset_of_mem" -> "data", "roption.coe_some" -> "data", "subalgebra.mul_mem" -> "algebra", "vector.tendsto_insert_nth" -> "topology", "lipschitz_with.dist_left" -> "topology", "commute.cast_nat_mul_left" -> "algebra", "primrec.dom_denumerable" -> "computability", "turing.reaches\:2080.tail" -> "computability", "bitraversable.tsnd_eq_snd_id'" -> "control", "measure_theory.ae_eq_fun.lintegral_mono" -> "analysis", "hash_map.mem_insert" -> "data", "category_theory.functor.to_cocone_\[Iota]_app" -> "category_theory", "le_not_le_of_lt" -> "init", "valuation.is_equiv_of_map_strict_mono" -> "algebra", "category_theory.image_to_kernel_map_epi_of_epi_of_zero" -> "algebra", "exists_pair_ne" -> "logic", "is_add_submonoid.smul_mem" -> "algebra", "uniform_space.compact_iff_seq_compact" -> "topology", "num.bit0_of_bit0" -> "data", "complex.abs_of_nat" -> "data", "prod.swap_swap_eq" -> "data", "complex.add_re" -> "data", "ordinal.CNF_sorted" -> "set_theory", "polynomial.nat_degree_comp_le" -> "data", "category_theory.uncurry.map_app" -> "category_theory", "measure_theory.ae_eq_fun.measurable" -> "analysis", "computation.lift_rel_map" -> "data", "set.nonempty.mul" -> "algebra", "polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero" -> "data", "computable.nat_strong_rec" -> "computability", "lipschitz_with.of_edist_le" -> "topology", "real.sin_pos_of_pos_of_le_one" -> "data", "generalized_continued_fraction.exists_int_eq_of_part_denom" -> "algebra", "primrec.option_map" -> "computability", "min_add_add_left" -> "algebra", "tactic.ring_exp.pow_p_pf_singleton" -> "tactic", "pnat.exists_prime_and_dvd" -> "data", "set.compl_Union" -> "data", "monoid_algebra.lift_single" -> "data", "nat.succ_div_of_dvd" -> "data", "measure_theory.measure.finite_at_filter.inf_of_right" -> "analysis", "multiset.rel_map" -> "data", "classical.cases_on" -> "init", "affine_map.comp_assoc" -> "algebra", "category_theory.sum.associator_map_inl_inr" -> "category_theory", "category_theory.limits.prod_functor_map_app" -> "category_theory", "ideal.mem_quotient_iff_mem" -> "algebra", "coe_subset_nonunits" -> "algebra", "deriv_within_cexp" -> "analysis", "vector.remove_nth_insert_nth" -> "data", "finset.map_refl" -> "data", "zmod.neg_val'" -> "data", "category_theory.abelian.pseudoelement.sub_of_eq_image" -> "category_theory", "pnat.bit1_le_bit1" -> "data", "set.piecewise_insert" -> "data", "matrix.transpose_row" -> "data", "list.nil_sigma" -> "data", "set.mem_to_finset" -> "data", "is_greatest_union_iff" -> "order", "set.indicator_self_add_compl_apply" -> "data", "nat.sub_lt_sub_left_iff" -> "data", "affine_subspace.span_Union" -> "algebra", "measurable.neg" -> "analysis", "circle_deg1_lift.floor_map_map_zero_le" -> "dynamics", "pnat.gcd_rel_right" -> "data", "finsupp.ker_lsingle" -> "algebra", "differentiable_on.const_smul" -> "analysis", "mvqpf.cofix.dest_mk" -> "data", "norm_eq_zero" -> "analysis", "list.sum_join" -> "data", "filter.comap_comap" -> "order", "multiset.nodup_ext" -> "data", "ite_mul_one" -> "algebra", "exists_open_with_compact_closure" -> "topology", "lie_group_core.to_lie_group" -> "geometry", "ordinal.power_le_power_iff_right" -> "set_theory", "is_open_empty" -> "topology", "power_series.inv_mul" -> "algebra", "finset.sum_piecewise" -> "algebra", "subsemiring.closure_eq" -> "algebra", "lower_bounds_Ico" -> "order", "nat.pow_right_strict_mono" -> "data", "ennreal.mul_max" -> "data", "set.preimage_add_right_zero" -> "algebra", "pow_eq_zero'" -> "algebra", "list.append_eq_nil" -> "data", "local_homeomorph.of_set_source" -> "topology", "finset.prod_product'" -> "algebra", "has_deriv_at.div" -> "analysis", "differentiable_within_at.sum" -> "analysis", "localization_map.map_map" -> "algebra", "onote.repr_power" -> "set_theory", "quotient.lift_beta" -> "data", "tsum_nonpos" -> "topology", "list.nodupkeys_cons" -> "data", "prod.fst_swap" -> "data", "set.image_swap_eq_preimage_swap" -> "data", "zmod.cast_int_cast" -> "data", "subalgebra.list_sum_mem" -> "algebra", "mv_polynomial.eval_rename_prodmk" -> "data", "opposite.unop_inv" -> "algebra", "submonoid.le_comap_of_map_le" -> "algebra", "filter.add_assoc" -> "order", "matrix.is_unit_nonsing_inv_det" -> "algebra", "fin.sum_univ_cast_succ" -> "data", "cardinal.omega_le_aleph'" -> "set_theory", "ideal.quotient.maximal_of_is_field" -> "algebra", "category_theory.functor.equiv_functor_map" -> "category_theory", "is_R_or_C.abs_cast_nat" -> "data", "polynomial.induction_on'" -> "data", "polynomial.leading_coeff_comp" -> "data", "bilin_form.zero_right" -> "algebra", "multilinear_map.continuous_of_bound" -> "analysis", "prime_spectrum.zero_locus_empty_iff_eq_top" -> "algebraic_geometry", "category_theory.limits.prod.associator_hom" -> "category_theory", "units.coe_gpow" -> "algebra", "inv_lt_inv'" -> "algebra", "mem_segment_translate" -> "analysis", "cardinal.mk_bounded_subset_le" -> "set_theory", "punit.inv_eq" -> "algebra", "norm_num.le_neg_pos" -> "tactic", "stream.unfolds_head_eq" -> "data", "finmap.keys_val" -> "data", "seq.of_list_append" -> "data", "filter.Liminf_le_Liminf_of_le" -> "order", "omega.symmod_add_one_self" -> "tactic", "nat.to_add_pow" -> "algebra", "list.sublists'_reverse" -> "data", "iterated_deriv_succ'" -> "analysis", "submodule.neg_mem_iff" -> "algebra", "right_ord_continuous.comp" -> "order", "filter.eventually.prod_mk_nhds" -> "topology", "abelianization.lift.of" -> "algebra", "multiset.eq_repeat'" -> "data", "set.Ioc_inter_Ioc" -> "data", "polynomial.div_by_monic_one" -> "data", "set.preimage_bInter" -> "data", "equiv.coe_mul_right" -> "data", "pnat.one_coprime" -> "data", "algebraic_geometry.PresheafedSpace.id_c_app" -> "algebraic_geometry", "category_theory.limits.cocones.whiskering_equivalence_functor" -> "category_theory", "submodule.lt_iff_le_and_exists" -> "algebra", "matrix.to_lin_one" -> "algebra", "is_irreducible.nonempty" -> "topology", "pgame.domineering.move_left_smaller" -> "set_theory", "pnat.one_gcd" -> "data", "add_subgroup.mem_inf" -> "algebra", "set.mk_preimage_prod_left_eq_if" -> "data", "Ioo_mem_nhds_within_Ici" -> "topology", "category_theory.preadditive.comp_neg" -> "category_theory", "measure_theory.tendsto_measure_Union" -> "analysis", "pgame.left_response_spec" -> "set_theory", "times_cont_diff_at.neg" -> "analysis", "differentiable.cos" -> "analysis", "Module.monoidal_category.pentagon" -> "algebra", "category_theory.equivalence.equivalence_mk'_unit_inv" -> "category_theory", "matrix.range_diagonal" -> "algebra", "presented_group.to_group.unique" -> "algebra", "add_semiconj_by.zero_left" -> "algebra", "cardinal.lift_mk_eq" -> "set_theory", "continuous_linear_equiv.coe_fn_of_bijective" -> "analysis", "le_add_of_sub_right_le" -> "algebra", "self_div_two_le_harmonic_two_pow" -> "analysis", "fixed_points.next_eq" -> "order", "le_of_mul_le_mul_left" -> "algebra", "tendsto_locally_uniformly_on_univ" -> "topology", "has_fderiv_within_at_id" -> "analysis", "continuous_linear_equiv.comp_times_cont_diff_on_iff" -> "analysis", "list.perm.product_left" -> "data", "measure_theory.simple_func.const_mul_eq_map" -> "analysis", "list.mem_permutations_aux2'" -> "data", "nat.succ_add" -> "init", "not_exists_not" -> "logic", "pos_num.divmod_to_nat" -> "data", "padic_norm_e.nonarchimedean'" -> "data", "fact.bit1.pos" -> "data", "measure_theory.ae_eq_fun.lintegral_zero" -> "analysis", "list.eq_nil_of_suffix_nil" -> "data", "is_R_or_C.of_real_bit1" -> "data", "set.inj_on.right_inv_on_of_left_inv_on" -> "data", "multiset.union_le" -> "data", "add_units.min_coe" -> "algebra", "set.preimage_mul_const_Icc_of_neg" -> "data", "metric.dist_le_diam_of_mem" -> "topology", "measure_theory.lintegral_congr" -> "analysis", "cardinal.mk_range_eq_lift" -> "set_theory", "not_surjective_fintype_infinite" -> "data", "measurable_to_encodable" -> "analysis", "or_iff_not_and_not" -> "logic", "lagrange.eq_zero_of_eval_eq_zero" -> "algebra", "set.image_mul_right'" -> "algebra", "quadratic_form.map_zero" -> "algebra", "nat.elim_succ" -> "computability", "typevec.typevec_cases_nil\:2082_append_fun" -> "data", "fintype.prod_eq_one" -> "data", "category_theory.op_equiv_symm_apply" -> "category_theory", "has_fderiv_within_at.sub_const" -> "analysis", "is_irreducible.image" -> "topology", "primrec_pred.comp" -> "computability", "typevec.drop_fun_id" -> "data", "is_greatest_pair" -> "order", "cardinal.pow_le" -> "set_theory", "zsqrtd.sqrtd_im" -> "data", "prod.lt_def" -> "init", "polynomial.coeff_sub" -> "data", "local_equiv.prod_trans" -> "data", "nonempty_quotient_iff" -> "data", "is_basis.total_comp_repr" -> "algebra", "function.is_periodic_pt.apply" -> "dynamics", "supr_range" -> "order", "list.length_concat" -> "data", "asymptotics.is_O_snd_prod'" -> "analysis", "concave_on.convex_hypograph" -> "analysis", "vector.to_list_map" -> "data", "filter.eventually_of_mem" -> "order", "rat.mul_self_num" -> "data", "mul_mul_inv_of_self_cancel" -> "algebra", "ideal.quotient_inf_to_pi_quotient_bijective" -> "algebra", "inducing_is_closed" -> "topology", "znum.zneg_pred" -> "data", "filter.eventually_eq.is_min_filter_iff" -> "order", "add_one_pow_unbounded_of_pos" -> "algebra", "filter.has_basis.lift" -> "order", "set.eq_preimage_subtype_val_iff" -> "data", "nat.le_rec_on_succ'" -> "data", "equiv.coe_plift" -> "data", "measure_theory.lintegral_supr_directed" -> "analysis", "filter.preimage_mem_comap" -> "order", "fixed_points.is_integral" -> "algebra", "emetric.nonempty_compacts.to_closeds.uniform_embedding" -> "topology", "normed_group.tendsto_nhds_zero" -> "analysis", "iterated_fderiv_zero_apply" -> "analysis", "znum.cast_bit0" -> "data", "mvqpf.cofix.dest_corec\:2081" -> "data", "is_add_submonoid.smul_coe" -> "algebra", "measure_theory.induced_outer_measure_eq_infi" -> "analysis", "category_theory.nat_trans.exchange" -> "category_theory", "compact_iff_compact_univ" -> "topology", "convex.norm_image_sub_le_of_norm_deriv_within_le" -> "analysis", "digits_of_digits" -> "data", "padic_int.norm_lt_one_mul" -> "data", "multiset.nodup_range" -> "data", "multiset.to_finset_nsmul" -> "data", "filter.eventually_eq.add" -> "order", "turing.tr_eval_dom" -> "computability", "array.to_list_length" -> "data", "bilin_form.neg_right" -> "algebra", "uniformity_prod" -> "topology", "omega.nat.exists_clause_holds_core" -> "tactic", "finset.sum_ite_eq'" -> "algebra", "seq1.map_id" -> "data", "measure_theory.simple_func.coe_mul" -> "analysis", "list.cons_injective" -> "data", "pnat.xgcd_type.is_special_iff" -> "data", "image_le_of_deriv_right_lt_deriv_boundary'" -> "analysis", "is_preconnected_iff_preconnected_space" -> "topology", "affine_subspace.mk'_nonempty" -> "algebra", "add_submonoid.localization_map.add_equiv_of_add_equiv_mk'" -> "algebra", "finset.fold_singleton" -> "data", "affine_subspace.coe_direction_eq_vsub_set" -> "algebra", "times_cont_diff.times_cont_diff_fderiv_apply" -> "analysis", "continuous_on_id" -> "topology", "char_zero_of_inj_zero" -> "algebra", "filter.infi_sets_eq" -> "order", "local_equiv.refl_target" -> "data", "finset.nonempty_encodable" -> "data", "digits_eq_nil_iff_eq_zero" -> "data", "deriv_within_inv" -> "analysis", "t2_separation" -> "topology", "neg_le_sub_right_of_le_add" -> "algebra", "list.kerase_nil" -> "data", "cardinal.lift_nat_cast" -> "set_theory", "int.coe_nat_le" -> "data", "turing.list_blank.induction_on" -> "computability", "continuous_linear_map.is_complete_ker" -> "topology", "num.shiftl_to_nat" -> "data", "real.sin_pi_over_two_pow_succ" -> "analysis", "list.perm.kreplace" -> "data", "finset.mem_of_min" -> "data", "nat.lt_iff_le_not_le" -> "init", "num.gcd_to_nat_aux" -> "data", "times_cont_mdiff_within_at_inter" -> "geometry", "category_theory.discrete.equivalence_unit_iso" -> "category_theory", "quotient_group.coe_pow" -> "algebra", "mv_polynomial.eval\:2082_eq_eval_map" -> "data", "omega.int.push_neg_equiv" -> "tactic", "pgame.lt_iff_le_not_le" -> "set_theory", "function.surjective.exists" -> "logic", "list.disjoint_append_left" -> "data", "prime_multiset.prod_dvd_iff'" -> "data", "equiv.arrow_congr'_symm" -> "data", "category_theory.monoidal.tensor_obj_map" -> "category_theory", "znum.cast_lt" -> "data", "quotient_add_group.eq_class_eq_left_coset" -> "algebra", "filter.tendsto_at_top_add_const_right" -> "order", "tendsto_neg_nhds_within_Ioi" -> "topology", "add_subgroup.coe_top" -> "algebra", "mem_uniformity_is_closed" -> "topology", "finset.mem_powerset" -> "data", "multiset.sub_cons" -> "data", "functor.comp.seq_pure" -> "control", "seq.head_dropn" -> "data", "finite_dimensional.findim_eq_dim" -> "algebra", "list.last_mem" -> "data", "times_cont_diff_within_at_inter" -> "analysis", "category_theory.limits.biprod.hom_ext'" -> "category_theory", "tactic.ring_exp.simple_pf_exp_one" -> "tactic", "nnreal.div_eq_div_iff" -> "data", "multiset.mem_join" -> "data", "polynomial.monic.nat_degree_mul" -> "data", "category_theory.functor.cocones_obj" -> "category_theory", "dense_sInter_of_open" -> "topology", "function.injective.map_at_top_finset_prod_eq" -> "order", "multiset.nat.nodup_antidiagonal" -> "data", "uniform_space.separation_prod" -> "topology", "nat.sub_mono_left_strict" -> "tactic", "set.Ici_top" -> "data", "linear_equiv.symm_apply_eq" -> "algebra", "is_coprime.dvd_of_dvd_mul_left" -> "algebra", "set.union_subset_union_left" -> "data", "tsum_eq_single" -> "topology", "finset.prod_dvd_of_coprime" -> "algebra", "le_neg_add_iff_add_le" -> "algebra", "left_ord_continuous.mono" -> "order", "ordinal.deriv_limit" -> "set_theory", "subsemiring.add_mem" -> "algebra", "cSup_inter_le" -> "order", "ring.fractional_ideal.mem_zero_iff" -> "algebra", "add_monoid.closure_singleton" -> "algebra", "measure_theory.measure.restrict_zero" -> "analysis", "computation.lift_rel_return_left" -> "data", "multiset.subset.trans" -> "data", "nat.prime.multiplicity_self" -> "data", "znum.lt_to_int" -> "data", "mem_closure_iff_nhds_within_ne_bot" -> "topology", "set.diff_subset_iff" -> "data", "gaussian_int.norm_le_norm_mul_left" -> "data", "mem_lower_bounds" -> "order", "prod.ext" -> "data", "measure_theory.measure.dirac_bind" -> "analysis", "int.of_nat_eq_coe" -> "init", "lucas_lehmer.s_zmod_eq_s" -> "number_theory", "measure_theory.outer_measure.trim_trim" -> "analysis", "exp_neg_inv_glue.f_aux_deriv" -> "analysis", "list.tail_sum" -> "data", "ennreal.sub_eq_zero_of_le" -> "data", "category_theory.faithful.of_comp_iso" -> "category_theory", "times_cont_mdiff_on_of_locally_times_cont_mdiff_on" -> "geometry", "ring_hom.codomain_trivial_iff_range_trivial" -> "algebra", "category_theory.limits.cones.forget_obj" -> "category_theory", "mul_le_of_le_inv_mul" -> "algebra", "finset.sum_update_of_mem" -> "algebra", "measure_theory.measure_bUnion" -> "analysis", "submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero" -> "algebra", "function.injective.comp_inj_on" -> "data", "is_lub_pair" -> "order", "vector.nth_update_nth_of_ne" -> "data", "subsemiring.srange_subtype" -> "algebra", "opposite.unop_op" -> "data", "category_theory.nat_iso.op_hom" -> "category_theory", "is_local_max_on.is_local_max" -> "topology", "pfun.core_res" -> "data", "monoid_algebra.lift_unique'" -> "data", "set.Union_add_left_image" -> "algebra", "pequiv.symm_single" -> "data", "ordinal.one_lt_omega" -> "set_theory", "lie_subalgebra.ext" -> "algebra", "rel_iso.symm_apply_apply" -> "order", "complex.lim_eq_lim_im_add_lim_re" -> "data", "one_div_mul_sub_mul_one_div_eq_one_div_add_one_div" -> "algebra", "is_R_or_C.inv_zero" -> "data", "submodule.quot_equiv_of_eq_bot_symm_apply" -> "algebra", "rat.coe_int_inj" -> "data", "norm_num.dvd_eq_nat" -> "tactic", "list.mfoldr_cons" -> "data", "list.cons_sublist_cons_iff" -> "data", "Sup_Prop_eq" -> "order", "mv_polynomial.C_inj" -> "data", "neg_le" -> "algebra", "differentiable_within_at.comp'" -> "analysis", "list.forall\:2082_zip" -> "data", "submodule.range_of_le" -> "algebra", "is_least.union" -> "order", "nat.fact_dvd_fact" -> "data", "real.sqrt_mul_self" -> "data", "topological_fiber_bundle_core.local_triv_trans" -> "topology", "list.traverse_append" -> "control", "int.mul_lt_mul_of_neg_left" -> "init", "right_ord_continuous.iterate" -> "order", "nat.choose_succ_self_right" -> "data", "pmf.coe_le_one" -> "analysis", "ideal.map_comap_le" -> "algebra", "set.add_singleton" -> "algebra", "category_theory.action_category.hom_as_subtype" -> "category_theory", "approximates_linear_on.mono_num" -> "analysis", "is_extr_on.on_preimage" -> "order", "monoid_hom.to_fun_eq_coe" -> "algebra", "lcm_eq_one_iff" -> "algebra", "list.ext" -> "data", "ring_hom.map_eq_zero" -> "algebra", "le_cinfi" -> "order", "linear_map.neg_apply" -> "algebra", "real.sin_pi_div_two" -> "analysis", "list.nodup_diff" -> "data", "pequiv.equiv_to_pequiv_to_matrix" -> "data", "is_greatest.unique" -> "order", "is_basis_empty_bot" -> "algebra", "list.chain'.append_overlap" -> "data", "stream.drop_drop" -> "data", "is_local_min.sup" -> "topology", "is_linear_map.mk'_apply" -> "algebra", "norm_num.le_bit1_bit1" -> "tactic", "seq.tail_nil" -> "data", "uniform.continuous_on_iff'_right" -> "topology", "lipschitz_with.diam_image_le" -> "topology", "times_cont_diff_at_top" -> "analysis", "turing.eval_maximal\:2081" -> "computability", "tensor_algebra.\[Iota]_comp_lift" -> "algebra", "int.neg_succ_of_nat_eq" -> "init", "matrix.comp_to_matrix_mul" -> "algebra", "filter.lift_le" -> "order", "hyperreal.gt_of_tendsto_zero_of_neg" -> "data", "computable.id" -> "computability", "is_irreducible_iff_sUnion_closed" -> "topology", "measure_theory.l1.simple_func.uniform_embedding" -> "analysis", "localization.ring_equiv_of_quotient_apply" -> "algebra", "nat.dvd_fact" -> "data", "is_coprime.of_prod_right" -> "algebra", "equiv.perm.sign_swap" -> "algebra", "polynomial.coeff_monomial_mul" -> "data", "finset.image_inter" -> "data", "real.exp_monotone" -> "data", "finset.le_inf_iff" -> "data", "list.perm.filter" -> "data", "ennreal.tendsto_of_real" -> "topology", "set.indicator_mul" -> "data", "ne_zero_of_lt" -> "algebra", "filter.mem_binfi" -> "order", "metric.Hausdorff_dist_comm" -> "topology", "is_min_on.max" -> "order", "add_monoid_hom.map_add_neg" -> "algebra", "add_submonoid.le_comap_of_map_le" -> "algebra", "succ_nsmul'" -> "algebra", "filter.tendsto_at_bot_of_add_bdd_below_left'" -> "order", "norm_num.pow_bit1" -> "tactic", "lt_mem_nhds" -> "topology", "equiv.symm_trans" -> "data", "filter.Inter_mem_sets" -> "order", "category_theory.op_op_equivalence_inverse" -> "category_theory", "pmf.bind_comm" -> "analysis", "measure_theory.outer_measure.is_caratheodory_compl_iff" -> "analysis", "inner_product_geometry.angle_neg_neg" -> "geometry", "invariant_basis_number_field" -> "algebra", "function.embedding.coe_image" -> "logic", "cardinal.power_mul" -> "set_theory", "add_monoid_algebra.mul_def" -> "data", "pequiv.trans_bot" -> "data", "affine.simplex.monge_plane_comm" -> "geometry", "pow_pos" -> "algebra", "fixed_points.minpoly.minimal_polynomial" -> "algebra", "algebraic_geometry.PresheafedSpace.mk_coe" -> "algebraic_geometry", "list.foldl_assoc" -> "data", "multiset.mem_product" -> "data", "deriv.lhopital_zero_nhds" -> "analysis", "ideal.quotient.maximal_ideal_iff_is_field_quotient" -> "algebra", "mul_gpow" -> "algebra", "filter.tendsto_at_bot_embedding" -> "order", "localization.induction_on" -> "algebra", "complex.tan_conj" -> "data", "is_R_or_C.bit0_im" -> "data", "supr_apply" -> "order", "nat.zero_lt_bit1" -> "init", "computation.lift_rel_bind" -> "data", "ordinal.power_right_inj" -> "set_theory", "frontier_Ioo" -> "topology", "category_theory.limits.pushout_cocone.mk_\[Iota]_app_right" -> "category_theory", "znum.zneg_pos" -> "data", "localization_map.algebra_map_eq" -> "algebra", "ring.fractional_ideal.zero_le" -> "algebra", "lt_neg_of_lt_neg" -> "algebra", "times_cont_mdiff_at.prod_mk" -> "geometry", "category_theory.limits.kernel_is_iso_comp_inv_comp_kernel_\[Iota]" -> "category_theory", "convex.combo_affine_apply" -> "analysis", "list.eq_of_sublist_of_length_le" -> "data", "padic.of_rat_eq" -> "data", "linarith.le_of_le_of_eq" -> "tactic", "nat.prime.dvd_choose_self" -> "data", "cardinal.mk_quotient_le" -> "set_theory", "refl_mem_uniformity" -> "topology", "multiset.sections_zero" -> "data", "fib_is_sol_fib_rec" -> "data", "let_eq" -> "init", "set.preimage_add_const_Iic" -> "data", "submodule.nonzero_mem_of_bot_lt" -> "algebra", "smooth_within_at_const" -> "geometry", "add_magma.free_add_semigroup.of_add_assoc" -> "algebra", "valuation.coe_coe" -> "algebra", "gaussian_int.to_real_im" -> "data", "padic_norm_z.padic_norm_e_of_padic_int" -> "data", "Algebra.of_self_iso_inv" -> "algebra", "category_theory.monad.algebra.hom.comp_f" -> "category_theory", "filter.germ.coe_eq" -> "order", "sup_eq_right" -> "order", "many_one_degree.le_refl" -> "computability", "set.image_neg_Ici" -> "data", "continuous_multilinear_map.norm_image_sub_le_of_bound" -> "analysis", "real.sqrt_inj" -> "data", "set.Ico_subset_Icc_union_Ioo" -> "data", "ennreal.div_zero_iff" -> "data", "nnreal.continuous.sub" -> "topology", "real.tan_nonneg_of_nonneg_of_le_pi_div_two" -> "analysis", "finset.card_attach_fin" -> "data", "gpow_mul_comm" -> "algebra", "ennreal.tendsto.mul" -> "topology", "monoid_hom.comap_ker" -> "algebra", "multiplicity.finite_int_iff_nat_abs_finite" -> "algebra", "add_subgroup.closure_union" -> "algebra", "inf_Sup_eq" -> "order", "strict_weak_order.erefl" -> "init", "mem_nhds_left" -> "topology", "category_theory.equivalence.symm_inverse" -> "category_theory", "or_eq_of_eq" -> "init", "category_theory.limits.pushout_cocone.mk_\[Iota]_app_zero" -> "category_theory", "set.Ico_subset_Ico_left" -> "data", "continuous_linear_map.op_norm_neg" -> "analysis", "set.prod_image_seq_comm" -> "data", "real.cau_seq_converges" -> "data", "mat_poly_equiv_symm_apply_coeff" -> "algebra", "pnat.mul_div_exact" -> "data", "if_eq_of_eq_false" -> "init", "list.sum_smul" -> "algebra", "pnat.ne_zero" -> "data", "real.one_le_exp" -> "data", "measure_theory.measure.mem_cofinite" -> "analysis", "submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul" -> "algebra", "pgame.equiv_refl" -> "set_theory", "is_bounded_bilinear_map.is_bounded_linear_map_deriv" -> "analysis", "subtype.connected_space" -> "topology", "ideal.is_jacobson_iff_Inf_maximal" -> "algebra", "pgame.mk_add_move_left_inl" -> "set_theory", "subring.ext'" -> "algebra", "add_submonoid.localization_map.lift_comp" -> "algebra", "turing.reaches\:2081_eq" -> "computability", "polynomial.aeval_alg_hom_apply" -> "data", "dense_embedding.inj_iff" -> "topology", "filter.tendsto_at_bot_at_bot_iff_of_monotone" -> "order", "nhds_of_nhds_within_of_nhds" -> "topology", "neg_lt_zero" -> "algebra", "subgroup.coe_supr_of_directed" -> "algebra", "uniform_continuous_fst" -> "topology", "submodule.quotient.nontrivial_of_lt_top" -> "algebra", "dvd_sub" -> "algebra", "ordinal.CNF_ne_zero" -> "set_theory", "euclidean_domain.mul_right_not_lt" -> "algebra", "measure_theory.integral_smul_measure" -> "analysis", "ordinal.power_one" -> "set_theory", "category_theory.category_of_elements.to_comma_map" -> "category_theory", "nat.mul_self_lt_mul_self" -> "data", "complex.sum_div_fact_le" -> "data", "set.countable.mono" -> "data", "is_basis.to_dual_range" -> "algebra", "category_theory.limits.colimit.pre_post" -> "category_theory", "is_R_or_C.two_ne_zero" -> "data", "filter.map_mono" -> "order", "list.exists_chain_of_relation_refl_trans_gen" -> "data", "fract_eq_fract" -> "algebra", "formal_multilinear_series.change_origin_summable_aux3" -> "analysis", "continuous_linear_map.smul_right_one_pow" -> "topology", "real.sin_pi_sub" -> "analysis", "ideal.radical_eq_jacobson" -> "algebra", "associates.mk_eq_zero" -> "algebra", "real.sqrt_mul_self_eq_abs" -> "data", "add_monoid_hom.map_indicator" -> "data", "submonoid.closure_Union" -> "algebra", "nonneg_add_comm_group.zero_lt_iff_nonneg_nonneg" -> "algebra", "uniform_space.completion.induction_on\:2082" -> "topology", "topological_group.t1_space" -> "topology", "function.cantor_surjective" -> "logic", "prod.snd_inv" -> "algebra", "lie_algebra.orthogonal.indefinite_diagonal_assoc" -> "algebra", "ring.direct_limit.of_injective" -> "algebra", "gcd_eq_normalize" -> "algebra", "measure_theory.simple_func.piecewise_univ" -> "analysis", "semidirect_product.lift_inr" -> "algebra", "multiplicity.one_left" -> "algebra", "category_theory.iso.comp_inv_eq" -> "category_theory", "le_is_glb_iff" -> "order", "sum.swap_swap" -> "data", "subalgebra.neg_mem" -> "algebra", "exp_neg_inv_glue.nonneg" -> "analysis", "real.volume_Ioc" -> "analysis", "multiset.fold_hom" -> "data", "free_magma.map_of" -> "algebra", "list.nth_le_reverse_aux1" -> "data", "lie_algebra.special_linear.sl_non_abelian" -> "algebra", "pnat.pos" -> "data", "subring.prod_mono_left" -> "algebra", "cauchy_seq_tendsto_of_is_complete" -> "topology", "euclidean_domain.gcd_self" -> "algebra", "nnreal.sub_sub_cancel_of_le" -> "data", "pnat.not_prime_one" -> "data", "submodule.smul_sup" -> "algebra", "filter.mem_infi_finite" -> "order", "is_max_on_const" -> "order", "nnreal.inv_one" -> "data", "finset.mem_erase_of_ne_of_mem" -> "data", "partrec.map_encode_iff" -> "computability", "ennreal.pow_ne_top" -> "data", "pnat.Ico.mem" -> "data", "convex.image_sub_lt_mul_sub_of_deriv_lt" -> "analysis", "function.commute.iterate_pos_le_iff_map_le" -> "order", "nat.one_div_le_one_div" -> "data", "coe_nnnorm" -> "analysis", "set.image_sub_const_Ioc" -> "data", "has_strict_fderiv_at.is_O_sub_rev" -> "analysis", "mul_left_continuous" -> "topology", "topological_space.open_nhds.map_id_obj" -> "topology", "measure_theory.measure.measure_univ_eq_zero" -> "analysis", "mul_semiring_action_hom.id_comp" -> "algebra", "real.sin_eq_zero_iff_of_lt_of_lt" -> "analysis", "relator.rel_exists_of_left_total" -> "logic", "injective_of_increasing" -> "order", "bitvec.to_nat_append" -> "data", "add_con.to_setoid_inj" -> "algebra", "uniform_continuous_iff_eventually" -> "topology", "galois_connection.dfun" -> "order", "real.uniform_continuous_inv" -> "topology", "category_theory.equivalence.cancel_unit_right_assoc'" -> "category_theory", "findim_vector_span_of_affine_independent" -> "algebra", "list.sublist_of_infix" -> "data", "mul_self_add_mul_self_eq_zero" -> "algebra", "multiplicity.eq_top_iff" -> "algebra", "multiset.disjoint_comm" -> "data", "equiv.set.sum_compl_apply_inr" -> "data", "subgroup.inv_mem_iff" -> "algebra", "finset.prod_attach_univ" -> "data", "prod.ext_iff" -> "data", "is_max_on.localize" -> "topology", "polynomial.restriction_one" -> "algebra", "filter.tendsto_at_bot_add" -> "order", "list.nil_bind" -> "init", "category_theory.limits.prod_left_unitor_inv_naturality" -> "category_theory", "measure_theory.simple_func.map_apply" -> "analysis", "ennreal.max_eq_zero_iff" -> "data", "subset_span_points" -> "algebra", "polynomial.dvd_term_of_is_root_of_dvd_terms" -> "data", "is_min_on.is_extr" -> "order", "matrix.rank_diagonal" -> "algebra", "set.interval_of_lt" -> "data", "finset.disjoint_union_right" -> "data", "rat.cast_mul" -> "data", "zsqrtd.norm_one" -> "data", "coe_homeomorph_of_strict_mono_continuous" -> "topology", "finset.prod_equiv" -> "data", "not_nonempty_fintype" -> "data", "open_subgroup.one_mem" -> "topology", "vsub_left_cancel" -> "algebra", "d_array.of_beq_eq_tt" -> "init", "roption.get_some" -> "data", "Module.monoidal_category.tensor_id" -> "algebra", "asymptotics.is_o_one_iff" -> "analysis", "linear_map.trace_aux_range" -> "algebra", "stream.homomorphism" -> "data", "submodule.colon_mono" -> "algebra", "real.pi_gt_sqrt_two_add_series" -> "data", "add_con.ext'" -> "algebra", "finset.sum_eq_zero_iff" -> "algebra", "finset.set_of_mem" -> "data", "fin.coe_cast" -> "data", "band_coe_iff" -> "init", "set.finite.convex_hull_eq_image" -> "analysis", "subring.coe_int_mem" -> "algebra", "Top.presheaf.pushforward.comp_inv_app" -> "topology", "ennreal.inv_ne_zero" -> "data", "bxor_ff" -> "init", "padic_int.exists_mem_range" -> "data", "asymptotics.is_o_iff_tendsto" -> "analysis", "two_pos" -> "algebra", "differentiable_at_snd" -> "analysis", "stream.tail_even" -> "data", "set.finite_bind" -> "data", "padic_norm_e.image" -> "data", "pequiv.single_subsingleton_eq_refl" -> "data", "con.coe_mul" -> "algebra", "finset.prod_add" -> "algebra", "dfinsupp.mk_sub" -> "data", "list.length_bind" -> "data", "rel.inv_inv" -> "data", "iterated_fderiv_within_inter_open" -> "analysis", "free_add_magma.traverse_add'" -> "algebra", "polynomial.splits_mul_iff" -> "algebra", "semiconj_by.neg_right" -> "algebra", "exists_is_basis_fintype" -> "algebra", "int.to_nat_sub" -> "init", "num.cast_inj" -> "data", "list.last_concat" -> "data", "tsum_of_norm_bounded" -> "analysis", "map_nhds_within" -> "topology", "category_theory.limits.types.colimit_equiv_quot_symm_apply" -> "category_theory", "category_theory.limits.fork.app_zero_right" -> "category_theory", "hyperreal.coe_mul" -> "data", "list.last'_is_some" -> "data", "category_theory.monoidal_functor.map_tensor" -> "category_theory", "algebra.adjoin_algebra_map" -> "algebra", "polynomial.aeval_C" -> "data", "measure_theory.restrict_mono_ae" -> "analysis", "metric.exists_dist_lt_of_Hausdorff_dist_lt'" -> "topology", "measurable_snd" -> "analysis", "add_con.le_def" -> "algebra", "int.modeq.modeq_of_modeq_mul_left" -> "data", "algebraic_closure.coe_to_step_of_le" -> "algebra", "submodule.prod_top" -> "algebra", "multiset.map_eq_zero" -> "data", "list.erase_dup_cons_of_not_mem" -> "data", "sym2.from_rel_irreflexive" -> "data", "commute.inv_left" -> "algebra", "finsupp.mem_support_finset_sum" -> "data", "iterated_deriv_eq_iterated_fderiv" -> "analysis", "to_bool_congr" -> "init", "algebra.smul_def" -> "algebra", "finsupp.ext_iff" -> "data", "tendsto_at_top_add_tendsto_right" -> "topology", "local_homeomorph.restr_univ" -> "topology", "dim_quotient_le" -> "algebra", "nat.pred_eq_sub_one" -> "data", "dioph.dvd_dioph" -> "number_theory", "monoid_algebra.of_apply" -> "data", "list.map_singleton" -> "init", "pgame.first_loses_of_equiv_iff" -> "set_theory", "galois_connection.lower_bounds_u_image_subset" -> "order", "padic_int.mod_part_lt_p" -> "data", "list.infix_iff_prefix_suffix" -> "data", "eq_div_iff" -> "algebra", "add_commute.add_right" -> "algebra", "le_of_mul_le_mul_right'" -> "algebra", "nat.lt_pow_self" -> "data", "local_homeomorph.to_homeomorph_symm_coe" -> "topology", "one_le_padic_val_nat_of_dvd" -> "data", "iterated_fderiv_apply_eq_iterated_deriv_mul_prod" -> "analysis", "polynomial.eval\:2082_X_pow" -> "data", "times_cont_diff_within_at_inter'" -> "analysis", "add_comm_group.direct_limit.of_f" -> "algebra", "filter.inter_mem_sets" -> "order", "subgroup.comap_inf" -> "algebra", "measure_theory.measure.count_apply_eq_top" -> "analysis", "stream.map_id" -> "data", "quotient_group_saturate" -> "topology", "nat.subtype.of_nat_surjective" -> "data", "nat.min_fac_aux_has_prop" -> "data", "pell.is_pell_nat" -> "number_theory", "set_coe_cast" -> "data", "times_cont_mdiff_within_at.times_cont_mdiff_at" -> "geometry", "category_theory.limits.image_mono_iso_source_hom_self_assoc" -> "category_theory", "list.head_le_sum" -> "data", "category_theory.tensoring_right_monoidal_\[CurlyEpsilon]_is_iso" -> "category_theory", "category_theory.sum.associator_obj_inl_inl" -> "category_theory", "ring_hom.one_def" -> "algebra", "asymptotics.is_O_with_of_le'" -> "analysis", "int.sub_nat_nat_of_lt" -> "init", "pell.yn_succ_succ" -> "number_theory", "pfunctor.M.agree_iff_agree'" -> "data", "nat.bit_le_bit1" -> "data", "int.normalize_of_nonneg" -> "algebra", "power_series.eq_zero_or_eq_zero_of_mul_eq_zero" -> "algebra", "circle_deg1_lift.semiconj_by_iff_semiconj" -> "dynamics", "nnreal.ne_iff" -> "data", "continuous_multilinear_map.norm_map_snoc_le" -> "analysis", "ennreal.tsum_sigma'" -> "topology", "set.surjective_onto_image" -> "data", "measure_theory.simple_func.piecewise_apply" -> "analysis", "complex.of_real_tanh_of_real_re" -> "data", "sub_le_self" -> "algebra", "Sup_pair" -> "order", "vector.head_cons" -> "data", "measure_theory.ae_eq_fun.mk_le_mk" -> "analysis", "pnat.dvd_iff" -> "data", "int.eq_one_of_mul_eq_self_right" -> "init", "has_strict_fderiv_at.const_sub" -> "analysis", "category_theory.abelian.image_\[Iota]_eq_image_\[Iota]" -> "category_theory", "polynomial.separable_def'" -> "algebra", "continuous_linear_map.coe_id'" -> "topology", "eq_add_of_sub_eq'" -> "algebra", "measure_theory.lintegral_zero" -> "analysis", "multiset.product_singleton" -> "data", "with_zero.coe_inv" -> "algebra", "coe_of_digits" -> "data", "bex.intro" -> "logic", "asymptotics.is_o.join" -> "analysis", "filter.realizer.mem_sets" -> "data", "padic_norm_e.eq_rat_norm" -> "data", "euclidean_geometry.angle_eq_zero_of_angle_eq_pi_right" -> "geometry", "relator.left_unique_flip" -> "logic", "semidirect_product.inl_aut" -> "algebra", "list.kinsert_def" -> "data", "one_lt_div" -> "algebra", "Ioc_mem_nhds_within_Ioi" -> "topology", "semiconj_by.sub_left" -> "algebra", "smodeq.refl" -> "algebra", "eq_of_eqv_lt" -> "init", "filter.is_bounded.is_cobounded_flip" -> "order", "cardinal.add_lt_omega" -> "set_theory", "subring.closure_le" -> "algebra", "set.eq_on.bij_on_iff" -> "data", "open_subgroup.coe_subgroup_le" -> "topology", "one_left_coset" -> "algebra", "localization.mk_one_eq_monoid_of_mk" -> "algebra", "cardinal.mul_lt_omega_iff_of_ne_zero" -> "set_theory", "submodule.mk_quotient_equiv_of_is_compl_apply" -> "algebra", "real.cos_arctan" -> "analysis", "finset.min'_le" -> "data", "nat.size_zero" -> "data", "con.ext_iff" -> "algebra", "finset.cons_eq_insert" -> "data", "list.prod_nil" -> "data", "nnreal.of_real_mono" -> "data", "card_pow_eq_one_eq_order_of_aux" -> "algebra", "nat.fib_zero" -> "data", "list.length_pos_of_mem" -> "data", "has_deriv_within_at.mul" -> "analysis", "tactic.abel.term_atomg" -> "tactic", "continuous_linear_equiv.symm_comp_self'" -> "topology", "vsub_mem_vector_span" -> "algebra", "euclidean_geometry.orthogonal_projection_mem" -> "geometry", "nonpos_of_mul_nonpos_right" -> "algebra", "function.injective.nonempty_apply_iff" -> "data", "pell.eq_pell_lem" -> "number_theory", "category_theory.functor.unop_obj" -> "category_theory", "euclidean_domain.mul_div_assoc" -> "algebra", "complex.cosh_neg" -> "data", "polynomial.splitting_field_aux.splits" -> "algebra", "ennreal.continuous_const_mul" -> "topology", "metric.mem_closure_range_iff" -> "topology", "has_fderiv_at_filter.const_smul_algebra" -> "analysis", "submodule.coe_zero" -> "algebra", "add_pos_of_pos_of_nonneg" -> "algebra", "finset.sum_lt_sum_of_nonempty" -> "algebra", "int.bit0_nonneg" -> "init", "zero_le_mul_right" -> "algebra", "polynomial.not_irreducible_C" -> "data", "matrix.to_blocks_from_blocks\:2081\:2082" -> "data", "set.range_sigma_mk" -> "data", "dist_vadd_cancel_right" -> "analysis", "ideal.radical_eq_Inf" -> "algebra", "card_perms_of_finset" -> "data", "list.sum_range_succ" -> "data", "set.mem_of_mem_diff" -> "data", "continuous_on_const" -> "topology", "fin.succ_above_pos" -> "data", "filter.germ.comp_tendsto'_coe" -> "order", "continuous_linear_map.has_deriv_at" -> "analysis", "complex.lim_im" -> "data", "multiset.antidiagonal_map_snd" -> "data", "isometric.point_reflection_dist_fixed" -> "analysis", "or_congr" -> "init", "submonoid.localization_map.mk'_sec" -> "algebra", "computation.destruct_ret" -> "data", "tendsto_pure_nhds" -> "topology", "ideal.radical_mul" -> "algebra", "set.Iio_union_right" -> "data", "poly.isp" -> "number_theory", "category_theory.monad.forget_creates_colimits.cocone_point_a" -> "category_theory", "submodule.span_empty" -> "algebra", "measure_theory.measure.compl_mem_cofinite" -> "analysis", "rank_le_domain" -> "algebra", "norm_num.mul_pos_neg" -> "tactic", "set.subset_bUnion_of_mem" -> "data", "dfinsupp.sum_add_index" -> "data", "category_theory.monoidal_category.unitors_equal" -> "category_theory", "if_eq_of_eq" -> "init", "num.lxor_to_nat" -> "data", "subsemiring.list_prod_mem" -> "algebra", "ring.direct_limit.of_add" -> "algebra", "filter.has_basis.forall_nonempty_iff_ne_bot" -> "order", "model_with_corners_prod_coe" -> "geometry", "formal_multilinear_series.comp_change_of_variables_blocks_fun" -> "analysis", "functor.comp.id_map" -> "control", "differentiable_at.csin" -> "analysis", "nat.lt_sub_left_of_add_lt" -> "data", "convex.is_linear_preimage" -> "analysis", "mv_polynomial.ext_iff" -> "data", "filter.has_basis.mem_of_superset" -> "order", "set.one_mem_one" -> "algebra", "add_units.max_coe" -> "algebra", "category_theory.equivalence.fun_inv_map" -> "category_theory", "free_abelian_group.lift.add'" -> "algebra", "gcd_monoid.irreducible_iff_prime" -> "algebra", "prod_mk_sum" -> "algebra", "nat.succ_le_of_lt" -> "init", "linear_map.ker_pi" -> "algebra", "polynomial.card_nth_roots" -> "data", "unique.ext_iff" -> "logic", "measurable_space.map_id" -> "analysis", "mul_inv_of_mul_self_cancel" -> "algebra", "finset.erase_empty" -> "data", "equiv.perm.cycle_of_one" -> "algebra", "list.revzip_swap" -> "data", "measure_theory.l1.eq" -> "analysis", "opposite.unop_mul" -> "algebra", "is_coprime_zero_right" -> "algebra", "computation.get_equiv" -> "data", "qpf.mem_supp" -> "data", "category_theory.monoidal_functor.map_right_unitor" -> "category_theory", "cardinal.power_lt_omega" -> "set_theory", "has_deriv_at.pow" -> "analysis", "category_theory.monoidal_category.left_unitor_conjugation" -> "category_theory", "abs_sub_le_iff" -> "algebra", "Ico_map_val_min_abs_nat_abs_eq_Ico_map_id" -> "number_theory", "submodule.comap_comp" -> "algebra", "commute.gpow_self" -> "algebra", "subring.closure_union" -> "algebra", "add_monoid_hom.range_eq_map" -> "algebra", "contracting_with.efixed_point_eq_of_edist_lt_top" -> "topology", "rel_embedding.map_rel_iff" -> "order", "vector.nth_tail" -> "data", "onote.oadd_mul" -> "set_theory", "with_top.coe_le_iff" -> "order", "computation.mem_bind" -> "data", "is_measurable_interval" -> "analysis", "equiv.to_embedding_coe_fn" -> "logic", "nnreal.rpow_le_one_of_one_le_of_nonpos" -> "analysis", "ring_equiv.image_eq_preimage" -> "data", "vsub_right_cancel_iff" -> "algebra", "zero_lt_one" -> "algebra", "set.empty_diff" -> "data", "quotient_map.of_quotient_map_compose" -> "topology", "real.le_sqrt_of_sqr_le" -> "data", "setoid.eq_eqv_class_of_mem" -> "data", "mul_div_right_comm" -> "algebra", "function.semiconj.maps_to_fixed_pts" -> "dynamics", "continuous_linear_equiv.coord_self" -> "analysis", "real.inner_le_Lp_mul_Lq_of_nonneg" -> "analysis", "padic_norm_e.add" -> "data", "fin.mk_one" -> "data", "measure_theory.l1.simple_func.of_simple_func_smul" -> "analysis", "measure_theory.dirac_ae_eq" -> "analysis", "has_fderiv_at_filter.prod" -> "analysis", "category_theory.coe_id" -> "category_theory", "injective_of_affine_independent" -> "algebra", "iff.elim_right" -> "init", "set.Inter_eq_Inter_finset'" -> "data", "measure_theory.measure.haar.prehaar_sup_le" -> "analysis", "list.map_subset" -> "data", "mv_power_series.coeff_inv" -> "algebra", "times_cont_diff_of_differentiable_iterated_deriv" -> "analysis", "measure_theory.ae_eq_fun.lift_rel_iff_coe_fn" -> "analysis", "free_group.red.not_step_singleton" -> "algebra", "int.neg_succ_of_nat_lt_zero" -> "init", "traversable.fold_map_hom" -> "control", "dist_le_tsum_dist_of_tendsto\:2080" -> "topology", "vector3.cons_fs" -> "number_theory", "submonoid.localization_map.mul_equiv_of_mul_equiv_eq_map_apply" -> "algebra", "category_theory.limits.im_obj" -> "category_theory", "int.neg_nonpos_of_nonneg" -> "init", "mem_interior_iff_mem_nhds" -> "topology", "nat.lt_of_lt_of_le" -> "init", "set.eq_empty_of_subset_empty" -> "data", "set.preimage_neg_Ioc" -> "data", "sub_lt_sub" -> "algebra", "multiset.card_cons" -> "data", "category_theory.comma.map_left_comp_inv_app_left" -> "category_theory", "zsqrtd.zero_re" -> "data", "zsqrtd.sq_le_add" -> "data", "polynomial.nat_degree_mul'" -> "data", "affine_map.to_fun_eq_coe" -> "algebra", "multiset.coe_card" -> "data", "polynomial.frange_of_subring" -> "algebra", "ennreal.top_div" -> "data", "continuous_on_Icc_extend_from_Ioo" -> "topology", "ideal.eq_jacobson_iff_Inf_maximal'" -> "algebra", "Group.coe_of" -> "algebra", "filter_basis.mem_filter_iff" -> "order", "asymptotics.is_o_norm_right" -> "analysis", "category_theory.limits.map_pair_iso_inv" -> "category_theory", "affine.triangle.orthocenter_mem_affine_span" -> "geometry", "list.find_eq_none" -> "data", "monoid_hom.prod_map_def" -> "algebra", "cau_seq.not_lim_zero_of_pos" -> "data", "finset.infi_finset_image" -> "data", "tsum_subtype" -> "topology", "Algebra.coe_comp" -> "algebra", "ideal.one_eq_top" -> "algebra", "gaussian_int.nat_abs_norm_mod_lt" -> "data", "primrec.option_is_some" -> "computability", "list.map_take" -> "data", "infi_split" -> "order", "mul_lt_mul_right" -> "algebra", "min_le_right_of_le" -> "algebra", "set.interval_self" -> "data", "category_theory.pi.sum_obj_obj" -> "category_theory", "real.cos_ne_zero_iff" -> "analysis", "equiv.trans_assoc" -> "data", "is_closed_map.comp" -> "topology", "omega.nat.preterm.val_add" -> "tactic", "list.nodup_map" -> "data", "measure_theory.norm_set_integral_le_of_norm_le_const_ae'" -> "analysis", "nat.coprime.mul_right" -> "data", "affine_subspace.span_union" -> "algebra", "differentiable_on.fst" -> "analysis", "metric.completion.uniform_continuous_dist" -> "topology", "set.le_eq_subset" -> "data", "zero_eq_nndist" -> "topology", "mul_lt_iff_lt_one_left" -> "algebra", "metric.frontier_ball_subset_sphere" -> "topology", "nat.sub_le_left_iff_le_add" -> "data", "finset.mem_inter" -> "data", "list.map_congr" -> "data", "list.length_remove_nth" -> "init", "nat.find_le" -> "algebra", "continuous_multilinear_map.map_zero" -> "topology", "magma.free_semigroup.lift_unique" -> "algebra", "function.commute.right_bij_on_fixed_pts_comp" -> "dynamics", "dvd_of_associated" -> "algebra", "localization_map.of_id" -> "algebra", "times_cont_diff.continuous_fderiv" -> "analysis", "alg_equiv.to_fun_apply" -> "algebra", "Module.Mon_Module_equivalence_Algebra.ring_add" -> "category_theory", "min_le_left" -> "init", "mem_ball_comp" -> "topology", "complex.zero_re" -> "data", "submonoid.mem_closure_singleton_self" -> "algebra", "submonoid.mem_Sup_of_mem" -> "algebra", "abs_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul" -> "analysis", "cardinal.sum_le_sup" -> "set_theory", "metric.Hausdorff_dist_empty'" -> "topology", "I_symm_one" -> "topology", "category_theory.limits.cocones.whiskering_obj" -> "category_theory", "cardinal.power_ne_zero" -> "set_theory", "measure_theory.outer_measure.exists_is_measurable_superset_of_trim_eq_zero" -> "analysis", "category_theory.limits.limit.lift_\[Pi]_assoc" -> "category_theory", "fin.cons_snoc_eq_snoc_cons" -> "data", "category_theory.arrow.w_assoc" -> "category_theory", "perfect_closure.quot_mk_eq_mk" -> "algebra", "seq.exists_of_mem_map" -> "data", "ring_hom.comp_apply" -> "algebra", "edist_le_range_sum_of_edist_le" -> "topology", "list.all_cons" -> "data", "simple_graph.adj_matrix_mul_vec_const_apply" -> "combinatorics", "pequiv.coe_mk_apply" -> "data", "list.count_cons_of_ne" -> "data", "associates.prod_eq_zero_iff" -> "algebra", "measurable_space.comap_comp" -> "analysis", "filter.le_iff_forall_inf_principal_compl" -> "order", "congr" -> "init", "nnreal.summable_coe" -> "topology", "std_simplex_eq_inter" -> "analysis", "filter.is_lawful_monad" -> "order", "mv_power_series.trunc_C" -> "algebra", "category_theory.currying_functor_obj_map" -> "category_theory", "tactic.ring.horner_add_horner_gt" -> "tactic", "nat.mul_mod_mul_right" -> "init", "list.length_iota" -> "data", "category_theory.limits.coequalizer.cofork_\[Iota]_app_one" -> "category_theory", "local_equiv.inv_image_trans_target" -> "data", "is_least.is_glb" -> "order", "finset.subset.refl" -> "data", "measure_theory.simple_func.restrict_preimage" -> "analysis", "set.inv_on.symm" -> "data", "nat.with_bot.lt_zero_iff" -> "data", "monoid_hom.prod_comp_prod_map" -> "algebra", "finset.insert_val" -> "data", "topological_space.open_nhds.map_id_obj_unop" -> "topology", "of_endo_map_action" -> "algebra", "strict_mono_of_monotone_of_injective" -> "order", "onote.NF.of_dvd_omega_power" -> "set_theory", "interior_Ioi" -> "topology", "cluster_pt.ne_bot" -> "topology", "to_matrix_to_bilin_form" -> "algebra", "finset.sum_attach_univ" -> "data", "padic_val_rat.padic_val_rat_self" -> "data", "finset.bind_subset_bind_of_subset_left" -> "data", "opposite.op_eq_iff_eq_unop" -> "data", "ideal.is_jacobson_iff_Inf_maximal'" -> "algebra", "finset.Ico.succ_top" -> "data", "polynomial.map_zero" -> "data", "list.perm.union_left" -> "data", "num.cast_to_nat" -> "data", "list.length_foldr_permutations_aux2" -> "data", "min_le_left_of_le" -> "algebra", "mvpfunctor.map_obj_append1" -> "data", "forall_true_iff'" -> "logic", "measure_theory.l1.simple_func.eq_iff" -> "analysis", "equiv.image_eq_preimage" -> "data", "set.range_inl_union_range_inr" -> "data", "ball.imp_left" -> "logic", "equiv.is_lawful_functor" -> "control", "real.sin_two_mul" -> "data", "padic_int.valuation_nonneg" -> "data", "is_cyclic_of_card_pow_eq_one_le" -> "algebra", "nat.gcd_def" -> "init", "set.Inter_eq_comp_Union_comp" -> "data", "real.pow_arith_mean_le_arith_mean_pow" -> "analysis", "int.sub_lt_sub" -> "init", "one_one_reducible.to_many_one" -> "computability", "filter.tendsto_at_top_add_left_of_le'" -> "order", "Liminf_nhds" -> "topology", "nsmul_nonneg" -> "algebra", "Cauchy.Cauchy_eq" -> "topology", "local_homeomorph.eq_on_source_iff" -> "topology", "uniform_continuous.dist" -> "topology", "approximates_linear_on.antilipschitz" -> "analysis", "zsqrtd.coe_int_im" -> "data", "polynomial.eval_sum" -> "data", "polynomial.monic.ne_zero_of_zero_ne_one" -> "data", "is_lub.of_subset_of_superset" -> "order", "set.finite.induction_on" -> "data", "ring.fractional_ideal.div_nonzero" -> "algebra", "category_theory.uncurry_natural_left_assoc" -> "category_theory", "state_t.run_pure" -> "init", "commute.symm_iff" -> "algebra", "linear_map.comp_zero" -> "algebra", "add_eq_of_eq_sub" -> "algebra", "associates.quot_mk_eq_mk" -> "algebra", "set.surj_on.inter_inter" -> "data", "list.reverse_core_eq" -> "data", "measure_theory.l1.norm_of_fun_eq_lintegral_norm" -> "analysis", "nat.zero_lt_bit0" -> "init", "eq_neg_of_eq_neg" -> "algebra", "is_bounded_linear_map.smul" -> "analysis", "closure_Ioo" -> "topology", "onote.NF.of_dvd_omega" -> "set_theory", "bilin_form.comp_left_comp_right" -> "algebra", "set.Iic_diff_Iio_same" -> "data", "set.Ioo_subset_Ico_self" -> "data", "nat.add_mod_eq_add_mod_right" -> "data", "Lim_nhds_within" -> "topology", "fintype.card_congr" -> "data", "power_series.coeff_X_pow_self" -> "algebra", "category_theory.full_subcategory_inclusion.obj" -> "category_theory", "list.append_right_cancel" -> "data", "finsupp.lmap_domain_supported" -> "algebra", "edist_ne_top_of_mem_ball" -> "topology", "cardinal.mk_Prop" -> "set_theory", "wseq.join_cons" -> "data", "ulift.smul_down'" -> "algebra", "submodule.is_principal.generator_mem" -> "algebra", "nat.div2_one" -> "init", "real.arccos_eq_pi_div_two_sub_arcsin" -> "analysis", "rel_iso.coe_fn_symm_mk" -> "order", "hyperreal.infinite_iff_infinitesimal_inv" -> "data", "dfinsupp.sum_single" -> "data", "enat.add_right_cancel_iff" -> "data", "is_bounded_linear_map.differentiable" -> "analysis", "char_poly_map_eval_self" -> "algebra", "category_theory.limits.pullback_cone.is_limit.hom_ext" -> "category_theory", "order_topology.t2_space" -> "topology", "hyperreal.infinite_pos_abs_iff_infinite_abs" -> "data", "filter.rmap_rmap" -> "order", "list.length_pos_of_sum_pos" -> "data", "list.nodup_cons_of_nodup" -> "data", "deriv_within_ccosh" -> "analysis", "unique_mdiff_within_at.mono" -> "geometry", "list.perm_comm" -> "data", "free_add_monoid.lift_apply" -> "algebra", "nhds_within_Ioi_ne_bot'" -> "topology", "turing.tape.map_move" -> "computability", "matrix.trace_one" -> "algebra", "finite_dimensional.trans" -> "algebra", "list.length_range" -> "data", "nat.eq_mul_of_div_eq_left" -> "data", "multiset.ndinter_cons_of_not_mem" -> "data", "ring.fractional_ideal.span_singleton_zero" -> "algebra", "sub_lt_iff_lt_add'" -> "algebra", "submonoid.localization_map.to_map_injective" -> "algebra", "filter.tendsto_Ixx_class_inf" -> "order", "int.of_nat_dvd_of_dvd_nat_abs" -> "data", "padic_int.mem_nonunits" -> "data", "asymptotics.is_O.of_bound" -> "analysis", "list.suffix_iff_eq_drop" -> "data", "list.take_repeat" -> "data", "int.sub_eq_add_neg" -> "init", "category_theory.monoidal_category.triangle_assoc_comp_left" -> "category_theory", "metric.nonempty_ball" -> "topology", "nat.succ_pred_eq_of_pos" -> "init", "nat.le_of_lt" -> "init", "or_of_or_of_imp_left" -> "logic", "nat.mod_eq_zero_of_dvd" -> "init", "complex.cos_pi_sub" -> "analysis", "list.chain'.iff_mem" -> "data", "filter.mp_sets" -> "order", "list.unzip_zip_right" -> "data", "cau_seq.eq_lim_of_const_equiv" -> "data", "directed.mono" -> "order", "exists_imp_exists" -> "init", "category_theory.prod_comp_snd" -> "category_theory", "set.maps_to_sUnion" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence_functor" -> "category_theory", "is_extr_on_const" -> "order", "is_group_hom.injective_of_trivial_ker" -> "algebra", "topological_space.is_open_sUnion_countable" -> "topology", "cauchy_seq_finset_of_geometric_bound" -> "analysis", "list.permutations_aux2_append" -> "data", "semidirect_product.lift_comp_inr" -> "algebra", "nat.Inf_le" -> "order", "set.union_add" -> "algebra", "adjoin_root.mk_self" -> "algebra", "nat.gcd_dvd_gcd_of_dvd_left" -> "data", "interval_integral.norm_integral_le_of_norm_le_const_ae" -> "analysis", "zmod.eq_iff_modeq_nat" -> "data", "monoid_hom.map_is_conj" -> "algebra", "int.ldiff_bit" -> "data", "bool.bxor_assoc" -> "data", "normalize_one" -> "algebra", "gaussian_int.nat_cast_complex_norm" -> "data", "list.perm.kunion_right" -> "data", "equiv.perm.disjoint_prod_right" -> "algebra", "differentiable_at.iterate" -> "analysis", "computation.ret_bind" -> "data", "composition_as_set.to_composition_boundaries" -> "combinatorics", "category_theory.discrete.equivalence_counit_iso" -> "category_theory", "add_subgroup.closure_le" -> "algebra", "pfunctor.M.head_mk" -> "data", "ordinal.lt_lift_iff" -> "set_theory", "is_local_min.on" -> "topology", "norm_num.clear_denom_add" -> "tactic", "is_compact.nonempty_Inter_of_directed_nonempty_compact_closed" -> "topology", "continuous_pow" -> "topology", "mul_equiv.apply_symm_apply" -> "data", "nat.bit_lt_bit_iff" -> "data", "neg_mul_eq_neg_mul_symm" -> "algebra", "is_open_union" -> "topology", "tactic.abel.term_neg" -> "tactic", "subset_interior_iff_subset_of_open" -> "topology", "real.pi_lt_3141593" -> "data", "nnreal.exists_le_has_sum_of_le" -> "topology", "mem_nhds_within_of_mem_nhds" -> "topology", "cau_seq.sub_lim_zero" -> "data", "is_glb_Ioo" -> "order", "localization_map.map_left_cancel" -> "algebra", "cardinal.power_def" -> "set_theory", "affine.triangle.orthocenter_eq_smul_vsub_vadd_circumcenter" -> "geometry", "local_equiv.map_source" -> "data", "ctop.realizer.is_closed_iff" -> "data", "circle_deg1_lift.map_sub_nat" -> "dynamics", "set.Iic_diff_right" -> "data", "cardinal_le_dim_of_linear_independent'" -> "algebra", "ennreal.tendsto.const_div" -> "topology", "encodable.encode_ff" -> "data", "complex.differentiable_at_cosh" -> "analysis", "ennreal.coe_sub" -> "data", "complex.one_re" -> "data", "category_theory.limits.pushout_cocone.mk_\[Iota]_app" -> "category_theory", "list.not_mem_nil" -> "init", "prime_spectrum.le_vanishing_ideal_zero_locus" -> "algebraic_geometry", "add_subgroup.comap_inf" -> "algebra", "fintype.pi_finset_univ" -> "data", "induced_id" -> "topology", "localization.ring_equiv_of_quotient_symm_mk" -> "algebra", "list.sorted_cons" -> "data", "localization_map.lin_coe_apply" -> "algebra", "list.ball_nil" -> "init", "local_homeomorph.is_O_congr" -> "analysis", "finsupp.sum_subtype_domain_index" -> "data", "omega.coeffs.val_between_map_mul" -> "tactic", "nnreal.of_real_lt_iff_lt_coe" -> "data", "ring.fractional_ideal.coe_ne_bot_iff_nonzero" -> "algebra", "function.injective.exists_ne" -> "logic", "ordinal.le_bsup" -> "set_theory", "le_iff_lt_or_eq" -> "init", "one_half_lt_one" -> "algebra", "multiset.map_subset_map" -> "data", "nat.gcd_one_right" -> "data", "multiset.filter_zero" -> "data", "nat.succ_pos'" -> "data", "add_submonoid.localization_map.add_equiv_of_localizations_symm_apply" -> "algebra", "deriv_within_neg" -> "analysis", "is_R_or_C.zero_re" -> "data", "quotient_group.range_ker_lift_injective" -> "algebra", "finsupp.antidiagonal_zero" -> "data", "set.image_eta" -> "data", "op_geom_series" -> "algebra", "module.direct_limit.lift_unique" -> "algebra", "set.bij_on_Inter" -> "data", "list.bind_ret_eq_map" -> "data", "centroid_mem_affine_span_of_nonempty" -> "algebra", "int.neg_nat_succ" -> "data", "set.interval_subset_interval_right" -> "data", "category_theory.limits.is_limit.uniq_cone_morphism" -> "category_theory", "is_valid_char_range_1" -> "init", "set.preimage_mul_const_Ioo" -> "data", "wseq.head_some_of_head_tail_some" -> "data", "nnreal.of_real_lt_of_real_iff'" -> "data", "rat.uniform_continuous_add" -> "topology", "stream.unfolds_eq" -> "data", "norm_num.int_mod_neg" -> "tactic", "traversable.to_list_eq_self" -> "control", "le_of_nhds_le_nhds" -> "topology", "padic_val_rat.padic_val_rat_of_int" -> "data", "one_div" -> "algebra", "category_theory.limits.limit.is_limit_lift" -> "category_theory", "filter.rtendsto_iff_le_comap" -> "order", "category_theory.limits.prod.lift_comp_comp" -> "category_theory", "filter.lift_principal" -> "order", "complex.I_ne_zero" -> "data", "summable.mul_right" -> "topology", "padic_seq.norm_const" -> "data", "list.unzip_nil" -> "data", "rel_iso.map_rel_iff''" -> "order", "mul_lt_one" -> "algebra", "subtype.restrict_def" -> "data", "with_one.coe_mul" -> "algebra", "filter.tendsto_at_bot_of_add_const_right" -> "order", "subring.map_bot" -> "algebra", "measurable.nnreal_coe" -> "analysis", "set.nonempty.snd" -> "data", "set.image_const_sub_Iio" -> "data", "polynomial.is_unit_map" -> "data", "tensor_algebra.lift_unique" -> "algebra", "add_group.gmultiples_eq_closure" -> "algebra", "category_theory.monoidal.Mon_functor_category_equivalence_counit_iso" -> "category_theory", "differentiable.div_const" -> "analysis", "tendsto_uniformly.tendsto_comp" -> "topology", "omega.nat.preterm.val_const" -> "tactic", "cauchy_seq_iff_le_tendsto_0" -> "topology", "nat.sub_le_sub_left_iff" -> "data", "max_min_distrib_right" -> "algebra", "is_absolute_value.abv_pos" -> "data", "mul_self_sub_one_eq" -> "algebra", "quadratic_form.pos_def.smul" -> "algebra", "monoid_hom.coe_fst" -> "algebra", "dist_le_range_sum_dist" -> "topology", "mv_power_series.X_pow_eq" -> "algebra", "lipschitz_with.weaken" -> "topology", "finset.prod_sdiff" -> "algebra", "alg_hom.map_smul" -> "algebra", "supr_eq_dif" -> "order", "turing.TM1.stmts_supports_stmt" -> "computability", "finset.bUnion_coe" -> "data", "onote.power_def" -> "set_theory", "filter.is_countably_generated_at_top" -> "order", "int.coe_nat_add_out" -> "init", "measurable_space.is_measurable_supr" -> "analysis", "card_units_lt" -> "algebra", "list.mem_of_mem_inter_right" -> "data", "filter.tendsto.add" -> "topology", "dense_embedding_pure" -> "topology", "is_closed_property" -> "topology", "alt_bilin_form.neg" -> "algebra", "continuous_ulift_up" -> "topology", "free_group.mul_mk" -> "algebra", "game.add_le_add_left" -> "set_theory", "measurable_pi_lambda" -> "analysis", "dioph.inject_dummies_lem" -> "number_theory", "category_theory.comonad.forget_map" -> "category_theory", "tactic.ring_exp.simple_pf_var_one" -> "tactic", "int.nat_abs_bit1_nonneg_step" -> "init", "localization_map.to_map_eq_zero_iff" -> "algebra", "order_iso.to_galois_connection" -> "order", "tactic.ring.horner_add_horner_lt" -> "tactic", "inv_lt_of_neg" -> "algebra", "zsqrtd.coe_int_sub" -> "data", "submodule.coe_set_eq" -> "algebra", "measure_theory.simple_func.lintegral_zero" -> "analysis", "polynomial.derivative_sum" -> "data", "list.mem_append_eq" -> "init", "is_alg_closed.degree_eq_one_of_irreducible" -> "algebra", "typevec.to_subtype_of_subtype" -> "data", "set.preimage_sub_const_Ioo" -> "data", "finset.filter_inter_filter_neg_eq" -> "data", "differentiable_on.sinh" -> "analysis", "sup_comm" -> "order", "nat.test_bit_ldiff" -> "init", "zmod.card_units" -> "algebra", "list.range'_eq_map_range" -> "data", "polynomial.exists_irreducible_of_degree_pos" -> "algebra", "finset.bUnion_preimage_singleton" -> "data", "linear_map.linear_proj_of_is_compl_of_proj" -> "algebra", "finsupp.supported_Inter" -> "algebra", "is_bounded_linear_map.fst" -> "analysis", "zmod.trace_pow_card" -> "algebra", "mv_power_series.coeff_zero_C" -> "algebra", "metric.nhds_basis_ball_inv_nat_pos" -> "topology", "function.surjective.surj_on" -> "data", "ennreal.rpow_eq_zero_iff" -> "analysis", "bit0_zero" -> "algebra", "ordinal.add_sub_add_cancel" -> "set_theory", "ring_hom.map_iterate_frobenius" -> "algebra", "complex.abs_of_real" -> "data", "matrix.empty_add_empty" -> "data", "complex.conj_inj" -> "data", "submodule.mem_sup_right" -> "algebra", "mul_le_mul_three" -> "algebra", "filter.univ_mem_sets" -> "order", "inv_lt_one'" -> "algebra", "submonoid.comap_infi" -> "algebra", "matrix.proj_diagonal" -> "algebra", "fin.eq_iff_veq" -> "data", "submonoid.localization_map.sec_spec" -> "algebra", "continuous.measurable2" -> "analysis", "continuous_linear_equiv.has_strict_fderiv_at" -> "analysis", "category_theory.over.colimit_\[Iota]_app" -> "category_theory", "differentiable_at.cexp" -> "analysis", "option_t.run_pure" -> "init", "measure_theory.simple_func.lintegral_restrict" -> "analysis", "is_compact.inter_Inter_nonempty" -> "topology", "is_open_map_smul_of_ne_zero" -> "topology", "complex.exp_nat_mul" -> "data", "emetric.ball_subset_closed_ball" -> "topology", "quadratic_form.lin_mul_lin_comp" -> "algebra", "multiset.card_zero" -> "data", "ennreal.of_real_le_iff_le_to_real" -> "data", "continuous_linear_map.is_bounded_linear_map_comp_right" -> "analysis", "with_zero.mul_right_inv" -> "algebra", "continuous_linear_map.ext_iff" -> "topology", "deriv.lhopital_zero_at_top" -> "analysis", "localization_map.integer_normalization_spec" -> "algebra", "padic_norm_e.add_eq_max_of_ne" -> "data", "mv_polynomial.C_0" -> "data", "abs_pos_of_ne_zero" -> "algebra", "lt_of_not_ge'" -> "algebra", "monoid_algebra.mul_apply" -> "data", "mul_le_iff_le_one_left" -> "algebra", "Algebra.of_self_iso_hom" -> "algebra", "mul_aut.inv_apply_self" -> "data", "Mod.comp_hom'" -> "category_theory", "inner_product_geometry.angle_smul_right_of_pos" -> "geometry", "with_top.add_top" -> "algebra", "int.div_eq_of_eq_mul_right" -> "data", "mv_polynomial.sum_to_iter_C" -> "data", "list.kerase_append_right" -> "data", "set.not_nonempty_iff_eq_empty" -> "data", "monoid_algebra.mul_zero" -> "data", "turing.eval_maximal" -> "computability", "equiv.coe_of_bijective" -> "data", "fraction_map.num_mul_denom_eq_num_iff_eq'" -> "algebra", "pgame.left_wins_of_equiv" -> "set_theory", "fin.vne_of_ne" -> "init", "has_mfderiv_within_at_const" -> "geometry", "lebesgue_number_lemma_of_metric_sUnion" -> "topology", "real.log_abs" -> "analysis", "hyperreal.not_infinitesimal_of_infinite_neg" -> "data", "is_max_on.is_local_max" -> "topology", "is_R_or_C.I_to_complex" -> "data", "midpoint_self" -> "algebra", "finset.choose_spec" -> "data", "is_seq_closed_iff_is_closed" -> "topology", "is_R_or_C.of_real_alg" -> "data", "set.mem_empty_eq" -> "data", "category_theory.limits.pushout.hom_ext" -> "category_theory", "decidable_linear_ordered_add_comm_group.tendsto_nhds" -> "topology", "times_cont_diff.comp_continuous_linear_map" -> "analysis", "linear_equiv.lie_conj_symm" -> "algebra", "category_theory.Monad.to_of_mon_end_iso_inv_app_to_nat_trans_app" -> "category_theory", "nat.Inf_def" -> "order", "measure_theory.ae_eq_fun.coe_fn_smul" -> "analysis", "filter.is_countably_generated.exists_antimono_seq" -> "order", "category_theory.adjunction.right_triangle_components" -> "category_theory", "continuous_at.continuous_within_at" -> "topology", "list.func.eq_of_equiv" -> "data", "subsemiring.coe_map" -> "algebra", "mul_ne_zero_iff" -> "algebra", "free_ring.coe_mul" -> "algebra", "qpf.fix.rec_eq" -> "data", "category_theory.comma.map_left_obj_right" -> "category_theory", "continuous_sup_rng_right" -> "topology", "neg_add_eq_sub" -> "algebra", "int.nat_abs_mul_self" -> "init", "open_add_subgroup.mem_coe_add_subgroup" -> "topology", "nat.primes.coe_pnat_nat" -> "data", "wseq.length_eq_map" -> "data", "stream.approx_zero" -> "data", "hash_map.valid.idx_enum_1" -> "data", "eq_false_intro" -> "init", "valuation.unit_map_eq" -> "algebra", "min_eq_left_of_lt" -> "init", "setoid.is_partition.pairwise_disjoint" -> "data", "finset.subset_iff" -> "data", "lower_bounds_mono" -> "order", "measure_theory.outer_measure.Union" -> "analysis", "lagrange.eval_interpolate" -> "algebra", "quotient.rep_spec" -> "data", "nat.size_one" -> "data", "open_embedding_of_embedding_open" -> "topology", "submonoid.localization_map.mk'_self'" -> "algebra", "set.mem_compl" -> "data", "list.perm.eq_nil" -> "data", "approximates_linear_on.to_local_homeomorph_coe" -> "analysis", "filter.mem_bot_sets" -> "order", "submodule.top_coe" -> "algebra", "linear_map.image_convex_hull" -> "analysis", "category_theory.abelian.pseudoelement.comp_apply" -> "category_theory", "fin.lt_iff_coe_lt_coe" -> "data", "differentiable_within_at.smul_algebra" -> "analysis", "with_top.add_one_le_of_lt" -> "data", "roption.of_to_option" -> "data", "principal_ideal_ring.irreducible_iff_prime" -> "algebra", "separation_rel_comap" -> "topology", "list.sigma_nil" -> "data", "subring.mem_Inf" -> "algebra", "linear_equiv.map_zero" -> "algebra", "filter.eventually_lift'_iff" -> "order", "finset.mono_of_fin_eq_mono_of_fin_iff" -> "data", "int.dvd_antisymm" -> "data", "list.nil_subset" -> "init", "nat.primrec'.prec'" -> "computability", "pgame.nim.non_zero_first_wins" -> "set_theory", "category_theory.limits.fork.app_zero_left" -> "category_theory", "multiset.card_smul" -> "data", "bool.band_comm" -> "data", "not_lt_of_gt" -> "init", "equiv.sum_assoc_apply_in1" -> "data", "finset.Ico.inter_consecutive" -> "data", "padic_int.valuation_p_pow_mul" -> "data", "set.mem_image_elim_on" -> "data", "is_min_on_const" -> "order", "sequentially_complete.seq_mem" -> "topology", "continuous_linear_map.comp_add" -> "topology", "hyperreal.coe_lt_coe" -> "data", "has_strict_fderiv_at.continuous_at" -> "analysis", "add_submonoid.mem_supr_of_directed" -> "algebra", "free_group.reduce.rev" -> "algebra", "ring_equiv.map_sub" -> "data", "rel_iso.injective" -> "order", "finset.range_subset" -> "data", "seq.nth_tail" -> "data", "nat.succ_div_of_not_dvd" -> "data", "circle_deg1_lift.translate_iterate" -> "dynamics", "metric.completion.dist_self" -> "topology", "ennreal.of_real_add" -> "data", "units.conj_pow" -> "algebra", "pequiv.trans_eq_some" -> "data", "fpow_injective" -> "algebra", "measure_theory.integral_finset_sum" -> "analysis", "category_theory.limits.biprod.braiding'_inv" -> "category_theory", "fderiv_sub" -> "analysis", "tendsto_subseq_of_bounded" -> "topology", "multiset.mem_inter" -> "data", "category_theory.limits.image.eq_fac" -> "category_theory", "has_fderiv_at.continuous_at" -> "analysis", "lie_neg" -> "algebra", "ceil_le" -> "algebra", "category_theory.non_preadditive_abelian.\[Sigma]_comp" -> "category_theory", "fin.is_lt" -> "data", "set.image_const_add_Ioo" -> "data", "measure_theory.measure.haar.prehaar_empty" -> "analysis", "finmap.erase_to_finmap" -> "data", "filter.mem_supr_sets" -> "order", "directed_on.mono" -> "order", "Cauchy.separated_pure_cauchy_injective" -> "topology", "ideal.le_jacobson" -> "algebra", "list.lookup_ext" -> "data", "alg_hom.ext_iff" -> "algebra", "finset.union_eq_empty_iff" -> "data", "measurable_equiv.trans_to_equiv" -> "analysis", "has_ftaylor_series_up_to.has_ftaylor_series_up_to_on" -> "analysis", "uniform_embedding.dense_embedding" -> "topology", "finmap.induction_on" -> "data", "measurable.is_lub" -> "analysis", "measure_theory.measure.haar_outer_measure_pos_of_is_open" -> "analysis", "structure_groupoid.local_invariant_prop.lift_prop_within_at_mono" -> "geometry", "deriv_within_sin" -> "analysis", "ne_false_of_self" -> "init", "semiquot.mem_pure" -> "data", "monoid_hom.coe_mrange" -> "algebra", "ideal.span_singleton_lt_span_singleton" -> "algebra", "category_theory.is_equivalence.inv_fun_map" -> "category_theory", "nsmul_add" -> "algebra", "gaussian_int.nat_abs_norm_eq" -> "data", "real.sin_square_pi_over_two_pow_succ" -> "analysis", "galois_coinsertion.u_sup_l" -> "order", "left_eq_sup" -> "order", "list.forall_mem_of_forall_mem_cons" -> "data", "has_strict_fderiv_at.eventually_right_inverse" -> "analysis", "supr_prod" -> "order", "int.lxor_bit" -> "data", "list.sublists_nil" -> "data", "real.sqrt_mul'" -> "data", "measure_theory.l1.simple_func.coe_smul" -> "analysis", "bitvec.of_nat_succ" -> "data", "differentiable_at_fpow" -> "analysis", "set.bUnion_eq_Union" -> "data", "Cauchy.mem_uniformity" -> "topology", "equiv.perm.same_cycle_apply" -> "algebra", "normed_ring.inverse_one_sub" -> "analysis", "mv_polynomial.monomial_add_single" -> "data", "mul_gpow_self" -> "algebra", "polynomial.splits_of_degree_eq_one" -> "algebra", "category_theory.limits.prod.map_iso_hom" -> "category_theory", "bitraversable.comp_tsnd" -> "control", "subsemiring.coe_mul" -> "algebra", "cau_seq.lt_of_lt_of_eq" -> "data", "nndist_comm" -> "topology", "category_theory.limits.is_limit.unique_up_to_iso_inv" -> "category_theory", "polynomial.commute_X" -> "data", "polynomial.mod_by_monic_eq_self_iff" -> "data", "equiv.perm.eq_sign_of_surjective_hom" -> "algebra", "lie_algebra.special_linear.Eb_val" -> "algebra", "measure_theory.measure.is_left_invariant_haar_measure" -> "analysis", "ring_hom.map_closure" -> "algebra", "inducing.tendsto_nhds_iff" -> "topology", "differentiable_on.neg" -> "analysis", "set.right_mem_Iic" -> "data", "continuous_linear_equiv.comp_continuous_iff" -> "topology", "add_units.eq_add_neg_iff_add_eq" -> "algebra", "inv_mul_lt_right_of_lt_mul" -> "algebra", "pequiv.mem_trans" -> "data", "category_theory.limits.coprod.inl_map" -> "category_theory", "measurable_const" -> "analysis", "div_le_one" -> "algebra", "mvpfunctor.map_eq" -> "data", "hyperreal.coe_eq_one" -> "data", "ennreal.inv_two_add_inv_two" -> "data", "mv_polynomial.map_C" -> "data", "polynomial.monic_of_injective" -> "data", "bounded_continuous_function.norm_coe_le_norm" -> "topology", "is_min_on_dual_iff" -> "order", "dim_bot" -> "algebra", "power_series.coeff_monomial" -> "algebra", "filter.map_infi_le" -> "order", "is_noetherian_of_submodule_of_noetherian" -> "algebra", "category_theory.functor.map_presheaf_obj_presheaf" -> "algebraic_geometry", "category_theory.non_preadditive_abelian.add_assoc" -> "category_theory", "list.insert_pos" -> "data", "complex.uniform_continuous_add" -> "topology", "is_connected_iff_sUnion_disjoint_open" -> "topology", "finset.Ico.val" -> "data", "category_theory.limits.image.pre_comp_comp" -> "category_theory", "formal_multilinear_series.continuous_on" -> "analysis", "deriv.lhopital_zero_at_bot_on_Iio" -> "analysis", "continuous_iff_is_closed" -> "topology", "nat.monotone_fact" -> "data", "add_monoid_hom.iterate_map_gsmul" -> "algebra", "has_le.le.lt_or_le" -> "algebra", "algebraic_geometry.PresheafedSpace.comp_c_app" -> "algebraic_geometry", "le_mul_of_one_le_of_le" -> "algebra", "nat.unpair_le_right" -> "data", "pow_left_inj" -> "algebra", "sub_le_iff_le_add'" -> "algebra", "is_R_or_C.of_real_int_cast" -> "data", "cardinal.mk_Union_le_sum_mk" -> "set_theory", "inv_of_one" -> "algebra", "has_fderiv_at_filter.iterate" -> "analysis", "pos_num.cmp_eq" -> "data", "continuous.sub" -> "topology", "is_glb_Ico" -> "order", "continuous_linear_map.mem_range" -> "topology", "computable.eqv" -> "computability", "affine_map.ext_iff" -> "algebra", "complex.exp_eq_one_iff" -> "analysis", "local_homeomorph.preimage_open_of_open_symm" -> "topology", "set.bInter_singleton" -> "data", "sub_gsmul" -> "algebra", "le_sub_iff_add_le'" -> "algebra", "findim_span_eq_card" -> "algebra", "category_theory.arrow.mk_right" -> "category_theory", "and_congr" -> "init", "has_ftaylor_series_up_to_on_zero_iff" -> "analysis", "finset.erase_subset" -> "data", "lie_add_group_core.to_topological_add_group" -> "geometry", "nat.strong_induction_on" -> "init", "int.div_zero" -> "data", "ordinal.sup_ord" -> "set_theory", "linarith.nat_le_subst" -> "tactic", "onote.repr_power_aux\:2082" -> "set_theory", "category_theory.limits.cocones.whiskering_equivalence_inverse" -> "category_theory", "ordinal.type_def'" -> "set_theory", "tensor_product.zero_tmul" -> "algebra", "distrib_mul_action_hom.map_zero" -> "algebra", "list.lookup_kinsert" -> "data", "ennreal.add_lt_add_iff_left" -> "data", "category_theory.discrete.equivalence_functor" -> "category_theory", "measurable_space.comap_le_iff_le_map" -> "analysis", "function.commute.iterate_le_of_map_le" -> "order", "seq.map_tail" -> "data", "eq_of_le_of_forall_ge_of_dense" -> "order", "category_theory.limits.types.coprod_map" -> "category_theory", "card_subgroup_dvd_card" -> "algebra", "union_mem_uniformity_sum" -> "topology", "cau_seq.tendsto_limit" -> "topology", "function.commute.comp_iterate" -> "logic", "set.mk_preimage_prod_right_eq_empty" -> "data", "linear_map.continuous_of_bound" -> "analysis", "ordinal.typein_inj" -> "set_theory", "local_equiv.trans_symm_self" -> "data", "function.semiconj.symm_adjoint" -> "order", "quotient.induction_on\:2083" -> "init", "set.Iic_union_Ioo_eq_Iio" -> "data", "add_lt_iff_neg_left" -> "algebra", "set.inter_subset_inter_left" -> "data", "semiconj_by.eq" -> "algebra", "set.preimage_id" -> "data", "uniform_embedding_comap" -> "topology", "ennreal.add_supr" -> "topology", "nndist_dist" -> "topology", "filter.eventually_eq.is_local_extr_iff" -> "topology", "exists_unique_of_exists_of_unique" -> "init", "summable_mul_right_iff" -> "topology", "units.coe_inv" -> "algebra", "padic.rat_dense" -> "data", "list.minimum_singleton" -> "data", "fraction_map.to_map_eq_zero_iff" -> "algebra", "multiplicity.pow_multiplicity_dvd" -> "algebra", "nat.lor_bit" -> "init", "equiv.perm.is_cycle_inv" -> "algebra", "add_neg_eq_iff_eq_add" -> "algebra", "pi_generate_from_eq_fintype" -> "topology", "submodule.mem_coe" -> "algebra", "submonoid.localization_map.eq_iff_eq" -> "algebra", "mem_nhds_within_Iio_iff_exists_Ico_subset" -> "topology", "closure_diff" -> "topology", "polynomial.nat_degree_prod_of_monic" -> "algebra", "int.bodd_coe" -> "data", "filter.tendsto_iff_ultrafilter" -> "order", "add_subgroup.map_map" -> "algebra", "set.mem_pi" -> "data", "function.inv_fun_eq_of_injective_of_right_inverse" -> "logic", "borel_eq_generate_from_of_subbasis" -> "analysis", "ideal.is_fg_degree_le" -> "algebra", "semiquot.ext_s" -> "data", "roption.map_map" -> "data", "is_lub_lt_iff" -> "order", "filter.monotone_lift" -> "order", "filter.mem_seq_sets_iff" -> "order", "is_measurable.prod" -> "analysis", "int.sub_nat_nat_elim" -> "init", "set.embedding_of_subset_apply_mk" -> "logic", "multiset.fmap_def" -> "data", "continuous_within_at.comp" -> "topology", "set.seq_eq_set_seq" -> "data", "multiset.sum_hom" -> "data", "primrec.nat_cases\:2081" -> "computability", "int.mul_self_lt_mul_self" -> "init", "prime_multiset.add_sub_of_le" -> "data", "monoid_hom.map_gpow" -> "algebra", "add_monoid_hom.mem_mrange" -> "algebra", "smooth_add" -> "geometry", "magma.free_semigroup.of_mul_assoc_left" -> "algebra", "times_cont_mdiff_within_at_fst" -> "geometry", "set.disjoint.union_right" -> "data", "pell.x_pos" -> "number_theory", "continuous_within_at_inter" -> "topology", "set.image_congr'" -> "data", "rel_embedding.acc" -> "order", "sylow.mk_vector_prod_eq_one_injective" -> "algebra", "submodule.span_smul_span" -> "algebra", "nnreal.coe_multiset_prod" -> "data", "nat.mod_mod" -> "data", "int.nat_abs_pow" -> "algebra", "set.set_of_false" -> "data", "refl_sesq_form.ortho_sym" -> "algebra", "pnat.mk_one" -> "data", "int.div_eq_iff_eq_mul_left" -> "data", "topological_space.sUnion_basis_of_is_open" -> "topology", "infi_sum" -> "order", "list.index_of_cons" -> "data", "submodule.quotient.mk_smul" -> "algebra", "sub_eq_iff_eq_add" -> "algebra", "inf_eq_right" -> "order", "Module.mono_of_ker_eq_bot" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_on_symm_of_mem_maximal_atlas" -> "geometry", "convex_cone.convex" -> "analysis", "category_theory.limits.types.limit_equiv_sections_apply" -> "category_theory", "free_group.quot_lift_on_mk" -> "algebra", "filter.eventually.prod_inl" -> "order", "nnreal.mul_finset_sup" -> "data", "ennreal.of_real_pos" -> "data", "tactic.abel.term_add_termg" -> "tactic", "polynomial.map_div_by_monic" -> "data", "ennreal.le_sub_add_self" -> "data", "int.lt_add_succ" -> "init", "set.mem_inv" -> "algebra", "holor.cprank_upper_bound" -> "data", "multiset.erase_add_left_neg" -> "data", "filter.germ.lift_pred_const" -> "order", "function.is_periodic_pt.iterate" -> "dynamics", "cardinal.lift_mul" -> "set_theory", "times_cont_diff.continuous" -> "analysis", "equiv.perm.swap_mul_self_mul" -> "algebra", "submonoid.list_prod_mem" -> "algebra", "poly.subst_eval" -> "number_theory", "differentiable.ccosh" -> "analysis", "free_monoid.one_def" -> "algebra", "differentiable_within_at_fpow" -> "analysis", "set.ord_connected_Inter" -> "data", "equiv.option_equiv_sum_punit_some" -> "data", "category_theory.op_op_equivalence_functor" -> "category_theory", "submodule.findim_le" -> "algebra", "times_cont_mdiff_const" -> "geometry", "mul_lt_mul_iff_right" -> "algebra", "category_theory.limits.biprod.inr_fst_assoc" -> "category_theory", "real.angle.angle_eq_iff_two_pi_dvd_sub" -> "analysis", "smooth_at_const" -> "geometry", "asymptotics.is_o.sub" -> "analysis", "pell.yn_zero" -> "number_theory", "set.Union_range_eq_Union" -> "data", "fintype.card_of_finset'" -> "data", "discrete_valuation_ring.iff_pid_with_one_nonzero_prime" -> "algebra", "set.nonempty_Ioi" -> "data", "nat.partrec'.of_eq" -> "computability", "iff_iff_eq" -> "logic", "pnat.coe_eq_one_iff" -> "data", "real.totally_bounded_Icc" -> "topology", "free_magma.traverse_eq" -> "algebra", "asymptotics.is_O_with_self_const_mul'" -> "analysis", "is_R_or_C.conj_involutive" -> "data", "metric.tendsto_uniformly_on_iff" -> "topology", "add_monoid_algebra.prod_single" -> "data", "turing.tape.move_right_n_head" -> "computability", "hyperreal.coe_eq_zero" -> "data", "is_open_singleton_true" -> "topology", "complex.of_real_ne_zero" -> "data", "add_commute.units_coe" -> "algebra", "enat.with_top_equiv_top" -> "data", "set.range_eq_empty" -> "data", "pgame.move_right_right_moves_neg_symm" -> "set_theory", "matrix.special_linear_group.inv_val" -> "algebra", "nhds_contain_boxes_of_singleton" -> "topology", "measure_theory.measure.map_comap_subtype_coe" -> "analysis", "add_monoid.coe_one" -> "algebra", "monoid_hom.ext_int" -> "data", "opt_param_eq" -> "init", "finset.prod_apply_dite" -> "algebra", "int.mod_two_ne_one" -> "data", "inv_lt_inv_iff" -> "algebra", "neg_one_mul" -> "algebra", "le_mul_of_one_le_right" -> "algebra", "set.nonempty_inter_iff_exists_left" -> "data", "gt_of_gt_of_ge" -> "init", "lt_add_of_neg_add_lt_left" -> "algebra", "is_R_or_C.ext_iff" -> "data", "pnat.coprime.gcd_mul_left_cancel_right" -> "data", "units.smul_eq_zero" -> "algebra", "pnat.eq" -> "data", "list.append_ne_nil_of_ne_nil_right" -> "data", "localization_map.mk'_eq_mul_mk'_one" -> "algebra", "finset.min_le_of_mem" -> "data", "set.finite.subset" -> "data", "hyperreal.infinite_neg_iff_infinite_of_neg" -> "data", "norm_norm'" -> "analysis", "ennreal.of_real_lt_iff_lt_to_real" -> "data", "setoid.exists_of_mem_partition" -> "data", "seq1.map_join" -> "data", "has_deriv_within_at.limsup_slope_le'" -> "analysis", "sequentially_complete.set_seq_mem" -> "topology", "category_theory.nat_iso.unop_hom" -> "category_theory", "norm_num.adc_bit1_one" -> "tactic", "polynomial.monic.as_sum" -> "data", "measurable.ennreal_sub" -> "analysis", "hyperreal.is_st_st" -> "data", "is_local_max.comp_antimono" -> "topology", "differentiable.smul" -> "analysis", "exists_mem_inter_of_exists_mem_inter_affine_span_of_affine_independent" -> "algebra", "div_self" -> "algebra", "continuous_on.prod_map" -> "topology", "not_and_not_right" -> "logic", "pgame.le_trans_aux" -> "set_theory", "euclidean_domain.gcd_val" -> "algebra", "infi_eq_of_tendsto" -> "topology", "ring_hom.coe_mk" -> "algebra", "category_theory.limits.types.lift_\[Pi]_apply'" -> "category_theory", "local_homeomorph.restr_source_inter" -> "topology", "magma.free_semigroup.lift_of" -> "algebra", "option.seq_some" -> "data", "polynomial.eisenstein_criterion_aux.eval_zero_mem_ideal_of_eq_mul_X_pow" -> "algebra", "finset.sum_bij" -> "algebra", "affine_subspace.inf_coe" -> "algebra", "set.image2_smul" -> "algebra", "sub_lt_iff_lt_add" -> "algebra", "category_theory.limits.inv_prod_comparison_map_snd_assoc" -> "category_theory", "smooth_manifold_with_corners.chart_mem_maximal_atlas" -> "geometry", "pell.xn_succ" -> "number_theory", "category_theory.uncurry_natural_right_assoc" -> "category_theory", "primrec\:2082.to_comp" -> "computability", "nnreal.half_lt_self" -> "data", "nat.subtype.le_succ_of_forall_lt_le" -> "data", "bitraversable.id_tsnd" -> "control", "nsmul_eq_mul'" -> "algebra", "list.sorted_insertion_sort" -> "data", "nat.le_add_one_iff" -> "data", "sub_div" -> "algebra", "multiset.union_le_union_right" -> "data", "filter.comap_const_of_mem" -> "order", "category_theory.abelian.pseudoelement.pseudo_zero_aux" -> "category_theory", "list.subset_append_of_subset_left" -> "data", "affine.triangle.eq_orthocenter_of_forall_mem_altitude" -> "geometry", "structure_groupoid.local_invariant_prop.lift_prop_within_at_congr_iff" -> "geometry", "bool.to_bool_false" -> "data", "nonempty_of_exists" -> "init", "one_one_equiv.to_many_one" -> "computability", "multiset.powerset_coe" -> "data", "set.union_eq_Union" -> "data", "multiset.filter_add" -> "data", "list.prod_take_mul_prod_drop" -> "data", "units.inv_mul_cancel_left" -> "algebra", "distrib_mul_action_hom.map_smul" -> "algebra", "lt_inv_mul_iff_mul_lt" -> "algebra", "linear_map.finsupp_sum" -> "algebra", "times_cont_mdiff_at_fst" -> "geometry", "category_theory.equiv_of_fully_faithful_symm_apply" -> "category_theory", "list.last_eq_nth_le" -> "data", "power_series.inv_eq_inv_aux" -> "algebra", "eq_zero_iff_of_associated" -> "algebra", "eq.substr" -> "init", "category_theory.equivalence.equivalence_mk'_counit_inv" -> "category_theory", "asymptotics.is_o_pow_id" -> "analysis", "ultrafilter_comap_pure_nhds" -> "topology", "list.disjoint_cons_right" -> "data", "closure_Iio" -> "topology", "image_norm_le_of_norm_deriv_right_le_deriv_boundary" -> "analysis", "asymptotics.is_O_with.join" -> "analysis", "set.preimage_const_mul_Iio_of_neg" -> "data", "Inf_union" -> "order", "coe_monoid_hom" -> "algebra", "multiset.sub_add_cancel" -> "data", "list.count_filter" -> "data", "ring.direct_limit.of_f" -> "algebra", "set.inclusion_injective" -> "data", "multiset.cons_erase" -> "data", "has_fderiv_at_iff_is_o_nhds_zero" -> "analysis", "eq_one_of_left_cancel_mul_self" -> "algebra", "infi_eq_top" -> "order", "sup_le" -> "order", "onote.zero_def" -> "set_theory", "has_fderiv_at.smul_algebra" -> "analysis", "submodule.ker_liftq" -> "algebra", "tendsto_indicator_bUnion_finset" -> "order", "int.cast_injective" -> "data", "mv_power_series.X_inj" -> "algebra", "summable.comp_injective" -> "topology", "gold_irrational" -> "data", "measure_theory.measure.haar.prehaar_pos" -> "analysis", "fraction_map.is_integer_of_is_unit_denom" -> "algebra", "asymptotics.is_O.congr" -> "analysis", "is_unit_one" -> "algebra", "measure_theory.simple_func.const_zero" -> "analysis", "local_equiv.eq_on_source.symm'" -> "data", "hyperreal.infinitesimal_iff_infinite_inv" -> "data", "padic_int.ideal_eq_span_pow_p" -> "data", "quotient.sound'" -> "data", "category_theory.limits.coprod_map_id_id" -> "category_theory", "complex.arg_neg_one" -> "analysis", "inv_le_one_of_one_le" -> "algebra", "local_homeomorph.of_set_symm" -> "topology", "nat.mul_le_mul_left" -> "init", "Top.presheaf.stalk_pushforward.comp" -> "topology", "ideal.mem_supr_of_mem" -> "algebra", "real.quotient_mk_eq_mk" -> "data", "ennreal.lt_iff_exists_add_pos_lt" -> "data", "int.le_div_iff_mul_le" -> "data", "dvd_normalize_iff" -> "algebra", "wseq.destruct_congr_iff" -> "data", "punit.Sup_eq" -> "algebra", "real.one_lt_rpow_of_pos_of_lt_one_of_neg" -> "analysis", "ennreal.to_nnreal_eq_zero_iff" -> "data", "multiset.Ico.eq_cons" -> "data", "degree_scale_roots" -> "algebra", "list.zip_map'" -> "data", "add_semiconj_by.units_coe" -> "algebra", "with_one.cases_on" -> "algebra", "unique_mdiff_on.unique_mdiff_on_preimage" -> "geometry", "has_fderiv_at.lim_real" -> "analysis", "category_theory.limits.pushout_cocone.mk_inr" -> "category_theory", "segment_eq_image'" -> "analysis", "CommRing.colimits.cocone_naturality_components" -> "algebra", "filter.tendsto_pure_left" -> "order", "hyperreal.not_infinite_neg_add_infinite_pos" -> "data", "not_mem_affine_span_diff_of_affine_independent" -> "algebra", "inv_image.irreflexive" -> "init", "uniform.continuous_at_iff'_left" -> "topology", "add_commute.all" -> "algebra", "option.some_orelse" -> "data", "tsum_sigma" -> "topology", "list.is_infix.trans" -> "data", "complex.has_deriv_at_sinh" -> "analysis", "differentiable_on.smul" -> "analysis", "measure_theory.l1.simple_func.norm_Integral_le_one" -> "analysis", "set.image_compl_preimage" -> "data", "emetric.Hausdorff_edist_comm" -> "topology", "pfun.core_def" -> "data", "int.cast_inj" -> "data", "fin.coe_mul" -> "data", "set.bInter_union" -> "data", "list.nil_subperm" -> "data", "lt_asymm" -> "init", "real.continuous_tan" -> "analysis", "topological_fiber_bundle_core.mem_triv_change_source" -> "topology", "int.of_nat_sub" -> "init", "category_theory.under.limit_X" -> "category_theory", "bool.bnot_band" -> "data", "abstract_completion.continuous_extend" -> "topology", "subalgebra.coe_int_mem" -> "algebra", "category_theory.limits.is_image.self_lift" -> "category_theory", "pythagorean_triple.mul_iff" -> "number_theory", "is_noetherian_iff_well_founded" -> "algebra", "has_deriv_within_at.cexp" -> "analysis", "fin.coe_val_of_lt" -> "data", "int.mul_le_mul_of_nonneg_left" -> "init", "wseq.join_think" -> "data", "composition.ext_iff" -> "combinatorics", "polynomial.degree_mod_by_monic_lt" -> "data", "real.cos_one_pos" -> "data", "list.perm.map" -> "data", "list.nodup_reverse" -> "data", "pi_Lp.smul_apply" -> "topology", "uniform.continuous_at_iff'_right" -> "topology", "continuous_linear_map.op_norm_extend_le" -> "analysis", "fin.eq_of_veq" -> "init", "palindrome.reverse_eq" -> "data", "mvpfunctor.M.dest'_eq_dest'" -> "data", "list.pairwise.imp_mem" -> "data", "polynomial.coeff_restriction'" -> "algebra", "set.disjoint_union_left" -> "data", "int.to_nat_eq_max" -> "data", "category_theory.adjunction.core_hom_equiv.hom_equiv_naturality_right_symm" -> "category_theory", "ring_equiv.to_ring_hom_refl" -> "data", "filter.monotone_principal" -> "order", "mul_nonneg_iff_right_nonneg_of_pos" -> "algebra", "category_theory.faithful.div_faithful" -> "category_theory", "category_theory.limits.diagram_of_cones.mk_of_has_limits_obj" -> "category_theory", "category_theory.iso.refl_inv" -> "category_theory", "Top.presheaf.pushforward.id_hom_app'" -> "topology", "has_fderiv_within_at_snd" -> "analysis", "ideal.mem_leading_coeff" -> "algebra", "traversable.naturality'" -> "control", "list.bind_map" -> "data", "int.distrib_left" -> "init", "char_p.int_coe_eq_int_coe_iff" -> "algebra", "emetric.cauchy_seq_iff'" -> "topology", "lists'.mem_cons" -> "set_theory", "hyperreal.infinitesimal_mul" -> "data", "real.mul_self_sqrt" -> "data", "ordinal.lift_min" -> "set_theory", "bdd_above_empty" -> "order", "discrete_valuation_ring.unit_mul_pow_congr_pow" -> "algebra", "subgroup.gpow_mem" -> "algebra", "real.sin_pi_div_sixteen" -> "analysis", "submodule.mul_one" -> "algebra", "mul_semiring_action_hom.comp_apply" -> "algebra", "prod.swap_swap" -> "data", "ordinal.sup_succ" -> "set_theory", "set.subset_diff_singleton" -> "data", "int.gcd_zero_left" -> "algebra", "fin.prod_univ_zero" -> "data", "is_integral_neg" -> "algebra", "subgroup.closure_eq_of_le" -> "algebra", "subsemiring.coe_mk'" -> "algebra", "measure_theory.measure_Inter_eq_infi_nat" -> "analysis", "finset.prod_involution" -> "algebra", "polynomial.mod_X_sub_C_eq_C_eval" -> "data", "dfinsupp.subtype_domain_sum" -> "data", "rat.cast_bit0" -> "data", "is_submonoid.power_subset" -> "algebra", "conj_inv" -> "algebra", "primrec.nat_bit1" -> "computability", "omega.coeffs.dvd_val_between" -> "tactic", "is_local_min.comp_antimono" -> "topology", "list.map_pmap" -> "data", "nat.zero_sub" -> "init", "filter.sup_bind" -> "order", "submodule.range_subtype" -> "algebra", "matrix.add_dot_product" -> "data", "emetric.diam_singleton" -> "topology", "multiset.prod_hom" -> "data", "rat.le_def" -> "data", "denumerable.encode_of_nat" -> "data", "category_theory.limits.cone.extend_\[Pi]" -> "category_theory", "is_R_or_C.bit1_im" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence.unit_iso_inv_app_hom_app" -> "category_theory", "linear_equiv_iso_Module_iso_inv" -> "algebra", "nat.le_rec_on_succ_left" -> "data", "many_one_equiv.le_congr_left" -> "computability", "measure_theory.outer_measure.le_trim" -> "analysis", "measure_theory.l1.coe_pos_part" -> "analysis", "list.find_cons_of_pos" -> "data", "normal_of_eq_add_cosets" -> "algebra", "category_theory.limits.prod.left_unitor_hom" -> "category_theory", "convex_hull_eq_union_convex_hull_finite_subsets" -> "analysis", "int.bodd_add_div2" -> "data", "uniform_space.completion.map_unique" -> "topology", "binfi_inf" -> "order", "finset.gsmul_sum" -> "algebra", "asymptotics.is_o_iff_forall_is_O_with" -> "analysis", "complex.uniform_continuous_mul_const" -> "topology", "category_theory.preadditive.mono_of_kernel_zero" -> "category_theory", "qpf.liftp_iff_of_is_uniform" -> "data", "matrix.subsingleton_of_empty_left" -> "data", "nnreal.continuous_coe" -> "topology", "linear_map.antilipschitz_of_bound" -> "analysis", "add_semiconj_by.neg_symm_left" -> "algebra", "nonempty_preirreducible_inter" -> "topology", "power_series.constant_coeff_inv_of_unit" -> "algebra", "subalgebra.to_submodule_injective" -> "algebra", "has_fpower_series_on_ball.tendsto_uniformly_on" -> "analysis", "list.mmap_with_index_eq_mmap_enum" -> "data", "filter.tendsto.nndist" -> "topology", "cauchy_seq_of_tendsto_nhds" -> "topology", "fintype.univ_punit" -> "data", "dioph.ex_dioph" -> "number_theory", "interval_integrable.add" -> "analysis", "is_coprime_self" -> "algebra", "is_add_subgroup.trivial_eq_closure" -> "algebra", "nat.even_succ" -> "data", "affine_subspace.inter_nonempty_of_nonempty_of_sup_direction_eq_top" -> "algebra", "nnreal.rpow_eq_zero_iff" -> "analysis", "upper_bounds_Iic" -> "order", "equiv.add_equiv_symm_apply" -> "data", "ideal.map_radical_of_surjective" -> "algebra", "model_with_corners_self_local_equiv" -> "geometry", "pgame.domineering.move_right_card" -> "set_theory", "add_comm_group.direct_limit.of_neg" -> "algebra", "function.injective_surj_inv" -> "logic", "exp_neg_inv_glue.f_aux_limit" -> "analysis", "or.elim3" -> "logic", "quotient.induction_on" -> "init", "primrec.bind_decode_iff" -> "computability", "submodule.eq_bot_of_zero_eq_one" -> "algebra", "cardinal.type_cardinal" -> "set_theory", "fin.ne_of_vne" -> "init", "abs_pos_iff" -> "algebra", "function.iterate_add_apply" -> "logic", "finset.sum_apply_ite" -> "algebra", "mul_sub_mul_div_mul_nonpos_iff" -> "algebra", "nat.lt_of_sub_lt_sub_left" -> "data", "is_R_or_C.I_mul_I" -> "data", "fraction_map.mul_inv_cancel" -> "algebra", "filter.has_basis_iff" -> "order", "smooth.smooth_at" -> "geometry", "lim_spec" -> "topology", "many_one_equiv.congr_left" -> "computability", "supr_eq_supr_finset" -> "data", "int.modeq.modeq_zero_iff" -> "data", "prod.snd_eq_iff" -> "data", "lt_inv_mul_of_mul_lt" -> "algebra", "eventually_eq_nhds_within_of_eq_on" -> "topology", "function.is_periodic_id" -> "dynamics", "prime_spectrum.zero_locus_supr" -> "algebraic_geometry", "decidable.imp_or_distrib" -> "logic", "monotone_const" -> "order", "infi_exists" -> "order", "orthogonal_projection_fn_mem" -> "analysis", "real.continuous_abs" -> "topology", "max_lt_iff" -> "algebra", "enat.ne_top_of_lt" -> "data", "polynomial.leading_coeff_mul'" -> "data", "category_theory.monoidal_category.associator_inv_naturality" -> "category_theory", "commute.self_cast_int_mul" -> "algebra", "pi_Lp.sub_apply" -> "topology", "Gromov_Hausdorff.Hausdorff_dist_optimal_le_HD" -> "topology", "filter.tendsto_at_top_at_bot" -> "order", "option.id_traverse" -> "control", "category_theory.nat_iso.cancel_nat_iso_hom_right_assoc" -> "category_theory", "has_sum.sigma_of_has_sum" -> "topology", "matrix.add_cons" -> "data", "category_theory.functor.flip_obj_map" -> "category_theory", "set.not_not_mem" -> "data", "le_of_add_le_add_left" -> "algebra", "complex.sin_sq_add_cos_sq" -> "data", "category_theory.Monad.to_Mon_one" -> "category_theory", "indicator_eventually_le_indicator" -> "order", "computable.nat_elim" -> "computability", "summable_of_summable_nnnorm" -> "analysis", "zmod.cast_add'" -> "data", "category_theory.monoidal_category.right_unitor_tensor_inv" -> "category_theory", "min_comm" -> "init", "bool.eq_tt_of_bnot_eq_ff" -> "data", "list.inter_nil" -> "data", "gaussian_int.to_complex_re" -> "data", "generalized_continued_fraction.nth_of_eq_some_of_nth_int_fract_pair_stream_fr_ne_zero" -> "algebra", "list.chain_of_chain_map" -> "data", "ennreal.zero_lt_one" -> "data", "multiset.sum_repeat" -> "data", "lt_of_inv_lt_inv" -> "algebra", "set.nonempty.mono" -> "data", "int.norm_cast_real" -> "analysis", "rat.coe_int_num" -> "data", "multiset.union_add_distrib" -> "data", "nnreal.inv_eq_one_div" -> "data", "filter.bot_sets_eq" -> "order", "tendsto_inv" -> "topology", "stream.nth_approx" -> "data", "not.decidable_imp_symm" -> "logic", "measure_theory.l1.simple_func.norm_eq_integral" -> "analysis", "nat.fpow_pos_of_pos" -> "algebra", "mvpfunctor.liftr_iff" -> "data", "measure_theory.extend_empty" -> "analysis", "nhds_within_inter'" -> "topology", "real.sqrt_sqr" -> "data", "exists_and_distrib_right" -> "logic", "subtype.preimage_val_eq_preimage_val_iff" -> "data", "relation.refl_trans_gen.cases_tail" -> "logic", "has_deriv_at_iff_tendsto" -> "analysis", "monoid_hom.map_frobenius" -> "algebra", "circle_deg1_lift.tendsto_translation_number_of_dist_bounded_aux" -> "dynamics", "category_theory.over.w_assoc" -> "category_theory", "metric.Hausdorff_dist_closure\:2081" -> "topology", "dist_pi_def" -> "topology", "polynomial.eq_C_of_degree_eq_zero" -> "data", "upper_bounds_Ico" -> "order", "alist.mem_insert" -> "data", "pfun.res_univ" -> "data", "int.bodd_two" -> "data", "real.volume_Icc" -> "analysis", "cardinal.lt_power_cof" -> "set_theory", "turing.TM1to1.step_aux_read" -> "computability", "hyperreal.not_infinite_of_infinitesimal" -> "data", "nnreal.has_sum_coe" -> "topology", "submonoid.mrange_inl" -> "algebra", "one_add_mul_le_pow" -> "algebra", "finset.prod_range_mul_prod_Ico" -> "algebra", "add_neg_self" -> "algebra", "ideal.span_singleton_mul_right_unit" -> "algebra", "prime_spectrum.gc" -> "algebraic_geometry", "ordinal.lift_type" -> "set_theory", "wseq.head_terminates_of_nth_terminates" -> "data", "polynomial.degree_add_eq_of_leading_coeff_add_ne_zero" -> "data", "denumerable.raise_sorted" -> "data", "open_add_subgroup.add_mem" -> "topology", "emetric.mem_ball_self" -> "topology", "set.image_const_sub_Ioo" -> "data", "nat.log_pow" -> "data", "measure_theory.l1.simple_func.integral_l1_eq_integral" -> "analysis", "submonoid.localization_map.of_mul_equiv_of_dom_comp_symm" -> "algebra", "div_le_div_of_nonpos_of_le" -> "algebra", "option.some_bind'" -> "data", "list.mem_lookup_all" -> "data", "nat.bitwise_swap" -> "init", "complex.tanh_conj" -> "data", "free_group.to_group.range_subset" -> "algebra", "nat.bitwise_zero_right" -> "init", "vector_allp_cons" -> "number_theory", "function.is_fixed_pt_id" -> "dynamics", "add_con.ext" -> "algebra", "real.sin_gt_sub_cube" -> "analysis", "nnreal.inner_le_Lp_mul_Lq" -> "analysis", "finset.mem_of_max" -> "data", "is_R_or_C.inv_I" -> "data", "nat.partrec'.comp'" -> "computability", "algebra.mem_adjoin_iff" -> "algebra", "inv_le_inv_iff" -> "algebra", "dfinsupp.support_eq_empty" -> "data", "equiv.perm.mem_support" -> "algebra", "measure_theory.integrable_on_univ" -> "analysis", "has_sum_sum" -> "topology", "computable.option_some" -> "computability", "dual_pair.mem_of_mem_span" -> "algebra", "opposite.op_eq_one_iff" -> "algebra", "initial_seg.coe_fn_mk" -> "set_theory", "free_semigroup.mul_seq" -> "algebra", "has_sum_iff_has_sum" -> "topology", "fpow_nonneg_of_nonneg" -> "algebra", "pfunctor.map_eq" -> "data", "bind_ext_congr" -> "init", "add_subgroup.subset_closure" -> "algebra", "Top.epi_iff_surjective" -> "topology", "multiset.erase_dup_cons" -> "data", "int.of_nat_mul_sub_nat_nat" -> "init", "UniformSpace.coe_of" -> "topology", "category_theory.monoidal.associator_hom_apply" -> "category_theory", "polynomial.coeff_expand_mul" -> "algebra", "finset.fold_min_le" -> "data", "set.dual_Iic" -> "data", "int.div_le_div" -> "data", "mem_closure_iff_nhds" -> "topology", "tangent_bundle.smooth_proj" -> "geometry", "fin.mul_def" -> "init", "times_cont_diff.times_cont_diff_within_at" -> "analysis", "function.is_periodic_pt.right_of_add" -> "dynamics", "add_monoid_hom.to_fun_eq_coe" -> "algebra", "joined_in.joined_subtype" -> "topology", "traversable.foldr.of_free_monoid_comp_free_mk" -> "control", "category_theory.limits.cones.postcompose_obj_\[Pi]" -> "category_theory", "is_lub.nonempty" -> "order", "is_open_prod_iff" -> "topology", "category_theory.adjunction.cocones_iso_component_hom_app" -> "category_theory", "submodule.disjoint_def" -> "algebra", "is_least.unique" -> "order", "unique_diff_within_at.inter" -> "analysis", "add_localization.mk_eq_add_monoid_of_mk'" -> "algebra", "is_G\[Delta]_bInter_of_open" -> "topology", "measure_theory.measure.finite_at_bot" -> "analysis", "is_least_pair" -> "order", "nat.lor_zero" -> "data", "cardinal_le_dim_of_linear_independent" -> "algebra", "ennreal.two_pos" -> "data", "mul_pos_of_neg_of_neg" -> "algebra", "tendsto_iff_dist_tendsto_zero" -> "topology", "ordinal.zero_or_succ_or_limit" -> "set_theory", "adjoin_root.coe_injective" -> "algebra", "wseq.nth_congr" -> "data", "linear_map.coprod_apply" -> "algebra", "deriv_within_sub" -> "analysis", "with_bot.coe_add" -> "algebra", "decidable.not_imp_not" -> "logic", "monoid_hom.iterate_map_mul" -> "algebra", "polynomial.monomial_zero_right" -> "data", "finmap.insert_singleton_eq" -> "data", "cau_seq.exists_gt" -> "data", "affine_subspace.lt_iff_le_and_exists" -> "algebra", "list.nil_prefix" -> "data", "finset.bind_to_finset" -> "data", "finset.one_lt_card_iff" -> "data", "turing.partrec_to_TM2.clear_ok" -> "computability", "bool_iff_false" -> "init", "filter.comap_lift'_eq2" -> "order", "finset.card_univ" -> "data", "hyperreal.infinite_neg_iff_infinite_pos_neg" -> "data", "list.mem_join_of_mem" -> "data", "vector.tail_val" -> "data", "nonempty_Prop" -> "logic", "finset.center_mass_segment" -> "analysis", "differentiable_within_at_inv" -> "analysis", "polynomial.integral_normalization_eval\:2082_eq_zero" -> "data", "d_array.of_beq_aux_eq_ff" -> "init", "equiv.forall\:2083_congr" -> "data", "dim_pos_iff_nontrivial" -> "algebra", "nat.partrec.code.eval_const" -> "computability", "differentiable_at.ccos" -> "analysis", "filter.is_ultrafilter.eventually_or" -> "order", "nat.choose_succ_self" -> "data", "pell.modeq_of_xn_modeq" -> "number_theory", "hyperreal.st_mul" -> "data", "category_theory.limits.binary_bicone.to_cone_\[Pi]_app_right" -> "category_theory", "wseq.to_list'_think" -> "data", "mul_right_inv" -> "algebra", "continuous_within_at_Iio_iff_Iic" -> "topology", "measure_theory.l1.simple_func.to_simple_func_eq_to_fun" -> "analysis", "submodule.mul_mem_mul" -> "algebra", "bool.eq_ff_of_bnot_eq_tt" -> "data", "partrec.comp" -> "computability", "set.image_const_sub_Ici" -> "data", "computation.mem_promises" -> "data", "category_theory.limits.lim_map_\[Pi]_assoc" -> "category_theory", "computation.exists_of_mem_parallel" -> "data", "circle_deg1_lift.transnum_aux_seq_dist_lt" -> "dynamics", "set.Union_const" -> "data", "differentiable_at.cosh" -> "analysis", "equiv.perm.inv_apply_self" -> "data", "category_theory.over.iterated_slice_backward_obj" -> "category_theory", "inf_le_right" -> "order", "div_lt_div_of_lt_left" -> "algebra", "power_series.order_le" -> "algebra", "ring.closure_subset" -> "algebra", "pythagorean_triple_comm" -> "number_theory", "mul_le_of_le_one_of_le" -> "algebra", "add_submonoid.localization_map.of_add_equiv_of_add_equiv" -> "algebra", "ennreal.of_real_coe_nnreal" -> "data", "by_contradiction" -> "logic", "linear_map.general_linear_group.general_linear_equiv_to_linear_map" -> "algebra", "linear_map.injective_iff_surjective_of_findim_eq_findim" -> "algebra", "filter.map_prod" -> "order", "asymptotics.is_o.mul" -> "analysis", "AddMon.coe_of" -> "algebra", "continuous_stone_cech_unit" -> "topology", "pythagorean_triple.is_primitive_classified_aux" -> "number_theory", "circle_deg1_lift.mono" -> "dynamics", "padic_norm.div" -> "data", "computable.equiv\:2082" -> "computability", "has_deriv_within_at.sin" -> "analysis", "submodule.range_snd" -> "algebra", "image_closure_subset_closure_image" -> "topology", "primrec.option_bind\:2081" -> "computability", "continuous_linear_map.coe_sub'" -> "topology", "category_theory.bundled.coe_mk" -> "category_theory", "set.Icc_inter_Icc_eq_singleton" -> "data", "finset.property_of_mem_map_subtype" -> "data", "submodule.mem_sup" -> "algebra", "pnat.Ico.card" -> "data", "continuous_on_of_locally_continuous_on" -> "topology", "category_theory.kernel_comp_cokernel" -> "algebra", "units.unop_pow" -> "algebra", "list.forall\:2082_comp_perm_eq_perm_comp_forall\:2082" -> "data", "matrix.vec_mul_empty" -> "data", "category_theory.limits.cospan_map_inl" -> "category_theory", "tendsto_uniformity_iff_dist_tendsto_zero" -> "topology", "list.rotate_rotate" -> "data", "category_theory.equivalence.fun_inv_id_assoc_hom_app" -> "category_theory", "tsum_comp_le_tsum_of_inj" -> "topology", "is_coprime.of_mul_left_left" -> "algebra", "local_homeomorph.coe_trans" -> "topology", "ring_equiv.to_opposite_symm_apply" -> "data", "zsqrtd.not_divides_square" -> "data", "is_greatest.insert" -> "order", "category_theory.limits.types.\[Iota]_desc_apply" -> "category_theory", "multiset.prod_hom_rel" -> "data", "strict_mono.const_add" -> "algebra", "is_extr_on.comp_mono" -> "order", "units.to_Aut_inv" -> "category_theory", "category_theory.mono_of_mono_fac" -> "category_theory", "le_of_not_gt" -> "init", "list.append_inj_right" -> "data", "polynomial.separable_C" -> "algebra", "nat.sub_self_add" -> "init", "has_deriv_at.mul" -> "analysis", "filter.map_principal" -> "order", "filter.exists_le_of_tendsto_at_bot" -> "order", "list.tendsto_insert_nth'" -> "topology", "nat.eq_zero_of_dvd_of_div_eq_zero" -> "data", "is_absolute_value.abv_sub" -> "data", "equiv.ring_equiv_symm_apply" -> "data", "seq.head_eq_destruct" -> "data", "category_theory.functor.punit_ext'" -> "category_theory", "complex.cos_of_real_im" -> "data", "int.coe_nat_nonneg" -> "data", "setoid.mem_classes" -> "data", "is_preconnected_Ioi" -> "topology", "is_open.open_embedding_subtype_coe" -> "topology", "measure_theory.measure.finite_at_filter.eventually" -> "analysis", "local_homeomorph.restr_trans" -> "topology", "vector_allp.imp" -> "number_theory", "differentiable_on.comp" -> "analysis", "filter.tendsto_at_bot_add_const_left" -> "order", "list.disjoint_of_subset_right" -> "data", "is_open_sum_iff" -> "topology", "finsupp.smul_single'" -> "data", "matrix.special_linear_group.to_lin_one" -> "algebra", "is_basis.to_dual_to_dual" -> "algebra", "ennreal.of_real_le_of_real" -> "data", "isometry.edist_eq" -> "topology", "set.preimage_const_mul_Iic_of_neg" -> "data", "polynomial.map_root_of_splits" -> "algebra", "category_theory.over.coe_hom" -> "category_theory", "ordinal.lt_of_add_lt_add_right" -> "set_theory", "neg_nonpos_of_nonneg" -> "algebra", "filter.comap_pure" -> "order", "tensor_product.neg_tmul" -> "algebra", "preorder_hom.id_to_fun" -> "order", "list.mem_of_ne_of_mem" -> "data", "category_theory.limits.prod.lift_snd_assoc" -> "category_theory", "list.tfae_of_forall" -> "data", "cardinal.powerlt_le_powerlt_left" -> "set_theory", "ring_hom.map_matrix_apply" -> "data", "fract_nonneg" -> "algebra", "free_group.red.not_step_nil" -> "algebra", "embedding_graph" -> "topology", "subtype.eta" -> "init", "ideal.mem_map_of_mem" -> "algebra", "array.rev_list_reverse" -> "data", "rel.core_union" -> "data", "lists'.of_list_subset" -> "set_theory", "set.Iio_subset_Iio_iff" -> "data", "lucas_lehmer.X.right_distrib" -> "number_theory", "local_homeomorph.image_trans_source" -> "topology", "monoid_hom.one_apply" -> "algebra", "qpf.fix.mk_dest" -> "data", "neg_gsmul" -> "algebra", "convex_on_iff_div" -> "analysis", "measure_theory.outer_measure.coe_zero" -> "analysis", "list.cons_head'_tail" -> "data", "bounded_continuous_function.continuous_evalx" -> "topology", "pythagorean_triple.zero" -> "number_theory", "with_zero.div_eq_iff_mul_eq" -> "algebra", "nat.add_zero" -> "init", "is_compl.inf_left_eq_bot_iff" -> "order", "is_R_or_C.mul_im" -> "data", "measure_theory.simple_func.restrict_lintegral" -> "analysis", "affine_map.mk'_linear" -> "algebra", "convex.strict_antimono_of_deriv_neg" -> "analysis", "int.coe_lcm" -> "algebra", "category_theory.mono_iff_injective" -> "category_theory", "finset.weighted_vsub_indicator_subset" -> "algebra", "is_integral_algebra_map" -> "algebra", "continuous_within_at_Icc_iff_Iic" -> "topology", "add_monoid_hom.prod_comp_prod_map" -> "algebra", "mv_polynomial.C_eq_coe_nat" -> "data", "euclidean_geometry.dist_eq_of_angle_eq_angle_of_angle_ne_pi" -> "geometry", "category_theory.limits.cokernel_zero_iso_target_inv" -> "category_theory", "interval_integral.norm_integral_le_of_norm_le_const" -> "analysis", "linear_independent.ne_zero" -> "algebra", "continuous_linear_equiv.comp_differentiable_at_iff" -> "analysis", "nat.lt_of_div_lt_div" -> "data", "list.index_of_nth" -> "data", "real.is_conjugate_exponent_conjugate_exponent" -> "data", "euclidean_domain.xgcd_aux_fst" -> "algebra", "turing.list_blank.head_mk" -> "computability", "polynomial.splits_comp_of_splits" -> "algebra", "eq_sub_of_add_eq" -> "algebra", "with_bot.coe_eq_zero" -> "algebra", "rel_iso.coe_fn_mk" -> "order", "typevec.snd_prod_mk" -> "data", "filter.mem_inf_principal" -> "order", "monotone.add_const" -> "algebra", "polynomial.expand_X" -> "algebra", "rel_iso.map_inf" -> "order", "measure_theory.measure.bind_apply" -> "analysis", "alist.union_assoc" -> "data", "equiv.perm.one_apply" -> "data", "ideal.is_local_of_is_maximal_radical" -> "algebra", "category_theory.non_preadditive_abelian.add_neg" -> "category_theory", "linear_map.ker_eq_bot_of_cancel" -> "algebra", "mv_power_series.coeff_monomial'" -> "algebra", "multiset.erase_cons_tail" -> "data", "is_least.is_least_iff_eq" -> "order", "sub_zero" -> "algebra", "rat.cast_bit1" -> "data", "category_theory.monad.algebra.EilenbergMoore_to_category_struct_to_has_hom_hom" -> "category_theory", "category_theory.limits.coprod.map_iso_inv" -> "category_theory", "segment_eq_image\:2082" -> "analysis", "frontier_eq_closure_inter_closure" -> "topology", "finset.prod_range_zero" -> "algebra", "vector_ex_iff_exists" -> "number_theory", "simple_graph.edge_symm" -> "combinatorics", "ordered_ring.mul_le_mul_of_nonneg_right" -> "algebra", "submonoid.coe_Inf" -> "algebra", "ring.fractional_ideal.coe_mem_one" -> "algebra", "category_theory.functor_to_types.map_hom_map_inv_apply" -> "category_theory", "emetric.ball_subset_ball" -> "topology", "measure_theory.simple_func.coe_le" -> "analysis", "function.comp.right_id" -> "init", "int.to_nat_coe_nat" -> "data", "rel_embedding.is_irrefl" -> "order", "lagrange.eval_basis_ne" -> "algebra", "iterated_deriv_within_one" -> "analysis", "exists_unique.elim" -> "init", "fderiv_fst" -> "analysis", "has_sum_le_inj" -> "topology", "lie_algebra.equiv.of_subalgebras_apply" -> "algebra", "polynomial.leading_coeff_pow'" -> "data", "eq_true_of_and_eq_true_left" -> "init", "enat.ne_top_iff_dom" -> "data", "is_measurable.sInter" -> "analysis", "polynomial.nat_degree_neg" -> "data", "continuous_linear_map.comp_continuous_multilinear_map_coe" -> "topology", "bool.to_bool_coe" -> "data", "finset.sum_insert" -> "algebra", "times_cont_diff_iff_times_cont_diff_at" -> "analysis", "circle_deg1_lift.le_floor_map_map_zero" -> "dynamics", "list.sublist.filter_map" -> "data", "valuation.is_equiv_of_val_le_one" -> "algebra", "mv_polynomial.eval_sum" -> "data", "ordinal.add_sub_cancel" -> "set_theory", "roption.ne_none_iff" -> "data", "int.sub_right_lt_of_lt_add" -> "init", "nat.mul_self_le_mul_self" -> "data", "iterated_fderiv_eq_equiv_comp" -> "analysis", "finset.filter_union" -> "data", "set.pi_eq_empty_iff" -> "data", "submodule.exists" -> "algebra", "complex.nat_cast_re" -> "data", "nat.le_succ_of_pred_le" -> "init", "circle_deg1_lift.commute_sub_int" -> "dynamics", "commute.pow_left" -> "algebra", "free_semigroup.traverse_mul" -> "algebra", "nat.mkpair_lt_mkpair_left" -> "data", "nnreal.inv_mul_cancel" -> "data", "deriv_const_smul" -> "analysis", "ideal.radical_inf" -> "algebra", "infi_range" -> "order", "category_theory.Monad.Mon_to_Monad_map_to_nat_trans_app" -> "category_theory", "max_eq_left" -> "init", "vector.continuous_at_remove_nth" -> "topology", "category_theory.limits.prod_left_unitor_inv_naturality_assoc" -> "category_theory", "qpf.recF_eq_of_Wequiv" -> "data", "filter.lift_const" -> "order", "submodule.closed_complemented.has_closed_complement" -> "topology", "image_le_of_deriv_right_lt_deriv_boundary" -> "analysis", "ordinal.typein_apply" -> "set_theory", "equiv_of_is_basis_symm_trans" -> "algebra", "ideal.is_prime.radical_le_iff" -> "algebra", "poly.remap_eval" -> "number_theory", "affine_subspace.mem_affine_span_insert_iff" -> "algebra", "mul_neg_eq_neg_mul_symm" -> "algebra", "iff_true" -> "init", "fderiv_id'" -> "analysis", "asymptotics.is_o.add" -> "analysis", "category_theory.limits.is_limit.cone_points_iso_of_nat_iso_hom" -> "category_theory", "filter.is_countably_generated.exists_countable_infi_principal" -> "order", "composition.sigma_composition_eq_iff" -> "analysis", "finset.sum_eq_fold" -> "algebra", "mv_power_series.coeff_zero_eq_constant_coeff" -> "algebra", "mv_polynomial.eq_zero_iff" -> "data", "is_extr_filter_dual_iff" -> "order", "int.add_mod" -> "data", "pgame.right_response_spec" -> "set_theory", "pnat.mod_le" -> "data", "matrix.det_eq_zero_of_column_eq_zero" -> "algebra", "complex.of_real_zero" -> "data", "pos_num.to_int_eq_succ_pred" -> "data", "qpf.has_good_supp_iff" -> "data", "function.update_noteq" -> "logic", "infi_pair" -> "order", "continuous_fst" -> "topology", "finset.inter_union_self" -> "data", "continuous_multilinear_map.map_sum" -> "topology", "euclidean_domain.xgcd_aux_val" -> "algebra", "unique_of_exists_unique" -> "init", "cardinal.mk_fin" -> "set_theory", "eq_of_dist_eq_zero" -> "topology", "pgame.nim.exists_ordinal_move_left_eq" -> "set_theory", "prod.map_snd" -> "data", "sym_bilin_form.ortho_sym" -> "algebra", "continuous_on_snd" -> "topology", "real.is_conjugate_exponent.one_div_nonneg" -> "data", "multiset.mem_sigma" -> "data", "monotone.add" -> "algebra", "nat.mul_sub_left_distrib" -> "init", "hash_map.valid.erase_aux" -> "data", "nnreal.exists_pos_sum_of_encodable" -> "analysis", "nat.mul_pred_right" -> "init", "multiset.sum_singleton" -> "data", "submodule.range_liftq" -> "algebra", "group.normal_closure_mono" -> "algebra", "nat.div_eq_zero_iff" -> "data", "topological_space.opens.map_comp_obj" -> "topology", "prime_spectrum.vanishing_ideal_Union" -> "algebraic_geometry", "int.add_le_of_le_neg_add" -> "init", "pgame.numeric.move_left" -> "set_theory", "is_measurable_Ioo" -> "analysis", "primrec.comp\:2082" -> "computability", "convex_cone.mem_comap" -> "analysis", "int.gcd_eq_left" -> "algebra", "nat.lxor_trichotomy" -> "data", "sub_left_lt_of_lt_add" -> "algebra", "inv_le_inv" -> "algebra", "list.sublist.refl" -> "data", "times_cont_diff_at_succ_iff_has_fderiv_at" -> "analysis", "totally_bounded.closure" -> "topology", "equiv.summable_iff_of_support" -> "topology", "subsemiring.coe_prod" -> "algebra", "category_theory.core.id_hom" -> "category_theory", "metric.is_closed_sphere" -> "topology", "matrix_equiv_tensor.inv_fun_zero" -> "algebra", "contracting_with.tendsto_iterate_fixed_point" -> "topology", "submonoid.localization_map.mk'_self" -> "algebra", "set.finite.add" -> "algebra", "real.rpow_def_of_pos" -> "analysis", "list.func.get_sub" -> "data", "category_theory.limits.diagram_of_cones.cone_points_obj" -> "category_theory", "category_theory.monoidal_of_has_finite_coproducts.tensor_hom" -> "category_theory", "exists_has_deriv_at_eq_zero" -> "analysis", "smooth_snd" -> "geometry", "mv_polynomial.coeff_sum" -> "data", "function.support_inv" -> "data", "not_lt_of_lt" -> "init", "filter.germ.map\:2082_coe" -> "order", "filter.basis_sets" -> "order", "gcd_mul_lcm" -> "algebra", "finset.mem_disj_union" -> "data", "category_theory.abelian.full_image_factorisation" -> "category_theory", "Mon_.assoc_flip" -> "category_theory", "nat.not_prime_mul" -> "data", "bit0_gsmul" -> "algebra", "list.modify_nth_tail_id" -> "data", "unique_factorization_domain.integer_of_integral" -> "algebra", "category_theory.limits.span_map_snd" -> "category_theory", "nat.decreasing_induction_succ_left" -> "data", "finsupp.single_multiset_sum" -> "data", "measure_theory.simple_func.integral_smul" -> "analysis", "pequiv.trans_symm_eq_iff_forall_is_some" -> "data", "measure_theory.l1.simple_func.uniform_continuous" -> "analysis", "and_iff_not_or_not" -> "logic", "multiset.mem_sections" -> "data", "finset.Ico.filter_lt_of_ge" -> "data", "inv_of_eq_right_inv" -> "algebra", "list.cons_eq_append_iff" -> "data", "measure_theory.simple_func.integral_add" -> "analysis", "add_submonoid.prod_bot_sup_bot_prod" -> "algebra", "ideal.jacobson_eq_self_of_is_maximal" -> "algebra", "free_group.to_group.of" -> "algebra", "finset.prod_apply" -> "algebra", "nnreal.div_lt_iff" -> "data", "has_fderiv_within_at.snd" -> "analysis", "subalgebra.fg_bot" -> "algebra", "set.piecewise_same" -> "data", "group.closure_eq_mclosure" -> "algebra", "one_sub_gold_conj" -> "data", "add_con.ker_lift_mk" -> "algebra", "continuous_linear_map.uncurry_left_apply" -> "analysis", "concave_on_const" -> "analysis", "real.deriv_sinh" -> "analysis", "ideal.zero_mem" -> "algebra", "ring_hom.eq_rat_cast" -> "data", "uniform_space.core_eq" -> "topology", "norm_image_sub_le_of_norm_deriv_le_segment_01'" -> "analysis", "set.dual_Icc" -> "data", "multiset.card_erase_of_mem" -> "data", "cardinal.zero_lt_one" -> "set_theory", "unique_diff_on_Iic" -> "analysis", "has_sum_geometric_two'" -> "analysis", "qpf.Wequiv.symm" -> "data", "local_equiv.coe_trans" -> "data", "Liminf_eq_of_le_nhds" -> "topology", "with_one.lift_one" -> "algebra", "finmap.insert_insert_of_ne" -> "data", "measure_theory.integral_eq" -> "analysis", "le_of_forall_le'" -> "algebra", "initial_seg.coe_coe_fn" -> "set_theory", "multiset.subset_ndunion_left" -> "data", "pnat.xgcd_type.flip_b" -> "data", "is_local_max_on.comp_mono" -> "topology", "inner_product_geometry.norm_add_square_eq_norm_square_add_norm_square'" -> "geometry", "local_homeomorph.continuous_on_symm" -> "topology", "subring.mem_prod" -> "algebra", "finset.prod_Ico_eq_mul_inv" -> "algebra", "subring.sum_mem" -> "algebra", "matrix.diagonal_mul_diagonal'" -> "data", "is_measurable_eball" -> "analysis", "prod.snd_swap" -> "data", "ring.fractional_ideal.coe_ideal_span_singleton" -> "algebra", "list.filter_map_filter" -> "data", "lebesgue_number_lemma" -> "topology", "concave_on_id" -> "analysis", "gsmul_eq_smul" -> "algebra", "submonoid.coe_supr_of_directed" -> "algebra", "finset.infi_insert" -> "data", "bool.tt_eq_to_bool_iff" -> "data", "rat.uniform_continuous_abs" -> "topology", "filter.seq_eq_filter_seq" -> "order", "emetric.inf_edist_zero_of_mem" -> "topology", "with_zero.cases_on" -> "algebra", "ring.fractional_ideal.coe_zero" -> "algebra", "pnat.coprime.mul_right" -> "data", "gpow_sub" -> "algebra", "map_ext_congr" -> "init", "derivation.ext" -> "algebra", "complex.conj_bit1" -> "data", "unique_diff_within_at.prod" -> "analysis", "cardinal.lift_mk_fin" -> "set_theory", "zmod.exists_pow_two_eq_prime_iff_of_mod_four_eq_three" -> "number_theory", "primrec.of_equiv_symm_iff" -> "computability", "submodule.mul_comm" -> "algebra", "mul_lt_of_lt_of_le_one'" -> "algebra", "onote.repr_mul" -> "set_theory", "mul_sub_right_distrib" -> "algebra", "filter.comap_ne_bot" -> "order", "measure_theory.measure.le_restrict_apply" -> "analysis", "composition_as_set.boundaries_nonempty" -> "combinatorics", "differentiable_within_at.const_add" -> "analysis", "measure_theory.sum_measure_preimage_singleton" -> "analysis", "complex.sin_int_mul_pi" -> "analysis", "finsupp.sum_comap_domain" -> "data", "homeomorph.to_local_homeomorph_source" -> "topology", "continuous_linear_map.op_norm_le_bound" -> "analysis", "ennreal.top_ne_nat" -> "data", "pi.multiset_prod_apply" -> "algebra", "measure_theory.simple_func.restrict_apply" -> "analysis", "ring_hom.apply_apply" -> "algebra", "is_bounded_linear_map.fderiv_within" -> "analysis", "multiset.singleton_add" -> "data", "continuous_linear_equiv.is_O_sub" -> "analysis", "relation.refl_gen.to_refl_trans_gen" -> "logic", "polynomial.leading_coeff_monomial" -> "data", "measure_theory.l1.integral_eq" -> "analysis", "local_equiv.image_inter_source_eq'" -> "data", "subsemiring.one_mem" -> "algebra", "polynomial.monic_mul_leading_coeff_inv" -> "data", "is_cau_of_decreasing_bounded" -> "data", "int.mod_lt_of_pos" -> "data", "cauchy_seq_of_edist_le_of_summable" -> "topology", "ordinal.le_nfp_self" -> "set_theory", "measure_theory.ae_eq_fun.to_germ_injective" -> "analysis", "list.any_of_mem" -> "data", "iff_def" -> "logic", "measure_theory.simple_func.fin_meas_supp_iff_support" -> "analysis", "minimal_polynomial.irreducible" -> "algebra", "list.enum_from_nth" -> "data", "int.modeq.modeq_of_modeq_mul_right" -> "data", "equiv.perm.inv_eq_iff_eq" -> "algebra", "matrix.mul_apply" -> "data", "nat.totient_le" -> "data", "nat.psub_add" -> "data", "add_magma.free_add_semigroup.lift_unique" -> "algebra", "nat.lxor_eq_zero" -> "data", "bilin_form.lin_mul_lin_comp_left" -> "algebra", "localization_map.is_integer_add" -> "algebra", "pos_num.cast_one'" -> "data", "le_inv_mul_iff_mul_le" -> "algebra", "nat.one_le_pow'" -> "data", "category_theory.limits.braid_natural_assoc" -> "category_theory", "complex.log_neg_one" -> "analysis", "field.direct_limit.inv_mul_cancel" -> "algebra", "set.smul_set_empty" -> "algebra", "polynomial.mod_def" -> "data", "add_submonoid.localization_map.mk'_add_cancel_right" -> "algebra", "semiconj_by.cast_nat_mul_left" -> "algebra", "complex.of_real_mul" -> "data", "fin.succ_lt_succ_iff" -> "data", "ring_hom.coe_prod_map" -> "algebra", "multiset.coe_prod" -> "data", "is_unit_iff_of_associated" -> "algebra", "differentiable.sum" -> "analysis", "cardinal.mul_eq_self" -> "set_theory", "functor.comp.run_map" -> "control", "pfun.dom_of_mem_fix" -> "data", "lipschitz_with.sub" -> "analysis", "polynomial.smul_eval" -> "algebra", "polynomial.nat_degree_remove_factor'" -> "algebra", "local_equiv.eq_on_source.source_eq" -> "data", "matrix.det_adjugate_eq_one" -> "algebra", "lipschitz_with.neg" -> "analysis", "add_neg_cancel_left" -> "algebra", "written_in_ext_chart_comp" -> "geometry", "local_homeomorph.symm_symm" -> "topology", "computation.results_think_iff" -> "data", "turing.partrec_to_TM2.move\:2082_ok" -> "computability", "mvfunctor.liftr_last_rel_iff" -> "control", "complex.cos_two_mul'" -> "data", "fderiv_within_fst" -> "analysis", "complex.exp_add_mul_I" -> "data", "filter.realizer.top_\[Sigma]" -> "data", "set.powerset_empty" -> "data", "associates.irreducible_iff_prime_iff" -> "algebra", "add_le_add_iff_right" -> "algebra", "continuous_sup_dom" -> "topology", "submodule.of_le_apply" -> "algebra", "dfinsupp.map_range_single" -> "data", "list.erase_dup_idempotent" -> "data", "pequiv.symm_trans_rev" -> "data", "midpoint_comm" -> "algebra", "encodable.encode_tt" -> "data", "submonoid.localization_map.mk'_spec" -> "algebra", "finsupp.mem_antidiagonal_support" -> "data", "alist.keys_nodup" -> "data", "mul_lt_mul_iff_left" -> "algebra", "num.cast_to_znum_neg" -> "data", "rat.one_mul" -> "data", "computable.nat_cases" -> "computability", "strict_antimono_of_deriv_neg" -> "analysis", "emetric.inf_edist_le_inf_edist_add_Hausdorff_edist" -> "topology", "generalized_continued_fraction.int_fract_pair.nth_stream_fr_nonneg" -> "algebra", "div_lt_div'" -> "algebra", "norm_sub_norm_le" -> "analysis", "emetric.is_closed_subsets_of_is_closed" -> "topology", "pnat.xgcd_type.finish_is_special" -> "data", "multiplicity.finite_mul_aux" -> "algebra", "add_subgroup.range_gmultiples_hom" -> "algebra", "mem_maximal_atlas_iff" -> "geometry", "local_equiv.trans_refl_restr" -> "data", "function.support_inf" -> "data", "semiconj_by.inv_inv_symm" -> "algebra", "local_homeomorph.continuous_within_at_iff_continuous_within_at_comp_left" -> "topology", "left_ord_continuous.map_Sup" -> "order", "measure_theory.outer_measure.coe_add" -> "analysis", "category_theory.monoidal_category.tensor_left_tensor_inv_app" -> "category_theory", "equiv.coe_trans" -> "data", "eq_bot_of_singletons_open" -> "topology", "ennreal.Inf_add" -> "data", "bitvec.of_fin_to_fin" -> "data", "finsupp.single_eq_single_iff" -> "data", "category_theory.functor.map_cone_X" -> "category_theory", "homological_complex.image_map_\[Iota]" -> "algebra", "cau_seq.lim_add" -> "data", "uniform_space.completion.is_add_group_hom_map" -> "topology", "associates.le_mul_right" -> "algebra", "power_series.inv_eq_zero" -> "algebra", "category_theory.functor.unop_map" -> "category_theory", "semiquot.exists_mem" -> "data", "to_bilin_form_to_matrix" -> "algebra", "composition.size_up_to_succ'" -> "combinatorics", "fin.mem_find_of_unique" -> "data", "real.tan_surjective" -> "analysis", "monoid_hom.prod_unique" -> "algebra", "set.maps_to_range" -> "data", "nat.prime_three" -> "data", "nat.zero_max" -> "data", "dvd.elim_left" -> "algebra", "left_dvd_or_dvd_right_of_dvd_prime_mul" -> "algebra", "nat.lt_of_le_of_lt" -> "init", "nat.sub_le_iff" -> "data", "metric.nonempty_compacts.dist_eq" -> "topology", "local_homeomorph.mdifferentiable.mdifferentiable_at" -> "geometry", "inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two" -> "analysis", "localization.monoid_of_eq_of" -> "algebra", "prime_spectrum.punit" -> "algebraic_geometry", "linear_order.convex_on_of_lt" -> "analysis", "measure_theory.measure.add_le_add_left" -> "analysis", "bool_eq_false" -> "init", "uniform_space.completion.dense" -> "topology", "generalized_continued_fraction.convergents'_stable_of_terminated" -> "algebra", "hyperreal.infinite_neg_iff_infinite_and_neg" -> "data", "ring.fractional_ideal.span_singleton_one" -> "algebra", "ring_char.spec" -> "algebra", "rat_add_continuous_lemma" -> "data", "CommRing.colimits.cocone_naturality" -> "algebra", "induced_generate_from_eq" -> "topology", "nat.dist.def" -> "data", "pfun.as_subtype_eq_of_mem" -> "data", "finset.eq_univ_iff_forall" -> "data", "complex.cos_add_two_pi" -> "analysis", "list.map_eq_nil" -> "data", "array.read_eq_read'" -> "init", "add_subgroup.mem_supr_of_mem" -> "algebra", "tactic.ring_exp.atom_to_sum_pf" -> "tactic", "category_theory.curry.map_app_app" -> "category_theory", "int.sub_one_le_of_lt" -> "init", "multiset.add_cons" -> "data", "list.sublists_len_aux_append" -> "data", "le_antisymm_iff" -> "init", "tendsto_uniformly_on.tendsto_locally_uniformly_on" -> "topology", "smul_eq_mul" -> "algebra", "set.image2_union_left" -> "data", "list.perm.length_eq" -> "data", "list.maximum_singleton" -> "data", "subring.coe_bot" -> "algebra", "category_theory.limits.image.fac_lift" -> "category_theory", "is_R_or_C.re_le_abs" -> "data", "add_submonoid.localization_map.mk'_add" -> "algebra", "complex.log_exp" -> "analysis", "cardinal.mk_preimage_of_injective_of_subset_range" -> "set_theory", "mv_polynomial.pderivative_monomial" -> "data", "subtype.map_injective" -> "data", "int.add_mod_self_left" -> "data", "category_theory.adjunction.core_hom_equiv.hom_equiv_naturality_left" -> "category_theory", "measure_theory.l1.continuous_pos_part" -> "analysis", "open_add_subgroup.ext_iff" -> "topology", "add_con.Inf_to_setoid" -> "algebra", "num.mod_to_nat" -> "data", "emetric.tendsto_locally_uniformly_on_iff" -> "topology", "list.filter_eq_self" -> "data", "mul_action.mem_orbit_smul" -> "algebra", "interior_closed_ball" -> "analysis", "is_clopen_compl_iff" -> "topology", "num_dvd_of_is_root" -> "algebra", "coinduced_sup" -> "topology", "category_theory.iso.to_equiv_id" -> "category_theory", "stream.mem_of_nth_eq" -> "data", "real.rpow_pos_of_pos" -> "analysis", "category_theory.limits.pullback.lift_fst_assoc" -> "category_theory", "mv_polynomial.total_degree_sub" -> "data", "turing.list_blank.cons_head_tail" -> "computability", "tactic.group.gpow_trick_one" -> "tactic", "polynomial.degree_div_le" -> "data", "ennreal.div_pos_iff" -> "data", "continuous_linear_map.ratio_le_op_norm" -> "analysis", "alg_equiv.to_Algebra_iso_inv" -> "algebra", "con.lift_on_beta" -> "algebra", "pnat.gcd_rel_left'" -> "data", "measure_theory.integrable.norm" -> "analysis", "list.mem_keys_of_mem" -> "data", "nat.two_step_induction" -> "init", "nat.mod_mul_right_div_self" -> "data", "complex.cpow_add" -> "analysis", "composition.blocks_pos'" -> "combinatorics", "set.Ioc_self" -> "data", "nnreal.rpow_le_one" -> "analysis", "finset.mul_card_le" -> "algebra", "polynomial.factor_dvd_of_not_is_unit" -> "algebra", "equiv_of_dim_eq_lift_dim" -> "algebra", "subsemiring.closure_Union" -> "algebra", "subring.zero_mem" -> "algebra", "fraction_map.to_map_ne_zero_of_mem_non_zero_divisors" -> "algebra", "complex.norm_sq_of_real" -> "data", "nat.coprime_of_dvd" -> "data", "dense_of_subset_dense" -> "topology", "perfect_closure.int_cast" -> "algebra", "emetric.diam_union'" -> "topology", "computation.lift_rel.trans" -> "data", "tsum_Union_decode2" -> "topology", "algebraic_geometry.PresheafedSpace.id_c" -> "algebraic_geometry", "hyperreal.epsilon_lt_pos" -> "data", "bool.bor_inr" -> "data", "primrec.nat_elim'" -> "computability", "topological_space.opens.map_id_obj'" -> "topology", "formal_multilinear_series.comp_id" -> "analysis", "differentiable_on.rpow_of_one_le" -> "analysis", "set.eq_on.eventually_eq_nhds_within" -> "topology", "pSet.equiv.refl" -> "set_theory", "set.singleton_mul" -> "algebra", "initial_seg.antisymm_symm" -> "set_theory", "list.subset_def" -> "data", "int.even_mul" -> "data", "list.forall\:2082_eq_eq_eq" -> "data", "irrational.mul_rat" -> "data", "add_submonoid.map_supr" -> "algebra", "free_comm_ring.induction_on" -> "algebra", "archimedean_iff_nat_lt" -> "algebra", "lebesgue_number_lemma_seq" -> "topology", "one_le_inv_of_le_one" -> "algebra", "rel_iso.coe_mul" -> "order", "uniform_space.to_core_to_topological_space" -> "topology", "polynomial.pow_comp" -> "data", "filter.infi_eq_generate" -> "order", "category_theory.eq_to_hom_trans_assoc" -> "category_theory", "nat.div2_succ" -> "init", "vector_space.erange_coe" -> "algebra", "onote.repr_sub" -> "set_theory", "finset.coe_univ" -> "data", "submodule.le_comap_map" -> "algebra", "equiv.perm.is_swap_of_subtype" -> "algebra", "category_theory.prod.swap_map" -> "category_theory", "typevec.drop_append1'" -> "data", "category_theory.limits.limit.pre_post" -> "category_theory", "Top.stalk_to_fiber_injective" -> "topology", "is_bounded_linear_map.zero" -> "analysis", "traversable.foldl_map" -> "control", "bex_of_exists" -> "logic", "category_theory.limits.diagram_of_cones.mk_of_has_limits_map_hom" -> "category_theory", "polynomial.is_unit_of_self_mul_dvd_separable" -> "algebra", "homological_complex.homology_map_2" -> "algebra", "tangent_cone_inter_nhds" -> "analysis", "free_comm_ring.is_supported_sub" -> "algebra", "cau_seq.mul_not_equiv_zero" -> "data", "tsum_eq_tsum_of_has_sum_iff_has_sum" -> "topology", "continuous_quot_lift" -> "topology", "free_abelian_group.hom_equiv_apply" -> "algebra", "filter.tendsto.uniformity_symm" -> "topology", "trunc.out_eq" -> "data", "equiv.perm.gpow_apply_eq_of_apply_apply_eq_self" -> "algebra", "category_theory.limits.bicone.to_binary_bicone_inr" -> "category_theory", "linear_equiv.injective" -> "algebra", "continuous_linear_equiv.of_bijective_symm_apply_apply" -> "analysis", "set.eq_on_of_left_inv_on_of_right_inv_on" -> "data", "int.lcm_self" -> "algebra", "uniform_space.completion.nonempty_completion_iff" -> "topology", "CommRing.colimits.quot_one" -> "algebra", "category_theory.limits.cofork.left_app_one" -> "category_theory", "dfinsupp.subtype_domain_zero" -> "data", "category_theory.equivalence.inv_fun_id_assoc_hom_app" -> "category_theory", "list.func.add_nil" -> "data", "seq.mem_append_left" -> "data", "pSet.equiv.symm" -> "set_theory", "finset.prod_dite_eq'" -> "algebra", "set.preimage_empty" -> "data", "ordinal.log_not_one_lt" -> "set_theory", "category_theory.limits.pullback.condition_assoc" -> "category_theory", "lt_neg_add_iff_add_lt" -> "algebra", "mem_of_is_lub_of_is_closed" -> "topology", "abs_two" -> "algebra", "neg_div_neg_eq" -> "algebra", "trunc.ind" -> "data", "multiset.revzip_powerset_aux_perm_aux'" -> "data", "add_aut.mul_apply" -> "data", "simple_graph.adj_matrix_vec_mul_apply" -> "combinatorics", "function.bijective_id" -> "init", "le_nhds_iff" -> "topology", "uniform_continuous_comap" -> "topology", "category_theory.limits.is_colimit.hom_ext" -> "category_theory", "int.of_nat_add_neg_succ_of_nat" -> "init", "set.surj_on_empty" -> "data", "exists_has_deriv_at_eq_zero'" -> "analysis", "nat.partrec.code.comp_prim" -> "computability", "times_cont_mdiff_within_at_inter'" -> "geometry", "free_semigroup.pure_seq" -> "algebra", "finset.weighted_vsub_of_point_insert" -> "algebra", "nhds_within_Ico_eq_nhds_within_Iio" -> "topology", "real.tendsto_inv" -> "topology", "category_theory.limits.is_image.fac_lift" -> "category_theory", "filter.germ.const_bot" -> "order", "zero_lie" -> "algebra", "prime.ne_one" -> "algebra", "open_embedding.target" -> "topology", "set.Iic_disjoint_Ioc" -> "data", "measure_theory.outer_measure.map_id" -> "analysis", "nat.coprime_one_left" -> "data", "sub_one_lt" -> "algebra", "finset.has_sum_compl_iff" -> "topology", "left_ord_continuous.map_sup" -> "order", "game.le_refl" -> "set_theory", "ring_equiv.to_ring_hom_apply_symm_to_ring_hom_apply" -> "data", "with_top.sum_lt_top" -> "algebra", "measure_theory.simple_func.is_measurable_preimage" -> "analysis", "finset.sum_eq_sum_Ico_succ_bot" -> "algebra", "num.test_bit_to_nat" -> "data", "hyperreal.not_infinite_neg" -> "data", "mv_power_series.inv_mul" -> "algebra", "finset.prod_range_div" -> "algebra", "set.preimage_sub_const_Ici" -> "data", "polynomial.nat_degree_mul_le" -> "data", "zmod.val_one" -> "data", "localization_map.mk'_self'" -> "algebra", "int.mul_neg_of_pos_of_neg" -> "init", "infi_singleton" -> "order", "complex.log_of_real_re" -> "analysis", "category_theory.pi.eval_map" -> "category_theory", "matrix.is_adjoint_pair_equiv" -> "algebra", "commute.zero_left" -> "algebra", "list.forall\:2082_take" -> "data", "Module.coe_comp" -> "algebra", "equiv.naturality" -> "control", "ring.fractional_ideal.mem_one_iff" -> "algebra", "mul_le_mul'" -> "algebra", "nat.cast_le" -> "data", "submodule.annihilator_supr" -> "algebra", "ideal.span_singleton_le_span_singleton" -> "algebra", "ordinal.lift_lift" -> "set_theory", "turing.TM2to1.tr_respects_aux" -> "computability", "eq_of_one_div_eq_one_div" -> "algebra", "has_deriv_within_at_id" -> "analysis", "nat.primrec.prec1" -> "computability", "mem_pregroupoid_of_eq_on_source" -> "geometry", "equiv.mul_equiv_symm_apply" -> "data", "list.nth_le_map_rev" -> "data", "summable.neg" -> "topology", "continuous_on_if'" -> "topology", "group.subset_closure" -> "algebra", "composition_as_set.blocks_partial_sum" -> "combinatorics", "generalized_continued_fraction.int_fract_pair.succ_nth_stream_eq_some_iff" -> "algebra", "int.add_sub_cancel" -> "init", "finset.mem_def" -> "data", "units.coe_lift_right" -> "algebra", "real.cos_lt_cos_of_nonneg_of_le_pi" -> "analysis", "asymptotics.is_o.triangle" -> "analysis", "one_one_reducible.trans" -> "computability", "finset.mono_of_fin_unique'" -> "data", "and.assoc" -> "init", "power_series.coeff_of_lt_order" -> "algebra", "is_ring_hom.map_neg" -> "algebra", "multiset.erase_dup_ext" -> "data", "add_con.ker_apply_eq_preimage" -> "algebra", "not_irreducible_zero" -> "algebra", "galois_connection.dual" -> "order", "real.le_mk_of_forall_le" -> "data", "algebra.tensor_product.mul_assoc" -> "algebra", "category_theory.over.over_right" -> "category_theory", "pgame.neg_def" -> "set_theory", "submonoid.localization_map.map_spec" -> "algebra", "fraction_map.is_unit_denom_of_num_eq_zero" -> "algebra", "encodable.decode_nat" -> "data", "add_aut.apply_inv_self" -> "data", "monoid_hom.coe_mk" -> "algebra", "set.image_smul_prod" -> "algebra", "string.le_iff_to_list_le" -> "data", "mem_nonunits_iff" -> "algebra", "local_homeomorph.trans_target" -> "topology", "nat.div_eq_of_eq_mul_left" -> "init", "has_fderiv_at.mul_const" -> "analysis", "continuous_linear_map.ker_cod_restrict" -> "topology", "pi.smul_apply" -> "algebra", "finset.image_val" -> "data", "power_series.coeff_X" -> "algebra", "d_array.of_beq_eq_ff" -> "init", "nhds_within_Ioo_eq_nhds_within_Iio" -> "topology", "is_open_map.is_open_range" -> "topology", "nat.div_lt_of_lt_mul" -> "data", "ideal.comap_injective_of_surjective" -> "algebra", "lower_bounds_Icc" -> "order", "pos_num.cast_lt" -> "data", "cardinal.mul_lt_of_lt" -> "set_theory", "summable.summable_compl_iff" -> "topology", "ordinal.omega_ne_zero" -> "set_theory", "convex.neg_preimage" -> "analysis", "int.ne_neg_of_pos" -> "init", "one_div_lt_one_div" -> "algebra", "continuous_linear_equiv.homothety_inverse" -> "analysis", "filter.eventually_eq.is_local_min_iff" -> "topology", "set.preimage_mul_right_one" -> "algebra", "int.modeq.modeq_add_cancel_left" -> "data", "filter.tendsto_at_top_at_top_iff_of_monotone" -> "order", "ideal.mem_leading_coeff_nth" -> "algebra", "add_submonoid.mem_prod" -> "algebra", "measure_theory.simple_func.mul_eq_map\:2082" -> "analysis", "int.mod_abs" -> "data", "or.elim" -> "init", "metric.nhds_basis_ball" -> "topology", "list.mem_union_left" -> "data", "ordinal.zero_mod" -> "set_theory", "filter.one_mul" -> "order", "list.insert_neg" -> "data", "measure_theory.ae_eq_fun.coe_fn_mk" -> "analysis", "nnreal.coe_rpow" -> "analysis", "pequiv.mem_single_iff" -> "data", "mv_polynomial.coe_zero" -> "algebra", "set.nonempty_Ioo" -> "data", "int.cast_lt_zero" -> "data", "metric.ball_subset" -> "topology", "turing.TM1to1.tr_tape'_move_right" -> "computability", "affine_subspace.mem_direction_iff_eq_vsub_right" -> "algebra", "list.eq_of_sorted_of_perm" -> "data", "set.image_bInter_subset" -> "data", "category_theory.monoidal.left_unitor_hom_app" -> "category_theory", "category_theory.comma.map_right_obj_left" -> "category_theory", "nat.mul_comm" -> "init", "dfinsupp.prod_sum_index" -> "data", "exists_subset_affine_independent_affine_span_eq_top" -> "algebra", "finset.prod_Ico_add" -> "algebra", "measure_theory.ae_eq_bot" -> "analysis", "deriv_forall_lt_or_forall_gt_of_forall_ne" -> "analysis", "metric.uniformity_basis_dist" -> "topology", "set.Iio_subset_Iic_union_Ioo" -> "data", "rel_embedding.collapse_apply" -> "set_theory", "pell.xz_sub" -> "number_theory", "set.nonempty_Iic" -> "data", "cancel_factors.div_subst" -> "tactic", "polynomial.X_pow_mul_assoc" -> "data", "list.nat.length_antidiagonal" -> "data", "subalgebra.ext" -> "algebra", "multiset.nodup_singleton" -> "data", "finset.subtype_map" -> "data", "local_equiv.coe_symm_mk" -> "data", "multiset.repeat_zero" -> "data", "zmodeq_of_digits_digits" -> "data", "hyperreal.coe_max" -> "data", "padic_norm_z.add_eq_max_of_ne" -> "data", "mv_polynomial.eval_eq" -> "data", "nat.lt_of_test_bit" -> "data", "submonoid.map_sup_comap_of_surjective" -> "algebra", "submodule.fg_sup" -> "algebra", "iterated_fderiv_within_univ" -> "analysis", "matrix.from_blocks_apply\:2082\:2081" -> "data", "plift.down_up" -> "init", "real.sin_zero" -> "data", "units.mul_right_inj" -> "algebra", "finset.sum_pow_mul_eq_add_pow" -> "algebra", "ideal.span_mul_span" -> "algebra", "mul_nonneg" -> "algebra", "is_closed_map.of_inverse" -> "topology", "exists_floor" -> "algebra", "commute.cast_int_mul_right" -> "algebra", "ennreal.mul_eq_mul_right" -> "data", "guard_false" -> "control", "nat.sub_add_eq_max" -> "data", "pell.dz_val" -> "number_theory", "category_theory.over.mk_left" -> "category_theory", "is_open_Inter_prop" -> "topology", "deriv_within_mul_const" -> "analysis", "norm_num.int_cast_zero" -> "tactic", "times_cont_mdiff_within_at_snd" -> "geometry", "category_theory.monoidal_category.pentagon_inv" -> "category_theory", "cardinal.sup_le_sup" -> "set_theory", "list.mem_zip" -> "data", "category_theory.quotient.induction" -> "category_theory", "inner_product_geometry.angle_zero_left" -> "geometry", "with_top.top_ne_nat" -> "data", "category_theory.limits.span_right" -> "category_theory", "int.gcd_pos_of_non_zero_right" -> "algebra", "finsupp.lsubtype_domain_apply" -> "algebra", "erased.bind_eq_out" -> "data", "mul_mul_div" -> "algebra", "mdifferentiable_within_at.mono" -> "geometry", "mul_le_one" -> "algebra", "closure_lt_subset_le" -> "topology", "convex.antimono_of_deriv_nonpos" -> "analysis", "matrix.zero_apply" -> "data", "add_commute.units_neg_right_iff" -> "algebra", "measure_theory.ae_mono" -> "analysis", "list.nth_le_join" -> "data", "int.neg_mul_neg" -> "init", "set.ord_connected_singleton" -> "data", "trunc.exists_rep" -> "data", "measurable_equiv.measurable_coe_iff" -> "analysis", "affine_subspace.direction_sup" -> "algebra", "category_theory.limits.is_limit.of_nat_iso.cone_fac" -> "category_theory", "function.surjective.exists\:2083" -> "logic", "nhds_add" -> "topology", "list.nodup_sublists_len" -> "data", "padic_int.ker_to_zmod_pow" -> "data", "isometric.to_real_linear_equiv_apply" -> "analysis", "holor.cprank_max_1" -> "data", "set.abs_sub_right_of_mem_interval" -> "data", "padic_norm_z.padic_val_of_cong_pow_p" -> "data", "monoid_algebra.mul_single_one_apply" -> "data", "measure_theory.measure.map_mul_left_eq_self" -> "analysis", "is_measurable.is_null_measurable" -> "analysis", "pow_succ" -> "algebra", "finset.sum_involution" -> "algebra", "real.cos_square" -> "data", "add_submonoid.mem_supr_of_mem" -> "algebra", "set.disjoint.preimage" -> "data", "psigma.ext_iff" -> "data", "smooth_fst" -> "geometry", "nat.two_not_dvd_two_mul_sub_one" -> "data", "continuous_multilinear_map.has_sum_eval" -> "analysis", "d_array.read_write_of_ne" -> "init", "tendsto_multiset_prod" -> "topology", "list.tail_cons" -> "data", "abs_abs_sub_abs_le_abs_sub" -> "algebra", "function.bij_on_fixed_pts_comp" -> "dynamics", "cardinal.lift_zero" -> "set_theory", "is_R_or_C.of_real_add" -> "data", "measurable_neg" -> "analysis", "partrec\:2082.unpaired" -> "computability", "metric.Hausdorff_dist_zero_iff_closure_eq_closure" -> "topology", "convex_on.subset" -> "analysis", "real.continuous_rpow_of_pos" -> "analysis", "set.Union_diff" -> "data", "normed_ring.summable_geometric_of_norm_lt_1" -> "analysis", "finsupp.sum_single_index" -> "data", "set.ord_connected_Ici" -> "data", "embedding.tendsto_nhds_iff" -> "topology", "linear_map.map_smul" -> "algebra", "mv_polynomial.iter_to_sum_X" -> "data", "asymptotics.is_o.prod_left_snd" -> "analysis", "polynomial.separable.map" -> "algebra", "finset.infi_union" -> "data", "is_measurable.compl" -> "analysis", "ff_band" -> "init", "lipschitz_with.dist" -> "topology", "category_theory.id_nonzero" -> "category_theory", "real.uniform_continuous_mul_const" -> "topology", "int.eq_one_of_mul_eq_one_left" -> "data", "continuous_linear_map.coe_subtype_val" -> "topology", "num.cast_zero'" -> "data", "ordinal.lt_omega" -> "set_theory", "int.add_lt_of_lt_sub_right" -> "init", "power_series.mul_inv" -> "algebra", "list.last_repeat_succ" -> "data", "category_theory.prod.sectl_obj" -> "category_theory", "subsemiring.prod_mono_right" -> "algebra", "list.nodup_inter_of_nodup" -> "data", "filter.realizer.map_\[Sigma]" -> "data", "continuous.lim_eq" -> "topology", "nat.bit_le" -> "data", "int.modeq.symm" -> "data", "has_mfderiv_within_at_inter'" -> "geometry", "finset.max_insert" -> "data", "has_ftaylor_series_up_to_on_succ_iff_right" -> "analysis", "is_preconnected_interval" -> "topology", "submodule.zero_eq_bot" -> "algebra", "filter.germ.mk'_eq_coe" -> "order", "is_extr_on.comp_antimono" -> "order", "ideal.radical_le_jacobson" -> "algebra", "tendsto_coe_int_real_at_top_iff" -> "topology", "set.disjoint_iff_inter_eq_empty" -> "data", "add_left_comm" -> "algebra", "inner_product_geometry.angle_eq_pi_iff" -> "geometry", "subsemiring.mem_closure_iff_exists_list" -> "algebra", "metric.tendsto_nhds_nhds" -> "topology", "adjoin_root.mk_C" -> "algebra", "filter.comap_top" -> "order", "not_nonempty_pempty" -> "logic", "turing.blank_extends.below_of_le" -> "computability", "fderiv.snd" -> "analysis", "add_con.mk'_surjective" -> "algebra", "omega.update_eq" -> "tactic", "filter.seq_pure" -> "order", "rat.commute_cast" -> "data", "set.preimage_diff" -> "data", "pos_tangent_cone_at_univ" -> "analysis", "finmap.mem_iff" -> "data", "dist_le_of_le_geometric_of_tendsto\:2080" -> "analysis", "ordinal.log_zero" -> "set_theory", "rat.zero_mk_nat" -> "data", "uniform_space_eq" -> "topology", "ideal.comap_lt_comap_of_integral_mem_sdiff" -> "algebra", "bounded_continuous_function.dist_coe_le_dist" -> "topology", "generalized_continued_fraction.convergent_eq_num_div_denom" -> "algebra", "continuous_on_if" -> "topology", "ordinal.power_lt_power_iff_right" -> "set_theory", "has_deriv_at.rpow" -> "analysis", "times_cont_diff_at.sum" -> "analysis", "pgame.subsequent.left_move" -> "set_theory", "continuous_multilinear_curry_fin1_symm_apply" -> "analysis", "measure_theory.measure.haar.index_empty" -> "analysis", "nnreal.coe_bit0" -> "data", "fintype.eq_of_subsingleton_of_sum_eq" -> "data", "matrix.bit0_apply" -> "data", "pgame.move_left_mk" -> "set_theory", "real.le_sqrt" -> "data", "scale_roots_eval\:2082_eq_zero_of_eval\:2082_div_eq_zero" -> "algebra", "ordinal.is_limit.pos" -> "set_theory", "affine_span_eq_top_of_affine_independent_of_card_eq_findim_add_one" -> "algebra", "exists_eq'" -> "logic", "associates.factors_mul" -> "algebra", "is_min_filter.add" -> "order", "complex.conj_involutive" -> "data", "hyperreal.coe_eq_coe" -> "data", "filter.prod_map_at_bot_eq" -> "order", "ordinal.cof_sup_le_lift" -> "set_theory", "nnreal.one_le_rpow_of_pos_of_le_one_of_nonpos" -> "analysis", "restrict_scalars_ker" -> "algebra", "list.argmax_mem" -> "data", "set.univ_eq_true_false" -> "data", "ennreal.half_pos" -> "data", "padic_int.pow_p_dvd_int_iff" -> "data", "dioph.pell_dioph" -> "number_theory", "two_smul" -> "algebra", "finset.mem_cons" -> "data", "pos_num.bit1_of_bit1" -> "data", "add_magma.free_add_semigroup.of_add" -> "algebra", "is_R_or_C.mul_self_abs" -> "data", "computation.orelse_ret" -> "data", "emetric.Hausdorff_edist_def" -> "topology", "bool.bor_comm" -> "data", "hyperreal.coe_min" -> "data", "finset.prod_filter_ne_one" -> "algebra", "algebra.tensor_product.one_def" -> "algebra", "list.sizeof_lt_sizeof_of_mem" -> "data", "ennreal.to_real_of_real_mul" -> "data", "pell.yn_modeq_a_sub_one" -> "number_theory", "has_fderiv_at_filter.is_O_sub" -> "analysis", "cardinal.nat_eq_lift_eq_iff" -> "set_theory", "algebraic_closure.of_step_succ" -> "algebra", "filter.eventually_le.congr" -> "order", "affine.simplex.monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub" -> "geometry", "category_theory.limits.diagram_of_cones.mk_of_has_limits_cone_points" -> "category_theory", "set.Icc_subset_Ioc_iff" -> "data", "measure_theory.simple_func.fin_meas_supp.mul" -> "analysis", "well_founded_submodule_gt" -> "algebra", "filter.tendsto_prod_self_iff" -> "order", "continuous_linear_map.has_sum" -> "analysis", "local_equiv.symm_image_inter_target_eq'" -> "data", "measure_theory.lebesgue_length_eq_infi_Ioo" -> "analysis", "dvd_of_dvd_neg" -> "algebra", "nat.modeq.modeq_iff_dvd'" -> "data", "alg_hom.id_comp" -> "algebra", "lt_mul_of_one_lt_of_le" -> "algebra", "stream.corec'_eq" -> "data", "div_neg_of_neg_of_pos" -> "algebra", "measure_theory.integrable_congr" -> "analysis", "zsqrtd.of_int_im" -> "data", "int.even_add" -> "data", "category_theory.prod.sectr_obj" -> "category_theory", "Limsup_nhds" -> "topology", "stream.map_append_stream" -> "data", "is_open_add_right" -> "topology", "equiv_iso_iso_inv" -> "category_theory", "int.add_neg_cancel_right" -> "init", "is_bounded_linear_map_continuous_multilinear_map_comp_linear" -> "analysis", "matrix.vec_mul_one" -> "data", "filter.mem_traverse_sets" -> "order", "add_commute.zero_left" -> "algebra", "matrix.adjugate_def" -> "algebra", "add_right_cancel_iff" -> "algebra", "category_theory.limits.has_colimit.iso_of_nat_iso_\[Iota]_hom" -> "category_theory", "with_top.none_eq_top" -> "order", "ideal.is_prime_radical" -> "algebra", "turing.list_blank.head_cons" -> "computability", "totally_bounded_empty" -> "topology", "irrational_sqrt_rat_iff" -> "data", "free_group.red.step.to_red" -> "algebra", "convex.norm_image_sub_le_of_norm_has_fderiv_within_le'" -> "analysis", "mul_inv_cancel_left'" -> "algebra", "list.sublists_eq_sublists'" -> "data", "is_basis.ext" -> "algebra", "is_G\[Delta]_sInter" -> "topology", "stream.inits_tail" -> "data", "is_open_supr_iff" -> "topology", "ideal.map_surjective_of_surjective" -> "algebra", "fin.coe_of_nat_eq_mod'" -> "data", "prod_X_sub_smul.monic" -> "algebra", "is_closed_empty" -> "topology", "euclidean_geometry.angle_nonneg" -> "geometry", "filter.countable_binfi_eq_infi_seq'" -> "order", "lists'.mem_equiv_left" -> "set_theory", "is_closed.closure_subset" -> "topology", "ordinal.lift_down" -> "set_theory", "map_supr_of_continuous_at_of_monotone" -> "topology", "trans_of" -> "init", "dist_self" -> "topology", "is_basis.mk_eq_dim'" -> "algebra", "ennreal.coe_lt_coe" -> "data", "filter.lift'_lift_assoc" -> "order", "order_top.ext" -> "order", "asymptotics.is_o.smul" -> "analysis", "refl_of" -> "init", "zero_pow'" -> "algebra", "metric.inf_dist_empty" -> "topology", "subsemiring.closure_univ" -> "algebra", "category_theory.limits.braid_natural" -> "category_theory", "ideal.exists_le_maximal" -> "algebra", "list.any_iff_exists" -> "data", "continuous_const" -> "topology", "complex.cos_int_mul_two_pi" -> "analysis", "category_theory.limits.cofork.condition" -> "category_theory", "ennreal.inv_eq_zero" -> "data", "local_equiv.eq_on_source.trans'" -> "data", "linear_map.coe_restrict_scalars_eq_coe" -> "algebra", "measure_theory.integral_eq_zero_of_ae" -> "analysis", "ring_equiv.coe_ring_hom" -> "data", "is_R_or_C.abs_ne_zero" -> "data", "nonempty_of_not_bdd_above" -> "order", "cau_seq.inv_aux" -> "data", "metric.mem_closure_iff" -> "topology", "measurable.sub" -> "analysis", "set.diff_union_self" -> "data", "continuous_linear_equiv.fst_equiv_of_right_inverse" -> "topology", "category_theory.limits.limit.post_\[Pi]" -> "category_theory", "smooth.comp_smooth_on" -> "geometry", "polynomial.irreducible_of_monic" -> "data", "stream.cycle_eq" -> "data", "is_algebraic_iff_is_integral" -> "algebra", "nonempty.forall" -> "logic", "add_comm_group.is_Z_bilin.zero_left" -> "topology", "finset.min_eq_inf_with_top" -> "data", "list.partition_eq_filter_filter" -> "init", "surj_on_Ioc_of_monotone_surjective" -> "data", "category_theory.comma.map_right_map_right" -> "category_theory", "add_group.subset_closure" -> "algebra", "metric.lipschitz_inf_dist" -> "topology", "submodule.mkq_map_self" -> "algebra", "circle_equiv_apply" -> "number_theory", "filter.eventually_comap" -> "order", "deriv_within_pow'" -> "analysis", "category_theory.is_iso.inv_comp" -> "category_theory", "submodule.ker_inl" -> "algebra", "setoid.refl" -> "init", "set.piecewise_eq_on_compl" -> "data", "differentiable_on_fpow" -> "analysis", "continuous_within_at.preimage_mem_nhds_within" -> "topology", "stream.nth_succ_iterate" -> "data", "nat.le_of_mul_le_mul_left" -> "init", "computation.has_bind_eq_bind" -> "data", "nat.size_bit1" -> "data", "convex_on_iff_convex_epigraph" -> "analysis", "relator.rel_eq" -> "logic", "finsupp.map_domain_support" -> "data", "is_totally_disconnected_singleton" -> "topology", "exists_nat_one_div_lt" -> "algebra", "set.surj_on.maps_to_inv_fun_on" -> "data", "set.Inter_eq_Inter_finset" -> "data", "padic_val_rat.padic_val_rat_le_padic_val_rat_iff" -> "data", "filter.eventually_inf_principal" -> "order", "fin.cast_succ_inj" -> "data", "list.map_length_split_wrt_composition" -> "combinatorics", "measure_theory.simple_func.smul_apply" -> "analysis", "omega.rhs_correct" -> "tactic", "list.tendsto_nhds" -> "topology", "add_units.add_right_symm" -> "data", "is_coprime.add_mul_right_left" -> "algebra", "category_theory.evaluation_obj_map" -> "category_theory", "pfun.preimage_eq" -> "data", "submodule.span_Union" -> "algebra", "list.sorted_of_sorted_cons" -> "data", "nat.div_one" -> "init", "polynomial.not_monic_zero" -> "data", "real.neg_one_le_cos" -> "data", "fintype.card_of_subsingleton" -> "data", "nat.pred_eq_of_eq_succ" -> "data", "mem_of_mem_nhds_within" -> "topology", "asymptotics.is_o.add_is_O" -> "analysis", "category_theory.monad.comparison_map_f" -> "category_theory", "galois_connection.l_Sup" -> "order", "bitraversable.tfst_eq_fst_id" -> "control", "neg_add_lt_right_of_lt_add" -> "algebra", "ennreal.tendsto_nat_nhds_top" -> "topology", "polynomial.prime_of_degree_eq_one" -> "data", "category_theory.comma.map_left_id_inv_app_right" -> "category_theory", "filter.has_basis.mem_lift_iff" -> "order", "add_submonoid.localization_map.add_mk'_eq_mk'_of_add" -> "algebra", "set.finite.bdd_above" -> "data", "le_infi_comp" -> "order", "padic_int.ker_to_zmod" -> "data", "computable.of_nat" -> "computability", "complex.of_real_neg" -> "data", "trans_trichotomous_right" -> "order", "submodule.lt_add_iff_not_mem" -> "algebra", "multiset.nodup_sigma" -> "data", "mv_polynomial.exists_coeff_ne_zero" -> "data", "differentiable_at.fderiv_prod" -> "analysis", "mul_le_mul" -> "algebra", "times_cont_mdiff_iff_times_cont_diff" -> "geometry", "set.preimage_range" -> "data", "ennreal.rpow_lt_rpow_of_exponent_gt" -> "analysis", "is_R_or_C.norm_sq_inv" -> "data", "nat.dvd_antisymm" -> "init", "filter.eventually_eq_of_mem" -> "order", "polynomial.degree_mod_by_monic_le" -> "data", "add_neg_eq_zero" -> "algebra", "list.cons_bind" -> "init", "set.bij_on.to_local_equiv_inv_fun" -> "data", "real.deriv_sin" -> "analysis", "normed_field.norm_div" -> "analysis", "perfect_closure.r.sound" -> "algebra", "multiset.countp_cons_of_pos" -> "data", "differentiable_on.sub_const" -> "analysis", "dvd_of_digits_sub_of_digits" -> "data", "submonoid.top_prod_top" -> "algebra", "real.sin_pi" -> "analysis", "finset.nonempty.ne_empty" -> "data", "list.nodup_range'" -> "data", "measure_theory.l1.simple_func.neg_to_simple_func" -> "analysis", "finset.prod_dite_eq" -> "algebra", "filter.eventually_eq.filter_mono" -> "order", "polynomial.separable_prod'" -> "algebra", "finset.filter_filter" -> "data", "padic_int.is_unit_denom" -> "data", "polynomial.comp_C" -> "data", "measure_theory.ae_eq_fun.lintegral_coe_fn" -> "analysis", "int.cast_neg_succ_of_nat" -> "data", "one_one_equiv.congr_right" -> "computability", "fraction_map.is_unit_map_of_injective" -> "algebra", "set.image_sub_const_Ici" -> "data", "set.nonempty.closure" -> "topology", "nhds_bot_order" -> "topology", "is_bounded_linear_map.id" -> "analysis", "is_bounded_linear_map.neg" -> "analysis", "Gromov_Hausdorff.GH_space.to_GH_space_rep" -> "topology", "matrix.diagonal_zero" -> "data", "cau_seq.completion.of_rat_inv" -> "data", "roption.some_inj" -> "data", "ctop.realizer.ext" -> "data", "pos_num.nat_size_pos" -> "data", "algebra.tensor_product.tmul_mul_tmul" -> "algebra", "matrix.col_apply" -> "data", "asymptotics.is_O_refl" -> "analysis", "filter.tendsto_at_bot_of_add_bdd_below_right" -> "order", "with_bot.le_coe_get_or_else" -> "order", "mem_span_points" -> "algebra", "set.subset_sInter" -> "data", "real.mk_le" -> "data", "set.finite_pure" -> "data", "submonoid.localization_map.mk'_eq_iff_eq" -> "algebra", "metric.totally_bounded_iff" -> "topology", "norm_num.lt_bit1_bit0" -> "tactic", "equiv.coe_prod_comm" -> "data", "dvd_neg_iff_dvd" -> "algebra", "seq.eq_of_bisim" -> "data", "submonoid.localization_map.eq_iff_exists" -> "algebra", "category_theory.limits.biprod.symmetry'_assoc" -> "category_theory", "category_theory.pi.eval_obj" -> "category_theory", "rel.comp_right_id" -> "data", "rat.cast_injective" -> "data", "mv_polynomial.eval_X" -> "data", "category_theory.limits.kernel_is_iso_comp_inv" -> "category_theory", "list.perm.product" -> "data", "add_submonoid.localization_map.add_equiv_of_add_equiv_eq" -> "algebra", "div_sq_cancel" -> "algebra", "subring.exists" -> "algebra", "equiv.to_local_equiv_coe" -> "data", "category_theory.over.forget_map" -> "category_theory", "category_theory.arrow.hom_mk_right" -> "category_theory", "finset.infi_coe" -> "data", "multiset.length_sort" -> "data", "measurable_space.mk_of_closure_sets" -> "analysis", "nat.fib_le_fib_succ" -> "data", "multiset.range_le" -> "data", "has_fpower_series_on_ball.radius_pos" -> "analysis", "Hausdorffification.induction_on" -> "algebra", "mem_nhds_within_Ici_iff_exists_Ico_subset" -> "topology", "finset.prod_mul_distrib" -> "algebra", "multiset.mem_add" -> "data", "category_theory.whisker_left_twice" -> "category_theory", "finsupp.support_single_subset" -> "data", "ennreal.of_real_lt_of_real_iff" -> "data", "function.Union_pnat_pts_of_period" -> "dynamics", "category_theory.iso.inv_hom_id_app" -> "category_theory", "add_eq_zero_iff'" -> "algebra", "list.disjoint.symm" -> "data", "polynomial.eval\:2082_finset_sum" -> "data", "filter.eventually_at_top" -> "order", "complex.of_real_cosh_of_real_re" -> "data", "list.erase_nil" -> "data", "ring_equiv.symm_apply_apply" -> "data", "simple_graph.adj_matrix_mul_vec_apply" -> "combinatorics", "nat.pos_of_ne_zero" -> "init", "units.min_coe" -> "algebra", "matrix_equiv_tensor.to_fun_alg_hom_apply" -> "algebra", "is_path_connected.mem_path_component" -> "topology", "submodule.findim_quotient_le" -> "algebra", "finset.sdiff_eq_empty_iff_subset" -> "data", "equiv.perm.sign_cycle" -> "algebra", "ennreal.coe_to_nnreal_le_self" -> "data", "tactic.abel.zero_termg" -> "tactic", "real.cos_le_cos_of_nonneg_of_le_pi" -> "analysis", "imp_or_distrib'" -> "logic", "add_submonoid.localization_map.is_unit_comp" -> "algebra", "polynomial.eval\:2082_map" -> "data", "set.image_mul_right_Icc'" -> "data", "add_lt_of_lt_neg_add" -> "algebra", "measure_theory.measure.haar_caratheodory_measurable" -> "analysis", "quadratic_form.polar_add" -> "algebra", "category_theory.under.map_obj_hom" -> "category_theory", "measure_theory.lintegral_mono'" -> "analysis", "list.nth_le_of_fn" -> "data", "filter.eventually_eq.mdifferentiable_within_at_iff" -> "geometry", "category_theory.limits.coprod.pentagon" -> "category_theory", "polynomial.splits_of_degree_le_one" -> "algebra", "pnat.to_pnat'_coe" -> "data", "category_theory.limits.is_colimit.desc_cocone_morphism_hom" -> "category_theory", "multiset.prod_bind" -> "data", "finmap.ext" -> "data", "finset.sdiff_idem" -> "data", "seq.join_nil" -> "data", "filter.prod_eq_bot" -> "order", "functor.comp.applicative_id_comp" -> "control", "nat.factors_unique" -> "data", "pell.xy_succ_succ" -> "number_theory", "set.nonempty_of_mem" -> "data", "cardinal.bit0_eq_self" -> "set_theory", "has_strict_fderiv_at.mem_implicit_to_local_homeomorph_target" -> "analysis", "ordinal.lift_mul" -> "set_theory", "euclidean_geometry.angle_eq_angle_of_dist_eq" -> "geometry", "list.mem_keys_of_mem_keys_kerase" -> "data", "norm_num.min_fac_ne_bit0" -> "tactic", "multiset.rel_bind" -> "data", "differentiable_on.smul_algebra" -> "analysis", "nat.pred_one_add" -> "data", "exists_le_mul_self" -> "algebra", "summable_of_ne_finset_zero" -> "topology", "qpf.Wrepr_equiv" -> "data", "continuous_linear_equiv.coe_prod" -> "topology", "convex_iff_sum_mem" -> "analysis", "submonoid.closure_eq" -> "algebra", "ordinal.nat_lt_card" -> "set_theory", "category_theory.limits.types.coprod" -> "category_theory", "subgroup.closure_Union" -> "algebra", "equiv.range_eq_univ" -> "data", "multilinear_map.snoc_add" -> "algebra", "isometric.image_symm" -> "topology", "uniform_continuous.nndist" -> "topology", "sym2.vmem_other_spec" -> "data", "algebraic_geometry.PresheafedSpace.stalk_map.id" -> "algebraic_geometry", "turing.to_partrec.step_ret_eval" -> "computability", "list.filter_map_cons_none" -> "data", "set.monotone_set_of" -> "data", "pgame.impartial.first_loses_symm'" -> "set_theory", "commute.right_comm" -> "algebra", "nat.dist_zero_right" -> "data", "submodule.coe_sub" -> "algebra", "matrix.nonsing_inv_nonsing_inv" -> "algebra", "set.image_neg_Ioo" -> "data", "mem_left_add_coset_iff" -> "algebra", "semiquot.is_pure.min" -> "data", "times_cont_mdiff_within_at_iff_times_cont_diff_within_at" -> "geometry", "wseq.mem_cons" -> "data", "list.lookmap_nil" -> "data", "has_deriv_within_at_univ" -> "analysis", "hyperreal.infinite_iff_not_exists_st" -> "data", "zsqrtd.bit1_re" -> "data", "int.pow_dvd_of_le_of_pow_dvd" -> "data", "equiv.subtype_equiv_codomain_symm_apply" -> "data", "prime_multiset.prod_of_pnat_list" -> "data", "abs_add_three" -> "algebra", "dist_le_Ico_sum_of_dist_le" -> "topology", "nnreal.coe_mono" -> "data", "metric.tendsto_at_top" -> "topology", "pfun.image_union" -> "data", "int.nonneg_or_nonneg_neg" -> "init", "matrix.row_vec_mul" -> "data", "zero_gsmul" -> "algebra", "refl" -> "init", "ordinal.lift_is_succ" -> "set_theory", "list.nodup_sublists'" -> "data", "fin.succ_rec_on_zero" -> "data", "mul_lt_one'" -> "algebra", "with_top.sum_lt_top_iff" -> "algebra", "primrec.option_guard" -> "computability", "generalized_continued_fraction.of_part_num_eq_one" -> "algebra", "polynomial.splits_of_splits_mul" -> "algebra", "path_connected_space_iff_connected_space" -> "topology", "metric.diam_le_of_forall_dist_le" -> "topology", "padic_seq.norm_equiv" -> "data", "isometry.continuous" -> "topology", "filter.has_basis.eq_binfi" -> "order", "fin.zero_le" -> "data", "metric.Hausdorff_dist_self_zero" -> "topology", "circle_deg1_lift.transnum_aux_seq_def" -> "dynamics", "euclidean_geometry.reflection_apply" -> "geometry", "associates.out_mul" -> "algebra", "units.mk0_inj" -> "algebra", "subsemiring.exists" -> "algebra", "nat.dist_add_add_left" -> "data", "computable.list_nth" -> "computability", "list.mem_rotate" -> "data", "nat.partrec.code.const_prim" -> "computability", "pell.eq_pell" -> "number_theory", "has_fderiv_within_at_iff_has_deriv_within_at" -> "analysis", "measure_theory.lintegral_eq_zero_iff" -> "analysis", "ennreal.coe_le_coe" -> "data", "finset.union_eq_right_iff_subset" -> "data", "nnreal.sub_eq_zero" -> "data", "and.imp" -> "init", "real.pow_arith_mean_le_arith_mean_pow_of_even" -> "analysis", "category_theory.coe_hom_inv_id" -> "category_theory", "times_cont_mdiff.smooth" -> "geometry", "set.Iic_union_Icc_eq_Iic" -> "data", "inv_of_div" -> "algebra", "is_local_extr.congr" -> "topology", "padic_seq.norm_eq_norm_app_of_nonzero" -> "data", "int.sub_lt_self" -> "init", "semidirect_product.map_comp_inr" -> "algebra", "set.image_eq_image" -> "data", "submonoid.closure_singleton_eq" -> "algebra", "ennreal.sub_mul_ge" -> "data", "nat.find_greatest_is_greatest" -> "data", "le_Sup_of_le" -> "order", "category_theory.limits.binary_fan.is_limit.lift'_val" -> "category_theory", "set.image_id" -> "data", "ennreal.of_real_add_le" -> "data", "has_strict_fderiv_at.const_add" -> "analysis", "pnat.gcd_b_eq" -> "data", "function.injective.inj_on" -> "data", "is_bounded_bilinear_map.differentiable_on" -> "analysis", "mvpfunctor.M.dest_corec'" -> "data", "norm_num.min_fac_helper_3" -> "tactic", "polynomial.splits_iff_exists_multiset" -> "algebra", "norm_num.sle_bit0_bit1" -> "tactic", "con.to_setoid_inj" -> "algebra", "filter.has_basis.eventually_iff" -> "order", "set.Ioo_subset_Ioc_union_Ico" -> "data", "real.sqrt_two_add_series_step_down" -> "data", "multiset.powerset_len_aux_nil" -> "data", "complex.sin_arg" -> "analysis", "list.chain'.iff" -> "data", "alg_equiv.map_zero" -> "algebra", "multiset.repeat_le_coe" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence.counit_iso_inv_app_app_hom" -> "category_theory", "submonoid.localization_map.mk'_eq_iff_mk'_eq" -> "algebra", "ereal.neg_le_of_neg_le" -> "data", "int.div_le_of_le_mul" -> "data", "measure_theory.outer_measure.is_caratheodory_iff_le" -> "analysis", "sum_bernoulli" -> "number_theory", "has_fpower_series_on_ball.analytic_at" -> "analysis", "path_connected_space_iff_univ" -> "topology", "measure_theory.integrable_of_bounded" -> "analysis", "is_strict_total_order'.swap" -> "order", "list.cons_bag_inter_of_neg" -> "data", "times_cont_mdiff.times_cont_mdiff_on" -> "geometry", "finset.prod_preimage'" -> "data", "fin.sum_univ_eq_sum_range" -> "data", "turing.partrec_to_TM2.tr_eval" -> "computability", "ordinal.power_le_power_right" -> "set_theory", "normed_algebra.to_nonzero" -> "analysis", "dfinsupp.neg_apply" -> "data", "nhds_nil" -> "topology", "is_glb.of_image" -> "order", "stream.eq_of_bisim" -> "data", "band_eq_true_eq_eq_tt_and_eq_tt" -> "init", "submonoid.localization_map.eq" -> "algebra", "set.Icc_subset_Icc_left" -> "data", "proj_I_I" -> "topology", "finset.sigma_eq_bind" -> "data", "free_group.map.comp" -> "algebra", "is_local_max_on.add" -> "topology", "eq_one_of_mul_self_left_cancel" -> "algebra", "discrete_valuation_ring.ideal_eq_span_pow_irreducible" -> "algebra", "is_compl.disjoint" -> "order", "finset.measurable_sum" -> "analysis", "category_theory.comma.map_left_map_right" -> "category_theory", "list.perm_induction_on" -> "data", "category_theory.abelian.pseudoelement.pseudo_pullback" -> "category_theory", "mv_polynomial.mem_restrict_total_degree" -> "algebra", "measure_theory.lintegral_nnnorm_add" -> "analysis", "omega.coeffs.val_between_add_val_between" -> "tactic", "real.sqrt_lt" -> "data", "pgame.add_assoc_equiv" -> "set_theory", "composition.ne_ones_iff" -> "combinatorics", "asymptotics.is_O_const_mul_self" -> "analysis", "set.countable_range" -> "data", "measurable.ennreal_mul" -> "analysis", "padic.coe_zero" -> "data", "local_ring.mem_maximal_ideal" -> "algebra", "vector.to_list_drop" -> "data", "is_cyclic.card_order_of_eq_totient" -> "algebra", "seq.mem_cons_iff" -> "data", "filter.germ.lift_pred_const_iff" -> "order", "nat_add_zero" -> "init", "ordinal.induction_on" -> "set_theory", "continuous_linear_map.norm_id_field" -> "analysis", "set.nonempty.ne_empty" -> "data", "list.func.equiv_trans" -> "data", "measure_theory.l1.zero_to_fun" -> "analysis", "monotone.map_bdd_above" -> "order", "finset.min'_mem" -> "data", "Hausdorffification.lift_eq" -> "algebra", "traversable.mfoldl_to_list" -> "control", "turing.partrec_to_TM2.K'.elim_update_main" -> "computability", "category_theory.limits.cokernel_condition_apply" -> "category_theory", "norm_num.clear_denom_le" -> "tactic", "has_strict_fderiv_at.implicit_to_local_homeomorph_self" -> "analysis", "category_theory.over.forget_obj" -> "category_theory", "finset.disjoint_right" -> "data", "set.surj_on_iff_exists_bij_on_subset" -> "data", "is_glb.nonempty" -> "order", "measure_theory.outer_measure.dirac_caratheodory" -> "analysis", "nnreal.coe_sub" -> "data", "primrec.or" -> "computability", "differentiable_within_at.sqrt" -> "analysis", "nat.add_units_eq_zero" -> "data", "submonoid.comap_id" -> "algebra", "nat.find_greatest_of_ne_zero" -> "data", "topological_fiber_bundle_core.mem_local_triv'_target" -> "topology", "multiset.card_bind" -> "data", "seq.of_mem_append" -> "data", "set.bUnion_subset_bUnion" -> "data", "int.gcd_mul_left" -> "algebra", "Set.Union_lem" -> "set_theory", "unique_diff_within_at.eq" -> "analysis", "dfinsupp.finite_supp" -> "data", "finset.sorted_last_eq_max'" -> "data", "is_open.is_measurable" -> "analysis", "continuous_multilinear_map.uncurry_right_norm" -> "analysis", "semiquot.univ_unique" -> "data", "set.bind_def" -> "data", "function.semiconj.id_left" -> "logic", "mdifferentiable_at.has_mfderiv_at" -> "geometry", "list.argmin_eq_none" -> "data", "add_right_surjective" -> "algebra", "primrec.list_cons" -> "computability", "category_theory.quotient.comp_mk" -> "category_theory", "category_theory.nat_iso.of_components.inv_app" -> "category_theory", "category_theory.limits.cone_of_cone_uncurry_\[Pi]_app" -> "category_theory", "continuous_infi_rng" -> "topology", "proper_space_of_compact_closed_ball_of_le" -> "topology", "typevec.repeat_eq_nil" -> "data", "nat.pow_dvd_pow_of_dvd" -> "data", "tactic.ring.unfold_div" -> "tactic", "stream.nth_succ" -> "data", "geom_series\:2082_zero" -> "algebra", "category_theory.tensoring_right_monoidal_\[Mu]_is_iso_inv_app" -> "category_theory", "fderiv_const_apply" -> "analysis", "turing.TM1to1.supports_stmt_write" -> "computability", "list.tendsto_cons" -> "topology", "mul_le_of_le_of_le_one" -> "algebra", "pgame.zero_le_iff_neg_le_zero" -> "set_theory", "category_theory.functor.map_arrow_obj_hom" -> "category_theory", "metric.uniformity_basis_dist_le" -> "topology", "linear_equiv.image_eq_preimage" -> "algebra", "set.inj_on_iff_injective" -> "data", "finset.disjoint_bind_right" -> "data", "has_sum_subtype_iff_of_support_subset" -> "topology", "Inf_sup_eq" -> "order", "continuous_multilinear_map.prod_apply" -> "topology", "asymptotics.is_O_with.trans_is_o" -> "analysis", "bounded_continuous_function.dist_le" -> "topology", "power_series.coeff_C" -> "algebra", "filter.tendsto.congr'" -> "order", "enorm.map_neg" -> "analysis", "matrix.reindex_lie_equiv_apply" -> "algebra", "enorm.finite_dist_eq" -> "analysis", "int.mod_two_ne_zero" -> "data", "iff.rfl" -> "init", "zmod.cast_mod_nat" -> "data", "matrix.diagonal_add" -> "data", "infi_neg" -> "order", "is_open_range_sigma_mk" -> "topology", "joined.trans" -> "topology", "add_units.ext_iff" -> "algebra", "mul_nsmul_left" -> "algebra", "mvqpf.cofix.dest_corec" -> "data", "infi_uniformity" -> "topology", "mul_add_eq_mul_add_iff_sub_mul_add_eq" -> "algebra", "is_open_Union" -> "topology", "is_add_submonoid.coe_add" -> "algebra", "function.embedding.min_injective" -> "set_theory", "smooth_within_at_fst" -> "geometry", "measure_theory.integral_mono" -> "analysis", "bit0_mul" -> "algebra", "category_theory.limits.binary_cofan.mk_\[Iota]_app_right" -> "category_theory", "deriv_id'" -> "analysis", "sup_eq_bot_iff" -> "order", "prod.zero_eq_mk" -> "algebra", "times_cont_mdiff_snd" -> "geometry", "is_cau_of_mono_bounded" -> "data", "typevec.subtype_val_diag_sub" -> "data", "list.length_append" -> "init", "function.commute.refl" -> "logic", "real.sin_eq_zero_iff" -> "analysis", "list.comp_traverse" -> "control", "ennreal.mul_eq_mul_left" -> "data", "localization_map.lift_mk'_spec" -> "algebra", "is_basis.to_dual_eq_repr" -> "algebra", "polynomial.derivative_smul" -> "data", "measure_theory.measure.join_map_dirac" -> "analysis", "subtype.edist_eq" -> "topology", "measure_theory.integral_map_measure" -> "analysis", "finsupp.sum_neg_index" -> "data", "computable.vector_length" -> "computability", "peirce'" -> "logic", "continuous_at.comp" -> "topology", "matrix.mul_vec_one" -> "data", "filter.tendsto.inv'" -> "analysis", "image_norm_le_of_liminf_right_slope_norm_lt_deriv_boundary" -> "analysis", "normalize_lcm" -> "algebra", "ring_hom.ext_zmod" -> "data", "tactic.ring_exp.add_pf_sum_overlap" -> "tactic", "zmod.cast_unit_of_coprime" -> "data", "lfp_eq" -> "order", "set.sUnion_mono" -> "data", "roption.eq_some_iff" -> "data", "exists_Ioc_subset_of_mem_nhds'" -> "topology", "linear_map.map_neg\:2082" -> "algebra", "polynomial.coeff_restriction" -> "algebra", "multiset.antidiagonal_cons" -> "data", "set.preimage_mul_const_Ioc" -> "data", "smodeq.add" -> "algebra", "algebraic_geometry.SheafedSpace.mk_coe" -> "algebraic_geometry", "free_comm_ring.is_supported_of" -> "algebra", "char_p.char_ne_zero_of_fintype" -> "algebra", "last_digit_ne_zero" -> "data", "dense_inter_of_G\[Delta]" -> "topology", "if_ctx_congr_prop" -> "init", "multiset.prod_cons" -> "data", "nhds_within_inter" -> "topology", "measurable.of_neg" -> "analysis", "tensor_product.lift.tmul" -> "algebra", "of_heq_true" -> "init", "deriv_within_inter" -> "analysis", "int.le_add_of_neg_add_le" -> "init", "has_mfderiv_within_at.mdifferentiable_within_at" -> "geometry", "setoid.ker_lift_injective" -> "data", "padic.rat_dense'" -> "data", "list.nat.nodup_antidiagonal" -> "data", "topological_space.opens.map_comp_hom_app" -> "topology", "submodule.is_principal.span_singleton_generator" -> "algebra", "semiquot.mem_pure'" -> "data", "uniform_space.completion.comap_coe_eq_uniformity" -> "topology", "hyperreal.lt_neg_of_pos_of_infinitesimal" -> "data", "padic.coe_add" -> "data", "mul_action.of_quotient_stabilizer_smul" -> "algebra", "nat.eq_zero_of_gcd_eq_zero_right" -> "data", "primrec\:2082.left" -> "computability", "ideal.span_eq" -> "algebra", "set_coe.exists'" -> "data", "local_homeomorph.prod_symm" -> "topology", "equiv.coe_inv" -> "data", "is_G\[Delta].union" -> "topology", "nat.mul_lt_mul'" -> "init", "submonoid.coe_map" -> "algebra", "list.lookup_is_some" -> "data", "measure_theory.outer_measure.Inf_gen_empty" -> "analysis", "equiv.apply_eq_iff_eq_symm_apply" -> "data", "list.func.equiv_symm" -> "data", "real.nnnorm_two" -> "analysis", "supr_comm" -> "order", "topological_fiber_bundle_core.local_triv'_trans" -> "topology", "digits_last" -> "data", "with_top.top_mul" -> "algebra", "measure_theory.induced_outer_measure_eq" -> "analysis", "set.Iic_diff_Iio" -> "data", "omega.nat.le_and_le_iff_eq" -> "tactic", "prime_multiset.prod_inf" -> "data", "list.length_insert_of_mem" -> "data", "perfect_closure.mk_mul_mk" -> "algebra", "continuous_at_of_locally_uniform_approx_of_continuous_at" -> "topology", "has_ftaylor_series_up_to_zero_iff" -> "analysis", "subring.map_sup" -> "algebra", "unique_mdiff_on.eq" -> "geometry", "nat.sum_four_squares" -> "number_theory", "measure_theory.integrable_on_empty" -> "analysis", "ideal.mul_le_left" -> "algebra", "int.sub_one_lt_iff" -> "data", "int.add_pos" -> "init", "add_submonoid.localization_map.of_add_equiv_of_add_equiv_apply" -> "algebra", "nat.gcd_mul_lcm" -> "data", "add_submonoid.closure_mono" -> "algebra", "nat.add_div_eq_of_le_mod_add_mod" -> "data", "list.exists_of_mem_keys" -> "data", "abs_le_max_abs_abs" -> "algebra", "complex.uniform_continuous_im" -> "topology", "ordinal.lt_sup" -> "set_theory", "is_R_or_C.norm_sq_to_real" -> "data", "category_theory.limits.cones.whiskering_map_hom" -> "category_theory", "set.empty_subset" -> "data", "continuous_equiv_fun_basis" -> "analysis", "submonoid.localization_map.lift_injective_iff" -> "algebra", "pnat.lcm_coe" -> "data", "set.inter_left_comm" -> "data", "set.disjoint_image_image" -> "data", "cau_seq.completion.of_rat_sub" -> "data", "finset.card_eq_sum_card_image" -> "algebra", "category_theory.limits.prod.lift_snd" -> "category_theory", "wseq.destruct_flatten" -> "data", "onote.scale_eq_mul" -> "set_theory", "pell.yz_succ" -> "number_theory", "nat.mul_eq_zero" -> "data", "stream.bisim_simple" -> "data", "list.forall\:2082_refl" -> "data", "finset.sum_equiv" -> "data", "category_theory.limits.biproduct.hom_ext" -> "category_theory", "polynomial.degree_lt_wf" -> "data", "cardinal.add_one_of_omega_le" -> "set_theory", "matrix_equiv_tensor.inv_fun_add" -> "algebra", "Mon.colimits.quot_mul" -> "algebra", "typevec.last_fun_append_fun" -> "data", "set.preimage_add_const_Ioi" -> "data", "finset.prod_insert" -> "algebra", "Lim_eq" -> "topology", "prod_le_borel_prod" -> "analysis", "complex.cos_add_sin_I" -> "data", "le_min" -> "init", "heq_of_eq_mp" -> "logic", "order_of_pow" -> "algebra", "list.kerase_cons_ne" -> "data", "add_submonoid.localization_map.mk'_zero" -> "algebra", "is_noetherian_of_fg_of_noetherian" -> "algebra", "dim_mul_dim'" -> "algebra", "filter.tendsto_at_top_add_left_of_le" -> "order", "cardinal.mk_punit" -> "set_theory", "function.semiconj.surj_on_range" -> "data", "measure_theory.l1.integral_smul" -> "analysis", "add_con.add_con_gen_of_add_con" -> "algebra", "auto.not_forall_eq" -> "tactic", "has_sum.sub" -> "topology", "list.erase_subset" -> "data", "has_fderiv_at.smul" -> "analysis", "path_component_subset_component" -> "topology", "mdifferentiable_on_atlas_symm" -> "geometry", "category_theory.monad.forget_creates_limits.lifted_cone_\[Pi]_app_f" -> "category_theory", "div_nonpos_of_nonpos_of_nonneg" -> "algebra", "measure_theory.l1.coe_coe" -> "analysis", "ordinal.is_normal.nfp_le" -> "set_theory", "unique_diff_on_Ioc" -> "analysis", "set.bij_on.inv_on_inv_fun_on" -> "data", "polynomial.leading_coeff_hom_apply" -> "data", "list.forall_mem_cons" -> "data", "list.perm.append_right" -> "data", "measure_theory.integrable.congr" -> "analysis", "add_subgroup.gsmul_mem" -> "algebra", "interior_eq_nhds" -> "topology", "gt.lt" -> "algebra", "symmetrize_mono" -> "topology", "add_lt_of_neg_of_lt" -> "algebra", "measure_theory.ae_eq_fun.integrable.neg" -> "analysis", "irreducible.is_unit_or_is_unit" -> "algebra", "option.iget_of_mem" -> "data", "has_fderiv_within_at.neg" -> "analysis", "with_top.sum_eq_top_iff" -> "algebra", "continuous_sup_rng_left" -> "topology", "category_theory.limits.is_limit.hom_lift" -> "category_theory", "of_add_nsmul" -> "algebra", "ordinal.is_normal.limit_lt" -> "set_theory", "multiset.le_union_left" -> "data", "eq.subset" -> "data", "list.rel_map" -> "data", "hyperreal.st_le_of_le" -> "data", "finset.prod_nonneg_of_card_nonpos_even" -> "analysis", "add_con.symm" -> "algebra", "finset.ext" -> "data", "omega.nat.exists_clause_holds" -> "tactic", "partrec.bind" -> "computability", "dim_range_add_dim_ker" -> "algebra", "ordering.compares.eq_lt" -> "algebra", "mem_closure_of_tendsto" -> "topology", "wseq.to_seq_of_seq" -> "data", "finset.prod_product" -> "algebra", "submonoid.dense_induction" -> "algebra", "omega.nat.neg_free_neg_elim" -> "tactic", "linear_map.id_apply" -> "algebra", "category_theory.limits.is_limit.cone_points_iso_of_equivalence_hom" -> "category_theory", "polynomial.degree_eq_zero_of_is_unit" -> "data", "finset.disjoint_empty_right" -> "data", "set.smul_set_mono" -> "algebra", "measure_theory.measure.coe_add" -> "analysis", "nnreal.inv_le_of_le_mul" -> "data", "complex.differentiable_sinh" -> "analysis", "complex.cos_nat_mul_two_pi" -> "analysis", "set.preimage_const_sub_Iic" -> "data", "nat.add_mul_div_left" -> "init", "set.card_le_of_subset" -> "data", "free_add_monoid.zero_def" -> "algebra", "differentiable_within_at.sub_const" -> "analysis", "ordinal.limit_le" -> "set_theory", "int.le_add_of_neg_add_le_right" -> "init", "algebra.tensor_product.alg_equiv_of_linear_equiv_triple_tensor_product_apply" -> "algebra", "nat.succ_pnat_inj" -> "data", "cardinal.mk_unit" -> "set_theory", "bsupr_le_bsupr" -> "order", "stream.nth_zip" -> "data", "algebraic_closure.to_step_succ.exists_root" -> "algebra", "interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left" -> "analysis", "order.cof_le" -> "set_theory", "nat.sub_eq_iff_eq_add" -> "init", "gaussian_int.sum_two_squares_of_nat_prime_of_not_irreducible" -> "data", "bitvec.to_nat_eq_foldr_reverse" -> "data", "free_monoid.lift_restrict" -> "algebra", "is_R_or_C.div_re" -> "data", "seq.append_nil" -> "data", "is_local_max.congr" -> "topology", "gaussian_int.coe_nat_abs_norm" -> "data", "isometric.symm_trans_apply" -> "topology", "times_cont_diff_on.differentiable_on_iterated_deriv_within" -> "analysis", "add_con.Sup_def" -> "algebra", "stream.approx_succ" -> "data", "option.lift_or_get_choice" -> "data", "stream.odd_eq" -> "data", "mdifferentiable_within_at.mdifferentiable_at" -> "geometry", "alg_equiv.injective" -> "algebra", "hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos" -> "data", "local_homeomorph.trans_target''" -> "topology", "right_ord_continuous.map_Inf'" -> "order", "units.mul_right_dvd" -> "algebra", "category_theory.limits.kernel_zero_iso_source_hom" -> "category_theory", "ctop.realizer.nhds_\[Sigma]" -> "data", "polynomial.C_sub" -> "data", "dist_le_zero" -> "topology", "mv_polynomial.homogeneous_component_zero" -> "algebra", "zmod.gauss_lemma" -> "number_theory", "set.mem_image" -> "data", "finset.fold_congr" -> "data", "zmod.val_mul" -> "data", "mvpfunctor.W_rec_eq" -> "data", "vector_allp_iff_forall" -> "number_theory", "is_coprime.add_mul_right_right_iff" -> "algebra", "is_local_extr.has_deriv_at_eq_zero" -> "analysis", "list.pw_filter_cons_of_neg" -> "data", "int.coe_nat_pos" -> "data", "continuous_within_at_Ioc_iff_Ioi" -> "topology", "filter.le_map_comap_of_surjective" -> "order", "continuous_multilinear_map.cons_add" -> "topology", "category_theory.limits.has_zero_object.from_zero_ext" -> "category_theory", "has_fderiv_at_filter.comp" -> "analysis", "pgame.le_of_le_of_equiv" -> "set_theory", "hash_map.not_contains_empty" -> "data", "nat.sum_totient" -> "data", "polynomial.mod_by_monic_eq_of_not_monic" -> "data", "set.finite.is_measurable" -> "analysis", "complex.norm_sq_add" -> "data", "submodule.comap_subtype_self" -> "algebra", "multiples.zero_mem" -> "algebra", "finset.exists_min_image" -> "data", "is_coprime.prod_right_iff" -> "algebra", "category_theory.equivalence.functor_unit" -> "category_theory", "nat.zero_shiftr" -> "init", "list.nodup_union" -> "data", "bitraversable.tfst_comp_tfst" -> "control", "Exists.fst" -> "logic", "sum.map_id_id" -> "data", "pgame.numeric.le_move_right" -> "set_theory", "affine.simplex.sum_point_weights_with_circumcenter" -> "geometry", "fderiv.comp" -> "analysis", "dim_pos_iff_exists_ne_zero" -> "algebra", "cau_seq.completion.of_rat_zero" -> "data", "matrix.bit1_apply_ne" -> "data", "uniform_embedding_subtype_coe" -> "topology", "finset.coe_mul" -> "algebra", "category_theory.equivalence.inverse_inv" -> "category_theory", "many_one_degree.le_add_right" -> "computability", "ordinal.lt_cof_type" -> "set_theory", "filter.tendsto_at_top_add_nonneg_left" -> "order", "finsupp.order_iso_multiset_apply" -> "data", "traversable.mfoldl.of_free_monoid_comp_free_mk" -> "control", "omega.clause.holds_append" -> "tactic", "associates.mk_dvd_mk" -> "algebra", "set.monotone_powerset" -> "data", "measure_theory.lebesgue_length_empty" -> "analysis", "turing.TM0.machine.map_step" -> "computability", "real.log_neg_iff" -> "analysis", "formal_multilinear_series.comp_coeff_zero" -> "analysis", "has_ftaylor_series_up_to.continuous" -> "analysis", "pos_num.le_iff_cmp" -> "data", "list.argmin_mem" -> "data", "category_theory.faithful_reflects_mono" -> "category_theory", "filter.monotone_lift'" -> "order", "multiset.nodup_iff_ne_cons_cons" -> "data", "multiset.Ico.eq_zero_iff" -> "data", "linear_equiv.map_sum" -> "algebra", "list.forall\:2082_and_left" -> "data", "let_value_heq" -> "init", "padic_norm.values_discrete" -> "data", "multiset.mem_of_subset" -> "data", "cluster_pt.of_le_nhds'" -> "topology", "monoid_hom.id_apply" -> "algebra", "multiset.case_strong_induction_on" -> "data", "power_series.coeff_comp_monomial" -> "algebra", "equiv.perm.cycle_of_apply_of_not_same_cycle" -> "algebra", "set.insert_subset" -> "data", "euclidean_domain.xgcd_aux_rec" -> "algebra", "nat.one_le_bit0" -> "init", "composition.inv_embedding_comp" -> "combinatorics", "ideal.map_Sup" -> "algebra", "filter.mem_map" -> "order", "surjective_of_linear_independent_of_span" -> "algebra", "linear_map.map_finsupp_total" -> "algebra", "int.add_left_neg" -> "init", "pell.n_lt_xn" -> "number_theory", "mvqpf.supp_eq" -> "data", "div_lt_iff'" -> "algebra", "setoid.eq_of_mem_eqv_class" -> "data", "filter.eventually_eq_iff_exists_mem" -> "order", "ennreal.to_real_le_to_real" -> "data", "stream.ext" -> "data", "cardinal.aleph_zero" -> "set_theory", "free_abelian_group.seq_sub" -> "algebra", "vector3.cons_elim_cons" -> "number_theory", "finset.exists_le" -> "data", "matrix.reindex_alg_equiv_symm_apply" -> "algebra", "complex.exp_ne_zero" -> "data", "contracting_with.dist_le_mul" -> "topology", "principal_seg.trans_top" -> "set_theory", "int.gcd_one_left" -> "algebra", "is_local_max_on.neg" -> "topology", "semidirect_product.right_hom_comp_inl" -> "algebra", "matrix.smul_std_basis_matrix" -> "data", "left_ord_continuous.le_iff" -> "order", "list.sublists_append" -> "data", "set.preimage_subset_iff" -> "data", "localization_map.integer_normalization_map_to_map" -> "algebra", "circle_deg1_lift.commute_add_nat" -> "dynamics", "mv_polynomial.indicator_mem_restrict_degree" -> "algebra", "ring.fractional_ideal.div_one" -> "algebra", "category_theory.limits.binary_fan.mk_\[Pi]_app_left" -> "category_theory", "free_group.prod.inv" -> "algebra", "category_theory.nat_trans.vcomp_app'" -> "category_theory", "approximates_linear_on.continuous" -> "analysis", "subring.closure_mono" -> "algebra", "list.suffix_refl" -> "data", "ennreal.tendsto_nhds_top" -> "topology", "nat.mod_mul_left_div_self" -> "data", "finset.sum_dite" -> "algebra", "cardinal.mk_real" -> "data", "real.rpow_arith_mean_le_arith_mean_rpow" -> "analysis", "continuous_linear_equiv.uniform_embedding" -> "analysis", "measure_theory.lebesgue_outer_le_length" -> "analysis", "eq_neg_iff_eq_neg" -> "algebra", "category_theory.id_of_comp_right_id" -> "category_theory", "add_add_add_comm" -> "algebra", "summable_geometric_of_norm_lt_1" -> "analysis", "linear_map.ext" -> "algebra", "dlist.to_list_append" -> "data", "if_true" -> "init", "equiv.perm.sign_subtype_perm" -> "algebra", "set.image2_swap" -> "data", "primrec.nat_bit" -> "computability", "subring.mk'_to_add_subgroup" -> "algebra", "Top.presheaf_to_Types_obj" -> "topology", "galois_connection.u_inf" -> "order", "semiconj_by.units_inv_right" -> "algebra", "algebraic_geometry.SheafedSpace.id_base" -> "algebraic_geometry", "Gromov_Hausdorff.candidates_b_of_candidates_mem" -> "topology", "uniform_space.completion.map_coe" -> "topology", "fin.find_spec" -> "data", "pnat.gcd_props" -> "data", "set.ord_connected_univ" -> "data", "uniform_space.completion.continuous_map\:2082" -> "topology", "multiset.le_cons_of_not_mem" -> "data", "add_group.closure_subset" -> "algebra", "pnat.xgcd_type.finish_v" -> "data", "set.eq_on.symm" -> "data", "int.coe_nat_mul_out" -> "init", "finsupp.mem_support_on_finset" -> "data", "mvfunctor.map_map" -> "control", "list.foldl_with_index_aux_spec_cons" -> "data", "refl_sesq_form.eq_zero" -> "algebra", "int.sub_nat_nat_eq_coe" -> "init", "set.maps_to.union_union" -> "data", "mul_pos" -> "algebra", "skew_adjoint_lie_subalgebra_equiv_apply" -> "algebra", "le_mul_of_one_le_left'" -> "algebra", "encodable.encode_inr" -> "data", "matrix.det_diagonal" -> "algebra", "has_deriv_within_at.rpow" -> "analysis", "add_submonoid.localization_map.eq" -> "algebra", "mnat_monoid_hom_ext" -> "algebra", "category_theory.limits.image.lift_fac_assoc" -> "category_theory", "filter.germ.const_inf" -> "order", "int.add_mod_eq_add_mod_right" -> "data", "finset.sup_eq_union" -> "data", "set.piecewise_eq_on" -> "data", "category_theory.limits.parallel_pair_map_left" -> "category_theory", "set.Icc_diff_right" -> "data", "typevec.split_drop_fun_last_fun" -> "data", "filter.has_basis.ge_iff" -> "order", "dfinsupp.support_single_ne_zero" -> "data", "cau_seq.lt_lim" -> "data", "smul_smul" -> "algebra", "set.Icc_subset_interval" -> "data", "linear_pmap.le_Sup" -> "algebra", "plift.ext" -> "tactic", "mem_nhds_within_Ici_iff_exists_Icc_subset'" -> "topology", "monoid_algebra.exists_left_inverse_of_injective" -> "algebra", "category_theory.limits.coequalizer.cofork_\[Pi]" -> "category_theory", "submodule.span_le" -> "algebra", "gpow_neg" -> "algebra", "rel_embedding.coe_fn_inj" -> "order", "filter.eventually_const" -> "order", "option.is_none_iff_eq_none" -> "data", "quadratic_form.lin_mul_lin_add" -> "algebra", "is_min_on.inter" -> "order", "free_group.red.enum.complete" -> "algebra", "norm_unit_one" -> "algebra", "polynomial.eval_mul_X_sub_C" -> "data", "lt_of_incomp_of_lt" -> "init", "set.nonempty_Ico" -> "data", "alg_equiv.map_neg" -> "algebra", "is_R_or_C.norm_sq_div" -> "data", "pgame.impartial.not_first_wins" -> "set_theory", "measure_theory.simple_func.coe_map" -> "analysis", "cau_seq.mul_lim_zero_right" -> "data", "normed_field.exists_one_lt_norm" -> "analysis", "is_compl.left_le_iff" -> "order", "cauchy_seq_finset_of_summable_norm" -> "analysis", "primrec.to_comp" -> "computability", "fintype.choose_spec" -> "data", "prime_spectrum.is_closed_zero_locus" -> "algebraic_geometry", "category_theory.curry.obj_obj_map" -> "category_theory", "algebra.lmul_left_apply" -> "algebra", "uniformity_eq_comap_nhds_zero'" -> "topology", "pfun.image_inter" -> "data", "has_fderiv_within_at.unique_diff_within_at" -> "analysis", "units.ext" -> "algebra", "real.has_deriv_at_cos" -> "analysis", "ennreal.tsum_prod" -> "topology", "is_R_or_C.abs_zero" -> "data", "finset.nonempty_of_ne_empty" -> "data", "units.mul_right_symm" -> "data", "category_theory.comonad.cofree_map_f" -> "category_theory", "continuous_on_Ioc_extend_from_Ioo" -> "topology", "multiset.mem_cons_of_mem" -> "data", "finsupp.support_sum" -> "data", "rel_embedding.injective" -> "order", "category_theory.non_preadditive_abelian.sub_def" -> "category_theory", "nat.bit1_le" -> "data", "inv_of_eq_group_inv" -> "algebra", "tangent_map_within_comp_at" -> "geometry", "not.intro" -> "init", "uniform_space.completion.uniform_continuous_map" -> "topology", "filter.inf_map_at_bot_ne_bot_iff" -> "order", "pnat.factor_multiset_gcd" -> "data", "padic.of_rat_sub" -> "data", "classical.dec_eq" -> "logic", "gt_irrefl" -> "init", "add_comm_group.is_Z_bilin.sub_left" -> "topology", "affine_subspace.top_coe" -> "algebra", "list.rel_filter_map" -> "data", "int.bodd_neg" -> "data", "euclidean_geometry.inter_eq_singleton_orthogonal_projection_fn" -> "geometry", "set.mem_image_eq" -> "data", "quot.exists_rep" -> "init", "category_theory.curry_natural_left_assoc" -> "category_theory", "list.length_le_of_infix" -> "data", "circle_deg1_lift.continuous_pow" -> "dynamics", "asymptotics.is_O_with_zero_right_iff" -> "analysis", "le_add_of_neg_le_sub_left" -> "algebra", "tactic.ring_exp.mul_coeff_pf_one_mul" -> "tactic", "emetric.mem_closed_ball_self" -> "topology", "hash_map.find_erase_eq" -> "data", "filter.le_comap_map" -> "order", "inner_product_geometry.angle_self_neg_of_nonzero" -> "geometry", "hash_map.valid.modify" -> "data", "primrec.vector_length" -> "computability", "finite_dimensional.not_linear_independent_of_infinite" -> "algebra", "category_theory.limits.prod.pentagon_assoc" -> "category_theory", "alg_equiv.map_mul" -> "algebra", "set.Ioi_subset_Ici_self" -> "data", "category_theory.iso.conj_Aut_hom" -> "category_theory", "list.length_of_fn" -> "data", "polynomial.degree_lt_mono" -> "algebra", "list.join_append" -> "data", "free_group.reduce.idem" -> "algebra", "classical.not_ball" -> "logic", "is_cobounded_ge_nhds" -> "topology", "bot_apply" -> "order", "polynomial.monic_X_pow_sub" -> "data", "inv_gpow" -> "algebra", "fintype.injective_iff_surjective" -> "data", "ordinal.power_omega" -> "set_theory", "category_theory.iso_whisker_right_hom" -> "category_theory", "units.op_pow" -> "algebra", "submonoid.closure_union" -> "algebra", "times_cont_diff_within_at.congr_of_eventually_eq" -> "analysis", "mul_bit1" -> "algebra", "alg_hom.map_pow" -> "algebra", "prime_multiset.to_of_nat_multiset" -> "data", "add_subgroup.mem_supr_of_directed" -> "algebra", "alt_sesq_form.neg" -> "algebra", "ennreal.tsum_le_tsum" -> "topology", "rat.cast_lt_zero" -> "data", "fin.coe_cast_lt" -> "data", "rat.le_total" -> "data", "Sup_empty" -> "order", "complex.sinh_sub" -> "data", "measure_theory.inner_content_le" -> "analysis", "left_mem_segment" -> "analysis", "finset.prod_fin_eq_prod_range" -> "data", "turing.tape.move_right_left" -> "computability", "ext_chart_continuous_at_symm'" -> "geometry", "complex.continuous_linear_map.re_norm" -> "analysis", "subspace.coe_prod_equiv_of_closed_compl_symm" -> "analysis", "cardinal.power_nat_le" -> "set_theory", "nontrivial_of_invariant_basis_number" -> "algebra", "set.mem_image2_eq" -> "data", "smooth.mul" -> "geometry", "holor.zero_mul" -> "data", "nat.mul_le_mul" -> "init", "set.subset_union_left" -> "data", "list.nth_le_split_wrt_composition_aux" -> "combinatorics", "filter.at_top_basis" -> "order", "lt_base_pow_length_digits'" -> "data", "ordinal.limit_rec_on_succ" -> "set_theory", "multiset.disjoint_map_map" -> "data", "set.Iio_subset_Iio_union_Ico" -> "data", "has_deriv_within_at.const_add" -> "analysis", "bounded_continuous_function.coe_zero" -> "topology", "midpoint_eq_iff" -> "algebra", "ordinal.omega_pos" -> "set_theory", "zero_div" -> "algebra", "Class.diff_hom" -> "set_theory", "finset.fold_op_distrib" -> "data", "filter.eventually_top" -> "order", "nat.lt_add_of_zero_lt_left" -> "init", "omega.coeffs.val_eq_of_le" -> "tactic", "asymm_of" -> "init", "submodule.fg_of_fg_map_of_fg_inf_ker" -> "algebra", "polynomial.degree_mul_leading_coeff_inv" -> "data", "enat.coe_add" -> "data", "prime_spectrum.coe_vanishing_ideal" -> "algebraic_geometry", "filter.prod_lift'_lift'" -> "order", "finsupp.unique_single_eq_iff" -> "data", "differentiable.pow" -> "analysis", "analytic_at.comp" -> "analysis", "num.bit1_of_bit1" -> "data", "list.not_mem_range_self" -> "data", "le_non_zero_divisors_of_domain" -> "algebra", "monoid.closure_singleton" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_on_indep_chart" -> "geometry", "digits_zero_of_eq_zero" -> "data", "localization_map.eq_zero_of_fst_eq_zero" -> "algebra", "abstract_completion.uniform_continuous_compare" -> "topology", "measurable.ennreal_induction" -> "analysis", "set_is_basis_of_linear_independent_of_card_eq_findim" -> "algebra", "ordinal.lift_zero" -> "set_theory", "set.Iio_union_Ici" -> "data", "abstract_completion.uniform_continuous_map\:2082" -> "topology", "ennreal.to_real_max" -> "data", "ideal.is_jacobson_iff_prime_eq" -> "algebra", "submonoid.localization_map.mul_equiv_of_localizations_right_inv_apply" -> "algebra", "measure_theory.measure.haar.chaar_mem_cl_prehaar" -> "analysis", "filter.lift_lift'_same_eq_lift'" -> "order", "nat.primrec.const" -> "computability", "inducing.comp" -> "topology", "inner_product_space.of_core.inner_smul_left" -> "analysis", "continuous_within_at.closure_le" -> "topology", "list.subperm.subset" -> "data", "category_theory.over.comp_left" -> "category_theory", "continuous_linear_map.comp_id" -> "topology", "multiset.mem_erase_of_ne" -> "data", "has_strict_fderiv_at.smul_algebra_const" -> "analysis", "real.two_le_pi" -> "analysis", "localization.mul_equiv_of_quotient_symm_mk'" -> "algebra", "filter.mem_at_bot_sets" -> "order", "lt_min_iff" -> "algebra", "lower_bounds_Ici" -> "order", "differentiable_at_fst" -> "analysis", "local_homeomorph.restr_eq_of_source_subset" -> "topology", "add_con.lift_unique" -> "algebra", "category_theory.adjunction.counit_naturality" -> "category_theory", "finset.inter_sdiff" -> "data", "supr_split_single" -> "order", "embedding.compact_iff_compact_image" -> "topology", "set.ord_connected_Icc" -> "data", "ideal.comap_inf" -> "algebra", "set.inter_self" -> "data", "add_le_of_le_sub_left" -> "algebra", "norm_num.is_prime_helper" -> "tactic", "mul_action.inv_smul_smul" -> "algebra", "ordinal.lift_add" -> "set_theory", "add_subgroup.exists" -> "algebra", "choose_le_middle" -> "data", "submodule.sum_mem" -> "algebra", "formal_multilinear_series.has_fpower_series_on_ball" -> "analysis", "list.prod_append" -> "data", "circle_deg1_lift.le_iterate_pos_iff" -> "dynamics", "emetric.ball_disjoint" -> "topology", "measurable.infi_Prop" -> "analysis", "add_submonoid.map_inr" -> "algebra", "interior_interior" -> "topology", "not_lt" -> "init", "continuous.dist" -> "topology", "inner_product_geometry.norm_sub_square_eq_norm_square_add_norm_square_iff_angle_eq_pi_div_two" -> "geometry", "vector.cons_head" -> "data", "polynomial.nat_degree_int_cast" -> "data", "abs_of_neg" -> "algebra", "polynomial.nat_degree_X_pow_sub_C" -> "data", "semidirect_product.lift_unique" -> "algebra", "pequiv.to_matrix_swap" -> "data", "differentiable.fst" -> "analysis", "is_max_on_univ_iff" -> "order", "fintype.pi_finset_disjoint_of_disjoint" -> "data", "set.singleton_nonempty" -> "data", "subsemiring.mem_to_add_submonoid" -> "algebra", "real.le_rpow_add" -> "analysis", "option.map_injective" -> "data", "enorm.top_map" -> "analysis", "continuous_linear_equiv.comp_differentiable_on_iff" -> "analysis", "eq_div_of_mul_eq" -> "algebra", "sub_eq_zero" -> "algebra", "multiset.map_id'" -> "data", "continuous_within_at.comp'" -> "topology", "polynomial.map_multiset_prod" -> "data", "mul_inv_cancel_left" -> "algebra", "category_theory.monoidal_of_has_finite_products.right_unitor_hom" -> "category_theory", "polynomial.degree_le_iff_coeff_zero" -> "data", "category_theory.limits.coprod.map_iso_hom" -> "category_theory", "measure_theory.measure.restrict_le_self" -> "analysis", "set.Ioc_union_Ioo_eq_Ioo" -> "data", "quotient.fin_choice_aux_eq" -> "data", "continuous_on_empty" -> "topology", "multiset.prod_map_add" -> "data", "mdifferentiable_on_univ" -> "geometry", "model_prod_range_prod_id" -> "geometry", "nat.coprime_or_dvd_of_prime" -> "data", "measure_theory.lintegral_Union" -> "analysis", "category_theory.limits.cocones.precompose_map_hom" -> "category_theory", "is_measurable.of_compl" -> "analysis", "list.subset_append_left" -> "init", "tendsto_uniformly_on.tendsto_comp" -> "topology", "nat.ppred_eq_none" -> "data", "is_greatest.is_greatest_iff_eq" -> "order", "ideal.quotient.eq" -> "algebra", "asymptotics.is_o.trans_is_O" -> "analysis", "finset.prod_filter" -> "algebra", "summable.sigma_factor" -> "topology", "associates.mk_one" -> "algebra", "pnat.coprime.factor_eq_gcd_left" -> "data", "le_mul_of_inv_mul_le" -> "algebra", "nhds_within_Ioi_self_ne_bot" -> "topology", "affine_subspace.direction_eq_top_iff_of_nonempty" -> "algebra", "con.lift_comp_mk'" -> "algebra", "mv_polynomial.degrees_X" -> "data", "composition.single_blocks" -> "combinatorics", "list.choose_property" -> "data", "asymptotics.is_O_of_le'" -> "analysis", "uniform_embedding.comp" -> "topology", "matrix.diagonal_apply_ne" -> "data", "submodule.map_subtype_le" -> "algebra", "ext_chart_preimage_mem_nhds_within'" -> "geometry", "complex.conj_re" -> "data", "is_open_sigma_iff" -> "topology", "gcd_dvd_gcd_mul_left" -> "algebra", "list.prod_rotate_eq_one_of_prod_eq_one" -> "data", "eq_iff_eq_cancel_left" -> "logic", "mul_sub_le_image_sub_of_le_deriv" -> "analysis", "multiset.cons_swap" -> "data", "ennreal.infi_add" -> "data", "fintype.right_inverse_bij_inv" -> "data", "category_theory.limits.parallel_pair_functor_obj" -> "category_theory", "dvd_and_not_dvd_iff" -> "algebra", "category_theory.limits.limit.cone_\[Pi]" -> "category_theory", "list.mem_map_of_injective" -> "data", "forall_2_true_iff" -> "logic", "filter.Limsup_le_Limsup" -> "order", "basic_smooth_bundle_core.mem_atlas_iff" -> "geometry", "real.is_conjugate_exponent.sub_one_pos" -> "data", "list.lookup_kerase" -> "data", "turing.TM0.map_init" -> "computability", "category_theory.category_of_elements.comma_equivalence_functor" -> "category_theory", "function.mem_periodic_pts" -> "dynamics", "mv_power_series.constant_coeff_inv" -> "algebra", "semiconj_by.inv_right_iff" -> "algebra", "category_theory.abelian.mono_of_epi_of_mono_of_mono" -> "category_theory", "le_inf_sup" -> "order", "localization.mul_equiv_of_quotient_symm_mk" -> "algebra", "frobenius_add" -> "algebra", "metric.inf_dist_le_inf_dist_add_Hausdorff_dist" -> "topology", "set.mem_of_mem_inter_left" -> "data", "polynomial.monic.def" -> "data", "bitvec.add_lsb_div_two" -> "data", "free_add_magma.pure_bind" -> "algebra", "measure_theory.outer_measure.is_caratheodory_Union_lt" -> "analysis", "relation.comp_iff" -> "logic", "polynomial.integral_normalization_coeff_ne_nat_degree" -> "data", "is_add_group_hom.neg_ker_zero'" -> "algebra", "int.sub_nat_nat_of_ge" -> "init", "free_add_magma.add_map_seq" -> "algebra", "continuous_linear_map.apply_ker" -> "topology", "convex.translate_preimage_left" -> "analysis", "multiset.forall_mem_map_iff" -> "data", "list.kinsert_nodupkeys" -> "data", "summable_geometric_two" -> "analysis", "composition.one_le_blocks'" -> "combinatorics", "list.sorted_ordered_insert" -> "data", "enat.to_with_top_lt" -> "data", "submodule.coe_quot_equiv_of_eq_bot_symm" -> "algebra", "normalize_associated" -> "algebra", "enat.get_coe" -> "data", "inner_add_left" -> "analysis", "order.sequence_of_cofinals.encode_mem" -> "order", "has_deriv_at.lhopital_zero_nhds_left" -> "analysis", "relation.refl_trans_gen_of_transitive_reflexive" -> "logic", "set.mem_sUnion" -> "data", "list.pairwise_of_sublist" -> "data", "polynomial.splits_one" -> "algebra", "commute.fpow_right" -> "algebra", "add_equiv.map_sum" -> "algebra", "mul_lt_one_of_lt_one_of_le_one" -> "algebra", "div_le_div_left" -> "algebra", "sum.traverse_eq_map_id" -> "control", "nhds_mul" -> "topology", "primrec.nat_cases" -> "computability", "nnreal.rpow_lt_rpow_of_exponent_lt" -> "analysis", "has_fderiv_within_at_inv" -> "analysis", "add_monoid_hom.prod_map_def" -> "algebra", "array.to_array_to_list" -> "data", "measure_theory.norm_integral_le_of_norm_le" -> "analysis", "uniform_continuous.add" -> "topology", "bilin_form.coe_fn_to_linear_map" -> "algebra", "computable.to\:2082" -> "computability", "filter.has_basis.tendsto_Ixx_class" -> "order", "uniform_space.completion.map_comp" -> "topology", "gfp_gfp" -> "order", "cau_seq.mul_lim_zero_left" -> "data", "differentiable_on.mul" -> "analysis", "complex.exp_add" -> "data", "multiset.filter_le_filter" -> "data", "list.mem_erase_of_ne" -> "data", "int.coe_nat_mod" -> "data", "interval_integrable.trans" -> "analysis", "subring.neg_mem" -> "algebra", "computation.lift_rel_def" -> "data", "exists_Ioo_extr_on_Icc" -> "analysis", "eckmann_hilton.mul_comm" -> "algebra", "exists_preirreducible" -> "topology", "nat.le_sub_right_iff_add_le" -> "data", "is_local_max.bicomp_mono" -> "topology", "is_R_or_C.conj_bit0" -> "data", "is_basis.range" -> "algebra", "associates.map_subtype_coe_factors'" -> "algebra", "hash_map.valid.insert" -> "data", "function.is_periodic_pt.eq_of_apply_eq" -> "dynamics", "bdd_above_Ioc" -> "order", "multiset.prod_map_prod_map" -> "data", "order_embedding.map_le_iff" -> "order", "category_theory.Monad.assoc_func_app" -> "category_theory", "category_theory.whisker_right_id" -> "category_theory", "list.index_of_nth_le" -> "data", "is_basis.le_span" -> "algebra", "ideal.eq_jacobson_iff_Inf_maximal" -> "algebra", "is_open_const" -> "topology", "finset.sum_nonpos" -> "algebra", "rat.lift_binop_eq" -> "data", "is_closed.is_closed_le" -> "topology", "localization_map.mk'_self''" -> "algebra", "finset.piecewise_coe" -> "data", "int.bit1_val" -> "data", "category_theory.prod.swap_obj" -> "category_theory", "category_theory.limits.types.limit_ext" -> "category_theory", "linear_map.comp_cod_restrict" -> "algebra", "complex.mk_eq_add_mul_I" -> "data", "localization.r_eq_r'" -> "algebra", "add_equiv.to_AddCommMon_iso_hom" -> "algebra", "continuous_of_le_add_edist" -> "topology", "vadd_eq_add" -> "algebra", "monotone.le_is_glb_image" -> "order", "mvqpf.mem_supp" -> "data", "mv_polynomial.eval\:2082_prod" -> "data", "complex.lim_abs" -> "data", "nat.lxor_assoc" -> "data", "pequiv.symm_injective" -> "data", "matrix.empty_mul_vec" -> "data", "units.coe_neg_one" -> "algebra", "alist.empty_union" -> "data", "seq.destruct_eq_nil" -> "data", "sup_le_sup_right" -> "order", "set.ord_connected_Ioi" -> "data", "convex_on.map_sum_le" -> "analysis", "linear_map.range_eq_top" -> "algebra", "tensor_product.lift_mk" -> "algebra", "vector3.append_add" -> "number_theory", "bilin_form.map_sum_left" -> "algebra", "category_theory.functor.congr_obj" -> "category_theory", "matrix.update_row_ne" -> "data", "composition.lt_size_up_to_index_succ" -> "combinatorics", "category_theory.limits.prod_right_unitor_inv_naturality" -> "category_theory", "and_congr_right" -> "init", "finset.le_sup" -> "data", "times_cont_mdiff.continuous" -> "geometry", "neg_of_mul_neg_right" -> "algebra", "set.ord_connected_Iio" -> "data", "map_seq" -> "control", "set.card_image_of_inj_on" -> "data", "int.gcd_one_right" -> "algebra", "is_open_analytic_at" -> "analysis", "is_preconnected_Icc" -> "topology", "mem_powers_iff_mem_gpowers" -> "algebra", "category_theory.End.mul_def" -> "category_theory", "equiv.perm.apply_inv_self" -> "data", "set.range_unique" -> "data", "strict_mono.bot_preimage_bot'" -> "order", "finset.summable" -> "topology", "list.foldl_with_index_aux_eq_foldl_with_index_aux_spec" -> "data", "circle_deg1_lift.exists_eq_add_translation_number" -> "dynamics", "ex_of_psig" -> "init", "imp.swap" -> "logic", "topological_fiber_bundle_core.local_triv'_fst" -> "topology", "localization_map.map_right_cancel" -> "algebra", "mv_polynomial.C_mul'" -> "data", "not_true" -> "init", "is_clopen_iff" -> "topology", "dioph.dioph_pfun_comp1" -> "number_theory", "ideal.quotient.mk_eq_mk" -> "algebra", "localization_map.mk'_mul" -> "algebra", "not_false" -> "init", "subtype.mk_eq_mk" -> "data", "symmetrize_rel_subset_self" -> "topology", "nat.partrec'.rfind_opt" -> "computability", "padic.norm_eq_pow_val" -> "data", "rel.mem_image" -> "data", "submodule.le_def" -> "algebra", "equiv.set_value_eq" -> "data", "to_add_one" -> "algebra", "set.neg_subset_neg" -> "algebra", "monoid_algebra.mul_apply_right" -> "data", "nonneg_add_comm_group.not_zero_pos" -> "algebra", "algebra.tensor_product.mul_apply" -> "algebra", "is_open_map_snd" -> "topology", "add_con.add_con_gen_idem" -> "algebra", "turing.list_blank.nth_modify_nth" -> "computability", "times_cont_diff.add" -> "analysis", "is_R_or_C.abs_nonneg" -> "data", "category_theory.functor.left_op_obj" -> "category_theory", "has_fderiv_within_at.unique_diff_within_at_of_continuous_linear_equiv" -> "analysis", "nat.sub_lt_iff" -> "data", "tactic.ring_exp.simple_pf_prod_one" -> "tactic", "enat.with_top_equiv_symm_lt" -> "data", "has_mfderiv_within_at_univ" -> "geometry", "nat.primrec'.prim_iff" -> "computability", "function.iterate_zero_apply" -> "logic", "asymptotics.is_o.prod_rightl" -> "analysis", "int.add_neg_cancel_left" -> "init", "int.lcm_assoc" -> "algebra", "set.one_subset" -> "algebra", "nat.cofinite_eq_at_top" -> "order", "complex.norm_sq_I" -> "data", "differentiable_at.mul" -> "analysis", "emetric.mem_ball'" -> "topology", "dim_map_le" -> "algebra", "con.sup_eq_con_gen" -> "algebra", "pnat.dvd_lcm_right" -> "data", "asymptotics.is_O.of_const_mul_right" -> "analysis", "add_con.induction_on" -> "algebra", "multiset.map_union" -> "data", "submonoid.mul_mem" -> "algebra", "linear_independent_Union_finite" -> "algebra", "open_subgroup.mul_mem" -> "topology", "measure_theory.l1.simple_func.of_simple_func_neg" -> "analysis", "relator.rel_imp" -> "logic", "matrix.mul_apply'" -> "data", "pfun.core_restrict" -> "data", "finset.filter_ne'" -> "data", "has_fderiv_at.lim" -> "analysis", "add_monoid_hom.coe_of_mdense" -> "algebra", "vsub_right_cancel" -> "algebra", "set.Union_eq_range_sigma" -> "data", "mul_sub_lt_image_sub_of_lt_deriv" -> "analysis", "pi.const_zero" -> "algebra", "real.sin_pos_of_pos_of_le_two" -> "data", "wseq.lift_rel.refl" -> "data", "add_submonoid.coe_subtype" -> "algebra", "nat.prime.mul_eq_prime_pow_two_iff" -> "data", "exp_neg_inv_glue.f_aux_iterated_deriv" -> "analysis", "set.sUnion_subset_iff" -> "data", "interior_Ioo" -> "topology", "multiset.eq_zero_of_forall_not_mem" -> "data", "tensor_product.sum_tmul" -> "algebra", "onote.NF.snd'" -> "set_theory", "ennreal.tendsto_to_nnreal" -> "topology", "image_le_of_deriv_right_le_deriv_boundary" -> "analysis", "set.mem_prod_eq" -> "data", "prod.mk_eq_zero" -> "algebra", "uniform_space.mem_nhds_iff" -> "topology", "deriv_within_zero_of_not_differentiable_within_at" -> "analysis", "frontier_lt_subset_eq" -> "topology", "add_self_div_two" -> "algebra", "pnat.coprime.gcd_mul_left_cancel" -> "data", "pythagorean_triple.normalize" -> "number_theory", "euclidean_domain.mul_div_cancel_left" -> "algebra", "measurable_binfi" -> "analysis", "submodule.coe_sort_coe" -> "algebra", "hyperreal.not_infinite_zero" -> "data", "has_ftaylor_series_up_to_on.has_strict_fderiv_at" -> "analysis", "succ_nsmul" -> "algebra", "set.smul_set_union" -> "algebra", "dense_range.comp" -> "topology", "nat.bit0_lt" -> "init", "nat.mul_div_left" -> "init", "prod.fst_zero" -> "algebra", "multiset.sum_smul" -> "algebra", "dense_range_iff_closure_range" -> "topology", "is_measurable.Union_Prop" -> "analysis", "mv_power_series.monomial_mul_monomial" -> "algebra", "W.depth_lt_depth_mk" -> "data", "add_le_add_left" -> "algebra", "complex.sinh_of_real_im" -> "data", "monoid_algebra.mul_single_apply" -> "data", "nat.gcd_pos_of_pos_left" -> "data", "linear_map.range_id" -> "algebra", "set.compl_eq_univ_diff" -> "data", "list.rotate_cons_succ" -> "data", "AddCommGroup.kernel_iso_ker_over_inv_left_to_fun_val" -> "algebra", "iff.to_eq" -> "init", "matrix.nonsing_inv_apply" -> "algebra", "gcd_is_unit_iff" -> "algebra", "circle_deg1_lift.translation_number_eq_of_dist_bounded" -> "dynamics", "asymptotics.is_O_iff_is_O_with" -> "analysis", "filter.nonempty_of_mem_sets" -> "order", "turing.proj_map_nth" -> "computability", "filter.mem_principal_self" -> "order", "discrete_valuation_ring.irreducible_iff_uniformizer" -> "algebra", "znum.cast_to_int" -> "data", "smodeq.bot" -> "algebra", "submodule.eq_top_of_disjoint" -> "algebra", "generalized_continued_fraction.int_fract_pair.one_le_succ_nth_stream_b" -> "algebra", "polynomial.smul_eval_smul" -> "algebra", "set.prod_subset_preimage_snd" -> "data", "free_add_semigroup.lift_unique" -> "algebra", "finmap.mem_def" -> "data", "pos_of_mul_pos_left" -> "algebra", "is_group_hom.trivial_ker_iff_eq_one" -> "algebra", "times_cont_diff_at.comp" -> "analysis", "list.pmap_eq_map" -> "data", "filter.realizer.bot_F" -> "data", "simple_graph.adj_matrix_apply" -> "combinatorics", "set.Iic_disjoint_Ioi" -> "data", "continuous_multilinear_map.bounds_bdd_below" -> "analysis", "hyperreal.not_real_of_infinitesimal_ne_zero" -> "data", "measure_theory.measure.measurable_dirac" -> "analysis", "finite_field.pow_card_sub_one_eq_one" -> "algebra", "list.not_mem_cons_of_ne_of_not_mem" -> "data", "add_con.coe_zero" -> "algebra", "continuous_subtype_coe" -> "topology", "cau_seq.lt_of_eq_of_lt" -> "data", "multiset.count_erase_self" -> "data", "euclidean_geometry.orthogonal_projection_vsub_mem_direction" -> "geometry", "equiv.perm.one_lt_nonfixed_point_card_of_ne_one" -> "algebra", "pgame.right_wins_of_equiv_iff" -> "set_theory", "free_comm_ring.is_supported_zero" -> "algebra", "finset.card_erase_le" -> "data", "list.remove_nth_eq_nth_tail" -> "data", "Class.mem_univ" -> "set_theory", "enat.top_eq_none" -> "data", "real.sqrt_aux_nonneg" -> "data", "AddCommGroup.has_limit.lift_apply" -> "algebra", "has_deriv_at.congr_of_eventually_eq" -> "analysis", "is_unit.map" -> "algebra", "le_add_iff_nonneg_right" -> "algebra", "list.perm.prod_eq'" -> "data", "category_theory.limits.cofork.right_app_one" -> "category_theory", "lipschitz_with.list_prod" -> "topology", "inf_le_left'" -> "order", "encodable.encode_injective" -> "data", "lt_sub_iff_add_lt" -> "algebra", "pmf.bind_apply" -> "analysis", "list.eq_of_mem_singleton" -> "data", "category_theory.limits.colimit.pre_map'" -> "category_theory", "affine_subspace.direction_inf_of_mem" -> "algebra", "set.indicator_nonpos'" -> "data", "is_scalar_tower.algebra_map_smul" -> "algebra", "cast_proof_irrel" -> "init", "finsupp.coe_lsum" -> "algebra", "equiv_equiv_iso_inv" -> "category_theory", "category_theory.limits.biprod.braiding'_eq_braiding" -> "category_theory", "has_deriv_within_at.sub" -> "analysis", "equiv.symm_to_local_equiv" -> "data", "real.mk_le_of_forall_le" -> "data", "set.disjoint_left" -> "data", "exists_and_distrib_left" -> "logic", "category_theory.monoidal.Mon_functor_category_equivalence.functor_obj_map_hom" -> "category_theory", "not_irreducible_one" -> "algebra", "monic_scale_roots_iff" -> "algebra", "opposite.op_inj_iff" -> "data", "mul_semiring_action_hom.map_neg" -> "algebra", "set.set_of_app_iff" -> "data", "padic_norm.neg" -> "data", "set.bInter_mono" -> "data", "category_theory.cancel_epi" -> "category_theory", "measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto_ae" -> "analysis", "cardinal.summable_cantor_function" -> "data", "add_monoid_hom.coe_prod_map" -> "algebra", "finset.union_empty" -> "data", "two_dvd_bit1" -> "algebra", "complex.log_zero" -> "analysis", "set.inter_subset_inter" -> "data", "is_basis.equiv_fun_apply" -> "algebra", "zsqrtd.add_le_add_left" -> "data", "pell.asq_pos" -> "number_theory", "stream.cons_nth_inits_core" -> "data", "quotient_group.ker_lift_injective" -> "algebra", "polynomial.add_comp" -> "data", "submonoid.localization_map.lift_id" -> "algebra", "set.Ioc_eq_empty" -> "data", "mem_affine_span_iff_eq_affine_combination" -> "algebra", "of_digits_neg_one" -> "data", "list.count_pos" -> "data", "affine_map.vsub_apply" -> "algebra", "circle_deg1_lift.translation_number_eq_of_semiconj_by" -> "dynamics", "linear_recurrence.sol_eq_of_eq_init" -> "algebra", "pnat.factor_multiset_lcm" -> "data", "normed_algebra.zero_ne_one" -> "analysis", "submonoid.coe_bot" -> "algebra", "list.inter_eq_nil_iff_disjoint" -> "data", "card_quotient_dvd_card" -> "algebra", "pullback_nonzero" -> "algebra", "countable_Inter_mem_sets" -> "order", "fpow_neg" -> "algebra", "AddCommGroup.image_map" -> "algebra", "mul_action.orbit_eq_iff" -> "algebra", "list.revzip_sublists" -> "data", "lt_iff_lt_of_le_iff_le" -> "algebra", "padic_seq.eq_zero_iff_equiv_zero" -> "data", "multiset.le_inter" -> "data", "mul_fpow" -> "algebra", "finset.card_disjoint_union" -> "data", "compact_of_finite_subfamily_closed" -> "topology", "min_le_iff" -> "algebra", "linear_equiv.continuous_symm" -> "analysis", "zsqrtd.norm_zero" -> "data", "filter.map_map" -> "order", "turing.reaches\:2080_eq" -> "computability", "ennreal.top_mul" -> "data", "category_theory.limits.biprod.inl_snd_assoc" -> "category_theory", "zmod.val_cast_of_lt" -> "data", "rel.image_inter" -> "data", "linear_map.ker_zero" -> "algebra", "linear_independent_of_zero_eq_one" -> "algebra", "free_add_semigroup.lift_of" -> "algebra", "measure_theory.l1.simple_func.dist_to_simple_func" -> "analysis", "nat.le_succ_of_le" -> "init", "measure_theory.ae_eq_fun.integrable.smul" -> "analysis", "category_theory.limits.cones.postcompose_map_hom" -> "category_theory", "hyperreal.is_st_le_of_le" -> "data", "continuous_at.add" -> "topology", "vadd_vsub_assoc" -> "algebra", "function.surjective.prod_map" -> "data", "cardinal.lt_cof_power" -> "set_theory", "is_R_or_C.conj_re" -> "data", "polynomial.map_neg" -> "data", "multiplicity.dvd_of_multiplicity_pos" -> "algebra", "tendsto_locally_uniformly_on.comp" -> "topology", "measure_theory.simple_func_sequence_tendsto" -> "analysis", "typevec.repeat_eq_iff_eq" -> "data", "wseq.head_of_seq" -> "data", "mul_action.mem_fixed_by" -> "algebra", "nat.not_even_bit1" -> "data", "measure_theory.measure.eq_zero_of_not_nonempty" -> "analysis", "multiset.erase_add_right_neg" -> "data", "category_theory.limits.cocones.forget_obj" -> "category_theory", "list.perm.eq_singleton" -> "data", "eq_iff_iff" -> "logic", "hyperreal.infinite_pos_mul_infinite_neg" -> "data", "has_fpower_series_at.radius_pos" -> "analysis", "hyperreal.not_real_of_infinite" -> "data", "category_theory.unop_id" -> "category_theory", "function.involutive.right_inverse" -> "logic", "pgame.add_move_right_inl" -> "set_theory", "bounded_continuous_function.forall_coe_zero_iff_zero" -> "topology", "measure_theory.l1.simple_func.coe_sub" -> "analysis", "lt_of_neg_of_one_div_lt_one_div" -> "algebra", "real.log_exp" -> "analysis", "cau_seq.const_lt" -> "data", "set.indicator_empty" -> "data", "pfun.pure_defined" -> "data", "has_fderiv_at.differentiable_at" -> "analysis", "mul_lt_one_of_nonneg_of_lt_one_right" -> "algebra", "mul_semiring_action_hom.map_smul" -> "algebra", "lt_add_of_lt_of_nonneg'" -> "algebra", "equiv.perm.is_cycle_swap_mul_aux\:2081" -> "algebra", "set.image_sub_const_Iic" -> "data", "mem_nhds_sets" -> "topology", "pnat.mk_lt_mk" -> "data", "hyperreal.epsilon_mul_omega" -> "data", "nhds_prod_eq" -> "topology", "category_theory.under.post_map_left" -> "category_theory", "ext_chart_at_to_inv" -> "geometry", "category_theory.uncurry.obj_obj" -> "category_theory", "hyperreal.infinitesimal_neg" -> "data", "polynomial.leading_coeff_X" -> "data", "lcm_dvd_lcm" -> "algebra", "mv_polynomial.total_degree_multiset_prod" -> "data", "multiset.mem_pmap" -> "data", "separated_equiv" -> "topology", "model_with_corners.left_inv'" -> "geometry", "filter.frequently_principal" -> "order", "pfun.mem_dom" -> "data", "pequiv.matrix_mul_apply" -> "data", "asymptotics.is_O_fst_prod" -> "analysis", "add_left_neg" -> "algebra", "linear_map.comap_injective" -> "algebra", "int.succ_pred" -> "data", "fin.find_min" -> "data", "filter.eventually_eq.deriv_eq" -> "analysis", "linear_order.ext" -> "order", "computation.results_of_terminates" -> "data", "mul_inv_le_of_le_mul" -> "algebra", "multiplicative.is_subgroup" -> "algebra", "list.mfoldl_nil" -> "data", "finset.map_filter" -> "data", "interval_integral.deriv_within_integral_of_tendsto_ae_left" -> "analysis", "list.filter_congr" -> "data", "interval_integral.integral_has_deriv_within_at_of_tendsto_ae_left" -> "analysis", "submodule.subtype_comp_of_le" -> "algebra", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_map_hom_app" -> "category_theory", "free_comm_ring.is_supported_upwards" -> "algebra", "exists_compact_superset" -> "topology", "add_commute.neg_left_iff" -> "algebra", "category_theory.non_preadditive_abelian.coimage.fac" -> "category_theory", "equiv.refl_symm" -> "data", "list.func.equiv_of_eq" -> "data", "filter.mem_infi_finite'" -> "order", "is_subgroup.mul_mem_cancel_right" -> "algebra", "category_theory.comonad.cofree_obj_A" -> "category_theory", "linear_map.map_sub" -> "algebra", "filter.comap_inf" -> "order", "filter.mem_rcomap'" -> "order", "midpoint_sub_left" -> "algebra", "cmp_swap" -> "algebra", "localization_map.ext_iff" -> "algebra", "circle_deg1_lift.coe_mk" -> "dynamics", "multiset.le_ndinsert_self" -> "data", "differentiable_on.div_const" -> "analysis", "lipschitz_with_iff_dist_le_mul" -> "topology", "setoid.symm" -> "init", "set.mem_bUnion" -> "data", "cardinal.ord_le_ord" -> "set_theory", "quotient.lift_on_beta\:2082" -> "data", "finset.inter_self" -> "data", "real.is_conjugate_exponent.conj_eq" -> "data", "prime_spectrum.zero_locus_inf" -> "algebraic_geometry", "int.div_mul_cancel_of_mod_eq_zero" -> "data", "compl_sup" -> "order", "bounded_continuous_function.coe_const" -> "topology", "list.nil_eq_append_iff" -> "data", "differentiable.csin" -> "analysis", "nat.lt_of_succ_lt" -> "init", "array.rev_list_foldr_aux" -> "data", "is_R_or_C.ext" -> "data", "rat.zero_iff_num_zero" -> "data", "matrix.map_zero" -> "data", "dist_le_of_trajectories_ODE" -> "analysis", "finset.weighted_vsub_of_point_indicator_subset" -> "algebra", "int.neg_succ_of_nat_of_nat" -> "init", "nat.not_succ_lt_self" -> "data", "int.neg_le_of_neg_le" -> "init", "function.semiconj.maps_to_range" -> "data", "ordinal.CNF_fst_le" -> "set_theory", "list.enum_from_map_snd" -> "data", "finsupp.map_domain_single" -> "data", "is_integral_iff_is_integral_closure_finite" -> "algebra", "list.func.pointwise_nil" -> "data", "lipschitz_with.edist_le_mul" -> "topology", "rat.num_div_eq_of_coprime" -> "data", "polynomial.eval\:2082_eq_eval_map" -> "data", "circle_deg1_lift.translation_number_le_of_le_add" -> "dynamics", "int.sub_lt_of_sub_lt" -> "init", "list.nth_of_mem" -> "data", "int.zero_shiftr" -> "data", "list.drop_append_of_le_length" -> "data", "free_group.red.nil_iff" -> "algebra", "exists_pos_add_of_lt" -> "algebra", "submodule.ext" -> "algebra", "submodule.prod_mono" -> "algebra", "has_strict_fderiv_at.prod" -> "analysis", "category_theory.limits.coprod.inr_desc" -> "category_theory", "pure_id_seq" -> "init", "computation.mem_of_get_eq" -> "data", "with_bot.coe_le_coe" -> "order", "lagrange.interpolate_add" -> "algebra", "not_not_of_not_imp" -> "logic", "category_theory.monad.forget_creates_colimits.lifted_cocone_is_colimit_desc_f" -> "category_theory", "is_coprime.add_mul_right_left_iff" -> "algebra", "category_theory.op_op_obj" -> "category_theory", "vector.eq" -> "data", "mv_power_series.coeff_one" -> "algebra", "category_theory.limits.coequalizer.\[Pi]_desc_assoc" -> "category_theory", "times_cont_diff_within_at.prod_map" -> "analysis", "polynomial.splitting_field.splits" -> "algebra", "set.Icc_union_Ico_eq_Ico" -> "data", "free_group.red.singleton_iff" -> "algebra", "ring_hom.coe_srange" -> "algebra", "dfinsupp.subtype_domain_def" -> "data", "measure_theory.lintegral_nnnorm_eq_lintegral_edist" -> "analysis", "dfinsupp.sum_neg_index" -> "data", "multiset.le_ndunion_right" -> "data", "mv_power_series.constant_coeff_X" -> "algebra", "add_monoid_hom.map_int_cast_smul" -> "algebra", "finset.map_singleton" -> "data", "dvd_add_self_right" -> "algebra", "category_theory.functor.right_op_map" -> "category_theory", "continuous_within_at_of_not_mem_closure" -> "topology", "interval_integral.integral_cases" -> "analysis", "free_monoid.mul_def" -> "algebra", "list.sublists_len_aux_zero" -> "data", "complex.inv_im" -> "data", "nnreal.continuous_sub" -> "topology", "category_theory.Kleisli.id_def" -> "category_theory", "asymptotics.is_O.trans" -> "analysis", "is_noetherian_of_linear_equiv" -> "algebra", "prod_pow_prime_padic_val_nat" -> "data", "finsupp.total_on_range" -> "algebra", "finset.powerset_insert" -> "data", "nat.dvd_of_mod_eq_zero" -> "init", "no_top" -> "order", "measure_theory.ae_eq_fun.coe_fn_one" -> "analysis", "list.perm_lookup" -> "data", "turing.TM0.univ_supports" -> "computability", "has_sum_mul_right_iff" -> "topology", "category_theory.monoidal_category.tensor_right_iff" -> "category_theory", "open_subgroup.inv_mem" -> "topology", "int.le_refl" -> "init", "finset.sum_range_induction" -> "algebra", "measure_theory.outer_measure.top_apply" -> "analysis", "neg_eq_zero" -> "algebra", "composition.eq_single_iff" -> "combinatorics", "has_fderiv_at.prod_map" -> "analysis", "mul_le_iff_le_one_right" -> "algebra", "add_monoid_hom.range_top_of_surjective" -> "algebra", "fintype.one_lt_card_iff_nontrivial" -> "data", "topological_space.open_nhds.inclusion_map_iso_hom" -> "topology", "list.append_bind" -> "init", "list.nodup_cons" -> "data", "mem_gpowers_iff_mem_range_order_of" -> "algebra", "associates.factors_prod" -> "algebra", "finsupp.single_swap" -> "data", "sum.swap_left_inverse" -> "data", "seq.join_cons_cons" -> "data", "relation.refl_trans_gen.trans_induction_on" -> "logic", "measurable_space.dynkin_system.of_measurable_space_le_of_measurable_space_iff" -> "analysis", "generalized_continued_fraction.nth_cont_eq_succ_nth_cont_aux" -> "algebra", "list.mem_insert_of_mem" -> "data", "lucas_lehmer.X.coe_mul" -> "number_theory", "ordinal.CNF_rec_zero" -> "set_theory", "cau_seq.completion.of_rat_add" -> "data", "nat.bit0_lt_bit1_iff" -> "data", "pfun.mem_core_res" -> "data", "category_theory.monad.comparison_obj_a" -> "category_theory", "gaussian_int.mod_def" -> "data", "semiquot.bind_def" -> "data", "submonoid.closure_empty" -> "algebra", "polynomial.mul_X_pow_eq_zero" -> "data", "list.foldr_map'" -> "data", "inf_le_left_of_le" -> "order", "pell.xy_modeq_of_modeq" -> "number_theory", "hash_map.find_insert" -> "data", "linear_map.mul_eq_one_comm" -> "algebra", "max_add_add_right" -> "algebra", "formal_multilinear_series.change_origin_radius" -> "analysis", "is_local_min_on_const" -> "topology", "filter.ne_bot.mono" -> "order", "ennreal.tsum_eq_top_of_eq_top" -> "topology", "mem_nhds_unbounded" -> "topology", "finset.sep_def" -> "data", "nat.fact_mul_fact_dvd_fact" -> "data", "real.mk_near_of_forall_near" -> "data", "finset.union_assoc" -> "data", "nnreal.mul_sup" -> "data", "mv_power_series.is_unit_constant_coeff" -> "algebra", "free_magma.map_mul'" -> "algebra", "exists_unique.intro2" -> "logic", "lie_subalgebra.mem_map_submodule" -> "algebra", "vector.head_of_fn" -> "data", "set.Icc_subset_Icc_right" -> "data", "set.image_swap_prod" -> "data", "finset.card_le_mul_card_image" -> "algebra", "div_add_div_same" -> "algebra", "add_con.inf_iff_and" -> "algebra", "Gromov_Hausdorff.GH_dist_eq_Hausdorff_dist" -> "topology", "mv_polynomial.rename_eval\:2082" -> "data", "metric.is_open_iff" -> "topology", "add_localization.induction_on" -> "algebra", "nhds_within_Ioc_eq_nhds_within_Ioi" -> "topology", "is_max_on.min" -> "order", "abelianization.lift.unique" -> "algebra", "complex.cos_pi_div_two" -> "analysis", "complex.bit0_im" -> "data", "subgroup.le_normalizer" -> "algebra", "category_theory.limits.pullback_cone.condition" -> "category_theory", "nat.mul_div_cancel_left" -> "init", "affine_map.homothety_add" -> "algebra", "abs_neg_one_pow" -> "algebra", "dvd_neg_of_dvd" -> "algebra", "set.finite_le_nat" -> "data", "int.add_le_of_le_sub_left" -> "init", "semiconj_by.one_left" -> "algebra", "submonoid.map_strict_mono_of_injective" -> "algebra", "polynomial.support_integral_normalization" -> "data", "sum.forall" -> "data", "inv.is_add_group_hom" -> "algebra", "add_submonoid.mem_closure_singleton" -> "algebra", "continuous_map.continuous_ev" -> "topology", "subset_sequential_closure" -> "topology", "unique_diff_on_empty" -> "analysis", "real.rpow_lt_one" -> "analysis", "complex.deriv_exp" -> "analysis", "fintype.card_pi" -> "data", "continuous_linear_map.proj_pi" -> "topology", "option.not_is_some" -> "data", "nat.lt_mul_of_div_lt" -> "data", "relation.reflexive_join" -> "logic", "list.nodupkeys_erase_dupkeys" -> "data", "filter.inf_eq_bot_iff" -> "order", "metric.inf_dist_zero_of_mem" -> "topology", "category_theory.limits.image.lift_fac" -> "category_theory", "circle_deg1_lift.translation_number_eq_of_tendsto_aux" -> "dynamics", "add_submonoid.localization_map.add_equiv_of_localizations_left_neg_apply" -> "algebra", "free_group.red.cons_cons_iff" -> "algebra", "reader_t.run_monad_map" -> "init", "sub_pos_of_lt" -> "algebra", "filter.germ.const_abs" -> "order", "lt_one_add" -> "algebra", "tactic.abel.term_add_constg" -> "tactic", "inv_eq_of_mul_eq_one" -> "algebra", "dist_le_norm_add_norm" -> "analysis", "hash_map.contains_iff" -> "data", "category_theory.limits.im_map" -> "category_theory", "matrix.diagonal_map" -> "data", "irreducible.not_unit" -> "algebra", "polynomial.derivative_zero" -> "data", "linear_equiv.map_sub" -> "algebra", "lie_algebra.map_lie" -> "algebra", "matrix.smul_eq_diagonal_mul" -> "data", "local_homeomorph.continuous_on" -> "topology", "mv_polynomial.total_degree_one" -> "data", "homeomorph.homeomorph_mk_coe_symm" -> "topology", "multiset.nodup_pi" -> "data", "is_lub.upper_bounds_eq" -> "order", "semidirect_product.inv_right" -> "algebra", "list.subset_of_cons_subset" -> "init", "polynomial.splits_of_is_unit" -> "algebra", "multiset.nodup_zero" -> "data", "set.ord_connected_of_Ioo" -> "data", "convex_cone.ext'_iff" -> "analysis", "valuation.is_equiv.trans" -> "algebra", "category_theory.iso.conj_comp" -> "category_theory", "lists.is_list_to_list" -> "set_theory", "list.kunion_nil" -> "data", "units.mul_inv_of_eq" -> "algebra", "complex.I_re" -> "data", "computation.get_eq_of_mem" -> "data", "topological_space.first_countable_topology.tendsto_subseq" -> "topology", "set.subset_of_mem_powerset" -> "data", "category_theory.over.creates_connected.raise_cone_X" -> "category_theory", "linear_equiv.skew_prod_apply" -> "algebra", "add_monoid_hom.eq_of_eq_on_mtop" -> "algebra", "primrec.vector_tail" -> "computability", "list.index_of_of_not_mem" -> "data", "uniform_space.separated_of_uniform_continuous" -> "topology", "is_R_or_C.I_im" -> "data", "subring.mem_closure" -> "algebra", "nat.partrec.code.evaln_bound" -> "computability", "subgroup.bot_normal" -> "algebra", "matrix.reindex_linear_equiv_symm_apply" -> "algebra", "matrix.vec_mul_vec_cons" -> "data", "filter.prod_comm'" -> "order", "set.right_inv_on.comp" -> "data", "is_coprime.add_mul_left_left_iff" -> "algebra", "int.of_nat_mod" -> "data", "cond_a_a" -> "init", "fish_assoc" -> "control", "set.image_preimage" -> "data", "measure_theory.measure.haar.index_union_eq" -> "analysis", "homeomorph.dense_embedding" -> "topology", "list.reverse_range'" -> "data", "filter.eventually_eq.comp_tendsto" -> "order", "trans_trichotomous_left" -> "order", "fish_pure" -> "control", "list.nth_le_zero" -> "data", "add_subgroup.coe_infi" -> "algebra", "equiv.refl_to_local_equiv" -> "data", "list.mem_bind" -> "data", "function.commute.comp_right" -> "logic", "set.Union_mul_right_image" -> "algebra", "list.head_mul_tail_prod'" -> "data", "finite_dimensional.proper" -> "analysis", "multiset.dvd_prod" -> "data", "set.image_neg_Icc" -> "data", "is_linear_map.is_linear_map_smul'" -> "algebra", "set.inter_union_diff" -> "data", "wseq.join_join" -> "data", "continuous_subtype_mk" -> "topology", "uniform_space.separation_quotient.map_comp" -> "topology", "list.tail_append_singleton_of_ne_nil" -> "data", "exists_vector_zero" -> "number_theory", "segment_eq_Icc'" -> "analysis", "sym2.from_rel_prop" -> "data", "eventually_nhds_within_iff" -> "topology", "category_theory.limits.cones.ext_hom_hom" -> "category_theory", "is_R_or_C.conj_bijective" -> "data", "cardinal.aleph'_le_of_limit" -> "set_theory", "category_theory.abelian.pseudoelement.pseudo_zero_def" -> "category_theory", "times_cont_diff_on.sub" -> "analysis", "omega.coeffs.val_neg" -> "tactic", "free_group.reduce.eq_of_red" -> "algebra", "is_closed.closure_subset_iff" -> "topology", "seq.corec_eq" -> "data", "monotone.iterate" -> "order", "nat.shiftl_zero" -> "init", "finset.subset_def" -> "data", "fin.tail_cons" -> "data", "topological_fiber_bundle_core.open_target'" -> "topology", "submonoid.comap_sup_map_of_injective" -> "algebra", "rescale_to_shell" -> "analysis", "category_theory.prod_preserves_connected_limits.forget_cone_\[Pi]" -> "category_theory", "finsupp.support_curry" -> "data", "exp_neg_inv_glue.f_aux_zero_eq" -> "analysis", "fin.comp_tail" -> "data", "discriminant_lt_zero" -> "algebra", "enat.add_one_le_of_lt" -> "data", "topological_space.compacts.finset_sup_val" -> "topology", "mk_eq_mk_of_basis" -> "algebra", "ordinal.le_lift_iff" -> "set_theory", "category_theory.of_type_functor_map" -> "category_theory", "finset.sum_image'" -> "algebra", "set.insert_eq_of_mem" -> "data", "add_monoid.closure_mono" -> "algebra", "matrix_is_adjoint_pair_bilin_form" -> "algebra", "set.preimage_mul_const_Ici_of_neg" -> "data", "cardinal.cantor_function_injective" -> "data", "set.singleton_subset_iff" -> "data", "int.sign_eq_neg_one_of_neg" -> "init", "fderiv_const" -> "analysis", "polynomial.leading_coeff_mul" -> "data", "zmod.nat_abs_mod_two" -> "data", "mul_self_nonneg" -> "algebra", "equiv.set.of_eq_symm_apply" -> "data", "measure_theory.measure.haar_measure_apply" -> "analysis", "multiset.mem_pi" -> "data", "int.add_mod_eq_add_mod_left" -> "data", "list.length_product" -> "data", "omega.nat.preform.sat_of_implies_of_sat" -> "tactic", "finsupp.support_single_ne_zero" -> "data", "nnreal.rpow_neg" -> "analysis", "list.perm.bind_left" -> "data", "matrix.is_skew_adjoint_bracket" -> "algebra", "category_theory.nat_iso.cancel_nat_iso_hom_right" -> "category_theory", "free_comm_ring.is_supported_add" -> "algebra", "norm_image_sub_le_of_norm_deriv_right_le_segment" -> "analysis", "set.subset.antisymm" -> "data", "has_fderiv_at_filter.const_smul" -> "analysis", "nat.min_fac_le_div" -> "data", "filter.map_comap_of_surjective" -> "order", "category_theory.split_epi.id_assoc" -> "category_theory", "has_strict_fderiv_at_const" -> "analysis", "finset.sizeof_lt_sizeof_of_mem" -> "data", "hyperreal.is_st_real_iff_eq" -> "data", "norm_num.clear_denom_div" -> "tactic", "polynomial.ext_iff" -> "data", "differentiable_at.const_sub" -> "analysis", "complex.arg_zero" -> "analysis", "nat.size_shiftl" -> "data", "homeomorph.is_o_congr" -> "analysis", "symmetric_rel_inter" -> "topology", "nat.eq_of_test_bit_eq" -> "data", "nat.find_greatest_of_not" -> "data", "has_sum_iff_tendsto_nat_of_nonneg" -> "topology", "ennreal.tendsto_inv_iff" -> "topology", "sub_eq_add_neg" -> "algebra", "is_R_or_C.re_sq_le_norm_sq" -> "data", "finset.sum_Ico_eq_add_neg" -> "algebra", "fin.coe_mk" -> "data", "fderiv_zero_of_not_differentiable_at" -> "analysis", "filter.ultrafilter_pure" -> "order", "nat.mul_lt_mul" -> "init", "computation.bind_promises" -> "data", "borel_comap" -> "analysis", "open_subgroup.mem_coe_subgroup" -> "topology", "real.mk_pos" -> "data", "pnat.coprime.mul" -> "data", "times_cont_diff.prod_map" -> "analysis", "finset.inter_filter" -> "data", "monotone_mul_left_of_nonneg" -> "algebra", "list.length_injective_iff" -> "data", "subsemiring.forall" -> "algebra", "equiv.sum_assoc_apply_in3" -> "data", "zero_ne_one" -> "algebra", "int.nat_cast_eq_coe_nat" -> "data", "model_with_corners.continuous_symm" -> "geometry", "psigma.eq" -> "init", "finsupp.le_def" -> "data", "linear_map.inl_eq_prod" -> "algebra", "set.maps_to_Inter_Inter" -> "data", "add_lt_add_left" -> "algebra", "multiset.powerset_zero" -> "data", "equiv.perm.swap_mul_swap_mul_swap" -> "algebra", "continuous_linear_map.coe_comp" -> "topology", "lipschitz_with.id" -> "topology", "int.le_sub_left_of_add_le" -> "init", "int.coe_succ_pos" -> "init", "set_coe.ext" -> "data", "centroid_mem_affine_span_of_card_eq_add_one" -> "algebra", "category_theory.pi.comap_id_hom_app" -> "category_theory", "sesq_form.sub_left" -> "algebra", "sigma.mk.inj_iff" -> "data", "metric.completion.uniformity_dist" -> "topology", "power_series.constant_coeff_C" -> "algebra", "is_basis_inl_union_inr" -> "algebra", "set.bInter_empty" -> "data", "function.right_inverse.iterate" -> "logic", "matrix.special_linear_group.one_val" -> "algebra", "list.self_mem_range_succ" -> "data", "category_theory.functor.op_obj" -> "category_theory", "nat.add_div" -> "data", "is_unit_int" -> "algebra", "multiset.nodup_attach" -> "data", "list.map_foldl_erase" -> "data", "AddGroup.coe_of" -> "algebra", "is_subgroup_Union_of_directed" -> "algebra", "list.prod_of_fn" -> "data", "category_theory.limits.biproduct.\[Iota]_\[Pi]_self" -> "category_theory", "filter.lift'_inf_principal_eq" -> "order", "dist_triangle" -> "topology", "homeomorph.trans_to_local_homeomorph" -> "topology", "category_theory.monoidal_of_has_finite_products.left_unitor_hom" -> "category_theory", "finsupp.to_multiset_map" -> "data", "dlist.to_list_of_list" -> "data", "measure_theory.simple_func.fin_meas_supp_iff" -> "analysis", "int.nat_succ_eq_int_succ" -> "data", "finset.prod_map" -> "algebra", "set.compl_empty" -> "data", "finset.inter_subset_right" -> "data", "ennreal.add_lt_add" -> "data", "measure_theory.measure.join_map_join" -> "analysis", "prod.map_mk" -> "data", "univ_eq_singleton_of_card_one" -> "data", "category_theory.nat_trans.id_app" -> "category_theory", "set.union_distrib_Inter_right" -> "data", "zsqrtd.nonneg_cases" -> "data", "set.disjoint_of_subset_left" -> "data", "submonoid.map_infi_comap_of_surjective" -> "algebra", "is_add_submonoid.list_sum_mem" -> "algebra", "ring_hom.eq_int_cast'" -> "data", "tendsto.min" -> "topology", "ennreal.mul_left_mono" -> "data", "finsupp.support_inf" -> "data", "pow_mul_comm'" -> "algebra", "finsupp.eval_add_hom_apply" -> "data", "finset.prod_Ico_succ_top" -> "algebra", "exists_rat_gt" -> "algebra", "nat.bit1_ne" -> "init", "metric.diam_eq_zero_of_unbounded" -> "topology", "closure_Ioi'" -> "topology", "continuous_linear_map.is_bounded_linear_map_comp_left" -> "analysis", "list.foldl_map" -> "data", "function.nmem_support" -> "data", "self_le_neg" -> "algebra", "ennreal.of_real_lt_of_real_iff_of_nonneg" -> "data", "convex_Inter" -> "analysis", "multiset.sup_add" -> "data", "set.diff_diff_comm" -> "data", "interior_Iio" -> "topology", "measure_theory.set_integral_const" -> "analysis", "to_topological_space_comap" -> "topology", "is_group_hom.trivial_ker_of_injective" -> "algebra", "and.elim" -> "init", "times_cont_diff_on.sum" -> "analysis", "analytic_at.sub" -> "analysis", "stream.drop_succ" -> "data", "function.inv_fun_comp" -> "logic", "padic_norm.padic_norm_p_lt_one" -> "data", "filter.pure_seq_eq_map" -> "order", "differentiable_on.add" -> "analysis", "continuous_linear_map.sub_apply'" -> "topology", "set.diff_eq" -> "data", "unique.exists_iff" -> "logic", "inner_product_space.of_core.inner_self_eq_norm_square" -> "analysis", "nat.cast_ite" -> "data", "canonically_ordered_semiring.pow_le_pow_of_le_left" -> "algebra", "padic_int.coe_zero" -> "data", "set.Ioc_union_Ioc_left" -> "data", "mv_polynomial.coe_monomial" -> "algebra", "padic_norm_e.eq_padic_norm" -> "data", "quadratic_form.polar_smul" -> "algebra", "forall_elim_eq_left" -> "tactic", "continuous_le_dom" -> "topology", "submodule.coe_eq_coe" -> "algebra", "pi.ring_hom_apply" -> "algebra", "category_theory.has_hom.hom.unop_op" -> "category_theory", "nat.prime.multiplicity_pow_self" -> "data", "galois_connection.compose" -> "order", "has_fderiv_within_at_inter" -> "analysis", "smooth_const" -> "geometry", "zero_lt_iff" -> "algebra", "zero_le_one'" -> "algebra", "power_series.coeff_zero_one" -> "algebra", "interval_integral.fderiv_integral" -> "analysis", "semidirect_product.one_left" -> "algebra", "list.length_permutations" -> "data", "multiset.filter_cons_of_pos" -> "data", "set.mem_smul_set" -> "algebra", "alist.lookup_eq_none" -> "data", "set.mem_image3" -> "data", "list.erasep_append_left" -> "data", "category_theory.limits.biprod.inl_map_assoc" -> "category_theory", "of_not_not" -> "logic", "uniform_space.separation_quotient.map_id" -> "topology", "polynomial.monomial_one_eq_X_pow" -> "data", "ideal.integral_closure.comap_ne_bot" -> "algebra", "with_top.lt_iff_exists_coe" -> "order", "list.any_nil" -> "data", "category_theory.limits.pullback_cone.mk_\[Pi]_app_one" -> "category_theory", "ennreal.rpow_le_rpow_of_exponent_ge" -> "analysis", "finset.card_powerset" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence.counit_iso_hom_app_app_hom" -> "category_theory", "submodule.span_eq_bot" -> "algebra", "ordinal.div_self" -> "set_theory", "AddCommGroup.as_hom_apply" -> "algebra", "symm_trans_mem_times_cont_diff_groupoid" -> "geometry", "times_cont_diff_on.comp'" -> "analysis", "alg_hom.coe_ring_hom_injective" -> "algebra", "measure_theory.ae_eq_fun.comp_mk" -> "analysis", "submodule.comap_infi" -> "algebra", "set.singleton_prod" -> "data", "div_eq_inv_mul" -> "algebra", "measure_theory.measure.haar_outer_measure_exists_open" -> "analysis", "local_equiv.of_set_coe" -> "data", "filter.add_le_add" -> "order", "is_open_coinduced" -> "topology", "set.Ioc_subset_Ioc" -> "data", "measure_theory.integral_eq_lintegral_max_sub_lintegral_min" -> "analysis", "cardinal.mk_Iic_real" -> "data", "is_noetherian_ring_closure" -> "algebra", "is_basis.to_dual_ker" -> "algebra", "complex.sin_add_pi_div_two" -> "analysis", "nat.galois_connection_mul_div" -> "order", "category_theory.coev_ev_assoc" -> "category_theory", "linear_equiv.uniform_embedding" -> "analysis", "real.sin_sub_sin" -> "analysis", "affine_subspace.le_def" -> "algebra", "cardinal.prod_le_prod" -> "set_theory", "setoid.lift_unique" -> "data", "finset.prod_subset" -> "algebra", "localization_map.mk'_add" -> "algebra", "category_theory.limits.cokernel.condition_assoc" -> "category_theory", "ext_chart_at_coe" -> "geometry", "equiv.coe_refl" -> "data", "nonneg_add_comm_group.pos_def" -> "algebra", "set.union_distrib_right" -> "data", "nnreal.coe_Sup" -> "data", "dim_span_set" -> "algebra", "padic_seq.norm_nonarchimedean" -> "data", "category_theory.comma.id_right" -> "category_theory", "mv_polynomial.eval\:2082_X" -> "data", "ring.fractional_ideal.mem_coe" -> "algebra", "measure_theory.l1.simple_func.integral_add" -> "analysis", "relation.eqv_gen_mono" -> "logic", "category_theory.biprod.of_components_comp" -> "category_theory", "nat.even_iff" -> "data", "real.abs_log_sub_add_sum_range_le" -> "analysis", "convex_on.convex_le" -> "analysis", "with_zero.mul_inv_cancel" -> "algebra", "function.injective2.eq_iff" -> "logic", "cardinal.one_le_bit1" -> "set_theory", "norm_num.adc_one_bit1" -> "tactic", "inner_product_geometry.sin_angle_add_angle_sub_add_angle_sub_eq_zero" -> "geometry", "set.compl_singleton_eq" -> "data", "is_complete_image_iff" -> "topology", "continuous_multilinear_map.continuous_eval_left" -> "analysis", "category_theory.induct_on_objects" -> "category_theory", "is_trans.swap" -> "order", "filter.comap_mul_comap_le" -> "order", "local_equiv.eq_on_source.restr" -> "data", "nnreal.lt_iff_exists_rat_btwn" -> "data", "finset.mem_coe" -> "data", "nat.zero_add" -> "init", "ideal.map_inf_comap_of_surjective" -> "algebra", "lucas_lehmer.X.bit1_snd" -> "number_theory", "filter.comap_const_of_not_mem" -> "order", "multilinear_map.map_sum_finset_aux" -> "algebra", "monotone.le_map_supr2" -> "order", "category_theory.monoidal.tensor_unit_obj" -> "category_theory", "set.preimage_mul_left_one'" -> "algebra", "one_le_pow_iff" -> "algebra", "equiv.prod_assoc_apply" -> "data", "nat.sub_add_cancel" -> "init", "list.head_add_tail_sum" -> "data", "Sup_image" -> "order", "set.singleton_eq_singleton_iff" -> "data", "category_theory.limits.fork.is_limit.hom_ext" -> "category_theory", "euclidean_geometry.angle_add_angle_eq_pi_of_angle_eq_pi" -> "geometry", "is_bounded_bilinear_map.map_sub_right" -> "analysis", "mv_power_series.inv_of_unit_eq" -> "algebra", "has_fderiv_within_at.congr" -> "analysis", "measure_theory.simple_func.const_lintegral" -> "analysis", "category_theory.prod.associator_map" -> "category_theory", "uniform_space.uniform_continuous_quotient_lift\:2082" -> "topology", "norm_neg" -> "analysis", "category_theory.monoidal_category.left_assoc_tensor_obj" -> "category_theory", "complex.norm_sq_mul" -> "data", "int.neg_succ_mul_neg_succ" -> "data", "nat.bit_ff" -> "data", "quotient.induction_on'" -> "data", "measure_theory.outer_measure.of_content_pos_of_is_open" -> "analysis", "list.sum_take_map_length_lt1" -> "data", "matrix.add_mul" -> "data", "ordinal.bsup_type" -> "set_theory", "set.countable.sUnion" -> "data", "rel_embedding.is_partial_order" -> "order", "pfun.lift_graph" -> "data", "affine_subspace.direction_le" -> "algebra", "set.finite_of_finite_image" -> "data", "enorm.map_add_le" -> "analysis", "mv_polynomial.coeff_mul_X" -> "data", "minimal_polynomial.algebra_map" -> "algebra", "is_local_max.max" -> "topology", "set.image_const_add_Icc" -> "data", "inf_of_le_left" -> "order", "compl_Sup" -> "order", "pnat.bit0_le_bit1" -> "data", "measure_theory.lintegral_rw\:2081" -> "analysis", "contracting_with.tendsto_iterate_efixed_point'" -> "topology", "of_add_add" -> "algebra", "list.rotate'_nil" -> "data", "linear_pmap.mk_apply" -> "algebra", "four_pos" -> "algebra", "tendsto_uniformly_on.comp" -> "topology", "fin.snoc_init_self" -> "data", "is_integral_sub" -> "algebra", "is_totally_separated_empty" -> "topology", "set.Ico_subset_Ico_right" -> "data", "has_sum.unique" -> "topology", "set.preimage_comp" -> "data", "add_subgroup.is_open_mono" -> "topology", "composition.length_le" -> "combinatorics", "measure_theory.nonempty_of_measure_ne_zero" -> "analysis", "cardinal.cantor_function_aux_ff" -> "data", "filter.mem_of_finite_Union_ultrafilter" -> "order", "is_noetherian_submodule_right" -> "algebra", "bnot_bnot" -> "init", "times_cont_diff_at_const" -> "analysis", "exists_unique.unique2" -> "logic", "pow_le_pow_of_le_left" -> "algebra", "qpf.cofix.bisim" -> "data", "quot.indep_coherent" -> "init", "closure_eq_compl_interior_compl" -> "topology", "set.preimage_const_of_not_mem" -> "data", "open_embedding.to_local_equiv_target" -> "topology", "set.Ico_subset_Ico_iff" -> "data", "measurable_space.dynkin_system.has_univ" -> "analysis", "num.pred_to_nat" -> "data", "map_nonunit" -> "algebra", "pgame.domineering.card_of_mem_right" -> "set_theory", "valuation.map_one" -> "algebra", "tendsto_list_sum" -> "topology", "power_series.coeff_order" -> "algebra", "set.Ici_subset_Icc_union_Ici" -> "data", "rec_subsingleton" -> "init", "fderiv_inv" -> "analysis", "band_tt" -> "init", "onote.NF_below.repr_lt" -> "set_theory", "dvd_symm_of_irreducible" -> "algebra", "ennreal.div_le_of_le_mul" -> "data", "cont_t.ext" -> "control", "finite_dimensional.eq_of_le_of_findim_eq" -> "algebra", "real.rpow_sub'" -> "analysis", "infi_insert" -> "order", "finset.mem_union_right" -> "data", "has_deriv_at_of_has_deriv_at_of_ne" -> "analysis", "inner_smul_right" -> "analysis", "complex.sin_pi_div_two_sub" -> "analysis", "free_magma.pure_seq" -> "algebra", "pow_abs" -> "algebra", "abs_le" -> "algebra", "pell.pell_zd_re" -> "number_theory", "measure_theory.ae_eq_fun.to_germ_eq" -> "analysis", "valuation.is_equiv.refl" -> "algebra", "nat.find_greatest_eq" -> "data", "mv_polynomial.coeff_coe" -> "algebra", "ring.fractional_ideal.bot_eq_zero" -> "algebra", "nhds_within_Iio_self_ne_bot'" -> "topology", "category_theory.image_to_kernel_map_epi_of_zero_of_mono" -> "algebra", "or_self" -> "init", "convex_on_fpow" -> "analysis", "is_order_right_adjoint.unique" -> "order", "euclidean_domain.gcd_one_left" -> "algebra", "linear_equiv.apply_symm_apply" -> "algebra", "sub_neg_of_lt" -> "algebra", "bool.to_bool_eq" -> "data", "polynomial.exists_multiset_of_splits" -> "algebra", "set.sUnion_range" -> "data", "semiconj_by.one_right" -> "algebra", "zmod.ring_hom_eq_of_ker_eq" -> "data", "cardinal.aleph'_le" -> "set_theory", "submodule.is_principal.mem_iff_eq_smul_generator" -> "algebra", "list.forall_mem_pw_filter" -> "data", "poly_equiv_tensor.inv_fun_add" -> "algebra", "convex_Ici" -> "analysis", "polynomial.degree_separable_eq_card_roots" -> "algebra", "relation.refl_trans_gen.single" -> "logic", "pgame.move_left_right_moves_neg" -> "set_theory", "divp_mk0" -> "algebra", "sesq_form.add_left" -> "algebra", "divp_mul_divp" -> "algebra", "neg_add_le_iff_le_add" -> "algebra", "prod.fst_sub" -> "algebra", "Gromov_Hausdorff.to_GH_space_eq_to_GH_space_iff_isometric" -> "topology", "prod.exists" -> "data", "real.angle.coe_neg" -> "analysis", "finsupp.sub_apply" -> "data", "primrec.nat_div2" -> "computability", "ideal.map_inf_le" -> "algebra", "with_top.coe_eq_coe" -> "order", "smodeq.comap" -> "algebra", "real.sinh_arsinh" -> "analysis", "multiset.nodup_inter_right" -> "data", "real.norm_two" -> "analysis", "num.of_nat_inj" -> "data", "complex.abs_exp_eq_iff_re_eq" -> "data", "is_null_measurable_iff" -> "analysis", "nat.one_le_bit0_iff" -> "data", "module.direct_limit.exists_of" -> "algebra", "is_min_on.bicomp_mono" -> "order", "has_strict_fderiv_at.prod_map" -> "analysis", "finmap.empty_to_finmap" -> "data", "category_theory.nat_trans.id_app'" -> "category_theory", "monoid_algebra.single_mul_single" -> "data", "matrix.dot_product_add" -> "data", "initial_seg.cod_restrict_apply" -> "set_theory", "equiv.mul_def" -> "data", "local_homeomorph.map_target" -> "topology", "is_add_subgroup.gsmul_mem" -> "algebra", "ennreal.bit0_eq_top_iff" -> "data", "lt_sub" -> "algebra", "fin.mk_val" -> "data", "nat.div_le_div_right" -> "data", "cinfi_const" -> "order", "ring.fractional_ideal.fractional_div_of_nonzero" -> "algebra", "units.inv_mul_cancel_right" -> "algebra", "emetric.diam_closed_ball" -> "topology", "isometric.point_reflection_involutive" -> "analysis", "Gromov_Hausdorff.HD_below_aux2" -> "topology", "vector_allp_singleton" -> "number_theory", "module.ker_algebra_map_End" -> "algebra", "list.mem_pure" -> "data", "ite_pow" -> "algebra", "prime_multiset.to_of_pnat_multiset" -> "data", "with_top.coe_bit0" -> "algebra", "roption.mem_restrict" -> "data", "contracting_with.one_sub_K_ne_zero" -> "topology", "linear_map.comp_pmap_apply" -> "algebra", "set.Icc_diff_left" -> "data", "finset.mem_product" -> "data", "zmod.cast_nat_abs_val_min_abs" -> "data", "multiset.powerset_len_aux_zero" -> "data", "lie_algebra.orthogonal.indefinite_diagonal_transform" -> "algebra", "subgroup.mem_supr_of_directed" -> "algebra", "linear_map.comp_ker_subtype" -> "algebra", "polynomial.linear_independent_powers_iff_eval\:2082" -> "algebra", "category_theory.functor.const.obj_map" -> "category_theory", "localization_map.mk'_eq_iff_eq_mul" -> "algebra", "add_group.exists_list_of_mem_closure" -> "algebra", "category_theory.limits.coprod.triangle" -> "category_theory", "fderiv_within.fst" -> "analysis", "prod.fst_vadd" -> "algebra", "real.rpow_le_rpow" -> "analysis", "set.mem_diff_singleton_empty" -> "data", "mul_left_cancel'" -> "algebra", "matrix.lie_conj_apply" -> "algebra", "ordinal.add_lt_omega" -> "set_theory", "ideal.comap_map_of_surjective" -> "algebra", "list.eq_nil_of_length_eq_zero" -> "init", "opposite.unop_zero" -> "algebra", "left_comm" -> "init", "normed_field.tendsto_norm_inverse_nhds_within_0_at_top" -> "analysis", "category_theory.uncurry_id_eq_ev" -> "category_theory", "dlist.to_list_singleton" -> "data", "ennreal.coe_inv_two" -> "data", "mul_le_mul_of_nonpos_right" -> "algebra", "finset.prod_add_prod_le'" -> "algebra", "subsemiring.map_sup" -> "algebra", "euclidean_domain.eq_div_of_mul_eq_left" -> "algebra", "real.tanh_eq_sinh_div_cosh" -> "data", "nhds_within_restrict" -> "topology", "rat.cast_floor" -> "algebra", "set.indicator_add" -> "data", "local_homeomorph.eq_on_source.target_eq" -> "topology", "measure_theory.integral_non_measurable" -> "analysis", "nnreal.of_real_add_of_real" -> "data", "lt_add_of_sub_right_lt" -> "algebra", "complex.iter_deriv_exp" -> "analysis", "lipschitz_with.const" -> "topology", "padic_seq.norm_values_discrete" -> "data", "finsupp.finite_supp" -> "data", "linear_equiv.ker" -> "algebra", "implicit_function_data.has_strict_fderiv_at" -> "analysis", "perfect_closure.neg_mk" -> "algebra", "equiv.perm.of_subtype_apply_of_not_mem" -> "algebra", "pfun.preimage_union" -> "data", "decidable.not_imp_symm" -> "logic", "homeomorph.continuous" -> "topology", "real.cos_eq_one_iff_of_lt_of_lt" -> "analysis", "multiset.nodup_ndinsert" -> "data", "not_exists" -> "logic", "finset.lt_fold_min" -> "data", "fintype.card_units_int" -> "data", "multiset.nodup_erase_of_nodup" -> "data", "category_theory.braided_functor.comp_to_monoidal_functor" -> "category_theory", "set.sInter_insert" -> "data", "primrec.list_nth" -> "computability", "union_lower_bounds_subset_lower_bounds_inter" -> "order", "add_lt_add_of_lt_of_le" -> "algebra", "local_homeomorph.eq_on_source_refl" -> "topology", "category_theory.functor.associator_inv_app" -> "category_theory", "rat.cast_pos" -> "data", "poly.const_eval" -> "number_theory", "subalgebra.mem_res" -> "algebra", "measurable_space.dynkin_system.generate_from_eq" -> "analysis", "measurable_space.monotone_comap" -> "analysis", "is_absolute_value.mem_uniformity" -> "topology", "category_theory.prod.sectr_map" -> "category_theory", "relation.flip_comp" -> "logic", "generalized_continued_fraction.zeroth_continuant_eq_h_one" -> "algebra", "matrix.neg_apply" -> "data", "norm_pow_le" -> "analysis", "continuous_linear_equiv.continuous" -> "topology", "ideal.exists_sub_one_mem_and_mem" -> "algebra", "computable.nat_bodd" -> "computability", "finset.prod_attach" -> "algebra", "measure_theory.measure_bUnion_finset_le" -> "analysis", "filter.exists_ultrafilter" -> "order", "times_cont_diff_within_at_const" -> "analysis", "omega.rhs_correct_aux" -> "tactic", "stream.head_cons" -> "data", "cau_seq.lim_const" -> "data", "function.surjective.forall" -> "logic", "category_theory.limits.id_zero_equiv_iso_zero_apply_inv" -> "category_theory", "wseq.lift_rel_think_right" -> "data", "mul_inv_mul_self" -> "algebra", "smooth_inv" -> "geometry", "continuous_linear_map.ker_closed_complemented_of_finite_dimensional_range" -> "analysis", "ennreal.pow_ne_zero" -> "data", "pow_dvd_pow_of_dvd" -> "algebra", "finset.weighted_vsub_of_point_eq_of_sum_eq_zero" -> "algebra", "pmf.pure_map" -> "analysis", "measure_theory.measure.join_apply" -> "analysis", "uniform_inducing.comp" -> "topology", "skew_adjoint_lie_subalgebra_equiv_symm_apply" -> "algebra", "local_equiv.restr_target" -> "data", "units.is_open" -> "analysis", "matrix.transpose_add" -> "data", "category_theory.limits.kernel_iso_of_eq_trans" -> "category_theory", "finsupp.ext" -> "data", "ideal.ext" -> "algebra", "int.nat_abs_pow_two" -> "algebra", "option.to_list_nodup" -> "data", "nnreal.coe_max" -> "data", "set.eq_empty_or_nonempty" -> "data", "category_theory.limits.biprod.map_iso_hom" -> "category_theory", "nnreal.eq_div_iff" -> "data", "zero_le_padic_val_rat_of_nat" -> "data", "function.maps_to_fixed_pts_comp" -> "dynamics", "pgame.impartial.equiv_iff_sum_first_loses" -> "set_theory", "is_open_prod" -> "topology", "list.span_eq_take_drop" -> "data", "floor_coe" -> "algebra", "isometric.map_midpoint" -> "analysis", "complex.exp_of_real_re" -> "data", "nat.lt_of_add_lt_add_right" -> "init", "matrix.to_bilin_form_comp" -> "algebra", "valuation.is_equiv.ne_zero" -> "algebra", "local_of_unique_nonzero_prime" -> "algebra", "localization_map.map_comp_map" -> "algebra", "mvqpf.liftp_iff_of_is_uniform" -> "data", "matrix.head_cons" -> "data", "sub_half" -> "algebra", "linear_equiv.refl_to_linear_map" -> "algebra", "polynomial.splits_zero" -> "algebra", "hyperreal.not_infinite_of_exists_st" -> "data", "list.index_of_cons_eq" -> "data", "asymptotics.is_O_with_norm_right" -> "analysis", "nat.choose_self" -> "data", "set.Ioo_subset_Ioi_self" -> "data", "writer_t.ext" -> "control", "set.subsingleton.eq_singleton_of_mem" -> "data", "real.log_pos" -> "analysis", "continuous_update" -> "topology", "holor.cprank_max_sum" -> "data", "has_sum.add_compl" -> "topology", "filter.mem_prod_iff" -> "order", "category_theory.iso.inv_hom_id_app_assoc" -> "category_theory", "mv_polynomial.vars_X" -> "data", "category_theory.is_iso.inv_hom_id" -> "category_theory", "interior_Ici" -> "topology", "SemiRing.coe_of" -> "algebra", "multiset.inter_le_right" -> "data", "ennreal.continuous_of_real" -> "topology", "measure_theory.mem_ae_iff" -> "analysis", "circle_deg1_lift.map_lt_of_translation_number_lt_int" -> "dynamics", "zsqrtd.nonneg_antisymm" -> "data", "bifunctor.snd_comp_fst" -> "control", "polynomial.mul_div_eq_iff_is_root" -> "data", "category_theory.functor.map_presheaf_map_c" -> "algebraic_geometry", "category_theory.limits.coprod.map_desc" -> "category_theory", "rel.inv_def" -> "data", "con.comap_eq" -> "algebra", "ennreal.mul_le_mul_right" -> "data", "tsum_sigma'" -> "topology", "norm_num.min_fac_bit0" -> "tactic", "add_units.add_neg_cancel_left" -> "algebra", "list.nodup_iff_count_le_one" -> "data", "nat.succ_lt_succ" -> "init", "is_basis.to_matrix_update" -> "algebra", "typevec.drop_fun_subtype_val" -> "data", "circle_deg1_lift.le_ceil_map_map_zero" -> "dynamics", "eq_of_vsub_eq_zero" -> "algebra", "closure_univ" -> "topology", "con.ker_lift_injective" -> "algebra", "mvqpf.supp_preservation_iff_liftp_preservation" -> "data", "finsupp.lmap_domain_total" -> "algebra", "pnat.prod_factor_multiset" -> "data", "real.arctan_neg" -> "analysis", "zmod.eisenstein_lemma" -> "number_theory", "set.preimage_const_mul_Ici_of_neg" -> "data", "linear_pmap.map_sub" -> "algebra", "free_add_semigroup.traverse_add" -> "algebra", "ordinal.nat_cast_power" -> "set_theory", "finset.not_mem_of_mem_powerset_of_not_mem" -> "data", "has_deriv_within_at.csin" -> "analysis", "category_theory.comma.map_left_id_hom_app_left" -> "category_theory", "local_equiv.right_inv" -> "data", "is_integer_of_is_root_of_monic" -> "algebra", "filter.eventually_congr" -> "order", "cardinal.nat_lt_omega" -> "set_theory", "wseq.to_list'_cons" -> "data", "finset.sum_le_sum" -> "algebra", "computable.vector_to_list" -> "computability", "localization_map.eq" -> "algebra", "add_monoid_hom.fst_comp_inr" -> "algebra", "finset.mul_mem_mul" -> "algebra", "category_theory.whisker_right_twice" -> "category_theory", "nat.mul_one" -> "init", "ball_true_iff" -> "logic", "basic_smooth_bundle_core.mem_chart_target_iff" -> "geometry", "category_theory.pi.comap_eval_iso_eval_inv_app" -> "category_theory", "uniformity_eq_uniformity_closure" -> "topology", "measure_theory.simple_func.mem_image_of_mem_range_restrict" -> "analysis", "is_glb_binfi" -> "order", "complex.exp_list_sum" -> "data", "convex_image_has_deriv_at" -> "analysis", "local_homeomorph.subtype_restr_symm_trans_subtype_restr" -> "topology", "setoid.classes_eqv_classes" -> "data", "local_homeomorph.image_open_of_open'" -> "topology", "metric.Hausdorff_dist_empty" -> "topology", "filter.eventually_at_bot" -> "order", "with_zero.div_mul_cancel" -> "algebra", "cardinal.mk_sep" -> "set_theory", "function.semiconj\:2082.comp_eq" -> "logic", "polynomial.degree_add_eq_of_degree_lt" -> "data", "list.lookup_kinsert_ne" -> "data", "category_theory.limits.limit.pre_\[Pi]" -> "category_theory", "times_cont_mdiff_at.congr_of_eventually_eq" -> "geometry", "mul_lt_mul_of_pos_left" -> "algebra", "pmf.bind_pure" -> "analysis", "function.left_inverse_surj_inv" -> "logic", "omega.nat.push_neg_equiv" -> "tactic", "array.push_back_idx" -> "init", "push_neg.not_eq" -> "tactic", "Gromov_Hausdorff.GH_dist_le_Hausdorff_dist" -> "topology", "tactic.ring_exp.pow_p_pf_succ" -> "tactic", "linear_map.proj_std_basis_ne" -> "algebra", "applicative.map_seq_map" -> "control", "eq_zero_of_zero_dvd" -> "algebra", "is_cau_seq.cauchy\:2082" -> "data", "list.erase_append_right" -> "data", "fin.last_pos" -> "data", "is_R_or_C.mul_inv_cancel" -> "data", "is_R_or_C.re_to_real" -> "data", "smooth_at_univ" -> "geometry", "linear_pmap.neg_apply" -> "algebra", "cardinal.one_lt_two" -> "set_theory", "euclidean_geometry.vsub_orthogonal_projection_mem_direction" -> "geometry", "is_open_univ" -> "topology", "finite_field.sum_pow_units" -> "algebra", "rel_embedding.is_refl" -> "order", "category_theory.limits.fork.of_\[Iota]_app_one" -> "category_theory", "nat.primrec'.to_prim" -> "computability", "nat.gcd_dvd" -> "data", "polynomial.splitting_field_aux.adjoin_roots" -> "algebra", "erased.mk_out" -> "data", "cardinal.zero_power_le" -> "set_theory", "convex_cone.pointed_of_positive_cone" -> "analysis", "module.dual.eval_apply" -> "algebra", "array.to_list_nth_le_aux" -> "data", "affine_subspace.lt_def" -> "algebra", "int.neg_ne_of_pos" -> "init", "measure_theory.outer_measure.Sup_apply" -> "analysis", "is_closed_iff_cluster_pt" -> "topology", "rat.div_int_inj" -> "data", "metric.bounded_closure_of_bounded" -> "topology", "is_topological_fiber_bundle_fst" -> "topology", "gcd_one_left" -> "algebra", "nhdset_of_mem_uniformity" -> "topology", "dioph.proj_dioph" -> "number_theory", "matrix.to_blocks_from_blocks\:2081\:2081" -> "data", "continuous_linear_map.mul_def" -> "topology", "Inf_eq_infi" -> "order", "hyperreal.infinitesimal_epsilon" -> "data", "nat.perm_of_prod_eq_prod" -> "data", "stream.mem_interleave_left" -> "data", "has_strict_fderiv_at.local_inverse_tendsto" -> "analysis", "left_coset_equiv_rel" -> "algebra", "set.nonempty_compl" -> "data", "well_founded.well_founded_iff_has_max'" -> "order", "measure_theory.l1.of_fun_eq_of_fun" -> "analysis", "finsupp.prod_to_multiset" -> "data", "mul_action.mem_orbit_self" -> "algebra", "is_R_or_C.one_re" -> "data", "finset.inter_subset_inter_left" -> "data", "multiset.inf_union" -> "data", "set.insert_def" -> "data", "one_pow" -> "algebra", "mul_inv_rev" -> "algebra", "stream.nth_zero_cons" -> "data", "filter.strict_mono_subseq_of_tendsto_at_top" -> "order", "nonempty_embedding_to_cardinal" -> "set_theory", "multiset.mem_cons" -> "data", "matrix.linear_equiv_matrix_symm_mul" -> "algebra", "ennreal.tsum_eq_supr_nat" -> "topology", "category_theory.iso.trans_refl" -> "category_theory", "nnreal.div_eq_iff" -> "data", "nat.prime.dvd_fact" -> "data", "is_measurable.bInter" -> "analysis", "category_theory.limits.biprod.map_iso_inv" -> "category_theory", "dense_range.nonempty" -> "topology", "d_array.of_beq_aux_eq_tt" -> "init", "category_theory.limits.types.limit_equiv_sections_symm_apply" -> "category_theory", "complex.cpow_nat_cast" -> "analysis", "tensor_product.ext_threefold" -> "algebra", "closure_eq_iff_is_closed" -> "topology", "pgame.move_left_left_moves_neg_symm" -> "set_theory", "add_submonoid.ext'" -> "algebra", "set.mem_preimage" -> "data", "list.suffix_cons" -> "data", "measure_theory.integrable_on.integrable" -> "analysis", "matrix.scalar_apply_ne" -> "data", "two_ne_zero" -> "algebra", "polynomial.apply_eq_coeff" -> "data", "polynomial.eval\:2082_C" -> "data", "directed_on_image" -> "order", "emetric.inf_edist_empty" -> "topology", "convex_cone.mem_bot" -> "analysis", "list.nodup_iota" -> "data", "nat_ceil_lt_add_one" -> "algebra", "semidirect_product.right_hom_inl" -> "algebra", "list.Ico.eq_nil_of_le" -> "data", "computable.encode_iff" -> "computability", "local_equiv.trans_refl_restr'" -> "data", "cau_seq.inv_mul_cancel" -> "data", "measure_theory.lebesgue_outer_singleton" -> "analysis", "monoid_hom.mrange_eq_map" -> "algebra", "lcm_dvd_lcm_mul_left_right" -> "algebra", "set.Iic_union_Ioc_eq_Iic" -> "data", "associates.le_of_mul_le_mul_left" -> "algebra", "is_R_or_C.conj_to_real" -> "data", "category_theory.iso.refl_trans" -> "category_theory", "complex.uniform_continuous_neg" -> "topology", "submodule.smul_def" -> "algebra", "alist.keys_erase" -> "data", "nat.find_pos" -> "data", "is_max_filter_const" -> "order", "set.mem_Ioc" -> "data", "array.to_list_nth_le'" -> "data", "classical.cases" -> "logic", "metric.nhds_within_basis_ball" -> "topology", "nat.add_div_left" -> "init", "list.forall_mem_inter_of_forall_left" -> "data", "add_subgroup.closure_empty" -> "algebra", "add_monoid_hom.zero_apply" -> "algebra", "deriv.lhopital_zero_nhds'" -> "analysis", "is_R_or_C.conj_of_real" -> "data", "wseq.flatten_congr" -> "data", "set.disjoint_singleton_right" -> "data", "with_bot.coe_one" -> "algebra", "embedding_sigma_mk" -> "topology", "matrix.det_zero" -> "algebra", "list.mem_append_left" -> "init", "principal_subtype" -> "topology", "prod.mk_add_mk" -> "algebra", "mem_irreducible_component" -> "topology", "pos_num.to_nat_eq_succ_pred" -> "data", "submodule.map_supr" -> "algebra", "one_inv" -> "algebra", "category_theory.iso.symm_self_id_assoc" -> "category_theory", "asymptotics.is_o_const_smul_left" -> "analysis", "inducing.continuous_iff" -> "topology", "associates.units_eq_one" -> "algebra", "norm_num.adc_bit1_bit0" -> "tactic", "has_strict_fderiv_at.to_local_inverse" -> "analysis", "set.indicator_zero" -> "data", "list.pairwise_map" -> "data", "asymptotics.is_O_with.is_O" -> "analysis", "set.prod_quotient_preimage_eq_image" -> "data", "finset.prod_range_succ" -> "algebra", "gpow_neg_one" -> "algebra", "has_deriv_at.csinh" -> "analysis", "affine_map.homothety_zero" -> "algebra", "category_theory.limits.cokernel_image_\[Iota]_inv" -> "category_theory", "times_cont_mdiff_at.continuous_at" -> "geometry", "polynomial.mem_support_derivative" -> "data", "list.perm.bag_inter_left" -> "data", "monoid_hom.map_pth_root" -> "algebra", "mul_le_mul_left_of_neg" -> "algebra", "has_strict_deriv_at.comp" -> "analysis", "category_theory.limits.cones.postcompose_equivalence_functor" -> "category_theory", "smooth_at.prod_map" -> "geometry", "is_min_on.of_is_local_min_on_of_convex_on" -> "analysis", "list.prod_hom_rel" -> "data", "separated_def'" -> "topology", "set.surjective_onto_range" -> "data", "linear_equiv.arrow_congr_apply" -> "algebra", "enorm.map_smul" -> "analysis", "is_bounded_linear_map.snd" -> "analysis", "dual_tensor_hom_apply" -> "algebra", "adjoin_root.coe_alg_hom" -> "algebra", "equiv.perm.disjoint_mul_right" -> "algebra", "isometric.dist_eq" -> "topology", "measure_theory.exists_is_measurable_superset_of_measure_eq_zero" -> "analysis", "cardinal.card_le_of_finset" -> "set_theory", "irrational.add_cases" -> "data", "list.length_insert_nth" -> "data", "hyperreal.coe_add" -> "data", "finsupp.restrict_dom_comp_subtype" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_of_locally_lift_prop_on" -> "geometry", "finset.exists_nat_subset_range" -> "data", "tensor_product.tmul_add" -> "algebra", "int.div_self" -> "data", "exp_neg_inv_glue.f_aux_deriv_zero" -> "analysis", "and_eq_of_eq_true_right" -> "init", "znum.div_to_int" -> "data", "subtype.equivalence" -> "data", "infi_le" -> "order", "mvpfunctor.comp_W_path_cases_on" -> "data", "submodule.prod_comap_inr" -> "algebra", "hyperreal.infinite_neg_neg_of_infinite_pos" -> "data", "measurable_space.dynkin_system.has_diff" -> "analysis", "ideal.eq_top_iff_one" -> "algebra", "padic_int.norm_eq_pow_val" -> "data", "pnat.gcd_b'_coe" -> "data", "midpoint_smul_smul" -> "algebra", "subring.comap_infi" -> "algebra", "list.lookup_kerase_ne" -> "data", "eq_zero_of_add_self_left_cancel" -> "algebra", "set.compl_sInter" -> "data", "category_theory.functor.map_cone_inv_X" -> "category_theory", "multiset.map_injective" -> "data", "add_div" -> "algebra", "category_theory.preimage_iso_map_iso" -> "category_theory", "pi.list_sum_apply" -> "algebra", "divp_self" -> "algebra", "fintype.card_pos_iff" -> "data", "filter.tendsto_at_top_at_top_of_monotone" -> "order", "cardinal.mk_bool" -> "set_theory", "finset.filter_and" -> "data", "filter.map_sup" -> "order", "generalized_continued_fraction.exists_s_a_of_part_num" -> "algebra", "surj_on_Iio_of_monotone_surjective" -> "data", "finset.exists_mem_empty_iff" -> "data", "cardinal.omega_le_bit1" -> "set_theory", "category_theory.limits.inv_prod_comparison_map_snd" -> "category_theory", "filter.germ.lift_rel_const" -> "order", "nat.primrec.id" -> "computability", "matrix.smul_eq_mul_diagonal" -> "data", "polynomial.nat_degree_mul" -> "data", "many_one_degree.le_add_left" -> "computability", "add_monoid_hom.coe_inj" -> "algebra", "list.chain_map" -> "data", "all_mem_nhds" -> "topology", "multiset.mem_powerset_len" -> "data", "znum.dvd_iff_mod_eq_zero" -> "data", "differentiable_at.cos" -> "analysis", "rat.num_neg_eq_neg_num" -> "data", "continuous_on_open_iff" -> "topology", "int.shiftl_neg" -> "data", "list.perm.pmap" -> "data", "norm_num.lt_bit1_bit1" -> "tactic", "nat.cast_add_one" -> "data", "disjoint.symm" -> "order", "matrix.cons_mul_vec" -> "data", "dfinsupp.support_add" -> "data", "linear_map.map_neg" -> "algebra", "localization.r_iff_exists" -> "algebra", "equiv.tsum_eq_tsum_of_has_sum_iff_has_sum" -> "topology", "has_mfderiv_within_at.congr_mono" -> "geometry", "isometric.midpoint_fixed" -> "analysis", "primrec.snd" -> "computability", "dense_inducing.continuous" -> "topology", "int.one_pos" -> "init", "category_theory.equivalence.cancel_counit_right" -> "category_theory", "category_theory.eq_to_iso.hom" -> "category_theory", "add_subgroup.sum_mem" -> "algebra", "mv_polynomial.ext" -> "data", "norm_add_square_eq_norm_square_add_norm_square" -> "analysis", "strict_mono.nat" -> "order", "category_theory.functor_to_types.map_comp_apply" -> "category_theory", "asymptotics.is_o.congr" -> "analysis", "set.image2_congr" -> "data", "measure_theory.lebesgue_length_eq_infi_Icc" -> "analysis", "function.commute.iterate_pos_lt_iff_map_lt'" -> "order", "has_deriv_at_filter.add" -> "analysis", "units.coe_map" -> "algebra", "set.Icc_subset_Icc_iff" -> "data", "gpow_add_one" -> "algebra", "norm_sub_le_of_geometric_bound_of_has_sum" -> "analysis", "localization.ring_equiv_of_quotient_mk'" -> "algebra", "subgroup.mem_Sup_of_mem" -> "algebra", "prime_spectrum.comap_continuous" -> "algebraic_geometry", "fpow_neg_succ_of_nat" -> "algebra", "separation_rel_eq_inter_closure" -> "topology", "finsupp.support_add" -> "data", "convex_iff_pointwise_add_subset" -> "analysis", "option.map_none" -> "data", "or.imp_right" -> "init", "ulift.inv_down" -> "algebra", "set.sUnion_bUnion" -> "data", "measure_theory.norm_integral_le_of_norm_le_const" -> "analysis", "fintype.sum_unique" -> "data", "is_linear_order.swap" -> "order", "finset.le_fold_min" -> "data", "ideal.radical_sup" -> "algebra", "add_units.coe_eq_zero" -> "algebra", "is_local_max_on.max" -> "topology", "int.add_le_add_right" -> "init", "asymptotics.is_O_with_const_one" -> "analysis", "ordinal.add_mul_succ" -> "set_theory", "nat.mod_one" -> "init", "add_submonoid.mem_closure" -> "algebra", "pell.d_pos" -> "number_theory", "continuous_at.integral_sub_linear_is_o_ae" -> "analysis", "isometric.coe_one" -> "topology", "complex.cpow_eq_zero_iff" -> "analysis", "nhds_is_add_hom" -> "topology", "category_theory.limits.coprod.inr_desc_assoc" -> "category_theory", "cardinal.add_eq_max" -> "set_theory", "compact_space.uniform_continuous_of_continuous" -> "topology", "category_theory.adjunction.functoriality_counit_app_hom" -> "category_theory", "category_theory.functor.const.op_obj_unop_hom_app" -> "category_theory", "nat.zero_land" -> "data", "list.map_drop" -> "data", "list.chain_map_of_chain" -> "data", "euclidean_geometry.angle_eq_right" -> "geometry", "or_of_or_of_imp_of_imp" -> "logic", "finset.sup_le" -> "data", "real.tendsto_pow_mul_exp_neg_at_top_nhds_0" -> "analysis", "adic_completion.of_apply" -> "algebra", "linear_map.flip_inj" -> "algebra", "int.cast_zero" -> "data", "add_submonoid.localization_map.add_equiv_of_add_equiv_eq_map_apply" -> "algebra", "fin.strict_mono_iff_lt_succ" -> "data", "pnat.gcd_rel_right'" -> "data", "category_theory.category_of_elements.to_comma_obj" -> "category_theory", "alg_hom.to_linear_map_apply" -> "algebra", "inner_product_geometry.angle_add_angle_eq_pi_of_angle_eq_pi" -> "geometry", "real.tan_lt_tan_of_nonneg_of_lt_pi_div_two" -> "analysis", "order_iso.left_ord_continuous" -> "order", "orthogonal_projection_fn_inner_eq_zero" -> "analysis", "subsemiring.multiset_prod_mem" -> "algebra", "list.map_subset_iff" -> "data", "cardinal.lt_ord" -> "set_theory", "pfunctor.M.mk_dest" -> "data", "not_le_of_gt" -> "init", "sub_nonneg" -> "algebra", "dvd_dvd_of_associated" -> "algebra", "Exists.some_spec" -> "logic", "sub_ne_zero_of_ne" -> "algebra", "times_cont_diff_on_of_continuous_on_differentiable_on_deriv" -> "analysis", "pow_order_of_eq_one" -> "algebra", "affine.simplex.ext_iff" -> "algebra", "uniform_space.completion.ext" -> "topology", "nhds_contain_boxes.comm" -> "topology", "set.Ioi_diff_Ioi" -> "data", "order_embedding.well_founded" -> "order", "category_theory.over.iterated_slice_backward_forget_forget" -> "category_theory", "function.semiconj.bij_on_image" -> "data", "matrix.coe_scalar" -> "data", "filter.principal_eq_iff_eq" -> "order", "fderiv_within_const_mul" -> "analysis", "turing.to_partrec.step_ret_then" -> "computability", "topological_group.ext" -> "topology", "set.Ico_subset_Ico" -> "data", "associates.prime.le_or_le" -> "algebra", "has_deriv_at_gronwall_bound_shift" -> "analysis", "local_homeomorph.map_source" -> "topology", "category_theory.over.hom_mk_left" -> "category_theory", "subgroup.mem_coe" -> "algebra", "prime_multiset.prod_of_nat_multiset" -> "data", "has_deriv_within_at.const_mul" -> "analysis", "finset.sum_centroid_weights_eq_one_of_card_ne_zero" -> "algebra", "continuous_within_at_Ico_iff_Iio" -> "topology", "ordinal.power_lt_power_left_of_succ" -> "set_theory", "turing.tr_eval" -> "computability", "differentiable.const_add" -> "analysis", "neg_nonpos" -> "algebra", "category_theory.limits.prod_lift_fst_snd" -> "category_theory", "ennreal.sub_half" -> "data", "polynomial.integral_normalization_coeff_nat_degree" -> "data", "mem_id_rel" -> "topology", "uniform_space.completion.extension\:2082_coe_coe" -> "topology", "dim_range_le" -> "algebra", "has_deriv_at_filter.iterate" -> "analysis", "algebra.linear_map_apply" -> "algebra", "zsqrtd.le_of_le_le" -> "data", "nat.div_le_div_left" -> "data", "quotient.exact'" -> "data", "nat.binary_rec_zero" -> "init", "Inf_le_Inf_of_subset_insert_top" -> "order", "circle_deg1_lift.pow_monotone" -> "dynamics", "Hausdorffification.lift_of" -> "algebra", "upper_bounds_union" -> "order", "equiv.coe_fn_mk" -> "data", "submonoid.map_comap_le" -> "algebra", "rel_embedding.is_strict_order" -> "order", "mul_mono_nonpos" -> "tactic", "multiset.quot_mk_to_coe'" -> "data", "function.update_same" -> "logic", "bdd_below.insert" -> "order", "filter.eventually_eq.times_cont_mdiff_within_at_iff" -> "geometry", "has_fderiv_within_at.const_smul" -> "analysis", "nonempty.map" -> "logic", "div_le_one_of_neg" -> "algebra", "turing.list_blank.nth_succ" -> "computability", "list.mem_union" -> "data", "category_theory.comma.map_right_obj_hom" -> "category_theory", "int.bodd_mul" -> "data", "filter.tendsto_at_top_of_add_bdd_above_left" -> "order", "fin.sum_univ_zero" -> "data", "submodule.pow_subset_pow" -> "algebra", "multiset.card_sections" -> "data", "norm_num.add_neg_pos_neg" -> "tactic", "alist.insert_union" -> "data", "is_conj_iff_eq" -> "algebra", "has_strict_fderiv_at.to_implicit_function" -> "analysis", "nat.succ_sub_succ_eq_sub" -> "init", "category_theory.limits.is_terminal.hom_ext" -> "category_theory", "holor_index.drop_take" -> "data", "mul_left_inj'" -> "algebra", "linear_map.trace_aux_def" -> "algebra", "Cauchy.uniform_inducing_pure_cauchy" -> "topology", "generalized_continued_fraction.exists_conts_a_of_num" -> "algebra", "metric.ball_eq_ball'" -> "topology", "nat.bit_le_bit1_iff" -> "data", "category_theory.limits.colimit.\[Iota]_desc_assoc" -> "category_theory", "cardinal.mk_option" -> "set_theory", "int.lt_sub_left_of_add_lt" -> "init", "ring.fractional_ideal.coe_mul" -> "algebra", "nat.sub_sub_assoc" -> "data", "mv_polynomial.X_pow_eq_single" -> "data", "add_group.closure_subset_iff" -> "algebra", "category_theory.comma.map_left_comp_hom_app_right" -> "category_theory", "filter.pure_injective" -> "order", "add_con.sup_eq_add_con_gen" -> "algebra", "closed_ball_pi" -> "topology", "measure_theory.measure.regular.outer_regular_eq" -> "analysis", "ennreal.coe_to_real" -> "data", "multiplicity.is_greatest" -> "algebra", "unique.default_eq" -> "logic", "uniform.continuous_iff'_right" -> "topology", "subtype.refl" -> "data", "filter.realizer.tendsto_iff" -> "data", "linear_pmap.coprod_apply" -> "algebra", "wseq.lift_rel_bind" -> "data", "tactic.ring_exp.mul_pf_c_c" -> "tactic", "matrix.add_apply" -> "data", "zsqrtd.one_re" -> "data", "has_strict_fderiv_at.has_fderiv_at" -> "analysis", "seq.destruct_nil" -> "data", "strict_mono.id_le" -> "order", "filter.is_cobounded.mono" -> "order", "asymm" -> "init", "complex.differentiable_cosh" -> "analysis", "set.Ioo_subset_Ioc_self" -> "data", "filter.tendsto_at_bot" -> "order", "multiset.erase_dup_le" -> "data", "finsupp.sum_sub_index" -> "data", "set.compl_Inter" -> "data", "real.tendsto_log_one_zero" -> "analysis", "if_true_right_eq_or" -> "init", "smooth_on.times_cont_mdiff_on" -> "geometry", "galois_insertion.l_infi_u" -> "order", "set.mem_bUnion_iff" -> "data", "is_R_or_C.add_conj" -> "data", "asymptotics.is_O_const_mul_right_iff'" -> "analysis", "surj_on_Ioo_of_monotone_surjective" -> "data", "measure_theory.ae_eq_fun.zero_to_germ" -> "analysis", "free_comm_ring.is_supported_mul" -> "algebra", "filter.has_basis_principal" -> "order", "set.forall_insert_of_forall" -> "data", "polynomial.div_X_mul_X_add" -> "data", "primrec.option_orelse" -> "computability", "sup_le_sup" -> "order", "seq.destruct_cons" -> "data", "typevec.drop_fun_prod" -> "data", "stream.drop_zip" -> "data", "polynomial.prod_X_sub_C_coeff_card_pred" -> "algebra", "nat.find_eq_zero" -> "data", "polynomial.degree_C" -> "data", "subsemiring.mem_map" -> "algebra", "int.neg_succ_of_nat_inj_iff" -> "init", "submodule.mem_inf" -> "algebra", "char_p.char_is_prime_of_two_le" -> "algebra", "category_theory.limits.types.sigma_desc" -> "category_theory", "power_series.coeff_def" -> "algebra", "is_greatest.union" -> "order", "group.conjugates_subset_normal" -> "algebra", "nat.lcm_comm" -> "data", "bilin_form.is_pair_self_adjoint_equiv" -> "algebra", "real.volume_Ico" -> "analysis", "buffer.read_eq_read'" -> "data", "local_homeomorph.inv_fun_eq_coe" -> "topology", "midpoint_unique" -> "algebra", "computable.decode" -> "computability", "filter.tendsto_const_pure" -> "order", "int.mul_nonpos_of_nonpos_of_nonneg" -> "init", "int.le_sub_one_iff" -> "data", "wseq.to_list'_nil" -> "data", "finset.subset_image_iff" -> "data", "category_theory.monoidal.associator_inv_app" -> "category_theory", "ideal.mul_unit_mem_iff_mem" -> "algebra", "category_theory.limits.\[Iota]_colim_map_assoc" -> "category_theory", "array.to_list_nth" -> "data", "list.Ico.append_consecutive" -> "data", "complex.abs_im_le_abs" -> "data", "eventually_nhds_iff" -> "topology", "list.rotate_eq_rotate'" -> "data", "lfp_comp" -> "order", "category_theory.nat_trans.left_op_app" -> "category_theory", "is_preconnected_iff_subset_of_disjoint" -> "topology", "polynomial.factor_dvd_of_degree_ne_zero" -> "algebra", "nnreal.geom_mean_le_arith_mean2_weighted" -> "analysis", "set.mem_union_right" -> "data", "complex.arg_I" -> "analysis", "omega.nat.preterm.val_sub_subst" -> "tactic", "stream.even_tail" -> "data", "inv_eq_iff_inv_eq" -> "algebra", "inf_assoc" -> "order", "tangent_cone_congr" -> "analysis", "ordinal.CNF_aux" -> "set_theory", "filter.germ.const_max" -> "order", "is_add_unit.add_right_inj" -> "algebra", "norm_num.not_refl_false_intro" -> "tactic", "sub_lt_of_abs_sub_lt_right" -> "algebra", "mul_equiv.symm_apply_apply" -> "data", "cau_seq.zero_apply" -> "data", "finset.exists_mem_insert" -> "data", "category_theory.iso.self_symm_id" -> "category_theory", "category_theory.over.construct_products.cones_equiv_inverse_obj_\[Pi]_app" -> "category_theory", "rat.cast_one" -> "data", "real.tan_eq_sin_div_cos" -> "data", "category_theory.limits.cone_morphism.ext" -> "category_theory", "set.preimage_const_sub_Iio" -> "data", "measurable_equiv.measurable" -> "analysis", "lipschitz_with.subtype_coe" -> "topology", "set.pairwise_disjoint.elim" -> "data", "quotient.exact" -> "init", "submonoid.mrange_snd" -> "algebra", "tactic.ring.mul_assoc_rev" -> "tactic", "is_min_filter.congr" -> "order", "div_nonneg_of_nonpos" -> "algebra", "pgame.add_lt_add" -> "set_theory", "polynomial.single_eq_C_mul_X" -> "data", "finite_dimensional.of_finset_basis" -> "algebra", "list.drop_eq_nth_le_cons" -> "data", "primrec.vector_nth" -> "computability", "is_bounded_linear_map.sub" -> "analysis", "tangent_bundle_proj_continuous" -> "geometry", "finite_field.frobenius_pow" -> "algebra", "metric.frontier_closed_ball_subset_sphere" -> "topology", "local_homeomorph.coe_coe" -> "topology", "category_theory.limits.is_colimit.of_nat_iso.cocone_fac" -> "category_theory", "pnat.coe_le_coe" -> "data", "category_theory.monad.forget_creates_colimits.lifted_cocone_\[Iota]_app_f" -> "category_theory", "list.map_repeat" -> "data", "ulift.smul_down" -> "algebra", "nat.one_le_bit1" -> "init", "euclidean_geometry.orthogonal_projection_vadd_eq_self" -> "geometry", "add_monoid_hom.prod_apply" -> "algebra", "submonoid.localization_map.lift_spec_mul" -> "algebra", "measure_theory.tendsto_lintegral_of_dominated_convergence" -> "analysis", "setoid.ker_def" -> "data", "cardinal.fintype_card" -> "set_theory", "circle_deg1_lift.ext_iff" -> "dynamics", "ordering.swap_or_else" -> "algebra", "linear_recurrence.eq_mk_of_is_sol_of_eq_init" -> "algebra", "inf_left_comm" -> "order", "category_theory.sum.inl__map" -> "category_theory", "neg_add" -> "algebra", "vector.m_of_fn_roption_some" -> "computability", "lie_algebra.equiv.of_injective_apply" -> "algebra", "multiset.pmap_eq_map" -> "data", "finset.empty_mem_powerset" -> "data", "mvpfunctor.M.map_dest" -> "data", "Set.mem_powerset" -> "set_theory", "monoid_hom.flip_apply" -> "algebra", "pgame.relabel_move_left'" -> "set_theory", "is_min_on.on_preimage" -> "order", "mem_right_coset" -> "algebra", "ordinal.succ_log_def" -> "set_theory", "mul_eq_zero_of_right" -> "algebra", "finset.induction" -> "data", "nat.eq_zero_of_le_half" -> "data", "euclidean_domain.xgcd_zero_left" -> "algebra", "list.length_attach" -> "data", "multiset.erase_dup_cons_of_mem" -> "data", "filter.bind_le" -> "order", "list.lookup_all_nil" -> "data", "of_mul_mul" -> "algebra", "finset.sum_range_sub_of_monotone" -> "algebra", "ceil_le_floor_add_one" -> "algebra", "set.finite.card_to_finset" -> "data", "lie_algebra.morphism.comp_apply" -> "algebra", "ring_hom.map_matrix_mul" -> "data", "free_add_monoid.lift_of_comp_eq_map" -> "algebra", "associates.out_mk" -> "algebra", "has_fderiv_within_at_of_not_mem_closure" -> "analysis", "has_mfderiv_at.congr_of_eventually_eq" -> "geometry", "omega.nat.unsat_of_unsat_sub_elim" -> "tactic", "metric.continuous_on_iff'" -> "topology", "ennreal.to_real_lt_to_real" -> "data", "is_closed_property3" -> "topology", "generalized_continued_fraction.int_fract_pair.coe_to_int_fract_pair" -> "algebra", "list.diff_sublist" -> "data", "complex.lim_conj" -> "data", "wseq.mem_map" -> "data", "list.func.nil_add" -> "data", "times_cont_diff_on.congr" -> "analysis", "partrec.sum_cases_right" -> "computability", "norm_num.sle_bit0_bit0" -> "tactic", "orthogonal_projection_inner_eq_zero" -> "analysis", "matrix.smul_mul" -> "data", "dense_inducing.tendsto_comap_nhds_nhds" -> "topology", "dense_range.prod" -> "topology", "algebraic_geometry.SheafedSpace.id_c" -> "algebraic_geometry", "multiset.mem_filter_map" -> "data", "fin.coe_last" -> "data", "category_theory.over.post_map_left" -> "category_theory", "filter.principal_bind" -> "order", "eventually_nhds_with_of_forall" -> "topology", "metric.closure_closed_ball" -> "topology", "ennreal.inv_lt_inv" -> "data", "multiset.Ico.zero_bot" -> "data", "pow_injective_of_lt_order_of" -> "algebra", "filter.le_lift'" -> "order", "finset.prod_hom_rel" -> "algebra", "pequiv.injective_of_forall_is_some" -> "data", "list.exists_mem_cons_of_exists" -> "data", "asymptotics.is_O_with_refl" -> "analysis", "multilinear_map.map_sum" -> "algebra", "free_group.sum.one" -> "algebra", "inner_neg_left" -> "analysis", "monotone.map_min" -> "algebra", "function.is_periodic_pt_minimal_period" -> "dynamics", "unique_diff_on.eq" -> "analysis", "cau_seq_iff_cauchy_seq" -> "topology", "int.of_nat_nat_abs_eq_of_nonneg" -> "init", "is_open_map_fst" -> "topology", "roption.mem_coe" -> "data", "list.infix_cons" -> "data", "units.smul_ne_zero" -> "algebra", "category_theory.limits.limit.cone_point_unique_up_to_iso_hom_comp" -> "category_theory", "cau_seq.lt_irrefl" -> "data", "neg_mul_comm" -> "algebra", "polynomial.derivative_sub" -> "data", "submodule.annihilator_bot" -> "algebra", "polynomial.eval_bit1" -> "data", "generalized_continued_fraction.of_correctness_of_terminated_at" -> "algebra", "is_bounded_linear_map.tendsto" -> "analysis", "is_preconnected_of_forall_pair" -> "topology", "ne_comm" -> "logic", "alg_equiv.symm_comp" -> "algebra", "semidirect_product.ext" -> "algebra", "seq.coinduction" -> "data", "symm_le_uniformity" -> "topology", "measure_theory.lintegral_add" -> "analysis", "fin.pred_add_one" -> "data", "bool.bnot_inj" -> "data", "list.mem_filter" -> "data", "filter.compl_mem_hyperfilter_of_finite" -> "order", "nat.unpair_lt" -> "data", "int.modeq.refl" -> "data", "affine_independent_of_subsingleton" -> "algebra", "local_equiv.of_set_target" -> "data", "add_con.add_con_gen_eq" -> "algebra", "int.bodd_bit" -> "data", "category_theory.biprod.of_components_snd" -> "category_theory", "gaussian_int.norm_sq_le_norm_sq_of_re_le_of_im_le" -> "data", "linear_map.map_smul\:2082" -> "algebra", "category_theory.limits.cones.equivalence_of_reindexing_functor_obj" -> "category_theory", "int.coe_nat_eq_zero" -> "data", "is_bounded_bilinear_map.differentiable_within_at" -> "analysis", "le_div_iff_of_neg'" -> "algebra", "ennreal.supr_add" -> "topology", "principal_seg.of_element_apply" -> "set_theory", "with_zero.coe_ne_zero" -> "algebra", "nnreal.sum_div" -> "data", "add_commute.neg_right" -> "algebra", "set.image_mul_left'" -> "algebra", "coeff_scale_roots_nat_degree" -> "algebra", "complex.sinh_neg" -> "data", "is_unit.mul_right_inj" -> "algebra", "matrix.is_add_monoid_hom_mul_left" -> "data", "category_theory.limits.cofork.of_\[Pi]_app_zero" -> "category_theory", "nat.prime.pow_dvd_fact_iff" -> "data", "pos_num.dvd_to_nat" -> "data", "wseq.productive_congr" -> "data", "nat.fact_le" -> "data", "real.cos_add_pi" -> "analysis", "rat.cast_lt" -> "data", "equiv.is_lawful_functor'" -> "control", "primrec.bor" -> "computability", "category_theory.limits.types.filtered_colimit.r_equiv" -> "category_theory", "lucas_lehmer.X.mul_snd" -> "number_theory", "is_absolute_value.abv_one" -> "data", "pgame.add_comm_le" -> "set_theory", "category_theory.limits.prod.symmetry'" -> "category_theory", "nat.unpair_le_left" -> "data", "set.mem_image_elim" -> "data", "continuous_linear_equiv.comp_differentiable_iff" -> "analysis", "set.Iio_diff_Iio" -> "data", "mul_eq_of_eq_inv_mul" -> "algebra", "category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_of_cocone" -> "category_theory", "tangent_cone_univ" -> "analysis", "times_cont_mdiff_within_at_const" -> "geometry", "mul_right_continuous" -> "topology", "category_theory.iso.trans_conj_Aut" -> "category_theory", "multiset.le_inf" -> "data", "is_open_induced_eq" -> "topology", "is_max_filter.filter_mono" -> "order", "finset.ssubset_insert" -> "data", "finset.sort_nodup" -> "data", "abstract_completion.extension\:2082_coe_coe" -> "topology", "subtype.coe_image_univ" -> "data", "subgroup.mem_top" -> "algebra", "mem_nhds_within_Ioi_iff_exists_mem_Ioc_Ioo_subset" -> "topology", "uniform_space.completion.is_add_group_hom_extension" -> "topology", "continuous_linear_map.one_apply" -> "topology", "int.cast_mul" -> "data", "list.mem_cons_self" -> "init", "polynomial.degree_add_div_by_monic" -> "data", "set.Ici_def" -> "data", "equiv.point_reflection_apply" -> "data", "encodable.decode_one" -> "data", "nat.prime.not_coprime_iff_dvd" -> "data", "ordinal.nat_cast_ne_zero" -> "set_theory", "pow_ne_zero" -> "algebra", "tendsto_at_top_div" -> "analysis", "multiset.repeat_one" -> "data", "category_theory.limits.cofan.mk_\[Pi]_app" -> "category_theory", "add_monoid_hom.lipschitz_of_bound" -> "analysis", "add_left_inj" -> "algebra", "left_add_coset_right_add_coset" -> "algebra", "Sup_range" -> "order", "list.length_of_sublists_len" -> "data", "ring_hom.map_fpow" -> "algebra", "le_of_max_le_left" -> "algebra", "nat.mkpair_lt_mkpair_right" -> "data", "group.mem_closure" -> "algebra", "is_preirreducible.is_preconnected" -> "topology", "local_homeomorph.continuous_on_iff_continuous_on_comp_left" -> "topology", "submodule.mem_sup_left" -> "algebra", "hyperreal.not_infinite_mul" -> "data", "is_max_on.max" -> "order", "category_theory.functor.op_hom_map_app" -> "category_theory", "times_cont_mdiff_at.comp" -> "geometry", "not_lt_iff_eq_or_lt" -> "algebra", "ennreal.one_lt_rpow" -> "analysis", "is_connected.is_preconnected" -> "topology", "submodule.mul_assoc" -> "algebra", "measure_theory.eventually_eq_dirac" -> "analysis", "monotonicity.or" -> "meta", "lt_add_of_pos_left" -> "algebra", "Inf_Prop_eq" -> "order", "monoid_algebra.mul_apply_left" -> "data", "filter.map_at_top_eq" -> "order", "contracting_with.apriori_dist_iterate_fixed_point_le" -> "topology", "nat.sub_self" -> "init", "multiset.zero_le" -> "data", "set.mem_of_subset_of_mem" -> "data", "encodable.decode_list_zero" -> "data", "ideal.radical_idem" -> "algebra", "to_add_of_add" -> "algebra", "path_connected_subset_basis" -> "topology", "array.to_list_of_heq" -> "data", "linear_independent_set_iff_affine_independent_vadd_union_singleton" -> "algebra", "mvpfunctor.const.get_mk" -> "data", "multiset.ndinter_le_right" -> "data", "pi.multiset_sum_apply" -> "algebra", "filter.infi_ne_bot_iff_of_directed" -> "order", "int.lt_iff_le_and_ne" -> "init", "tensor_product.add_tmul" -> "algebra", "is_coprime.prod_left" -> "algebra", "is_min_filter.comp_antimono" -> "order", "nat.one_ne_bit1" -> "init", "cardinal.mk_plift_of_true" -> "set_theory", "continuous_multilinear_map.curry_left_apply" -> "analysis", "emetric.is_closed_ball" -> "topology", "ordinal.is_limit.one_lt" -> "set_theory", "mv_polynomial.eval\:2082_congr" -> "data", "real.norm_coe_nat" -> "analysis", "tendsto_locally_uniformly_on.continuous_on" -> "topology", "finmap.disjoint.symm_iff" -> "data", "continuous_linear_map.coe_neg'" -> "topology", "list.count_eq_one_of_mem" -> "data", "option.naturality" -> "control", "is_extr_on.is_local_extr" -> "topology", "fintype.card_of_subtype" -> "data", "matrix.ext_iff" -> "data", "gaussian_int.to_complex_add" -> "data", "continuous_linear_equiv.coe_symm_comp_coe" -> "topology", "set.exists_range_iff" -> "data", "measure_theory.simple_func.exists_range_iff" -> "analysis", "measure_theory.integrable_on.union" -> "analysis", "real.pi_lt_315" -> "data", "ennreal.tendsto_coe" -> "topology", "composition.mono_of_fin_boundaries" -> "combinatorics", "real.sin_pi_div_thirty_two" -> "analysis", "add_monoid_hom.mrange_top_of_surjective" -> "algebra", "local_homeomorph.eq_of_eq_on_source_univ" -> "topology", "galois_connection.is_lub_l_image" -> "order", "real.log_zero" -> "analysis", "rat.add_zero" -> "data", "ideal.exists_coeff_mem_comap_sdiff_comap_of_root_mem_sdiff" -> "algebra", "multiset.id_traverse" -> "data", "list.filter_map_cons_some" -> "data", "not_prime_one" -> "algebra", "irreducible_component_property" -> "topology", "convex_on.map_center_mass_le" -> "analysis", "nnreal.rpow_add'" -> "analysis", "ring_hom.map_list_prod" -> "algebra", "asymptotics.is_O_prod_left" -> "analysis", "asymptotics.is_O_const_smul_right" -> "analysis", "filter.is_countably_generated_seq" -> "order", "times_cont_mdiff.comp" -> "geometry", "bounded_continuous_function.dist_zero_of_empty" -> "topology", "monoid.coe_one" -> "algebra", "list.sorted_merge" -> "data", "pequiv.refl_apply" -> "data", "quotient_group.range_ker_lift_surjective" -> "algebra", "measure_theory.l1.to_fun_of_fun" -> "analysis", "linear_recurrence.is_sol_mk_sol" -> "algebra", "subring.mem_inf" -> "algebra", "has_strict_deriv_at_const" -> "analysis", "prime_multiset.prod_of_nat_list" -> "data", "mv_polynomial.coe_mul" -> "algebra", "relation.refl_trans_gen.head" -> "logic", "Inf_univ" -> "order", "localization_map.mk'_spec'" -> "algebra", "zorn.chain_closure_total" -> "order", "mem_own_left_coset" -> "algebra", "ennreal.of_real_eq_zero" -> "data", "abstract_completion.extend_unique" -> "topology", "category_theory.types_id" -> "category_theory", "set.eq_univ_of_subset" -> "data", "power_series.ext_iff" -> "algebra", "finset.ssubset_iff_of_subset" -> "data", "prime_spectrum.zero_locus_vanishing_ideal_eq_closure" -> "algebraic_geometry", "cardinal.lift_power" -> "set_theory", "gaussian_int.norm_eq_zero" -> "data", "is_R_or_C.abs_of_real" -> "data", "list.mem_last'_eq_last" -> "data", "asymptotics.is_o_const_iff_is_o_one" -> "analysis", "quotient_group.coe_gpow" -> "algebra", "matrix.det_one" -> "algebra", "iterated_deriv_within_eq_iterated_fderiv_within" -> "analysis", "function.injective.image_injective" -> "data", "multiset.nodup_powerset" -> "data", "set.surj_on_sUnion" -> "data", "has_fderiv_within_at.smul_const" -> "analysis", "filter.rtendsto'_def" -> "order", "set.Icc_def" -> "data", "finset.prod_dite" -> "algebra", "continuous_linear_map.equiv_prod_of_surjective_of_is_compl_apply" -> "analysis", "ordinal.mul_div_cancel" -> "set_theory", "norm_num.inv_div_one" -> "tactic", "rat.uniform_continuous_neg" -> "topology", "nat.lcm_self" -> "data", "continuous_induced_rng'" -> "topology", "nat.gcd_mul_right_left" -> "data", "subsemiring.gc_map_comap" -> "algebra", "cauchy_product" -> "data", "equiv.point_reflection_fixed_iff_of_module" -> "analysis", "continuous_linear_map.pi_eq_zero" -> "topology", "scale_roots_aeval_eq_zero_of_aeval_div_eq_zero" -> "algebra", "mul_lt_of_lt_inv_mul" -> "algebra", "irrational_rat_add_iff" -> "data", "lcm_eq_normalize" -> "algebra", "finsupp.subtype_domain_sub" -> "data", "wseq.lift_rel_o.imp_right" -> "data", "category_theory.monad.forget_creates_limits.cone_point_a" -> "category_theory", "finsupp.support_erase" -> "data", "compact_iff_finite_subcover" -> "topology", "category_theory.adjunction.unit_naturality" -> "category_theory", "primrec.pred" -> "computability", "set.compl_Ioi" -> "data", "wseq.tail_think" -> "data", "circle_deg1_lift.le_map_map_zero" -> "dynamics", "algebra_map_matrix_apply" -> "algebra", "continuous_linear_equiv.norm_pos" -> "analysis", "prod.eq_iff_fst_eq_snd_eq" -> "data", "units.smul_inv_smul" -> "algebra", "finset.bdd_above" -> "data", "with_top.mul_top" -> "algebra", "commute.fpow_left" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_within_at_congr_of_eventually_eq" -> "geometry", "pfunctor.M.is_path_cons" -> "data", "num.gcd_to_nat" -> "data", "sum.lex_inl_inl" -> "data", "multiset.coe_nodup" -> "data", "differentiable_on_univ" -> "analysis", "commute.inv_right'" -> "algebra", "nat.not_coprime_of_dvd_of_dvd" -> "data", "affine_map.coe_const" -> "algebra", "linear_equiv.of_submodule_apply" -> "algebra", "eq_iff_eq_of_sub_eq_sub" -> "algebra", "list.sum_map_hom" -> "data", "setoid.eqv_classes_disjoint" -> "data", "filter.lift_lift'_assoc" -> "order", "ennreal.to_real_mul_top" -> "data", "filter.mem_lift'_sets" -> "order", "monoid_hom.range_eq_map" -> "algebra", "finmap.lift_on\:2082_to_finmap" -> "data", "metric.sum.dist_eq_glue_dist" -> "topology", "punit.sup_eq" -> "algebra", "mv_polynomial.dim_mv_polynomial" -> "algebra", "algebra.tensor_product.algebra_map_apply" -> "algebra", "mv_power_series.constant_coeff_C" -> "algebra", "add_submonoid.localization_map.lift_injective_iff" -> "algebra", "polynomial.eval\:2082_endomorphism_algebra_map" -> "data", "add_monoid_hom.comp_assoc" -> "algebra", "forall_eq" -> "logic", "pfunctor.M.agree'_refl" -> "data", "mul_inv_cancel_of_invertible" -> "algebra", "category_theory.limits.coprod.inr_map_assoc" -> "category_theory", "inv_mul_le_iff_le_mul'" -> "algebra", "borel_eq_generate_Iio" -> "analysis", "prod.fst_neg" -> "algebra", "nat.lxor_right_inj" -> "data", "le_of_mul_le_mul_right" -> "algebra", "computable.const" -> "computability", "quotient.ind" -> "init", "nnreal.val_eq_coe" -> "data", "padic_val_nat.div" -> "data", "equiv.symm_image_image" -> "data", "eq_of_forall_ge_iff" -> "algebra", "formal_multilinear_series.comp_summable_nnreal" -> "analysis", "sub_lt_self" -> "algebra", "int.cast_pos" -> "data", "is_G\[Delta].inter" -> "topology", "finset.sup_mono" -> "data", "category_theory.limits.walking_pair.equiv_bool_symm_apply_ff" -> "category_theory", "linear_map.range_coe" -> "algebra", "hyperreal.infinite_pos_mul_of_infinite_pos_not_infinitesimal_pos" -> "data", "subalgebra.add_mem" -> "algebra", "list.length_zip" -> "data", "nat.lt_sub_right_iff_add_lt" -> "data", "multiset.pmap_cons" -> "data", "set.to_finset_univ" -> "data", "homological_complex.kernel_map_condition_assoc" -> "algebra", "equiv.perm.cycle_of_apply_of_same_cycle" -> "algebra", "monoid_hom.id_to_functor" -> "category_theory", "nat.ppred_eq_some" -> "data", "set.diff_inter_diff" -> "data", "ideal.mul_le_right" -> "algebra", "metric.continuous_inf_dist_pt" -> "topology", "mv_power_series.map_id" -> "algebra", "nat.gcd_mul_right_right" -> "data", "finsupp.add_apply" -> "data", "wseq.head_think" -> "data", "finset.map_insert" -> "data", "linear_equiv.of_linear_apply" -> "algebra", "submodule.coe_add" -> "algebra", "derivation.map_zero" -> "algebra", "finsupp.neg_apply" -> "data", "nat.le.intro" -> "init", "primrec.fin_val_iff" -> "computability", "differentiable_on.exp" -> "analysis", "ordering.swap_swap" -> "init", "rat.num_denom_mk" -> "data", "tangent_map_within_tangent_bundle_proj" -> "geometry", "list.mfoldl_cons" -> "data", "nat.coprime.pow" -> "data", "tendsto_prod_uniformity_snd" -> "topology", "power_series.constant_coeff_one" -> "algebra", "ennreal.infi_mul" -> "data", "typevec.drop_fun_from_append1_drop_last" -> "data", "dfinsupp.erase_ne" -> "data", "category_theory.limits.limit.lift_pre" -> "category_theory", "traversable.mfoldr.of_free_monoid_comp_free_mk" -> "control", "irrational_nrt_of_n_not_dvd_multiplicity" -> "data", "gaussian_int.div_def" -> "data", "unique_mdiff_on.inter" -> "geometry", "units.neg_mul" -> "algebra", "is_unit.mul_left_dvd" -> "algebra", "cardinal.mk_bUnion_le" -> "set_theory", "list.rotate'_length_mul" -> "data", "deriv_within_smul" -> "analysis", "measure_theory.measure.finite_at_filter.inf_of_left" -> "analysis", "finset.center_mass_empty" -> "analysis", "nhds_bind_nhds" -> "topology", "ideal.map_is_prime_of_surjective" -> "algebra", "continuous_at.prod_map" -> "topology", "is_R_or_C.abs_of_nat" -> "data", "pfunctor.M.eq_of_bisim" -> "data", "category_theory.under.under_morphism.ext" -> "category_theory", "nat.lxor_comm" -> "data", "finset.ssubset_iff" -> "data", "finset.val_lt_iff" -> "data", "equiv.trans_apply" -> "data", "add_submonoid.localization_map.mk'_surjective" -> "algebra", "set.preimage_mul_const_Iic_of_neg" -> "data", "cardinal.mk_subset_ge_of_subset_image_lift" -> "set_theory", "set.Ici_inter_Iic" -> "data", "units.coe_one" -> "algebra", "category_theory.biprod.unipotent_lower_hom" -> "category_theory", "dfinsupp.filter_pos_add_filter_neg" -> "data", "set.image_neg_Iio" -> "data", "int.neg_eq_of_add_eq_zero" -> "init", "complex.exp_conj" -> "data", "monotone.mul_strict_mono" -> "algebra", "ereal.coe_real_inj'" -> "data", "complex.int_cast_re" -> "data", "filter.frequently_imp_distrib_left" -> "order", "padic_norm.nonneg" -> "data", "measure_theory.l1.of_fun_zero" -> "analysis", "int.neg_add_cancel_left" -> "init", "multiset.coe_nodupkeys" -> "data", "vector.of_fn_nth" -> "data", "pi.mul_apply" -> "algebra", "set.surj_on.comp" -> "data", "is_measurable.Inter_Prop" -> "analysis", "category_theory.monad.forget_creates_colimits.new_cocone_X" -> "category_theory", "continuous_linear_equiv.times_cont_diff_on_comp_iff" -> "analysis", "is_bounded_linear_map.is_O_comp" -> "analysis", "nat.find_greatest_zero" -> "data", "is_open_map_sigma_mk" -> "topology", "linear_independent_span" -> "algebra", "polynomial.degree_one_le" -> "data", "function.comp_app" -> "init", "add_submonoid.localization_map.mk'_add_cancel_left" -> "algebra", "Ioo_mem_nhds_within_Iio" -> "topology", "local_homeomorph.restr_coe" -> "topology", "equiv.forall\:2082_congr'" -> "data", "subring.top_prod_top" -> "algebra", "category_theory.iso.hom_inv_id_app_assoc" -> "category_theory", "add_subgroup.le_normalizer" -> "algebra", "int.neg_mul_eq_mul_neg" -> "init", "fixed_points.coe_algebra_map" -> "algebra", "set.finite_subset_Union" -> "data", "mv_polynomial.is_homogeneous.inj_right" -> "algebra", "fderiv_within.snd" -> "analysis", "int.modeq.exists_unique_equiv" -> "data", "emetric.mem_closed_ball" -> "topology", "category_theory.limits.cocones.precompose_equivalence_unit_iso" -> "category_theory", "fin.succ_above_descend" -> "data", "uniform_embedding_subtype_emb" -> "topology", "category_theory.limits.types.filtered_colimit.r_eq" -> "category_theory", "filter.tendsto_at_top_of_add_const_right" -> "order", "opposite.coe_unop_add_hom" -> "algebra", "canonically_ordered_semiring.zero_lt_one" -> "algebra", "mdifferentiable_within_at_inter'" -> "geometry", "multiset.mem_ndunion" -> "data", "set.eq_or_mem_of_mem_insert" -> "data", "polynomial.root_mul_left_of_is_root" -> "data", "free_group.induction_on" -> "algebra", "ordinal.le_zero" -> "set_theory", "polynomial.card_roots_sub_C" -> "data", "metric.to_glue_r_isometry" -> "topology", "qpf.recF_eq" -> "data", "filter.pure_le_iff" -> "order", "le_of_lt" -> "init", "functor.map_id" -> "control", "filter.eventually.filter_mono" -> "order", "cardinal.card_typein_lt" -> "set_theory", "ideal.comap_is_maximal_of_surjective" -> "algebra", "local_homeomorph.restr_to_local_equiv'" -> "topology", "eq_false_of_not_eq_true" -> "init", "measure_theory.measure.bind_bind" -> "analysis", "is_closed_prod" -> "topology", "dist_le_Ico_sum_dist" -> "topology", "ceil_sub_int" -> "algebra", "padic_norm.of_int" -> "data", "differentiable_snd" -> "analysis", "is_ring_hom.of_semiring" -> "algebra", "con.to_submonoid_inj" -> "algebra", "mul_action.inv_smul_eq_iff" -> "algebra", "norm_add_le" -> "analysis", "fderiv_within_sub_const" -> "analysis", "vsub_set_empty" -> "algebra", "set.neg_preimage" -> "algebra", "one_lt_inv_of_inv" -> "algebra", "category_theory.comma.comp_left" -> "category_theory", "pow_mul" -> "algebra", "pos_num.size_eq_nat_size" -> "data", "category_theory.over.hom_mk_right" -> "category_theory", "polynomial.degree_add_le" -> "data", "bool.cond_to_bool" -> "data", "category_theory.limits.coprod.associator_hom" -> "category_theory", "has_fpower_series_at.continuous_at" -> "analysis", "decidable.le_or_lt" -> "init", "vadd_left_cancel" -> "algebra", "monotone.le_map_Sup" -> "order", "complex.is_cau_seq_abs" -> "data", "quadratic_form.to_matrix_comp" -> "algebra", "strict_fderiv_of_cont_diff" -> "analysis", "list.lookup_all_sublist" -> "data", "primrec.option_iget" -> "computability", "padic_int.coe_mul" -> "data", "hash_map.find_empty" -> "data", "is_R_or_C.abs_div" -> "data", "nhds_is_mul_hom" -> "topology", "category_theory.limits.prod_functor_obj_map" -> "category_theory", "prod.swap_left_inverse" -> "data", "int.shiftl_add" -> "data", "filter.has_basis.has_basis_self_subset" -> "order", "stream.corec_id_f_eq_iterate" -> "data", "array.read_foreach" -> "data", "pell.eq_pow_of_pell" -> "number_theory", "deriv_within_csin" -> "analysis", "prod.snd_injective" -> "data", "one_lt_gold" -> "data", "bilin_form.comp_left_apply" -> "algebra", "add_con.map_apply" -> "algebra", "list.last_eq_of_concat_eq" -> "data", "has_deriv_at.lhopital_zero_right_on_Ioo" -> "analysis", "measure_theory.l1.simple_func.integral_congr" -> "analysis", "list.perm.diff" -> "data", "set.powerset_inter" -> "data", "int.ne_of_nat_abs_ne_nat_abs_of_nonneg" -> "init", "wseq.nth_terminates_le" -> "data", "inv_le_one'" -> "algebra", "add_units.coe_le_coe" -> "algebra", "convex.mem_to_cone" -> "analysis", "composition.blocks_fun_congr" -> "combinatorics", "rat.of_int_eq_mk" -> "data", "filter.germ.map\:2082_const" -> "order", "list.perm_cons" -> "data", "subtype.map_id" -> "data", "function.support_sum" -> "data", "generate_from_mono" -> "topology", "finset.eq_of_card_le_one_of_prod_eq" -> "algebra", "list.subset_erase_dup" -> "data", "has_mfderiv_within_at.nhds_within" -> "geometry", "submonoid.comap_surjective_of_injective" -> "algebra", "linear_map.surjective_of_injective" -> "algebra", "list.mem_permutations_aux_of_perm" -> "data", "cardinal.mk_preimage_of_injective_lift" -> "set_theory", "set.image_add_const_Ioi" -> "data", "additive.normal_add_subgroup_iff" -> "algebra", "category_theory.iso.symm_hom" -> "category_theory", "ring_hom.iterate_map_gsmul" -> "algebra", "list.exists_erase_eq" -> "data", "power_series.coeff_zero_mul_X" -> "algebra", "nat.odd_mul_odd_div_two" -> "data", "multiset.powerset_aux_perm_powerset_aux'" -> "data", "is_local_min.congr" -> "topology", "submonoid.comap_inf_map_of_injective" -> "algebra", "finmap.erase_erase" -> "data", "times_cont_diff_on.continuous_on_fderiv_within" -> "analysis", "function.is_fixed_pt.is_periodic_pt" -> "dynamics", "set.inv_subset" -> "algebra", "pgame.mk_lt_mk" -> "set_theory", "pfun.image_mono" -> "data", "gt_of_mul_lt_mul_neg_left" -> "algebra", "nat.prime_def_lt" -> "data", "relation.trans_gen.to_refl" -> "logic", "nat.dvd_mul_right" -> "init", "continuous_linear_map.smul_right_apply" -> "topology", "continuous_multilinear_curry_left_equiv_symm_apply" -> "analysis", "power_series.constant_coeff_zero" -> "algebra", "nat.div_eq_of_lt_le" -> "init", "nat.even_bit0" -> "data", "fin.coe_injective" -> "data", "mv_polynomial.eval\:2082_eq'" -> "data", "is_local_max.min" -> "topology", "mem_nhds_right" -> "topology", "ordinal.lift.principal_seg_coe" -> "set_theory", "normed_ring.inverse_continuous_at" -> "analysis", "list.length_map_accumr" -> "init", "multiset.range_zero" -> "data", "nnreal.coe_eq" -> "data", "equiv.perm.disjoint_one_left" -> "algebra", "hash_map.keys_empty" -> "data", "subtype.exists_set_subtype" -> "data", "topological_fiber_bundle_core.open_source'" -> "topology", "cluster_pt_principal_iff_frequently" -> "topology", "add_con.mem_coe" -> "algebra", "set.image_const_sub_Ico" -> "data", "submonoid.mem_sup_left" -> "algebra", "div_div_div_cancel_right" -> "algebra", "zsqrtd.zero_im" -> "data", "finsupp.prod_ite_eq'" -> "data", "dfinsupp.sum_sub_index" -> "data", "div_mul_eq_div_mul_one_div" -> "algebra", "category_theory.End.one_def" -> "category_theory", "segment_eq_image" -> "analysis", "ennreal.infi_sum" -> "data", "filter.tendsto_at_bot_add_nonpos_right" -> "order", "pell.eq_of_xn_modeq_lem1" -> "number_theory", "pgame.le_of_restricted" -> "set_theory", "mem_left_coset_left_coset" -> "algebra", "cardinal.eq_one_iff_subsingleton_and_nonempty" -> "set_theory", "finset.powerset_empty" -> "data", "measure_theory.ae_eq_fun.edist_zero_eq_coe" -> "analysis", "mul_action_hom.comp_apply" -> "algebra", "measure_theory.l1.of_fun_eq_mk" -> "analysis", "model_with_corners.continuous" -> "geometry", "quadratic_form.polar_comm" -> "algebra", "mvfunctor.of_mem_supp" -> "control", "finset.sum_range_sub'" -> "algebra", "cancel_factors.add_subst" -> "tactic", "and_or_distrib_right" -> "logic", "set.image_const_add_Ioc" -> "data", "filter.prod_ne_bot" -> "order", "sum_hom_units_eq_zero" -> "algebra", "compact_covered_by_mul_left_translates" -> "topology", "complete_univ" -> "topology", "inner_product_geometry.angle_comm" -> "geometry", "polynomial.derivative_X" -> "data", "free_add_monoid.add_def" -> "algebra", "multiset.card_erase_le" -> "data", "finsupp.filter_single_of_pos" -> "data", "measure_theory.ae_eq_fun.coe_fn_neg" -> "analysis", "list.insert_nil" -> "data", "cauchy_seq_finset_of_norm_bounded" -> "analysis", "nat.lxor_self" -> "data", "set.image2_inter_subset_left" -> "data", "nat.mod_two_ne_zero" -> "data", "category_theory.iso.cancel_iso_hom_right" -> "category_theory", "rel_embedding.is_preorder" -> "order", "mul_equiv.to_Mon_iso_inv" -> "algebra", "list.sublists_aux\:2081_bind" -> "data", "min_right_comm" -> "algebra", "local_equiv.ext" -> "data", "setoid.ext'" -> "data", "uniform_inducing.uniform_continuous_iff" -> "topology", "finmap.insert_insert" -> "data", "filter.tendsto_principal" -> "order", "zmod.val_eq_zero" -> "data", "is_prime.to_maximal_ideal" -> "algebra", "nat.le_of_le_of_sub_le_sub_right" -> "init", "ring_hom.ker_eq_bot_iff_eq_zero" -> "algebra", "ideal.integral_closure.is_maximal_of_is_maximal_comap" -> "algebra", "ideal.is_primary.to_is_prime" -> "algebra", "irrational.neg" -> "data", "list.perm.append" -> "data", "semiconj_by.gpow_right" -> "algebra", "list.prod_take_of_fn" -> "data", "nat.cast_bit1" -> "data", "fin.init_snoc" -> "data", "metric.ball_zero" -> "topology", "holor.mul_scalar_mul" -> "data", "ennreal.coe_le_iff" -> "data", "presented_group.to_group.inv" -> "algebra", "measure_theory.integrable_at_filter.inf_of_left" -> "analysis", "tsum_supr_decode2" -> "topology", "ordinal.le_min" -> "set_theory", "zmod.coe_val_min_abs" -> "data", "is_R_or_C.abs_to_complex" -> "data", "category_theory.limits.fork.equalizer_ext" -> "category_theory", "set.Ioi_subset_Ioc_union_Ioi" -> "data", "continuous_linear_map.coe_add" -> "topology", "ring_hom.iterate_map_frobenius" -> "algebra", "function.iterate_zero" -> "logic", "add_ite" -> "algebra", "add_submonoid.ext'_iff" -> "algebra", "nat.add_mod_add_ite" -> "data", "add_submonoid.mem_bot" -> "algebra", "submodule.lt_of_le_of_findim_lt_findim" -> "algebra", "pi.comp_one" -> "algebra", "inv_inj" -> "algebra", "linear_independent.to_subtype_range" -> "algebra", "polynomial.map_mod_div_by_monic" -> "data", "Cauchy.nonempty_Cauchy_iff" -> "topology", "mem_uniformity_of_uniform_continuous_invariant" -> "topology", "add_submonoid.localization_map.exists_of_sec_mk'" -> "algebra", "primrec.decode2" -> "computability", "pnat.mod_add_div" -> "data", "category_theory.monad.algebra.EilenbergMoore_to_category_struct_comp" -> "category_theory", "is_asymm.swap" -> "order", "real.of_near" -> "data", "polynomial.degree_eq_nat_degree" -> "data", "dioph.dioph_fn_comp1" -> "number_theory", "real.continuous_log" -> "analysis", "category_theory.is_equivalence.functor_unit_comp" -> "category_theory", "of_to_bool_true" -> "init", "cardinal.ord.order_embedding_coe" -> "set_theory", "filter.mem_of_finite_sUnion_ultrafilter" -> "order", "is_local_min_on.neg" -> "topology", "div_lt_div_right" -> "algebra", "finset.Ico_\:2124.card" -> "data", "Set.mem_union" -> "set_theory", "finmap.empty_union" -> "data", "compl_injective" -> "order", "function.injective.comp" -> "init", "subring.gc_map_comap" -> "algebra", "submodule.comap_snd" -> "algebra", "submodule.ker_mkq" -> "algebra", "sigma.exists" -> "data", "bilin_form.smul_right" -> "algebra", "ennreal.coe_of_nnreal_hom" -> "data", "rat.sub_def" -> "data", "prime_spectrum.zero_locus_sup" -> "algebraic_geometry", "category_theory.limits.is_colimit.unique_up_to_iso_inv" -> "category_theory", "stream.exists_of_mem_map" -> "data", "continuous_linear_map.coe_apply'" -> "topology", "rat.cast_min" -> "data", "gaussian_int.to_complex_def" -> "data", "isometric.vadd_const_to_equiv" -> "analysis", "mv_polynomial.degrees_sub" -> "data", "nhds_eq_nhds_emetric_ball" -> "topology", "matrix.zero_empty" -> "data", "denumerable.prod_of_nat_val" -> "data", "set.ord_connected.interval_subset" -> "data", "multiset.prod_zero" -> "data", "free_monoid.hom_eq" -> "algebra", "stream.nth_tails" -> "data", "function.support_subset_iff'" -> "data", "relation.refl_trans_gen_idem" -> "logic", "set.preimage_const_mul_Icc_of_neg" -> "data", "finset.exists_ne_zero_of_sum_ne_zero" -> "algebra", "has_fderiv_at.const_sub" -> "analysis", "quotient_group.lift_mk'" -> "algebra", "mv_polynomial.monomial_eq" -> "data", "is_basis.to_dual_inj" -> "algebra", "nat.right_distrib" -> "init", "asymptotics.is_O.const_mul_left" -> "analysis", "filter.eq_Inf_of_mem_sets_iff_exists_mem" -> "order", "has_deriv_at_filter_const" -> "analysis", "category_theory.yoneda.obj_map_id" -> "category_theory", "mv_power_series.coeff_zero_eq_constant_coeff_apply" -> "algebra", "list.filter_filter" -> "data", "nat.exists_eq_add_of_lt" -> "data", "add_eq_zero_iff_eq_zero_of_nonneg" -> "algebra", "int.add_neg" -> "init", "contracting_with.dist_fixed_point_fixed_point_of_dist_le'" -> "topology", "nat.test_bit_succ" -> "init", "asymptotics.is_O_norm_right" -> "analysis", "pgame.lt_irrefl" -> "set_theory", "multiset.pairwise_of_nodup" -> "data", "category_theory.differential_object.hom.id_f" -> "category_theory", "cardinal.wf" -> "set_theory", "continuous_at.preimage_mem_nhds" -> "topology", "nat.one_lt_pow" -> "data", "measurable_add" -> "analysis", "gsmul_int_one" -> "algebra", "list.nth_le_split_wrt_composition" -> "combinatorics", "partrec.merge" -> "computability", "ordinal.card_eq_zero" -> "set_theory", "polynomial.map_list_prod" -> "data", "metric.mem_iff_inf_dist_zero_of_closed" -> "topology", "pairwise_disjoint_fiber" -> "data", "alist.union_empty" -> "data", "prod.fst_add" -> "algebra", "linear_map.range_eq_of_proj" -> "algebra", "submodule.comap_coe" -> "algebra", "mat_poly_equiv_eval" -> "algebra", "has_fderiv_within_at.smul_algebra" -> "analysis", "metric.ball_subset_closed_ball" -> "topology", "nat.zero_ne_one" -> "init", "relation.refl_trans_gen.total_of_right_unique" -> "logic", "mv_polynomial.hom_C" -> "data", "set.image_union" -> "data", "is_group_hom.one_ker_inv" -> "algebra", "computation.mem_parallel" -> "data", "array.push_back_rev_list" -> "data", "mv_polynomial.total_degree_list_prod" -> "data", "uniform_space.compact_space_iff_seq_compact_space" -> "topology", "finsupp.filter_curry" -> "data", "list.index_of_eq_length" -> "data", "ennreal.coe_two" -> "data", "metric.uniform_continuous_inf_dist_Hausdorff_dist" -> "topology", "Set.pair_inj" -> "set_theory", "nat.bit0_lt_bit1" -> "init", "ennreal.sum_le_tsum" -> "topology", "dvd_add" -> "algebra", "module.algebra_map_End_apply" -> "algebra", "category_theory.pre_id" -> "category_theory", "incomp_trans_of" -> "init", "ring_hom.ext_iff" -> "algebra", "measure_theory.lintegral_edist_lt_top" -> "analysis", "polynomial.roots_prod_X_sub_C" -> "data", "list.perm.kunion_left" -> "data", "is_preconnected.intermediate_value\:2082" -> "topology", "cau_seq.const_lim_zero" -> "data", "subsemiring.mem_closure" -> "algebra", "category_theory.over.iso_mk_hom_left" -> "category_theory", "complex.cos_sub_sin_I" -> "data", "lipschitz_with.iterate" -> "topology", "is_unit_iff_ne_zero" -> "algebra", "category_theory.monoidal_category.unitors_equal.cells_3_4" -> "category_theory", "has_deriv_within_at.limsup_norm_slope_le" -> "analysis", "real.pi_div_two_pos" -> "analysis", "tendsto_inv_at_top_zero" -> "analysis", "set.bUnion_subset" -> "data", "pgame.not_lt" -> "set_theory", "multiset.join_add" -> "data", "measurable_space.is_measurable_infi" -> "analysis", "prod.mk_eq_one" -> "algebra", "submodule.comap_smul'" -> "algebra", "is_bounded_bilinear_map.is_O'" -> "analysis", "closed_ball_Icc" -> "topology", "left_ord_continuous.map_Sup'" -> "order", "has_deriv_within_at.sinh" -> "analysis", "supr_bool_eq" -> "order", "has_deriv_within_at_inter" -> "analysis", "nat.cast_add_one_ne_zero" -> "algebra", "cInf_upper_bounds_eq_cSup" -> "order", "int.cast_le" -> "data", "mul_div_mul_left" -> "algebra", "tendsto_of_tendsto_of_tendsto_of_le_of_le'" -> "topology", "turing.TM2to1.add_bottom_map" -> "computability", "linear_equiv_iso_Module_iso_hom" -> "algebra", "turing.frespects_eq" -> "computability", "image.is_submonoid" -> "algebra", "vector3.append_cons" -> "number_theory", "option.lift_or_get_some_some" -> "data", "pythagorean_triple.coprime_classification" -> "number_theory", "affine_map.decomp" -> "algebra", "convex.norm_image_sub_le_of_norm_has_deriv_within_le" -> "analysis", "hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg" -> "data", "linear_map.to_add_monoid_hom_coe" -> "algebra", "affine_subspace.direction_mk'" -> "algebra", "is_subgroup.inv_mem_iff" -> "algebra", "nat.even.add" -> "data", "category_theory.adjunction.cocones_iso_component_inv_app" -> "category_theory", "category_theory.functor.to_cone_X" -> "category_theory", "sup_eq_max" -> "order", "has_sum.summable" -> "topology", "pgame.le_refl" -> "set_theory", "free_abelian_group.lift.ext" -> "algebra", "category_theory.limits.prod.left_unitor_inv" -> "category_theory", "ordinal.lift_card" -> "set_theory", "encodable.decode_option_succ" -> "data", "finset.image_const" -> "data", "ordinal.lift_down'" -> "set_theory", "local_equiv.prod_coe_symm" -> "data", "list.exists_of_mem_join" -> "data", "int.sub_nat_nat_of_sub_eq_zero" -> "init", "submonoid.localization_map.of_mul_equiv_of_localizations_eq_iff_eq" -> "algebra", "polynomial.ring_hom_eval\:2082_algebra_map_int" -> "data", "fin.succ_last" -> "data", "category_theory.functor.map_hom_inv" -> "category_theory", "localization_map.mk'_surjective" -> "algebra", "free_add_semigroup.traverse_eq" -> "algebra", "set.indicator_preimage_of_not_mem" -> "data", "category_theory.arrow.lift_mk'_left" -> "category_theory", "finset.mem_union" -> "data", "complex.of_real_smul" -> "data", "measure_theory.outer_measure.trim_le_trim" -> "analysis", "lucas_lehmer.mersenne_int_ne_zero" -> "number_theory", "power_series.is_unit_constant_coeff" -> "algebra", "generalized_continued_fraction.second_continuant_aux_eq" -> "algebra", "measure_theory.integral_eq_lintegral_of_nonneg_ae" -> "analysis", "alg_hom.injective_cod_restrict" -> "algebra", "real.Ioo_eq_ball" -> "topology", "zsqrtd.add_im" -> "data", "is_add_group_hom.injective_of_trivial_ker" -> "algebra", "category_theory.under.under_left" -> "category_theory", "ideal.sup_mul_right_self" -> "algebra", "decidable_linear_ordered_add_comm_group.eq_of_abs_sub_nonpos" -> "algebra", "div_mul_cancel_of_invertible" -> "algebra", "category_theory.nat_trans.congr_app" -> "category_theory", "list.mem_of_mem_erase" -> "data", "turing.TM2to1.tr_eval_dom" -> "computability", "group.closure_subset" -> "algebra", "quadratic_form.discr_smul" -> "algebra", "real.pi_gt_three" -> "data", "fin.val_mul" -> "data", "encodable.decode_of_equiv" -> "data", "nat.coprime_primes" -> "data", "category_theory.limits.coprod_map_comp_id" -> "category_theory", "list.sublists'_singleton" -> "data", "list.filter_of_map" -> "data", "nat.mod_add_div" -> "init", "set.union_left_comm" -> "data", "continuous.neg" -> "topology", "ring.fractional_ideal.map_comp" -> "algebra", "ennreal.lt_iff_exists_coe" -> "data", "polynomial.eval\:2082_monomial" -> "data", "prime_spectrum.is_open_iff" -> "algebraic_geometry", "inner_div_norm_mul_norm_eq_neg_one_iff" -> "analysis", "computation.parallel_congr_left" -> "data", "linear_map.ker_prod" -> "algebra", "ring_hom.mem_srange" -> "algebra", "finsupp.sum_ite_eq" -> "data", "is_add_group_hom.add" -> "algebra", "tendsto_nhds_unique'" -> "topology", "strict_mono.add_monotone" -> "algebra", "finset.fold_max_lt" -> "data", "is_absolute_value.abs_abv_sub_le_abv_sub" -> "data", "add_con.add" -> "algebra", "filter.tendsto.inv" -> "topology", "zmod.cast_one'" -> "data", "le_max_iff" -> "algebra", "set.bUnion_preimage_singleton" -> "data", "list.chain'.rel_head'" -> "data", "circle_deg1_lift.iterate_pos_lt_iff" -> "dynamics", "list.lookmap_of_forall_not" -> "data", "category_theory.monad.forget_creates_colimits.new_cocone_\[Iota]" -> "category_theory", "has_fderiv_at_filter_real_equiv" -> "analysis", "fintype.subtype_card" -> "data", "nhds_within_Ico_eq_nhds_within_Ici" -> "topology", "linear_independent.total_repr" -> "algebra", "linear_map.trace_aux_eq" -> "algebra", "deriv_add" -> "analysis", "ennreal.inv_one" -> "data", "finset.mem_insert" -> "data", "uniform_space.of_core_eq_to_core" -> "topology", "nat.mod_eq_sub_mod" -> "init", "add_left_iterate" -> "algebra", "filter.tendsto_at_bot'" -> "order", "inv_inv" -> "algebra", "decidable.le_iff_le_iff_lt_iff_lt" -> "algebra", "affine.simplex.inner_monge_point_vsub_face_centroid_vsub" -> "geometry", "nat.lt_add_one_iff" -> "data", "is_unit_pow" -> "algebra", "circle_deg1_lift.commute_add_int" -> "dynamics", "ordered_ring.mul_le_mul_of_nonneg_left" -> "algebra", "finsupp.sum_zero_index" -> "data", "multiset.nodup_inter_left" -> "data", "with_top.nat_ne_top" -> "data", "filter.tendsto_infi" -> "order", "is_G\[Delta]_Inter" -> "topology", "nnreal.tendsto_coe" -> "topology", "measure_theory.integrable.sub" -> "analysis", "power_series.X_dvd_iff" -> "algebra", "nhds_translation" -> "topology", "filter.exists_lt_of_tendsto_at_bot" -> "order", "filter.frequently_or_distrib_right" -> "order", "pell.yn_modeq_two" -> "number_theory", "category_theory.limits.biprod.braiding_hom" -> "category_theory", "set.range_nonempty" -> "data", "lt_mul_of_inv_mul_lt_right" -> "algebra", "generalized_continued_fraction.terminated_at_iff_s_none" -> "algebra", "filter.comap_supr" -> "order", "nat.le_rec_on_succ" -> "data", "ordinal.mul_add" -> "set_theory", "dfinsupp.prod_subtype_domain_index" -> "data", "tensor_product.ext" -> "algebra", "asymptotics.is_o_refl_left" -> "analysis", "cardinal.cof_is_regular" -> "set_theory", "omega.nat.nnf_equiv" -> "tactic", "finsupp.sigma_sum" -> "data", "measurable_equiv.symm_to_equiv" -> "analysis", "infi_eq_if" -> "order", "nat.partrec.code.eval_eq_rfind_opt" -> "computability", "exists_deriv_eq_zero'" -> "analysis", "ennreal.supr_add_supr_of_monotone" -> "topology", "set.dual_Ici" -> "data", "set.sInter_union" -> "data", "algebra.tensor_product.include_left_apply" -> "algebra", "mdifferentiable_on_iff_differentiable_on" -> "geometry", "nat.lt_one_add_iff" -> "data", "pfunctor.M.bisim_equiv" -> "data", "polynomial.coeff_expand_mul'" -> "algebra", "multiset.le_erase_dup" -> "data", "finset.sum_filter" -> "algebra", "has_fderiv_at.has_fderiv_at_filter" -> "analysis", "wseq.lift_rel_o.imp" -> "data", "cardinal.omega_ne_zero" -> "set_theory", "category_theory.limits.biprod.lift_desc_assoc" -> "category_theory", "ordinal.is_normal.nfp_fp" -> "set_theory", "finsupp.lsingle_range_le_ker_lapply" -> "algebra", "free_add_magma.traverse_pure" -> "algebra", "continuous_induced_dom" -> "topology", "differentiable_on.prod" -> "analysis", "surj_on_Iic_of_monotone_surjective" -> "data", "multiset.eq_union_left" -> "data", "linear_map.mk_continuous_apply" -> "analysis", "add_subgroup.top_prod_top" -> "algebra", "zmod.prime_ne_zero" -> "data", "padic_val_rat_def" -> "data", "order_iso.map_bot" -> "order", "zero_eq_mul_self" -> "algebra", "mvqpf.comp.get_map" -> "data", "filter.at_bot_countable_basis" -> "order", "subsemiring.closure_eq_of_le" -> "algebra", "lie_algebra.equiv.apply_symm_apply" -> "algebra", "UniformSpace.coe_comp" -> "topology", "add_halves" -> "algebra", "convex.is_path_connected" -> "analysis", "list.sum_append" -> "data", "enat.with_top_equiv_symm_coe" -> "data", "cauchy_map_iff" -> "topology", "mv_polynomial.is_homogeneous_zero" -> "algebra", "circle_deg1_lift.translation_number_of_eq_add_int" -> "dynamics", "complex.of_real_eq_coe" -> "data", "pequiv.trans_single_of_mem" -> "data", "linear_equiv.coe_of_eq_apply" -> "algebra", "free_magma.pure_bind" -> "algebra", "smooth_manifold_with_corners.compatible" -> "geometry", "model_with_corners_prod_to_local_equiv" -> "geometry", "monotone.mul" -> "algebra", "int.neg_succ_of_nat_mul_neg_of_nat" -> "init", "con.Sup_def" -> "algebra", "measure_theory.induced_outer_measure_exists_set" -> "analysis", "nat.sub_le" -> "init", "set.to_finset_inj" -> "data", "norm_num.add_pos_neg_neg" -> "tactic", "uniformity_subtype" -> "topology", "list.perm.nil_eq" -> "data", "submodule.inf_orthogonal" -> "analysis", "set.mem_seq_iff" -> "data", "decidable.le_of_not_lt" -> "init", "linear_pmap.sup_le" -> "algebra", "eq_inv_mul_of_mul_eq" -> "algebra", "category_theory.iso.symm_symm_eq" -> "category_theory", "finset.sum_singleton" -> "algebra", "multiset.Ico.map_sub" -> "data", "has_fderiv_at.const_mul" -> "analysis", "filter.is_basis.mem_filter_basis_iff" -> "order", "lt_neg" -> "algebra", "measurable.max" -> "analysis", "set.finite.compact_convex_hull" -> "analysis", "metric.second_countable_of_almost_dense_set" -> "topology", "category_theory.fork_\[Iota]_comp_cofork_\[Pi]_assoc" -> "algebra", "monoid_hom.eq_on_closure" -> "algebra", "set.eq_empty_of_not_nonempty" -> "data", "filter.mem_hyperfilter_of_finite_compl" -> "order", "list.reverse_reverse" -> "data", "lt_of_mul_lt_mul_left'" -> "algebra", "is_irreducible.is_preirreducible" -> "topology", "list.chain_of_chain_cons" -> "data", "finset.inter_distrib_right" -> "data", "closed_embedding_sigma_mk" -> "topology", "ring.fractional_ideal.exists_eq_span_singleton_mul" -> "algebra", "vector_span_eq_top_of_affine_independent_of_card_eq_findim_add_one" -> "algebra", "pgame.lt_of_lt_of_le" -> "set_theory", "complex.sin_two_pi" -> "analysis", "nat.modeq.modeq_mul_left'" -> "data", "fin.eta" -> "data", "local_equiv.restr_univ" -> "data", "set.finite.dependent_image" -> "data", "finsupp_tensor_finsupp_single" -> "algebra", "multilinear_map.smul_apply" -> "algebra", "neg_div" -> "algebra", "filter.le_lift" -> "order", "lie_algebra.orthogonal.JD_transform" -> "algebra", "local_equiv.coe_trans_symm" -> "data", "local_homeomorph.continuous_at" -> "topology", "div_div_div_div_eq" -> "algebra", "category_theory.limits.has_image_map.factor_map" -> "category_theory", "set.image_const_add_Ici" -> "data", "measure_theory.outer_measure.union_null" -> "analysis", "mul_semiring_action_hom.id_apply" -> "algebra", "int.coe_nat_abs" -> "data", "category_theory.monoidal_of_has_finite_products.right_unitor_inv" -> "category_theory", "nat.le_sub_add" -> "data", "deriv.lhopital_zero_left_on_Ioo" -> "analysis", "multiset.to_finsupp_to_multiset" -> "data", "int.add_pos_of_nonneg_of_pos" -> "init", "approximates_linear_on.injective" -> "analysis", "category_theory.non_preadditive_abelian.add_comp" -> "category_theory", "set.union_mul" -> "algebra", "int.lt_add_one_of_le" -> "init", "continuous_linear_map.norm_def" -> "analysis", "norm_sub_mul_self" -> "analysis", "no_top_order.upper_bounds_univ" -> "order", "nhds_eq_comap_uniformity" -> "topology", "ordinal.type_lt" -> "set_theory", "multiset.range_succ" -> "data", "subtype.ne_of_val_ne" -> "init", "category_theory.differential_object.hom.ext" -> "category_theory", "tsum_prod" -> "topology", "list.length_pos_of_mem_split_wrt_composition" -> "combinatorics", "mul_lt_of_le_one_of_lt'" -> "algebra", "principal_seg.trans_apply" -> "set_theory", "category_theory.limits.biprod.braiding_inv" -> "category_theory", "implicit_function_data.prod_map_implicit_function" -> "analysis", "support_scale_roots_eq" -> "algebra", "filter.eventually_eq.neg" -> "order", "complex.tanh_neg" -> "data", "sum.comp_traverse" -> "control", "ereal.coe_real_lt" -> "data", "filter.tendsto_at_top_of_monotone_of_subseq" -> "order", "is_bounded_bilinear_map_smul_algebra" -> "analysis", "is_R_or_C.norm_sq_pos" -> "data", "generalized_continued_fraction.first_continuant_aux_eq_h_one" -> "algebra", "has_deriv_at.has_deriv_at_filter" -> "analysis", "algebra.left_comm" -> "algebra", "le_nhds_of_cauchy_adhp" -> "topology", "category_theory.dite_comp" -> "category_theory", "pgame.numeric_rec" -> "set_theory", "equiv.set.apply_range_symm" -> "data", "generalized_continued_fraction.first_denominator_eq" -> "algebra", "free_abelian_group.map_neg" -> "algebra", "real.angle.coe_two_pi" -> "analysis", "with_zero.coe_inj" -> "algebra", "uniform_continuous_sub" -> "topology", "locally_finite_of_finite" -> "topology", "list.nodup_of_nodup_append_left" -> "data", "eq_one_div_of_mul_eq_one_left" -> "algebra", "polynomial.le_nat_degree_of_ne_zero" -> "data", "free_group.to_group.one" -> "algebra", "complex.norm_sq_eq_zero" -> "data", "add_subgroup.zero_mem" -> "algebra", "bounded_continuous_function.continuous_comp" -> "topology", "comp_symm_mem_uniformity_sets" -> "topology", "measure_theory.lintegral_const" -> "analysis", "harmonic_tendsto_at_top" -> "analysis", "matrix.mul_nonsing_inv" -> "algebra", "padic_norm.one" -> "data", "category_theory.limits.biprod.inl_fst" -> "category_theory", "mvqpf.cofix.dest_corec'" -> "data", "set.right_mem_Icc" -> "data", "smul_ite" -> "algebra", "differentiable_within_at.csin" -> "analysis", "cardinal.eq_of_add_eq_of_omega_le" -> "set_theory", "set.empty_add" -> "algebra", "nat.find_greatest_le" -> "data", "complex.eq_conj_iff_real" -> "data", "traversable.traverse_map" -> "control", "convex.affine_image" -> "analysis", "num.of_nat_to_znum" -> "data", "iff_congr" -> "init", "tendsto_of_uniform_continuous_subtype" -> "topology", "category_theory.epi_comp" -> "category_theory", "polynomial.coe_mul" -> "algebra", "pgame.star_first_wins" -> "set_theory", "multiset.zero_ndunion" -> "data", "ennreal.zero_div" -> "data", "neg_pow" -> "algebra", "measure_theory.measure.haar.chaar_self" -> "analysis", "nat.lt_of_succ_le" -> "init", "nat.succ_pnat_coe" -> "data", "list.nil_union" -> "data", "matrix.diagonal_comp_std_basis" -> "algebra", "simple_graph.card_neighbor_set_eq_degree" -> "combinatorics", "mul_lt_mul_of_lt_of_le" -> "algebra", "finset.sum_bij'" -> "algebra", "set.mem_compl_eq" -> "data", "polynomial.C_pow" -> "data", "is_compl_compl" -> "order", "ordinal.succ_le" -> "set_theory", "free_group.to_group.inv" -> "algebra", "category_theory.functor.map_conj_Aut" -> "category_theory", "int.neg_zero" -> "init", "uniform_continuous_on_iff_restrict" -> "topology", "Module.Mon_Module_equivalence_Algebra.inverse_obj_2" -> "category_theory", "polynomial.mod_by_monic_one" -> "data", "equiv.swap_core_comm" -> "data", "add_lt_of_lt_of_nonpos'" -> "algebra", "multiset.card_pos_iff_exists_mem" -> "data", "normed_ring.inverse_add_norm_diff_second_order" -> "analysis", "le_Sup" -> "order", "linear_map.pi_apply" -> "algebra", "open_embedding.prod" -> "topology", "list.sublists_perm_sublists'" -> "data", "continuous_linear_equiv.ext" -> "topology", "category_theory.curry.obj_obj_obj" -> "category_theory", "list.nodupkeys_singleton" -> "data", "multiset.countp_le_of_le" -> "data", "asymptotics.is_O_with.prod_rightl" -> "analysis", "Set.choice_is_func" -> "set_theory", "metric.exists_dist_lt_of_Hausdorff_dist_lt" -> "topology", "local_homeomorph.preimage_interior" -> "topology", "convex_on_univ_of_deriv_mono" -> "analysis", "nnreal.coe_one" -> "data", "list.pmap_congr" -> "data", "category_theory.limits.colimit.\[Iota]_pre_assoc" -> "category_theory", "category_theory.equivalence.equivalence_mk'_counit" -> "category_theory", "add_con.ker_rel" -> "algebra", "filter.lift_lift_same_le_lift" -> "order", "con.Inf_to_setoid" -> "algebra", "has_fpower_series_on_ball.mono" -> "analysis", "filter.mem_infi_iff" -> "order", "multiset.inf_eq_inter" -> "data", "real.pi_pos" -> "analysis", "list.tendsto_remove_nth" -> "topology", "linear_map.snd_eq_coprod" -> "algebra", "sub_eq_zero_iff_eq" -> "algebra", "mvqpf.recF_eq" -> "data", "function.is_periodic_pt.mul_const" -> "dynamics", "category_theory.over.iterated_slice_equiv_counit_iso" -> "category_theory", "polynomial.monic_pow" -> "data", "list.infix_of_suffix" -> "data", "continuous_linear_map.has_fderiv_at" -> "analysis", "range_quadrant" -> "geometry", "dense_sInter_of_G\[Delta]" -> "topology", "category_theory.limits.image.ext" -> "category_theory", "sigma.eq" -> "init", "pequiv.of_set_univ" -> "data", "rat.cast_eq_zero" -> "data", "iterated_fderiv_within_inter" -> "analysis", "continuous_supr_rng" -> "topology", "set.bij_on.union" -> "data", "nat.coprime.coprime_div_left" -> "data", "local_homeomorph.eventually_left_inverse'" -> "topology", "hyperreal.coe_pos" -> "data", "real.sqrt_two_add_series_step_up" -> "data", "convex_Ico" -> "analysis", "category_theory.monoidal.left_unitor_inv_app" -> "category_theory", "equiv.ext" -> "data", "nat.mod_pow_succ" -> "init", "monotone.infi_comp_eq" -> "order", "dfinsupp.filter_apply_neg" -> "data", "int.dvd_of_mul_dvd_mul_left" -> "data", "le_bot_iff" -> "order", "asymptotics.is_O_const_of_tendsto" -> "analysis", "measure_theory.tendsto_integral_of_l1" -> "analysis", "set.image_add_const_Iio" -> "data", "finset.has_sum_iff_compl" -> "topology", "times_cont_mdiff_at_top" -> "geometry", "complex.norm_eq_abs" -> "analysis", "filter.germ.const_inj" -> "order", "add_equiv.to_AddMon_iso_inv" -> "algebra", "pgame.equiv_nim_iff_grundy_value_eq" -> "set_theory", "continuous.mul" -> "topology", "nat.partrec'.vec.prim" -> "computability", "computation.results.terminates" -> "data", "sum_add_tsum_compl" -> "topology", "category_theory.adjunction.monad_\[Eta]_app" -> "category_theory", "cau_seq.le_total" -> "data", "measure_theory.measure.haar.chaar_nonneg" -> "analysis", "inner_self_eq_norm_square" -> "analysis", "roption.bind_some_eq_map" -> "data", "uniformity_has_basis_closed" -> "topology", "set.singleton_pi" -> "data", "closure_Icc" -> "topology", "interval_integral.norm_integral_le_integral_norm_Ioc" -> "analysis", "is_open_iff_ball_subset" -> "topology", "AddCommGroup.lift_\[Pi]_apply" -> "algebra", "category_theory.over.iterated_slice_forward_forget" -> "category_theory", "equiv.subtype_preimage_symm_apply_coe_pos" -> "data", "order_embedding.is_well_order" -> "order", "real.Inf_lt" -> "data", "linear_equiv.of_top_apply" -> "algebra", "with_top.coe_add" -> "algebra", "is_unit_iff_dvd_one" -> "algebra", "stream.map_tail" -> "data", "bilin_form.add_left" -> "algebra", "is_open_map_sum" -> "topology", "Top.presheaf_to_Types_map" -> "topology", "with_top.well_founded_lt" -> "order", "category_theory.monoidal_of_has_finite_products.left_unitor_inv" -> "category_theory", "metric.Hausdorff_dist_image" -> "topology", "onote.split_dvd" -> "set_theory", "iterated_fderiv_succ_apply_right" -> "analysis", "tensor_product.ite_tmul" -> "algebra", "nat.size_pow" -> "data", "category_theory.comma.map_right_comp_inv_app_right" -> "category_theory", "computation.destruct_think" -> "data", "nat.one_lt_bit1" -> "init", "set.image_add" -> "algebra", "matrix.trace_mul_comm" -> "algebra", "lt_neg_add_of_add_lt" -> "algebra", "finset.sum_range_add_sum_Ico" -> "algebra", "rel.image_subset" -> "data", "onote.repr_inj" -> "set_theory", "int.neg_le_neg" -> "init", "free_add_semigroup.map_add" -> "algebra", "fderiv_within_snd" -> "analysis", "category_theory.equivalence.refl_functor" -> "category_theory", "nat.le_sub_right_of_add_le" -> "data", "ennreal.coe_zero" -> "data", "measure_theory.ae_eq_fun.lintegral_mk" -> "analysis", "equiv.perm.sign_mul" -> "algebra", "finset.sigma_image_fst_preimage_mk" -> "data", "continuous.integrable_on_compact" -> "analysis", "finset.inter_insert_of_mem" -> "data", "category_theory.limits.cones.whiskering_obj" -> "category_theory", "set.preimage_subset_preimage_iff" -> "data", "category_theory.monad.algebra.hom.id_f" -> "category_theory", "rat.coe_int_num_of_denom_eq_one" -> "data", "units.neg_inv" -> "algebra", "eq_of_le_of_forall_le_of_dense" -> "order", "is_R_or_C.conj_eq_zero" -> "data", "num.of_to_nat" -> "data", "set.nonempty.some_mem" -> "data", "set.preimage_eq" -> "data", "asymptotics.is_o_const_mul_right_iff'" -> "analysis", "filter.principal_ne_bot_iff" -> "order", "filter.eventually_prod_iff" -> "order", "ring_hom.is_unit_map" -> "algebra", "multiset.revzip_powerset_aux" -> "data", "smooth_at.prod_mk" -> "geometry", "roption.map_none" -> "data", "wseq.equiv.ext" -> "data", "submodule.comap_mkq_embedding_eq" -> "algebra", "finset.map_subset_iff_subset_preimage" -> "data", "sym_sesq_form.sym" -> "algebra", "lcm_comm" -> "algebra", "filter.map_bot" -> "order", "cardinal.mk_compl_of_omega_le" -> "set_theory", "times_cont_mdiff_on_iff_times_cont_diff_on" -> "geometry", "gcd_mul_right" -> "algebra", "approximates_linear_on.to_local_homeomorph_target" -> "analysis", "pnat.xgcd_type.flip_is_reduced" -> "data", "int.le_of_lt" -> "init", "lt_sub_iff_add_lt'" -> "algebra", "pfunctor.M.mk_inj" -> "data", "complex.of_real_exp" -> "data", "directed_on_iff_directed" -> "order", "is_measurable_range_inr" -> "analysis", "continuous_linear_map.ker_coe" -> "topology", "category_theory.split_mono.id_assoc" -> "category_theory", "fintype.prod_apply" -> "algebra", "rel_iso.of_surjective_coe" -> "order", "ennreal.max_zero_left" -> "data", "category_theory.monoidal_category.tensor_left_iff" -> "category_theory", "option.map_eq_some'" -> "data", "set.image2_empty_left" -> "data", "localization.induction_on\:2083" -> "algebra", "multiset.foldl_add" -> "data", "monoid_algebra.alg_hom_ext" -> "data", "ordered_ring.mul_lt_mul_of_pos_left" -> "algebra", "finset.pi_val" -> "data", "list.prod_reverse" -> "data", "local_homeomorph.of_set_univ_eq_refl" -> "topology", "continuous_multilinear_map.op_norm_add_le" -> "analysis", "decidable.not_exists_not" -> "logic", "has_lt.lt.false" -> "algebra", "nat.primrec'.nil" -> "computability", "mul_mul_mul_comm" -> "algebra", "unit_of_invertible_inv" -> "algebra", "category_theory.limits.prod_right_unitor_hom_naturality_assoc" -> "category_theory", "nat.choose_mul_fact_mul_fact" -> "data", "set.Iio_subset_Iic_self" -> "data", "list.rel_sections" -> "data", "bifunctor.fst_id" -> "control", "monoid_hom.comp_coprod" -> "algebra", "ordinal.add_absorp_iff" -> "set_theory", "category_theory.biprod.of_components_eq" -> "category_theory", "int.lcm_comm" -> "algebra", "is_measurable.Union" -> "analysis", "differentiable_within_at.const_smul_algebra" -> "analysis", "local_ring.le_maximal_ideal" -> "algebra", "nat.dvd_add_iff_left" -> "init", "convex_on.smul" -> "analysis", "ideal.subset_span" -> "algebra", "group.subset_conjugates_of_set" -> "algebra", "multiset.card_range" -> "data", "one_nsmul" -> "algebra", "finset.affine_combination_of_eq_one_of_eq_zero" -> "algebra", "homeomorph.refl_to_local_homeomorph" -> "topology", "div_mul_cancel_of_imp" -> "algebra", "int.le_neg_add_of_add_le" -> "init", "finset.union_val" -> "data", "nat.pred_succ" -> "init", "neg_lt_sub_right_of_lt_add" -> "algebra", "category_theory.monoidal.Mon_functor_category_equivalence_unit_iso" -> "category_theory", "set_is_basis_of_span_eq_top_of_card_eq_findim" -> "algebra", "add_con.coe_add" -> "algebra", "nat.bit1_lt_bit0" -> "init", "finsupp.induction" -> "data", "ring_hom.map_mul" -> "algebra", "fin.coe_sub_nat" -> "data", "add_subgroup.mem_closure" -> "algebra", "mul_self_eq_one_iff" -> "algebra", "has_mfderiv_within_at.congr_of_eventually_eq" -> "geometry", "set.image_comp" -> "data", "prod.fst_inv" -> "algebra", "one_div_lt_of_neg" -> "algebra", "subgroup.coe_mk" -> "algebra", "filter.tendsto_at_bot_add_right_of_ge" -> "order", "ring_hom.prod_apply" -> "algebra", "add_localization.add_equiv_of_quotient_apply" -> "algebra", "continuous_multilinear_map.map_add_univ" -> "topology", "map_nhds" -> "topology", "category_theory.functor.image_preimage" -> "category_theory", "localization_map.is_unit_comp" -> "algebra", "nat.modeq.modeq_add" -> "data", "function.left_id" -> "init", "mdifferentiable.continuous" -> "geometry", "real.sqrt_sqr_eq_abs" -> "data", "subgroup.prod_mono" -> "algebra", "list.filter_false" -> "data", "preimage_interior_subset_interior_preimage" -> "topology", "generalized_continued_fraction.succ_nth_fib_le_of_nth_denom" -> "algebra", "category_theory.limits.eq_zero_of_image_eq_zero" -> "category_theory", "interior_empty" -> "topology", "ennreal.zero_ne_top" -> "data", "polynomial.degree_eq_iff_nat_degree_eq" -> "data", "pnat.gcd_eq_left" -> "data", "ideal.radical_top" -> "algebra", "bounded_continuous_function.arzela_ascoli\:2081" -> "topology", "quotient_add_group.range_ker_lift_surjective" -> "algebra", "is_measurable.congr" -> "analysis", "complex.exists_forall_abs_polynomial_eval_le" -> "analysis", "add_eq_of_eq_neg_add" -> "algebra", "measure_theory.hahn_decomposition" -> "analysis", "submodule.quotient.mk_zero" -> "algebra", "is_R_or_C.of_real_im" -> "data", "array.mem_to_list_enum" -> "data", "add_submonoid.mrange_inl_sup_mrange_inr" -> "algebra", "filter.limsup_const" -> "order", "is_local_min_on.bicomp_mono" -> "topology", "category_theory.preadditive.neg_comp_neg_assoc" -> "category_theory", "int.div_eq_of_eq_mul_left" -> "data", "category_theory.op_equiv_apply" -> "category_theory", "polynomial.is_root_of_eval\:2082_map_eq_zero" -> "data", "cSup_singleton" -> "order", "interval_integral.integral_symm" -> "analysis", "continuous_apply" -> "topology", "game.add_left_neg" -> "set_theory", "finset.coe_filter" -> "data", "cardinal.lift_mk_le" -> "set_theory", "category_theory.is_iso.iso.inv_hom" -> "category_theory", "polynomial.eval\:2082_restriction" -> "algebra", "computation.equiv_ret_of_mem" -> "data", "commute.inv_left'" -> "algebra", "polynomial.nat_degree_prod" -> "algebra", "not_of_not_imp" -> "logic", "function.right_inverse.injective" -> "logic", "submodule.lt_top_of_findim_lt_findim" -> "algebra", "free_abelian_group.map_pure" -> "algebra", "inv_lt_inv''" -> "algebra", "category_theory.functor.map_hom_congr" -> "category_theory", "filter.tendsto_fst" -> "order", "hyperreal.lt_of_is_st_lt" -> "data", "finset.coe_image" -> "data", "ennreal.le_of_real_iff_to_real_le" -> "data", "neg_add_eq_of_eq_add" -> "algebra", "typevec.last_fun_subtype_val" -> "data", "list.last'_append_of_ne_nil" -> "data", "ennreal.supr_sub" -> "data", "padic.const_equiv" -> "data", "uniform_space.completion.uniform_continuous_completion_separation_quotient_equiv" -> "topology", "le_mul_iff_one_le_right'" -> "algebra", "denumerable.of_nat_encode" -> "data", "finsupp.mem_span_iff_total" -> "algebra", "category_theory.preadditive.neg_comp" -> "category_theory", "equiv.conj_comp" -> "data", "nsmul_le_nsmul" -> "algebra", "le_neg_add_of_add_le" -> "algebra", "is_open_iff_mem_nhds" -> "topology", "mul_lt_one_of_lt_one_of_le_one'" -> "algebra", "set.preimage_const_mul_Ico_of_neg" -> "data", "Module.Mon_Module_equivalence_Algebra.inverse_obj_one" -> "category_theory", "fixed_points.of_eval\:2082" -> "algebra", "is_R_or_C.conj_conj" -> "data", "filter.tendsto_at_bot_principal" -> "order", "dfinsupp.zip_with_def" -> "data", "set.sInter_eq_Inter" -> "data", "function.semiconj.comp_right" -> "logic", "pnat.xgcd_type.step_wf" -> "data", "category_theory.op_op_map" -> "category_theory", "function.semiconj.iterate_right" -> "logic", "list.count_bag_inter" -> "data", "pow_bit1" -> "algebra", "finsupp.frange_single" -> "data", "category_theory.limits.biprod.symmetry" -> "category_theory", "pell.pell_zd_succ_succ" -> "number_theory", "additive.normal_add_subgroup" -> "algebra", "subring.top_prod" -> "algebra", "filter.map_pure" -> "order", "computation.length_ret" -> "data", "nat.lt_trans" -> "init", "continuous_on_iff" -> "topology", "polynomial.ne_zero_of_monic_of_zero_ne_one" -> "data", "nat.add_one_le_iff" -> "data", "set.sUnion_eq_univ_iff" -> "data", "nat.Sup_def" -> "order", "measure_theory.measure_Union_null" -> "analysis", "list.minimum_eq_none" -> "data", "antilipschitz_with.mul_le_dist" -> "topology", "free_abelian_group.map_zero" -> "algebra", "nat.fact_zero" -> "data", "add_monoid.exists_list_of_mem_closure" -> "algebra", "cau_seq.lim_eq_of_equiv_const" -> "data", "option.bind_comm" -> "data", "multiset.nodup_erase_eq_filter" -> "data", "padic.cast_eq_of_rat_of_nat" -> "data", "filter.mem_add" -> "order", "linear_independent_iff_not_mem_span" -> "algebra", "multiset.inf_singleton" -> "data", "list.mem_join" -> "data", "lie_skew" -> "algebra", "submodule.ker_of_le" -> "algebra", "add_submonoid.mem_comap" -> "algebra", "emetric.Hausdorff_edist_le_of_inf_edist" -> "topology", "cardinal.is_strong_limit.is_limit" -> "set_theory", "has_fderiv_within_at.add" -> "analysis", "vadd_mem_span_points_of_mem_span_points_of_mem_vector_span" -> "algebra", "differentiable_within_at.inv" -> "analysis", "category_theory.limits.pullback.lift_snd_assoc" -> "category_theory", "ordinal.typein_le_typein" -> "set_theory", "ennreal.coe_nat_mono" -> "data", "typevec.split_fun_inj" -> "data", "rat.denom_dvd" -> "data", "emetric.is_open_iff" -> "topology", "prod.edist_eq" -> "topology", "band_eq_false_eq_eq_ff_or_eq_ff" -> "init", "filter.comap_ne_bot_iff" -> "order", "multiset.ndinsert_le" -> "data", "category_theory.monoidal.right_unitor_hom_app" -> "category_theory", "nat.eq_zero_of_add_eq_zero_right" -> "init", "inv_mul_mul_self" -> "algebra", "metric.inf_dist_le_inf_dist_of_subset" -> "topology", "exist_quadratic_eq_zero" -> "algebra", "lt_inv_of_neg" -> "algebra", "add_commute.right_comm" -> "algebra", "filter.tendsto_at_top_add_nonneg_left'" -> "order", "mv_polynomial.eval\:2082_comp_right" -> "data", "list.prefix_concat" -> "data", "matrix.empty_vec_mul" -> "data", "matrix.dot_product_cons" -> "data", "category_theory.limits.types.initial" -> "category_theory", "setoid.eq_iff_rel_eq" -> "data", "strict_mono_mul_left_of_pos" -> "algebra", "is_local_max.comp_mono" -> "topology", "cau_seq.not_lim_zero_of_not_congr_zero" -> "data", "measure_theory.outer_measure.of_function_eq" -> "analysis", "nat.partrec'.of_part" -> "computability", "convex_sInter" -> "analysis", "primrec.dom_bool" -> "computability", "asymptotics.is_O_with_norm_left" -> "analysis", "add_commute.zero_right" -> "algebra", "list.filter_map_eq_filter" -> "data", "times_cont_diff_of_differentiable_iterated_fderiv" -> "analysis", "int.sub_left_lt_of_lt_add" -> "init", "nndist_triangle" -> "topology", "omega.int.preform.sat_or" -> "tactic", "circle_deg1_lift.lt_map_of_int_lt_translation_number" -> "dynamics", "sequentially_complete.set_seq_mono" -> "topology", "prod.fst_prod" -> "algebra", "nnnorm_zero" -> "analysis", "hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos" -> "data", "denumerable.list_of_nat_zero" -> "data", "neg_lt_sub_iff_lt_add" -> "algebra", "polynomial.nat_degree_eq_of_degree_eq" -> "data", "nat.eq_zero_of_add_eq_zero" -> "init", "vector.mk_to_list" -> "data", "filter.supr_sets_eq" -> "order", "finsupp.sum_sum_index" -> "data", "measure_theory.l1.of_fun_sub" -> "analysis", "polynomial.ne_zero_of_monic" -> "data", "ring_equiv.bijective" -> "data", "measure_theory.simple_func.is_measurable_fiber" -> "analysis", "list.sublist_cons_of_sublist" -> "data", "Class.to_Set_of_Set" -> "set_theory", "filter.germ.max_def" -> "order", "add_localization.mk_zero_eq_add_monoid_of_mk" -> "algebra", "polynomial.separable.inj_of_prod_X_sub_C" -> "algebra", "iterated_fderiv_within_inter'" -> "analysis", "fderiv_within_add" -> "analysis", "list.map_id'" -> "data", "nat.lt_add_left" -> "init", "lt_base_pow_length_digits" -> "data", "set.maps_to.mono" -> "data", "filter.is_ultrafilter.unique" -> "order", "linear_map.map_zero" -> "algebra", "mv_polynomial.eval\:2082_mul_monomial" -> "data", "cau_seq.completion.inv_mk" -> "data", "function.commute.self_iterate" -> "logic", "measure_theory.outer_measure.measure_of_eq_coe" -> "analysis", "measure_theory.simple_func.pair_apply" -> "analysis", "primorial_le_4_pow" -> "number_theory", "differentiable.iterate" -> "analysis", "ennreal.continuous_mul_const" -> "topology", "frontier_Ici" -> "topology", "int.units_inv_eq_self" -> "data", "joined.mem_path_component" -> "topology", "dense_range.nhds_within_ne_bot" -> "topology", "prime_multiset.coe_pnat_injective" -> "data", "has_deriv_at.const_add" -> "analysis", "multiset.to_finset_union" -> "data", "has_deriv_at.iterate" -> "analysis", "add_submonoid.localization_map.add_equiv_of_add_equiv_eq_map" -> "algebra", "is_coprime.mul_add_left_left" -> "algebra", "neg_add_self" -> "algebra", "turing.mem_eval" -> "computability", "traversable.id_sequence" -> "control", "ordinal.type_le'" -> "set_theory", "cardinal.extend_function_of_lt" -> "set_theory", "filter.sup_join" -> "order", "category_theory.limits.types.image_map" -> "category_theory", "continuous_id'" -> "topology", "uniform_embedding.prod" -> "topology", "nat.div_eq_of_lt" -> "init", "list.singleton_sublist" -> "data", "asymptotics.is_O_with_zero" -> "analysis", "add_comm_group.direct_limit.lift_sub" -> "algebra", "complex.add_im" -> "data", "submodule.span_mono" -> "algebra", "finsupp.mem_support_multiset_sum" -> "data", "list.ne_of_not_mem_cons" -> "data", "multiset.add_comm" -> "data", "is_linear_map.with_bound" -> "analysis", "linear_equiv.refl_apply" -> "algebra", "znum.bit0_of_bit0" -> "data", "ordinal.mul_le_mul" -> "set_theory", "hyperreal.infinitesimal_sub_is_st" -> "data", "prime_multiset.prod_dvd_iff" -> "data", "setoid.ext_iff" -> "data", "category_theory.biprod.inr_of_components" -> "category_theory", "int.nat_abs_of_nat" -> "init", "circle_deg1_lift.map_map_zero_le" -> "dynamics", "measure_theory.outer_measure.restrict_apply" -> "analysis", "list.append_ne_nil_of_ne_nil_left" -> "data", "stream.head_zip" -> "data", "simple_graph.mem_neighbor_set" -> "combinatorics", "add_subgroup.coe_gsmul" -> "algebra", "submonoid.map_injective_of_injective" -> "algebra", "associates.prod_le_prod_iff_le" -> "algebra", "zmod.mul_inv_eq_gcd" -> "data", "bool.to_bool_not" -> "data", "pfun.mem_restrict" -> "data", "category_theory.functor.map_presheaf_map_f" -> "algebraic_geometry", "set.finite.image" -> "data", "set.image_singleton" -> "data", "ennreal.coe_eq_one" -> "data", "category_theory.limits.cokernel.\[Pi]_desc" -> "category_theory", "continuous_linear_equiv.has_fderiv_at" -> "analysis", "localization_map.injective" -> "algebra", "is_measurable_ball" -> "analysis", "quadratic_form.associated_comp" -> "algebra", "cmp_using_eq_gt" -> "init", "mv_polynomial.is_id" -> "data", "nat.partrec.code.prec_prim" -> "computability", "category_theory.functor.id_map" -> "category_theory", "finset.mem_attach" -> "data", "nat.add_mul_mod_self_right" -> "init", "asymptotics.is_o.trans_tendsto" -> "analysis", "finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero" -> "algebra", "add_localization.add_equiv_of_quotient_mk" -> "algebra", "computable.sum_inr" -> "computability", "primrec.nat_bodd_div2" -> "computability", "asymptotics.is_O_with_fst_prod" -> "analysis", "linear_equiv.of_linear_symm_apply" -> "algebra", "exists_nhds_half_neg" -> "topology", "filter.tendsto_finset_image_at_top_at_top" -> "order", "matrix.neg_vec_mul" -> "data", "ordinal.bsup_le" -> "set_theory", "setoid.ext" -> "data", "filter.eventually_eq.sub" -> "order", "set.subsingleton.image" -> "data", "has_deriv_at_filter.sub_const" -> "analysis", "measurable_inv" -> "analysis", "power_series.order_eq_nat" -> "algebra", "add_nonpos" -> "algebra", "circle_deg1_lift.translation_number_eq_int_iff" -> "dynamics", "exists_prop" -> "logic", "subring.mk'_to_submonoid" -> "algebra", "iterated_fderiv_within_one_apply" -> "analysis", "is_R_or_C.inv_im" -> "data", "submonoid.localization_map.mk'_mul" -> "algebra", "znum.of_int_cast" -> "data", "list.length_cons" -> "init", "tactic.ring_exp.mul_pf_zero" -> "tactic", "subalgebra.range_subset" -> "algebra", "exists_int_pow_near" -> "algebra", "finset.sum_le_sum_of_subset_of_nonneg" -> "algebra", "fn_min_mul_fn_max" -> "algebra", "real.sin_add_two_pi" -> "analysis", "not_bdd_above_iff" -> "order", "add_subgroup.mem_closure_singleton" -> "algebra", "category_theory.limits.cocone.of_cofork_\[Iota]" -> "category_theory", "add_submonoid.coe_injective" -> "algebra", "add_units.coe_add_right" -> "data", "norm_num.rat_cast_neg" -> "tactic", "pgame.lt_def" -> "set_theory", "bnot_eq_ff_eq_eq_tt" -> "init", "measurable.add" -> "analysis", "finite_dimensional.exists_is_basis_finite" -> "algebra", "continuous_linear_map.coe_inj" -> "topology", "filter.is_compl_principal" -> "order", "ordinal.power_dvd_power" -> "set_theory", "filter.eventually.mono" -> "order", "submodule.mem_orthogonal'" -> "analysis", "hyperreal.st_add" -> "data", "iterated_fderiv_zero_eq_comp" -> "analysis", "list.insert_of_mem" -> "data", "is_local_max_on.inf" -> "topology", "category_theory.functor.id_obj" -> "category_theory", "category_theory.limits.zero_of_comp_mono" -> "category_theory", "filter.prod_same_eq" -> "order", "hash_map.mk_valid" -> "data", "prime_multiset.coe_prod" -> "data", "linear_map.range_cod_restrict" -> "algebra", "ordinal.enum_le_enum" -> "set_theory", "is_lub_of_is_glb_of_tendsto" -> "topology", "linear_map.prod_map_apply" -> "algebra", "set.preimage_const_add_Ioi" -> "data", "joined_in_iff_joined" -> "topology", "set.preimage_const_sub_Ioo" -> "data", "le_add_of_neg_le_sub_right" -> "algebra", "equiv.perm.disjoint_mul_left" -> "algebra", "set.union_diff_cancel" -> "data", "local_homeomorph.image_open_of_open" -> "topology", "nat.sqrt_le_sqrt" -> "data", "complex.bit1_im" -> "data", "mdifferentiable_within_at.congr_mono" -> "geometry", "finset.map_val" -> "data", "of_digits_mod" -> "data", "category_theory.functor_to_types.inv_hom_id_app_apply" -> "category_theory", "is_bounded_bilinear_map_apply" -> "analysis", "AddCommGroup.coe_of" -> "algebra", "list.ne_and_not_mem_of_not_mem_cons" -> "data", "measure_theory.extend_eq" -> "analysis", "emetric.uniform_continuous_iff" -> "topology", "nat.sub_sub_sub_cancel_right" -> "data", "metric.continuous_at_iff'" -> "topology", "nat.lcm_one_right" -> "data", "metric.ball_mem_nhds" -> "topology", "continuous_linear_equiv.coe_refl" -> "topology", "function.inv_fun_on_eq" -> "logic", "not_imp_eq_of_eq_false_right" -> "init", "eq_irreducible_component" -> "topology", "real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le" -> "analysis", "measure_theory.simple_func.const_mul_lintegral" -> "analysis", "rat.mk_pnat_eq" -> "data", "is_closed_Iic" -> "topology", "commute.fpow_fpow_self" -> "algebra", "ring_hom.closure_preimage_le" -> "algebra", "interval_integral.integral_interval_sub_left" -> "analysis", "filter.map_def" -> "order", "differentiable_on.restrict_scalars" -> "analysis", "pgame.impartial.first_wins_symm'" -> "set_theory", "free_group.red.step.length" -> "algebra", "commute.zero_right" -> "algebra", "int.neg_lt_sub_left_of_lt_add" -> "init", "mvqpf.supp_map" -> "data", "subsemiring.ext'_iff" -> "algebra", "eq_top_mono" -> "order", "traversable.pure_traverse" -> "control", "real.continuous_rpow_aux2" -> "analysis", "has_fderiv_at_filter.fst" -> "analysis", "zmod.val_injective" -> "data", "multiset.Ico.succ_singleton" -> "data", "multiset.coe_erase_dup" -> "data", "model_with_corners.to_local_equiv_coe_symm" -> "geometry", "is_basis.mem_span" -> "algebra", "zero_le_one" -> "algebra", "add_localization.r_iff_exists" -> "algebra", "traversable.mfoldl.unop_of_free_monoid" -> "control", "hyperreal.neg_of_infinite_neg" -> "data", "is_measurable_range_inl" -> "analysis", "is_preconnected.eq_univ_of_unbounded" -> "topology", "metric.lipschitz_inf_dist_pt" -> "topology", "mul_aut.apply_inv_self" -> "data", "measure_theory.l1.simple_func.eq'" -> "analysis", "add_le_iff_nonpos_right" -> "algebra", "finsupp.subtype_domain_zero" -> "data", "real.sqrt_two_add_series_one" -> "analysis", "list.nodup_filter" -> "data", "nat.div_def" -> "init", "bounded_continuous_function.dist_eq" -> "topology", "finset.prod_apply_ite" -> "algebra", "list.eq_or_ne_mem_of_mem" -> "data", "list.tail_suffix" -> "data", "monoid_hom.eq_lift_of_surjective" -> "algebra", "set.diff_Union" -> "data", "except_t.run_pure" -> "init", "measure_theory.measure.regular.conj" -> "analysis", "irrefl_of" -> "init", "dfinsupp.lmk_apply" -> "data", "pos_num.cmp_to_nat_lemma" -> "data", "add_lt_of_neg_of_lt'" -> "algebra", "metric.bounded_iff_ediam_ne_top" -> "topology", "set.Ioo_subset_Ioo_iff" -> "data", "exists_nhds_half" -> "topology", "mem_ball_symmetry" -> "topology", "turing.TM2to1.add_bottom_modify_nth" -> "computability", "set.Union_empty" -> "data", "ring.fractional_ideal.fractional_mul" -> "algebra", "polynomial.eval\:2082_hom" -> "data", "filter.tendsto_at_top_add" -> "order", "linear_map.le_ker_iff_map" -> "algebra", "euclidean_domain.mod_self" -> "algebra", "mvpfunctor.M.dest_corec" -> "data", "onote.add_NF_below" -> "set_theory", "nat.partrec.of_eq_tot" -> "computability", "lists.lt_sizeof_cons'" -> "set_theory", "equiv.set.sum_compl_apply_inl" -> "data", "quot.lift\:2082_mk" -> "data", "zmod.exists_pow_two_eq_prime_iff_of_mod_four_eq_one" -> "number_theory", "is_connected.closure" -> "topology", "euclidean_domain.gcd.induction" -> "algebra", "padic_int.sub_zmod_repr_mem" -> "data", "ordinal.log_le_self" -> "set_theory", "mvpfunctor.M.dest_map" -> "data", "le_add_of_le_of_nonneg" -> "algebra", "add_submonoid.localization_map.mk'_sec" -> "algebra", "holor_index.drop_drop" -> "data", "is_closed_discrete" -> "topology", "turing.blank_extends.refl" -> "computability", "pSet.resp.euc" -> "set_theory", "add_magma.free_add_semigroup.of_add_assoc_left" -> "algebra", "module.card_fintype" -> "algebra", "upper_bounds_mono" -> "order", "matrix.ring_hom.map_det" -> "algebra", "set.right_inv_on.congr_left" -> "data", "Inf_image" -> "order", "multilinear_map.cons_add" -> "algebra", "dvd_antisymm_of_normalize_eq" -> "algebra", "iterated_fderiv_within_eq_equiv_comp" -> "analysis", "bind_pure" -> "init", "dfinsupp.prod_finset_sum_index" -> "data", "set.mem_compl_image" -> "data", "nat.shiftl_sub" -> "init", "finset.bInter_finset_image" -> "data", "category_theory.limits.image.fac" -> "category_theory", "onote.oadd_lt_oadd_2" -> "set_theory", "finset.sup_union" -> "data", "tt_eq_ff_eq_false" -> "init", "ordinal.is_normal.fp_iff_deriv" -> "set_theory", "closed_under_restriction'" -> "geometry", "set.snd_image_prod" -> "data", "nat.coprime.mul_dvd_of_dvd_of_dvd" -> "data", "nhds_within_ne_bot_of_mem" -> "topology", "differentiable_at.sum" -> "analysis", "nnreal.sub_zero" -> "data", "bilin_form.to_matrix_smul" -> "algebra", "pnat.xgcd_type.finish_is_reduced" -> "data", "initial_seg.refl_apply" -> "set_theory", "category_theory.limits.cocones.whiskering_map_hom" -> "category_theory", "metric.mem_ball" -> "topology", "dense_embedding.prod" -> "topology", "ennreal.to_real_sum" -> "data", "set.preimage_const_sub_Ioc" -> "data", "pgame.zero_first_loses" -> "set_theory", "set.ext" -> "data", "category_theory.functor.cocones_map_app" -> "category_theory", "monoid_hom.lift_of_surjective_comp" -> "algebra", "finset.prod_singleton" -> "algebra", "frontier_Iic" -> "topology", "mul_right_cancel" -> "algebra", "fpow_sub_one" -> "algebra", "pow_mul'" -> "algebra", "function.minimal_period_pos_of_mem_periodic_pts" -> "dynamics", "add_commute.neg_left" -> "algebra", "list.rotate_eq_take_append_drop" -> "data", "multiset.sub_le_sub_left" -> "data", "int.lcm_one_left" -> "algebra", "set.sInter_singleton" -> "data", "computation.empty_promises" -> "data", "int.norm_cast_rat" -> "analysis", "is_least.bdd_below" -> "order", "finset.map_empty" -> "data", "is_compact.finite_measure_of_nhds_within" -> "analysis", "set.compl_Iic" -> "data", "list.singleton_perm_singleton" -> "data", "category_theory.limits.mono_of_is_limit_parallel_pair" -> "category_theory", "pgame.lt_iff_neg_gt" -> "set_theory", "classical.epsilon_spec" -> "init", "option.to_finset_none" -> "data", "equiv.set.range_apply" -> "data", "int.of_nat_mul_neg_succ_of_nat" -> "init", "exists_deriv_eq_zero" -> "analysis", "nhds_le_uniformity" -> "topology", "Mod.hom.ext_iff" -> "category_theory", "polynomial.zero_mod_by_monic" -> "data", "monoid_hom.iterate_map_frobenius" -> "algebra", "has_ftaylor_series_up_to_on_succ_iff_left" -> "analysis", "set.insert_diff_of_not_mem" -> "data", "mem_smul_set_iff_inv_smul_mem" -> "algebra", "quotient_add_group.induction_on'" -> "algebra", "tactic.ring_exp.pow_p_pf_zero" -> "tactic", "pgame.add_le_add_right" -> "set_theory", "is_local_extr_on.comp_continuous_on" -> "topology", "rat.cast_coe_nat" -> "data", "list.continuous_at_length" -> "topology", "top_sup_eq" -> "order", "of_digits_lt_base_pow_length" -> "data", "generalized_continued_fraction.squash_gcf_eq_self_of_terminated" -> "algebra", "mv_polynomial.is_homogeneous_one" -> "algebra", "is_closed_univ" -> "topology", "div_le_div_iff" -> "algebra", "finsupp.to_multiset_zero" -> "data", "mv_polynomial.map_range_eq_map" -> "algebra", "bxor_self" -> "init", "ideal.jacobson_eq_bot" -> "algebra", "is_glb.unique" -> "order", "subalgebra.fg_def" -> "algebra", "finset.le_max_of_mem" -> "data", "times_cont_mdiff_within_at.of_succ" -> "geometry", "nsmul_add_comm" -> "algebra", "pgame.lt_asymm" -> "set_theory", "compact_univ_pi" -> "topology", "tactic.abel.unfold_sub" -> "tactic", "monotone.map_Inf_le" -> "order", "multiset.mem_to_list" -> "data", "le_or_lt" -> "algebra", "fderiv.comp_deriv" -> "analysis", "subset_Icc_cInf_cSup" -> "order", "nat.ldiff_bit" -> "init", "is_local_min_on.sub" -> "topology", "int.even_bit0" -> "data", "is_submonoid.coe_one" -> "algebra", "real.exp_le_exp" -> "data", "dfinsupp.sum_neg" -> "data", "asymptotics.is_o_const_iff" -> "analysis", "category_theory.Comonad.comp_to_nat_trans" -> "category_theory", "multiset.countp_pos_of_mem" -> "data", "free_ring.coe_surjective" -> "algebra", "nontrivial_of_ne" -> "logic", "to_add_injective" -> "algebra", "int.cast_id" -> "data", "ordinal.le_cof_type" -> "set_theory", "valuation.is_equiv.of_eq" -> "algebra", "times_cont_diff_within_at.sub" -> "analysis", "interval_integral.integral_const" -> "analysis", "real.pi_gt_3141592" -> "data", "eq_one_of_pow_eq_one" -> "algebra", "abstract_completion.extend_comp_coe" -> "topology", "set.bij_on.to_local_equiv_source" -> "data", "set.update_preimage_univ_pi" -> "data", "real.rpow_le_rpow_of_exponent_le" -> "analysis", "embedding.comp" -> "topology", "encodable.decode_sigma_val" -> "data", "fin.succ_pred" -> "data", "max_le_iff" -> "algebra", "local_homeomorph.restr_source" -> "topology", "ennreal.sub_eq_zero_iff_le" -> "data", "category_theory.monad.forget_creates_limits.new_cone_\[Pi]" -> "category_theory", "multiset.foldr_cons" -> "data", "partrec.map" -> "computability", "associates.mul_eq_one_iff" -> "algebra", "list.count_concat" -> "data", "times_cont_mdiff_on_chart" -> "geometry", "encodable.Union_decode2_cases" -> "data", "filter.tendsto_at_top_mono" -> "order", "le_neg_of_le_neg" -> "algebra", "list.subset_inter" -> "data", "int.lt_add_of_neg_add_lt_left" -> "init", "closure_Ici" -> "topology", "polynomial.expand_one" -> "algebra", "continuous_linear_map.isometry_iff_norm_image_eq_norm" -> "analysis", "sub_le_of_abs_sub_le_left" -> "algebra", "mv_polynomial.C_mul_monomial" -> "data", "wseq.lift_rel_join" -> "data", "asymptotics.is_o_const_smul_left_iff" -> "analysis", "cauchy.comap'" -> "topology", "int.dist_cast_rat" -> "topology", "measure_theory.integrable_on_const" -> "analysis", "con.mem_coe" -> "algebra", "hyperreal.infinitesimal_neg_iff" -> "data", "filter.tendsto_at_top_of_add_bdd_above_left'" -> "order", "list.kerase_of_not_mem_keys" -> "data", "filter.is_cobounded_top" -> "order", "pequiv.of_set_eq_some_iff" -> "data", "list.reverse_eq_nil" -> "data", "ennreal.rpow_neg" -> "analysis", "finset.insert_inter_of_not_mem" -> "data", "real.is_conjugate_exponent.one_div_ne_zero" -> "data", "monoid.image_closure" -> "algebra", "nat.binary_rec_eq" -> "init", "function.equiv.refl" -> "init", "equiv.subtype_equiv_codomain_symm_apply_eq" -> "data", "matrix.cramer_column_self" -> "algebra", "finset.sdiff_inter_self_left" -> "data", "set.subset_compl_iff_disjoint" -> "data", "filter.generate_Union" -> "order", "coe_ff" -> "init", "list.eq_repeat'" -> "data", "category_theory.limits.cones.postcompose_equivalence_unit_iso" -> "category_theory", "associates.prod_mk" -> "algebra", "category_theory.limits.biprod.braid_natural" -> "category_theory", "ordinal.is_normal.le_nfp" -> "set_theory", "nat.nat_zero_eq_zero" -> "init", "ordinal.is_normal.sup" -> "set_theory", "list.nodup_concat" -> "data", "num.of_nat_to_znum_neg" -> "data", "mv_polynomial.eval\:2082_hom_X" -> "data", "ordinal.lift_type_eq" -> "set_theory", "zmod.val_coe_unit_coprime" -> "data", "set.finite_Union" -> "data", "units.norm_pos" -> "analysis", "is_preconnected_Iic" -> "topology", "mul_le_mul_iff_right" -> "algebra", "list.keys_nil" -> "data", "le_mul_of_inv_mul_le_right" -> "algebra", "set.Union_disjointed_of_mono" -> "data", "is_open_compl_iff" -> "topology", "asymptotics.is_o_norm_left" -> "analysis", "nnreal.rpow_le_rpow" -> "analysis", "category_theory.limits.kernel_fork.\[Iota]_of_\[Iota]" -> "category_theory", "measure_theory.lintegral_eq_supr_eapprox_lintegral" -> "analysis", "metric.to_inductive_limit_isometry" -> "topology", "set.indicator_univ" -> "data", "local_homeomorph.to_homeomorph_coe" -> "topology", "real.sqrt_le" -> "data", "max_eq_right" -> "init", "category_theory.Monad.Monad_Mon_equiv_counit_iso" -> "category_theory", "joined_in.mem" -> "topology", "fin.coe_eq_cast_succ" -> "data", "real.sqrt_two_add_series_nonneg" -> "analysis", "turing.tape.map_write" -> "computability", "fintype.card_bool" -> "data", "with_bot.coe_lt_coe" -> "order", "list.mem_foldr_permutations_aux2" -> "data", "metric.inf_dist_le_dist_of_mem" -> "topology", "pfunctor.M.default_consistent" -> "data", "rel.codom_inv" -> "data", "has_fderiv_within_at.has_deriv_within_at" -> "analysis", "euclidean_domain.mul_div_cancel" -> "algebra", "quadratic_form.equivalent.trans" -> "algebra", "lists'.mem_of_subset'" -> "set_theory", "nat.primrec'.of_prim" -> "computability", "fin.comp_snoc" -> "data", "cau_seq.completion.of_rat_neg" -> "data", "ordinal.zero_power" -> "set_theory", "list.drop_one" -> "data", "topological_space.open_nhds.inclusion_map_iso_inv" -> "topology", "mem_nhds_within_Iio_iff_exists_Ioo_subset" -> "topology", "measure_theory.simple_func.zero_lintegral" -> "analysis", "free_group.map.inv" -> "algebra", "multiset.Ico.pred_singleton" -> "data", "quotient_prod_linear_equiv" -> "algebra", "int.cast_bit0" -> "data", "many_one_degree.le_trans" -> "computability", "list.erase_cons_head" -> "data", "ordinal.mul_is_limit" -> "set_theory", "has_deriv_within_at.inv" -> "analysis", "circle_deg1_lift.map_lt_of_translation_number_lt_nat" -> "dynamics", "list.perm.count_eq" -> "data", "convex_Iic" -> "analysis", "computation.bind_ret'" -> "data", "sesq_form.neg_left" -> "algebra", "is_local_max_on.min" -> "topology", "linear_pmap.eq_of_le_of_domain_eq" -> "algebra", "norm_num.ne_zero_of_pos" -> "tactic", "range_proj_I" -> "topology", "measure_theory.measure.haar.le_index_mul" -> "analysis", "category_theory.pi.id_apply" -> "category_theory", "filter.sup_principal" -> "order", "polynomial.degree_pow'" -> "data", "bilin_form.add_right" -> "algebra", "filter.tendsto_of_not_nonempty" -> "order", "lt_add_iff_pos_left" -> "algebra", "category_theory.over.w" -> "category_theory", "affine.simplex.mk_of_point_points" -> "algebra", "ordinal.cof_eq_zero" -> "set_theory", "set.union_diff_cancel_right" -> "data", "ordinal.add_le_of_limit" -> "set_theory", "polynomial.separable.of_dvd" -> "algebra", "set.subset_subset_Union" -> "data", "nat.find_min" -> "init", "is_null_measurable_of_complete" -> "analysis", "mdifferentiable_on_const" -> "geometry", "list.product_nil" -> "data", "multiplicative.is_mul_hom" -> "algebra", "fintype.card_empty" -> "data", "functor.comp.run_pure" -> "control", "submodule.is_compl_orthogonal_of_is_complete" -> "analysis", "set.univ_eq_empty_iff" -> "data", "mv_power_series.zero_mul" -> "algebra", "filter.exists_le_of_tendsto_at_top" -> "order", "real.pow_nat_rpow_nat_inv" -> "analysis", "mul_gsmul_left" -> "algebra", "set.maps_to.inter" -> "data", "Cauchy.dense_embedding_pure_cauchy" -> "topology", "nat.add_lt_add" -> "init", "continuous.inv" -> "topology", "primrec.fin_curry\:2081" -> "computability", "padic_int.coe_add" -> "data", "filter.filter_eq_iff" -> "order", "real.abs_rpow_le_abs_rpow" -> "analysis", "real.tanh_neg" -> "data", "set.eval_image_univ_pi" -> "data", "tendsto_iff_of_dist" -> "topology", "alist.extract_eq_lookup_erase" -> "data", "polynomial.aeval_def" -> "data", "fin.cast_succ_zero" -> "data", "lt_is_lub_iff" -> "order", "prime_spectrum.subset_zero_locus_vanishing_ideal" -> "algebraic_geometry", "filter.rtendsto_def" -> "order", "times_cont_mdiff.of_le" -> "geometry", "metric.diam_subsingleton" -> "topology", "measure_theory.lintegral_infi_ae" -> "analysis", "ring.direct_limit.lift_pow" -> "algebra", "order_of_eq_one_iff" -> "algebra", "multiset.attach_zero" -> "data", "wseq.mem_rec_on" -> "data", "one_open_separated_mul" -> "topology", "filter.infi_ne_bot_iff_of_directed'" -> "order", "filter.lift_lift'_same_le_lift'" -> "order", "is_open_set_pi" -> "topology", "complex.of_real_cos_of_real_re" -> "data", "measure_theory.simple_func.mem_restrict_range" -> "analysis", "matrix.tail_cons" -> "data", "add_submonoid.localization_map.lift_unique" -> "algebra", "traversable.traverse_comp" -> "control", "multiset.powerset_len_coe'" -> "data", "mul_aut.inv_def" -> "data", "category_theory.equivalence.trans_functor" -> "category_theory", "linear_map.id_comp" -> "algebra", "ordinal.add_is_normal" -> "set_theory", "continuous_at_iff_continuous_left_right" -> "topology", "linear_map.map_le_range" -> "algebra", "continuous_linear_equiv.self_comp_symm" -> "topology", "set.card_insert" -> "data", "tangent_bundle.smooth_within_at_proj" -> "geometry", "nat.succ_add_eq_succ_add" -> "init", "topological_fiber_bundle_core.mem_local_triv_at_source" -> "topology", "unique.eq_default" -> "logic", "commute.gpow_right" -> "algebra", "matrix.reindex_symm_apply" -> "algebra", "mdifferentiable_at_atlas" -> "geometry", "topological_space.opens.ext_iff" -> "topology", "set.left_mem_Icc" -> "data", "measure_theory.extend_Union_le_tsum_nat" -> "analysis", "is_preconnected_of_forall" -> "topology", "affine.simplex.monge_point_mem_monge_plane" -> "geometry", "finset.lt_inf_iff" -> "data", "hyperreal.infinitesimal_sub_st" -> "data", "cau_seq.add_lim_zero" -> "data", "mul_lt_of_lt_one_of_le" -> "algebra", "unit.ext" -> "tactic", "roption.eq_none_iff'" -> "data", "pfunctor.M.iselect_cons" -> "data", "norm_num.sle_bit1_bit1" -> "tactic", "alg_equiv.map_add" -> "algebra", "category_theory.limits.functor_category_limit_cone_X" -> "category_theory", "generalized_continued_fraction.of_h_eq_int_fract_pair_seq1_fst_b" -> "algebra", "linear_map.inl_injective" -> "algebra", "Gromov_Hausdorff.to_GH_space_lipschitz" -> "topology", "list.empty_eq" -> "data", "set.image_add_const_Ici" -> "data", "free_ring.map_of" -> "algebra", "polynomial.monic.ne_zero" -> "data", "category_theory.abelian.exact_iff" -> "category_theory", "turing.partrec_to_TM2.tr_respects" -> "computability", "complex.abs_exp_sub_one_le" -> "data", "continuous_of_uniform_approx_of_continuous" -> "topology", "has_strict_deriv_at.smul" -> "analysis", "zsqrtd.smuld_val" -> "data", "principal_seg.cod_restrict_top" -> "set_theory", "local_homeomorph.trans_assoc" -> "topology", "setoid.le_def" -> "data", "polynomial.eval\:2082_neg" -> "data", "ordering.compares.eq_gt" -> "algebra", "algebra.lmul_right_apply" -> "algebra", "finsupp.total_map_domain" -> "algebra", "joined_in.of_line" -> "topology", "category_theory.whisker_right_app" -> "category_theory", "category_theory.abelian.pseudoelement.pseudo_exact_of_exact" -> "category_theory", "simple_graph.mem_edge_finset" -> "combinatorics", "list.chain_succ_range'" -> "data", "int.mod_eq_of_lt" -> "data", "int.neg_of_neg_pos" -> "init", "category_theory.limits.cofork.of_\[Pi]_app_one" -> "category_theory", "add_left_injective" -> "algebra", "rat.dist_eq" -> "topology", "semidirect_product.right_inl" -> "algebra", "eq.congr" -> "logic", "mul_self_iff_eq_one" -> "algebra", "geom_sum\:2082_mul_comm" -> "algebra", "real.continuous_rpow" -> "analysis", "qpf.liftr_iff" -> "data", "ordinal.add_le_add_iff_right" -> "set_theory", "filter.map_eq_comap_of_inverse" -> "order", "mat_poly_equiv_char_matrix" -> "algebra", "vector3.cons_fz" -> "number_theory", "function.iterate_succ'" -> "logic", "pos_num.cast_inj" -> "data", "gronwall_bound_\[CurlyEpsilon]0" -> "analysis", "closure_le_eq" -> "topology", "nat.partrec.rfind'" -> "computability", "bdd_above_Iic" -> "order", "convex_hull_diam" -> "analysis", "subalgebra.multiset_sum_mem" -> "algebra", "add_submonoid.coe_map" -> "algebra", "real.fpow_arith_mean_le_arith_mean_fpow" -> "analysis", "circle_deg1_lift.iterate_le_of_map_le_add_int" -> "dynamics", "filter.mem_iff_inf_principal_compl" -> "order", "primrec.list_index_of\:2081" -> "computability", "finset.inter_right_comm" -> "data", "linarith.int.coe_nat_bit0_mul" -> "tactic", "tensor_product.lift_compr\:2082" -> "algebra", "measure_theory.all_ae_tendsto_of_real_norm" -> "analysis", "set.union_self" -> "data", "linear_equiv.coord_self" -> "algebra", "generalized_continued_fraction.part_num_eq_s_a" -> "algebra", "uniformity_edist" -> "topology", "sum.elim_inl" -> "data", "quadratic_form.map_sub" -> "algebra", "computable.vector_nth" -> "computability", "cardinal.mk_ord_out" -> "set_theory", "bitraversable.tsnd_id" -> "control", "list.eq_cons_of_length_one" -> "data", "summable_geometric_of_abs_lt_1" -> "analysis", "semidirect_product.one_right" -> "algebra", "asymptotics.is_o_const_mul_right_iff" -> "analysis", "multiset.rel_join" -> "data", "with_top.lattice_eq_DLO" -> "order", "bex_or_distrib" -> "logic", "int.coe_nat_lt_coe_nat_iff" -> "init", "polynomial.next_coeff_C_eq_zero" -> "data", "padic_int.zero_ne_one" -> "data", "ordinal.card_omega" -> "set_theory", "times_cont_mdiff_at.prod_map" -> "geometry", "sub_floor_div_mul_lt" -> "algebra", "ring_hom.map_add" -> "algebra", "polynomial.has_fderiv_at" -> "analysis", "exists_of_exists_unique" -> "init", "eq_of_heq" -> "init", "has_fderiv_within_at.congr_mono" -> "analysis", "category_theory.limits.limit.cone_point_unique_up_to_iso_hom_comp_assoc" -> "category_theory", "is_glb.insert" -> "order", "tangent_bundle.times_cont_mdiff_on_proj" -> "geometry", "convex.combo_to_vadd" -> "analysis", "submodule.map_bot" -> "algebra", "encodable.encode_of_equiv" -> "data", "matrix.head_transpose" -> "data", "nnreal.coe_multiset_sum" -> "data", "ordinal.lt_div" -> "set_theory", "mul_self_mul_inv" -> "algebra", "set.image2_add" -> "algebra", "is_open_lt" -> "topology", "one_lt_pow" -> "algebra", "local_homeomorph.eq_on_source.restr" -> "topology", "ordinal.cof_type" -> "set_theory", "int.of_nat_nonneg" -> "init", "is_open_inter" -> "topology", "asymptotics.is_O_with.exists_nonneg" -> "analysis", "ordinal.cof_type_le" -> "set_theory", "category_theory.iso.cancel_iso_inv_left" -> "category_theory", "prime_spectrum.zero_locus_span" -> "algebraic_geometry", "ordinal.nat_lt_omega" -> "set_theory", "turing.list_blank.nth_map" -> "computability", "ideal.mem_of_polynomial" -> "algebra", "set.surj_on.inv_on_inv_fun_on" -> "data", "set.preimage_const_mul_Iic" -> "data", "ring.direct_limit.lift_of" -> "algebra", "nat.prime_def_le_sqrt" -> "data", "dim_prod" -> "algebra", "one_le_mul" -> "algebra", "polynomial.coeff_X_pow" -> "data", "rat.add_def" -> "data", "euclidean_geometry.vsub_orthogonal_projection_mem_direction_orthogonal" -> "geometry", "category_theory.category_of_elements.ext" -> "category_theory", "filter.comap_lift_eq" -> "order", "zero_sub" -> "algebra", "local_homeomorph.of_set_trans'" -> "topology", "add_semiconj_by.eq" -> "algebra", "principal_seg.equiv_lt_top" -> "set_theory", "znum.cast_zero" -> "data", "ideal.mul_top" -> "algebra", "turing.tape.move_right_nth" -> "computability", "list.rotate'_zero" -> "data", "category_theory.limits.cocone.category_to_category_struct_id_hom" -> "category_theory", "list.sublist.exists_perm_append" -> "data", "pSet.definable.eq" -> "set_theory", "turing.tape.map_fst" -> "computability", "has_fpower_series_on_ball.tendsto_locally_uniformly_on'" -> "analysis", "submodule.comap_id" -> "algebra", "submodule.mul_le_mul_right" -> "algebra", "borel_eq_generate_Ioi" -> "analysis", "polynomial.coeff_add" -> "data", "measurable_space.comap_map_le" -> "analysis", "multiset.rel_cons_right" -> "data", "rat.cast_of_int" -> "data", "category_theory.under.forget_map" -> "category_theory", "midpoint_sub_sub" -> "algebra", "list.kerase_append_left" -> "data", "symm_of_uniformity" -> "topology", "matrix.from_blocks_apply\:2082\:2082" -> "data", "filter.mem_top_sets" -> "order", "funext" -> "init", "mv_polynomial.sum_monomial" -> "data", "free_monoid.lift_eval_of" -> "algebra", "category_theory.category_of_elements.id_val" -> "category_theory", "many_one_equiv.le_congr_right" -> "computability", "strict_mono.div_const" -> "algebra", "set.bij_on.image_eq" -> "data", "measure_theory.l1.coe_sub" -> "analysis", "mem_left_coset" -> "algebra", "with_top.some_eq_coe" -> "order", "list.zip_swap" -> "data", "finset.image_val_of_inj_on" -> "data", "cSup_le_iff" -> "order", "tangent_map_comp_at" -> "geometry", "function.uncurry_bicompr" -> "logic", "multiset.inf_ndinsert" -> "data", "real.cos_pi_div_sixteen" -> "analysis", "multiset.union_add_inter" -> "data", "smooth_on.neg" -> "geometry", "finset.Ico.filter_le_of_le" -> "data", "finset.prod_univ_pi" -> "data", "measure_theory.integral_add" -> "analysis", "set.preimage_const_sub_Icc" -> "data", "int.add_lt_add_left" -> "init", "onote.oadd_add" -> "set_theory", "semidirect_product.lift_comp_inl" -> "algebra", "with_zero.div_zero" -> "algebra", "add_neg'" -> "algebra", "neg_add_eq_iff_eq_add" -> "algebra", "cardinal.omega_le" -> "set_theory", "filter.mem_infi" -> "order", "finset.insert_idem" -> "data", "mem_normalizer_fintype" -> "algebra", "tendsto_list_prod" -> "topology", "localization.mul_equiv_of_quotient_apply" -> "algebra", "top_apply" -> "order", "category_theory.connected_zigzag" -> "category_theory", "char_poly_nat_degree_eq_dim" -> "algebra", "eventually_nhds_within_nhds_within" -> "topology", "pgame.lt_def_le" -> "set_theory", "set.piecewise_insert_of_ne" -> "data", "units.exists_iff_ne_zero" -> "algebra", "measure_theory.sum_measure_le_measure_univ" -> "analysis", "ordinal.sup_lt_ord" -> "set_theory", "typevec.fst_prod_mk" -> "data", "real.log_le_log" -> "analysis", "is_linear_map.map_sub" -> "algebra", "is_max_filter.max" -> "order", "list.nodup_of_nodup_cons" -> "data", "metric.completion.dist_eq" -> "topology", "linarith.zero_mul_eq" -> "tactic", "typevec.last_fun_comp" -> "data", "tactic.group.gpow_trick_one'" -> "tactic", "seq_compact_space.tendsto_subseq" -> "topology", "submonoid.localization_map.mul_equiv_of_mul_equiv_eq" -> "algebra", "lim_norm_zero'" -> "analysis", "digits_add" -> "data", "array.pop_back_idx" -> "init", "nat.prime.pos" -> "data", "ordinal.nat_cast_inj" -> "set_theory", "int.sub_nat_nat_add_right" -> "init", "cInf_singleton" -> "order", "convex_halfspace_ge" -> "analysis", "tactic.ring_exp.mul_pf_sum" -> "tactic", "finset.prod_const" -> "algebra", "nnreal.inv_rpow" -> "analysis", "filter.inf_map_at_top_ne_bot_iff" -> "order", "riesz_lemma" -> "analysis", "subsemiring.comap_comap" -> "algebra", "cardinal.power_add" -> "set_theory", "metric.diam_empty" -> "topology", "affine_subspace.ext" -> "algebra", "polynomial.nodup_of_separable_prod" -> "algebra", "tsum_eq_tsum_of_ne_zero_bij" -> "topology", "add_le_of_nonpos_of_le'" -> "algebra", "padic_norm.padic_norm_p" -> "data", "nat.subtype.exists_succ" -> "data", "primrec.nat_elim" -> "computability", "measurable_space.dynkin_system.has_union" -> "analysis", "enat.to_with_top_coe" -> "data", "tactic.abel.subst_into_smul" -> "tactic", "filter.frequently_or_distrib_left" -> "order", "function.surjective.preimage_injective" -> "data", "rat.cast_add" -> "data", "finsupp.sum_single" -> "data", "real.continuous_cosh" -> "analysis", "is_basis.repr_total" -> "algebra", "functor.comp.functor_id_comp" -> "control", "finset.prod_update_of_mem" -> "algebra", "measurable.sum_rec" -> "analysis", "continuous_linear_map.is_closed_ker" -> "topology", "dim_le_of_injective" -> "algebra", "list.foldr_cons" -> "data", "computable.list_cons" -> "computability", "category_theory.preadditive.comp_sum_assoc" -> "category_theory", "category_theory.limits.types.sigma_\[Iota]" -> "category_theory", "eq_cosets_of_normal" -> "algebra", "mnat_monoid_hom_eq" -> "algebra", "quadratic_eq_zero_iff" -> "algebra", "cardinal.lift_lt_univ" -> "set_theory", "continuous_Inf_rng" -> "topology", "polynomial.separable_def" -> "algebra", "nat.cast_bit0" -> "data", "metric.sum.one_dist_le'" -> "topology", "geom_sum_Ico_mul" -> "algebra", "category_theory.nat_trans.right_op_app" -> "category_theory", "add_submonoid.mem_coe" -> "algebra", "vadd_right_cancel_iff" -> "algebra", "generalized_continued_fraction.continuants_recurrence" -> "algebra", "real.arccos_cos" -> "analysis", "multiset.cons_bind" -> "data", "measure_theory.simple_func.monotone_approx" -> "analysis", "polynomial.mod_by_monic_X_sub_C_eq_C_eval" -> "data", "ordinal.nat_cast_le" -> "set_theory", "image_le_of_liminf_slope_right_lt_deriv_boundary'" -> "analysis", "dioph.ex1_dioph" -> "number_theory", "concave_on.concave_le" -> "analysis", "nat.add_def" -> "data", "bounded_continuous_function.coe_neg" -> "topology", "joined_in.trans" -> "topology", "ring.direct_limit.induction_on" -> "algebra", "mem_closure_of_continuous" -> "topology", "add_semiconj_by.units_of_coe" -> "algebra", "eventually_countable_ball" -> "order", "list.append_inj_left'" -> "data", "subgroup.normal_of_comm" -> "algebra", "algebraic_geometry.SheafedSpace.id_c_app" -> "algebraic_geometry", "is_local_min_const" -> "topology", "add_submonoid.localization_map.lift_mk'_spec" -> "algebra", "measure_theory.simple_func_sequence_tendsto'" -> "analysis", "category_theory.non_preadditive_abelian.sub_comp" -> "category_theory", "char.veq_of_eq" -> "init", "is_max_on.on_preimage" -> "order", "applicative_transformation.preserves_seq" -> "control", "finsupp.sum_map_domain_index" -> "data", "one_one_equiv.trans" -> "computability", "false_of_true_eq_false" -> "init", "homeomorph.induced_eq" -> "topology", "submodule.smul_assoc" -> "algebra", "add_neg_of_neg_of_nonpos" -> "algebra", "num.cast_of_znum" -> "data", "dfinsupp.map_range_def" -> "data", "pos_num.min_fac_to_nat" -> "data", "hyperreal.not_infinite_add" -> "data", "lt_mul_of_lt_of_one_lt'" -> "algebra", "mul_inv_le_iff_le_mul" -> "algebra", "linear_map.comp_id" -> "algebra", "matrix.to_lin_of_equiv" -> "algebra", "set.image_mul_left" -> "algebra", "hyperreal.coe_inv" -> "data", "list.nodup_enum_map_fst" -> "data", "deriv_id''" -> "analysis", "lucas_lehmer.X.add_fst" -> "number_theory", "equiv.perm.sign_bij_aux_inj" -> "algebra", "finmap.mem_list_to_finmap" -> "data", "list.chain.imp" -> "data", "gcd_comm" -> "algebra", "continuous_linear_equiv.snd_equiv_of_right_inverse" -> "topology", "subtype.range_val" -> "data", "list.pairwise_map_of_pairwise" -> "data", "measure_theory.measure.haar.index_defined" -> "analysis", "computable.part" -> "computability", "complex.of_real_re" -> "data", "cardinal.aleph'_aleph_idx" -> "set_theory", "Set.image.mk" -> "set_theory", "inner_product_geometry.sin_angle_mul_norm_mul_norm" -> "geometry", "add_le_iff_nonpos_left" -> "algebra", "nhds_mono" -> "topology", "add_monoid_hom.comap_ker" -> "algebra", "multiset.quot_mk_to_coe" -> "data", "set.Ico_union_Icc_eq_Icc" -> "data", "set.mem_image2_of_mem" -> "data", "implicit_function_data.right_map_implicit_function" -> "analysis", "add_group.mem_closure_union_iff" -> "algebra", "ring.direct_limit.of_mul" -> "algebra", "subgroup.mem_bot" -> "algebra", "uniformity_sum_of_open_aux" -> "topology", "polynomial.leading_coeff_zero" -> "data", "finite_dimensional_direction_affine_span_of_finite" -> "algebra", "ennreal.top_add" -> "data", "finset.sdiff_inter_self_right" -> "data", "omega.int.neg_free_neg_elim" -> "tactic", "pfun.preimage_mono" -> "data", "add_right_cancel" -> "algebra", "cardinal.aleph'_omega" -> "set_theory", "not_bdd_below_iff" -> "order", "smooth_on_univ" -> "geometry", "ideal.mul_mem_mul" -> "algebra", "computation.parallel_congr_lem" -> "data", "filter.has_basis_binfi_principal'" -> "order", "is_closed_union" -> "topology", "continuous_linear_equiv.bijective" -> "topology", "monoid_hom.eq_on_inv" -> "algebra", "list.perm.erasep" -> "data", "category_theory.full_subcategory_inclusion.map" -> "category_theory", "array.mem_rev_list" -> "data", "nat.mul_left_inj" -> "data", "times_cont_diff_on.continuous_on_fderiv_within_apply" -> "analysis", "Module.Mon_Module_equivalence_Algebra.functor_obj" -> "category_theory", "free_group.red.trans" -> "algebra", "set.Ici_diff_Ioi_same" -> "data", "polynomial.eval\:2082_algebra_map_int_X" -> "data", "set.compl_sUnion" -> "data", "local_equiv.restr_coe" -> "data", "gold_sub_gold_conj" -> "data", "cardinal.lift_one" -> "set_theory", "set.image_preimage_eq_of_subset" -> "data", "fin.coe_cast_succ" -> "data", "ring.fractional_ideal.map_equiv_refl" -> "algebra", "interval_integrable.sub" -> "analysis", "times_cont_mdiff_on_chart_symm" -> "geometry", "additive.is_add_monoid_hom" -> "algebra", "filter.has_basis.restrict_subset" -> "order", "nat.pow_succ" -> "init", "int.le_trans" -> "init", "free_ring.coe_zero" -> "algebra", "list.length_take" -> "init", "enat.with_top_equiv_le" -> "data", "finset.singleton_subset_iff" -> "data", "primrec.dom_fintype" -> "computability", "lcm_mul_left" -> "algebra", "canonically_ordered_semiring.mul_pos" -> "algebra", "zsqrtd.nonneg_iff_zero_le" -> "data", "equiv.arrow_congr'_apply" -> "data", "Module.monoidal_category.tensor_comp" -> "algebra", "neg_convex_on_iff" -> "analysis", "prod.snd_prod" -> "algebra", "asymptotics.is_o.trans_is_O_with" -> "analysis", "complex.abs_mul" -> "data", "finset.min_eq_none" -> "data", "finsupp.map_range_zero" -> "data", "list.eq_of_infix_of_length_eq" -> "data", "equiv.to_local_equiv_source" -> "data", "measure_theory.outer_measure.sum_apply" -> "analysis", "nat.cast_max" -> "data", "is_measurable_Iic" -> "analysis", "ennreal.sub_add_self_eq_max" -> "data", "discrete_valuation_ring.has_unit_mul_pow_irreducible_factorization.unique_irreducible" -> "algebra", "set.Iio_union_Ico_eq_Iio" -> "data", "filter.lift_mono'" -> "order", "nnreal.coe_tsum" -> "topology", "strict_mono.const_mul" -> "algebra", "int.add_right_neg" -> "init", "is_open.is_connected_iff_is_path_connected" -> "topology", "mul_eq_zero_of_left" -> "algebra", "strict_mono.top_preimage_top'" -> "order", "infi_top" -> "order", "filter.ultrafilter_ultrafilter_of" -> "order", "finset.filter_true_of_mem" -> "data", "punit.bot_eq" -> "algebra", "map_infi_of_continuous_at_of_monotone" -> "topology", "ne_zero_of_one_div_ne_zero" -> "algebra", "tangent_map_tangent_bundle_proj" -> "geometry", "finset.card_le_card_of_inj_on" -> "data", "category_theory.functor.empty_ext'" -> "category_theory", "power_series.coeff_one_X" -> "algebra", "polynomial.leading_coeff_C" -> "data", "list.cons_bag_inter_of_pos" -> "data", "emetric.closed_ball_subset_closed_ball" -> "topology", "function.embedding.to_fun_eq_coe" -> "logic", "set.maps_to_bInter" -> "data", "equiv.set.univ_symm_apply" -> "data", "finset.Ico.to_finset" -> "data", "has_deriv_at.scomp" -> "analysis", "concave_on.add" -> "analysis", "is_integral_of_noetherian'" -> "algebra", "list.rotate'_mod" -> "data", "associates.rel_associated_iff_map_eq_map" -> "algebra", "ereal.neg_neg" -> "data", "turing.tape.mk'_nth_nat" -> "computability", "map_infi_of_continuous_at_of_monotone'" -> "topology", "set.finite.seq" -> "data", "list.concat_nil" -> "data", "hyperreal.is_st_sub" -> "data", "int.pred_neg_pred" -> "data", "alist.erase_erase" -> "data", "free_group.red.step.cons_bnot_rev" -> "algebra", "linear_map.inl_apply" -> "algebra", "add_submonoid.localization_map.map_spec" -> "algebra", "lt_abs" -> "algebra", "hyperreal.epsilon_ne_zero" -> "data", "mdifferentiable_on_id" -> "geometry", "with_one.coe_inj" -> "algebra", "times_cont_mdiff_on_of_mem_maximal_atlas" -> "geometry", "abstract_completion.induction_on" -> "topology", "nat.bit_tt" -> "data", "set.Ico_eq_empty" -> "data", "measure_theory.lintegral_eq_nnreal" -> "analysis", "linear_independent_of_span_eq_top_of_card_eq_findim" -> "algebra", "category_theory.limits.binary_bicone.to_cocone_X" -> "category_theory", "cardinal.mk_compl_eq_mk_compl_finite_same" -> "set_theory", "category_theory.functor.flip_map_app" -> "category_theory", "local_homeomorph.eq_on_source.source_eq" -> "topology", "Mon.colimits.quot_one" -> "algebra", "subset_connected_component" -> "topology", "category_theory.graded_object.comap_eq_trans" -> "category_theory", "Top.sheaf_condition.fork_\[Pi]_app_walking_parallel_pair_zero" -> "topology", "add_monoid_hom.map_neg" -> "algebra", "subgroup.bot_prod_bot" -> "algebra", "int.default_eq_zero" -> "data", "filter.frequently.forall_exists_of_at_bot" -> "order", "add_submonoid.localization_map.lift_add_left" -> "algebra", "is_open_bUnion" -> "topology", "finset.sum_preimage'" -> "data", "bitraversable.tfst_eq_fst_id'" -> "control", "gsmul_lie" -> "algebra", "int.nat_abs_bit0" -> "init", "generalized_continued_fraction.first_continuant_eq" -> "algebra", "list_all_congr" -> "number_theory", "pgame.impartial.first_loses_symm" -> "set_theory", "filter.pure_bind" -> "order", "uniform_space.mem_nhds_iff_symm" -> "topology", "list.disjoint_of_disjoint_append_right_left" -> "data", "interior_maximal" -> "topology", "ennreal.not_mem_Ioo_self_sub" -> "data", "roption.mem_of_option" -> "data", "nat.partrec'.cons" -> "computability", "set.inter_eq_compl_compl_union_compl" -> "data", "category_theory.limits.cones.functoriality_obj_X" -> "category_theory", "set.right_inv_on.surj_on" -> "data", "fin.succ_succ_ne_one" -> "data", "set.ord_connected_iff_interval_subset" -> "data", "tactic.ring.horner_add_const" -> "tactic", "open_subgroup.is_open" -> "topology", "int.units_nat_abs" -> "data", "ordinal.enum_type" -> "set_theory", "monoid_hom.eq_of_eq_on_top" -> "algebra", "monoid_hom.map_iterate_pth_root" -> "algebra", "finsupp.prod_map_range_index" -> "data", "is_preconnected_Ici" -> "topology", "finset.inter_val_nd" -> "data", "turing.reaches\:2080.trans" -> "computability", "list.exists_mem_of_length_pos" -> "data", "is_bounded_bilinear_map.times_cont_diff" -> "analysis", "is_measurable.Inter" -> "analysis", "commute.cast_nat_mul_cast_nat_mul" -> "algebra", "set.preimage_neg_Iic" -> "data", "refl_bilin_form.eq_zero" -> "algebra", "finite_field.prod_univ_units_id_eq_neg_one" -> "algebra", "sym_sesq_form.is_refl" -> "algebra", "filter.inter_mem_inf_sets" -> "order", "category_theory.functor.to_cocone_X" -> "category_theory", "lt_floor_add_one" -> "algebra", "category_theory.sum.associator_obj_inr" -> "category_theory", "interval_integral.deriv_within_integral_right" -> "analysis", "le_add_of_neg_add_le" -> "algebra", "map_csupr_of_continuous_at_of_monotone" -> "topology", "cInf_insert" -> "order", "function.injective.has_sum_iff" -> "topology", "linear_map.map_le_map_iff" -> "algebra", "eq_self_iff_true" -> "init", "finsupp.prod_finset_sum_index" -> "data", "Inf_empty" -> "order", "vector3.insert_fz" -> "number_theory", "bdd_below.inter_of_right" -> "order", "finsupp.supported_union" -> "algebra", "supr_pos" -> "order", "category_theory.limits.equalizer.condition_assoc" -> "category_theory", "nat.primrec.swap'" -> "computability", "measurable.ennreal_coe" -> "analysis", "vadd_vsub" -> "algebra", "ordinal.nat_lt_limit" -> "set_theory", "filter.nmem_hyperfilter_of_finite" -> "order", "equiv.summable_iff" -> "topology", "decidable.le_imp_le_iff_lt_imp_lt" -> "algebra", "has_deriv_within_at.limsup_slope_le" -> "analysis", "add_subgroup.closure_eq_of_le" -> "algebra", "tendsto_const_nhds_within" -> "topology", "nat.mul_le_mul_right" -> "init", "add_neg_cancel_right" -> "algebra", "polynomial.eval\:2082_mul" -> "data", "pi_generate_from_eq" -> "topology", "has_deriv_at_iff_tendsto_slope" -> "analysis", "le_of_forall_lt" -> "algebra", "buffer.ext" -> "data", "polynomial.is_splitting_field.splits_iff" -> "algebra", "linear_pmap.le_of_eq_locus_ge" -> "algebra", "zsqrtd.sq_le_of_le" -> "data", "function.inv_fun_on_mem" -> "logic", "list.eq_nil_of_sublist_nil" -> "data", "num.zero_add" -> "data", "finsupp.sum_apply" -> "data", "list.nodup_append_comm" -> "data", "int.sub_add_cancel" -> "init", "cardinal.one_lt_omega" -> "set_theory", "free_group.red.step.append_left_iff" -> "algebra", "multiset.Ico.filter_lt_of_le_bot" -> "data", "floor_mono" -> "algebra", "order_of_dvd_of_pow_eq_one" -> "algebra", "free_abelian_group.seq_add" -> "algebra", "list.init_append_last" -> "data", "asymptotics.is_O_with.sum" -> "analysis", "padic_int.norm_lt_one_iff_dvd" -> "data", "field.closure_subset" -> "algebra", "vsub_add_vsub_cancel" -> "algebra", "polynomial.comp_X" -> "data", "subgroup.map_sup" -> "algebra", "convex_on_pow_of_even" -> "analysis", "submodule.smul_mono_left" -> "algebra", "dfinsupp.erase_same" -> "data", "hyperreal.infinite_iff_infinite_pos_abs" -> "data", "filter.tendsto.inf" -> "order", "finset.insert_val_of_not_mem" -> "data", "set.Iio_union_Icc_eq_Iic" -> "data", "ordinal.div_mul_cancel" -> "set_theory", "finset.sum_eq_single" -> "algebra", "set.image_subset_preimage_of_inverse" -> "data", "lt_mul_iff_one_lt_right'" -> "algebra", "ideal.quotient.mk_surjective" -> "algebra", "filter.le_comap_top" -> "order", "add_subgroup.coe_coe" -> "algebra", "padic_val_nat_def" -> "data", "complex.norm_sq_inv" -> "data", "list.doubleton_eq" -> "data", "set.insert_union" -> "data", "real.neg_one_le_sin" -> "data", "cau_seq.trichotomy" -> "data", "imp_eq_of_eq_true_left" -> "init", "bot_eq_zero" -> "algebra", "primrec.subtype_mk" -> "computability", "submonoid.localization_map.map_comp_map" -> "algebra", "Class.empty_hom" -> "set_theory", "subsemiring.mem_mk'" -> "algebra", "ring_equiv.to_fun_eq_coe_fun" -> "data", "unique_diff_on.unique_diff_within_at" -> "analysis", "filter.image_mem_sets" -> "order", "cardinal.one_lt_bit0" -> "set_theory", "tactic.abel.zero_term" -> "tactic", "continuous_linear_equiv.is_O_comp" -> "analysis", "list.pairwise.and" -> "data", "list.nth_rotate" -> "data", "linarith.mul_neg" -> "tactic", "mul_mono_nonneg" -> "tactic", "is_R_or_C.nat_cast_re" -> "data", "derivation.smul_apply" -> "algebra", "add_monoid_hom.coprod_comp_inl" -> "algebra", "finite_dimensional.lt_omega_of_linear_independent" -> "algebra", "list.is_suffix.trans" -> "data", "equiv.trans_to_local_equiv" -> "data", "polynomial.map_expand" -> "algebra", "is_coprime_comm" -> "algebra", "set.Union_image_preimage_sigma_mk_eq_self" -> "data", "affine.simplex.monge_point_vsub_face_centroid_eq_weighted_vsub_of_points_with_circumcenter" -> "geometry", "real.tan_neg" -> "data", "derivation.to_fun_eq_coe" -> "algebra", "mv_polynomial.eval\:2082_hom_congr" -> "data", "function.partial_inv_left" -> "logic", "measure_theory.ae_eq_fun.edist_self" -> "analysis", "neg_lt" -> "algebra", "AddCommGroup.injective_of_mono" -> "algebra", "eq_zero_of_abs_eq_zero" -> "algebra", "finset.bInter_singleton" -> "data", "inv_inj'" -> "algebra", "equiv.perm.card_support_swap" -> "algebra", "submodule.gc_map_comap" -> "algebra", "set.Icc_subset_Iio_iff" -> "data", "exists_eq_right" -> "logic", "nnreal.coe_add" -> "data", "finset.sum_boole_mul" -> "algebra", "Icc_mem_nhds_within_Ici" -> "topology", "not_is_unit_zero" -> "algebra", "category_theory.arrow.id_right" -> "category_theory", "is_greatest.nonempty" -> "order", "category_theory.limits.is_limit.hom_ext" -> "category_theory", "znum.add_one" -> "data", "has_fderiv_at_filter_const" -> "analysis", "cluster_pt.mono" -> "topology", "is_glb_Inf" -> "order", "turing.partrec_to_TM2.K'.elim_update_stack" -> "computability", "multiset.filter_inter" -> "data", "le_compl_of_le_compl" -> "order", "ideal.radical_eq_top" -> "algebra", "nnreal.summable_geometric" -> "analysis", "measure_theory.restrict_congr" -> "analysis", "max_sub_min_eq_abs" -> "algebra", "set.range_restrict" -> "data", "pow_inv_comm" -> "algebra", "finset.piecewise_eq_of_mem" -> "data", "submodule.quotient.mk_surjective" -> "algebra", "cardinal.lt_succ" -> "set_theory", "local_homeomorph.trans_symm_eq_symm_trans_symm" -> "topology", "equiv.perm.sign_of_subtype" -> "algebra", "Set.choice_mem" -> "set_theory", "set.finite_range_find_greatest" -> "data", "set.Iic_subset_Iic" -> "data", "pequiv.single_trans_of_eq_none" -> "data", "category_theory.limits.coprod.map_desc_assoc" -> "category_theory", "associates.factors'_cong" -> "algebra", "submonoid.localization_map.mul_equiv_of_localizations_apply" -> "algebra", "linear_map.pi_comp" -> "algebra", "set.sInter_eq_comp_sUnion_compl" -> "data", "pequiv.single_trans_single_of_ne" -> "data", "circle_deg1_lift.map_int_of_map_zero" -> "dynamics", "category_theory.symmetric_of_has_finite_products_to_braided_category_braiding" -> "category_theory", "filter.prod_principal_principal" -> "order", "inducing.map_nhds_eq" -> "topology", "alist.insert_insert_of_ne" -> "data", "fderiv_add_const" -> "analysis", "measure_theory.outer_measure.map_map" -> "analysis", "semiconj_by.units_of_coe" -> "algebra", "multiset.mem_ndinsert_self" -> "data", "has_strict_fderiv_at.smul" -> "analysis", "submonoid.mem_carrier" -> "algebra", "add_con.Sup_eq_add_con_gen" -> "algebra", "set.union_nonempty" -> "data", "embedding.continuous_iff" -> "topology", "fderiv.comp_fderiv_within" -> "analysis", "continuous_linear_map.coe_prod_map'" -> "topology", "measure_theory.measure_bUnion_finset" -> "analysis", "finset.has_sum" -> "topology", "tangent_map_within_univ" -> "geometry", "preserves_limits_iso_hom_\[Pi]" -> "category_theory", "associates.eq_of_prod_eq_prod" -> "algebra", "padic_norm.nonzero" -> "data", "list.init_eq_of_concat_eq" -> "data", "ne_zero_of_abs_ne_zero" -> "algebra", "int.even_iff" -> "data", "dfinsupp.eq_mk_support" -> "data", "int.add_le_add_left" -> "init", "computation.get_ret" -> "data", "list.foldl_nil" -> "data", "finset.prod_extend_by_one" -> "algebra", "function.semiconj.inj_on_image" -> "data", "multiset.sub_add'" -> "data", "seq.nats_nth" -> "data", "is_unit_iff_exists_inv'" -> "algebra", "continuous_linear_equiv.comp_has_fderiv_at_iff" -> "analysis", "affine_map.homothety_one" -> "algebra", "tactic.ring_exp.simple_pf_sum_zero" -> "tactic", "compl_le_compl" -> "order", "rat.add_mul" -> "data", "has_deriv_at.lhopital_zero_left_on_Ioc" -> "analysis", "ordinal.type_mul" -> "set_theory", "filter.tendsto.smul" -> "topology", "equiv.to_local_equiv_target" -> "data", "complex.sinh_add_cosh" -> "data", "free_group.red.step.sublist" -> "algebra", "measure_theory.l1.simple_func.coe_add" -> "analysis", "complex.norm_sq_pos" -> "data", "fderiv_within_smul" -> "analysis", "list.rotate_nil" -> "data", "norm_sub_rev" -> "analysis", "filter.tendsto_add_at_top_nat" -> "order", "mvqpf.fix.rec_unique" -> "data", "ideal.mem_infi" -> "algebra", "real.cosh_sq_sub_sinh_sq" -> "data", "AddCommGroup.image.lift_fac" -> "algebra", "and_iff_right_of_imp" -> "logic", "set.preimage_inter" -> "data", "pow_lt_pow_of_lt_one" -> "algebra", "complex.cpow_int_cast" -> "analysis", "convex_univ" -> "analysis", "multiplicity.ne_zero_of_finite" -> "algebra", "category_theory.under.mk_right" -> "category_theory", "category_theory.abelian.coimages.coimage_strong_epi_mono_factorisation_e_strong_epi" -> "category_theory", "nhds_zero_symm" -> "topology", "commute.inv_left_iff'" -> "algebra", "list.sublist_of_suffix" -> "data", "fderiv_deriv" -> "analysis", "multiset.nodup_add_of_nodup" -> "data", "filter.eventually_eq.is_extr_filter_iff" -> "order", "list.diff_append" -> "data", "category_theory.eq_to_hom_op" -> "category_theory", "summable.subtype" -> "topology", "nat.dvd_prime_two_le" -> "data", "ring_hom.mem_range" -> "algebra", "zmod.val_lt" -> "data", "subtype.coe_image" -> "data", "submodule.smul_singleton" -> "algebra", "linear_map.quot_ker_equiv_range_symm_apply_image" -> "algebra", "typevec.last_fun_to_subtype" -> "data", "measure_theory.measure_diff_of_ae_le" -> "analysis", "int.sub_lt_sub_right" -> "init", "asymptotics.is_O_with.of_bound" -> "analysis", "category_theory.limits.prod.associator_naturality_assoc" -> "category_theory", "has_deriv_within_at_inter'" -> "analysis", "is_absolute_value.abv_inv" -> "data", "matrix.bit1_apply" -> "data", "ordinal.mul_right_inj" -> "set_theory", "subring.coe_ssubset_coe" -> "algebra", "set.indicator_preimage" -> "data", "deriv_csin" -> "analysis", "bool.exists_bool" -> "data", "free_monoid.map_comp" -> "algebra", "matrix.adjugate_eq_one_of_card_eq_one" -> "algebra", "list.sorted_singleton" -> "data", "norm_num.subst_into_add" -> "tactic", "filter.Liminf_le_Limsup" -> "order", "ennreal.inv_ne_top" -> "data", "set.sInter_bUnion" -> "data", "group.mem_closure_union_iff" -> "algebra", "add_monoid_algebra.single_mul_single" -> "data", "Set.mem_pair_sep" -> "set_theory", "interior_eq_iff_open" -> "topology", "tactic.ring_exp.pow_pf_zero" -> "tactic", "turing.to_partrec.code.id_eval" -> "computability", "function.comp_iterate_pred_of_pos" -> "logic", "padic_norm_e.eq_padic_norm'" -> "data", "nat.bodd_bit0" -> "data", "function.iterate_id" -> "logic", "local_equiv.trans_source'" -> "data", "pequiv.to_matrix_bot" -> "data", "complex.abs_pos" -> "data", "multiset.prod_eq_zero" -> "data", "has_deriv_at.ccos" -> "analysis", "computation.lift_rel_aux.swap" -> "data", "continuous_linear_map.to_span_singleton_norm" -> "analysis", "continuous_on.comp_continuous" -> "topology", "nat.coe_cast_ring_hom" -> "data", "pnat.lt_add_one_iff" -> "data", "is_bounded_bilinear_map_comp_multilinear" -> "analysis", "category_theory.limits.cocones.functoriality_obj_\[Iota]_app" -> "category_theory", "compl_unique" -> "order", "finset.prod_bij" -> "algebra", "pos_num.sub'_one" -> "data", "is_R_or_C.of_real_inj" -> "data", "subring.coe_zero" -> "algebra", "dioph.dioph_fn_comp" -> "number_theory", "fixed_points.prev_le" -> "order", "turing.partrec_to_TM2.head_stack_ok" -> "computability", "inv_pow'" -> "algebra", "set.mk_preimage_prod_right_eq_if" -> "data", "subgroup.coe_prod" -> "algebra", "finset.prod_range_succ'" -> "algebra", "is_lub_empty" -> "order", "opposite.op_eq_zero_iff" -> "algebra", "complex.norm_int" -> "analysis", "int.exists_greatest_of_bdd" -> "data", "submonoid.monotone_comap" -> "algebra", "category_theory.discrete.nat_iso_app" -> "category_theory", "real.volume_Ioo" -> "analysis", "wseq.map_cons" -> "data", "monoid_hom.snd_comp_inl" -> "algebra", "le_abs_self" -> "algebra", "measure_theory.l1.simple_func.coe_coe" -> "analysis", "real.has_deriv_at_cosh" -> "analysis", "int.coe_nat_le_coe_nat_of_le" -> "init", "finset.union_val_nd" -> "data", "pgame.zero_le_add_right_neg" -> "set_theory", "set.image_add_const_Ioo" -> "data", "emetric.nhds_basis_eball" -> "topology", "ennreal.to_nnreal_coe" -> "data", "add_localization.zero_rel" -> "algebra", "set.left_mem_Ici" -> "data", "asymptotics.is_O_with.right_le_add_of_lt_1" -> "analysis", "list.suffix_union_right" -> "data", "eq_pth_root_iff" -> "algebra", "smooth_within_at.prod_mk" -> "geometry", "vector.nth_cons_zero" -> "data", "eventually_residual" -> "topology", "real.sinh_neg" -> "data", "list.prod_take_succ" -> "data", "matrix.zero_dot_product" -> "data", "set.eq_on.trans" -> "data", "cau_seq.completion.of_rat_div" -> "data", "pos_num.to_nat_pos" -> "data", "bifunctor.id_fst" -> "control", "fin.zero_ne_one" -> "data", "measure_theory.eventually_dirac" -> "analysis", "mem_inv_smul_set_iff" -> "algebra", "mvpfunctor.id_map" -> "data", "measure_theory.l1.neg_to_fun" -> "analysis", "bit1_mul" -> "algebra", "convex_cone.ext'" -> "analysis", "hyperreal.infinite_omega" -> "data", "asymptotics.is_O_with.of_const_mul_right" -> "analysis", "linear_equiv.inv_fun_apply" -> "algebra", "geom_sum_mul_neg" -> "algebra", "is_add_unit.coe_lift_right" -> "algebra", "is_extr_on.neg" -> "order", "uniform_space.complete_of_convergent_controlled_sequences" -> "topology", "times_cont_mdiff_within_at.comp" -> "geometry", "gcd_mul_left" -> "algebra", "structure_groupoid.is_local_structomorph_within_at_local_invariant_prop" -> "geometry", "real.angle.coe_int_mul_eq_gsmul" -> "analysis", "category_theory.under.mk_left" -> "category_theory", "finset.range_mono" -> "data", "ennreal.mul_eq_top" -> "data", "primrec.fin_curry" -> "computability", "function.iterate_succ" -> "logic", "pow_le_pow" -> "algebra", "units.ext_iff" -> "algebra", "filter.germ.coe_add" -> "order", "list.perm.pairwise_iff" -> "data", "submonoid.localization_map.lift_eq_iff" -> "algebra", "set.eq_on.surj_on_iff" -> "data", "tsum_add" -> "topology", "filter.prod_comap_comap_eq" -> "order", "finset.univ_map_equiv_to_embedding" -> "data", "list.subperm.diff_right" -> "data", "int.coe_cast_add_hom" -> "data", "linear_map.range_prod_eq" -> "algebra", "finset.sup_singleton" -> "data", "polynomial.factor_dvd_of_nat_degree_ne_zero" -> "algebra", "add_nonneg" -> "algebra", "is_lub_Ioo" -> "order", "preorder_hom.comp_id" -> "order", "digits_one" -> "data", "filter.map_at_top_eq_of_gc" -> "order", "filter.at_top_basis'" -> "order", "equiv.set.sum_diff_subset_symm_apply_of_not_mem" -> "data", "norm_num.adc_bit0_one" -> "tactic", "list.sum_take_map_length_split_wrt_composition" -> "combinatorics", "generalized_continued_fraction.of_denom_mono" -> "algebra", "smul_algebra_right_apply" -> "algebra", "nat.le_mkpair_right" -> "data", "tangent_cone_at.lim_zero" -> "analysis", "has_mfderiv_at_id" -> "geometry", "metric.diam_le_of_forall_dist_le_of_nonempty" -> "topology", "has_deriv_at_iff_has_fderiv_at" -> "analysis", "nnreal.div_mul_eq_mul_div" -> "data", "category_theory.iso.hom_comp_eq_id" -> "category_theory", "interval_integral.integral_has_deriv_at_of_tendsto_ae_left" -> "analysis", "le_inv" -> "algebra", "ideal.span_singleton_prime" -> "algebra", "polynomial.leading_coeff_eq_zero_iff_deg_eq_bot" -> "data", "measure_theory.integral_mono_of_nonneg" -> "analysis", "is_coprime_one_right" -> "algebra", "is_measurable_interior" -> "analysis", "gsmul_mul" -> "algebra", "polynomial.coeff_eq_zero_of_nat_degree_lt" -> "data", "nat.add_le_add_left" -> "init", "category_theory.uncurry.obj_map" -> "category_theory", "equiv.perm.mem_fin_pairs_lt" -> "algebra", "mvqpf.recF_eq'" -> "data", "finsupp.support_on_finset" -> "data", "category_theory.pi.comap_map" -> "category_theory", "ideal.radical_mono" -> "algebra", "differentiable_within_at_pow" -> "analysis", "category_theory.limits.walking_parallel_pair_hom_id" -> "category_theory", "list.chain.iff_mem" -> "data", "well_founded.lt_succ" -> "order", "list.erase_of_not_mem" -> "data", "polynomial.eval_add" -> "data", "measure_theory.measure.Inf_apply" -> "analysis", "lagrange.degree_interpolate_lt" -> "algebra", "list.diff_eq_filter_of_nodup" -> "data", "complex.I_im" -> "data", "nat.add_one" -> "init", "cardinal.mk_subtype_le" -> "set_theory", "function.support_subset_comp" -> "data", "finset.range_add_one" -> "data", "continuous_linear_equiv.coe_def_rev" -> "topology", "computation.length_thinkN" -> "data", "supr_false" -> "order", "deriv_smul_const" -> "analysis", "set.compl_union_self" -> "data", "Top.sheaf_condition.fork_\[Pi]_app_walking_parallel_pair_one" -> "topology", "category_theory.action_category.stabilizer_iso_End_apply" -> "category_theory", "is_greatest_Icc" -> "order", "ordinal.is_normal.bsup_eq" -> "set_theory", "list.lex.cons_iff" -> "data", "equiv.Pi_congr_left'_apply" -> "data", "ennreal.coe_finset_prod" -> "data", "mem_nhds_within_Iic_iff_exists_Icc_subset'" -> "topology", "function.embedding.coe_prod_map" -> "logic", "multiset.coe_fold_l" -> "data", "monoid_hom.snd_comp_inr" -> "algebra", "is_open_fold" -> "topology", "lim_norm_zero" -> "analysis", "midpoint_add_left" -> "algebra", "complex.sinh_zero" -> "data", "differentiable.smul_algebra_const" -> "analysis", "int.add_sub_assoc" -> "init", "pos_num.cmp_swap" -> "data", "not_false_iff" -> "init", "cardinal.aleph_lt" -> "set_theory", "norm_num.le_bit0_bit0" -> "tactic", "Set.mk_eq" -> "set_theory", "measure_theory.ae_eq_fun.coe_fn_comp\:2082" -> "analysis", "filter.eventually_eq.eventually" -> "order", "is_measurable.inl_image" -> "analysis", "finset.sdiff_union_of_subset" -> "data", "measure_theory.l1.simple_func.sub_to_simple_func" -> "analysis", "linear_map.uncurry_left_apply" -> "algebra", "polynomial.div_X_eq_zero_iff" -> "data", "mem_vector_span_iff_eq_weighted_vsub" -> "algebra", "finset.eq_affine_combination_subset_iff_eq_affine_combination_subtype" -> "algebra", "fin.coe_succ_eq_succ" -> "data", "set.fst_image_prod" -> "data", "path_component_in_univ" -> "topology", "multiset.coe_disjoint" -> "data", "set.Ici_subset_Ici" -> "data", "asymptotics.is_o.right_is_O_add" -> "analysis", "mdifferentiable_of_mem_atlas" -> "geometry", "to_topological_space_bot" -> "topology", "homeomorph.compact_image" -> "topology", "matrix.empty_vec_mul_vec" -> "data", "omega.nat.preterm.val_constant" -> "tactic", "fintype.card_le_of_injective" -> "data", "measure_theory.integrable_iff_edist" -> "analysis", "composition.size_up_to_size_up_to_add" -> "analysis", "set.range_subset_iff" -> "data", "set.subset_union_of_subset_right" -> "data", "direct_sum.mk_neg" -> "algebra", "one_ne_zero" -> "algebra", "category_theory.limits.mono_of_source_iso_zero" -> "category_theory", "function.is_periodic_pt.left_of_add" -> "dynamics", "measure_theory.simple_func.preimage_eq_empty_iff" -> "analysis", "category_theory.limits.types.pi_map" -> "category_theory", "dfinsupp.support_mk_subset" -> "data", "list.forall_mem_singleton" -> "data", "matrix.mul_eq_mul" -> "data", "forall_quotient_iff" -> "data", "cardinal.add_lt_of_lt" -> "set_theory", "order_dual.dual_le" -> "order", "ennreal.sub_add_cancel_of_le" -> "data", "is_compl_bot_top" -> "order", "is_open_neg" -> "topology", "vector3.eq_nil" -> "number_theory", "cardinal.bit0_lt_omega" -> "set_theory", "polynomial.separable_prod_X_sub_C_iff'" -> "algebra", "category_theory.zero_not_simple" -> "category_theory", "reader_t.run_bind" -> "init", "set.indicator_le_indicator" -> "data", "is_bounded_ge_nhds" -> "topology", "one_div_one_div" -> "algebra", "measure_theory.ae_iff" -> "analysis", "fg_adjoin_of_finite" -> "algebra", "ideal.is_local.mem_jacobson_or_exists_inv" -> "algebra", "nnreal.div_add'" -> "data", "submonoid.localization_map.lift_unique" -> "algebra", "differentiable.cexp" -> "analysis", "equiv.symm_comp_self" -> "data", "is_R_or_C.abs_pos" -> "data", "contracting_with.edist_inequality" -> "topology", "is_local_max_on.fderiv_within_eq_zero" -> "analysis", "pnat.xgcd_type.step_v" -> "data", "unique_mdiff_on_univ" -> "geometry", "composition.size_up_to_succ" -> "combinatorics", "is_closed_Union_prop" -> "topology", "ordinal.omin_mem" -> "set_theory", "emetric.pos_of_mem_ball" -> "topology", "fderiv_smul" -> "analysis", "category_theory.monoidal.Mon_functor_category_equivalence.functor_obj_obj_mul" -> "category_theory", "traversable.fold_mfoldr_cons" -> "control", "list.count_erase_self" -> "data", "turing.partrec_to_TM2.tr_init" -> "computability", "set.eq_of_subset_of_card_le" -> "data", "mdifferentiable_within_at_iff_differentiable_within_at" -> "geometry", "mul_inv_eq_of_eq_mul" -> "algebra", "complex.conj_of_real" -> "data", "is_closed_property2" -> "topology", "multiset.eq_of_mem_map_const" -> "data", "prime.not_unit" -> "algebra", "prime_multiset.coe_nat_of_prime" -> "data", "list.nat.mem_antidiagonal" -> "data", "ext_chart_model_space_eq_id" -> "geometry", "bool.band_intro" -> "data", "polynomial.splits_C" -> "algebra", "linear_independent.of_subtype_range" -> "algebra", "category_theory.functor_to_types.map_id_apply" -> "category_theory", "continuous_linear_equiv.comp_has_fderiv_within_at_iff'" -> "analysis", "cardinal.aleph_idx_lt" -> "set_theory", "with_bot.some_lt_some" -> "order", "stone_cech_unit_dense" -> "topology", "pow_nonneg" -> "algebra", "linear_map.lcongr_fun" -> "algebra", "finset.comp_sup_eq_sup_comp" -> "data", "matrix_equiv_tensor.inv_fun_smul" -> "algebra", "decidable.not_or_iff_and_not" -> "init", "measure_theory.measure.restrict_apply_eq_zero'" -> "analysis", "linear_map.map_comap_eq" -> "algebra", "zero_le'" -> "algebra", "ideal.mem_map_C_iff" -> "algebra", "lt_div_iff" -> "algebra", "num.ldiff_to_nat" -> "data", "wseq.head_congr" -> "data", "cauchy_map_iff'" -> "topology", "adjoin_root.mul_div_root_cancel" -> "algebra", "int.cast_ne_zero" -> "data", "polynomial.eval_bit0" -> "data", "filter.map_at_bot_eq" -> "order", "setoid.is_partition.sUnion_eq_univ" -> "data", "typevec.prod_map_id" -> "data", "category_theory.graded_object.comap_eq_inv_app" -> "category_theory", "algebra.tensor_product.assoc_aux_1" -> "algebra", "infi_congr" -> "order", "metric.completion.uniformity_dist'" -> "topology", "with_top.zero_lt_coe" -> "algebra", "strict_mono.mul_monotone'" -> "algebra", "filter_basis.generate" -> "order", "is_linear_map.image_convex_hull" -> "analysis", "measure_theory.l1.integral_neg" -> "analysis", "free_group.red.inv_of_red_of_ne" -> "algebra", "ennreal.infi_mul_left" -> "topology", "submodule.prod_bot" -> "algebra", "category_theory.limits.cospan_one" -> "category_theory", "computation.tail_think" -> "data", "multiset.count_le_count_cons" -> "data", "multiset.cons_add" -> "data", "list.Ico.trichotomy" -> "data", "ennreal.add_infi" -> "data", "ideal.mem_span_singleton'" -> "algebra", "set.finite_range" -> "data", "finset.supr_insert_update" -> "data", "polynomial.mod_by_monic_add_div" -> "data", "list.Ico.filter_le_of_le_bot" -> "data", "add_subgroup.coe_Inf" -> "algebra", "submodule.mem_smul_span_singleton" -> "algebra", "differentiable.smul_const" -> "analysis", "fderiv_id" -> "analysis", "submodule.mul_subset_mul" -> "algebra", "units.map_comp" -> "algebra", "fin.mk_succ_pos" -> "data", "ennreal.supr_coe_nat" -> "data", "mvqpf.comp.map_mk" -> "data", "polynomial.splits_of_exists_multiset" -> "algebra", "sub_lt_sub_of_le_of_lt" -> "algebra", "real.one_le_pi_div_two" -> "analysis", "nat.gcd_div" -> "data", "category_theory.limits.prod.right_unitor_hom" -> "category_theory", "set.inter_empty" -> "data", "constr_eq" -> "algebra", "sym2.mem_other_spec" -> "data", "local_of_unique_max_ideal" -> "algebra", "int.exists_gcd_one" -> "algebra", "cardinal.mk_out" -> "set_theory", "matrix.col_cons" -> "data", "cau_seq.neg_apply" -> "data", "finset.inf_mono" -> "data", "differentiable_at.snd" -> "analysis", "alist.singleton_entries" -> "data", "multiset.sum_bind" -> "data", "frontier_union_subset" -> "topology", "lucas_lehmer.s_zmod_eq_s_mod" -> "number_theory", "category_theory.limits.cocone_morphism.ext" -> "category_theory", "asymptotics.is_o.right_is_O_sub" -> "analysis", "add_lt_add_iff_left" -> "algebra", "finsupp.dom_lcongr_single" -> "algebra", "semiconj_by.zero_right" -> "algebra", "finset.bInter_coe" -> "data", "nat.succ_mul" -> "init", "set.singleton_prod_singleton" -> "data", "enat.inf_eq_min" -> "data", "real.abs_div_sqrt_one_add_lt" -> "analysis", "list.length_map\:2082" -> "init", "eq_add_of_neg_add_eq" -> "algebra", "continuous_linear_map.exists_right_inverse_of_surjective" -> "analysis", "category_theory.iso.hom_congr_apply" -> "category_theory", "euclidean_domain.val_dvd_le" -> "algebra", "computable_pred.of_eq" -> "computability", "with_top.not_top_le_coe" -> "order", "int.sign_of_succ" -> "init", "list.foldl_with_index_eq_foldl_enum" -> "data", "category_theory.iso.trans_conj" -> "category_theory", "ennreal.mul_infi" -> "data", "turing.partrec_to_TM2.K'.elim_update_rev" -> "computability", "list.range'_concat" -> "data", "measure_theory.ae_eq_fun.one_to_germ" -> "analysis", "filter.tendsto.edist" -> "topology", "finset.Ico.succ_top'" -> "data", "measure_theory.outer_measure.Inf_eq_of_function_Inf_gen" -> "analysis", "multiset.erase_dup_cons_of_not_mem" -> "data", "set.mem_union_eq" -> "data", "norm_num.add_neg_neg" -> "tactic", "measure_theory.outer_measure.smul_apply" -> "analysis", "set.compl_image_set_of" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_at_symm_of_mem_maximal_atlas" -> "geometry", "finsupp.sum_zero" -> "data", "pgame.grundy_value_def" -> "set_theory", "continuous_multilinear_map.map_sub" -> "topology", "pow_le_one_iff" -> "algebra", "multiset.to_finsupp_singleton" -> "data", "category_theory.limits.pullback_cone.mk_fst" -> "category_theory", "ring_hom.iterate_map_zero" -> "algebra", "pnat.count_factor_multiset" -> "data", "lucas_lehmer.X.int_coe_snd" -> "number_theory", "nndist_triangle_left" -> "topology", "set.inv_inv" -> "algebra", "linear_map.comap_map_eq" -> "algebra", "set.union_Inter" -> "data", "category_theory.limits.cocone_of_split_epi_\[Iota]_app_zero" -> "category_theory", "linear_pmap.fst_apply" -> "algebra", "int.eq_zero_of_dvd_of_nat_abs_lt_nat_abs" -> "data", "fin.succ_above_last" -> "data", "lt_or_eq_of_le" -> "init", "cardinal.mk_Union_le" -> "set_theory", "list.pw_filter_eq_self" -> "data", "nat.pow_eq_pow" -> "algebra", "ordinal.add_lt_omega_power" -> "set_theory", "set.mem_set_of_eq" -> "data", "padic_norm_e.nonneg" -> "data", "uniformity_eq_comap_nhds_zero" -> "topology", "set.nonempty_of_ssubset" -> "data", "one_div_mul_add_mul_one_div_eq_one_div_add_one_div" -> "algebra", "prod.map_def" -> "data", "finset.sum_preimage" -> "data", "lt_succ_floor" -> "algebra", "nat.sub_eq_zero_iff_le" -> "init", "list.nodup_filter_map" -> "data", "gpow_of_nat" -> "algebra", "zsqrtd.add_lt_add_left" -> "data", "disjoin_many_one_reducible" -> "computability", "quotient.hrec_on'_mk'" -> "data", "norm_le_of_mem_closed_ball" -> "analysis", "measure_theory.extend_mono'" -> "analysis", "nnreal.le_of_forall_lt_one_mul_lt" -> "data", "filter.tendsto_id'" -> "order", "computable.fin_app" -> "computability", "iter_deriv_fpow" -> "analysis", "list.permutations_aux_cons" -> "data", "submodule.to_add_submonoid_eq" -> "algebra", "filter.mem_infi_sets_finset" -> "order", "neg_lt_sub_left_of_lt_add" -> "algebra", "category_theory.monoidal.right_unitor_inv_apply" -> "category_theory", "unique_diff_on_Ioi" -> "analysis", "finmap.lookup_insert" -> "data", "left_ord_continuous.map_cSup" -> "order", "relation.trans_gen.tail'_iff" -> "logic", "filter.eventually_lift'_powerset_eventually" -> "order", "category_theory.limits.bicone.to_cocone_X" -> "category_theory", "nat.one_mod" -> "data", "convex_iff_div" -> "analysis", "quadratic_form.associated_to_quadratic_form" -> "algebra", "list.permutations_aux2_snd_nil" -> "data", "continuous_linear_map.id_apply" -> "topology", "of_add_neg" -> "algebra", "category_theory.abelian.images.image.fac" -> "category_theory", "is_min_filter.comp_tendsto" -> "order", "multiplicative.is_subgroup_iff" -> "algebra", "category_theory.limits.cocone.of_pushout_cocone_X" -> "category_theory", "list.foldr_with_index_eq_foldr_enum" -> "data", "finset.sum_Ico_succ_top" -> "algebra", "continuous_within_at_fst" -> "topology", "local_equiv.eq_on_source.target_eq" -> "data", "uniform_continuous_add" -> "topology", "semilattice_inf.ext" -> "order", "set.sInter_eq_bInter" -> "data", "eq_one_div_of_mul_eq_one" -> "algebra", "list.subperm_of_subset_nodup" -> "data", "is_add_unit.add_left_inj" -> "algebra", "function.semiconj\:2082.iterate" -> "logic", "denumerable.raise_chain" -> "data", "subtype.coe_mk" -> "data", "list.drop_left" -> "data", "list.singleton_append" -> "data", "complex.exp_sum" -> "data", "option.none_orelse'" -> "data", "inf_nhds_at_bot" -> "topology", "category_theory.limits.cospan_map_inr" -> "category_theory", "polynomial.map_eq_zero" -> "data", "set.image2_image_right" -> "data", "times_cont_mdiff_on.continuous_on_tangent_map_within_aux" -> "geometry", "applicative_transformation.preserves_pure" -> "control", "is_open_induced_iff" -> "topology", "ordinal.cof_bsup_le" -> "set_theory", "multiset.le_sub_add" -> "data", "polynomial.le_degree_of_ne_zero" -> "data", "onote.NF_below.fst" -> "set_theory", "category_theory.tensoring_right_monoidal_to_lax_monoidal_functor_\[CurlyEpsilon]" -> "category_theory", "multiset.count_sub" -> "data", "dim_quotient_add_dim" -> "algebra", "prime.ne_zero" -> "algebra", "ennreal.top_rpow_of_pos" -> "analysis", "measurable_add_right" -> "analysis", "finsupp.single_add_erase" -> "data", "derive_fintype.finset_above.mem_union_left" -> "tactic", "int.sub_eq_zero_of_eq" -> "init", "category_theory.limits.limit.post_post" -> "category_theory", "Module.epi_of_range_eq_top" -> "algebra", "finmap.not_mem_empty" -> "data", "list.perm.singleton_eq" -> "data", "abstract_completion.dense_inducing" -> "topology", "ext_chart_preimage_mem_nhds" -> "geometry", "matrix_equiv_tensor.inv_fun_algebra_map" -> "algebra", "initial_seg.coe_fn_to_rel_embedding" -> "set_theory", "group.image_closure" -> "algebra", "isometry_subtype_coe" -> "topology", "submonoid.localization_map.lift_comp" -> "algebra", "list.mmap_with_index_aux_eq_mmap_with_index_aux_spec" -> "data", "option.bind_eq_some'" -> "data", "set.preimage_mul_const_Ioi" -> "data", "turing.blank_rel.equivalence" -> "computability", "category_theory.monoidal_functor.comp_\[Mu]_is_iso" -> "category_theory", "is_open_Inter" -> "topology", "list.exists_of_kerase" -> "data", "real.sin_neg" -> "data", "galois_connection.u_top" -> "order", "ring_hom.lift_of_surjective_comp" -> "algebra", "compact_of_finite_subcover" -> "topology", "ext_chart_at_continuous_on" -> "geometry", "min_eq_right_of_lt" -> "init", "list.pairwise_of_pairwise_map" -> "data", "real.cos_pi_over_two_pow" -> "analysis", "category_theory.Monad.Monad_Mon_equiv_inverse" -> "category_theory", "filter.germ.lift_rel_coe" -> "order", "list.suffix_append" -> "data", "has_deriv_within_at.nhds_within" -> "analysis", "Top.subpresheaf_to_Types_obj" -> "topology", "filter.tendsto_at_top_at_top" -> "order", "topological_space.opens.supr_def" -> "topology", "times_cont_diff_on_snd" -> "analysis", "primrec.to\:2082" -> "computability", "set.right_mem_interval" -> "data", "category_theory.limits.coprod.inr_map" -> "category_theory", "euclidean_domain.lcm_eq_zero_iff" -> "algebra", "matrix.mul_vec_zero" -> "data", "add_monoid.image_closure" -> "algebra", "semiconj_by.pow_right" -> "algebra", "tangent_map_id" -> "geometry", "equivalence_of_one_one_equiv" -> "computability", "dvd_iff_dvd_of_digits" -> "data", "times_cont_diff.sub" -> "analysis", "cInf_union" -> "order", "finset.subset_union_right" -> "data", "is_coprime.of_add_mul_right_right" -> "algebra", "primrec\:2082.of_nat_iff" -> "computability", "forall_eq'" -> "logic", "nat.ppred_eq_pred" -> "data", "inv_le_inv_of_le" -> "algebra", "set.Ioc_union_Ioc_eq_Ioc" -> "data", "equiv.perm.sign_symm_trans_trans" -> "algebra", "cardinal.succ_is_regular" -> "set_theory", "algebraic_closure.adjoin_monic.exists_root" -> "algebra", "list.lookup_nil" -> "data", "nhds_order_unbounded" -> "topology", "algebra.coe_top" -> "algebra", "set.diff_Inter" -> "data", "asymptotics.is_O.congr_left" -> "analysis", "inv_le_of_neg" -> "algebra", "fin.ne_iff_vne" -> "data", "normed_field.nnnorm_inv" -> "analysis", "is_compact.image" -> "topology", "add_submonoid.localization_map.symm_comp_of_add_equiv_of_localizations_apply" -> "algebra", "eq_neg_add_iff_add_eq" -> "algebra", "or_comm" -> "init", "gc_nhds" -> "topology", "bdd_below_bdd_above_iff_subset_Icc" -> "order", "smooth_on_id" -> "geometry", "list.pairwise_filter_map" -> "data", "polynomial.leading_coeff_one" -> "data", "composition.boundary_last" -> "combinatorics", "complex.conj_conj" -> "data", "tactic.abel.zero_smulg" -> "tactic", "lt_of_mul_lt_mul_neg_right" -> "tactic", "category_theory.Monad.of_to_mon_end_iso_hom_app_hom" -> "category_theory", "int.add_left_comm" -> "init", "set.sigma_to_Union_bijective" -> "data", "has_strict_fderiv_at.to_local_left_inverse" -> "analysis", "open_of_uniformity_sum_aux" -> "topology", "category_theory.equivalence.trans_inverse" -> "category_theory", "list.nodup_erase_eq_filter" -> "data", "nhds_le_nhds_iff" -> "topology", "add_submonoid.localization_map.lift_spec_add" -> "algebra", "continuous_linear_map.is_O_comp" -> "analysis", "bifunctor.map_equiv_apply" -> "data", "sigma.ext_iff" -> "data", "set.preimage_mul_right_one'" -> "algebra", "gsmul_of_nat" -> "algebra", "function.bijective.iterate" -> "logic", "set.preimage_set_of_eq" -> "data", "div_lt_one_of_neg" -> "algebra", "linear_equiv.symm_trans_apply" -> "algebra", "segment_same" -> "analysis", "ennreal.sub_le_iff_le_add" -> "data", "norm_num.int_div_neg" -> "tactic", "complex.sin_square" -> "data", "category_theory.equivalence.pow_zero" -> "category_theory", "free_abelian_group.seq_zero" -> "algebra", "equiv.swap_apply_def" -> "data", "category_theory.iso.trans_mk" -> "category_theory", "finset.sum_lt_sum_of_subset" -> "algebra", "rat.mk_eq_div" -> "data", "differentiable.sub_const" -> "analysis", "quotient_group.induction_on" -> "algebra", "monoid_hom.snd_comp_prod" -> "algebra", "many_one_degree.of_le_of'" -> "computability", "mvqpf.Wequiv.symm" -> "data", "is_compact.is_least_Inf" -> "topology", "Gromov_Hausdorff.isometry_optimal_GH_injl" -> "topology", "has_fderiv_at.add" -> "analysis", "category_theory.limits.kernel.lift_zero" -> "category_theory", "nnnorm_neg" -> "analysis", "category_theory.limits.is_colimit.cocone_points_iso_of_equivalence_inv" -> "category_theory", "relation.trans_gen.trans_left" -> "logic", "pnat.xgcd_type.is_reduced_iff" -> "data", "add_localization.mk_eq_add_monoid_of_mk'_apply" -> "algebra", "list.exists_cons_of_ne_nil" -> "data", "set.preimage_add_left_zero" -> "algebra", "subring.mem_top" -> "algebra", "uniform_continuous_id" -> "topology", "finset.affine_combination_vsub" -> "algebra", "is_noetherian_ring.irreducible_induction_on" -> "algebra", "unique.ext" -> "logic", "category_theory.under.iso_mk_inv_right" -> "category_theory", "continuous_linear_equiv.subsingleton_or_nnnorm_symm_pos" -> "analysis", "nat.abs_cast" -> "data", "fin.coe_cast_add" -> "data", "nhds_within_le_comap" -> "topology", "list.tail_eq_of_cons_eq" -> "data", "int.sub_le_self" -> "init", "closed_embedding.closed_iff_image_closed" -> "topology", "turing.tape.move_left_mk'" -> "computability", "function.support_neg" -> "data", "is_R_or_C.is_cau_seq_abs" -> "data", "with_top.add_lt_top" -> "algebra", "matrix.dot_product_comm" -> "data", "group.normal_closure_subset_iff" -> "algebra", "summable_mul_left_iff" -> "topology", "relation.symmetric_join" -> "logic", "category_theory.unop_comp" -> "category_theory", "roption.get_eq_iff_eq_some" -> "data", "category_theory.limits.cospan_map_id" -> "category_theory", "category_theory.non_preadditive_abelian.\[CapitalDelta]_\[Sigma]" -> "category_theory", "real.has_deriv_at_exp" -> "analysis", "stream.append_append_stream" -> "data", "zsqrtd.coe_nat_im" -> "data", "nat.cast_min" -> "data", "differentiable_within_at.cos" -> "analysis", "filter.mem_one" -> "order", "list.chain'_of_chain'_map" -> "data", "rat_mul_continuous_lemma" -> "data", "category_theory.monoidal_category.tensor_right_map" -> "category_theory", "convex_singleton" -> "analysis", "continuous_at.tendsto" -> "topology", "enat.to_with_top_zero'" -> "data", "turing.TM0.machine.map_respects" -> "computability", "finsupp.to_multiset_add" -> "data", "real.rpow_lt_rpow_of_exponent_gt" -> "analysis", "nat.partrec'.comp\:2081" -> "computability", "has_fderiv_at_id" -> "analysis", "is_alg_closed.of_exists_root" -> "algebra", "has_fderiv_at_unique" -> "analysis", "nat.lt_of_succ_lt_succ" -> "init", "list.perm.inter" -> "data", "list.diff_cons" -> "data", "int.coe_gcd" -> "algebra", "ring_hom.domain_nontrivial" -> "algebra", "multiset.disjoint_to_finset" -> "data", "polynomial.nat_degree_le_of_degree_le" -> "data", "measure_theory.l1.simple_func.edist_eq" -> "analysis", "int.dvd_iff_mod_eq_zero" -> "data", "neg_div'" -> "algebra", "finset.sdiff_eq_self_iff_disjoint" -> "data", "equiv.id_map" -> "control", "list.lookup_all_eq_nil" -> "data", "cardinal.prod_const" -> "set_theory", "multiset.mem_of_le" -> "data", "function.injective.no_zero_divisors" -> "algebra", "mul_lt_mul'" -> "algebra", "nat.min_fac_eq_two_iff" -> "data", "equiv.perm.support_swap" -> "algebra", "padic_int.mul_inv" -> "data", "category_theory.limits.cone.of_pullback_cone_\[Pi]" -> "category_theory", "is_basis.dual_basis_is_basis" -> "algebra", "differentiable_on.sub" -> "analysis", "nat.bit0_ne" -> "init", "set.piecewise_eq_of_not_mem" -> "data", "mdifferentiable_within_at_const" -> "geometry", "measure_theory.outer_measure.dirac_apply" -> "analysis", "pequiv.to_matrix_refl" -> "data", "linear_map.smul_comp" -> "algebra", "pgame.lt_of_lt_of_equiv" -> "set_theory", "polynomial.irreducible_X" -> "data", "ennreal.finset_sum_supr_nat" -> "topology", "dense_bInter_of_G\[Delta]" -> "topology", "finset.erase_val" -> "data", "finset.attach_map_val" -> "data", "mdifferentiable_within_at_id" -> "geometry", "hyperreal.infinite_mul_of_infinite_not_infinitesimal" -> "data", "finite_field.exists_root_sum_quadratic" -> "algebra", "le_or_gt" -> "init", "nat.add_div_le_add_div" -> "data", "filter.seq_mem_seq_sets" -> "order", "ring_hom.injective_iff" -> "algebra", "mem_right_add_coset_right_add_coset" -> "algebra", "sup_left_idem" -> "order", "has_deriv_at.const_smul" -> "analysis", "Top.presheaf.germ_res" -> "topology", "polynomial.nat_degree_expand" -> "algebra", "complex.of_real_int_cast" -> "data", "wseq.exists_of_mem_map" -> "data", "ideal.map_le_of_le_comap" -> "algebra", "subgroup.coe_to_submonoid" -> "algebra", "direct_sum.induction_on" -> "algebra", "unique_mdiff_within_at_iff_unique_diff_within_at" -> "geometry", "closure_compl" -> "topology", "eq_mpr_heq" -> "logic", "group.subset_normal_closure" -> "algebra", "Module.id_apply" -> "algebra", "matrix.lie_conj_symm_apply" -> "algebra", "convex_cone.smul_mem_iff" -> "analysis", "turing.reaches\:2080.head" -> "computability", "monoid_hom.mul_apply" -> "algebra", "function.injective2.right" -> "logic", "category_theory.limits.coequalizer.hom_ext" -> "category_theory", "finsupp.count_to_multiset" -> "data", "set.preimage_singleton_nonempty" -> "data", "tendsto_nhds_unique" -> "topology", "functor.ext" -> "control", "int.neg_of_nat_add" -> "init", "frobenius_neg" -> "algebra", "nnreal.half_pos" -> "data", "tangent_bundle_model_space_chart_at" -> "geometry", "finset.prod_add_prod_eq" -> "algebra", "set.Ioo_subset_Ioc_union_Ioo" -> "data", "finset.union_subset_union" -> "data", "inv_mul_eq_iff_eq_mul" -> "algebra", "edist_le_tsum_of_edist_le_of_tendsto\:2080" -> "topology", "wseq.map_ret" -> "data", "metric.isometry_on_inr" -> "topology", "finset.range_image_pred_top_sub" -> "data", "is_absolute_value.abv_pow" -> "data", "free_add_magma.pure_seq" -> "algebra", "measure_theory.norm_set_integral_le_of_norm_le_const_ae''" -> "analysis", "finset.mono_of_fin_last" -> "data", "lift_nhds_left" -> "topology", "list.mfoldr_eq_foldr" -> "data", "nnreal.continuous_of_real" -> "topology", "real.add_one_le_exp_of_nonneg" -> "data", "measurable.ennnorm" -> "analysis", "is_coprime.dvd_of_dvd_mul_right" -> "algebra", "topological_space.opens.supr_mk" -> "topology", "submodule.map_zero" -> "algebra", "multiset.card_powerset" -> "data", "category_theory.limits.coprod_map_comp_id_assoc" -> "category_theory", "int.neg_add_le_of_le_add" -> "init", "omega.lin_comb_holds" -> "tactic", "function.commute.symm" -> "logic", "tensor_product.ext_fourfold" -> "algebra", "units.mul_inv_cancel_right" -> "algebra", "real.norm_eq_abs" -> "analysis", "filter.is_countably_generated.tendsto_of_seq_tendsto" -> "order", "free_group.quot_mk_eq_mk" -> "algebra", "with_bot.add_bot" -> "algebra", "strict_mono.lt_iff_lt" -> "order", "nat.lt_pred_iff" -> "data", "frobenius_inj" -> "algebra", "gt_trans" -> "init", "times_cont_diff.sum" -> "analysis", "ordinal.power_mul" -> "set_theory", "metric.inf_dist_singleton" -> "topology", "category_theory.comp_dite" -> "category_theory", "sub_add_eq_sub_sub_swap" -> "algebra", "traversable.mfoldr_map" -> "control", "ordering.compares_iff_of_compares_impl" -> "algebra", "units.coe_mul" -> "algebra", "normal.splits" -> "algebra", "is_coprime.mul_add_right_right" -> "algebra", "computation.orelse_empty" -> "data", "ideal.integral_closure.comap_lt_comap" -> "algebra", "localization_map.map_id" -> "algebra", "compact_singleton" -> "topology", "coord_norm'" -> "analysis", "one_div_le_one_div_of_neg" -> "algebra", "set.preimage_union" -> "data", "add_comm_group.direct_limit.lift_zero" -> "algebra", "bit0_lt_bit0" -> "algebra", "module.End.exists_eigenvalue" -> "algebra", "polynomial.ext" -> "data", "bor_eq_true_eq_eq_tt_or_eq_tt" -> "init", "differentiable_at.congr_of_eventually_eq" -> "analysis", "is_subgroup.trivial_eq_closure" -> "algebra", "complex.differentiable_exp" -> "analysis", "finset.update_eq_piecewise" -> "data", "nat.pow_succ_log_gt_self" -> "data", "nnreal.sub_def" -> "data", "category_theory.monoidal.left_unitor_hom_apply" -> "category_theory", "nnreal.coe_mul" -> "data", "filter.eventually_le.is_local_max_on" -> "topology", "category_theory.limits.coprod.symmetry" -> "category_theory", "submodule.mul_le_mul_left" -> "algebra", "wseq.dropn_tail" -> "data", "rat.num_zero" -> "data", "fintype.univ_of_subsingleton" -> "data", "multiset.Ico.filter_lt_of_ge" -> "data", "fintype.card_coe" -> "data", "int.lt_add_of_neg_add_lt_right" -> "init", "pnat.factor_multiset_of_prime" -> "data", "set.subset_Inter" -> "data", "alg_equiv_iso_Algebra_iso_inv" -> "algebra", "pSet.mem_Union" -> "set_theory", "Mon_.id_hom'" -> "category_theory", "category_theory.limits.colimit.hom_ext" -> "category_theory", "power_series.X_pow_eq" -> "algebra", "euclidean_geometry.exists_unique_dist_eq_of_affine_independent" -> "geometry", "well_founded.lt_sup" -> "order", "function.is_periodic_pt.trans_dvd" -> "dynamics", "euclidean_domain.gcd_dvd_right" -> "algebra", "relation.comp_assoc" -> "logic", "summable_geometric_two'" -> "analysis", "nat.mod_mul_left_mod" -> "data", "measure_theory.mem_ae_map_iff" -> "analysis", "has_fderiv_within_at.smul_algebra_const" -> "analysis", "polynomial.is_local_ring_hom_expand" -> "algebra", "tfae_mem_nhds_within_Ioi" -> "topology", "stone_cech_extend_extends" -> "topology", "modeq_eleven_digits_sum" -> "data", "ideal.coe_closure" -> "topology", "opposite.op_inv" -> "algebra", "localization.ind" -> "algebra", "CommMon.coe_of" -> "algebra", "mul_sub_mul_div_mul_neg_iff" -> "algebra", "set.subset_image_diff" -> "data", "matrix.cons_add" -> "data", "multiset.coe_count" -> "data", "has_deriv_at.has_fderiv_at_equiv" -> "analysis", "topological_space.opens.subset_coe" -> "topology", "to_uniform_space_eq" -> "topology", "polynomial.algebra_map_apply" -> "data", "list.pw_filter_idempotent" -> "data", "zmod.expand_card" -> "algebra", "category_theory.equivalence.symm_counit_iso" -> "category_theory", "sequentially_complete.seq_is_cauchy_seq" -> "topology", "ring.fractional_ideal.mul_left_mono" -> "algebra", "filter.extraction_of_frequently_at_top" -> "order", "findim_span_set_eq_card" -> "algebra", "differentiable_at.mul_const" -> "analysis", "con.lift_apply_mk'" -> "algebra", "approximates_linear_on.mono_set" -> "analysis", "filter.has_basis.eq_generate" -> "order", "of_add_gsmul" -> "algebra", "set.preimage_eq_preimage" -> "data", "mul_le_iff_le_one_left'" -> "algebra", "coe_add_monoid_hom" -> "algebra", "enat.add_eq_top_iff" -> "data", "affine.simplex.direction_monge_plane" -> "geometry", "filter.tendsto_id" -> "order", "real.Inf_def" -> "data", "findim_euclidean_space" -> "analysis", "open_embedding.to_local_equiv_source" -> "topology", "mv_power_series.X_pow_dvd_iff" -> "algebra", "multilinear_map.sum_apply" -> "algebra", "list.sublist.diff_right" -> "data", "smul_add" -> "algebra", "lift_of_splits" -> "algebra", "filter.frequently_high_scores" -> "order", "local_equiv.refl_trans" -> "data", "int.add_one_le_of_lt" -> "init", "int.lt_neg_add_of_add_lt" -> "init", "pnat.mk_coe" -> "data", "alg_hom.coe_to_monoid_hom" -> "algebra", "norm_num.le_one_bit0" -> "tactic", "fixed_points.prev_eq" -> "order", "set.indicator_le'" -> "data", "submonoid.map_supr_comap_of_surjective" -> "algebra", "if_ctx_simp_congr_prop" -> "init", "ennreal.inv_le_iff_le_mul" -> "data", "ennreal.coe_finset_sum" -> "data", "list.map\:2082_nil" -> "data", "nat.primrec'.comp\:2081" -> "computability", "category_theory.over.colimit_X" -> "category_theory", "category_theory.Monad.of_Mon_str_\[Eta]" -> "category_theory", "roption.bind_some" -> "data", "euclidean_domain.gcd_zero_right" -> "algebra", "sub_eq_sub_iff_sub_eq_sub" -> "algebra", "real.Sup_of_not_bdd_above" -> "data", "category_theory.nat_trans.sum_app_inr" -> "category_theory", "span_lt_of_subset_of_card_lt_findim" -> "algebra", "gaussian_int.to_complex_mul" -> "data", "filter.map_add_at_top_eq_nat" -> "order", "ennreal.tsum_add" -> "topology", "ideal.map_pi" -> "algebra", "int.neg_div_of_dvd" -> "data", "cSup_intro" -> "order", "mul_self_pos" -> "algebra", "ext_chart_at_open_source" -> "geometry", "nat.pred_sub" -> "data", "times_cont_diff_at.prod_map" -> "analysis", "functor.map_comp_map" -> "control", "algebra.of_id_apply" -> "algebra", "mfderiv_within_const" -> "geometry", "linarith.nat_lt_subst" -> "tactic", "submonoid.ext'" -> "algebra", "abs_sub_lt_iff" -> "algebra", "list.foldl1_eq_foldr1" -> "data", "int.add_comm" -> "init", "localization.ring_equiv_of_quotient_of" -> "algebra", "category_theory.comma.map_right_id_inv_app_right" -> "category_theory", "one_lt_mul_of_lt_of_le" -> "algebra", "add_pow_char" -> "algebra", "padic_int.pmul_comm" -> "data", "measure_theory.integrable.add_measure" -> "analysis", "neg_add_le_of_le_add" -> "algebra", "exists_pow_eq_one" -> "algebra", "pequiv.ext" -> "data", "category_theory.monoidal_functor.comp_to_lax_monoidal_functor" -> "category_theory", "has_sum.add" -> "topology", "nat.div_eq_iff_eq_mul_left" -> "data", "measure_theory.ae_eq_fun.coe_fn_mul" -> "analysis", "pgame.equiv_zero_iff_grundy_value" -> "set_theory", "cardinal.mk_le_mk_of_subset" -> "set_theory", "cau_seq.lim_eq_lim_of_equiv" -> "data", "function.embedding.ext_iff" -> "logic", "cardinal.cantor_function_aux_tt" -> "data", "has_fderiv_at_filter_fst" -> "analysis", "nonempty_of_not_bdd_below" -> "order", "omega.nat.unsat_of_unsat_dnf" -> "tactic", "is_strict_weak_order_of_is_total_preorder" -> "init", "fintype.linear_order.is_well_order" -> "data", "list.filter_eq_foldr" -> "data", "add_submonoid.coe_coe" -> "algebra", "not_unbounded_iff" -> "order", "list.sublist_append_left" -> "data", "continuous_linear_map.is_O_sub" -> "analysis", "polynomial.degree_monomial" -> "data", "pnat.gcd_dvd_right" -> "data", "submonoid.localization_map.mk'_spec'" -> "algebra", "ennreal.add_lt_add_iff_right" -> "data", "asymptotics.is_O_with_bot" -> "analysis", "int.of_nat_mul_of_nat" -> "init", "measure_theory.simple_func.seq_apply" -> "analysis", "set.preimage_subset_image_of_inverse" -> "data", "is_R_or_C.zero_im" -> "data", "derivation.map_algebra_map" -> "algebra", "category_theory.limits.binary_fan.\[Pi]_app_right" -> "category_theory", "div_lt_iff_of_neg" -> "algebra", "category_theory.monad.forget_creates_colimits.lifted_cocone_X" -> "category_theory", "Set.induction_on" -> "set_theory", "is_basis.to_dual_apply" -> "algebra", "polynomial.leading_coeff_add_of_degree_lt" -> "data", "multiset.disjoint_right" -> "data", "int.mod_add_div_aux" -> "data", "set.not_mem_empty" -> "data", "uniform_space.ring_sep_quot" -> "topology", "bounded_continuous_function.coe_add" -> "topology", "nnreal.bdd_above_coe" -> "data", "complex.has_deriv_at_sin" -> "analysis", "nat.pow_le_pow_of_le_left" -> "init", "emetric.cauchy_iff" -> "topology", "set.seq_of_forall_finite_exists" -> "data", "dist_triangle_right" -> "topology", "cardinal.aleph_succ" -> "set_theory", "category_theory.comma.nat_trans_app" -> "category_theory", "char_poly_sub_diagonal_degree_lt" -> "algebra", "category_theory.iso_whisker_right_inv" -> "category_theory", "and_not_self_iff" -> "logic", "nnreal.div_div_eq_div_mul" -> "data", "category_theory.abelian.pseudoelement.eq_zero_iff" -> "category_theory", "normal_subgroup_of_comm_group" -> "algebra", "filter.prod_lift_lift" -> "order", "category_theory.monoidal.functor_category.tensor_obj_obj" -> "category_theory", "add_submonoid.localization_map.neg_unique" -> "algebra", "supr_empty" -> "order", "ennreal.nhds_coe_coe" -> "topology", "disjoint_bot_right" -> "order", "measure_theory.simple_func.map_const" -> "analysis", "ideal.jacobson_eq_iff_jacobson_quotient_eq_bot" -> "algebra", "pnat.sub_coe" -> "data", "pi_norm_le_iff" -> "analysis", "times_cont_diff_at.differentiable" -> "analysis", "matrix.special_linear_group.one_apply" -> "algebra", "is_coprime.mul_add_right_left" -> "algebra", "qpf.fix.ind_aux" -> "data", "nat.one_le_pow" -> "data", "mono_of_deriv_nonneg" -> "analysis", "nnreal.nndist_eq" -> "topology", "int.mod_neg" -> "data", "measure_theory.measure_union_null" -> "analysis", "closure_Ico" -> "topology", "submonoid.copy_eq" -> "algebra", "pgame.move_right_left_moves_neg" -> "set_theory", "to_topological_space_top" -> "topology", "ring_hom.coe_inj" -> "algebra", "monoid_hom.coprod_unique" -> "algebra", "pell.xn_add" -> "number_theory", "fin.mk_zero" -> "data", "open_add_subgroup.coe_injective" -> "topology", "ordinal.lt_succ" -> "set_theory", "category_theory.pi.comap_comp_hom_app" -> "category_theory", "set.ssubset_iff_of_subset" -> "data", "vector.comp_traverse" -> "data", "minimal_polynomial.coeff_zero_eq_zero" -> "algebra", "add_submonoid.localization_map.mk'_add_eq_mk'_of_add" -> "algebra", "hyperreal.infinite_pos_iff_infinite_and_pos" -> "data", "category_theory.comma.map_left_id_inv_app_left" -> "category_theory", "mul_mem_nonunits_left" -> "algebra", "add_comm_group.is_Z_bilin.zero" -> "topology", "ennreal.rpow_lt_one" -> "analysis", "primrec.list_find_index\:2081" -> "computability", "nnreal.mul_rpow" -> "analysis", "complex.cos_sub_pi_div_two" -> "analysis", "uniform_continuous.prod_mk_left" -> "topology", "mv_polynomial.rename_injective" -> "data", "mdifferentiable_within_at.continuous_within_at" -> "geometry", "set.eq_univ_iff_forall" -> "data", "category_theory.monad.forget_obj" -> "category_theory", "bundle_trivialization.coe_coe" -> "topology", "mul_nsmul_assoc" -> "algebra", "matrix.trace_transpose_mul" -> "algebra", "poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2" -> "algebra", "ring_equiv.map_one" -> "data", "asymptotics.is_O.add" -> "analysis", "ring.fractional_ideal.map_equiv_apply" -> "algebra", "convex_on.translate_left" -> "analysis", "filter.eventually_eq.refl" -> "order", "znum.of_int'_eq" -> "data", "stream.coinduction" -> "data", "filter.has_basis.tendsto_iff" -> "order", "linarith.mul_nonpos" -> "tactic", "set.image2_image2_left" -> "data", "filter.germ.induction_on\:2083" -> "order", "open_subgroup.coe_subset" -> "topology", "inf_le_right_of_le" -> "order", "cardinal.one_lt_iff_nontrivial" -> "set_theory", "nat.one_lt_two_pow'" -> "data", "submonoid.localization_map.is_unit_comp" -> "algebra", "is_scalar_tower.aeval_apply" -> "algebra", "fintype.sum_sum_type" -> "data", "preserves_limits_iso_hom_\[Pi]_assoc" -> "category_theory", "pgame.nim.grundy_value" -> "set_theory", "times_cont_diff.times_cont_diff_at" -> "analysis", "lcm_dvd" -> "algebra", "quotient_group.coe_mul" -> "algebra", "surjective_of_continuous'" -> "topology", "nat.one_pow" -> "data", "Class.Union_hom" -> "set_theory", "option.guard_eq_some'" -> "data", "pell.xn_modeq_x2n_sub" -> "number_theory", "real.cos_pi_div_eight" -> "analysis", "inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul" -> "analysis", "padic_seq.lift_index_right" -> "data", "imp_intro" -> "logic", "sub_right_comm" -> "algebra", "category_theory.functor.left_unitor_hom_app" -> "category_theory", "padic.coe_neg" -> "data", "filter.germ.map_id" -> "order", "has_deriv_within_at.comp" -> "analysis", "function.left_inverse.injective" -> "init", "ennreal.mul_inv_cancel" -> "data", "ordinal.omega_is_limit" -> "set_theory", "compact_covered_by_add_left_translates" -> "topology", "nat.prime.multiplicity_choose" -> "data", "set.indicator_neg" -> "data", "concave_on.translate_right" -> "analysis", "asymptotics.is_O.congr'" -> "analysis", "int.sub_left_le_of_le_add" -> "init", "is_max_on.is_extr" -> "order", "finset.inter_assoc" -> "data", "except_t.ext" -> "init", "list.eq_or_mem_of_mem_cons" -> "init", "mem_subalgebra_of_subring" -> "algebra", "int.neg_mul_eq_neg_mul_symm" -> "init", "matrix.dot_product_neg" -> "data", "list.sum_map_mul_left" -> "data", "finset.ext_iff" -> "data", "computation.exists_of_mem_map" -> "data", "finset.empty_subset" -> "data", "nat.le_of_succ_le_succ" -> "init", "array.read_mem" -> "init", "multiset.disjoint_union_right" -> "data", "subgroup.range_gpowers_hom" -> "algebra", "emetric.is_open_ball" -> "topology", "polynomial.fderiv" -> "analysis", "int.normalize_of_neg" -> "algebra", "znum.mod_to_int" -> "data", "iterated_fderiv_within_zero_eq_comp" -> "analysis", "finset.coe_union" -> "data", "deriv_exp" -> "analysis", "mul_lt_one_of_le_one_of_lt_one'" -> "algebra", "multiset.card_lt_of_lt" -> "data", "int.modeq.exists_unique_equiv_nat" -> "data", "lipschitz_with.of_le_add" -> "topology", "sub_le_sub_iff_left" -> "algebra", "add_subgroup.top_prod" -> "algebra", "nat.coprime_div_gcd_div_gcd" -> "data", "set.inter_bUnion" -> "data", "category_theory.limits.cone.naturality_concrete" -> "category_theory", "ordinal.lift_pred" -> "set_theory", "polynomial.of_irreducible_expand" -> "algebra", "finset.union_eq_left_iff_subset" -> "data", "ctop.to_topsp_is_topological_basis" -> "data", "mdifferentiable_at_iff_differentiable_at" -> "geometry", "complex.uniform_continuous_re" -> "topology", "functor.map_equiv_refl" -> "data", "has_strict_fderiv_at_iff_has_strict_deriv_at" -> "analysis", "multiset.naturality" -> "data", "ring_hom.iterate_map_add" -> "algebra", "pfun.mem_image" -> "data", "subtype.image_preimage_coe" -> "data", "filter.tendsto.eventually_interval_integrable_ae" -> "analysis", "filter.tendsto.limsup_eq" -> "topology", "category_theory.limits.coprod.left_unitor_hom" -> "category_theory", "subtype.val_prop" -> "data", "list.erase_cons" -> "data", "inner_product_geometry.angle_le_pi" -> "geometry", "category_theory.non_preadditive_abelian.sub_self" -> "category_theory", "mem_left_coset_iff" -> "algebra", "encodable.choose_spec" -> "data", "submodule.fg_def" -> "algebra", "finset.union_sdiff_symm" -> "data", "nat.succ_mul_succ_eq" -> "init", "mv_power_series.mul_add" -> "algebra", "quotient_add_group.eq" -> "algebra", "set.subset_diff" -> "data", "set.countable.exists_surjective" -> "data", "free_comm_ring.is_supported_neg" -> "algebra", "has_strict_deriv_at_inv" -> "analysis", "zmod.cast_pow'" -> "data", "nat.eq_zero_of_zero_dvd" -> "init", "principal_ideal_ring.associates_irreducible_iff_prime" -> "algebra", "ordered_add_comm_group.add_lt_add_left" -> "algebra", "filter.eventually_bind" -> "order", "hyperreal.infinite_pos_omega" -> "data", "submonoid.localization_map.of_mul_equiv_of_dom_eq" -> "algebra", "times_cont_mdiff_at.mdifferentiable_at" -> "geometry", "abs_sub_square" -> "algebra", "int.zero_mul" -> "init", "finset.image_mono" -> "data", "sub_le_sub_left" -> "algebra", "nnreal.of_real_le_of_real_iff" -> "data", "linear_independent_unique" -> "algebra", "linear_equiv.trans_apply" -> "algebra", "ring_hom.map_div" -> "algebra", "equiv.refl_to_embedding" -> "logic", "computation.get_bind" -> "data", "gfp_eq" -> "order", "polynomial.subsingleton_of_monic_zero" -> "data", "has_strict_deriv_at_fpow" -> "analysis", "ordinal.div_lt" -> "set_theory", "homological_complex.image_to_kernel_map_comp_kernel_map_assoc" -> "algebra", "is_max_filter.sub" -> "order", "hyperreal.not_infinite_neg_of_infinite_pos" -> "data", "derivation.map_smul" -> "algebra", "relation.join_of_equivalence" -> "logic", "sdiff_le_sdiff" -> "order", "list.chain'.imp_head" -> "data", "embedding_id" -> "topology", "monoid_hom.map_multiset_prod" -> "data", "tendsto_coe_nat_real_at_top_at_top" -> "topology", "semiconj_by.cast_int_mul_left" -> "algebra", "bilin_form.is_skew_adjoint_bracket" -> "algebra", "module.algebra_map_End_eq_smul_id" -> "algebra", "is_irreducible.closure" -> "topology", "zorn.succ_spec" -> "order", "ideal.zero_eq_bot" -> "algebra", "monoid_hom.injective_iff" -> "algebra", "is_clopen_inter" -> "topology", "metric.bounded_bUnion" -> "topology", "filter.has_basis.eq_infi" -> "order", "bilin_form.lin_mul_lin_comp" -> "algebra", "has_deriv_within_at.congr_of_eventually_eq" -> "analysis", "supr_insert" -> "order", "list.perm_middle" -> "data", "minimal_polynomial.not_is_unit" -> "algebra", "filter.eventually_eq_inf_principal_iff" -> "order", "right_ord_continuous.le_iff" -> "order", "linear_independent_sUnion_of_directed" -> "algebra", "asymptotics.is_O_const_mul_left_iff" -> "analysis", "filter.mem_at_top_sets" -> "order", "set.prod_eq" -> "data", "euclidean_domain.mod_zero" -> "algebra", "times_cont_mdiff_within_at_congr" -> "geometry", "fin.add_one_pos" -> "data", "ideal.mem_sup_right" -> "algebra", "bor_ff" -> "init", "subtype.trans" -> "data", "euclidean_geometry.orthogonal_projection_vadd_smul_vsub_orthogonal_projection" -> "geometry", "pnat.bot_eq_zero" -> "data", "filter.le_of_map_le_map_inj_iff" -> "order", "quotient_group.open_coe" -> "topology", "inv_neg" -> "algebra", "equiv.coe_const_vadd" -> "algebra", "measure_theory.lintegral_sum_measure" -> "analysis", "measure_theory.ae_eq_fun.zero_def" -> "analysis", "complex.cos_two_mul" -> "data", "galois_insertion.l_u_eq" -> "order", "is_integral_of_subring" -> "algebra", "free_group.to_group_eq_prod_map" -> "algebra", "is_open_map.functor_obj_val" -> "topology", "dim_span" -> "algebra", "quadratic_form.coe_fn_neg" -> "algebra", "category_theory.iso.hom_inv_id_app" -> "category_theory", "ring_hom.ext_nat" -> "data", "Class.fval_ex" -> "set_theory", "times_cont_diff_on_of_differentiable_on_deriv" -> "analysis", "complex.exp_bound" -> "data", "div_mul_eq_mul_div" -> "algebra", "is_bounded_bilinear_map.has_fderiv_at" -> "analysis", "add_submonoid.localization_map.map_add_left" -> "algebra", "finsupp.emb_domain_eq_map_domain" -> "data", "ordinal.sub_sub" -> "set_theory", "sigma_mk_injective" -> "data", "zero_lt_iff_ne_zero" -> "algebra", "int.eq_zero_of_dvd_of_nonneg_of_lt" -> "data", "sym2.congr_right" -> "data", "add_units.coe_lt_coe" -> "algebra", "function.support_prod_mk" -> "data", "is_asymm.is_antisymm" -> "order", "measure_theory.l1.sub_to_fun" -> "analysis", "measure_theory.l1.mk_to_fun" -> "analysis", "polynomial.coeff_eq_zero_of_degree_lt" -> "data", "submodule.smul_mem_smul" -> "algebra", "inv_ne_zero" -> "algebra", "continuous_multilinear_map.smul_apply" -> "topology", "real.log_nonpos" -> "analysis", "derivation.Rsmul_apply" -> "algebra", "polynomial.nat_degree_X" -> "data", "localization_map.surj" -> "algebra", "measure_theory.mem_dirac_ae_iff" -> "analysis", "subgroup.is_open_of_mem_nhds" -> "topology", "set.pairwise_on.mono'" -> "data", "filter.eventually.self_of_nhds" -> "topology", "convex_Ioc" -> "analysis", "lipschitz_with.le_add_mul" -> "topology", "dense_inducing.continuous_extend_of_cauchy" -> "topology", "is_coprime_one_left" -> "algebra", "finset.insert_eq_of_mem" -> "data", "function.left_inverse_inv_fun" -> "logic", "submodule.mem_Sup_of_mem" -> "algebra", "continuous_linear_equiv.comp_has_fderiv_at_iff'" -> "analysis", "times_cont_diff_neg" -> "analysis", "list.le_maximum_of_mem'" -> "data", "continuous_inf_dom_right" -> "topology", "ordinal.card_add" -> "set_theory", "poly.sub_eval" -> "number_theory", "multiset.erase_add_right_pos" -> "data", "pgame.grundy_value_nim_add_nim" -> "set_theory", "fin.pred_mk_succ" -> "data", "iterated_deriv_within_succ" -> "analysis", "measure_theory.norm_integral_le_integral_norm" -> "analysis", "equiv.left_inverse_symm" -> "data", "finset.prod_pow_eq_pow_sum" -> "algebra", "continuous_linear_map.smul_apply" -> "topology", "option.some_inj" -> "data", "mul_assoc" -> "algebra", "normed_ring.inverse_one_sub_norm" -> "analysis", "alist.keys_replace" -> "data", "category_theory.limits.cone_of_split_mono_\[Pi]_app_zero" -> "category_theory", "mul_lt_one_of_le_one_of_lt_one" -> "algebra", "is_R_or_C.char_zero_R_or_C" -> "data", "finset.card_eq_of_bijective" -> "data", "real.sin_add_pi" -> "analysis", "times_cont_mdiff_fst" -> "geometry", "finset.max_empty" -> "data", "hyperreal.coe_zero" -> "data", "div_mul_div_cancel" -> "algebra", "nat.primrec'.sqrt" -> "computability", "sub_le" -> "algebra", "category_theory.nat_trans.app_naturality" -> "category_theory", "infi_le_infi2" -> "order", "set.Inter_inter" -> "data", "ordinal.mod_eq_of_lt" -> "set_theory", "Class.union_hom" -> "set_theory", "frontier_Icc" -> "topology", "set.Iio_subset_Iic" -> "data", "unique_diff_within_at_inter'" -> "analysis", "list.foldl_eq_of_comm_of_assoc" -> "data", "ennreal.nat_ne_top" -> "data", "matrix.rank_vec_mul_vec" -> "algebra", "int.coe_nat_dvd_right" -> "data", "zsqrtd.coe_int_inj" -> "data", "contracting_with.dist_inequality" -> "topology", "with_zero.div_eq_div" -> "algebra", "finset.infi_insert_update" -> "data", "zsqrtd.ext" -> "data", "continuous_on_congr" -> "topology", "measure_theory.lintegral_supr_ae" -> "analysis", "partrec.rfind" -> "computability", "linear_map.ext\:2082" -> "algebra", "polynomial.expand_contract" -> "algebra", "and_self_right" -> "logic", "set.union_subset_union_right" -> "data", "measure_theory.ae_eq_fun.quot_mk_eq_mk" -> "analysis", "measure_theory.measure.le_add_left" -> "analysis", "polynomial.roots_prod" -> "data", "tangent_bundle.times_cont_mdiff_proj" -> "geometry", "add_localization.add_equiv_of_quotient_symm_mk'" -> "algebra", "pnat.gcd_coe" -> "data", "free_magma.mul_eq" -> "algebra", "omega.unsat_lin_comb_of" -> "tactic", "equiv.set.image_symm_preimage" -> "data", "num.nat_size_to_nat" -> "data", "filter.eq_of_map_eq_map_inj'" -> "order", "times_cont_diff.of_le" -> "analysis", "AddCommGroup.kernel_iso_ker_inv_comp_\[Iota]" -> "algebra", "set.nonempty.of_diff" -> "data", "category_theory.limits.cocone.whisker_X" -> "category_theory", "mul_action.fixed_eq_Inter_fixed_by" -> "algebra", "sub_pow_char_pow_of_commute" -> "algebra", "int.of_nat_zero" -> "init", "vector3.rec_on_nil" -> "number_theory", "is_max_on.on_subset" -> "order", "tactic.ring2.horner_expr.cseval_add" -> "tactic", "inducing_open" -> "topology", "category_theory.limits.pushout.condition_assoc" -> "category_theory", "metric.sum.dist_eq" -> "topology", "open_add_subgroup.mem_coe" -> "topology", "closed_embedding_id" -> "topology", "lt_of_not_ge" -> "init", "mul_action_hom.ext" -> "algebra", "complex.cos_of_real_re" -> "data", "mem_nhds_within_subtype" -> "topology", "ring_hom.ext_rat" -> "data", "add_monoid_hom.coe_range" -> "algebra", "turing.list_blank.bind_mk" -> "computability", "monotone_or" -> "order", "set.compl_inter_self" -> "data", "polynomial.C_comp" -> "data", "onote.NF.snd" -> "set_theory", "open_subgroup.mem_nhds_one" -> "topology", "semiquot.nonempty" -> "data", "add_con.lift_funext" -> "algebra", "category_theory.limits.has_equalizers_of_pullbacks_and_binary_products.pullback_fst_eq_pullback_snd" -> "category_theory", "wseq.map_append" -> "data", "zsqrtd.nonnegg_cases_left" -> "data", "zero_lt_mul_right" -> "algebra", "ptendsto'_nhds" -> "topology", "submodule.map_liftq" -> "algebra", "list.of_fn_eq_pmap" -> "data", "set.set_of_set" -> "data", "list.length_pos_of_sum_ne_zero" -> "data", "true_iff" -> "init", "continuous_at.div" -> "analysis", "subring.comap_comap" -> "algebra", "multiset.singleton_le" -> "data", "filter.mem_sets_of_superset" -> "order", "mul_le_mul_iff_left" -> "algebra", "filter.eventually.prod_mk" -> "order", "is_glb_Ioi" -> "order", "one_mul" -> "algebra", "category_theory.equivalence.counit_inv_functor_comp" -> "category_theory", "open_embedding.open_iff_preimage_open" -> "topology", "psigma.mk.inj_iff" -> "data", "measure_theory.measure.measurable_lintegral" -> "analysis", "measure_theory.simple_func.pos_part_map_norm" -> "analysis", "set.bInter_subset_of_mem" -> "data", "Sup_inf_eq" -> "order", "set.maps_to_sInter" -> "data", "ideal.mul_mem_left" -> "algebra", "ideal.is_primary_inf" -> "algebra", "has_deriv_at.lhopital_zero_at_top_on_Ioi" -> "analysis", "is_unit.mul_lift_right_inv" -> "algebra", "measure_theory.measure.restrict_Union_le" -> "analysis", "polynomial.nat_degree_le_of_dvd" -> "data", "lagrange.interpolate_empty" -> "algebra", "category_theory.limits.limit.map_\[Pi]" -> "category_theory", "norm_num.sle_one_bit0" -> "tactic", "group.conjugates_subset" -> "algebra", "pequiv.symm_trans" -> "data", "lt_mul_iff_one_lt_left" -> "algebra", "cardinal.power_one" -> "set_theory", "ordinal.mul_le_of_limit" -> "set_theory", "cardinal.lt_univ" -> "set_theory", "ordinal.is_normal.is_limit" -> "set_theory", "convex.sub" -> "analysis", "norm_num.sub_neg" -> "tactic", "option.eq_some_iff_get_eq" -> "data", "continuous_linear_map.unit_le_op_norm" -> "analysis", "matrix.cramer_map_is_linear" -> "algebra", "iff_iff_not_or_and_or_not" -> "logic", "uniform_continuous_const" -> "topology", "metric.bounded_singleton" -> "topology", "set.subset_union_right" -> "data", "encodable.decode_ge_two" -> "data", "matrix.col_add" -> "data", "list.mem_range'" -> "data", "add_monoid_algebra.mul_single_apply_aux" -> "data", "category_theory.ulift_functor_map" -> "category_theory", "semidirect_product.inr_inj" -> "algebra", "finsupp.map_domain_notin_range" -> "data", "list.filter_append" -> "init", "exp_neg_inv_glue.zero_of_nonpos" -> "analysis", "normed_space.inclusion_in_double_dual_isometry" -> "analysis", "is_R_or_C.smul_re" -> "data", "polynomial.C_add" -> "data", "group.mem_conjugates_of_set_iff" -> "algebra", "set.Ici_diff_Ici" -> "data", "measure_theory.outer_measure.trim_smul" -> "analysis", "adjoin_root.mk_X" -> "algebra", "measure_theory.induced_outer_measure_eq'" -> "analysis", "power_series.inv_of_unit_eq" -> "algebra", "list.reverse_repeat" -> "data", "real.rpow_def" -> "analysis", "wseq.head_terminates_of_mem" -> "data", "cardinal.mk_image_eq" -> "set_theory", "subgroup.coe_comap" -> "algebra", "exists_unique.intro" -> "init", "enat.coe_lt_top" -> "data", "tactic.ring_exp.mul_pf_c_prod" -> "tactic", "left_ord_continuous.map_is_greatest" -> "order", "subgroup.mem_closure" -> "algebra", "measure_theory.l1.continuous_neg_part" -> "analysis", "int.sign_eq_neg_one_iff_neg" -> "init", "enat.add_lt_add_iff_right" -> "data", "to_matrix_to_lin" -> "algebra", "mv_polynomial.eval\:2082_rename" -> "data", "times_cont_diff_within_at_nat" -> "analysis", "relation.trans_gen.tail'" -> "logic", "floor_fract" -> "algebra", "subtype.prop" -> "data", "ring_hom.coe_fst" -> "algebra", "nat.prime.eq_two_or_odd" -> "data", "finset.ne_empty_of_mem" -> "data", "isometric.coe_vadd_const" -> "analysis", "finset.prod_union" -> "algebra", "category_theory.nat_trans.unop_id" -> "category_theory", "commute.cast_int_mul_left" -> "algebra", "mul_action.mem_orbit_iff" -> "algebra", "power_series.coeff_zero_C" -> "algebra", "gt_iff_lt" -> "algebra", "composition_as_set.card_boundaries_eq_succ_length" -> "combinatorics", "finsupp.single_add" -> "data", "ordinal.mul_lt_of_lt_div" -> "set_theory", "sum.map_inl" -> "data", "primrec.nat_iff" -> "computability", "abstract_completion.uniform_continuous_extension\:2082" -> "topology", "Inf_le_Inf" -> "order", "is_subgroup.eq_trivial_iff" -> "algebra", "is_max_filter.filter_inf" -> "order", "filter.germ.induction_on\:2082" -> "order", "polynomial.derivative_pow" -> "data", "enat.get_add" -> "data", "mul_aut.mul_def" -> "data", "filter.tendsto.ne_bot" -> "order", "mv_polynomial.total_degree_eq" -> "data", "rat.cast_inv" -> "data", "matrix.smul_apply" -> "data", "set.enumerate_eq_none" -> "data", "free_group.map.mul" -> "algebra", "has_strict_fderiv_at_fst" -> "analysis", "galois_connection.l_unique" -> "order", "pfunctor.M.approx.P_mk" -> "data", "differentiable_within_at.fderiv_within_congr_mono" -> "analysis", "has_deriv_at.const_sub" -> "analysis", "tendsto_left_nhds_uniformity" -> "topology", "scale_roots_ne_zero" -> "algebra", "qpf.supp_eq" -> "data", "lie_submodule.quotient.mk_bracket" -> "algebra", "affine_subspace.coe_direction_eq_vsub_set_right" -> "algebra", "set.Ico_eq_empty_iff" -> "data", "decidable.peirce" -> "logic", "fin.univ_cast_succ" -> "data", "primrec\:2082.comp\:2082" -> "computability", "ordinal.univ_id" -> "set_theory", "filter.map_mul" -> "order", "vector.cons_val" -> "data", "ideal.quotient.zero_eq_one_iff" -> "algebra", "pell.xn_ge_a_pow" -> "number_theory", "is_R_or_C.norm_sq_neg" -> "data", "equiv.prod_punit_apply" -> "data", "local_ring.maximal_ideal_unique" -> "algebra", "submonoid.multiset_prod_mem" -> "algebra", "cancel_factors.neg_subst" -> "tactic", "is_order_right_adjoint_cSup" -> "order", "commute.all" -> "algebra", "eckmann_hilton.mul_assoc" -> "algebra", "sub_eq_sub_iff_add_eq_add" -> "algebra", "ennreal.mul_le_mul" -> "data", "linear_map.proj_comp_std_basis" -> "algebra", "measure_theory.lintegral_Union_le" -> "analysis", "filter.tendsto_at_bot_add_left_of_ge" -> "order", "continuous_multilinear_map.norm_def" -> "analysis", "ordinal.nat_cast_eq_zero" -> "set_theory", "unique_diff_on.prod" -> "analysis", "pfunctor.M.head'_eq_head" -> "data", "set.Iio_inter_Iio" -> "data", "list.mem_lookup_iff" -> "data", "multiset.Ico.filter_le_of_le_bot" -> "data", "list.pairwise.and_mem" -> "data", "cauchy_seq_of_edist_le_of_tsum_ne_top" -> "topology", "ordinal.mod_one" -> "set_theory", "con.mk'_surjective" -> "algebra", "order_embedding.lt_embedding_apply" -> "order", "list.head_eq_head'" -> "data", "galois_connection.is_lub_u" -> "order", "wseq.destruct_cons" -> "data", "continuous_of_strict_mono_surjective" -> "topology", "localization_map.lift_unique" -> "algebra", "vector.insert_nth_val" -> "data", "module_equiv_finsupp_apply_basis" -> "algebra", "multiset.count_cons_self" -> "data", "nat.add_sub_cancel'" -> "data", "real.angle.coe_zero" -> "analysis", "mv_polynomial.range_eval\:1d62" -> "algebra", "tendsto_nhds_within_of_tendsto_nhds_of_eventually_within" -> "topology", "pgame.add_lt_add_left" -> "set_theory", "matrix_equiv_tensor_apply_symm" -> "algebra", "monoid_hom.map_mul" -> "algebra", "iff_eq_true_of_eq" -> "init", "dfinsupp.filter_def" -> "data", "abstract_completion.map\:2082_coe_coe" -> "topology", "category_theory.whisker_left_app" -> "category_theory", "measure_theory.measure_eq_extend" -> "analysis", "galois_insertion.strict_mono_u" -> "order", "filter.ultrafilter_iff_compl_mem_iff_not_mem" -> "order", "nat.sub_lt_sub_right_iff" -> "data", "turing.TM1to0.tr_respects" -> "computability", "linear_equiv.conj_apply" -> "algebra", "pnat.xgcd_type.flip_is_special" -> "data", "linear_map.supr_range_std_basis" -> "algebra", "category_theory.groupoid.is_isomorphic_iff_nonempty_hom" -> "category_theory", "filter.comap_principal" -> "order", "asymptotics.is_O_with.exists_pos" -> "analysis", "pell.xn_modeq_x4n_add" -> "number_theory", "pmf.map_comp" -> "analysis", "primrec.cond" -> "computability", "bitvec.of_nat_to_nat" -> "data", "polynomial.coeff_C_mul_X" -> "data", "add_submonoid.mem_multiples" -> "algebra", "gsmul_neg_succ_of_nat" -> "algebra", "is_R_or_C.conj_inj" -> "data", "riesz_extension.exists_top" -> "analysis", "category_theory.limits.cocone.category_to_category_struct_to_has_hom_hom" -> "category_theory", "submodule.map_id" -> "algebra", "set.Union_disjointed" -> "data", "imp_eq_true_of_eq" -> "init", "formal_multilinear_series.apply_composition_update" -> "analysis", "is_closed_irreducible_component" -> "topology", "basic_smooth_bundle_core.coe_chart_at_fst" -> "geometry", "pgame.add_left_neg_equiv" -> "set_theory", "Mod.hom.ext" -> "category_theory", "bifunctor.map_equiv_refl_refl" -> "data", "differentiable.mul_const" -> "analysis", "multiset.countp_sub" -> "data", "monoid_algebra.submodule.exists_is_compl" -> "algebra", "continuous_multilinear_map.coe_coe" -> "topology", "setoid.ker_mk_eq" -> "data", "equiv.to_iso_hom" -> "category_theory", "int.add_le_add" -> "init", "is_clopen_univ" -> "topology", "to_topological_space_infi" -> "topology", "nat.add_sub_assoc" -> "init", "dual_pair.decomposition" -> "algebra", "list.forall\:2082_map_right_iff" -> "data", "alg_equiv.coe_refl" -> "algebra", "dim_le_of_surjective" -> "algebra", "submonoid.coe_subset_coe" -> "algebra", "ordinal.deriv_succ" -> "set_theory", "not_of_eq_false" -> "init", "real.exists_sup" -> "data", "nnreal.bot_eq_zero" -> "data", "mvpfunctor.supp_eq" -> "data", "list.eq_of_suffix_of_length_eq" -> "data", "ring_equiv.coe_mul_equiv" -> "data", "nnreal.one_lt_rpow" -> "analysis", "pnat.xgcd_type.v_eq_succ_vp" -> "data", "geom_sum\:2082_mul" -> "algebra", "measure_theory.measure.haar.index_union_le" -> "analysis", "has_sum_single" -> "topology", "power_series.coeff_zero_eq_constant_coeff_apply" -> "algebra", "algebra.mem_bot" -> "algebra", "circle_deg1_lift.iterate_pos_le_iff" -> "dynamics", "metric.uniformity_edist" -> "topology", "ftaylor_series_within_univ" -> "analysis", "nhds_within_Iio_ne_bot" -> "topology", "function.embedding.coe_sum_map" -> "logic", "category_theory.limits.coequalizer.condition" -> "category_theory", "filter.empty_in_sets_eq_bot" -> "order", "quotient.out_eq'" -> "data", "zmod.char_poly_pow_card" -> "algebra", "measure_theory.inner_content_Union_nat" -> "analysis", "cau_seq.completion.mk_mul" -> "data", "is_path_connected.union" -> "topology", "category_theory.limits.cokernel.\[Pi]_of_epi" -> "category_theory", "enat.lt_add_one" -> "data", "measure_theory.outer_measure.is_caratheodory_iff" -> "analysis", "submonoid.localization_map.of_mul_equiv_of_localizations_comp" -> "algebra", "complex.smul_im" -> "data", "smooth_on.prod_mk" -> "geometry", "continuous_linear_map.coe_proj_ker_of_right_inverse_apply" -> "topology", "opposite.unop_one" -> "algebra", "contracting_with.exists_fixed_point" -> "topology", "lie_subalgebra.coe_bracket" -> "algebra", "has_deriv_at.cexp" -> "analysis", "power_series.order_eq_top" -> "algebra", "padic_norm_e.nonarchimedean" -> "data", "list.nodupkeys_of_sublist" -> "data", "padic_norm_e.norm_p_lt_one" -> "data", "ordinal.add_le_add_right" -> "set_theory", "inv_le_one" -> "algebra", "add_units.neg_add" -> "algebra", "char_p.neg_one_ne_one" -> "algebra", "inner_product_space.of_core.inner_add_left" -> "analysis", "is_add_unit_iff_exists_neg'" -> "algebra", "nat.mul_mod_mul_left" -> "init", "measure_theory.lintegral_const_mul'" -> "analysis", "id_comp_rel" -> "topology", "option.to_finset_some" -> "data", "supr_supr_eq_right" -> "order", "num.succ'_to_nat" -> "data", "nat.of_add_mul" -> "algebra", "free_group.to_word.inj" -> "algebra", "real.sin_int_mul_pi" -> "analysis", "algebra.tensor_product.map_tmul" -> "algebra", "one_lt_mul_of_le_of_lt" -> "algebra", "add_submonoid.closure_singleton_eq" -> "algebra", "multiset.filter_sub" -> "data", "ideal.mem_inf" -> "algebra", "multiset.le_iff_subset" -> "data", "add_units.map_id" -> "algebra", "ennreal.coe_ne_top" -> "data", "interval_integral.integral_has_deriv_at_right" -> "analysis", "bilin_form.mul_to_matrix_mul" -> "algebra", "sym_bilin_form.sym" -> "algebra", "list.enum_nth" -> "data", "pgame.le_congr" -> "set_theory", "category_theory.abelian.coimages.coimage_strong_epi_mono_factorisation_to_mono_factorisation_m" -> "category_theory", "topological_space.opens.local_homeomorph_subtype_coe_target" -> "topology", "adjoin_root.lift_mk" -> "algebra", "bilin_form.is_adjoint_pair.sub" -> "algebra", "bor_self" -> "init", "has_fderiv_at_filter_iff_has_deriv_at_filter" -> "analysis", "category_theory.limits.prod_right_unitor_inv_naturality_assoc" -> "category_theory", "times_cont_diff_on_of_continuous_on_differentiable_on" -> "analysis", "nat.mul_self_lt_mul_self_iff" -> "data", "subtype.ext_iff" -> "data", "multiset.le_sum_of_subadditive" -> "data", "norm_num.int_sub_hack" -> "tactic", "mem_path_component_of_mem" -> "topology", "submodule.mem_supr" -> "algebra", "add_units.add_left_inj" -> "algebra", "add_submonoid.localization_map.lift_add_right" -> "algebra", "exists_subset_is_basis" -> "algebra", "Sup_singleton" -> "order", "multiset.inf_ndunion" -> "data", "interval_integral.integral_of_ge" -> "analysis", "measure_theory.l1.simple_func.norm_of_simple_func" -> "analysis", "is_least.insert" -> "order", "bundle_trivialization.continuous_at_proj" -> "topology", "nat.gcd.induction" -> "init", "list.map_reverse_core" -> "data", "measure_theory.integrable_const" -> "analysis", "continuous_linear_equiv.lipschitz" -> "analysis", "int.of_nat_mul" -> "init", "has_ftaylor_series_up_to.differentiable" -> "analysis", "category_theory.comma.map_left_obj_left" -> "category_theory", "encodable.encode_list_cons" -> "data", "nat.smul_def" -> "algebra", "zmod.ne_neg_self" -> "data", "cardinal.min_le" -> "set_theory", "rat.le_def'" -> "data", "basic_smooth_bundle_core.smooth_at_proj" -> "geometry", "category_theory.limits.is_colimit.uniq_cocone_morphism" -> "category_theory", "category_theory.limits.cone_of_split_mono_\[Pi]_app_one" -> "category_theory", "ideal.exists_coeff_ne_zero_mem_comap_of_root_mem" -> "algebra", "subring.mem_Sup_of_directed_on" -> "algebra", "multiset.le_filter" -> "data", "rat.totally_bounded_Icc" -> "topology", "pfunctor.approx.agree_children" -> "data", "padic_norm_z" -> "data", "asymptotics.is_o.trans_le" -> "analysis", "measure_theory.integrable_iff_of_real" -> "analysis", "category_theory.limits.types.jointly_surjective'" -> "category_theory", "power_series.coeff_map" -> "algebra", "polynomial.eval\:2082_comp" -> "data", "closure_ball" -> "analysis", "approximates_linear_on.inverse_continuous_on" -> "analysis", "finite_dimensional.fintype_card_le_findim_of_linear_independent" -> "algebra", "submonoid.exists" -> "algebra", "set.sUnion_image" -> "data", "differentiable_at.comp_differentiable_within_at" -> "analysis", "category_theory.limits.colimit.\[Iota]_post_assoc" -> "category_theory", "inv_ne_one" -> "algebra", "category_theory.induced_functor_obj" -> "category_theory", "add_submonoid.localization_map.of_add_equiv_of_dom_comp" -> "algebra", "mul_lt_mul''" -> "algebra", "imp_congr_eq" -> "init", "ring_hom.map_inv" -> "algebra", "category_theory.monoidal.tensor_unit_map" -> "category_theory", "measure_theory.simple_func.integrable_pair" -> "analysis", "ordered_comm_group.le_of_mul_le_mul_left" -> "algebra", "int.commute_cast" -> "data", "list.disjoint_left" -> "data", "not_lt_of_ge" -> "init", "con.sup_def" -> "algebra", "add_submonoid.localization_map.surj" -> "algebra", "is_compact.exists_is_glb" -> "topology", "sesq_form.ortho_smul_right" -> "algebra", "multiset.lt_cons_self" -> "data", "pi.vadd_apply" -> "algebra", "nat.le_sub_left_of_add_le" -> "data", "cardinal.ord_card_le" -> "set_theory", "category_theory.limits.image_\[Iota]_comp_eq_zero" -> "category_theory", "option.bind_some" -> "data", "category_theory.monoidal_functor.id_to_lax_monoidal_functor_\[Mu]" -> "category_theory", "measurable_mul_left" -> "analysis", "int.dvd_of_mul_dvd_mul_right" -> "data", "has_fderiv_at.comp_has_deriv_at" -> "analysis", "encodable.encode_none" -> "data", "free_abelian_group.seq_neg" -> "algebra", "padic_int.prime_p" -> "data", "is_closed_diagonal" -> "topology", "filter.at_bot_basis" -> "order", "int.add_lt_of_lt_neg_add" -> "init", "deriv_pow''" -> "analysis", "galois_connection.l_bot" -> "order", "lucas_lehmer.order_\[Omega]" -> "number_theory", "ennreal.inv_involutive" -> "data", "ring_hom.ker_is_prime" -> "algebra", "nat.triangle_succ" -> "data", "polynomial.degree_pos_of_eval\:2082_root" -> "data", "complex.abs_sub_le" -> "data", "metric.exists_dist_lt_of_inf_dist_lt" -> "topology", "commute.inv_inv" -> "algebra", "list.nodup_of_nodup_map" -> "data", "set.union_right_comm" -> "data", "abs_mul" -> "algebra", "multiset.filter_subset" -> "data", "set.preimage_mul_const_Ioc_of_neg" -> "data", "contracting_with.efixed_point_eq_of_edist_lt_top'" -> "topology", "commute.inv_right_iff" -> "algebra", "measure_theory.integral_nonpos_of_nonpos_ae" -> "analysis", "cont_t.run_cont_t_map_cont_t" -> "control", "list.length_split_wrt_composition" -> "combinatorics", "has_mfderiv_at_const" -> "geometry", "add_submonoid.prod_mono" -> "algebra", "set.inter_Union" -> "data", "circle_deg1_lift.map_add_one" -> "dynamics", "real.has_sum_pow_div_log_of_abs_lt_1" -> "analysis", "list.append_nil" -> "init", "ideal.comap_lt_comap_of_root_mem_sdiff" -> "algebra", "to_add_inv" -> "algebra", "category_theory.limits.has_zero_morphisms.ext" -> "category_theory", "add_submonoid.localization_map.map_id" -> "algebra", "nat.cast_zero" -> "data", "has_deriv_at.csin" -> "analysis", "real.zero_rpow_nonneg" -> "analysis", "finset.Ico.diff_right" -> "data", "submonoid.mrange_fst" -> "algebra", "category_theory.limits.cokernel_not_iso_of_nonzero" -> "category_theory", "real.cos_lt_cos_of_nonneg_of_le_pi_div_two" -> "analysis", "dfinsupp.support_single_subset" -> "data", "category_theory.monoidal_category.triangle_assoc_comp_right" -> "category_theory", "equiv.coe_ulift" -> "data", "isometric.continuous" -> "topology", "localization_map.epic_of_localization_map" -> "algebra", "finset.sum_Ico_consecutive" -> "algebra", "fract_add" -> "algebra", "multiplicity.one_right" -> "algebra", "seq.terminated_stable" -> "data", "set.sInter_Union" -> "data", "true_implies_iff" -> "init", "pi.zero_apply" -> "algebra", "submonoid.localization_map.map_left_cancel" -> "algebra", "lie_submodule.quotient.is_quotient_mk" -> "algebra", "nnreal.sub_le_self" -> "data", "real.sqrt_nonneg" -> "data", "denumerable.raise_lower'" -> "data", "linear_equiv.dim_eq_lift" -> "algebra", "multiset.nodup_iff_le" -> "data", "int.lt_add_of_neg_lt_sub_left" -> "init", "is_cyclic_of_order_of_eq_card" -> "algebra", "composition_as_set.blocks_fun_pos" -> "combinatorics", "localization_map.integer_normalization_eval\:2082_eq_zero" -> "algebra", "finite_dimensional.findim_pos_iff_exists_ne_zero" -> "algebra", "filter.eventually_sup" -> "order", "bifunctor.fst_comp_snd" -> "control", "alg_hom.to_linear_map_inj" -> "algebra", "analytic_at.add" -> "analysis", "list.repeat_sublist_repeat" -> "data", "partrec.none" -> "computability", "filter.generate_univ" -> "order", "category_theory.limits.limit_uncurry_iso_limit_comp_lim_hom_\[Pi]_\[Pi]" -> "category_theory", "complex.of_real_log" -> "analysis", "list.alternating_sum_eq_finset_sum" -> "data", "polynomial.coeff_X_zero" -> "data", "prime.dvd_of_dvd_pow" -> "algebra", "ennreal.coe_range_mem_nhds" -> "topology", "dfinsupp.add_apply" -> "data", "valuation.zero_iff" -> "algebra", "dvd.intro_left" -> "algebra", "category_theory.limits.cofork.left_app_one_assoc" -> "category_theory", "exists_ratio_deriv_eq_ratio_slope'" -> "analysis", "prime_spectrum.preimage_comap_zero_locus" -> "algebraic_geometry", "is_basis.dual_dim_eq" -> "algebra", "cauchy_seq_of_le_tendsto_0" -> "topology", "uniform_space.completion.coe_neg" -> "topology", "submonoid.mrange_inl_sup_mrange_inr" -> "algebra", "multiset.ndinter_le_left" -> "data", "prod.mk.inj_iff" -> "data", "measure_theory.measure.lift_linear_apply" -> "analysis", "deriv_within_smul_const" -> "analysis", "submodule.smul_mem_iff'" -> "algebra", "category_theory.monoidal.Mon_functor_category_equivalence.functor_obj_obj_one" -> "category_theory", "nat.mul_self_inj" -> "data", "eq_iff_modeq_int" -> "algebra", "deriv_within_rpow" -> "analysis", "measure_theory.measure.restrict_mono" -> "analysis", "local_homeomorph.coe_trans_symm" -> "topology", "local_homeomorph.mk_coe" -> "topology", "commute.add_left" -> "algebra", "list.sum_const_nat" -> "data", "eq_false_of_or_eq_false_right" -> "init", "semiquot.ext" -> "data", "add_subgroup.mem_bot" -> "algebra", "measure_theory.simple_func.smul_eq_map" -> "analysis", "punit.add_eq" -> "algebra", "wseq.mem_congr" -> "data", "submonoid.localization_map.of_mul_equiv_of_dom_comp" -> "algebra", "alist.keys_empty" -> "data", "tendsto_locally_uniformly.comp" -> "topology", "with_zero.zero_div" -> "algebra", "supr_le_supr_of_subset" -> "order", "category_theory.limits.cofork.\[Pi]_of_\[Pi]" -> "category_theory", "category_theory.functor.map_cocone_X" -> "category_theory", "contracting_with.edist_efixed_point_lt_top'" -> "topology", "measure_theory.le_to_measure_apply" -> "analysis", "tactic.ring.horner_pow" -> "tactic", "is_R_or_C.im_sq_le_norm_sq" -> "data", "nat.pow_dvd_pow_iff_pow_le_pow" -> "data", "finset.mem_mul" -> "algebra", "nat.xgcd_zero_left" -> "data", "implicit_function_data.map_pt_mem_to_local_homeomorph_target" -> "analysis", "omega.coeffs.val_between_eq_zero" -> "tactic", "topological_add_group.ext" -> "topology", "continuous_sigma_map" -> "topology", "free_comm_ring.lift_comp_of" -> "algebra", "fin.add_def" -> "init", "nat.mul_pred_left" -> "init", "free_semigroup.map_pure" -> "algebra", "ne_bot_of_gt" -> "order", "mv_polynomial.is_homogeneous.sum" -> "algebra", "multiset.count_repeat" -> "data", "forall_comm" -> "tactic", "add_group.closure_add_subgroup" -> "algebra", "set.prod_image_image_eq" -> "data", "string.empty_ne_str" -> "init", "mvqpf.comp_map" -> "data", "one_lt_mul_of_lt_of_le'" -> "algebra", "category_theory.over.iterated_slice_forward_obj" -> "category_theory", "finset.eq_of_veq" -> "data", "has_deriv_within_at.sub_const" -> "analysis", "primrec.option_some" -> "computability", "deriv_within_ccos" -> "analysis", "subring.prod_top" -> "algebra", "set.indicator_add_eq_right" -> "data", "list.length_pos_iff_exists_mem" -> "data", "polynomial.mul_coeff_zero" -> "data", "differentiable_on.mono" -> "analysis", "relator.rel_not" -> "logic", "cauchy_seq.is_cau_seq" -> "topology", "ideal.comap_top" -> "algebra", "emetric.diam_triple" -> "topology", "emetric.edist_le_diam_of_mem" -> "topology", "filter.tendsto.Ioc" -> "order", "function.commute.iterate_self" -> "logic", "Exists.snd" -> "logic", "linear_equiv.coe_uncurry_symm" -> "algebra", "infi_bool_eq" -> "order", "category_theory.category_of_elements.comma_equivalence_inverse" -> "category_theory", "group.closure_subgroup" -> "algebra", "int.eq_neg_succ_of_lt_zero" -> "init", "set.surj_on.union_union" -> "data", "matrix.lie_transpose" -> "algebra", "ennreal.mul_div_assoc" -> "data", "padic.of_rat_neg" -> "data", "multiset.sum_hom_rel" -> "data", "CommSemiRing.coe_of" -> "algebra", "polynomial.eval_one" -> "data", "not_le" -> "init", "free_group.one_eq_mk" -> "algebra", "one_one_reducible.disjoin_left" -> "computability", "ennreal.Sup_add" -> "topology", "exists_rat_lt" -> "algebra", "geom_series\:2082_with_one" -> "algebra", "ideal.sub_mem" -> "algebra", "order_of_eq_card_of_forall_mem_gpowers" -> "algebra", "quotient_group.induction_on'" -> "algebra", "localization.one_rel" -> "algebra", "pow_length_le_mul_of_digits" -> "data", "has_fderiv_at_filter.sub_const" -> "analysis", "Sup_mem_closure" -> "topology", "filter.mem_pmap" -> "order", "measure_theory.ae_eq_fun.edist_comm" -> "analysis", "submodule.findim_mono" -> "algebra", "category_theory.monoidal_of_has_finite_coproducts.associator_hom" -> "category_theory", "mv_polynomial.total_degree_pow" -> "data", "wseq.mem_of_mem_tail" -> "data", "nnreal.coe_list_prod" -> "data", "continuous_on.neg" -> "topology", "finset.not_mem_map_subtype_of_not_property" -> "data", "linear_map.pi_eq_zero" -> "algebra", "set.inter_empty_of_inter_sUnion_empty" -> "data", "CommRing.colimits.quot_add" -> "algebra", "eq_zero_of_neg_eq" -> "algebra", "list.prefix_or_prefix_of_prefix" -> "data", "int.bit_val" -> "data", "function.surjective_iff_has_right_inverse" -> "logic", "measure_theory.measure.measurable_join" -> "analysis", "complex.abs_add" -> "data", "le_of_one_div_le_one_div" -> "algebra", "localization.ring_equiv_of_quotient_symm_of" -> "algebra", "div_eq_filter_card" -> "number_theory", "list.lex.append_left" -> "data", "eq_inv_of_mul_right_eq_one" -> "algebra", "finmap.lookup_is_some" -> "data", "int.coe_nat_bit0" -> "data", "gold_conj_ne_zero" -> "data", "int.sub_nonpos_of_le" -> "init", "set.nonempty.left" -> "data", "filter.germ.map'_coe" -> "order", "num.le_to_nat" -> "data", "compact_std_simplex" -> "analysis", "real.rpow_lt_rpow" -> "analysis", "ennreal.to_real_nonneg" -> "data", "hyperreal.is_st_mul" -> "data", "smooth_id" -> "geometry", "set.singleton_add_singleton" -> "algebra", "fderiv_within_const_sub" -> "analysis", "partrec.some" -> "computability", "le_cInf_iff" -> "order", "or_eq_of_eq_true_right" -> "init", "supr_emptyset" -> "order", "add_con.coe_eq" -> "algebra", "is_closed.Inf_mem" -> "topology", "mv_polynomial.C_pow" -> "data", "convex.smul" -> "analysis", "int.coe_nat_one" -> "init", "is_open.interior_eq" -> "topology", "is_group_hom.one_iff_ker_inv'" -> "algebra", "function.commute.comp_left" -> "logic", "multiset.coe_inter" -> "data", "differentiable_within_at.rpow" -> "analysis", "onote.NF_below_iff_top_below" -> "set_theory", "nsmul_eq_mul" -> "algebra", "ordinal.card_nat" -> "set_theory", "mul_dvd_mul_iff_left" -> "algebra", "list.mem_keys" -> "data", "differentiable_at.fderiv_within_prod" -> "analysis", "norm_num.add_neg_pos_pos" -> "tactic", "uniform_space.completion.continuous_mul" -> "topology", "category_theory.functor.ext" -> "category_theory", "subtype.coe_preimage_self" -> "data", "semiconj_by.units_inv_right_iff" -> "algebra", "generalized_continued_fraction.int_fract_pair.succ_nth_stream_b_le_nth_stream_fr_inv" -> "algebra", "list.sum_take_succ" -> "data", "eq_orthogonal_projection_of_mem_of_inner_eq_zero" -> "analysis", "ennreal.tsum_mul_left" -> "topology", "num.of_nat_cast" -> "data", "is_local_extr.has_fderiv_at_eq_zero" -> "analysis", "category_theory.over.construct_products.cones_equiv_unit_iso_2" -> "category_theory", "mv_polynomial.eval\:2082_eq" -> "data", "category_theory.limits.binary_cofan.\[Iota]_app_right" -> "category_theory", "discrete_valuation_ring.of_has_unit_mul_pow_irreducible_factorization" -> "algebra", "int.mod_mul_right_mod" -> "data", "polynomial.C_0" -> "data", "ring_hom.map_multiset_sum" -> "algebra", "interval_integral.integral_has_strict_deriv_at_of_tendsto_ae_left" -> "analysis", "nnreal.tendsto_pow_at_top_nhds_0_of_lt_1" -> "analysis", "pnat.coprime.gcd_mul" -> "data", "int.mod_mod_of_dvd" -> "data", "list.perm.insert" -> "data", "measure_theory.simple_func.restrict_const_lintegral" -> "analysis", "padic_int.norm_units" -> "data", "category_theory.limits.walking_pair.swap_symm_apply_tt" -> "category_theory", "list.alternating_prod_cons_cons" -> "data", "subring.coe_supr_of_directed" -> "algebra", "fin.comp_cons" -> "data", "equiv.sigma_congr_right_symm_apply" -> "data", "filter.congr_sets" -> "order", "dioph.proj_dioph_of_nat" -> "number_theory", "set.infinite.to_subtype" -> "data", "cau_seq.lim_neg" -> "data", "finset.map_subset_map" -> "data", "structure_groupoid.id_mem" -> "geometry", "multiset.map_eq_map" -> "data", "multiset.erase_dup_add" -> "data", "prime_spectrum.zero_locus_union" -> "algebraic_geometry", "turing.pointed_map.mk_val" -> "computability", "category_theory.limits.cokernel_cofork.\[Pi]_of_\[Pi]" -> "category_theory", "array.ext'" -> "init", "mv_polynomial.degrees_mul" -> "data", "submodule.mem_colon'" -> "algebra", "linear_map.disjoint_std_basis_std_basis" -> "algebra", "set.image_image2" -> "data", "mv_power_series.coeff_mul" -> "algebra", "set.surj_on.congr" -> "data", "computation.lift_rel_aux.ret_left" -> "data", "le_of_lt_or_eq" -> "init", "finset.subset_product" -> "data", "continuous_add" -> "topology", "analytic_at.neg" -> "analysis", "continuous_bot" -> "topology", "relation.church_rosser" -> "logic", "has_sum.tsum_eq" -> "topology", "is_open.unique_diff_within_at" -> "analysis", "finsupp.eq_zero_of_zero_eq_one" -> "data", "category_theory.limits.epi_of_is_colimit_parallel_pair" -> "category_theory", "filter.mul_one" -> "order", "structure_groupoid.compatible_of_mem_maximal_atlas" -> "geometry", "order_iso.right_ord_continuous" -> "order", "normed_space.dual_def" -> "analysis", "inv_le" -> "algebra", "perfect_closure.nat_cast_eq_iff" -> "algebra", "option.is_none_none" -> "data", "nat.dvd_of_mul_dvd_mul_right" -> "init", "padic_val_nat_zero" -> "data", "isometric.point_reflection_self" -> "analysis", "dvd_iff_dvd_of_rel_right" -> "algebra", "buffer.lt_aux_3" -> "data", "linear_map.prod_eq_inf_comap" -> "algebra", "category_theory.iso.to_alg_equiv_inv_fun" -> "algebra", "has_fderiv_at.congr_of_eventually_eq" -> "analysis", "tsum_geometric_two" -> "analysis", "subgroup.ext'" -> "algebra", "le_div_iff" -> "algebra", "int.mul_pos" -> "init", "category_theory.limits.has_image_map.factor_map_assoc" -> "category_theory", "int.eq_succ_of_zero_lt" -> "init", "finset.supr_finset_image" -> "data", "set.image2_singleton_left" -> "data", "multiset.powerset_len_zero_right" -> "data", "Module.exact_iff" -> "algebra", "opposite.op_injective" -> "data", "fpow_of_nat" -> "algebra", "multiset.singleton_ne_zero" -> "data", "category_theory.limits.pushout_cocone.condition_assoc" -> "category_theory", "matrix.dot_product_diagonal" -> "data", "free_add_magma.map_pure" -> "algebra", "sum.lex_acc_inl" -> "data", "submonoid.range_subtype" -> "algebra", "mul_nsmul" -> "algebra", "set.Ioc_disjoint_Ioc" -> "data", "multiset.sup_le" -> "data", "list.mem_cons_eq" -> "init", "asymptotics.is_O_with.const_smul_left" -> "analysis", "computation.ret_orelse" -> "data", "ennreal.coe_min" -> "data", "multiset.erase_dup_subset'" -> "data", "function.is_periodic_pt_iff_minimal_period_dvd" -> "dynamics", "add_units.add_neg_cancel_right" -> "algebra", "ideal.is_jacobson_iso" -> "algebra", "continuous_multilinear_map.curry_uncurry_right" -> "analysis", "associates.factor_set.coe_add" -> "algebra", "is_lub_Iic" -> "order", "ring_hom.prod_unique" -> "algebra", "bool.cond_tt" -> "data", "supr_and'" -> "order", "gcd_eq_zero_iff" -> "algebra", "with_top.top_add" -> "algebra", "category_theory.adjunction.left_triangle_components" -> "category_theory", "inv_of_mul_self" -> "algebra", "fin.succ.inj" -> "data", "polynomial.degree_C_le" -> "data", "zero_le" -> "algebra", "seq.map_nil" -> "data", "measure_theory.lintegral_const_mul_le" -> "analysis", "rel_embedding.collapse_F.not_lt" -> "set_theory", "int.neg_neg" -> "init", "padic_norm_e.one'" -> "data", "list.length_of_fn_aux" -> "data", "generalized_continued_fraction.terminated_at_iff_s_terminated_at" -> "algebra", "rat.mk_nat_eq" -> "data", "matrix.linear_equiv_matrix_mul" -> "algebra", "asymptotics.is_o.add_add" -> "analysis", "polynomial.differentiable_within_at" -> "analysis", "set.diff_compl" -> "data", "set.bij_on.congr" -> "data", "category_theory.quotient.functor_map" -> "category_theory", "isometry.lipschitz" -> "topology", "nat.coprime_one_right_iff" -> "data", "seq.le_stable" -> "data", "polynomial.nat_degree_map" -> "data", "cardinal.bit0_ne_zero" -> "set_theory", "category_theory.nat_iso.cancel_nat_iso_inv_left" -> "category_theory", "measure_theory.simple_func.restrict_of_not_measurable" -> "analysis", "equiv.set.sum_diff_subset_apply_inl" -> "data", "summable_of_nnnorm_bounded" -> "analysis", "nnreal.mul_le_iff_le_inv" -> "data", "ennreal.infi_add_infi" -> "data", "topological_space.opens.inclusion_to_fun" -> "topology", "nat.prod_factors" -> "data", "multilinear_map.map_add" -> "algebra", "finsupp.single_zero" -> "data", "list.Ico.zero_bot" -> "data", "add_group.closure_mono" -> "algebra", "num.size_eq_nat_size" -> "data", "set.nonempty_image_iff" -> "data", "filter.tendsto_prod_iff" -> "order", "nat.min_fac_zero" -> "data", "interval_integral.integral_has_strict_deriv_at_left" -> "analysis", "ennreal.nhds_zero" -> "topology", "filter.mem_bind_sets'" -> "order", "monoid_hom.eq_of_eq_on_dense" -> "algebra", "filter.tendsto.Ioo" -> "order", "homeomorph.symm_comp_self" -> "topology", "dim_eq_of_surjective" -> "algebra", "cluster_pt.of_inf_right" -> "topology", "compact_space_uniformity" -> "topology", "ring_hom.cancel_right" -> "algebra", "measure_theory.outer_measure.Union_null" -> "analysis", "monoid_algebra.group_smul.linear_map_apply" -> "data", "mul_lt_iff_lt_one_right" -> "algebra", "ennreal.to_real_eq_zero_iff" -> "data", "nat.bit1_val" -> "init", "add_units.coe_map" -> "algebra", "mv_power_series.coeff_inv_aux" -> "algebra", "nat.choose_pos" -> "data", "inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four" -> "analysis", "is_R_or_C.conj_neg_I" -> "data", "category_theory.limits.fork.\[Iota]_of_\[Iota]" -> "category_theory", "filter.le_def" -> "order", "finsupp.lsum_apply" -> "algebra", "real.uniform_continuous_mul" -> "topology", "rank_add_le" -> "algebra", "composition_as_set.blocks_length" -> "combinatorics", "measure_theory.integral_add_measure" -> "analysis", "ennreal.coe_bit0" -> "data", "decidable.lt_trichotomy" -> "init", "Set.mem_singleton" -> "set_theory", "filter.is_countably_generated.countable_generating_set" -> "order", "polynomial.not_unit_X_sub_C" -> "algebra", "set.finite.mul" -> "algebra", "measure_theory.integrable_iff_norm" -> "analysis", "list.tfae_nil" -> "data", "int.gcd_dvd_gcd_of_dvd_left" -> "algebra", "nat.coprime.eq_one_of_dvd" -> "data", "computable.list_append" -> "computability", "multiset.erase_zero" -> "data", "con.ext'" -> "algebra", "int.gcd_dvd_gcd_mul_left_right" -> "algebra", "category_theory.limits.kernel.condition" -> "category_theory", "onote.repr_of_nat" -> "set_theory", "category_theory.iso.comp_hom_eq_id" -> "category_theory", "asymptotics.is_O.symm" -> "analysis", "is_closed_infi_iff" -> "topology", "category_theory.adjunction.equiv_homset_left_of_nat_iso_apply" -> "category_theory", "function.commute.iterate_pos_lt_iff_map_lt" -> "order", "measure_theory.outer_measure.Union_eq_of_caratheodory" -> "analysis", "ctop.realizer.is_open_iff" -> "data", "cardinal.one_lt_bit1" -> "set_theory", "cardinal.powerlt_aux" -> "set_theory", "prime_iff_of_associated" -> "algebra", "interval_integral.integral_sub" -> "analysis", "infi_infi_eq_right" -> "order", "ordinal.power_log_le" -> "set_theory", "polynomial.pairwise_coprime_X_sub" -> "data", "cardinal.mk_quot_le" -> "set_theory", "multiset.disjoint_add_left" -> "data", "is_compact.inter_right" -> "topology", "nat.lcm_one_left" -> "data", "filter.eventually_lt_of_limsup_lt" -> "order", "filter.countable_binfi_principal_eq_seq_infi" -> "order", "fin.succ_zero_eq_one" -> "data", "filter.tendsto_comap_iff" -> "order", "category_theory.under.forget_obj" -> "category_theory", "Mon_.comp_hom'" -> "category_theory", "mfderiv_within_zero_of_not_mdifferentiable_within_at" -> "geometry", "multiset.not_mem_of_nodup_cons" -> "data", "uniform_space.comap_quotient_le_uniformity" -> "topology", "metric.mem_closed_ball" -> "topology", "sum.inl_ne_inr" -> "data", "norm_num.le_bit0_bit1" -> "tactic", "topological_space.opens.comap_id" -> "topology", "ordinal.omega_le_cof" -> "set_theory", "prod_X_sub_smul.coeff" -> "algebra", "finsupp.subtype_domain_apply" -> "data", "finset.union_left_comm" -> "data", "set.infinite.exists_subset_card_eq" -> "data", "list.chain'.append" -> "data", "set.sInter_subset_sInter" -> "data", "list.exists_of_length_succ" -> "data", "dense_inducing.nhds_within_ne_bot" -> "topology", "equiv.perm.sign_aux_inv" -> "algebra", "ideal.gc_map_comap" -> "algebra", "polynomial.monomial_zero_left" -> "data", "relation.trans_gen.head'_iff" -> "logic", "list.disjoint_of_nodup_append" -> "data", "is_glb.of_subset_of_superset" -> "order", "Inf_le" -> "order", "sub_lt_self_iff" -> "algebra", "ordinal.mk_initial_seg" -> "set_theory", "euclidean_geometry.dist_reflection" -> "geometry", "is_R_or_C.div_im" -> "data", "list.repeat_add" -> "data", "norm_num.bit0_mul" -> "tactic", "int.div_eq_div_of_mul_eq_mul" -> "data", "deriv_pow'" -> "analysis", "set.eq_finite_Union_of_finite_subset_Union" -> "data", "affine.simplex.sum_circumcenter_weights_with_circumcenter" -> "geometry", "category_theory.monoidal_category.inv_tensor" -> "category_theory", "bit1_zero" -> "algebra", "affine_independent_set_of_affine_independent" -> "algebra", "free_group.sum_mk" -> "algebra", "is_open_mul_left" -> "topology", "equivalence_of_many_one_equiv" -> "computability", "applicative.pure_seq_eq_map'" -> "control", "ordinal.succ_eq_add_one" -> "set_theory", "asymptotics.is_o.is_O_with" -> "analysis", "padic.valuation_one" -> "data", "seq_compact.lebesgue_number_lemma_of_metric" -> "topology", "times_cont_mdiff_within_at.of_le" -> "geometry", "valuation.is_equiv.val_eq" -> "algebra", "mul_le_of_le_one_left" -> "algebra", "le_imp_le_iff_lt_imp_lt" -> "algebra", "multiset.to_finsupp_zero" -> "data", "dense_range.induction_on\:2083" -> "topology", "submonoid.localization_map.lift_mk'_spec" -> "algebra", "div_div_cancel'" -> "algebra", "finsupp.support_neg" -> "data", "set.union_assoc" -> "data", "mv_polynomial.monomial_add" -> "data", "exists_dual_vector" -> "analysis", "multiset.coe_keys" -> "data", "list.subperm.erase" -> "data", "cardinal.sum_mk" -> "set_theory", "ordinal.nat_cast_mul" -> "set_theory", "finset.Ico.eq_empty_iff" -> "data", "add_monoid_hom.add_apply" -> "algebra", "subgroup.mem_sup_left" -> "algebra", "isometric.edist_eq" -> "topology", "fraction_map.integer_normalization_eq_zero_iff" -> "algebra", "ring_hom.map_neg" -> "algebra", "is_unit.mem_submonoid_iff" -> "algebra", "add_comm_group.is_Z_bilin.zero_right" -> "topology", "le_nat_ceil" -> "algebra", "frontier_inter_subset" -> "topology", "multiset.pi_cons_injective" -> "data", "emetric.is_closed_ball_top" -> "topology", "subsemiring.range_fst" -> "algebra", "inv_lt_one" -> "algebra", "nat.find_greatest_spec_and_le" -> "data", "mul_dvd_mul_left" -> "algebra", "pgame.numeric.move_left_lt" -> "set_theory", "times_cont_diff_within_at.comp_continuous_linear_map" -> "analysis", "ordinal.type_fin" -> "set_theory", "option.not_is_some_iff_eq_none" -> "data", "list.lookmap_some" -> "data", "gaussian_int.to_complex_one" -> "data", "ordinal.typein_top" -> "set_theory", "is_lub_Sup" -> "order", "units.mul_inv_cancel_left" -> "algebra", "category_theory.Kleisli.comp_def" -> "category_theory", "linear_map.range_coprod" -> "algebra", "list.argmax_nil" -> "data", "padic_norm_e.mul'" -> "data", "zsqrtd.mul_im" -> "data", "max_min_distrib_left" -> "algebra", "euclidean_geometry.inter_eq_singleton_orthogonal_projection" -> "geometry", "list.forall_mem_map_iff" -> "data", "ennreal.add_sub_cancel_of_le" -> "data", "category_theory.iso.ext" -> "category_theory", "complex.conj_bijective" -> "data", "finsupp.sum_add" -> "data", "euclidean_domain.div_self" -> "algebra", "measure_theory.l1.neg_part_to_fun_eq_max" -> "analysis", "free_add_monoid.hom_eq" -> "algebra", "filter.is_bounded_sup" -> "order", "category_theory.functor.flip_obj_obj" -> "category_theory", "pi.linear_independent_std_basis" -> "algebra", "roption.not_mem_none" -> "data", "add_sub" -> "algebra", "iterated_fderiv_within_succ_apply_left" -> "analysis", "measure_theory.all_ae_of_real_F_le_bound" -> "analysis", "det_eq_sign_char_poly_coeff" -> "algebra", "prime_spectrum.comap_id" -> "algebraic_geometry", "multiplicative.simple_group_iff" -> "algebra", "con.map_apply" -> "algebra", "free_comm_ring.exists_finset_support" -> "algebra", "measure_theory.measure.coe_smul" -> "analysis", "submonoid.mrange_inr'" -> "algebra", "set.mk_preimage_prod_left" -> "data", "polynomial.map_injective" -> "data", "is_compl.inf_sup" -> "order", "hyperreal.infinite_iff_abs_lt_abs" -> "data", "category_theory.exists_zigzag'" -> "category_theory", "nat.succ_mul_choose_eq" -> "data", "relation.refl_trans_gen_lift'" -> "logic", "affine_map.line_map_apply_zero" -> "algebra", "dist_eq_zero" -> "topology", "nat.eq_or_lt_of_not_lt" -> "init", "fixed_points.smul_polynomial" -> "algebra", "subring.coe_prod" -> "algebra", "tactic.ring.add_neg_eq_sub" -> "tactic", "formal_multilinear_series.mem_comp_partial_sum_source_iff" -> "analysis", "set.left_mem_Ico" -> "data", "alg_equiv.bijective" -> "algebra", "fin.mk_eq_subtype_mk" -> "data", "is_add_group_hom.zero_ker_neg" -> "algebra", "monoid.exists_list_of_mem_closure" -> "algebra", "subset_tangent_cone_prod_left" -> "analysis", "nat.coprime_self" -> "data", "continuous_multilinear_map.mk_pi_ring_apply_one_eq_self" -> "analysis", "subsingleton_or_exists_ne" -> "logic", "filter.has_basis.ext" -> "order", "differentiable_within_at.csinh" -> "analysis", "measure_theory.simple_func.finset_sup_apply" -> "analysis", "finset.lt_fold_max" -> "data", "continuous_linear_map.pi_comp" -> "topology", "bool.default_bool" -> "data", "set.indicator_sub" -> "data", "real.sin_add_pi_div_two" -> "analysis", "continuous_multilinear_map.bound" -> "analysis", "finset.sum_subtype_eq_sum_filter" -> "algebra", "ennreal.rpow_lt_rpow" -> "analysis", "ordinal.zero_eq_type_empty" -> "set_theory", "linear_map.ker_smul'" -> "algebra", "lists.sizeof_pos" -> "set_theory", "nat.lt_of_add_lt_add_left" -> "init", "filter.sup_of_ultrafilters" -> "order", "irrational.of_neg" -> "data", "polynomial.has_deriv_within_at" -> "analysis", "real.continuous_inv" -> "topology", "distrib_mul_action_hom.ext_iff" -> "algebra", "multilinear_map.norm_image_sub_le_of_bound'" -> "analysis", "nat.primrec.pow" -> "computability", "nnreal.eq_iff" -> "data", "dioph.vec_ex1_dioph" -> "number_theory", "is_add_monoid_hom.of_add" -> "algebra", "measure_theory.lebesgue_outer_trim" -> "analysis", "fderiv_const_add" -> "analysis", "list.append_left_cancel" -> "data", "category_theory.bifunctor.map_id_comp" -> "category_theory", "complex.cosh_of_real_im" -> "data", "convex.norm_image_sub_le_of_norm_fderiv_le'" -> "analysis", "list.nth_modify_nth" -> "data", "iterated_fderiv_within_succ_apply_right" -> "analysis", "and_eq_of_eq" -> "init", "set.image_prod" -> "data", "convex_cone.mem_Inf" -> "analysis", "has_sum.has_sum_of_sum_eq" -> "topology", "pnat.factor_multiset_pow" -> "data", "pSet.equiv.euc" -> "set_theory", "gpow_bit0" -> "algebra", "list.prefix_iff_eq_append" -> "data", "set.inter_distrib_right" -> "data", "submodule.map_inf_eq_map_inf_comap" -> "algebra", "adic_completion.coe_eval" -> "algebra", "topological_space.compacts.sup_val" -> "topology", "emetric.inf_edist_union" -> "topology", "wseq.join_map_ret" -> "data", "equiv.prod_sum_distrib_apply_right" -> "data", "has_fpower_series_on_ball.analytic_at_of_mem" -> "analysis", "ulower.up_eq_up" -> "data", "dense_embedding.subtype" -> "topology", "complete_space_congr" -> "topology", "polynomial.map_sum" -> "data", "finsupp.mem_to_multiset" -> "data", "right_add_coset_mem_right_add_coset" -> "algebra", "measurable_space.dynkin_system.of_measurable_space_to_measurable_space" -> "analysis", "is_mul_hom.comp" -> "algebra", "multiset.sup_ndinsert" -> "data", "nat.lt_succ_of_le" -> "init", "stream.corec_def" -> "data", "complex.tanh_of_real_im" -> "data", "metric.complete_of_cauchy_seq_tendsto" -> "topology", "nat.mul_self_sub_mul_self_eq" -> "init", "zero_add" -> "algebra", "con.inf_iff_and" -> "algebra", "function.semiconj\:2082.comp" -> "logic", "subring.mem_closure_iff" -> "algebra", "times_cont_diff_on.continuous_on" -> "analysis", "is_coprime_zero_left" -> "algebra", "category_theory.iso.conj_Aut_mul" -> "category_theory", "ite_smul" -> "algebra", "finset.sum_mul" -> "algebra", "model_with_corners.target" -> "geometry", "free_add_monoid.of_def" -> "algebra", "measure_theory.integral_zero_measure" -> "analysis", "norm_num.mul_bit0'" -> "tactic", "neg_dvd" -> "algebra", "bitraversable.tfst_comp_tsnd" -> "control", "metric.is_closed_ball" -> "topology", "padic_norm_e.sub_rev" -> "data", "int.lcm_dvd" -> "algebra", "topological_space.opens.map_iso_inv_app" -> "topology", "mv_polynomial.coeff_X" -> "data", "list.perm.bag_inter_right" -> "data", "bit0_eq_zero" -> "algebra", "category_theory.limits.walking_pair.swap_apply_right" -> "category_theory", "measure_theory.lintegral_norm_eq_lintegral_edist" -> "analysis", "exists_prop_of_false" -> "logic", "iff_eq_of_eq_true_left" -> "init", "lt_mul_of_lt_of_one_lt" -> "algebra", "add_localization.induction_on\:2083" -> "algebra", "pnat.dvd_prime" -> "data", "isometric.isometry" -> "topology", "category_theory.quotient.comp_right" -> "category_theory", "finsupp.map_range_add" -> "data", "cau_seq.lim_le" -> "data", "num.lor_to_nat" -> "data", "function.comp_const_right" -> "init", "of_mul_inv" -> "algebra", "category_theory.kernel_comp_cokernel_assoc" -> "algebra", "filter.mem_inf_sets_of_left" -> "order", "nat.sub_le_right_of_le_add" -> "data", "denumerable.of_nat_of_decode" -> "data", "int.le_add_one" -> "data", "linear_equiv.of_injective_endo_right_inv" -> "algebra", "mul_two" -> "algebra", "filter.is_countably_generated.exists_seq" -> "order", "is_max_on.neg" -> "order", "span_lt_top_of_card_lt_findim" -> "algebra", "category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom" -> "category_theory", "traversable.naturality_pf" -> "control", "polynomial.degree_X_pow_sub_C" -> "data", "set.Iic_union_Ioi" -> "data", "lebesgue_number_lemma_of_metric" -> "topology", "measure_theory.simple_func.fin_meas_supp.map_iff" -> "analysis", "num.land_to_nat" -> "data", "int.mod_add_div" -> "data", "countable_bInter_mem_sets" -> "order", "set.bij_on.subset_range" -> "data", "primrec.list_of_fn" -> "computability", "category_theory.over.construct_products.cones_equiv_functor_2" -> "category_theory", "category_theory.monoidal_category.right_unitor_conjugation" -> "category_theory", "nat.succ_le_succ" -> "init", "complex.deriv_sin" -> "analysis", "add_units.map_comp" -> "algebra", "rel_iso.surjective" -> "order", "nat.test_bit_zero" -> "init", "smul_inv_smul'" -> "algebra", "bool.ff_ne_tt" -> "init", "filter.eventually_eq.symm" -> "order", "filter.lift_comm" -> "order", "zorn.chain_closure_succ_fixpoint_iff" -> "order", "free_magma.traverse_mul'" -> "algebra", "mul_equiv.ext" -> "data", "turing.to_partrec.code.exists_code" -> "computability", "cancel_factors.mul_subst" -> "tactic", "is_add_unit_of_add_eq_zero" -> "algebra", "category_theory.monoidal_category.associator_nat_iso_hom_app" -> "category_theory", "num.bit_to_nat" -> "data", "filter.rcomap_sets" -> "order", "nonempty_unique_or_exists_ne" -> "logic", "set.neg_subset" -> "algebra", "has_fpower_series_at.neg" -> "analysis", "add_submonoid.localization_map.map_right_cancel" -> "algebra", "continuous_supr_dom" -> "topology", "tendsto_locally_uniformly.continuous" -> "topology", "string.to_list_inj" -> "data", "finset.max'_le" -> "data", "ring_equiv.to_opposite_apply" -> "data", "polynomial.differentiable_on" -> "analysis", "vector.cons_head_tail" -> "data", "mv_polynomial.eval_indicator_apply_eq_zero" -> "algebra", "set.preimage_add_preimage_subset" -> "algebra", "cardinal.mk_rat" -> "data", "nat.fact_lt" -> "data", "continuous_linear_map.coe_snd'" -> "topology", "subring.prod_mono_right" -> "algebra", "int.bitwise_bit" -> "data", "inf_eq_top_iff" -> "order", "is_integral_of_mem_of_fg" -> "algebra", "category_theory.graded_object.zero_apply" -> "category_theory", "one_le_pow_of_one_le'" -> "algebra", "computation.lift_rel_of_mem" -> "data", "add_submonoid.localization_map.lift_eq" -> "algebra", "list.tfae_of_cycle" -> "data", "real.deriv_cos'" -> "analysis", "filter.tendsto.basis_left" -> "order", "nnreal.rpow_one" -> "analysis", "local_equiv.refl_source" -> "data", "computation.results.len_unique" -> "data", "nat.div_div_self" -> "data", "set.mem_union" -> "data", "multiplicity.multiplicity_pow_self" -> "algebra", "filter.prod_mono" -> "order", "measure_theory.outer_measure.le_inter_add_diff" -> "analysis", "pell.yn_succ" -> "number_theory", "multiset.singleton_coe" -> "data", "add_submonoid.mrange_snd" -> "algebra", "Top.prelocal_predicate.sheafify_of" -> "topology", "subsemiring.mem_inf" -> "algebra", "list.rel_mem" -> "data", "real.exp_strict_mono" -> "data", "quadratic_form.to_fun_eq_apply" -> "algebra", "interval_integral.FTC_filter.finite_at_inner" -> "analysis", "exp_neg_inv_glue.f_aux_has_deriv_at" -> "analysis", "fintype.sum_congr" -> "data", "norm_num.mul_neg_neg" -> "tactic", "mem_skew_adjoint_matrices_submodule" -> "algebra", "is_integral_tower_bot_of_is_integral" -> "algebra", "Cauchy.extend_pure_cauchy" -> "topology", "of_digits_digits" -> "data", "ordinal.mul_is_normal" -> "set_theory", "galois_coinsertion.u_supr_of_lu_eq_self" -> "order", "set.maps_to.congr" -> "data", "cardinal.aleph'_is_normal" -> "set_theory", "Set.eval_mk" -> "set_theory", "add_submonoid.subset_closure" -> "algebra", "deriv_div" -> "analysis", "finmap.union_to_finmap" -> "data", "linear_map.fun_congr_left_apply" -> "algebra", "differentiable_on.add_const" -> "analysis", "inner_smul_left" -> "analysis", "submodule.map_coe" -> "algebra", "self_mem_nhds_within" -> "topology", "set.preimage_injective" -> "data", "mul_action.orbit_equiv_quotient_stabilizer_symm_apply" -> "algebra", "div_one" -> "algebra", "cardinal_lt_omega_of_dim_lt_omega" -> "algebra", "category_theory.pi.sum_obj_map" -> "category_theory", "surreal.add_assoc" -> "set_theory", "iff_eq_of_eq_true_right" -> "init", "int.shiftl_neg_succ" -> "data", "upper_bounds_Icc" -> "order", "continuous_multilinear_map.fin0_apply_norm" -> "analysis", "int.nat_abs_one" -> "init", "mvqpf.supp_eq_of_is_uniform" -> "data", "finset.subset.trans" -> "data", "filter.has_basis.restrict" -> "order", "circle_deg1_lift.iterate_eq_of_map_eq_add_int" -> "dynamics", "with_top.coe_lt_coe" -> "order", "list.prod_cons" -> "data", "polynomial.hom_eval\:2082" -> "data", "ennreal.coe_mem_upper_bounds" -> "data", "asymptotics.is_o_congr" -> "analysis", "multiset.powerset_len_cons" -> "data", "mv_polynomial.is_noetherian_ring_fin" -> "algebra", "mem_ext_chart_source" -> "geometry", "compact_iff_compact_in_subtype" -> "topology", "measurable.of_inv" -> "analysis", "dist_le_of_le_geometric_two_of_tendsto\:2080" -> "analysis", "set.inv_subset_inv" -> "algebra", "le_mem_nhds" -> "topology", "znum.cast_one" -> "data", "submodule.coe_supr_of_directed" -> "algebra", "topological_space.open_nhds.inclusion_obj" -> "topology", "padic_norm.padic_norm_p_of_prime" -> "data", "eq_vadd_iff_vsub_eq" -> "algebra", "differentiable_at.const_smul_algebra" -> "analysis", "sup_top_eq" -> "order", "multiset.pure_def" -> "data", "nat.choose_symm" -> "data", "array.to_list_nth_le" -> "data", "strict_mono_mul_right_of_pos" -> "algebra", "continuous_multilinear_map.curry0_norm" -> "analysis", "category_theory.monoidal_category.unitors_equal.cells_15" -> "category_theory", "category_theory.limits.fork.app_zero_right_assoc" -> "category_theory", "finset.le_fold_max" -> "data", "holor.mul_assoc" -> "data", "multiset.Ico.inter_consecutive" -> "data", "qpf.cofix.bisim'" -> "data", "matrix.mul_smul" -> "data", "is_lub_Ioc" -> "order", "affine_subspace.affine_span_eq_Inf" -> "algebra", "left_inverse_inv" -> "algebra", "multiset.sup_singleton" -> "data", "is_open_map_smul_of_unit" -> "topology", "complex.deriv_cos" -> "analysis", "ideal.map_supr_comap_of_surjective" -> "algebra", "heq_self_iff_true" -> "init", "set.Ico_pnat_card" -> "data", "set.inj_on_preimage" -> "data", "associates.mk_pow" -> "algebra", "tendsto_of_liminf_eq_limsup" -> "topology", "times_cont_mdiff_within_at_id" -> "geometry", "sub_le_sub" -> "algebra", "normalize_eq_one" -> "algebra", "hash_map.find_insert_ne" -> "data", "differentiable_fst" -> "analysis", "list.perm.countp_eq" -> "data", "pnat.dvd_iff'" -> "data", "has_mfderiv_within_at.comp" -> "geometry", "subring.prod_bot_sup_bot_prod" -> "algebra", "hyperreal.infinite_neg_mul_infinite_neg" -> "data", "relation.transitive_refl_trans_gen" -> "logic", "has_deriv_at_filter.add_const" -> "analysis", "has_deriv_within_at.liminf_right_slope_norm_le" -> "analysis", "exists_lt_of_cInf_lt" -> "order", "continuous_linear_map.fst_prod_snd" -> "topology", "num.add_one" -> "data", "vsub_sub_vsub_cancel_left" -> "algebra", "enat.coe_ne_top" -> "data", "finsupp.coe_leval" -> "data", "stream.tail_inits" -> "data", "is_measurable.nhds_within_is_measurably_generated" -> "analysis", "UniformSpace.hom_ext" -> "topology", "cInf_le_cSup" -> "order", "category_theory.braided_functor.id_to_monoidal_functor" -> "category_theory", "category_theory.preadditive.sub_comp" -> "category_theory", "power_series.map_comp" -> "algebra", "fraction_map.num_denom_reduced" -> "algebra", "is_R_or_C.conj_im" -> "data", "mv_polynomial.C_1" -> "data", "set.image_factorization_eq" -> "data", "prod.lex_def" -> "data", "list.injective_foldl_comp" -> "data", "subgroup.exists" -> "algebra", "onote.le_def" -> "set_theory", "category_theory.limits.kernel.lift_\[Iota]" -> "category_theory", "asymptotics.is_O_comm" -> "analysis", "nat.bit_ne_zero" -> "data", "zsqrtd.nonneg_muld" -> "data", "asymptotics.is_O_with.trans" -> "analysis", "set.sigma_to_Union_injective" -> "data", "submonoid.localization_map.map_comp" -> "algebra", "linear_equiv.symm_symm" -> "algebra", "char_p.char_p_to_char_zero" -> "algebra", "generalized_continued_fraction.of_part_num_eq_one_and_exists_int_part_denom_eq" -> "algebra", "alist.mem_erase" -> "data", "lattice.ext" -> "order", "padic_int.appr_lt" -> "data", "mvpfunctor.comp_map" -> "data", "gronwall_bound_continuous_\[CurlyEpsilon]" -> "analysis", "set.inter_eq_self_of_subset_right" -> "data", "filter.is_ultrafilter.em" -> "order", "cau_seq.const_equiv" -> "data", "tendsto_pow_at_top_nhds_0_of_norm_lt_1" -> "analysis", "associated_mul_mul" -> "algebra", "list.head_eq_of_cons_eq" -> "data", "algebraic_geometry.PresheafedSpace.comp_base" -> "algebraic_geometry", "semiconj_by.neg_left_iff" -> "algebra", "finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one" -> "algebra", "dvd_dvd_iff_associated" -> "algebra", "submodule.mem_div_iff_smul_subset" -> "algebra", "add_subgroup.prod_mono_right" -> "algebra", "generalized_continued_fraction.terminated_stable" -> "algebra", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_comp_is_iso_hom" -> "category_theory", "open_embedding.source" -> "topology", "deriv_smul" -> "analysis", "continuous_top" -> "topology", "submonoid.localization_map.mk'_mul_cancel_left" -> "algebra", "category_theory.limits.pushout.inr_desc" -> "category_theory", "rat.cast_inj" -> "data", "turing.to_partrec.cont_eval_fix" -> "computability", "div_sub_div_same" -> "algebra", "deriv_within_div" -> "analysis", "znum.zneg_neg" -> "data", "smodeq.mono" -> "algebra", "pi.list_prod_apply" -> "algebra", "set.mem_inter_iff" -> "data", "con.lift_surjective_of_surjective" -> "algebra", "typevec.drop_fun_diag" -> "data", "monoid_hom.map_mclosure" -> "algebra", "continuous_edist" -> "topology", "int.add_lt_of_lt_sub_left" -> "init", "cardinal.mul_power" -> "set_theory", "polynomial.map_id" -> "data", "set.empty_inter" -> "data", "topological_space.opens.is_basis_iff_nbhd" -> "topology", "zsqrtd.nonneg_total" -> "data", "measure_theory.le_extend" -> "analysis", "category_theory.comma.map_right_obj_right" -> "category_theory", "free_group.red.step.cons_cons_iff" -> "algebra", "ring_hom.eq_nat_cast" -> "data", "constr_neg" -> "algebra", "add_aut.coe_one" -> "data", "contracting_with.edist_efixed_point_le" -> "topology", "measurable_inv'" -> "analysis", "nat.rfind_opt_dom" -> "computability", "category_theory.action_category.stabilizer_iso_End_symm_apply" -> "category_theory", "differentiable_on.inv" -> "analysis", "ennreal.inv_bijective" -> "data", "equiv.coe_plift_symm" -> "data", "asymptotics.is_o.mul_is_O" -> "analysis", "finset.image_subset_iff_subset_preimage" -> "data", "ring_hom.id_comp" -> "algebra", "div_le_div_iff'" -> "algebra", "add_submonoid.map_sup" -> "algebra", "embedding.mk'" -> "topology", "set.disjoint_singleton_left" -> "data", "omega.coeffs.val_except_eq_val_except" -> "tactic", "local_homeomorph.trans_target'" -> "topology", "ordinal.unbounded_of_unbounded_sUnion" -> "set_theory", "padic_val_rat.div" -> "data", "or.right_comm" -> "logic", "multiset.coe_to_list" -> "data", "add_submonoid.mem_sup_left" -> "algebra", "category_theory.image_to_kernel_map_zero_left" -> "algebra", "open_dom_of_pcontinuous" -> "topology", "is_closed_map_add_right" -> "topology", "category_theory.iso.to_equiv_fun" -> "category_theory", "add_con.lift_surjective_of_surjective" -> "algebra", "units.inv_eq_of_mul_eq_one" -> "algebra", "ite_eq_ff_distrib" -> "init", "set.image_mul_left_Icc'" -> "data", "equiv.inv_symm" -> "data", "set.finite.countable" -> "data", "rat.dist_cast" -> "topology", "continuous_linear_equiv.units_equiv_aut_apply_symm" -> "topology", "lipschitz_with.dist_right" -> "topology", "times_cont_diff_within_at_succ_iff_has_fderiv_within_at" -> "analysis", "add_subgroup.comap_top" -> "algebra", "equiv_functor.map_equiv_symm_apply" -> "control", "dist_norm_norm_le" -> "analysis", "complex.div_im" -> "data", "hyperreal.infinitesimal_inv_of_infinite" -> "data", "affine_subspace.mem_affine_span_singleton" -> "algebra", "multiset.add_union_distrib" -> "data", "set.surj_on_bUnion" -> "data", "complex.eq_conj_iff_re" -> "data", "le_imp_le_of_lt_imp_lt" -> "algebra", "is_R_or_C.of_real_neg" -> "data", "pnat.factor_multiset_mul" -> "data", "asymptotics.is_O_const_smul_left_iff" -> "analysis", "neg_add'" -> "algebra", "filter.tendsto_sub_at_top_nat" -> "order", "monoid_hom.mrange_top_iff_surjective" -> "algebra", "order_of_pos" -> "algebra", "measure_theory.le_infi2_lintegral" -> "analysis", "set.preimage_add_const_Iio" -> "data", "ennreal.zero_to_real" -> "data", "function.update_comp_eq_of_injective" -> "data", "homological_complex.kernel_map_condition" -> "algebra", "times_cont_diff_within_at.times_cont_diff_at" -> "analysis", "filter.ultrafilter_of_le" -> "order", "many_one_reducible_refl" -> "computability", "set.preimage_singleton_eq_empty" -> "data", "continuous_Prop" -> "topology", "norm_add_pow_two" -> "analysis", "multiset.filter_cons_of_neg" -> "data", "continuous_linear_equiv.trans_to_linear_equiv" -> "topology", "category_theory.limits.has_image.uniq" -> "category_theory", "uniform_space.completion.continuous.mul" -> "topology", "hyperreal.not_infinitesimal_of_infinite_pos" -> "data", "is_max_filter.neg" -> "order", "cardinal.mk_subtype_of_equiv" -> "set_theory", "holor_index.take_take" -> "data", "asymptotics.is_O_with.congr_right" -> "analysis", "category_theory.functor.const.op_obj_op_hom_app" -> "category_theory", "unique_factorization_domain.dvd_of_dvd_mul_right_of_no_prime_factors" -> "algebra", "list.mem_of_mem_last'" -> "data", "category_theory.pre_map" -> "category_theory", "roption.bind_assoc" -> "data", "filter.eventually.exists_measurable_mem" -> "analysis", "function.injective_id" -> "init", "finset.card_union_le" -> "data", "real.sin_pi_div_eight" -> "analysis", "finset.disjoint_val" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_on_of_locally_lift_prop_on" -> "geometry", "category_theory.limits.limit.lift_post" -> "category_theory", "equiv.perm.one_def" -> "data", "quadratic_form.equivalent.refl" -> "algebra", "composition.size_up_to_of_length_le" -> "combinatorics", "classical.dec" -> "logic", "list.nodup_sigma" -> "data", "ordinal.add_sub_cancel_of_le" -> "set_theory", "measure_theory.l1.integral_zero" -> "analysis", "submodule.restrict_scalars_mem" -> "algebra", "pnat.coe_bit1" -> "data", "setoid.ker_eq_lift_of_injective" -> "data", "ideal.span_singleton_eq_bot" -> "algebra", "power_series.monomial_zero_eq_C_apply" -> "algebra", "wseq.bind_assoc" -> "data", "wseq.lift_rel.swap" -> "data", "finset.mul_def" -> "algebra", "model_with_corners_self_coe_symm" -> "geometry", "linear_independent_iff_total_on" -> "algebra", "category_theory.adjunction.right_triangle_components_assoc" -> "category_theory", "mv_polynomial.total_degree_neg" -> "data", "list.lookup_all_nodup" -> "data", "prod_subset_compl_diagonal_iff_disjoint" -> "topology", "list.not_mem_append" -> "data", "category_theory.limits.prod_left_unitor_hom_naturality_assoc" -> "category_theory", "linear_map.range_le_ker_iff" -> "algebra", "directed.sequence_mono_nat" -> "data", "set.Iio_subset_Iic_union_Ico" -> "data", "add_submonoid.localization_map.add_equiv_of_localizations_apply" -> "algebra", "enat.pos_iff_one_le" -> "data", "continuous_id" -> "topology", "list.update_nth_eq_modify_nth" -> "data", "one_lt_of_inv_inv" -> "algebra", "linear_equiv.to_Module_iso_inv" -> "algebra", "ideal.is_maximal_of_is_maximal_disjoint" -> "algebra", "nat.succ_sub_one" -> "init", "norm_num.inv_one" -> "tactic", "pi_Lp.norm_eq" -> "topology", "discrete_valuation_ring.of_ufd_of_unique_irreducible" -> "algebra", "not_ball_of_bex_not" -> "logic", "tactic.ring_exp.pow_pp_pf_one" -> "tactic", "stream.nth_odd" -> "data", "category_theory.limits.cokernel_cofork.condition" -> "category_theory", "is_min_on.add" -> "order", "subgroup.mem_inf" -> "algebra", "filter.tendsto_at_bot_add_right_of_ge'" -> "order", "generalized_continued_fraction.convergent_eq_conts_a_div_conts_b" -> "algebra", "affine_subspace.direction_affine_span_insert" -> "algebra", "bifunctor.snd_fst" -> "control", "euclidean_domain.mod_lt" -> "algebra", "pgame.left_wins_of_equiv_iff" -> "set_theory", "uniform_space_comap_id" -> "topology", "nonneg_of_neg_nonpos" -> "algebra", "continuous_multilinear_map.sum_apply" -> "topology", "linarith.int.coe_nat_bit1_mul" -> "tactic", "measure_theory.measure.add_le_add_right" -> "analysis", "prod.snd_sum" -> "algebra", "function.semiconj.maps_to_image" -> "data", "mdifferentiable.comp" -> "geometry", "int.nat_abs_neg_of_nat" -> "data", "submonoid.localization_map.of_mul_equiv_of_localizations_apply" -> "algebra", "canonically_ordered_semiring.mul_le_mul_left'" -> "algebra", "nnreal.bdd_below_coe" -> "data", "times_cont_mdiff_on.continuous_on_tangent_map_within" -> "geometry", "rat.mk_pnat_denom" -> "data", "approximates_linear_on.lipschitz_sub" -> "analysis", "differentiable_within_at.congr_of_eventually_eq" -> "analysis", "nhds_Inf" -> "topology", "is_add_subgroup.mem_norm_comm" -> "algebra", "add_submonoid.localization_map.eq_iff_eq" -> "algebra", "polynomial.coeff_mk" -> "data", "mv_polynomial.eval\:2082_sum" -> "data", "mv_polynomial.is_homogeneous.add" -> "algebra", "stream.nth_nats" -> "data", "linear_map.map_add" -> "algebra", "is_add_submonoid.coe_zero" -> "algebra", "set.empty_pi" -> "data", "finset.fold_hom" -> "data", "stream.head_map" -> "data", "category_theory.prod.associator_obj" -> "category_theory", "real.sin_lt" -> "analysis", "int.to_nat_le_to_nat" -> "data", "list.length_repeat" -> "init", "subsemiring.coe_Sup_of_directed_on" -> "algebra", "antilipschitz_with.cod_restrict" -> "topology", "composition_as_set.to_composition_length" -> "combinatorics", "nat.lt_succ_self" -> "init", "filter.eventually_Sup" -> "order", "mv_polynomial.vars_C" -> "data", "open_subgroup.mem_coe_opens" -> "topology", "has_deriv_at_neg" -> "analysis", "int.neg_of_nat_eq_sub_nat_nat_zero" -> "init", "set.range_factorization_eq" -> "data", "metric.Hausdorff_dist_triangle'" -> "topology", "con.ker_apply_eq_preimage" -> "algebra", "filter.tendsto_map'_iff" -> "order", "category_theory.limits.biprod.symmetry'" -> "category_theory", "cardinal.nat_cast_le" -> "set_theory", "turing.tape.map_mk\:2081" -> "computability", "add_units.ext" -> "algebra", "pi.is_basis_fun\:2080" -> "algebra", "nnreal.coe_of_real" -> "data", "list.alternating_sum_cons_cons" -> "data", "eq_of_inf_eq_sup_eq" -> "order", "encodable.decode_list_succ" -> "data", "add_submonoid.localization_map.sec_spec" -> "algebra", "surjective_proj_I" -> "topology", "traversable.map_traverse'" -> "control", "nat.gcd_mul_left" -> "data", "finset.max'_singleton" -> "data", "imp_and_distrib" -> "logic", "algebraic_geometry.PresheafedSpace.restrict_carrier" -> "algebraic_geometry", "equiv.swap_comm" -> "data", "quadratic_form.zero_apply" -> "algebra", "list.forall_of_pairwise" -> "data", "mul_self_sub_mul_self" -> "algebra", "linear_map.inr_eq_prod" -> "algebra", "inv_pos" -> "algebra", "is_R_or_C.abs_of_nonneg" -> "data", "submodule.map_smul''" -> "algebra", "finset.disjoint_singleton" -> "data", "fintype.card_sum" -> "data", "ordinal.mod_lt" -> "set_theory", "cardinal.extend_function_finite" -> "set_theory", "finset.sum_congr" -> "algebra", "neg_eq_of_add_eq_zero" -> "algebra", "quotient_add_group.induction_on" -> "algebra", "finset.card_univ_diff" -> "data", "local_homeomorph.trans_symm_self" -> "topology", "asymptotics.is_O_with.prod_rightr" -> "analysis", "submonoid.mrange_inl'" -> "algebra", "eq.to_iff" -> "init", "vector3.rec_on_cons" -> "number_theory", "ring_hom.eq_on_set_closure" -> "algebra", "lucas_lehmer.int.coe_nat_two_pow_pred" -> "number_theory", "add_monoid_hom.iterate_map_smul" -> "algebra", "stream.nats_eq" -> "data", "emetric.ball_mem_nhds" -> "topology", "quotient.eq" -> "data", "real.arcsin_pos" -> "analysis", "equiv.coe_units_equiv_ne_zero" -> "data", "is_closed_sigma_mk" -> "topology", "metric.Hausdorff_dist_le_diam" -> "topology", "add_submonoid.comap_inf" -> "algebra", "real.is_conjugate_exponent.one_div_pos" -> "data", "unique_mdiff_within_at_univ" -> "geometry", "finset.sum_hom" -> "algebra", "prod.swap_right_inverse" -> "data", "subalgebra.sub_mem" -> "algebra", "mvfunctor.liftp_last_pred_iff" -> "control", "times_cont_mdiff_on_top" -> "geometry", "int.of_nat_add_of_nat" -> "init", "multiset.count_ne_zero" -> "data", "list.mem_of_fn" -> "data", "map_Inf_of_continuous_at_of_monotone" -> "topology", "set.interval_of_gt" -> "data", "has_deriv_within_at_iff_tendsto" -> "analysis", "mfderiv_within_congr" -> "geometry", "measure_theory.measure_eq_induced_outer_measure" -> "analysis", "local_equiv.trans_symm_eq_symm_trans_symm" -> "data", "perfect_closure.of_apply" -> "algebra", "contracting_with.one_sub_K_pos" -> "topology", "hyperreal.pos_of_infinite_pos" -> "data", "turing.partrec_to_TM2.tr_num_nat_end" -> "computability", "nat.gcd_self" -> "init", "complex.abs_re_le_abs" -> "data", "smooth_within_at_iff" -> "geometry", "pmf.bind_bind" -> "analysis", "mem_nhds_subtype" -> "topology", "category_theory.zero_mul_hom" -> "category_theory", "algebra.smul_mul_assoc" -> "algebra", "filter.lift'_id" -> "order", "pgame.le_iff_sub_nonneg" -> "set_theory", "is_closed_imp" -> "topology", "list.to_finset_eq" -> "data", "compact_Icc" -> "topology", "function.right_inverse_inv_fun" -> "logic", "int.of_nat_mul_neg_of_nat" -> "init", "measure_theory.simple_func.measurable" -> "analysis", "fpow_le_of_le" -> "algebra", "set.inter_preimage_subset" -> "data", "ordinal.succ_lt_of_not_succ" -> "set_theory", "has_strict_fderiv_at.has_strict_deriv_at" -> "analysis", "free_semigroup.map_mul" -> "algebra", "list.rotate_zero" -> "data", "is_coprime.pow_left" -> "algebra", "cardinal.sum_le_sum" -> "set_theory", "ideal.quotient_map_C_eq_zero" -> "algebra", "has_deriv_at_id" -> "analysis", "ordering.compares.eq_eq" -> "algebra", "Meas.coe_of" -> "analysis", "uniform_embedding_def" -> "topology", "filter.germ.coe_coe_mul_hom" -> "order", "is_coprime.add_mul_left_left" -> "algebra", "measure_theory.l1.dist_eq" -> "analysis", "filter.eventually_false_iff_eq_bot" -> "order", "filter.prod_pure_pure" -> "order", "is_bounded_linear_map.fderiv" -> "analysis", "structure_groupoid.local_invariant_prop.lift_prop_at_congr_iff_of_eventually_eq" -> "geometry", "measure_theory.measure.dirac_apply'" -> "analysis", "measure_theory.measure.map_id" -> "analysis", "rel.core_comp" -> "data", "function.directed_pts_of_period_pnat" -> "dynamics", "continuous_linear_equiv.map_eq_zero_iff" -> "topology", "matrix.det_update_row_add" -> "algebra", "turing.TM1to1.supports_stmt_read" -> "computability", "multiset.mem_bind" -> "data", "multiplicity.finite_of_finite_mul_left" -> "algebra", "category_theory.monoidal_category.unitors_equal.cells_1_4" -> "category_theory", "add_monoid_algebra.support_mul" -> "data", "nat.min_fac_dvd" -> "data", "uniform_space.completion.extension_map" -> "topology", "fin.univ_succ" -> "data", "circle_deg1_lift.ceil_map_map_zero_le" -> "dynamics", "is_add_submonoid.multiset_sum_mem" -> "algebra", "free_add_semigroup.map_pure" -> "algebra", "free_group.red.cons_cons" -> "algebra", "mul_self_le_mul_self" -> "algebra", "equiv.swap_swap" -> "data", "real.pi_gt_314" -> "data", "supr_univ" -> "order", "circle_deg1_lift.map_one_add" -> "dynamics", "measure_theory.measure_mono" -> "analysis", "is_local_min.deriv_eq_zero" -> "analysis", "mt" -> "init", "wseq.destruct_append" -> "data", "times_cont_diff_on.comp_continuous_linear_map" -> "analysis", "pnat.dvd_antisymm" -> "data", "int.to_nat_add" -> "data", "submonoid.localization_map.mul_inv_left" -> "algebra", "set.mem_of_mem_of_subset" -> "data", "filter.tendsto_pure" -> "order", "real.is_conjugate_exponent.sub_one_mul_conj" -> "data", "polynomial.expand_eq_sum" -> "algebra", "affine.simplex.points_with_circumcenter_point" -> "geometry", "continuous_at_id" -> "topology", "forall_or_distrib_left" -> "logic", "finsupp.on_finset_sum" -> "data", "set.subsingleton_singleton" -> "data", "algebra.tensor_product.lid_tmul" -> "algebra", "finset.image_image" -> "data", "zsqrtd.d_pos" -> "data", "has_fderiv_within_at.maps_to_tangent_cone" -> "analysis", "category_theory.nat_trans.vcomp_app" -> "category_theory", "category_theory.limits.kernel_condition_apply" -> "category_theory", "padic_val_rat.mul" -> "data", "mdifferentiable_at.mfderiv" -> "geometry", "finset.bInter_insert" -> "data", "prod.fst_eq_iff" -> "data", "eq_div_iff_mul_eq" -> "algebra", "typevec.append1_cases_append1" -> "data", "pnat.gcd_eq_left_iff_dvd" -> "data", "finmap.lookup_singleton_eq" -> "data", "inf_ind" -> "order", "mul_eq_zero" -> "algebra", "equiv.perm.same_cycle_inv_apply" -> "algebra", "false_of_true_iff_false" -> "init", "filter.mem_inf_sets" -> "order", "has_ftaylor_series_up_to_on_univ_iff" -> "analysis", "measure_theory.simple_func.ennreal_rat_embed_encode" -> "analysis", "compact_of_is_closed_subset" -> "topology", "monoid_hom.map_one" -> "algebra", "continuous_linear_equiv.symm_to_linear_equiv" -> "topology", "associates.prod_eq_one_iff" -> "algebra", "asymptotics.is_o.prod_rightr" -> "analysis", "bilin_form.map_sum_right" -> "algebra", "set.image_neg" -> "algebra", "nat.tendsto_pow_at_top_at_top_of_one_lt" -> "analysis", "algebra.bijective_algbera_map_iff" -> "algebra", "local_homeomorph.continuous_at_iff_continuous_at_comp_left" -> "topology", "polynomial.degree_eq_iff_nat_degree_eq_of_pos" -> "data", "not_and_of_not_right" -> "logic", "prime_of_associated" -> "algebra", "pythagorean_triple.is_primitive_classified_of_coprime" -> "number_theory", "num.size_to_nat" -> "data", "units.coe_neg" -> "algebra", "dfinsupp.sum_single_index" -> "data", "hyperreal.infinite_neg_def" -> "data", "normal_iff_eq_cosets" -> "algebra", "linear_map.ker_eq_bot_of_injective" -> "algebra", "palindrome.iff_reverse_eq" -> "data", "set.Ioc_union_Ioi_eq_Ioi" -> "data", "tactic.abel.unfold_smulg" -> "tactic", "nat.primrec'.unpair\:2082" -> "computability", "differentiable_at.exp" -> "analysis", "smooth_within_at_id" -> "geometry", "times_cont_diff_within_at.prod" -> "analysis", "equiv.perm.mul_apply" -> "data", "category_theory.currying_counit_iso_inv_app_app" -> "category_theory", "filter.tendsto_at_bot_at_bot" -> "order", "filter.Limsup_top" -> "order", "associates.prime_mk" -> "algebra", "cardinal.mk_singleton" -> "set_theory", "multiset.rel_zero_right" -> "data", "add_submonoid.coe_add" -> "algebra", "int.nat_abs_zero" -> "init", "ennreal.add_top" -> "data", "generalized_continued_fraction.numerators_recurrence" -> "algebra", "fact.succ.pos" -> "data", "Inf_apply" -> "order", "polynomial.eq_C_of_nat_degree_le_zero" -> "data", "pgame.star_lt_zero" -> "set_theory", "category_theory.limits.is_colimit.hom_desc" -> "category_theory", "function.injective.preimage_surjective" -> "data", "is_min_filter.neg" -> "order", "circle_deg1_lift.translation_number_le_of_le_add_int" -> "dynamics", "nat.prime.multiplicity_choose_aux" -> "data", "char_dvd_card_solutions_family" -> "algebra", "commute.mul_pow" -> "algebra", "measure_theory.le_to_outer_measure_caratheodory" -> "analysis", "is_cyclic.card_pow_eq_one_le" -> "algebra", "commute.div_right" -> "algebra", "perfect_closure.eq_iff'" -> "algebra", "measure_theory.induced_outer_measure_caratheodory" -> "analysis", "set.preimage_sub_const_Icc" -> "data", "differentiable_within_at.sub" -> "analysis", "times_cont_diff.times_cont_diff_on" -> "analysis", "exists_congr" -> "init", "filter.Inter_mem_sets_of_fintype" -> "order", "set.union_diff_cancel'" -> "data", "computable\:2082.comp\:2082" -> "computability", "uniform.tendsto_nhds_right" -> "topology", "measure_theory.ae_eq_fun.lintegral_add" -> "analysis", "primrec.band" -> "computability", "list.mem_append" -> "init", "primrec.vector_of_fn" -> "computability", "neg_of_mul_pos_right" -> "algebra", "base_pow_length_digits_le'" -> "data", "decidable.lt_or_gt_of_ne" -> "init", "list.foldl_join" -> "data", "add_magma.free_add_semigroup.map_of" -> "algebra", "vector.nth_update_nth_eq_if" -> "data", "function.right_id" -> "init", "multiset.ext" -> "data", "continuous_linear_map.op_norm_le_of_lipschitz" -> "analysis", "array.to_list_to_array" -> "data", "finset.card_compl" -> "data", "finset.insert_subset_insert" -> "data", "with_top.some_lt_some" -> "order", "has_groupoid_of_le" -> "geometry", "list.modify_nth_eq_take_cons_drop" -> "data", "list.of_mem_lookup" -> "data", "mul_le_mul_right" -> "algebra", "primrec.list_range" -> "computability", "category_theory.abelian.pseudoelement.zero_eq_zero'" -> "category_theory", "add_submonoid.localization_map.symm_comp_of_add_equiv_of_localizations_apply'" -> "algebra", "measure_theory.integrable.right_of_add_measure" -> "analysis", "primrec.subtype_val_iff" -> "computability", "set.pi_nonempty_iff" -> "data", "multiset.nodup_filter" -> "data", "is_coprime.of_mul_right_left" -> "algebra", "real.angle.sin_eq_iff_eq_or_add_eq_pi" -> "analysis", "semiconj_by.cast_nat_mul_cast_nat_mul" -> "algebra", "direct_sum.to_group_add" -> "algebra", "set.bij_on.mk" -> "data", "normal.is_integral" -> "algebra", "real.arcsin_le_pi_div_two" -> "analysis", "nonote.repr_add" -> "set_theory", "finsupp.erase_add" -> "data", "filter.prod_at_bot_at_bot_eq" -> "order", "local_homeomorph.trans_source''" -> "topology", "add_submonoid.map_le_iff_le_comap" -> "algebra", "is_local_max.sup" -> "topology", "pos_num.divmod_to_nat_aux" -> "data", "with_top.inf_eq_min" -> "order", "complex.sin_sub_pi_div_two" -> "analysis", "free_add_monoid.map_of" -> "algebra", "norm_num.rat_cast_bit1" -> "tactic", "submonoid.localization_map.eq_of_eq" -> "algebra", "normed_field.norm_one" -> "analysis", "dense_or_discrete" -> "order", "polynomial.monic.coeff_nat_degree" -> "data", "ennreal.bit0_inj" -> "data", "to_mul_zero" -> "algebra", "is_open_map.to_quotient_map" -> "topology", "directed.finset_le" -> "data", "category_theory.curry_natural_right_assoc" -> "category_theory", "left_ord_continuous.map_csupr" -> "order", "div_neg" -> "algebra", "sylow.exists_subgroup_card_pow_prime" -> "algebra", "add_magma.free_add_semigroup.lift_add" -> "algebra", "int.lt_add_of_sub_left_lt" -> "init", "is_glb.nhds_within_ne_bot" -> "topology", "deriv_within.comp" -> "analysis", "complex.continuous_linear_map.re_coe" -> "analysis", "int.eq_nat_abs_iff_mul" -> "number_theory", "quotient.eq_rel" -> "data", "turing.TM1to1.tr_respects" -> "computability", "has_fderiv_at_filter_iff_tendsto" -> "analysis", "rat.mk_zero" -> "data", "polynomial.degree_le_degree" -> "data", "unique_diff_within_at_congr" -> "analysis", "real.angle.cos_sin_inj" -> "analysis", "nat.mod_lt" -> "init", "list.not_bex_nil" -> "init", "hash_map.mk_as_list" -> "data", "ne_of_eq_of_ne" -> "init", "category_theory.limits.pushout_cocone.coequalizer_ext" -> "category_theory", "min_neg_neg" -> "algebra", "real.sqrt_mul" -> "data", "abv_sum_le_sum_abv" -> "data", "inv_mul_lt_left_of_lt_mul" -> "algebra", "omega.clauses.unsat_cons" -> "tactic", "irrational_sqrt_of_multiplicity_odd" -> "data", "set.disjoint_of_subset_right" -> "data", "isometric.symm_comp_self" -> "topology", "uniformity_eq_uniformity_interior" -> "topology", "category_theory.functor.prod_map" -> "category_theory", "category_theory.non_preadditive_abelian.\[CapitalDelta]_map_assoc" -> "category_theory", "auto_param_eq" -> "init", "category_theory.limits.has_colimit.iso_of_nat_iso_\[Iota]_hom_assoc" -> "category_theory", "ordinal.CNF_fst_le_log" -> "set_theory", "set.surj_on.bij_on_subset" -> "data", "ennreal.coe_mul_rpow" -> "analysis", "multiset.zero_ne_cons" -> "data", "hyperreal.coe_sub" -> "data", "linear_map.has_strict_deriv_at" -> "analysis", "subalgebra.prod_mem" -> "algebra", "Set.map_is_func" -> "set_theory", "measure_theory.measure.restrict_eq_zero" -> "analysis", "subset_interior_iff_open" -> "topology", "localization_map.map_mk'" -> "algebra", "uniform_space.completion.induction_on\:2083" -> "topology", "add_lt_of_le_of_neg" -> "algebra", "linear_equiv.of_eq_symm" -> "algebra", "category_theory.abelian.images.image_strong_epi_mono_factorisation_to_mono_factorisation_I" -> "category_theory", "imp_congr_ctx" -> "init", "mul_boole" -> "algebra", "filter.mem_or_mem_of_ultrafilter" -> "order", "ordinal.div_zero" -> "set_theory", "mv_power_series.one_mul" -> "algebra", "circle_deg1_lift.ext" -> "dynamics", "computation.get_promises" -> "data", "pgame.impartial.good_left_move_iff_first_wins" -> "set_theory", "set.singleton_mul_singleton" -> "algebra", "left_ord_continuous.map_supr" -> "order", "pnat.xgcd_type.start_is_special" -> "data", "function.embedding.coe_sigma_map" -> "logic", "category_theory.limits.types.image.lift_fac" -> "category_theory", "category_theory.functor.map_iso_inv" -> "category_theory", "continuous_multilinear_map.apply_zero_curry0" -> "analysis", "continuous_linear_equiv.continuous_at" -> "topology", "measure_theory.l1.simple_func.measurable" -> "analysis", "onote.NF_below.lt" -> "set_theory", "real.convex_iff_ord_connected" -> "analysis", "finset.Ico.disjoint_consecutive" -> "data", "interval_integral.integral_add_adjacent_intervals" -> "analysis", "category_theory.adjunction.equiv_homset_left_of_nat_iso_symm_apply" -> "category_theory", "filter.has_basis.mem_uniformity_iff" -> "topology", "lt_Sup_iff" -> "order", "times_cont_mdiff_of_locally_times_cont_mdiff_on" -> "geometry", "int.lt_of_to_nat_lt" -> "data", "list.mem_of_mem_cons_of_mem" -> "data", "differentiable_at.ccosh" -> "analysis", "mv_power_series.coeff_zero" -> "algebra", "composition.strict_mono_boundary" -> "combinatorics", "norm_le_pi_norm" -> "analysis", "nat.one_lt_bit0" -> "init", "ring.fractional_ideal.ne_zero_of_mul_eq_one" -> "algebra", "polynomial.X_comp" -> "data", "has_deriv_within_at.ccosh" -> "analysis", "subgroup.le_def" -> "algebra", "one_div_le" -> "algebra", "equiv.computable.trans" -> "computability", "category_theory.limits.cone.whisker_X" -> "category_theory", "Gromov_Hausdorff.GH_dist_le_nonempty_compacts_dist" -> "topology", "list.erasep_map" -> "data", "times_cont_mdiff_within_at.prod_mk" -> "geometry", "nat.add_one_ne_zero" -> "init", "valuation.ext_iff" -> "algebra", "filter.is_countably_generated.tendsto_iff_seq_tendsto" -> "order", "monoid_algebra.prod_single" -> "data", "set.preimage_neg_Ici" -> "data", "filter.infi_sup_left" -> "order", "dfinsupp.mem_support_iff" -> "data", "eq_inv_iff_mul_eq_one" -> "algebra", "set.eval_image_pi" -> "data", "rat.add_left_neg" -> "data", "list.pairwise_middle" -> "data", "function.semiconj.id_right" -> "logic", "is_closed.frontier_eq" -> "topology", "measure_theory.exists_nonempty_inter_of_measure_univ_lt_tsum_measure" -> "analysis", "is_unit.map'" -> "algebra", "measure_theory.measure.sum_apply" -> "analysis", "nat.pred_le_iff" -> "data", "filter.map_neg" -> "topology", "multiset.powerset_len_le_powerset" -> "data", "nat.mul_div_mul" -> "init", "relation.trans_gen.trans" -> "logic", "ordinal.succ_lt_succ" -> "set_theory", "mv_power_series.coeff_index_single_X" -> "algebra", "real.zero_rpow_le_one" -> "analysis", "is_compact.binary_compact_cover" -> "topology", "option.mem_to_finset" -> "data", "principal_seg.lt_le_apply" -> "set_theory", "ennreal.sub_self" -> "data", "multiset.bind_zero" -> "data", "typevec.drop_fun_to_subtype" -> "data", "category_theory.monoidal_category.tensor_right_tensor_hom_app" -> "category_theory", "nat.eq_zero_of_add_eq_zero_left" -> "init", "localization.mul_equiv_of_quotient_symm_monoid_of" -> "algebra", "nnreal.sub_lt_self" -> "data", "nat.sqrt_eq" -> "data", "continuous_proj_I" -> "topology", "submonoid.sup_eq_range" -> "algebra", "nat.coprime.mul" -> "data", "has_fderiv_within_at.mul_const" -> "analysis", "order_bot.ext" -> "order", "category_theory.over.iterated_slice_backward_map" -> "category_theory", "is_R_or_C.norm_sq_conj" -> "data", "emetric.inf_edist_singleton" -> "topology", "list.chain.imp'" -> "data", "wseq.to_list_cons" -> "data", "alist.perm_insert" -> "data", "cardinal.not_countable_real" -> "data", "subalgebra.one_mem" -> "algebra", "differentiable_at_pow" -> "analysis", "nat.prime.two_le" -> "data", "pfunctor.liftr_iff" -> "data", "measure_theory.measure.le_add_right" -> "analysis", "category_theory.limits.types.filtered_colimit.colimit_eq_iff" -> "category_theory", "list.sum_cons" -> "data", "nnreal.coe_indicator" -> "data", "alg_hom.comp_to_linear_map" -> "algebra", "submodule.sub_mem" -> "algebra", "int.gcd_assoc" -> "algebra", "norm_num.int_cast_one" -> "tactic", "multiset.insert_eq_cons" -> "data", "dvd_pow" -> "algebra", "function.is_periodic_pt.apply_iterate" -> "dynamics", "polynomial.map_C" -> "data", "nat.div_mod_eq_mod_mul_div" -> "data", "int.le_of_coe_nat_le_coe_nat" -> "init", "function.const_apply" -> "logic", "measure_theory.inner_content_of_is_compact" -> "analysis", "finset.prod_cancels_of_partition_cancels" -> "algebra", "exists_mem_multiset_dvd_of_prime" -> "algebra", "nat.gcd_eq_gcd_ab" -> "data", "subring.coe_subtype" -> "algebra", "category_theory.limits.span_map_id" -> "category_theory", "nat.dvd_trans" -> "init", "category_theory.limits.prod.map_fst" -> "category_theory", "list.continuous_remove_nth" -> "topology", "add_add_sub_cancel" -> "algebra", "list.length_fin_range" -> "data", "set.ball_empty_iff" -> "data", "subsemiring.coe_coe" -> "algebra", "is_compl.left_unique" -> "order", "differentiable_at_id" -> "analysis", "list.map_reverse" -> "data", "has_deriv_at_interval_right_endpoint_of_tendsto_deriv" -> "analysis", "interval_integral.integral_interval_sub_interval_comm" -> "analysis", "differentiable.log" -> "analysis", "multiset.count_inter" -> "data", "continuous_linear_map.lmul_left_norm" -> "analysis", "formal_multilinear_series.comp_coeff_zero''" -> "analysis", "punit.smul_eq" -> "algebra", "and_iff_left_of_imp" -> "logic", "has_deriv_within_at.add_const" -> "analysis", "add_monoid_hom.mrestrict_apply" -> "algebra", "is_R_or_C.norm_sq_zero" -> "data", "list.nodup_iff_sublist" -> "data", "multiset.bind_map" -> "data", "continuous_linear_equiv.apply_symm_apply" -> "topology", "nat_ceil_zero" -> "algebra", "findim_euclidean_space_fin" -> "analysis", "eckmann_hilton.mul" -> "algebra", "set.to_finset_inter" -> "data", "nnreal.of_real_mul" -> "data", "uniformity_translate" -> "topology", "list.perm.subperm_left" -> "data", "gsmul_neg" -> "algebra", "affine_map.vadd_apply" -> "algebra", "continuous_linear_map.bound" -> "analysis", "set.mem_Ico" -> "data", "hyperreal.coe_div" -> "data", "asymptotics.is_O_with_comm" -> "analysis", "quotient.map\:2082'_mk'" -> "data", "ordinal.is_normal.inj" -> "set_theory", "exists_finite_card_le_of_finite_of_linear_independent_of_span" -> "algebra", "function.left_inverse.right_inverse" -> "logic", "omega.term.val_mul" -> "tactic", "infi_eq_infi_finset" -> "data", "right_ord_continuous.lt_iff" -> "order", "measure_theory.norm_integral_le_lintegral_norm" -> "analysis", "right_eq_inf" -> "order", "set.image_const_sub_Iic" -> "data", "set.nonempty.to_subtype" -> "data", "subgroup.coe_top" -> "algebra", "cau_seq.mul_apply" -> "data", "function.mem_fixed_points" -> "dynamics", "minimal_polynomial.min" -> "algebra", "nat.eq_of_mul_eq_mul_right" -> "data", "pos_num.cast_to_nat" -> "data", "has_ftaylor_series_up_to_on.mono" -> "analysis", "affine_subspace.span_univ" -> "algebra", "stream.tail_const" -> "data", "continuous_inf_rng" -> "topology", "bdd_below_singleton" -> "order", "filter.liminf_congr" -> "order", "list.head_cons" -> "data", "open_subgroup.mem_coe" -> "topology", "nat.sub_sub_self" -> "init", "category_theory.eq_of_comp_right_eq'" -> "category_theory", "filter.frequently_comap" -> "order", "category_theory.cocones_obj" -> "category_theory", "geom_series\:2082_def" -> "algebra", "multiset.card_sigma" -> "data", "set.preimage_const_add_Ici" -> "data", "multiset.pairwise_coe_iff_pairwise" -> "data", "list.filter_eq_nil" -> "data", "norm_num.nat_mod" -> "tactic", "primrec.nat_div" -> "computability", "list.erasep_cons" -> "data", "Ioc_mem_nhds_within_Iio" -> "topology", "tensor_product.lift_aux.smul" -> "algebra", "list.argmin_concat" -> "data", "ennreal.nhds_top" -> "topology", "continuous_on_of_uniform_approx_of_continuous_on" -> "topology", "unique_mdiff_within_at.inter" -> "geometry", "exists_imp_exists'" -> "logic", "add_subgroup.mem_top" -> "algebra", "set.mem_Union" -> "data", "nat.bodd_add" -> "init", "mul_eq_one_iff_inv_eq" -> "algebra", "list.argmin_singleton" -> "data", "cau_seq.cauchy" -> "data", "category_theory.limits.has_limit.iso_of_nat_iso_hom_\[Pi]" -> "category_theory", "finset.card_insert_of_mem" -> "data", "sym2.from_rel_proj_prop" -> "data", "int.nat_abs_mul" -> "data", "omega.coeffs.val_eq_zero" -> "tactic", "finite_dimensional_of_dim_eq_zero" -> "algebra", "linear_map.id_coe" -> "algebra", "rat.mul_num" -> "data", "set.forall_prod_set" -> "data", "int.lt_add_of_pos_right" -> "init", "submodule.smul_le_right" -> "algebra", "polynomial.sum_over_range" -> "data", "stream.map_eq" -> "data", "set.range_ite_subset'" -> "data", "power_series.coeff_inv_of_unit" -> "algebra", "add_comm_group.direct_limit.of.zero_exact" -> "algebra", "mv_polynomial.degrees_indicator" -> "algebra", "int.cast_pow" -> "algebra", "set.Inter_subset" -> "data", "norm_image_sub_le_of_norm_deriv_le_segment" -> "analysis", "list.lookup_all_cons_ne" -> "data", "is_null_measurable.compl" -> "analysis", "multiset.coe_pmap" -> "data", "tendsto_nhds_within_of_tendsto_nhds" -> "topology", "equiv.perm.sign_one" -> "algebra", "ideal.span_le" -> "algebra", "ennreal.zero_lt_coe_iff" -> "data", "local_equiv.of_set_symm" -> "data", "add_subgroup.closure_eq" -> "algebra", "gcd_zero_right" -> "algebra", "pequiv.of_set_eq_refl" -> "data", "infi_true" -> "order", "nat.odd_of_mod_four_eq_one" -> "data", "list.sublist.subperm" -> "data", "tactic.ring.zero_horner" -> "tactic", "typevec.split_fun_comp" -> "data", "category_theory.limits.cone_left_op_of_cocone_X" -> "category_theory", "set.preimage_sub_const_Ioi" -> "data", "structure_groupoid.locality" -> "geometry", "znum.neg_of_int" -> "data", "multiset.sizeof_lt_sizeof_of_mem" -> "data", "continuous_multilinear_map.bounds_nonempty" -> "analysis", "deriv_neg'" -> "analysis", "vector.to_list_append" -> "data", "padic.of_rat_mul" -> "data", "isometry.injective" -> "topology", "ctop.realizer.mem_nhds" -> "data", "continuous_linear_map.coe_neg" -> "topology", "real.sinh_bijective" -> "analysis", "nat.partrec.some" -> "computability", "set.bij_on_empty" -> "data", "submonoid.gc_map_comap" -> "algebra", "onote.omega_le_oadd" -> "set_theory", "is_coprime.of_add_mul_left_right" -> "algebra", "function.minimal_period_pos_iff_mem_periodic_pts" -> "dynamics", "onote.lt_def" -> "set_theory", "euclidean_geometry.orthogonal_projection_mem_orthogonal" -> "geometry", "local_homeomorph.is_O_with_congr" -> "analysis", "finset.card_insert_le" -> "data", "polynomial.coeff_zero_eq_aeval_zero" -> "data", "list.suffix_iff_eq_append" -> "data", "nhds_within_restrict'" -> "topology", "multiset.not_mem_range_self" -> "data", "multiset.comp_traverse" -> "data", "polynomial.X_sub_C_ne_zero" -> "data", "is_coprime.mul_left" -> "algebra", "setoid.ker_iff_mem_preimage" -> "data", "rat.num_pos_iff_pos" -> "data", "mv_power_series.mul_one" -> "algebra", "polynomial.coeff_C_zero" -> "data", "monotone.le_map_sup" -> "order", "continuous_on_iff_is_closed" -> "topology", "ideal.add_mem_iff_left" -> "algebra", "linear_map.infi_ker_proj" -> "algebra", "metric.diam_nonneg" -> "topology", "quotient.map_mk" -> "data", "rel_embedding.is_trans" -> "order", "finset.singleton_bind" -> "data", "half_sub" -> "algebra", "list.rel_of_pairwise_cons" -> "data", "measure_theory.simple_func.lintegral_congr" -> "analysis", "int.gcd_mul_right" -> "algebra", "turing.TM2.stmts_supports_stmt" -> "computability", "filter.mem_sup_sets" -> "order", "add_subgroup.mem_sup_right" -> "algebra", "finset.sum_sdiff" -> "algebra", "norm_pos_iff" -> "analysis", "ext_chart_preimage_inter_eq" -> "geometry", "norm_num.nat_cast_bit1" -> "tactic", "fin.le_def" -> "init", "emetric.mem_nhds_iff" -> "topology", "nat.lt_trichotomy" -> "init", "set.empty_ne_univ" -> "data", "with_zero.mul_zero" -> "algebra", "minimal_polynomial.one" -> "algebra", "multiset.cons_coe" -> "data", "ordinal.limit_rec_on_limit" -> "set_theory", "ordinal.card_le_nat" -> "set_theory", "filter.is_countably_generated_of_seq" -> "order", "affine_subspace.vsub_mem_direction" -> "algebra", "enat.to_with_top_top" -> "data", "list.Ico.filter_le_of_top_le" -> "data", "pgame.first_loses_of_equiv" -> "set_theory", "padic_norm_e.triangle_ineq" -> "data", "category_theory.limits.types.coprod_inr" -> "category_theory", "fintype.prod_congr" -> "data", "power_series.coeff_inv" -> "algebra", "one_one_reducible_refl" -> "computability", "set.image2_mul" -> "algebra", "measure_theory.measure_sUnion" -> "analysis", "measure_theory.ae_eq_fun.edist_mk_mk" -> "analysis", "computation.empty_orelse" -> "data", "supr_congr_Prop" -> "order", "finset.card_mk" -> "data", "category_theory.nat_iso.app_hom" -> "category_theory", "measure_theory.simple_func.range_map" -> "analysis", "traversable.mfoldr_to_list" -> "control", "nat.le_succ" -> "init", "onote.NF.fst" -> "set_theory", "seq.map_nth" -> "data", "gpow_eq_mod_order_of" -> "algebra", "primrec.and" -> "computability", "is_add_subgroup_Union_of_directed" -> "algebra", "pell.eq_of_xn_modeq'" -> "number_theory", "complex.tan_of_real_re" -> "data", "category_theory.limits.colimit.pre_pre" -> "category_theory", "set.mem_Ioo_or_eq_endpoints_of_mem_Icc" -> "data", "is_local_min.comp_mono" -> "topology", "computation.thinkN_equiv" -> "data", "seq.ext" -> "data", "is_coprime.of_add_mul_left_left" -> "algebra", "ideal.jacobson_mono" -> "algebra", "times_cont_diff_at.of_le" -> "analysis", "computation.results_bind" -> "data", "padic_int.valuation_one" -> "data", "multiset.Ico.mem" -> "data", "left_ord_continuous.coe_to_order_embedding" -> "order", "polynomial.zero_comp" -> "data", "circle_deg1_lift.dist_pow_map_zero_mul_translation_number_le" -> "dynamics", "linear_independent.union" -> "algebra", "set.mem_range" -> "data", "direct_sum.apply_eq_component" -> "algebra", "is_min_filter_dual_iff" -> "order", "topological_fiber_bundle_core.is_open_map_proj" -> "topology", "Gromov_Hausdorff.Hausdorff_dist_optimal" -> "topology", "sum_range_diag_flip" -> "data", "free_group.red.enum.sound" -> "algebra", "ring_hom.eq_of_eq_on_stop" -> "algebra", "measure_theory.extend_Union_nat" -> "analysis", "computation.parallel_congr_right" -> "data", "category_theory.preadditive.comp_neg_assoc" -> "category_theory", "gsmul_sub" -> "algebra", "polynomial.coe_zero" -> "algebra", "category_theory.limits.cone.category_to_category_struct_to_has_hom_hom" -> "category_theory", "finset.map_eq_empty" -> "data", "power_series.trunc_zero" -> "algebra", "polynomial.C_inj" -> "data", "filter.antimono_seq_of_seq" -> "order", "measurable.inv" -> "analysis", "add_monoid_hom.map_add_eq_zero" -> "algebra", "subalgebra.is_algebraic_iff" -> "algebra", "ideal.ne_top_iff_one" -> "algebra", "measure_theory.is_left_invariant_conj'" -> "analysis", "interval_integral.integral_has_deriv_within_at_left" -> "analysis", "alg_equiv.to_lie_equiv_symm_apply" -> "algebra", "multiplicity.int.coe_nat_multiplicity" -> "algebra", "circle_deg1_lift.map_map_zero_lt" -> "dynamics", "matrix.reindex_linear_equiv_apply" -> "algebra", "list.append_sublist_append_left" -> "data", "is_R_or_C.mul_conj" -> "data", "frobenius_zero" -> "algebra", "metric.Hausdorff_dist_self_closure" -> "topology", "matrix.induction_on'" -> "data", "mvqpf.cofix.bisim\:2082" -> "data", "pnat.dvd_gcd" -> "data", "list.pairwise_gt_iota" -> "data", "rel.inv_id" -> "data", "multilinear_map.mk_pi_ring_apply" -> "algebra", "multiset.card_map" -> "data", "many_one_reducible.trans" -> "computability", "subsemiring.coe_to_submonoid" -> "algebra", "pfunctor.M.ext_aux" -> "data", "alg_hom.map_sum" -> "algebra", "tsum_geometric_of_abs_lt_1" -> "analysis", "computation.length_think" -> "data", "multiset.nodup_iff_count_le_one" -> "data", "list.erase_dup_cons_of_mem'" -> "data", "continuous_within_at.preimage_mem_nhds_within'" -> "topology", "wseq.mem_cons_iff" -> "data", "polynomial.map_X" -> "data", "rel.preimage_def" -> "data", "real.exp_lt_one_iff" -> "data", "is_unit_of_invertible" -> "algebra", "mul_equiv.to_CommMon_iso_inv" -> "algebra", "local_homeomorph.prod_coe_symm" -> "topology", "complex.cpow_one" -> "analysis", "rel.core_preimage_gc" -> "data", "char_p.cast_eq_mod" -> "algebra", "tendsto_at_top_csupr" -> "topology", "set.bex_image_iff" -> "data", "cardinal.lift_add" -> "set_theory", "real.continuous_exp" -> "analysis", "polynomial.roots_X_sub_C" -> "data", "function.iterate_succ_apply'" -> "logic", "structure_groupoid.local_invariant_prop.lift_prop_on_chart" -> "geometry", "is_separated_def'" -> "topology", "antilipschitz_with.to_right_inverse" -> "topology", "is_cyclic.image_range_card" -> "algebra", "has_fderiv_at_filter.has_deriv_at_filter" -> "analysis", "continuous_linear_map.coe_comp'" -> "topology", "local_homeomorph.subtype_restr_source" -> "topology", "onote.NF_repr_split'" -> "set_theory", "interval_integral.integral_has_strict_deriv_at_right" -> "analysis", "computable.bind_decode_iff" -> "computability", "category_theory.limits.is_colimit.cocone_points_iso_of_equivalence_hom" -> "category_theory", "one_dvd" -> "algebra", "list.pairwise_append" -> "data", "tactic.abel.term_atom" -> "tactic", "polynomial.expand_mul" -> "algebra", "edist_eq_zero" -> "topology", "set.union_inter_cancel_left" -> "data", "finset.disjoint_iff_ne" -> "data", "category_theory.prod_comp" -> "category_theory", "isometric.symm_apply_eq" -> "topology", "composition.ones_blocks_fun" -> "combinatorics", "nat.pow_le_iff_le_left" -> "data", "relation.refl_trans_gen_eq_self" -> "logic", "nat.pow_lt_iff_lt_right" -> "data", "differentiable.comp" -> "analysis", "caratheodory.shrink" -> "analysis", "multiset.pi_zero" -> "data", "is_glb_Ici" -> "order", "differentiable_on.const_add" -> "analysis", "char_p.ring_char_ne_one" -> "algebra", "option.map_eq_some" -> "data", "add_monoid.closure_subset" -> "algebra", "finsupp.single_of_emb_domain_single" -> "data", "finmap.mem_lookup_union_middle" -> "data", "category_theory.limits.is_colimit.hom_iso_hom" -> "category_theory", "measure_theory.simple_func.fin_meas_supp.map\:2082" -> "analysis", "real.angle.cos_eq_iff_eq_or_eq_neg" -> "analysis", "commute.neg_right_iff" -> "algebra", "finsupp.sum_fintype" -> "data", "finset.sum_filter_of_ne" -> "algebra", "filter.eventually.prod_inl_nhds" -> "topology", "polynomial.expand_monomial" -> "algebra", "complex.of_real_cos" -> "data", "not_forall_not" -> "logic", "function.surjective.forall\:2082" -> "logic", "matrix.row_smul" -> "data", "of_mul_to_mul" -> "algebra", "list.modify_nth_tail_length" -> "data", "char_poly_coeff_eq_prod_coeff_of_le" -> "algebra", "filter.is_countably_generated.comap" -> "order", "topological_space.seq_tendsto_iff" -> "topology", "is_min_filter.filter_mono" -> "order", "list.subset.trans" -> "init", "roption.get_mem" -> "data", "measure_theory.simple_func.map_lintegral" -> "analysis", "category_theory.limits.pullback_cone.equalizer_ext" -> "category_theory", "path_component.nonempty" -> "topology", "div_mul_cancel" -> "algebra", "multiset.prod_map_sum" -> "data", "norm_num.min_fac_helper_0" -> "tactic", "add_monoid_hom.coe_mrange_restrict" -> "algebra", "list.pw_filter_map" -> "data", "continuous_linear_map.mem_ker" -> "topology", "real.arcsin_eq_pi_div_two_sub_arccos" -> "analysis", "nat.partrec.code.evaln_prim" -> "computability", "list.ordered_insert_length" -> "data", "mul_ne_zero" -> "algebra", "equiv.swap_mul_self" -> "data", "continuous_coinduced_rng" -> "topology", "add_subgroup.coe_neg" -> "algebra", "nat.fpow_ne_zero_of_pos" -> "algebra", "continuous_multilinear_map.map_coord_zero" -> "topology", "nat.mul_assoc" -> "init", "continuous_on.preimage_interior_subset_interior_preimage" -> "topology", "mv_polynomial.coeff_eq_zero_of_total_degree_lt" -> "data", "is_R_or_C.abs_im_div_abs_le_one" -> "data", "finset.sup_subset" -> "data", "category_theory.limits.prod.pentagon" -> "category_theory", "pnat.mul_coe" -> "data", "category_theory.limits.coprod.right_unitor_hom" -> "category_theory", "nnreal.mul_eq_mul_left" -> "data", "multiset.rel_eq" -> "data", "finsupp.map_domain_comp" -> "data", "add_group.mclosure_neg_subset" -> "algebra", "list.subperm.antisymm" -> "data", "primrec.nat_sub" -> "computability", "localization_map.mk'_mul_mk'_eq_one" -> "algebra", "lie_algebra.special_linear.sl_bracket" -> "algebra", "submonoid.localization_map.of_mul_equiv_of_localizations_id" -> "algebra", "category_theory.functor.as_equivalence_inverse" -> "category_theory", "generalized_continued_fraction.denominators_recurrence" -> "algebra", "mv_polynomial.rename_X" -> "data", "cau_seq.lt_trans" -> "data", "submodule.mapq_mkq" -> "algebra", "free_group.of.inj" -> "algebra", "subsemiring.mem_coe" -> "algebra", "tendsto_of_monotone" -> "topology", "holor.mul_left_distrib" -> "data", "quotient_group.lift_mk" -> "algebra", "category_theory.limits.cocones.precompose_obj_\[Iota]" -> "category_theory", "gaussian_int.prime_of_nat_prime_of_mod_four_eq_three" -> "data", "continuous_multilinear_map.le_op_norm" -> "analysis", "monotone.supr_comp_eq" -> "order", "bdd_above_Ioo" -> "order", "generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp" -> "algebra", "set.subset_compl_comm" -> "data", "category_theory.iso.refl_symm" -> "category_theory", "rat.num_dvd" -> "data", "has_mfderiv_at.has_mfderiv_within_at" -> "geometry", "category_theory.prod_id_fst" -> "category_theory", "dioph.ext" -> "number_theory", "nat.min_fac_le" -> "data", "hyperreal.st_id_real" -> "data", "set.preimage_add_left_zero'" -> "algebra", "norm_tsum_le_tsum_norm" -> "analysis", "is_unit_iff_exists_inv" -> "algebra", "function.inv_on_fixed_pts_comp" -> "dynamics", "submodule.span_singleton_eq_bot" -> "algebra", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp_assoc" -> "category_theory", "category_theory.non_preadditive_abelian.epi_of_zero_cancel" -> "category_theory", "summable_nat_add_iff" -> "topology", "opposite.unop_eq_one_iff" -> "algebra", "matrix.transpose_neg" -> "data", "group.conjugates_of_set_subset'" -> "algebra", "inner_product_geometry.inner_eq_zero_iff_angle_eq_pi_div_two" -> "geometry", "Exists.imp" -> "logic", "has_deriv_at_filter.prod" -> "analysis", "eq_inv_iff_eq_inv" -> "algebra", "list.smul_sum" -> "algebra", "continuous_multilinear_map.map_piecewise_add" -> "topology", "continuous_mul" -> "topology", "set.bUnion_inter" -> "data", "eleven_dvd_iff" -> "data", "ordinal.CNF_pairwise_aux" -> "set_theory", "local_equiv.bij_on_source" -> "data", "semiconj_by.inv_right" -> "algebra", "convex.prod" -> "analysis", "subgroup.normal.mem_comm_iff" -> "algebra", "monotone.mul_strict_mono'" -> "algebra", "mul_action.injective_of_quotient_stabilizer" -> "algebra", "pgame.lt_iff_sub_pos" -> "set_theory", "local_equiv.restr_trans" -> "data", "with_top.zero_ne_top" -> "algebra", "set.compl_neg" -> "algebra", "multiset.le_sup" -> "data", "is_least.lower_bounds_eq" -> "order", "ring_hom.iterate_map_mul" -> "algebra", "has_mfderiv_at.comp" -> "geometry", "affine_map.continuous_iff" -> "topology", "measure_theory.measure_mono_null" -> "analysis", "complex.arg_one" -> "analysis", "real.rpow_nat_cast" -> "analysis", "set.indicator_of_mem" -> "data", "polynomial.continuous_eval" -> "topology", "category_theory.monoidal_category.unitors_equal.cells_4" -> "category_theory", "submonoid.map_comap_map" -> "algebra", "commute.self_fpow" -> "algebra", "denom_dvd_of_is_root" -> "algebra", "ne_iff_lt_or_gt" -> "init", "function.is_periodic_pt.mod" -> "dynamics", "nat.coprime.dvd_of_dvd_mul_right" -> "data", "ordinal.add_mul_limit" -> "set_theory", "nat.coprime.coprime_dvd_left" -> "data", "submodule.subtype_apply" -> "algebra", "nat.gcd_assoc" -> "data", "fin.coe_add" -> "data", "equiv.forall\:2083_congr'" -> "data", "primrec.of_equiv_symm" -> "computability", "sum.inl.inj_iff" -> "data", "list.Ico.filter_le" -> "data", "totally_bounded_of_forall_symm" -> "topology", "mem_nhds_induced" -> "topology", "matrix.reindex_transpose" -> "algebra", "set.Iio_diff_Iic" -> "data", "distrib_mul_action_hom.id_apply" -> "algebra", "measurable_equiv.coe_eq" -> "analysis", "emetric.Hausdorff_edist_closure" -> "topology", "matrix.update_column_apply" -> "data", "nhds_eq_uniformity_prod" -> "topology", "list.take_length" -> "data", "auto.not_exists_eq" -> "tactic", "list.merge_sort_cons_cons" -> "data", "nat.partrec.code.encode_lt_pair" -> "computability", "nat.prime.dvd_mul" -> "data", "list.mem_cons_iff" -> "init", "set.insert_subset_insert" -> "data", "linarith.mul_eq" -> "tactic", "set.left_inv_on.surj_on" -> "data", "enat.get_one" -> "data", "finmap.lookup_union_left" -> "data", "linear_map.compr\:2082_apply" -> "algebra", "equiv.mul_right_symm" -> "data", "list.Ico.eq_empty_iff" -> "data", "tactic.ring.horner_add_horner_eq" -> "tactic", "continuous_within_at_Icc_iff_Ici" -> "topology", "list.argmax_cons" -> "data", "neg_lt_sub_iff_lt_add'" -> "algebra", "circle_deg1_lift.map_int_add" -> "dynamics", "tactic.ring.const_add_horner" -> "tactic", "category_theory.limits.colimit.post_post" -> "category_theory", "computation.promises_congr" -> "data", "polynomial.irreducible_X_sub_C" -> "data", "caratheodory.shrink'" -> "analysis", "tactic.interactive.generalize_a_aux" -> "tactic", "add_monoid_hom.map_add" -> "algebra", "zmod.int_cast_surjective" -> "data", "real.has_deriv_at_rpow_zero_of_one_le" -> "analysis", "polynomial.coeff_monomial_zero_mul" -> "data", "equiv.sigma_congr_left_apply" -> "data", "measurable_inr" -> "analysis", "right_ord_continuous.mono" -> "order", "list.forall_mem_nil" -> "data", "nat.pow_add" -> "data", "lie_algebra.of_associative_algebra_hom_id" -> "algebra", "fin.init_update_last" -> "data", "subgroup.ext" -> "algebra", "multilinear_map.uncurry_curry_left" -> "algebra", "finset.prod_eq_fold" -> "algebra", "is_closed_bUnion" -> "topology", "add_semiconj_by.units_neg_symm_left" -> "algebra", "forall_prop_of_false" -> "logic", "ennreal.none_eq_top" -> "data", "nat.with_bot.coe_nonneg" -> "data", "add_monoid_hom.eq_of_eq_on_mdense" -> "algebra", "string.iterator.next_to_string_mk_iterator" -> "init", "mul_right_surjective" -> "algebra", "AddCommGroup.zero_apply" -> "algebra", "irrational.of_one_div" -> "data", "emetric.inf_edist_le_Hausdorff_edist_of_mem" -> "topology", "nat.prime.pred_pos" -> "data", "alist.lookup_is_some" -> "data", "int.sqrt_eq" -> "data", "list.mmap_with_index'_aux_eq_mmap_with_index_aux" -> "data", "category_theory.monoidal_functor.id_to_lax_monoidal_functor_\[CurlyEpsilon]" -> "category_theory", "deriv.lhopital_zero_right_on_Ico" -> "analysis", "submodule.mem_map_equiv" -> "algebra", "function.commute.iterate_pos_lt_of_map_lt'" -> "order", "continuous_linear_map.homothety_norm" -> "analysis", "ennreal.embedding_coe" -> "topology", "eventually_eventually_le_nhds" -> "topology", "multiset.sigma_add" -> "data", "is_submonoid.coe_pow" -> "algebra", "measure_theory.outer_measure.measure_inter_union" -> "analysis", "continuous_within_at.congr_of_eventually_eq" -> "topology", "category_theory.limits.map_pair_left" -> "category_theory", "traversable.to_list_spec" -> "control", "list.nth_modify_nth_ne" -> "data", "filter.is_ultrafilter.eventually_not" -> "order", "finsupp.map_domain_apply" -> "data", "pell.is_pell_norm" -> "number_theory", "multiset.cons_ne_zero" -> "data", "dfinsupp.sum_sum_index" -> "data", "neg_le_self" -> "algebra", "hyperreal.is_st_of_tendsto" -> "data", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge" -> "analysis", "computation.results_of_terminates'" -> "data", "power_series.constant_coeff_comp_C" -> "algebra", "cau_seq.lt_total" -> "data", "metric.emetric_ball" -> "topology", "fish_pipe" -> "control", "polynomial.coe_expand" -> "algebra", "finset.filter_eq'" -> "data", "filter.ne_bot.prod" -> "order", "measure_theory.measure.finite_at_filter.filter_mono_ae" -> "analysis", "measure_theory.ae_eq_fun.comp_eq_mk" -> "analysis", "lie_algebra.orthogonal.S_as_blocks" -> "algebra", "ideal.add_mem" -> "algebra", "int.mul_mod_left" -> "data", "convex_on_rpow" -> "analysis", "nat.bitwise_comm" -> "data", "mem_nhds_within_Iio_iff_exists_Ioo_subset'" -> "topology", "finset.image_union" -> "data", "cardinal.sup_eq_zero" -> "set_theory", "commute.gpow_gpow" -> "algebra", "tendsto_of_tendsto_of_tendsto_of_le_of_le" -> "topology", "lt_mul_iff_one_lt_left'" -> "algebra", "continuous_multilinear_map.norm_restr" -> "analysis", "category_theory.adjunction.hom_equiv_apply_eq" -> "category_theory", "category_theory.limits.kernel_not_iso_of_nonzero" -> "category_theory", "not_tendsto_at_top_of_tendsto_nhds" -> "topology", "nat.primrec'.comp'" -> "computability", "measure_theory.l1.simple_func.of_simple_func_eq_of_fun" -> "analysis", "alg_hom.map_nat_cast" -> "algebra", "wseq.append_nil" -> "data", "category_theory.limits.limit.map_pre'" -> "category_theory", "finset.card_le_of_inj_on" -> "data", "computation.head_ret" -> "data", "ideal.is_jacobson_of_surjective" -> "algebra", "enat.coe_get" -> "data", "complex.exp_eq_exp_iff_exp_sub_eq_one" -> "analysis", "exists_comm" -> "logic", "asymptotics.is_o_prod_left" -> "analysis", "mvqpf.cofix.abs_repr" -> "data", "is_seq_closed_of_is_closed" -> "topology", "module.direct_limit.to_module_totalize_of_le" -> "algebra", "set.exists_min_image" -> "data", "has_fderiv_within_at.fderiv_within" -> "analysis", "real.young_inequality" -> "analysis", "dioph.pow_dioph" -> "number_theory", "mul_equiv.map_eq_one_iff" -> "data", "multiset.rel_flip_eq" -> "data", "subgroup.normal_closure_eq_infi" -> "algebra", "has_strict_fderiv_at.congr_of_eventually_eq" -> "analysis", "cInf_le_of_le" -> "order", "ideal.is_maximal.eq_of_le" -> "algebra", "Gromov_Hausdorff.GH_dist_le_of_approx_subsets" -> "topology", "opposite.unop_neg" -> "algebra", "nat.div_eq_of_eq_mul_right" -> "init", "charted_space_self_atlas" -> "geometry", "ordinal.one_eq_lift_type_unit" -> "set_theory", "circle_deg1_lift.dist_map_zero_translation_number_le" -> "dynamics", "int.le_antisymm" -> "init", "set.union_diff_self" -> "data", "ennreal.inv_le_inv" -> "data", "category_theory.limits.wide_pushout_shape.wide_span_map" -> "category_theory", "set.subset_eq_empty" -> "data", "function.surjective.supr_comp" -> "order", "pos_num.nat_size_to_nat" -> "data", "Ioc_mem_nhds_within_Ici" -> "topology", "measure_theory.simple_func.support_eq" -> "analysis", "equiv.point_reflection_fixed_iff_of_bit0_injective" -> "data", "bilin_form.to_matrix_comp_right" -> "algebra", "has_sum.map" -> "topology", "fderiv_within_mul" -> "analysis", "turing.TM1.stmts_trans" -> "computability", "int.eq_one_of_mul_eq_self_left" -> "init", "mv_power_series.constant_coeff_inv_of_unit" -> "algebra", "int.sign_eq_one_iff_pos" -> "init", "hash_map.append_of_modify" -> "data", "derivation.map_one_eq_zero" -> "algebra", "supr_congr" -> "order", "prod.fst_vsub" -> "algebra", "linear_map.trace_mul_comm" -> "algebra", "add_units.coe_lift_right" -> "algebra", "Class.iota_ex" -> "set_theory", "finsupp.single_eq_same" -> "data", "list.kextract_eq_lookup_kerase" -> "data", "nat.prime.sum_two_squares" -> "number_theory", "int.gcd_zero_right" -> "algebra", "primrec.option_some_iff" -> "computability", "nat.min_fac_eq" -> "data", "iff_self" -> "init", "rec_heq_of_heq" -> "logic", "real.continuous_rpow_aux3" -> "analysis", "list.rel_nodup" -> "data", "cau_seq.le_antisymm" -> "data", "mv_polynomial.coeff_zero_X" -> "data", "polynomial.map_comp" -> "data", "category_theory.preimage_comp" -> "category_theory", "category_theory.whiskering_left_obj_map" -> "category_theory", "is_null_measurable.diff_null" -> "analysis", "category_theory.eq_to_iso_map" -> "category_theory", "ulower.up_down" -> "data", "has_fderiv_at_filter.add_const" -> "analysis", "algebra.tensor_product.mul_aux_apply" -> "algebra", "measure_theory.lintegral_edist_triangle" -> "analysis", "primrec.list_find_index" -> "computability", "zmod.cast_mul" -> "data", "filter.subtype_coe_map_comap" -> "order", "nnreal.rpow_lt_one_of_one_lt_of_neg" -> "analysis", "qpf.Wequiv.refl" -> "data", "gsmul_zero" -> "algebra", "ideal.bot_is_maximal" -> "algebra", "eq_add_of_add_neg_eq" -> "algebra", "subsemiring.coe_supr_of_directed" -> "algebra", "norm_num.mul_bit1_bit1" -> "tactic", "ring_hom.map_list_sum" -> "algebra", "times_cont_diff_at.continuous_at" -> "analysis", "int.div_le_self" -> "data", "classical.dec_pred" -> "logic", "is_local_max_on.sub" -> "topology", "findim_bot" -> "algebra", "fderiv_snd" -> "analysis", "category_theory.limits.binary_bicone.to_cone_\[Pi]_app_left" -> "category_theory", "cardinal.bit0_lt_bit1" -> "set_theory", "filter.principal_mono" -> "order", "measure_theory.l1.coe_zero" -> "analysis", "pfunctor.M.ext'" -> "data", "fderiv_within_deriv_within" -> "analysis", "primrec.nat_le" -> "computability", "asymptotics.is_O_with.const_mul_right'" -> "analysis", "nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul" -> "data", "real.sinh_injective" -> "analysis", "div_lt_iff" -> "algebra", "add_smul" -> "algebra", "pmf.pure_apply" -> "analysis", "circle_deg1_lift.translate_apply" -> "dynamics", "interval_integral.integral_Iic_sub_Iic" -> "analysis", "set.monotone_preimage" -> "data", "pgame.neg_congr" -> "set_theory", "fintype.prod_bool" -> "data", "list.chain'_pair" -> "data", "filter.germ.coe_smul'" -> "order", "padic_norm_e.norm_int_lt_pow_iff_dvd" -> "data", "pnat.pow_coe" -> "data", "mv_polynomial.coe_eval\:2082_hom" -> "data", "equiv.perm.is_cycle_swap" -> "algebra", "zero_mul" -> "algebra", "nnreal.tendsto_const_div_at_top_nhds_0_nat" -> "analysis", "times_cont_mdiff_at.of_le" -> "geometry", "continuous_linear_map.extend_unique" -> "analysis", "continuous_iff_coinduced_le" -> "topology", "heq_of_eq_of_heq" -> "init", "has_deriv_within_at.liminf_right_norm_slope_le" -> "analysis", "circle_deg1_lift.translation_number_lt_of_forall_lt_add" -> "dynamics", "set.union_compl_self" -> "data", "times_cont_mdiff_on_univ" -> "geometry", "list.sublists'_cons" -> "data", "frontier_compl" -> "topology", "le_min_iff" -> "algebra", "multiset.card_sub" -> "data", "free_abelian_group.zero_bind" -> "algebra", "lt_div_iff_of_neg" -> "algebra", "midpoint_add_right" -> "algebra", "has_fderiv_within_at.lim" -> "analysis", "set.Ico_union_Ico_eq_Ico" -> "data", "bilin_form.comp_right_apply" -> "algebra", "is_measurable_Icc" -> "analysis", "omega.int.is_nnf_nnf" -> "tactic", "free_semigroup.pure_bind" -> "algebra", "add_eq_zero_iff_eq_neg" -> "algebra", "category_theory.limits.colimit.cocone_morphism_hom" -> "category_theory", "nat.bit_decomp" -> "init", "iff_subst" -> "init", "is_add_group_hom.trivial_ker_of_injective" -> "algebra", "nat.add_sub_cancel_left" -> "init", "category_theory.sum.swap_map_inl" -> "category_theory", "equiv.perm.sign_prod_list_swap" -> "algebra", "vsub_set_mono" -> "algebra", "interval_integral.integral_same" -> "analysis", "isometric.neg_to_equiv" -> "topology", "set.subset_union_of_subset_left" -> "data", "add_monoid_hom.map_mrange" -> "algebra", "lfp_induct" -> "order", "cardinal.lift_omega" -> "set_theory", "category_theory.congr_app" -> "category_theory", "dist_sub_right" -> "analysis", "ordinal.power_succ" -> "set_theory", "not_and_distrib" -> "logic", "iterated_deriv_one" -> "analysis", "qpf.cofix.bisim_rel" -> "data", "continuous_swap" -> "topology", "open_mapping" -> "analysis", "add_subgroup.mem_infi" -> "algebra", "finset.tsum_subtype" -> "topology", "Module.Mon_Module_equivalence_Algebra.ring_mul" -> "category_theory", "category_theory.over.iterated_slice_equiv_unit_iso" -> "category_theory", "bilin_form.to_quadratic_form_apply" -> "algebra", "metric.bounded_of_compact_space" -> "topology", "pfun.coe_val" -> "data", "set.preimage_sub_const_Iio" -> "data", "set.ord_connected_dual" -> "data", "set.not_mem_of_mem_diff" -> "data", "polynomial.sum_C_index" -> "data", "real.cosh_pos" -> "data", "filter.nonempty_of_ne_bot" -> "order", "bool.eq_tt_of_ne_ff" -> "data", "Module.coe_of" -> "algebra", "finset.sdiff_self" -> "data", "measurable_neg_iff" -> "analysis", "padic_int.is_unit_iff" -> "data", "zero_lt_two" -> "algebra", "polynomial.leading_coeff_eq_zero" -> "data", "lt_of_sub_pos" -> "algebra", "set.Union_range_eq_sUnion" -> "data", "category_theory.equivalence.trans_counit_iso" -> "category_theory", "filter.mem_lift_sets" -> "order", "submodule.exists_finset_of_mem_supr" -> "algebra", "ordinal.nat_le_card" -> "set_theory", "category_theory.limits.binary_cofan.is_colimit.desc'_val" -> "category_theory", "not_ball" -> "logic", "affine.triangle.orthocenter_eq_monge_point" -> "geometry", "metric.closed_ball_subset_closed_ball" -> "topology", "wseq.destruct_map" -> "data", "tactic.abel.unfold_gsmul" -> "tactic", "category_theory.iso.conj_id" -> "category_theory", "rel_iso.ext" -> "order", "finsupp.erase_add_single" -> "data", "is_basis.equiv_fun_self" -> "algebra", "continuous_linear_map.sub_apply" -> "topology", "pos_num.cast_bit0" -> "data", "nat.partrec'.to_part" -> "computability", "category_theory.comma.map_left_map_left" -> "category_theory", "polynomial.coeff_one" -> "data", "norm_unit_mul_norm_unit" -> "algebra", "or.left_comm" -> "init", "set.prod_subset_iff" -> "data", "is_glb_of_mem_nhds" -> "topology", "add_magma.free_add_semigroup.of_add_assoc_right" -> "algebra", "differentiable_on_const" -> "analysis", "homological_complex.homology_map_condition" -> "algebra", "embedding_inr" -> "topology", "category_theory.currying_inverse_obj_obj_obj" -> "category_theory", "int.modeq.coe_nat_modeq_iff" -> "data", "algebraic_geometry.structure_sheaf_stalk_to_fiber_surjective" -> "algebraic_geometry", "linear_map.smul_apply" -> "algebra", "set.card_lt_card" -> "data", "category_theory.nat_trans.sum_app_inl" -> "category_theory", "is_closed.Sup_mem" -> "topology", "list.id_traverse" -> "control", "add_le_of_nonpos_of_le" -> "algebra", "nat.zero_ne_bit1" -> "init", "pell.xn_modeq_x2n_sub_lem" -> "number_theory", "real.arith_mean_le_rpow_mean" -> "analysis", "multiset.cons_ndunion" -> "data", "mvqpf.supp_preservation_iff_uniform" -> "data", "Gromov_Hausdorff.isometry_optimal_GH_injr" -> "topology", "cau_seq.completion.zero_ne_one" -> "data", "linear_independent_empty" -> "algebra", "multiset.coe_product" -> "data", "list.sorted.tail" -> "data", "std_simplex_subset_closed_ball" -> "analysis", "asymptotics.is_O_with.right_le_sub_of_lt_1" -> "analysis", "mem_nhds_uniformity_iff_right" -> "topology", "finset.map_embedding_apply" -> "data", "set.countable_Union" -> "data", "ideal.span_eq_bot" -> "algebra", "filter.is_basis.has_basis" -> "order", "coinduced_compose" -> "topology", "is_lub_bsupr" -> "order", "subtype.ext_iff_val" -> "data", "padic.valuation_p" -> "data", "submodule.linear_proj_of_is_compl_apply_right" -> "algebra", "has_deriv_at.sub" -> "analysis", "finset.bUnion_insert" -> "data", "add_subgroup.neg_mem_iff" -> "algebra", "finmap.mem_lookup_union" -> "data", "stream.mem_const" -> "data", "denumerable.decode_is_some" -> "data", "category_theory.arrow.lift_mk'_right" -> "category_theory", "set.comp_indicator" -> "data", "ne.irrefl" -> "init", "smooth.times_cont_mdiff" -> "geometry", "power_series.order_add_of_order_eq" -> "algebra", "real.dist_0_eq_abs" -> "topology", "int.nat_abs_ne_zero_of_ne_zero" -> "data", "computation.of_think_mem" -> "data", "has_fderiv_within_at.congr_of_eventually_eq" -> "analysis", "is_noetherian_ring_of_surjective" -> "algebra", "sesq_form.zero_left" -> "algebra", "is_lub_supr" -> "order", "nnreal.rpow_lt_one" -> "analysis", "tensor_product.uncurry_apply" -> "algebra", "category_theory.op_comp" -> "category_theory", "affine_subspace.coe_direction_eq_vsub_set_left" -> "algebra", "is_connected.nonempty" -> "topology", "add_commute.units_neg_left_iff" -> "algebra", "mv_polynomial.coe_X" -> "algebra", "squeeze_zero_norm'" -> "analysis", "asymptotics.is_o_neg_right" -> "analysis", "inv_of_mul" -> "algebra", "free_magma.map_pure" -> "algebra", "classical.strong_indefinite_description" -> "init", "filter.lift'_lift'_assoc" -> "order", "nat.bit_le_bit_iff" -> "data", "linear_equiv.bijective" -> "algebra", "nat.lt_succ_of_lt" -> "init", "deriv_within_exp" -> "analysis", "category_theory.biprod.unipotent_upper_hom" -> "category_theory", "lipschitz_with.pow" -> "topology", "roption.mem_unique" -> "data", "add_equiv.trans_apply" -> "data", "category_theory.iso_whisker_left_hom" -> "category_theory", "nat.even_sub" -> "data", "int.add_assoc_aux1" -> "init", "times_cont_mdiff_at_iff_times_cont_mdiff_on_nhds" -> "geometry", "set.eq_of_mem_singleton" -> "data", "is_closed.is_measurable" -> "analysis", "differentiable.const_sub" -> "analysis", "cardinal.eq" -> "set_theory", "linear_map.fun_congr_left_symm" -> "algebra", "nnreal.one_lt_rpow_of_pos_of_lt_one_of_neg" -> "analysis", "finset.image_singleton" -> "data", "ennreal.bit1_inj" -> "data", "summable_iff_vanishing_norm" -> "analysis", "interval_integral.deriv_integral_of_tendsto_ae_left" -> "analysis", "list.rotate_eq_self_iff_eq_repeat" -> "data", "multiplicative.normal_subgroup" -> "algebra", "polynomial.smul_X" -> "algebra", "is_open_map_mul_left" -> "topology", "ring_equiv.to_ring_hom_trans" -> "data", "mfderiv_within_comp" -> "geometry", "polynomial.roots_one" -> "data", "category_theory.equiv_of_fully_faithful_apply" -> "category_theory", "category_theory.under.hom_mk_right" -> "category_theory", "int.lt_of_sub_neg" -> "init", "ite_eq_iff" -> "logic", "cardinal.prod_eq_zero" -> "set_theory", "abstract_completion.continuous_map" -> "topology", "equiv.summable_iff_of_has_sum_iff" -> "topology", "image_norm_le_of_norm_deriv_right_le_deriv_boundary'" -> "analysis", "floor_zero" -> "algebra", "filter.map_lift_eq" -> "order", "nat.xgcd_aux_P" -> "data", "set.preimage_add_const_Icc" -> "data", "real.arcsin_neg" -> "analysis", "measure_theory.measure.finite_at_filter.integrable_at_filter" -> "analysis", "category_theory.limits.cone.of_pullback_cone_X" -> "category_theory", "pgame.impartial.no_good_left_moves_iff_first_loses" -> "set_theory", "submodule.map_le_iff_le_comap" -> "algebra", "int.nat_abs_eq_zero" -> "data", "finset.range_coe" -> "data", "set.add_mem_add" -> "algebra", "euclidean_domain.gcd_mul_lcm" -> "algebra", "onote.NF_below.snd" -> "set_theory", "finsupp.filter_smul" -> "data", "euclidean_domain.dvd_lcm_left" -> "algebra", "subrel.rel_embedding_apply" -> "order", "filter.germ.coe_tendsto" -> "order", "traversable.free.map_eq_map" -> "control", "nnreal.coe_nat_cast" -> "data", "abs_neg" -> "algebra", "category_theory.monoidal_category.right_unitor_product_aux_triangle" -> "category_theory", "tsum_sum" -> "topology", "multiset.prod_eq_foldr" -> "data", "equiv.swap_apply_of_ne_of_ne" -> "data", "subsemiring.pow_mem" -> "algebra", "gcd_eq_right_iff" -> "algebra", "int.sign_mul_abs" -> "data", "algebra.fg_trans" -> "algebra", "list.mem_of_mem_erasep" -> "data", "filter.Liminf_top" -> "order", "nat.mul_lt_mul_of_pos_left" -> "init", "enat.add_top" -> "data", "measurable_space.dynkin_system.has_Union" -> "analysis", "emetric.nonempty_of_Hausdorff_edist_ne_top" -> "topology", "category_theory.prod.inverse_associator_obj" -> "category_theory", "ennreal.tendsto_pow_at_top_nhds_0_of_lt_1" -> "analysis", "add_le_add_three" -> "algebra", "cardinal.lt_omega_iff_finite" -> "set_theory", "set.set_of_eq_eq_singleton" -> "data", "convex_hull_basis_eq_std_simplex" -> "analysis", "one_one_equiv.symm" -> "computability", "segment_translate_image" -> "analysis", "real.cos_zero" -> "data", "has_ftaylor_series_up_to.of_le" -> "analysis", "omega.nat.is_nnf_push_neg" -> "tactic", "finsupp.is_basis_single_one" -> "algebra", "nat.primrec'.const" -> "computability", "multiset.mem_powerset" -> "data", "dfinsupp.lsingle_apply" -> "data", "digits_lt_base" -> "data", "category_theory.equivalence.inv_fun_id_assoc_inv_app" -> "category_theory", "coe_homeomorph_of_strict_mono_surjective" -> "topology", "min_le_right" -> "init", "pi_Lp.dist" -> "topology", "continuous_mul_right" -> "topology", "formal_multilinear_series.geometric_bound_of_lt_radius" -> "analysis", "multiset.Ico.eq_zero_of_le" -> "data", "int.mem_to_nat'" -> "data", "has_fderiv_at.const_smul" -> "analysis", "multiset.prod_smul" -> "data", "is_bounded_bilinear_map.is_bounded_linear_map_left" -> "analysis", "antilipschitz_with_iff_le_mul_dist" -> "topology", "localization_map.eq_of_eq" -> "algebra", "fderiv.fst" -> "analysis", "differentiable.differentiable_at" -> "analysis", "finsupp.prod_add_index" -> "data", "filter.tendsto_iff_rtendsto" -> "order", "metric.mem_ball_self" -> "topology", "category_theory.yoneda_obj_obj" -> "category_theory", "ideal.comap_Inf'" -> "algebra", "onote.repr_power_aux\:2081" -> "set_theory", "measure_theory.lebesgue_outer_Ioo" -> "analysis", "wseq.map_id" -> "data", "filter.prod_map_at_top_eq" -> "order", "real.continuous_sqrt" -> "analysis", "measure_theory.norm_set_integral_le_of_norm_le_const_ae" -> "analysis", "ennreal.coe_eq_coe" -> "data", "nat.land_bit" -> "init", "list.sum_eq_foldr" -> "data", "ennreal.rpow_le_rpow_of_exponent_le" -> "analysis", "div_lt_div_right_of_neg" -> "algebra", "padic_norm_e.mul" -> "data", "function.hfunext" -> "logic", "rat.inv_def'" -> "data", "mul_eq_of_eq_mul_inv" -> "algebra", "has_fpower_series_at.comp" -> "analysis", "set.nonempty.image" -> "data", "finite_dimensional.iff_fg" -> "algebra", "algebra.tensor_product.mul_one" -> "algebra", "punit.not_lt" -> "algebra", "mul_right_cancel_iff" -> "algebra", "ennreal.top_to_nnreal" -> "data", "linear_map.coe_fn_sum" -> "algebra", "with_top.top_mul_top" -> "algebra", "finset.center_mass_segment'" -> "analysis", "subring.coe_to_add_subgroup" -> "algebra", "symm_of" -> "init", "category_theory.nat_iso.naturality_1" -> "category_theory", "primrec.option_cases" -> "computability", "state_t.ext" -> "init", "differentiable_at.csinh" -> "analysis", "omega.int.exists_clause_holds" -> "tactic", "measure_theory.l1.simple_func.norm_integral_le_norm" -> "analysis", "zsqrtd.neg_im" -> "data", "filter.germ.map_map" -> "order", "topological_fiber_bundle_core.local_triv_at_fst" -> "topology", "primrec\:2082.mkpair" -> "computability", "is_max_on.comp_antimono" -> "order", "measure_theory.simple_func.lintegral_eq_of_subset" -> "analysis", "complex.exp_of_real_im" -> "data", "nat.pow_log_le_self" -> "data", "int.mul_le_mul" -> "init", "list.nth_le_reverse_aux2" -> "data", "dense_inducing.extend_eq_of_tendsto" -> "topology", "subgroup.closure_union" -> "algebra", "associated_one_of_associated_mul_one" -> "algebra", "tt_bor" -> "init", "equiv.perm.ext" -> "data", "measure_theory.simple_func.fin_meas_supp.meas_preimage_singleton_ne_zero" -> "analysis", "ordinal.succ_lt_of_is_limit" -> "set_theory", "inv_mul_le_iff_le_mul" -> "algebra", "composition.length_pos_of_pos" -> "combinatorics", "category_theory.functor.cones_obj" -> "category_theory", "tactic.ring_exp.pow_pp_pf_c" -> "tactic", "polynomial.degree_X_le" -> "data", "padic_int.maximal_ideal_eq_span_p" -> "data", "pell.eq_pow_of_pell_lem" -> "number_theory", "matrix.one_apply_ne'" -> "data", "homological_complex.homology_map_condition_assoc" -> "algebra", "inf_le_inf_left" -> "order", "ennreal.measurable_of_measurable_nnreal" -> "analysis", "list.zip_map_left" -> "data", "is_add_hom.comp" -> "algebra", "filter.germ.coe_inv" -> "order", "finset.sum_mono_set_of_nonneg" -> "algebra", "fintype.exists_equiv_fin" -> "data", "normed_field.exists_norm_lt_one" -> "analysis", "encodable.encode_nat" -> "data", "complex.add_conj" -> "data", "is_min_on_univ_iff" -> "order", "nat.pow_le_iff_le_log" -> "data", "finset.card_ne_zero_of_mem" -> "data", "nat.mod_zero" -> "init", "nat.one_add" -> "data", "filter.tendsto.mono_left" -> "order", "many_one_degree.le_add_left'" -> "computability", "times_cont_diff_within_at_fst" -> "analysis", "dvd_mul_of_dvd_left" -> "algebra", "homeomorph.is_open_map" -> "topology", "multiset.filter_le" -> "data", "is_antisymm.swap" -> "order", "multiset.zero_inter" -> "data", "equiv.perm.fixed_point_card_lt_of_ne_one" -> "algebra", "category_theory.limits.limit.map_pre" -> "category_theory", "function.embedding.coe_fn_mk" -> "logic", "omega.nat.sat_sub_elim" -> "tactic", "ennreal.div_top" -> "data", "contracting_with.efixed_point_is_fixed_pt'" -> "topology", "primrec\:2082.unpaired'" -> "computability", "submodule.fg_pow" -> "algebra", "closure_prod_eq" -> "topology", "pow_one" -> "algebra", "disjoint_bot_left" -> "order", "sum.map_map" -> "data", "lucas_lehmer.X.neg_fst" -> "number_theory", "set.image2_inter_subset_right" -> "data", "set.Iic_subset_Iic_union_Ioc" -> "data", "subalgebra.gsmul_mem" -> "algebra", "sub_add_sub_cancel" -> "algebra", "is_coprime.of_mul_add_left_right" -> "algebra", "category_theory.limits.biprod.map_eq" -> "category_theory", "multiset.nodup_add" -> "data", "measure_theory.measure.bind_dirac" -> "analysis", "filter.tendsto_map'" -> "order", "continuous_linear_map.zero_comp" -> "topology", "tactic.ring.horner_def'" -> "tactic", "nat.exists_coprime" -> "data", "add_monoid_algebra.mul_zero" -> "data", "interval_integral.integral_interval_sub_interval_comm'" -> "analysis", "category_theory.equivalence.refl_unit_iso" -> "category_theory", "coe_fn_coe_base" -> "logic", "filter.tendsto.is_cobounded_under_le" -> "topology", "is_closed.mem_of_ge_of_forall_exists_gt" -> "topology", "mv_polynomial.map_restrict_dom_eval\:2097" -> "algebra", "add_submonoid.localization_map.lift_surjective_iff" -> "algebra", "category_theory.limits.prod.lift_map_assoc" -> "category_theory", "ennreal.one_le_rpow" -> "analysis", "category_theory.limits.cones.functoriality_obj_\[Pi]_app" -> "category_theory", "adic_completion.ext" -> "algebra", "affine.simplex.sum_monge_point_vsub_face_centroid_weights_with_circumcenter" -> "geometry", "prime_multiset.card_of_prime" -> "data", "algebra.tensor_product.include_right_apply" -> "algebra", "localization_map.exists_integer_multiple'" -> "algebra", "ordinal.mul_le_mul_right" -> "set_theory", "finite_field.card_units" -> "algebra", "omega.coeffs.val_between_eq_val_between" -> "tactic", "is_bounded_bilinear_map.has_fderiv_within_at" -> "analysis", "polynomial.eisenstein_criterion_aux.map_eq_C_mul_X_pow_of_forall_coeff_mem" -> "algebra", "equiv.perm.same_cycle_cycle" -> "algebra", "closure_eq_uniformity" -> "topology", "mem_nhds_within_Iic_iff_exists_Ioc_subset'" -> "topology", "iter_deriv_pow'" -> "analysis", "nat.dvd_iff_mod_eq_zero" -> "init", "free_add_magma.add_eq" -> "algebra", "cardinal.add_eq_right" -> "set_theory", "measure_theory.measure.haar.chaar_empty" -> "analysis", "isometric.neg_symm" -> "topology", "isometric.coe_add_left" -> "topology", "submonoid.comap_top" -> "algebra", "ne_of_lt" -> "init", "add_submonoid.mem_Sup_of_mem" -> "algebra", "differentiable.continuous" -> "analysis", "int.le_add_of_neg_add_le_left" -> "init", "decidable.not_and_distrib'" -> "logic", "exists_exists_eq_and" -> "logic", "list.forall\:2082_iff_zip" -> "data", "pnat.coprime.factor_eq_gcd_left_right" -> "data", "measure_theory.integral_undef" -> "analysis", "measurable_mul_right" -> "analysis", "power_series.coeff_mul" -> "algebra", "subgroup.mem_supr_of_mem" -> "algebra", "supr_and" -> "order", "ordinal.cof_ord_le" -> "set_theory", "linear_map.update_apply" -> "algebra", "algebra.map_bot" -> "algebra", "hyperreal.infinite_neg_add_infinite_neg" -> "data", "set.preimage_eq_preimage'" -> "data", "int.test_bit_bitwise" -> "data", "nat.div_le_self" -> "init", "is_local_max.has_fderiv_at_eq_zero" -> "analysis", "measure_theory.simple_func.approx_apply" -> "analysis", "function.mk_mem_periodic_pts" -> "dynamics", "ordinal.rel_iso_enum" -> "set_theory", "integral_closure.is_integral" -> "algebra", "finset.sum_sigma" -> "algebra", "pnat.mod_div_aux_spec" -> "data", "subsemiring.mk'_to_add_submonoid" -> "algebra", "nat.pos_pow_of_pos" -> "init", "finset.disjoint_self_iff_empty" -> "data", "fin.prod_univ_eq_prod_range" -> "data", "mul_equiv.map_one" -> "data", "finset.inter_empty" -> "data", "submonoid.localization_map.mk'_one" -> "algebra", "mv_polynomial.coeff_C" -> "data", "real.div_rpow" -> "analysis", "fderiv_within_const_smul" -> "analysis", "continuous_linear_map.restrict_scalars_coe_eq_coe'" -> "analysis", "subsemiring.coe_inf" -> "algebra", "set.finite.insert" -> "data", "measure_theory.outer_measure.le_of_content_compacts" -> "analysis", "to_bool_ff_iff" -> "init", "ennreal.of_real_mul" -> "data", "monoid_hom.inl_apply" -> "algebra", "nat.exists_eq_succ_of_ne_zero" -> "init", "right_coset_mem_right_coset" -> "algebra", "list.nodup_of_nodup_append_right" -> "data", "convex_hull_to_cone_eq_Inf" -> "analysis", "dvd_of_neg_dvd" -> "algebra", "local_equiv.map_target" -> "data", "caratheodory.step" -> "analysis", "char.of_nat_ne_of_ne" -> "init", "int.lt_iff_le_not_le" -> "init", "submodule.one_eq_span" -> "algebra", "galois_coinsertion.u_infi_of_lu_eq_self" -> "order", "lcm_dvd_lcm_mul_right" -> "algebra", "set.range_iff_surjective" -> "data", "int.neg_succ_of_nat_coe" -> "init", "add_submonoid.prod_top" -> "algebra", "sigma.forall" -> "data", "multiset.coe_ndinter" -> "data", "category_theory.non_preadditive_abelian.add_zero" -> "category_theory", "roption.map_eq_map" -> "data", "list.exists_mem_cons_of" -> "data", "nnreal.rpow_nat_cast" -> "analysis", "padic_int.to_zmod_spec" -> "data", "linear_independent_iff''" -> "algebra", "rat.cast_nonneg" -> "data", "asymptotics.is_O.prod_rightl" -> "analysis", "local_equiv.trans_target" -> "data", "Module.of_self_iso_inv" -> "algebra", "norm_num.not_prime_helper" -> "tactic", "strict_mono.const_mul'" -> "algebra", "semidirect_product.map_comp_inl" -> "algebra", "real.log_nonneg" -> "analysis", "lt_mul_of_lt_of_one_le" -> "algebra", "matrix.det_mul_aux" -> "algebra", "category_theory.eq_of_inv_eq_inv" -> "category_theory", "ordinal.zero_le" -> "set_theory", "continuous_inl" -> "topology", "category_theory.abelian.kernel_cokernel_eq_image_\[Iota]" -> "category_theory", "multiset.card_eq_card_of_rel" -> "data", "nat.min_fac_prime" -> "data", "submodule.coe_mem" -> "algebra", "polynomial.degree_pos_of_ne_zero_of_nonunit" -> "data", "multiset.pi.cons_swap" -> "data", "multiset.cons_ndinter_of_mem" -> "data", "finset.coe_nonempty" -> "data", "set.insert_prod" -> "data", "equiv.conj_refl" -> "data", "linear_map.quotient_inf_equiv_sup_quotient_symm_apply_right" -> "algebra", "int.modeq.modeq_of_dvd_of_modeq" -> "data", "int.not_even_iff" -> "data", "with_top.unop_sum" -> "algebra", "function.semiconj_of_is_lub" -> "order", "lt_add_of_neg_lt_sub_right" -> "algebra", "linear_map.mem_range_self" -> "algebra", "free_semigroup_free_magma_mul" -> "algebra", "polynomial.coeff_derivative" -> "data", "differentiable_at.sin" -> "analysis", "list.reverse_injective" -> "data", "ennreal.sub_mul" -> "data", "affine_span_singleton_union_vadd_eq_top_of_span_eq_top" -> "algebra", "padic_int.zmod_congr_of_sub_mem_span_aux" -> "data", "equiv.tsum_eq" -> "topology", "fderiv_within_smul_const" -> "analysis", "polynomial.deriv" -> "analysis", "padic_norm_e.eq_of_norm_add_lt_left" -> "data", "list.take'_left'" -> "data", "has_ftaylor_series_up_to_on.continuous_linear_map_comp" -> "analysis", "denumerable.list_of_nat_succ" -> "data", "complex.cosh_add" -> "data", "nnreal.sub_pos" -> "data", "category_theory.non_preadditive_abelian.epi_of_zero_cokernel" -> "category_theory", "list.concat_ne_nil" -> "data", "mv_polynomial.eval\:2082_eta" -> "data", "nat.partrec'.part_iff" -> "computability", "continuous_on.prod" -> "topology", "state_t.run_put" -> "init", "set.preimage_univ" -> "data", "int.pos_of_sign_eq_one" -> "init", "nat.le_of_lt_succ" -> "init", "joined_in.some_path_mem" -> "topology", "mul_action_hom.map_smul" -> "algebra", "add_lt_iff_neg_right" -> "algebra", "pure_le_nhds" -> "topology", "subring.exists_list_of_mem_closure" -> "algebra", "nat.sub_le_right_iff_le_add" -> "data", "measure_theory.simple_func.coe_range" -> "analysis", "subspace.coe_continuous_linear_proj_of_closed_compl'" -> "analysis", "zmod.val_eq_ite_val_min_abs" -> "data", "equiv.perm.same_cycle.refl" -> "algebra", "list.tail_repeat" -> "data", "or_iff_not_imp_right" -> "logic", "set.indicator_nonneg'" -> "data", "ideal.mul_le" -> "algebra", "is_glb_Icc" -> "order", "minimal_polynomial.prime" -> "algebra", "ennreal.coe_nat_le_coe_nat" -> "data", "category_theory.arrow.hom_mk'_left" -> "category_theory", "omega.int.nnf_equiv" -> "tactic", "free_group.prod.one" -> "algebra", "set.Ioi_def" -> "data", "eq_true" -> "init", "associates.one_or_eq_of_le_of_prime" -> "algebra", "fin.coe_nat_eq_last" -> "data", "euclidean_domain.gcd_dvd" -> "algebra", "measure_theory.l1.coe_neg" -> "analysis", "supr_supr_eq_left" -> "order", "computation.corec_eq" -> "data", "bool.of_nat_le_of_nat" -> "data", "finset.sum_le_sum_of_ne_zero" -> "algebra", "set.surj_on.right_inv_on_inv_fun_on" -> "data", "category_theory.limits.span_zero" -> "category_theory", "has_mfderiv_within_at.has_mfderiv_at" -> "geometry", "interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae" -> "analysis", "ennreal.sub_le_self" -> "data", "category_theory.equivalence.symm_functor" -> "category_theory", "set_coe.forall" -> "data", "lie_equiv_matrix'_apply" -> "algebra", "cau_seq.mul_equiv_zero" -> "data", "model_with_corners.left_inv" -> "geometry", "pgame.omega_left_wins" -> "set_theory", "fg_adjoin_singleton_of_integral" -> "algebra", "is_local_max_const" -> "topology", "pnat.coe_to_pnat'" -> "data", "function.surjective_id" -> "init", "mul_le_mul_right_of_neg" -> "algebra", "subsemiring.prod_mono_left" -> "algebra", "units.dvd_mul_right" -> "algebra", "list.prefix_append" -> "data", "zmod.int_coe_eq_int_coe_iff" -> "data", "is_totally_disconnected_of_is_totally_separated" -> "topology", "ennreal.to_real_top_mul" -> "data", "mul_neg_of_pos_of_neg" -> "algebra", "unique_mdiff_on.tangent_bundle_proj_preimage" -> "geometry", "classical.eq_false_or_eq_true" -> "init", "pSet.mk_type_func" -> "set_theory", "computable.vector_head" -> "computability", "computation.terminates_def" -> "data", "commute.self_cast_nat_mul_cast_nat_mul" -> "algebra", "pequiv.mul_matrix_apply" -> "data", "array.push_back_to_list" -> "data", "nnreal.mul_div_assoc'" -> "data", "hyperreal.st_infinite" -> "data", "mul_equiv.to_Mon_iso_hom" -> "algebra", "open_embedding_of_continuous_injective_open" -> "topology", "commute.units_inv_right" -> "algebra", "category_theory.limits.kernel_comp_is_iso_hom" -> "category_theory", "real.tan_arctan" -> "analysis", "alg_equiv.coe_ring_equiv_injective" -> "algebra", "ideal.add_eq_sup" -> "algebra", "add_monoid_hom.map_matrix_apply" -> "data", "set.prod_sub_preimage_iff" -> "data", "submodule.quotient.mk_neg" -> "algebra", "category_theory.under.iso_mk_hom_right" -> "category_theory", "set.finite.is_closed_convex_hull" -> "analysis", "cardinal.le_zero" -> "set_theory", "iff_true_left" -> "logic", "filter.map_lift'_eq" -> "order", "linear_map.mul_app" -> "algebra", "pnat.div_coe" -> "data", "valuation.map_sub_swap" -> "algebra", "irreducible_iff_nat_prime" -> "algebra", "abstract_completion.map_coe" -> "topology", "has_strict_fderiv_at.fst" -> "analysis", "filter.strict_mono_tendsto_at_top" -> "order", "polynomial.C_mul" -> "data", "ennreal.nhds_coe" -> "topology", "pgame.le_trans" -> "set_theory", "finset.sum_neg_distrib" -> "algebra", "mv_polynomial.degrees_zero" -> "data", "ordinal.type_subrel_lt" -> "set_theory", "is_open_iff_forall_mem_open" -> "topology", "primrec.eq" -> "computability", "real.sin_sq_le_one" -> "data", "polynomial.coeff_mul_X" -> "data", "add_left_surjective" -> "algebra", "category_theory.functor.equiv_counit_iso" -> "category_theory", "filter.tendsto_at_bot_mono" -> "order", "tensor_product.tmul_ite" -> "algebra", "is_greatest.is_lub" -> "order", "units.nhds" -> "analysis", "category_theory.non_preadditive_abelian.add_def" -> "category_theory", "Top.presheaf.pushforward.comp_hom_app" -> "topology", "fract_mul_nat" -> "algebra", "finset.union_right_comm" -> "data", "lt_sub_right_of_add_lt" -> "algebra", "euclidean_geometry.dist_square_smul_orthogonal_vadd_smul_orthogonal_vadd" -> "geometry", "has_deriv_at_neg'" -> "analysis", "fderiv_within_add_const" -> "analysis", "pequiv.single_trans_single" -> "data", "category_theory.iso.to_linear_equiv_inv_fun" -> "algebra", "int.dvd_lcm_left" -> "algebra", "nat.modeq.modeq_iff_dvd" -> "data", "int.neg_pred" -> "data", "map_cSup_of_continuous_at_of_monotone" -> "topology", "category_theory.pre_post_comm" -> "category_theory", "complex.abs_le_abs_re_add_abs_im" -> "data", "asymptotics.is_O.triangle" -> "analysis", "dist_pi_le_iff" -> "topology", "category_theory.limits.image.\[Iota]_zero" -> "category_theory", "equiv.perm.same_cycle_of_is_cycle" -> "algebra", "rel.preimage_mono" -> "data", "inner_smul_self_right" -> "analysis", "differentiable_at.const_add" -> "analysis", "finsupp.support_emb_domain" -> "data", "polynomial.nat_degree_coe_units" -> "data", "deriv_mul_const" -> "analysis", "has_deriv_at_const" -> "analysis", "euclidean_domain.gcd_dvd_left" -> "algebra", "is_R_or_C.smul_im'" -> "data", "finsupp.add_eq_zero_iff" -> "data", "cardinal.zero_powerlt" -> "set_theory", "nhds_within_union" -> "topology", "set.bInter_subset_bInter_right" -> "data", "vadd_right_cancel" -> "algebra", "category_theory.monoidal_category.unitors_equal.cells_9" -> "category_theory", "submonoid.coe_top" -> "algebra", "fpow_coe_nat" -> "algebra", "add_submonoid.sum_mem" -> "algebra", "euclidean_geometry.reflection_eq_iff_orthogonal_projection_eq" -> "geometry", "continuous_at.mul" -> "topology", "cau_seq.cauchy\:2083" -> "data", "polynomial.nat_degree_map'" -> "data", "list.diff_subset" -> "data", "multiset.foldl_swap" -> "data", "has_deriv_at.lhopital_zero_nhds_right" -> "analysis", "measure_theory.outer_measure.of_content_exists_open" -> "analysis", "real.rpow_zero" -> "analysis", "metric.diam_mono" -> "topology", "free_abelian_group.lift.neg" -> "algebra", "subring.ext" -> "algebra", "is_lub_Ico" -> "order", "edist_dist" -> "topology", "model_with_corners.unique_diff_at_image" -> "geometry", "category_theory.graded_object.comap_equiv_inverse" -> "category_theory", "set.subset.refl" -> "data", "add_subgroup.le_def" -> "algebra", "nat.pow_pos" -> "data", "finmap.keys_empty" -> "data", "category_theory.limits.prod_functor_obj_obj" -> "category_theory", "continuous_linear_map.restrict_scalars_coe_eq_coe" -> "analysis", "direct_sum.of_injective" -> "algebra", "category_theory.abelian.pseudo_equal_symm" -> "category_theory", "category_theory.limits.limit_iso_limit_curry_comp_lim_inv_\[Pi]" -> "category_theory", "list.append_sublist_append_right" -> "data", "bounded_continuous_function.lipschitz_comp" -> "topology", "category_theory.limits.biproduct.lift_desc_assoc" -> "category_theory", "cauchy.le_nhds_Lim" -> "topology", "valuation.map_mul" -> "algebra", "list.perm.eqv" -> "data", "ordinal.lift_type_lt" -> "set_theory", "filter.eventually_iff" -> "order", "is_scalar_tower.range_under_adjoin" -> "algebra", "linear_recurrence.eq_mk_of_is_sol_of_eq_init'" -> "algebra", "le_inv'" -> "algebra", "padic_int.eq_zero_or_eq_zero_of_mul_eq_zero" -> "data", "multiset.foldl_zero" -> "data", "nat.primrec'.vec_iff" -> "computability", "set.to_finset_insert" -> "data", "heq_of_eq_rec_right" -> "init", "hyperreal.coe_abs" -> "data", "norm_num.adc_bit0_bit1" -> "tactic", "ring_hom.map_units_inv" -> "algebra", "opposite.op_one" -> "algebra", "complex.two_sinh" -> "data", "set.image_const_sub_Ioi" -> "data", "rel_sup_add" -> "topology", "interval_integral.deriv_within_integral_left" -> "analysis", "nat.cast_pos" -> "data", "measure_theory.induced_outer_measure_preimage" -> "analysis", "one_one_reducible.of_equiv_symm" -> "computability", "pfun.mem_res" -> "data", "sequentially_complete.seq_pair_mem" -> "topology", "iterated_fderiv_succ_eq_comp_left" -> "analysis", "Sup_le_iff" -> "order", "eq_zero_of_mul_eq_self_left" -> "algebra", "abstract_completion.extend_map" -> "topology", "hyperreal.infinite_pos_add_not_infinite" -> "data", "finset.forall_mem_insert" -> "data", "free_group.to_word.mk" -> "algebra", "continuous_coinduced_dom" -> "topology", "submonoid.map_inf_comap_of_surjective" -> "algebra", "compl_supr" -> "order", "topological_space.opens.map_id_obj_unop" -> "topology", "Set.mem_pair" -> "set_theory", "erased.join_eq_out" -> "data", "free_add_monoid.lift_comp_of" -> "algebra", "eq_sub_of_add_eq'" -> "algebra", "nat.sqrt_lt" -> "data", "multilinear_map.uncurry_curry_right" -> "algebra", "interior_Iic" -> "topology", "continuous_linear_map.coe_zero" -> "topology", "galois_coinsertion.u_infi_l" -> "order", "nat.rfind_dom" -> "computability", "omega.pred_mono_2'" -> "tactic", "computation.of_results_think" -> "data", "generalized_continued_fraction.zero_le_of_continuants_aux_b" -> "algebra", "is_open_map.image_mem_nhds" -> "topology", "multiset.choose_mem" -> "data", "category_theory.functor.map_arrow_map_left" -> "category_theory", "int.gcd_dvd_gcd_mul_right" -> "algebra", "finset.eq_singleton_iff_unique_mem" -> "data", "primrec_rel.of_eq" -> "computability", "list.map_sub_range'" -> "data", "ennreal.div_self" -> "data", "is_linear_map.convex_hull_image" -> "analysis", "nat.bit1_ne_zero" -> "init", "lt_cSup_of_lt" -> "order", "gaussian_int.to_real_re" -> "data", "traversable.foldl_to_list" -> "control", "functor.of_mem_supp" -> "control", "set.diff_subset_diff_right" -> "data", "filter.eventually_eq.has_fderiv_at_filter_iff" -> "analysis", "fin.val_add" -> "data", "enat.to_with_top_top'" -> "data", "add_aut.inv_apply_self" -> "data", "zsqrtd.mul_nonneg" -> "data", "list.chain'_nil" -> "data", "prod.swap_prod_mk" -> "data", "equiv.pempty_sum_apply_inr" -> "data", "rat.abs_def" -> "data", "measure_theory.integral_smul" -> "analysis", "surj_on_Ico_of_monotone_surjective" -> "data", "finsupp.prod_pow" -> "data", "set.Ico_subset_Icc_union_Ico" -> "data", "compl_inj_iff" -> "order", "list.Ico.mem" -> "data", "deriv_within_add" -> "analysis", "set.mem_image_of_mem" -> "data", "continuous_linear_equiv.prod_apply" -> "topology", "finset.sum_eq_zero" -> "algebra", "filter.map_lift'_eq2" -> "order", "normed_field.exists_norm_lt" -> "analysis", "primrec.nat_add" -> "computability", "continuous_linear_equiv.map_zero" -> "topology", "list.nodup_of_sublist" -> "data", "lipschitz_with.to_right_inverse" -> "topology", "times_cont_diff_on_top" -> "analysis", "finset.sum_update_of_not_mem" -> "algebra", "gcd_monoid.prime_of_irreducible" -> "algebra", "pos_num.pred'_to_nat" -> "data", "multiset.mem_map" -> "data", "normalize_apply" -> "algebra", "int.modeq.modeq_mul_right'" -> "data", "mvfunctor.id_map" -> "control", "finset.pi_disjoint_of_disjoint" -> "data", "lt_add_of_pos_right" -> "algebra", "nat.gcd_dvd_gcd_mul_left_right" -> "data", "list.infix_append'" -> "data", "turing.tape.write_self" -> "computability", "lucas_lehmer.s_mod_succ" -> "number_theory", "wseq.head_terminates_of_head_tail_terminates" -> "data", "pure_id'_seq" -> "control", "multiset.eq_zero_of_subset_zero" -> "data", "filter.is_countably_generated_at_bot" -> "order", "locally_finite_subset" -> "topology", "continuous_linear_map.add_apply" -> "topology", "ennreal.one_sub_inv_two" -> "data", "wseq.seq_destruct_nil" -> "data", "frontier_Ioc" -> "topology", "lt_of_nat_ceil_lt" -> "algebra", "deriv_neg''" -> "analysis", "category_theory.monoidal_functor.id_\[CurlyEpsilon]_is_iso" -> "category_theory", "or_assoc" -> "init", "matrix.cons_val_one" -> "data", "add_comm_group.direct_limit.of_zero" -> "algebra", "partrec\:2082.comp\:2082" -> "computability", "inv_le'" -> "algebra", "measure_theory.supr_lintegral_le" -> "analysis", "finset.card_powerset_len" -> "data", "polynomial.coeff_contract" -> "algebra", "wseq.think_append" -> "data", "convex_Ioi" -> "analysis", "list.sublist_of_prefix" -> "data", "linear_equiv.to_fun_apply" -> "algebra", "ennreal.mul_pos" -> "data", "algebraic_closure.le_max_ideal" -> "algebra", "list.drop_length" -> "data", "finset.sdiff_union_self_eq_union" -> "data", "submodule.mul_mem_mul_rev" -> "algebra", "has_le.le.trans_eq" -> "algebra", "bool.band_assoc" -> "data", "euclidean_geometry.dist_square_eq_dist_orthogonal_projection_square_add_dist_orthogonal_projection_square" -> "geometry", "monoid_algebra.lift_of" -> "data", "metric.dist_mem_uniformity" -> "topology", "set.bij_on.comp" -> "data", "ennreal.not_lt_top" -> "data", "linear_equiv.of_injective_endo_left_inv" -> "algebra", "finset.inter_subset_left" -> "data", "finset.measurable_prod" -> "analysis", "list.func.get_set" -> "data", "equiv.to_pequiv_refl" -> "data", "nat.pow_le_iff_le_right" -> "data", "tendsto_at_top_supr_nat" -> "topology", "finsupp.infi_ker_lapply_le_bot" -> "algebra", "category_theory.prod.symmetry_inv_app" -> "category_theory", "set.add_comm" -> "algebra", "fin.succ_injective" -> "data", "has_sum_of_bounded_monoid_hom_of_has_sum" -> "analysis", "submodule.supr_eq_span" -> "algebra", "is_group_hom.inv_ker_one" -> "algebra", "local_homeomorph.eventually_left_inverse" -> "topology", "filter.unbounded_of_tendsto_at_top'" -> "order", "trunc.eq" -> "data", "finset.le_iff_subset" -> "data", "list.append_inj_left" -> "data", "direct_sum.to_group_sub" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_within_at_inter'" -> "geometry", "nhds_within_restrict''" -> "topology", "list.length_init" -> "data", "finset.prod_inv_distrib" -> "algebra", "polynomial.derivative_neg" -> "data", "deriv_fpow" -> "analysis", "nonneg_add_comm_group.nonneg_def" -> "algebra", "commute.units_of_coe" -> "algebra", "nat.add_mod_mod" -> "data", "deriv_sum" -> "analysis", "le_Inf_inter" -> "order", "forall_ge_le_of_forall_le_succ" -> "data", "num.cast_mul" -> "data", "galois_connection.monotone_l" -> "order", "times_cont_diff_top_iff_fderiv" -> "analysis", "list.foldr_with_index_aux_spec_cons" -> "data", "Vieta_formula_quadratic" -> "algebra", "measure_theory.l1.coe_add" -> "analysis", "finset.prod_subtype_map_embedding" -> "algebra", "times_cont_diff_within_at.continuous_linear_map_comp" -> "analysis", "differentiable_on.congr_mono" -> "analysis", "finset.filter_congr_decidable" -> "data", "is_local_max_on.inter" -> "topology", "commute.add_pow" -> "data", "rat.zero_of_num_zero" -> "data", "category_theory.iso.conj_Aut_apply" -> "category_theory", "uliftable.down_up" -> "control", "submonoid.localization_map.lift_spec" -> "algebra", "list.perm.append_left" -> "data", "set.image_seq" -> "data", "multilinear_map.map_smul" -> "algebra", "equiv.perm.pow_apply_eq_of_apply_apply_eq_self" -> "algebra", "vector.mem_iff_nth" -> "data", "mul_inv_cancel_right'" -> "algebra", "ring_equiv.surjective" -> "data", "finsupp.lcongr_single" -> "algebra", "category_theory.non_preadditive_abelian.sub_sub_sub" -> "category_theory", "monoid_hom.apply_apply" -> "algebra", "uniform_space.completion.dense\:2083" -> "topology", "ennreal.inv_le_iff_inv_le" -> "data", "affine_map.comp_apply" -> "algebra", "concave_on.comp_linear_map" -> "analysis", "fraction_ring.mk_eq_div" -> "algebra", "multiplicity.mul'" -> "algebra", "associates.dvd_out_iff" -> "algebra", "int.le_div_of_mul_le" -> "data", "nat.eq_prime_pow_of_dvd_least_prime_pow" -> "data", "is_conj_one_left" -> "algebra", "cauchy_iff_exists_le_nhds" -> "topology", "mvqpf.Wequiv.abs'" -> "data", "category_theory.discrete.nat_trans_app" -> "category_theory", "asymptotics.is_O_congr" -> "analysis", "add_commute.neg_right_iff" -> "algebra", "minimal_polynomial.ne_zero" -> "algebra", "mvqpf.corec_roll" -> "data", "nat.eq_of_mul_eq_mul_left" -> "init", "turing.TM1to1.exists_enc_dec" -> "computability", "nnreal.le_of_real_iff_coe_le" -> "data", "multiset.erase_of_not_mem" -> "data", "padic_norm_e.norm_p_pow" -> "data", "embedding_of_rat" -> "topology", "finset.card_insert_of_not_mem" -> "data", "subtype.ext_val" -> "data", "lie_equiv_matrix'_symm_apply" -> "algebra", "measure_theory.simple_func.eq_zero_of_mem_range_zero" -> "analysis", "polynomial.is_splitting_field.mul" -> "algebra", "int.sub_le_sub_left" -> "init", "padic_norm.zero" -> "data", "add_localization.ind" -> "algebra", "filter.is_cobounded_le_of_bot" -> "order", "lcm_eq_right_iff" -> "algebra", "filter.mk_of_closure_sets" -> "order", "real.is_topological_basis_Ioo_rat" -> "topology", "int.exists_least_of_bdd" -> "data", "complex.exists_root" -> "analysis", "wseq.join_nil" -> "data", "nnreal.coe_lt_coe" -> "data", "gronwall_bound_of_K_ne_0" -> "analysis", "subalgebra.range_le" -> "algebra", "indicator_norm_le_norm_self" -> "analysis", "is_R_or_C.of_real_mul" -> "data", "relator.rel_and" -> "logic", "finite_dimensional.dim_eq_card_basis" -> "algebra", "inf_idem" -> "order", "smooth_at_id" -> "geometry", "metric.bounded_range_iff" -> "topology", "category_theory.nat_trans_from_connected" -> "category_theory", "omega.int.le_and_le_iff_eq" -> "tactic", "multilinear_map.neg_apply" -> "algebra", "multiset.exists_multiset_eq_map_quot_mk" -> "data", "has_strict_fderiv_at.mem_implicit_to_local_homeomorph_of_complemented_target" -> "analysis", "set.surj_on_bUnion_bUnion" -> "data", "dim_eq_of_injective" -> "algebra", "subsemiring.ext" -> "algebra", "set.compl_inter" -> "data", "neg_mul_neg" -> "algebra", "closure_subset_iff_is_closed" -> "topology", "commute.neg_left_iff" -> "algebra", "roption.mem_assert_iff" -> "data", "punit.top_eq" -> "algebra", "unique_factorization_domain.dvd_of_dvd_mul_left_of_no_prime_factors" -> "algebra", "tendsto_neg_nhds_within_Iio" -> "topology", "finset.prod_pow_boole" -> "algebra", "num.zneg_to_znum" -> "data", "set.empty_card'" -> "data", "gfp_comp" -> "order", "sup_sdiff_same" -> "order", "category_theory.bifunctor.diagonal'" -> "category_theory", "ennreal.mul_top" -> "data", "subtype.coe_injective" -> "data", "int.gcd_mul_lcm" -> "algebra", "norm_num.clear_denom_simple_nat" -> "tactic", "set.indicator_indicator" -> "data", "real.range_cos" -> "analysis", "set.surj_on.union" -> "data", "function.support_prod" -> "data", "submodule.zero_mem" -> "algebra", "nat.zero_pow" -> "init", "finsupp.total_range" -> "algebra", "seq1.join_nil" -> "data", "cardinal.ord_aleph_is_limit" -> "set_theory", "valuation.map_inv" -> "algebra", "real.sqrt_two_add_series_monotone_left" -> "analysis", "alist.lookup_empty" -> "data", "multiset.erase_le" -> "data", "category_theory.faithful.div_comp" -> "category_theory", "mv_polynomial.is_homogeneous.prod" -> "algebra", "mv_polynomial.coe_C" -> "algebra", "int.coe_nat_mul_neg_succ" -> "data", "sub_eq_sub_add_sub" -> "algebra", "pgame.zero_lt" -> "set_theory", "formal_multilinear_series.id_apply_one'" -> "analysis", "adic_completion.eval_of" -> "algebra", "finset.Ico.filter_lt_of_le_bot" -> "data", "monotonicity.and" -> "meta", "multiset.mem_singleton" -> "data", "list.Ico.filter_le_of_bot" -> "data", "has_mfderiv_at_unique" -> "geometry", "ceil_mono" -> "algebra", "sub_right_inj" -> "algebra", "nonempty_pprod" -> "logic", "filter.germ.const_comp_tendsto'" -> "order", "znum.abs_to_znum" -> "data", "max_left_comm" -> "init", "iterated_deriv_succ" -> "analysis", "mvqpf.recF_eq_of_Wequiv" -> "data", "power_series.order_X" -> "algebra", "fin.succ_ne_zero" -> "data", "option.iget_some" -> "data", "filter.eventually_eq.eventually_eq_nhds" -> "topology", "relation.equivalence_join" -> "logic", "ordinal.mod_def" -> "set_theory", "polynomial.monic_mul" -> "data", "quot.out_eq" -> "data", "typevec.prod_id" -> "data", "is_unit.dvd" -> "algebra", "filter.eventually_le.is_max_filter" -> "order", "filter.map_le_iff_le_comap" -> "order", "lipschitz_with.mul" -> "topology", "I_extend_one" -> "topology", "finset.card_bind" -> "algebra", "lower_bounds_Ioi" -> "order", "rat.norm_cast_real" -> "analysis", "is_coprime.mul_add_left_right" -> "algebra", "functor.map_map" -> "control", "stream.nth_map" -> "data", "category_theory.action_as_functor_map" -> "category_theory", "add_con.comap_eq" -> "algebra", "sub_add" -> "algebra", "is_irreducible_irreducible_component" -> "topology", "opposite.coe_op_add_hom" -> "algebra", "has_deriv_at.lhopital_zero_at_bot" -> "analysis", "stream.zip_inits_tails" -> "data", "filter.germ.coe_lt" -> "order", "minimal_polynomial.coeff_zero_ne_zero" -> "algebra", "lists'.subset_nil" -> "set_theory", "add_semiconj_by.neg_neg_symm_iff" -> "algebra", "ordinal.iterate_le_nfp" -> "set_theory", "cinfi_le_cinfi" -> "order", "ideal.map_comap_map" -> "algebra", "cau_seq.mul_pos" -> "data", "le_of_not_le" -> "init", "zmod.cast_add" -> "data", "pequiv.to_matrix_symm" -> "data", "category_theory.limits.kernel_is_iso_comp_hom_comp_kernel_\[Iota]" -> "category_theory", "filter.infi_sets_eq_finite" -> "order", "iterated_fderiv_within_succ_eq_comp_right" -> "analysis", "list.find_cons_of_neg" -> "data", "local_equiv.prod_target" -> "data", "list.of_mem_filter" -> "data", "filter.is_bounded_under_inf" -> "order", "deriv_within_const_sub" -> "analysis", "finset.coe_ssubset" -> "data", "finset.sigma_preimage_mk_of_subset" -> "data", "matrix.adjugate_transpose" -> "algebra", "measurable.fst" -> "analysis", "continuous_sigma_mk" -> "topology", "one_div_lt_one_div_of_neg" -> "algebra", "finmap.not_mem_erase_self" -> "data", "add_neg_le_iff_le_add'" -> "algebra", "finset.forall_mem_empty_iff" -> "data", "differentiable_within_at.div" -> "analysis", "finmap.ext_lookup" -> "data", "add_equiv.coe_mk" -> "data", "open_add_subgroup.zero_mem" -> "topology", "lagrange.interpolate_smul" -> "algebra", "int.modeq.modeq_sub" -> "data", "nat.gcd_mul_dvd_mul_gcd" -> "data", "mv_polynomial.degrees_add" -> "data", "linear_equiv.skew_prod_symm_apply" -> "algebra", "polynomial.separable.mul" -> "algebra", "pgame.nim.equiv_iff_eq" -> "set_theory", "submonoid.comap_map_comap" -> "algebra", "equiv_of_is_basis_refl" -> "algebra", "is_R_or_C.norm_sq_sub" -> "data", "is_local_min_on.on_subset" -> "topology", "localization_map.mk'_eq_iff_mk'_eq" -> "algebra", "cau_seq.lim_eq_zero_iff" -> "data", "submonoid.coe_injective" -> "algebra", "eq.trans" -> "init", "finsupp.sum_ite_eq'" -> "data", "qpf.recF_eq'" -> "data", "continuous_linear_map.le_op_norm" -> "analysis", "has_deriv_at_filter.sum" -> "analysis", "circle_deg1_lift.commute_iff_commute" -> "dynamics", "ordinal.CNF_pairwise" -> "set_theory", "emetric.mem_closure_iff" -> "topology", "with_top.top_ne_zero" -> "algebra", "zmod.cast_self'" -> "data", "function.right_inverse_of_injective_of_left_inverse" -> "init", "rat.coe_int_eq_of_int" -> "data", "generalized_continued_fraction.int_fract_pair.nth_stream_fr_nonneg_lt_one" -> "algebra", "metric.isometry_on_inl" -> "topology", "matrix_equiv_tensor_apply" -> "algebra", "is_R_or_C.abs_re_le_abs" -> "data", "finsupp.supported_Union" -> "algebra", "reflexive_many_one_reducible" -> "computability", "category_theory.functor.sum_map_inl" -> "category_theory", "pell.eq_pell_zd" -> "number_theory", "finsupp.map_domain_add" -> "data", "inf_nhds_at_top" -> "topology", "erased.map_def" -> "data", "implicit_function_data.pt_mem_to_local_homeomorph_source" -> "analysis", "not_forall" -> "logic", "nat.zero_lor" -> "data", "ennreal.coe_bit1" -> "data", "le_of_max_le_right" -> "algebra", "initial_seg.init_iff" -> "set_theory", "is_open_map.continuous_on_range_of_left_inverse" -> "topology", "list.append_eq_append_iff" -> "data", "int.le_add_of_nonneg_left" -> "init", "list.foldl_op_eq_op_foldr_assoc" -> "data", "matrix.bit1_apply_eq" -> "data", "embedding_sigma_map" -> "topology", "mv_polynomial.eval\:2082_zero" -> "data", "map_nhds_induced_of_surjective" -> "topology", "list.nodup_append_of_nodup" -> "data", "padic.padic_norm_e_lim_le" -> "data", "le_of_forall_le_of_dense" -> "order", "convex.image_sub_le_mul_sub_of_deriv_le" -> "analysis", "traversable.fold_mfoldl_cons" -> "control", "category_theory.prod.fst_obj" -> "category_theory", "polynomial.monic.next_coeff_prod" -> "data", "dvd_lcm_left" -> "algebra", "set.subset.antisymm_iff" -> "data", "list.sublist.map" -> "data", "lower_bound_Ioc" -> "order", "list.to_finset_card_of_nodup" -> "data", "category_theory.equivalence.functor_as_equivalence" -> "category_theory", "norm_num.nat_cast_zero" -> "tactic", "list.concat_perm" -> "data", "is_least_Ici" -> "order", "inv_eq_one_div" -> "algebra", "computation.lift_rel_return_right" -> "data", "pfunctor.approx.P_corec" -> "data", "measure_theory.l1.simple_func.of_simple_func_eq_mk" -> "analysis", "filter.tendsto_congr" -> "order", "neg_zero" -> "algebra", "times_cont_mdiff_at.smooth_at" -> "geometry", "submodule.span_singleton_le_iff_mem" -> "algebra", "mvqpf.liftr_map_last'" -> "data", "nat.min_succ_succ" -> "init", "int.modeq.modeq_mul_right" -> "data", "nat.coprime_pow_primes" -> "data", "polynomial.deriv_within" -> "analysis", "distrib_mul_action_hom.coe_fn_coe" -> "algebra", "le_of_add_le_add_right" -> "algebra", "functor.comp.run_seq" -> "control", "times_cont_mdiff_on_fst" -> "geometry", "local_equiv.right_inv_on" -> "data", "nat.partrec.code.smn" -> "computability", "zmod.quadratic_reciprocity" -> "number_theory", "set.Union_inter" -> "data", "differentiable.add_const" -> "analysis", "pnat.xgcd_type.flip_x" -> "data", "polynomial.integral_normalization_aeval_eq_zero" -> "data", "nat.unpair_mkpair" -> "data", "finset.sum_filter_ne_zero" -> "algebra", "option.not_mem_none" -> "data", "real.rpow_nat_inv_pow_nat" -> "analysis", "add_semiconj_by.neg_symm_left_iff" -> "algebra", "measurable_space.is_measurable_Sup" -> "analysis", "Sup_eq_supr'" -> "order", "times_cont_diff_succ_iff_fderiv" -> "analysis", "filter.has_basis.Limsup_eq_infi_Sup" -> "order", "linear_map.sub_apply" -> "algebra", "cau_seq.completion.inv_zero" -> "data", "polynomial.degree_le_nat_degree" -> "data", "one_lt_one_div" -> "algebra", "list.singleton_eq" -> "data", "nat.of_le_succ" -> "data", "mul_gsmul_assoc" -> "algebra", "omega.fun_mono_2" -> "tactic", "symmetrize_mem_uniformity" -> "topology", "set.sInter_subset_of_mem" -> "data", "category_theory.prod_preserves_connected_limits.\[Gamma]\:2081_app" -> "category_theory", "algebraic_closure.is_algebraic" -> "algebra", "add_subgroup.coe_prod" -> "algebra", "set.bUnion_pair" -> "data", "finset.insert_erase_subset" -> "data", "quadratic_form.coe_fn_smul" -> "algebra", "mul_div_cancel_left_of_imp" -> "algebra", "le_max_right" -> "init", "measure_theory.l1.simple_func.uniform_inducing" -> "analysis", "with_top.coe_Inf" -> "order", "bitraversable.tfst_id" -> "control", "Set.mem_sep" -> "set_theory", "isometry_id" -> "topology", "list.zip_unzip" -> "data", "real.has_deriv_at_rpow_of_one_le" -> "analysis", "finsupp.mul_apply" -> "data", "finset.center_mass_eq_of_sum_1" -> "analysis", "additive.is_add_submonoid_iff" -> "algebra", "category_theory.limits.types.pi" -> "category_theory", "cardinal.powerlt_max" -> "set_theory", "cardinal.power_zero" -> "set_theory", "bsupr_le" -> "order", "finsupp.eq_zero_of_comap_domain_eq_zero" -> "data", "real.sqrt_prop" -> "data", "metric.lipschitz_inf_dist_set" -> "topology", "sum.map_traverse" -> "control", "ennreal.le_coe_iff" -> "data", "matrix.minor_empty" -> "data", "dfinsupp.single_smul" -> "data", "setoid.trans'" -> "data", "function.left_inverse.id" -> "init", "equiv.conj_apply" -> "data", "set.countable_singleton" -> "data", "real.is_conjugate_exponent.conjugate_eq" -> "data", "real.sqrt_two_add_series_zero" -> "analysis", "is_glb_infi" -> "order", "add_le_of_le_of_nonpos" -> "algebra", "prime_multiset.prod_sup" -> "data", "is_R_or_C.eq_conj_iff_real" -> "data", "polynomial.degree_eq_one_of_irreducible_of_root" -> "data", "cardinal.lift_id" -> "set_theory", "pgame.zero_right_moves" -> "set_theory", "multiset.cons_inter_of_neg" -> "data", "typevec.drop_fun_split_fun" -> "data", "rat.add_num_denom" -> "data", "int.mul_lt_mul_of_pos_left" -> "init", "distrib_mul_action_hom.map_neg" -> "algebra", "irreducible_of_prime" -> "algebra", "list.countp_nil" -> "data", "finite_field.cast_card_eq_zero" -> "algebra", "uniform_continuous.prod_mk_right" -> "topology", "submodule.mul_induction_on" -> "algebra", "is_group_hom.inv_iff_ker" -> "algebra", "ideal.is_local.le_jacobson" -> "algebra", "monoid_hom.iterate_map_gpow" -> "algebra", "seq1.join_join" -> "data", "continuous_linear_equiv.differentiable_at" -> "analysis", "filter.principal_eq_bot_iff" -> "order", "finsupp.single_sub" -> "data", "to_topological_space_inf" -> "topology", "complex.of_real_sinh_of_real_re" -> "data", "list.length_rotate'" -> "data", "smooth.smooth_on" -> "geometry", "submonoid.mem_Inf" -> "algebra", "ordinal.pred_le_self" -> "set_theory", "category_theory.limits.coprod.left_unitor_inv" -> "category_theory", "mul_mem_nonunits_right" -> "algebra", "is_add_hom.neg" -> "algebra", "wseq.destruct_think" -> "data", "normed_ring.inverse_add_norm_diff_nth_order" -> "analysis", "gold_conj_neg" -> "data", "ennreal.sub_le_sub" -> "data", "one_add_mul_le_pow'" -> "algebra", "real.pi_div_two_le_two" -> "analysis", "composition.blocks_fun_sigma_composition_aux" -> "analysis", "computation.exists_of_mem_bind" -> "data", "nnreal.add_div'" -> "data", "set.mem_of_mem_insert_of_ne" -> "data", "bool_of_nat_mem_Icc_of_mem_Icc_to_nat" -> "system", "multiset.mem_of_mem_filter" -> "data", "exists_unique_congr" -> "init", "nat.bodd_two" -> "init", "is_integral_domain.polynomial" -> "data", "multiset.cons_le_cons_iff" -> "data", "measure_theory.simple_func.integral_eq_lintegral" -> "analysis", "mv_polynomial.eval_indicator_apply_eq_one" -> "algebra", "asymptotics.is_o_bot" -> "analysis", "topological_space.opens.val_eq_coe" -> "topology", "set.inj_on_empty" -> "data", "polynomial.coeff_C" -> "data", "category_theory.limits.cospan_left" -> "category_theory", "mvpfunctor.W_path_dest_right_W_path_cases_on" -> "data", "stream.corec_id_id_eq_const" -> "data", "continuous_iff_le_induced" -> "topology", "nat.modeq.modeq_of_dvd" -> "data", "pi_Lp.edist" -> "topology", "category_theory.limits.colimit.w" -> "category_theory", "nat.succ_le_succ_iff" -> "data", "set.eq_of_subset_of_subset" -> "data", "is_add_subgroup.mem_add_center" -> "algebra", "mvpfunctor.M.bisim" -> "data", "initial_seg.le_add_apply" -> "set_theory", "category_theory.limits.prod.lift_comp_comp_assoc" -> "category_theory", "int.neg_succ_of_nat_coe'" -> "init", "real.pi_lower_bound_start" -> "data", "finsupp.lapply_apply" -> "algebra", "fintype.card_unit" -> "data", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp" -> "category_theory", "cardinal.lift_min" -> "set_theory", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le" -> "analysis", "presented_group.to_group.mul" -> "algebra", "contracting_with.fixed_point_is_fixed_pt" -> "topology", "ennreal.top_mul_top" -> "data", "real.borel_eq_generate_from_Iio_rat" -> "analysis", "closure_eq_self_union_frontier" -> "topology", "int.dvd_of_mod_eq_zero" -> "data", "monotone.map_inf" -> "order", "cardinal.mul_eq_right" -> "set_theory", "relation.trans_gen.trans_right" -> "logic", "int.of_nat_ge_zero" -> "init", "nat.one_lt_two_pow" -> "data", "initial_seg.lt_or_eq_apply_right" -> "set_theory", "equiv.symm_apply_eq" -> "data", "finset.card_fin" -> "data", "filter.inf_principal_ne_bot_iff" -> "order", "is_add_subgroup.neg_mem_iff" -> "algebra", "sym2.mk_has_mem" -> "data", "path_component_congr" -> "topology", "exists_nat_gt" -> "algebra", "function.iterate_succ_apply" -> "logic", "function.injective2.left" -> "logic", "set.diff_singleton_subset_iff" -> "data", "convex_halfspace_im_gt" -> "analysis", "list.map_diff" -> "data", "omega.coeffs.dvd_val" -> "tactic", "continuous_linear_map.smul_algebra_right_apply" -> "analysis", "mdifferentiable.mfderiv_within" -> "geometry", "finset.subset_univ" -> "data", "monoid_hom.mem_ker" -> "algebra", "dlist.to_list_empty" -> "data", "quadratic_form.polar_add_left" -> "algebra", "le_add_of_nonneg_right" -> "algebra", "list.foldr_ext" -> "data", "add_monoid_hom.functions_ext" -> "algebra", "Algebra.id_apply" -> "algebra", "pfunctor.M.isubtree_cons" -> "data", "differentiable_at.has_deriv_at" -> "analysis", "filter.tendsto_bot" -> "order", "set.union_diff_cancel_left" -> "data", "finsupp.emb_domain_inj" -> "data", "submodule.map_smul" -> "algebra", "list.mem_argmax_iff" -> "data", "continuous_linear_map.lmul_left_right_norm_le" -> "analysis", "is_closed.is_complete" -> "topology", "list.count_le_count_cons" -> "data", "complex.re_eq_add_conj" -> "data", "con.rel_eq_coe" -> "algebra", "cardinal.ord_lt_ord" -> "set_theory", "mv_polynomial.map_injective" -> "data", "submodule.not_le_iff_exists" -> "algebra", "int.add_div_of_dvd" -> "data", "has_fderiv_at_fst" -> "analysis", "injective_of_surjective" -> "algebra", "continuous.measurable" -> "analysis", "nat.one_ne_zero" -> "init", "category_theory.limits.inv_prod_comparison_map_fst_assoc" -> "category_theory", "category_theory.limits.prod_map_map_assoc" -> "category_theory", "subset_convex_hull" -> "analysis", "differentiable.const_mul" -> "analysis", "nat.bit_zero" -> "init", "UniformSpace.completion_hom_val" -> "topology", "ring.fractional_ideal.coe_coe_ideal" -> "algebra", "polynomial.eq_one_of_is_unit_of_monic" -> "data", "semiconj_by.mul_left" -> "algebra", "coe_sort_coe_base" -> "logic", "int.div_eq_zero_of_lt_abs" -> "data", "list.func.get_map'" -> "data", "sub_pow_char" -> "algebra", "ring.closure_subset_iff" -> "algebra", "finset.not_mem_empty" -> "data", "nat.two_not_dvd_two_mul_add_one" -> "data", "nat.fib_one" -> "data", "ordinal.infinite_pigeonhole_card" -> "set_theory", "multiset.rel_add_right" -> "data", "quadratic_form.comp_apply" -> "algebra", "add_submonoid.localization_map.mk'_eq_iff_eq_add" -> "algebra", "vector3.append_insert" -> "number_theory", "add_submonoid.coe_inf" -> "algebra", "and_or_distrib_left" -> "logic", "nat.cast_with_bot" -> "data", "mvpfunctor.comp.mk_get" -> "data", "approximates_linear_on.inverse_approx_map_sub" -> "analysis", "times_cont_diff.continuous_fderiv_apply" -> "analysis", "diagonal_eq_range_diagonal_map" -> "topology", "norm_num.inv_neg" -> "tactic", "infi_of_empty" -> "order", "continuous_linear_map.has_fderiv_within_at" -> "analysis", "submonoid.localization_map.mk'_surjective" -> "algebra", "option.ne_none_iff_exists" -> "data", "finset.left_eq_union_iff_subset" -> "data", "mem_perms_of_list_of_mem" -> "data", "category_theory.limits.has_zero_object.to_zero_ext" -> "category_theory", "ennreal.half_lt_self" -> "data", "model_with_corners.unique_diff_preimage" -> "geometry", "iff.symm" -> "init", "hyperreal.coe_neg" -> "data", "times_cont_diff_on.times_cont_diff_within_at" -> "analysis", "submodule.mem_comap" -> "algebra", "is_seq_compact.totally_bounded" -> "topology", "archimedean_iff_rat_lt" -> "algebra", "distrib_mul_action_hom.id_comp" -> "algebra", "multiset.ndinter_eq_zero_iff_disjoint" -> "data", "lcm_same" -> "algebra", "measure_theory.l1.integral_eq_norm_pos_part_sub" -> "analysis", "category_theory.biprod.column_nonzero_of_iso" -> "category_theory", "list.head_lookup_all" -> "data", "ennreal.one_eq_coe" -> "data", "is_measurable_Ioi" -> "analysis", "nat.mul_def" -> "data", "times_cont_diff_within_at_local_invariant_prop" -> "geometry", "primrec\:2082.comp" -> "computability", "lists'.cons_subset" -> "set_theory", "measure_theory.lebesgue_length_Ico" -> "analysis", "supr_subtype'" -> "order", "real.differentiable_at_cos" -> "analysis", "iterated_deriv_zero" -> "analysis", "circle_deg1_lift.tendsto_translation_number'" -> "dynamics", "filter.unbounded_of_tendsto_at_top" -> "order", "int.shiftr_neg_succ" -> "data", "equiv.point_reflection_involutive" -> "data", "tensor_product.rid_tmul" -> "algebra", "category_theory.yoneda.naturality" -> "category_theory", "category_theory.iso.eq_inv_comp" -> "category_theory", "metric.mem_of_closed'" -> "topology", "finmap.to_finmap_nil" -> "data", "list.eq_of_prefix_of_length_eq" -> "data", "metric.inf_dist_le_inf_dist_add_dist" -> "topology", "finset.prod_fiberwise" -> "data", "mul_ne_zero_comm" -> "algebra", "category_theory.limits.biprod.inr_map" -> "category_theory", "submodule.complete_of_finite_dimensional" -> "analysis", "Module.monoidal_category.associator_naturality" -> "algebra", "computation.destruct_eq_ret" -> "data", "computation.rel_of_lift_rel" -> "data", "vsub_eq_sub" -> "algebra", "finset.prod_filter_of_ne" -> "algebra", "list.argmax_two_self" -> "data", "finset.prod_flip" -> "algebra", "pgame.equiv_of_relabelling" -> "set_theory", "lt_or_gt_of_ne" -> "init", "I_extend_extends" -> "topology", "ordinal.power_limit" -> "set_theory", "category_theory.limits.prod.right_unitor_inv" -> "category_theory", "edist_le_Ico_sum_of_edist_le" -> "topology", "irrational.of_mul_self" -> "data", "linear_equiv.coe_prod" -> "algebra", "category_theory.monoidal_category.right_unitor_product_aux_perimeter" -> "category_theory", "polynomial.continuous_within_at" -> "analysis", "category_theory.nat_trans.op_app" -> "category_theory", "prod.one_eq_mk" -> "algebra", "multiset.add_le_add_left" -> "data", "differentiable_within_at_snd" -> "analysis", "fintype.card_fin" -> "data", "measurable.norm" -> "analysis", "filter.eq_infi_of_mem_sets_iff_exists_mem" -> "order", "vector.remove_nth_val" -> "data", "finset.product_val" -> "data", "measure_theory.limsup_lintegral_le" -> "analysis", "set.Inter_set_of" -> "data", "galois_insertion.u_injective" -> "order", "function.uncurry_curry" -> "init", "add_subgroup.mem_prod" -> "algebra", "nhds_le_of_le" -> "topology", "UniformSpace.coe_mk" -> "topology", "vector.tendsto_cons" -> "topology", "units.conj_pow'" -> "algebra", "function.comp.assoc" -> "init", "category_theory.monoidal_category.id_tensor_comp_tensor_id" -> "category_theory", "localization_map.mk'_one" -> "algebra", "bernoulli_def'" -> "number_theory", "list.length_pos_of_prod_ne_one" -> "data", "filter.is_bounded_under.mono" -> "order", "category_theory.abelian.pseudo_equal_refl" -> "category_theory", "mul_dvd_mul" -> "algebra", "polynomial.has_deriv_at" -> "analysis", "pfun.bind_defined" -> "data", "category_theory.adjunction.hom_equiv_naturality_right" -> "category_theory", "or_self_right" -> "logic", "dfinsupp.subtype_domain_finsupp_sum" -> "data", "finset.sum_Ico_reflect" -> "algebra", "padic_norm.sub" -> "data", "submonoid.localization_map.map_units" -> "algebra", "ring_equiv.to_CommRing_iso_hom" -> "algebra", "list.union_sublist_append" -> "data", "map_Sup_of_continuous_at_of_monotone'" -> "topology", "sup_eq_left" -> "order", "right_distrib" -> "algebra", "nnreal.div_eq_mul_one_div" -> "data", "finset.finite_to_set_to_finset" -> "data", "nat.sub_add_eq_add_sub" -> "data", "has_deriv_at.prod" -> "analysis", "enat.top_add" -> "data", "polynomial.splits_map_iff" -> "algebra", "frontier_ball" -> "analysis", "local_homeomorph.symm_source" -> "topology", "times_cont_diff_on.continuous_linear_map_comp" -> "analysis", "rat.not_irrational" -> "data", "list.repeat_perm" -> "data", "power_series.span_X_is_prime" -> "algebra", "inner_comm" -> "analysis", "int.gcd_div" -> "algebra", "num.mul_to_nat" -> "data", "is_absolute_value.abv_neg" -> "data", "preorder_hom.id_comp" -> "order", "nat.le_add_left" -> "init", "has_deriv_within_at_iff_tendsto_slope'" -> "analysis", "bilin_form.zero_left" -> "algebra", "submodule.mem_span" -> "algebra", "Top.mono_iff_injective" -> "topology", "continuous_list_prod" -> "topology", "monoid_hom.comp_id" -> "algebra", "minimal_polynomial.unique'" -> "algebra", "bex_def" -> "logic", "set.eq_on_indicator" -> "data", "onote.oadd_pos" -> "set_theory", "real.geom_mean_le_arith_mean_weighted" -> "analysis", "continuous_neg" -> "topology", "has_deriv_within_at_neg" -> "analysis", "localization_map.exists_integer_multiple" -> "algebra", "mv_polynomial.rename_prodmk_eval\:2082" -> "data", "category_theory.under.map_map_right" -> "category_theory", "filter.prod_infi_right" -> "order", "real.lt_Sup" -> "data", "polynomial.div_by_monic_eq_zero_iff" -> "data", "finsupp.map_domain_smul" -> "data", "complex.of_real_bit1" -> "data", "is_max_filter_dual_iff" -> "order", "add_submonoid.ext" -> "algebra", "is_max_on.of_is_local_max_of_convex_univ" -> "analysis", "category_theory.functor.hext" -> "category_theory", "matrix.mul_diagonal" -> "data", "computable_pred.rice" -> "computability", "category_theory.preadditive.sum_comp" -> "category_theory", "list.lookmap_congr" -> "data", "ordinal.min_le" -> "set_theory", "multiset.fold_eq_foldl" -> "data", "infi_of_empty'" -> "order", "multiset.filter_map_filter" -> "data", "omega.term.val_add" -> "tactic", "surjective_of_continuous" -> "topology", "decidable.or_iff_not_imp_right" -> "logic", "category_theory.coyoneda.naturality" -> "category_theory", "int.nat_abs_eq" -> "init", "is_seq_closed_of_def" -> "topology", "measure_theory.measure.count_apply" -> "analysis", "mv_power_series.constant_coeff_map" -> "algebra", "nnreal.coe_list_sum" -> "data", "smooth_on.prod_map" -> "geometry", "set.subset_diff_union" -> "data", "nat.sub_le_sub_left" -> "init", "lt_is_glb_iff" -> "order", "filter.comap_id" -> "order", "list.length_le_of_sublist" -> "init", "measure_theory.to_outer_measure_to_measure" -> "analysis", "hyperreal.is_st_unique" -> "data", "continuous_multilinear_map.uncurry0_norm" -> "analysis", "equiv.arrow_congr_apply" -> "data", "add_aut.one_def" -> "data", "bounded_convex_hull" -> "analysis", "polynomial.card_roots'" -> "data", "sesq_form.ortho_smul_left" -> "algebra", "pos_num.one_le_cast" -> "data", "uniform_continuous\:2082.bicompl" -> "topology", "open_add_subgroup.is_closed" -> "topology", "stream.tail_interleave" -> "data", "list.Ico.pairwise_lt" -> "data", "complex.continuous_linear_map.im_coe" -> "analysis", "finset.supr_insert" -> "data", "complex.log_one" -> "analysis", "add_monoid_hom.map_rat_module_smul" -> "algebra", "finset.sdiff_union_inter" -> "data", "affine_map.id_apply" -> "algebra", "mvqpf.cofix.bisim" -> "data", "smodeq.trans" -> "algebra", "metric.bounded_of_compact" -> "topology", "continuous_linear_equiv.coord_norm" -> "analysis", "polynomial.not_is_unit_X_sub_C" -> "data", "affine_map.line_map_zero" -> "algebra", "wseq.map_congr" -> "data", "right_ne_zero_of_mul" -> "algebra", "euclidean_domain.mod_one" -> "algebra", "list.erase_dup_cons_of_mem" -> "data", "measure_theory.ae_eq_fun.mk_mul_mk" -> "analysis", "filter.tendsto.frequently" -> "order", "tensor_product.direct_sum_lof_tmul_lof" -> "algebra", "cardinal.mk_Icc_real" -> "data", "le_sup_right_of_le" -> "order", "lie_ring.of_associative_ring_bracket" -> "algebra", "wseq.destruct_dropn" -> "data", "real.cos_pos_of_le_one" -> "data", "pSet.mem_powerset" -> "set_theory", "nat.zero_lt_one" -> "init", "Top.comp_app" -> "topology", "int.neg_of_nat_zero" -> "init", "num.div_to_nat" -> "data", "int.zero_nonneg" -> "init", "submodule.smul_mem_span_smul" -> "algebra", "set.range_const" -> "data", "ennreal.one_le_coe_iff" -> "data", "commute.inv_right_iff'" -> "algebra", "add_sub_sub_cancel" -> "algebra", "measurable_space.map_mono" -> "analysis", "category_theory.monad_hom.ext" -> "category_theory", "or.assoc" -> "init", "is_cyclic_of_subgroup_integral_domain" -> "algebra", "complex.im_sq_le_norm_sq" -> "data", "congr_fun" -> "init", "pell.dvd_of_ysq_dvd" -> "number_theory", "finsupp.restrict_dom_apply" -> "algebra", "uniform_continuous.neg" -> "topology", "fintype.card_pi_finset" -> "data", "set.Ioc_diff_Ioo_same" -> "data", "category_theory.limits.eq_zero_of_epi_kernel" -> "category_theory", "differentiable_at.rpow" -> "analysis", "pfunctor.approx.cofix_a_eq_zero" -> "data", "polynomial.map_dvd_map" -> "data", "prime_multiset.coe_pnat_nat" -> "data", "hyperreal.is_st_refl_real" -> "data", "interior_Ioc" -> "topology", "free_abelian_group.pure_bind" -> "algebra", "aux_has_sum_of_le_geometric" -> "analysis", "times_cont_mdiff_within_at_iff_nat" -> "geometry", "topological_space.opens.ext" -> "topology", "convex_hull_min" -> "analysis", "power_series.order_mul" -> "algebra", "finsupp.add_sub_single_one" -> "data", "measure_theory.simple_func.restrict_univ" -> "analysis", "add_con.ext_iff" -> "algebra", "equiv.perm.mul_def" -> "data", "option.eq_of_eq_some" -> "init", "polynomial.integral_normalization_coeff_ne_degree" -> "data", "fraction_map.num_mul_denom_eq_num_iff_eq" -> "algebra", "is_linear_map.is_linear_map_neg" -> "algebra", "cardinal.cantor_function_aux_eq" -> "data", "int.bit_decomp" -> "data", "is_coprime.of_add_mul_right_left" -> "algebra", "turing.list_blank.map_cons" -> "computability", "set.countable.bUnion" -> "data", "embedding_is_closed" -> "topology", "set.Ioc_def" -> "data", "finsupp.subtype_domain_sum" -> "data", "set.mem_insert_iff" -> "data", "int.cast_nonpos" -> "data", "turing.tr_reaches\:2081" -> "computability", "measure_theory.l1.dist_to_fun" -> "analysis", "nat.partrec.code.fixed_point" -> "computability", "rat.cast_mk" -> "data", "has_deriv_within_at.scomp" -> "analysis", "qpf.supp_preservation_iff_liftp_preservation" -> "data", "prod_generate_from_generate_from_eq" -> "topology", "pequiv.to_pequiv_mul_matrix" -> "data", "bifunctor.map_equiv_symm_apply" -> "data", "pi.is_basis_std_basis" -> "algebra", "rel_embedding.refl_apply" -> "order", "convex.to_cone_eq_Inf" -> "analysis", "Module.Mon_Module_equivalence_Algebra.ring_one" -> "category_theory", "turing.tape.exists_mk'" -> "computability", "set.mem_sep_eq" -> "data", "nat.two_mul_ne_two_mul_add_one" -> "data", "polynomial.degree_sub_le" -> "data", "category_theory.limits.coprod_map_id_comp" -> "category_theory", "emetric.cauchy_seq_iff_le_tendsto_0" -> "topology", "principal_seg.top_lt_top" -> "set_theory", "multiset.mem_erase_iff_of_nodup" -> "data", "nat.lt_add_of_pos_left" -> "init", "continuous_linear_equiv.fderiv_within" -> "analysis", "localization.mk_eq_monoid_of_mk'_apply" -> "algebra", "add_monoid_hom.continuous_of_bound" -> "analysis", "cardinal.add_one_le_succ" -> "set_theory", "list.filter_sublist_filter" -> "data", "set.Union_mul_left_image" -> "algebra", "set.empty_mul" -> "algebra", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_fst" -> "analysis", "uniform_embedding.embedding" -> "topology", "filter.is_countably_generated.eq_generate" -> "order", "convex_cone.pointed_iff_not_blunt" -> "analysis", "decidable.imp_or_distrib'" -> "logic", "set.mem_singleton" -> "data", "filter.tendsto_at_bot_mono'" -> "order", "real.coe_fib_eq" -> "data", "category_theory.abelian.pseudoelement.apply_eq_zero_of_comp_eq_zero" -> "category_theory", "is_closed.mem_of_tendsto" -> "topology", "uniform_space.completion.uniform_continuous_extension" -> "topology", "computation.lift_rel_return" -> "data", "continuous_quotient_lift" -> "topology", "vector.nth_update_nth_same" -> "data", "findim_eq_zero" -> "algebra", "asymptotics.is_O.prod_rightr" -> "analysis", "continuous_multilinear_map.map_smul_univ" -> "topology", "add_units.add_left_symm" -> "data", "free_comm_ring.restriction_of" -> "algebra", "set.nonempty.prod" -> "data", "submodule.quotient_equiv_of_is_compl_symm_apply" -> "algebra", "and.comm" -> "init", "equiv.point_reflection_midpoint_left" -> "algebra", "category_theory.equivalence.inverse_map_inj_iff" -> "category_theory", "measure_theory.ae_eq_fun.coe_fn_comp" -> "analysis", "rank_le_range" -> "algebra", "eq_of_nndist_eq_zero" -> "topology", "turing.TM1to1.step_aux_write" -> "computability", "ring.fractional_ideal.eq_span_singleton_of_principal" -> "algebra", "rat.cast_abs" -> "data", "polynomial.prime_of_degree_eq_one_of_monic" -> "data", "is_subgroup.of_div" -> "algebra", "list.sublist.subset" -> "data", "category_theory.monoidal_category.left_unitor_tensor" -> "category_theory", "filter.eventually_eq_bind" -> "order", "is_compact.bdd_below" -> "topology", "partrec\:2082.unpaired'" -> "computability", "ennreal.top_pow" -> "data", "set.compl_union" -> "data", "local_homeomorph.eq_on_source.eq_on" -> "topology", "multiplicity.multiplicity_pow_self_of_prime" -> "algebra", "ennreal.tsum_eq_supr_sum'" -> "topology", "vector.to_list_length" -> "data", "dense_embedding_of_rat" -> "topology", "finset.sum_insert_of_eq_zero_if_not_mem" -> "algebra", "set.eq_or_ssubset_of_subset" -> "data", "semilattice_sup.ext" -> "order", "computable.list_length" -> "computability", "is_bounded_bilinear_map.map_sub_left" -> "analysis", "sup_assoc" -> "order", "indicator_ae_eq_restrict_compl" -> "analysis", "hyperreal.omega_pos" -> "data", "ordinal.cof_eq_one_iff_is_succ" -> "set_theory", "lt_add_of_pos_of_le" -> "algebra", "is_compl.right_unique" -> "order", "rel.inv_comp" -> "data", "subgroup.closure_induction" -> "algebra", "multiset.subset.refl" -> "data", "composition.mem_range_embedding" -> "combinatorics", "filter.eventually_lift'_powerset" -> "order", "real.sqrt_exists" -> "data", "not_or_of_imp" -> "logic", "ennreal.lt_top_iff_ne_top" -> "data", "equiv_functor.map_equiv_apply" -> "control", "measure_theory.integrable.min_zero" -> "analysis", "finset.mem_insert_of_mem" -> "data", "contracting_with.efixed_point_is_fixed_pt" -> "topology", "finset.right_eq_union_iff_subset" -> "data", "zsqrtd.coe_int_val" -> "data", "free_magma.traverse_pure'" -> "algebra", "cInf_intro" -> "order", "uniform_continuous.prod_map" -> "topology", "minimal_polynomial.monic" -> "algebra", "padic_norm_z.mul" -> "data", "submonoid.map_le_iff_le_comap" -> "algebra", "continuous_linear_equiv.continuous_within_at" -> "topology", "is_lub.bdd_above" -> "order", "polynomial.eval\:2082_bit0" -> "data", "set.Ioc_union_Ici_eq_Ioi" -> "data", "cardinal.mk_le_of_injective" -> "set_theory", "nat.modeq.refl" -> "data", "nnreal.tendsto_of_real" -> "topology", "ideal.top_pow" -> "algebra", "iff_true_right" -> "logic", "category_theory.limits.equalizer.hom_ext" -> "category_theory", "nnreal.rpow_arith_mean_le_arith_mean_rpow" -> "analysis", "category_theory.monoidal_category.left_unitor_nat_iso_inv_app" -> "category_theory", "tendsto_finset_sum" -> "topology", "list.prefix_append_right_inj" -> "data", "dfinsupp.support_neg" -> "data", "submonoid.localization_map.comp_eq_of_eq" -> "algebra", "mem_of_is_closed_sequential" -> "topology", "list.mmap_with_index'_eq_mmap_with_index" -> "data", "normed_field.nhds_within_is_unit_ne_bot" -> "analysis", "typevec.snd_diag" -> "data", "finset.image_preimage_of_bij" -> "data", "bounded_continuous_function.coe_sub" -> "topology", "differentiable.smul_algebra" -> "analysis", "quotient_map.comp" -> "topology", "nnreal.of_real_lt_of_real_iff_of_nonneg" -> "data", "is_unit_unit" -> "algebra", "multiset.map_traverse" -> "data", "complex.two_cos" -> "data", "category_theory.non_preadditive_abelian.lift_\[Sigma]" -> "category_theory", "set.eq_on.mono" -> "data", "with_top.is_glb_Inf" -> "order", "nat.choose_symm_of_eq_add" -> "data", "pos_num.bit_to_nat" -> "data", "lie_algebra.special_linear.E_apply_zero" -> "algebra", "ordinal.typein_lt_type" -> "set_theory", "Gromov_Hausdorff.dist_GH_dist" -> "topology", "set.compl_image" -> "data", "cardinal.omega_le_aleph" -> "set_theory", "subring.map_le_iff_le_comap" -> "algebra", "neg_pos" -> "algebra", "units.eq_inv_mul_iff_mul_eq" -> "algebra", "filter.Iio_mem_at_bot" -> "order", "mem_subalgebra_of_subsemiring" -> "algebra", "string.str_ne_empty" -> "init", "set.preimage_congr" -> "data", "list.drop_drop" -> "data", "list.length_drop" -> "init", "measure_theory.measure.restrict_univ" -> "analysis", "submodule.coe_prod_equiv_of_is_compl'" -> "algebra", "finset.is_measurable" -> "analysis", "polynomial.separable_prod" -> "algebra", "multiset.length_ndinsert_of_mem" -> "data", "pnat.coprime.coprime_dvd_left" -> "data", "add_comm_group.direct_limit.of_add" -> "algebra", "linear_equiv.eq_symm_apply" -> "algebra", "equiv.traverse_eq_map_id" -> "control", "tensor_product.smul.aux_of" -> "algebra", "filter.is_bounded.mono" -> "order", "cardinal.bit1_lt_bit0" -> "set_theory", "rat.cast_div" -> "data", "list.cons_subperm_of_mem" -> "data", "filter.map_one" -> "order", "supr_image" -> "order", "subring.map_map" -> "algebra", "eq_true_of_and_eq_true_right" -> "init", "isometry.comp" -> "topology", "commute.self_pow" -> "algebra", "zmod.val_min_abs_def_zero" -> "data", "category_theory.exp_comparison_natural_left" -> "category_theory", "gsmul_add_comm" -> "algebra", "constr_sub" -> "algebra", "category_theory.abelian.images.image_strong_epi_mono_factorisation_e_strong_epi" -> "category_theory", "AddCommGroup.ext" -> "algebra", "smooth_on_iff" -> "geometry", "model_with_corners.mk_coe_symm" -> "geometry", "lists.equiv_atom" -> "set_theory", "int.neg_lt_of_neg_lt" -> "init", "filter.has_basis.prod" -> "order", "topological_space.opens.mem_supr" -> "topology", "multiset.countp_zero" -> "data", "filter.lift'_infi" -> "order", "nat.sub_eq_sub_min" -> "init", "sub_sub_cancel" -> "algebra", "ultrafilter_basis_is_basis" -> "topology", "list.func.length_neg" -> "data", "sym2.rel.is_equivalence" -> "data", "map_cluster_pt_of_comp" -> "topology", "list.minimum_le_of_mem" -> "data", "localization_map.map_comap" -> "algebra", "set.Union_pos" -> "data", "dvd_iff_dvd_of_rel_left" -> "algebra", "local_equiv.source_subset_preimage_target" -> "data", "ennreal.max_zero_right" -> "data", "add_subgroup.closure_univ" -> "algebra", "continuous_within_at.mem_closure" -> "topology", "free_group.red.sizeof_of_step" -> "algebra", "multiset.union_def" -> "data", "subring.mem_to_submonoid" -> "algebra", "inv_le_inv''" -> "algebra", "subgroup.mem_gpowers" -> "algebra", "set.left_inv_on.eq" -> "data", "multiset.fold_distrib" -> "data", "ring_hom.map_range" -> "algebra", "list.filter_nil" -> "init", "nnreal.coe_zero" -> "data", "pell.pell_zd_add" -> "number_theory", "real.exp_log" -> "analysis", "finsupp.lmap_domain_apply" -> "algebra", "lipschitz_with.iff_le_add_mul" -> "topology", "with_zero.coe_add" -> "algebra", "nnreal.nsmul_coe" -> "data", "cardinal.powerlt_succ" -> "set_theory", "int.add_mod_mod" -> "data", "lipschitz_with.of_le_add_mul" -> "topology", "mul_left_comm" -> "algebra", "turing.tape.right\:2080_nth" -> "computability", "nat.mod_eq_of_lt" -> "init", "category_theory.iso.conj_Aut_trans" -> "category_theory", "nat.bitwise_zero_left" -> "init", "category_theory.arrow.hom_mk'_right" -> "category_theory", "finset.prod_ite" -> "algebra", "list.concat_append" -> "data", "composition.disjoint_range" -> "combinatorics", "measure_theory.integral_dirac" -> "analysis", "filter.germ.coe_pos" -> "order", "dvd_of_mul_right_dvd" -> "algebra", "list.perm.symm" -> "data", "lt_add_of_pos_of_lt'" -> "algebra", "finset.prod_range_div'" -> "algebra", "ring_equiv.coe_add_equiv_refl" -> "data", "local_equiv.target_subset_preimage_source" -> "data", "nat.min_fac_sq_le_self" -> "data", "abstract_completion.uniform_continuous_map" -> "topology", "infi_apply" -> "order", "has_deriv_at.smul" -> "analysis", "primrec.list_map" -> "computability", "smul_pow" -> "algebra", "category_theory.limits.biproduct.lift_desc" -> "category_theory", "nat.partrec.of_eq" -> "computability", "mul_lt_mul_of_neg_right" -> "algebra", "nat.dvd_add_left" -> "data", "turing.list_blank.head_map" -> "computability", "vector_span_empty" -> "algebra", "lt_of_add_lt_add_left" -> "algebra", "real.mk_eq" -> "data", "category_theory.non_preadditive_abelian.add_comm" -> "category_theory", "mv_polynomial.pderivative_C" -> "data", "category_theory.limits.cones.postcompose_equivalence_inverse" -> "category_theory", "generalized_continued_fraction.of_terminated_at_n_iff_succ_nth_int_fract_pair_stream_eq_none" -> "algebra", "finset.eq_of_card_le_one_of_sum_eq" -> "algebra", "ideal.map.is_maximal" -> "algebra", "filter.germ.const_comp_tendsto" -> "order", "seq.head_cons" -> "data", "has_sum_iff_tendsto_nat_of_summable_norm" -> "analysis", "equiv.fun_unique_symm_apply" -> "data", "category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv" -> "category_theory", "complex.tanh_eq_sinh_div_cosh" -> "data", "list.erase_comm" -> "data", "bor_eq_false_eq_eq_ff_and_eq_ff" -> "init", "category_theory.graded_object.shift_functor_obj_apply" -> "category_theory", "category_theory.non_preadditive_abelian.neg_add_self" -> "category_theory", "has_fpower_series_at.coeff_zero" -> "analysis", "nat.partrec.code.encode_lt_comp" -> "computability", "multiset.rel.mono" -> "data", "linear_map.ker_std_basis" -> "algebra", "polynomial.ite_le_nat_degree_coeff" -> "data", "ordinal.lt_power_of_limit" -> "set_theory", "list.mem_map" -> "data", "category_theory.monoidal_category.right_unitor_tensor" -> "category_theory", "real.rpow_lt_rpow_iff" -> "analysis", "measure_theory.simple_func.const_apply" -> "analysis", "nat.even.sub" -> "data", "ennreal.add_right_inj" -> "data", "topological_space.second_countable_topology_induced" -> "topology", "list.kerase_cons_eq" -> "data", "hash_map.valid.contains_aux_iff" -> "data", "nat.xgcd_aux_rec" -> "data", "integral_closure_idem" -> "algebra", "complex.cos_square" -> "data", "mem_closure_of_continuous2" -> "topology", "wseq.head_some_of_nth_some" -> "data", "category_theory.differential_object.hom.comp_f" -> "category_theory", "list.nil_sublist" -> "data", "vadd_right_injective" -> "algebra", "category_theory.equivalence.adjointify_\[Eta]_\[CurlyEpsilon]" -> "category_theory", "one_one_equiv.congr_left" -> "computability", "list.nodup_bind" -> "data", "nnnorm_smul" -> "analysis", "list.insert.def" -> "data", "principal_seg.lt_top" -> "set_theory", "minimal_polynomial.unique" -> "algebra", "measure_theory.ae_restrict_iff" -> "analysis", "erased.map_out" -> "data", "multiset.ndinter_subset_left" -> "data", "linear_equiv.to_Module_iso'_inv" -> "algebra", "add_mul_self_eq" -> "algebra", "ideal.map_supr" -> "algebra", "set.Icc_union_Icc_eq_Icc" -> "data", "sup_Inf_eq" -> "order", "measure_theory.with_density_apply" -> "analysis", "polynomial.leading_coeff_pow" -> "data", "tactic.abel.unfold_smul" -> "tactic", "finset.sum_cancels_of_partition_cancels" -> "algebra", "filter.tendsto_iff_ptendsto" -> "order", "set.ball_image_iff" -> "data", "isometric.coe_add_right" -> "topology", "plift.down_inj" -> "logic", "has_fpower_series_on_ball.uniform_geometric_approx" -> "analysis", "is_comm_applicative.commutative_map" -> "control", "isometric.inv_apply_self" -> "topology", "nat.modeq.dvd_of_modeq" -> "data", "ulift.zero_down" -> "algebra", "equiv.perm.sign_eq_of_is_swap" -> "algebra", "polynomial.map_prod" -> "data", "pgame.zero_lt_star" -> "set_theory", "differentiable_within_at_const" -> "analysis", "multiset.subset_erase_dup'" -> "data", "mul_le_mul_left'" -> "algebra", "complex.deriv_cosh" -> "analysis", "false_iff_true" -> "init", "monotone.mul'" -> "algebra", "nat.le_sub_left_iff_add_le" -> "data", "zorn.chain_insert" -> "order", "ideal.map_radical_le" -> "algebra", "is_conj_trans" -> "algebra", "ordinal.lt_mul_of_limit" -> "set_theory", "gaussian_int.nat_cast_nat_abs_norm" -> "data", "finite_dimensional_bot" -> "algebra", "closure_image_mem_nhds_of_uniform_inducing" -> "topology", "euclidean_domain.eq_div_of_mul_eq_right" -> "algebra", "multiset.union_le_add" -> "data", "filter.eventually_eq.is_local_min_on_iff" -> "topology", "submodule.comap_top" -> "algebra", "qpf.fix.rec_unique" -> "data", "finsupp.not_mem_support_iff" -> "data", "false_implies_iff" -> "init", "pell.eq_of_xn_modeq" -> "number_theory", "finsupp.emb_domain_notin_range" -> "data", "setoid.trans" -> "init", "lucas_lehmer.X.bit0_snd" -> "number_theory", "nat.succ_div" -> "data", "neg_neg_sub_neg" -> "algebra", "category_theory.functor.map_cone_inv_\[Pi]" -> "category_theory", "finset.pi.cons_ne" -> "data", "homeomorph.image_symm" -> "topology", "traversable.map_traverse" -> "control", "strict_weak_order.etrans" -> "init", "is_closed_Ici" -> "topology", "topological_fiber_bundle_core.local_triv_at_ext_to_local_homeomorph" -> "topology", "cardinal.omega_pos" -> "set_theory", "has_deriv_within_at_iff_tendsto_slope" -> "analysis", "int.bit_zero" -> "data", "strict_mono.le_iff_le" -> "order", "add_eq_zero_iff_neg_eq" -> "algebra", "mv_polynomial.coeff_monomial" -> "data", "filter.generate_empty" -> "order", "quotient.ind\:2082'" -> "data", "nat.lt_add_of_pos_right" -> "init", "asymptotics.is_o.trans'" -> "analysis", "abs_lt" -> "algebra", "eq_inv_mul_iff_mul_eq" -> "algebra", "set.Icc_diff_both" -> "data", "nat.lt_succ_iff_lt_or_eq" -> "data", "set.sum_indicator_subset_of_eq_zero" -> "data", "list.func.mem_get_of_le" -> "data", "submonoid.localization_map.mk'_mul_eq_mk'_of_mul" -> "algebra", "monotone_closure" -> "topology", "linarith.int.coe_nat_mul_bit0" -> "tactic", "filter.tendsto_at_top_add_right_of_le" -> "order", "module.direct_limit.of_f" -> "algebra", "finset.attach_image_val" -> "data", "is_min_on.sup" -> "order", "typevec.append_fun_comp'" -> "data", "not_and" -> "logic", "measure_theory.lintegral_tsum" -> "analysis", "nnreal.rpow_le_rpow_of_exponent_ge" -> "analysis", "filter.ultrafilter_ultrafilter_of'" -> "order", "add_subgroup.mem_map" -> "algebra", "ideal.map_Inf" -> "algebra", "le_zero_iff_eq" -> "algebra", "has_fderiv_at.smul_const" -> "analysis", "nnnorm_sum_le" -> "analysis", "ennreal.inv_zero" -> "data", "list.erasep_cons_of_neg" -> "data", "topological_space.opens.mem_coe" -> "topology", "circle_deg1_lift.iterate_monotone" -> "dynamics", "fraction_map.exists_reduced_fraction" -> "algebra", "polynomial.C_bit1" -> "data", "setoid.sUnion_classes" -> "data", "ring.fractional_ideal.val_eq_coe" -> "algebra", "filter.frequently_or_distrib" -> "order", "circle_deg1_lift.lt_translation_number_of_forall_add_lt" -> "dynamics", "Top.subsheaf_to_Types_sheaf_condition" -> "topology", "fin.cases_succ" -> "data", "cau_seq.le_of_eq_of_le" -> "data", "mv_polynomial.map_id" -> "data", "is_topological_fiber_bundle.is_open_map_proj" -> "topology", "free_group.map_one" -> "algebra", "composition_as_set.ext_iff" -> "combinatorics", "int.lt_add_of_le_of_pos" -> "init", "real.pi_gt_31415" -> "data", "convex_hull_eq_union" -> "analysis", "lucas_lehmer.X.nat_coe_fst" -> "number_theory", "linear_equiv.of_injective_endo_to_fun" -> "algebra", "filter.eventually.prod_inr_nhds" -> "topology", "category_theory.limits.biprod.map_eq_map'" -> "category_theory", "abs_add" -> "algebra", "linear_equiv_matrix_symm_one" -> "algebra", "isometry.ediam_image" -> "topology", "measure_theory.l1.simple_func.of_simple_func_zero" -> "analysis", "nnreal.div_self" -> "data", "category_theory.limits.pullback_cone.mk_\[Pi]_app_left" -> "category_theory", "inner_product_geometry.angle_self" -> "geometry", "add_subgroup.map_supr" -> "algebra", "stream.nth_interleave_right" -> "data", "localization_map.eq_mk'_iff_mul_eq" -> "algebra", "fin.coe_two" -> "data", "of_digits_modeq'" -> "data", "add_sub_add_right_eq_sub" -> "algebra", "eq_comm" -> "init", "add_con.lift_on_beta" -> "algebra", "measure_theory.ae_eq_fun.smul_mk" -> "analysis", "mem_closure" -> "topology", "decidable.by_contradiction" -> "init", "is_coprime.of_mul_right_right" -> "algebra", "asymptotics.is_o.symm" -> "analysis", "relation.refl_trans_gen_iff_eq" -> "logic", "uniform_space.completion.induction_on" -> "topology", "category_theory.limits.cofork.coequalizer_ext" -> "category_theory", "many_one_reducible.mk" -> "computability", "subsemiring.prod_mono" -> "algebra", "add_lt_add" -> "algebra", "embedding_subtype_coe" -> "topology", "pos_of_mul_pos_right" -> "algebra", "category_theory.preadditive.epi_of_cancel_zero" -> "category_theory", "holor.slice_eq" -> "data", "add_submonoid.localization_map.of_add_equiv_of_dom_eq" -> "algebra", "padic_int.norm_lt_one_add" -> "data", "mvqpf.fix.ind" -> "data", "cardinal.min_eq" -> "set_theory", "times_cont_diff_const" -> "analysis", "complex.I_mul" -> "data", "stream.iterate_eq" -> "data", "convex_hull_ediam" -> "analysis", "vector.m_of_fn_pure" -> "data", "computable.cond" -> "computability", "nat.sqrt_succ_le_succ_sqrt" -> "data", "submodule.mem_span_singleton_self" -> "algebra", "power_series.constant_coeff_X" -> "algebra", "add_equiv.refl_apply" -> "data", "category_theory.split_mono.id" -> "category_theory", "measure_theory.ae_eq_fun.coe_fn_const" -> "analysis", "option.get_or_else_of_ne_none" -> "data", "set.mem_Ioo_or_eq_left_of_mem_Ico" -> "data", "buffer.lt_aux_2" -> "data", "category_theory.category_of_elements.\[Pi]_map" -> "category_theory", "free_abelian_group.lift_comp" -> "algebra", "lt_trichotomy" -> "init", "complex.of_real_one" -> "data", "measure_theory.ae_eq_fun.coe_fn_pos_part" -> "analysis", "ordinal.CNF_zero" -> "set_theory", "simple_graph.adj_matrix_mul_apply" -> "combinatorics", "eq_iff_eq_cancel_right" -> "logic", "filter.tendsto.congr" -> "order", "is_compact.is_closed" -> "topology", "polynomial.degree_div_lt" -> "data", "primrec.list_cases" -> "computability", "structure_groupoid.local_invariant_prop.lift_prop_within_at_of_lift_prop_at_of_mem_nhds" -> "geometry", "submodule.comap_zero" -> "algebra", "polynomial.degree_pos_of_root" -> "data", "nat.add_left_cancel" -> "init", "set.mem_range_self" -> "data", "add_submonoid.mrange_inl'" -> "algebra", "max.right_comm" -> "algebra", "affine_map.line_map_vadd_neg" -> "algebra", "ctop.mem_nhds_to_topsp" -> "data", "cau_seq.inv_apply" -> "data", "smooth_at.times_cont_mdiff_at" -> "geometry", "inv_unique" -> "algebra", "measure_theory.measure_Union" -> "analysis", "derive_fintype.finset_above.mem_union_right" -> "tactic", "list.eq_nil_iff_forall_not_mem" -> "data", "filter.join_pure" -> "order", "pi.add_apply" -> "algebra", "add_monoid_hom.coe_snd" -> "algebra", "cau_seq.completion.mk_eq_zero" -> "data", "nhds_within_eq_nhds_within" -> "topology", "nat.prime_def_lt'" -> "data", "add_equiv.map_sub" -> "data", "is_coprime.pow_right" -> "algebra", "inv_nonpos" -> "algebra", "has_fderiv_within_at.const_mul" -> "analysis", "nat.dist_eq_sub_of_le_right" -> "data", "set.finite.dinduction_on" -> "data", "int.neg_eq_neg_one_mul" -> "init", "bool.bnot_bor" -> "data", "ring.fractional_ideal.coe_span_singleton" -> "algebra", "pequiv.trans_single_of_eq_none" -> "data", "finset.eq_empty_of_forall_not_mem" -> "data", "pos_num.cast_bit1" -> "data", "has_deriv_at_inv" -> "analysis", "filter.eventually.curry" -> "order", "is_closed_iff_nhds" -> "topology", "is_unit.coe_lift_right" -> "algebra", "num.cast_le" -> "data", "category_theory.category_of_elements.from_comma_obj" -> "category_theory", "algebra.smul_def''" -> "algebra", "ennreal.lt_top_of_mul_lt_top_right" -> "data", "complex.norm_sq_zero" -> "data", "interval_integral.fderiv_within_integral_of_tendsto_ae" -> "analysis", "padic.of_rat_div" -> "data", "finset.sum_le_sum_of_subset" -> "algebra", "quadratic_form.smul_apply" -> "algebra", "list.unzip_cons" -> "data", "real.arccos_inj" -> "analysis", "ennreal.of_real_zero" -> "data", "set.preimage_sub_const_Ioc" -> "data", "matrix.head_val'" -> "data", "filter.order_bot.at_bot_eq" -> "order", "real.rpow_le_rpow_of_exponent_ge" -> "analysis", "div_fpow" -> "algebra", "complex.two_sin" -> "data", "add_submonoid.coe_infi" -> "algebra", "turing.to_partrec.step_normal_eval" -> "computability", "category_theory.monoidal.functor_category.tensor_obj_map" -> "category_theory", "list.minimum_mem" -> "data", "topological_space.opens.mk_inf_mk" -> "topology", "structure_groupoid.local_invariant_prop.lift_prop_on_of_mem_maximal_atlas" -> "geometry", "complex.of_real_add" -> "data", "segment_eq_Icc" -> "analysis", "set.Ioo_subset_Ioo_union_Ico" -> "data", "deriv_log'" -> "analysis", "equiv.sum_congr_apply" -> "data", "continuous_linear_map.op_norm_zero_iff" -> "analysis", "has_strict_fderiv_at.implicit_to_local_homeomorph_apply_ker" -> "analysis", "linear_map.proj_std_basis_same" -> "algebra", "list.Ico.length" -> "data", "list.mem_of_mem_head'" -> "data", "list.prod_map_hom" -> "data", "continuous_linear_map.le_op_norm_of_le" -> "analysis", "submonoid.ext" -> "algebra", "nat.factors_add_two" -> "data", "finset.filter_false" -> "data", "category_theory.nat_iso.of_components.hom_app" -> "category_theory", "continuous_multilinear_map.map_add" -> "topology", "free_add_monoid.lift_restrict" -> "algebra", "encodable.encode_some" -> "data", "mjoin_map_pure" -> "control", "mul_lt_iff_lt_one_left'" -> "algebra", "cfilter.of_equiv_val" -> "data", "is_semiring_hom.comp" -> "algebra", "matrix.cons_mul" -> "data", "wseq.destruct_congr" -> "data", "interval_integrable.smul" -> "analysis", "nat.one_lt_fact" -> "data", "list.drop_take" -> "data", "linear_map.ker_le_ker_comp" -> "algebra", "list.bag_inter_sublist_left" -> "data", "ne_of_ne_of_eq" -> "init", "nat.coprime.coprime_mul_right" -> "data", "real.neg_one_lt_div_sqrt_one_add" -> "analysis", "list.perm.foldl_eq" -> "data", "is_integral_of_is_scalar_tower" -> "algebra", "finset.filter_insert" -> "data", "measure_theory.measure.smul_apply" -> "analysis", "znum.add_zero" -> "data", "add_submonoid.localization_map.add_equiv_of_localizations_right_neg" -> "algebra", "inv_lt_inv_of_neg" -> "algebra", "ideal.add_mem_iff_right" -> "algebra", "inf_top_eq" -> "order", "well_founded.not_lt_min" -> "order", "mul_equiv.coe_mk" -> "data", "function.semiconj.surj_on_image" -> "data", "ennreal.sub_sub_cancel" -> "data", "filter_basis.mem_filter_of_mem" -> "order", "circle_deg1_lift.dist_map_map_zero_lt" -> "dynamics", "commute.units_inv_left_iff" -> "algebra", "list.nil_map\:2082" -> "data", "bounded_continuous_function.bounded_range" -> "topology", "rel_embedding.of_monotone_coe" -> "order", "list.Ico.not_mem_top" -> "data", "Cauchy.dense_inducing_pure_cauchy" -> "topology", "composition_as_set.lt_length'" -> "combinatorics", "category_theory.limits.prod.lift_fst_assoc" -> "category_theory", "matrix.tail_transpose" -> "data", "complex.sin_nat_mul_pi" -> "analysis", "continuous_linear_equiv.equiv_of_right_inverse_symm_apply" -> "topology", "polynomial.roots_zero" -> "data", "matrix.update_row_transpose" -> "data", "ennreal.coe_nat_lt_coe" -> "data", "free_comm_ring.map_of" -> "algebra", "mul_right_bound" -> "analysis", "submodule.mem_right_iff_eq_zero_of_disjoint" -> "algebra", "measure_theory.simple_func.fin_meas_supp.iff_lintegral_lt_top" -> "analysis", "asymptotics.is_O_with_snd_prod" -> "analysis", "set.inj_on.left_inv_on_inv_fun_on" -> "data", "lipschitz_with.add" -> "analysis", "uniform_space.uniform_continuous_quotient_lift" -> "topology", "prime_multiset.coe_pnat_of_prime" -> "data", "composition.size_up_to_index_le" -> "combinatorics", "relator.rel_or" -> "logic", "category_theory.limits.pullback.hom_ext" -> "category_theory", "category_theory.functor.equiv_unit_iso" -> "category_theory", "bilin_form.coe_fn_mk" -> "algebra", "times_cont_diff_on.differentiable_on" -> "analysis", "cardinal.univ_id" -> "set_theory", "squeeze_zero_norm" -> "analysis", "circle_deg1_lift.coe_mul" -> "dynamics", "linear_map.ker_comp" -> "algebra", "set.bUnion_insert" -> "data", "topological_fiber_bundle_core.mem_local_triv'_source" -> "topology", "polynomial.mem_map_range" -> "data", "polynomial.card_roots_X_pow_sub_C" -> "data", "tsum_comm" -> "topology", "AddCommGroup.kernel_iso_ker_over_hom_left_to_fun_val" -> "algebra", "pi.zero_comp" -> "algebra", "continuous_linear_map.lmul_right_norm" -> "analysis", "padic_val_rat.pow" -> "data", "free_semigroup.lift_of" -> "algebra", "finsupp.support_mul" -> "data", "metric.continuous_within_at_iff" -> "topology", "multiset.nodup_cons" -> "data", "euclidean_domain.zero_div" -> "algebra", "pos_num.cast_succ" -> "data", "category_theory.limits.binary_bicone.to_cocone_\[Iota]_app_right" -> "category_theory", "linear_map.pair_fst_snd" -> "algebra", "cau_seq.completion.inv_mul_cancel" -> "data", "nat.dvd_sub" -> "init", "finset.smul_sum" -> "algebra", "continuous_linear_equiv.eq_symm_apply" -> "topology", "closed_embedding.continuous" -> "topology", "homeomorph.self_comp_symm" -> "topology", "interior_inter" -> "topology", "computable.map_decode_iff" -> "computability", "list.Ico.inter_consecutive" -> "data", "list.not_perm_nil_cons" -> "data", "list.array_eq_of_fn" -> "data", "nat.subtype.of_nat_surjective_aux" -> "data", "algebra.tensor_product.tmul_pow" -> "algebra", "continuous_I_symm" -> "topology", "subgroup.coe_Inf" -> "algebra", "int.neg_succ_of_nat_mul_sub_nat_nat" -> "init", "isometric.apply_inv_self" -> "topology", "structure_groupoid.local_invariant_prop.lift_prop_on_congr_iff" -> "geometry", "category_theory.monoidal_of_has_finite_products.associator_hom" -> "category_theory", "ring_hom.map_zero" -> "algebra", "mv_polynomial.single_eq_C_mul_X" -> "data", "abstract_completion.uniform_continuous_compare_equiv_symm" -> "topology", "omega.update_eq_of_ne" -> "tactic", "magma.free_semigroup.of_mul_assoc_right" -> "algebra", "list.sublists_aux_eq_foldr.aux" -> "data", "finset.pi_empty" -> "data", "localization_map.sec_spec" -> "algebra", "convex_cone.map_map" -> "analysis", "has_strict_deriv_at.sub" -> "analysis", "image_sub_lt_mul_sub_of_deriv_lt" -> "analysis", "rat.nonneg_mul" -> "data", "polynomial.map_ne_zero" -> "data", "set.Iic_subset_Iio_union_Icc" -> "data", "nnreal.of_real_zero" -> "data", "circle_deg1_lift.coe_inj" -> "dynamics", "subgroup.comap_top" -> "algebra", "mv_polynomial.iter_to_sum_C_X" -> "data", "mvqpf.Wrepr_W_mk" -> "data", "finsupp.dim_eq" -> "algebra", "seq.zip_with_nth_none'" -> "data", "pow_dvd_pow_iff" -> "algebra", "convex.translate" -> "analysis", "vsub_set_singleton" -> "algebra", "ordinal.lift_succ" -> "set_theory", "tangent_bundle.times_cont_mdiff_at_proj" -> "geometry", "affine_subspace.sup_direction_le" -> "algebra", "fderiv_within.comp" -> "analysis", "set.empty_not_nonempty" -> "data", "primrec\:2082.const" -> "computability", "ennreal.zero_lt_sub_iff_lt" -> "data", "multiset.powerset_aux_eq_map_coe" -> "data", "differentiable_id" -> "analysis", "int.le_add_of_sub_left_le" -> "init", "upper_bounds_singleton" -> "order", "add_lie" -> "algebra", "continuous.smul" -> "topology", "padic_norm_z.pow" -> "data", "znum.mul_to_int" -> "data", "path_component_symm" -> "topology", "is_measurable_closure" -> "analysis", "tangent_map_comp" -> "geometry", "continuous_at_of_strict_mono_surjective" -> "topology", "submonoid.comap_strict_mono_of_surjective" -> "algebra", "multiset.map_filter_map_of_inv" -> "data", "filter.eventually.mp" -> "order", "ordinal.infinite_pigeonhole_set" -> "set_theory", "filter.prod_map_seq_comm" -> "order", "is_local_max.comp_continuous_on" -> "topology", "filter.limsup_eq_infi_supr_of_nat" -> "order", "hyperreal.infinite_neg_mul_infinite_pos" -> "data", "wseq.lift_rel_join.lem" -> "data", "modeq_nine_digits_sum" -> "data", "nnreal.rpow_le_rpow_iff" -> "analysis", "multiset.ndinsert_zero" -> "data", "subalgebra.mem_to_submodule" -> "algebra", "submonoid.localization_map.lift_mul_left" -> "algebra", "submonoid.one_mem" -> "algebra", "finset.mem_union_left" -> "data", "infi_or" -> "order", "fin.pred_succ" -> "data", "nat.gcd_le_right" -> "data", "ring_hom.id_apply" -> "algebra", "times_cont_mdiff.comp_times_cont_mdiff_on" -> "geometry", "category_theory.biprod.unipotent_upper_inv" -> "category_theory", "category_theory.limits.cocones.forget_map" -> "category_theory", "galois_coinsertion.u_l_eq" -> "order", "is_unit_map_iff" -> "algebra", "add_subgroup.ext" -> "algebra", "finsupp.support_smul" -> "data", "cardinal.mk_emptyc" -> "set_theory", "cau_seq.mk_to_fun" -> "data", "complex.ext" -> "data", "with_bot.coe_le" -> "order", "dist_add_add_le_of_le" -> "analysis", "ne_self_iff_false" -> "init", "category_theory.curry_natural_right" -> "category_theory", "is_compact.compl_mem_sets_of_nhds_within" -> "topology", "tangent_bundle.smooth_on_proj" -> "geometry", "list.exists_of_erasep" -> "data", "Set.omega_zero" -> "set_theory", "inter_mem_nhds_within" -> "topology", "nnreal.sub_self" -> "data", "finset_is_basis_of_span_eq_top_of_card_eq_findim" -> "algebra", "coe_frobenius_equiv" -> "algebra", "module.direct_limit.of.zero_exact" -> "algebra", "is_closed_Union" -> "topology", "linear_map.disjoint_inl_inr" -> "algebra", "CommRing.colimits.quot_neg" -> "algebra", "linear_map.coe_mk" -> "algebra", "free_abelian_group.induction_on'" -> "algebra", "commute.eq" -> "algebra", "contracting_with.edist_efixed_point_lt_top" -> "topology", "fintype.mem_pi_finset" -> "data", "nat.cast_sub" -> "data", "differentiable_on.snd" -> "analysis", "is_R_or_C.of_real_zero" -> "data", "bool.eq_ff_of_ne_tt" -> "data", "filter.germ.coe_comp_tendsto" -> "order", "primrec.id" -> "computability", "units.inv_mul_eq_iff_eq_mul" -> "algebra", "computation.return_def" -> "data", "real.cos_pi_div_two" -> "analysis", "matrix.neg_dot_product" -> "data", "turing.TM2.stmts\:2081_trans" -> "computability", "wseq.seq_destruct_think" -> "data", "relation.refl_trans_gen_closed" -> "logic", "submonoid.localization_map.mk'_mul_cancel_right" -> "algebra", "asymptotics.is_O_with_of_le" -> "analysis", "set.inj_on.bij_on_image" -> "data", "set.ne_insert_of_not_mem" -> "data", "is_compl.inf_right_eq_bot_iff" -> "order", "algebra.adjoin_eq_range" -> "algebra", "presented_group.to_group.of" -> "algebra", "cardinal.mk_pempty" -> "set_theory", "semiconj_by.add_left" -> "algebra", "forall_congr" -> "init", "typevec.drop_append1" -> "data", "set.inter_compl_self" -> "data", "let_value_eq" -> "init", "function.bij_on_periodic_pts" -> "dynamics", "norm_num.nat_cast_ne" -> "tactic", "bdd_below_insert" -> "order", "function.injective.ne" -> "logic", "submodule.ne_bot_iff" -> "algebra", "nat.mem_rfind" -> "computability", "finset.mk_coe" -> "data", "equiv.prod_assoc_sym_apply" -> "data", "category_theory.non_preadditive_abelian.add_neg_self" -> "category_theory", "set.preimage_sUnion" -> "data", "simple_graph.mem_edge_set" -> "combinatorics", "matrix.zero_mul" -> "data", "set.seq_def" -> "data", "list.count_le_of_sublist" -> "data", "multilinear_map.norm_image_sub_le_of_bound" -> "analysis", "valuation.is_equiv.map" -> "algebra", "Mon.colimits.cocone_naturality_components" -> "algebra", "ordinal.add_absorp" -> "set_theory", "zero_nsmul" -> "algebra", "skew_adjoint_matrices_lie_subalgebra_equiv_transpose_apply" -> "algebra", "set.preimage_preimage" -> "data", "turing.tape.write_nth" -> "computability", "is_R_or_C.of_real_re" -> "data", "ordinal.lt_sub" -> "set_theory", "abs_eq" -> "algebra", "with_one.lift_coe" -> "algebra", "add_monoid_hom.eq_lift_of_surjective" -> "algebra", "nat.modeq.modeq_and_modeq_iff_modeq_mul" -> "data", "measure_theory.simple_func.restrict_mono" -> "analysis", "list.sum_map_mul_right" -> "data", "multiset.disjoint_of_le_right" -> "data", "rat.mul_self_denom" -> "data", "eq_zero_of_right_cancel_add_self" -> "algebra", "finset.mem_of_mem_inter_left" -> "data", "measure_theory.measure.restrict_add" -> "analysis", "subgroup.normal.mem_comm" -> "algebra", "pythagorean_triple.ne_zero_of_coprime" -> "number_theory", "cardinal.finset_card_lt_omega" -> "set_theory", "measure_theory.lintegral_zero_measure" -> "analysis", "compact_iff_ultrafilter_le_nhds" -> "topology", "cardinal.mk_sUnion_le" -> "set_theory", "polynomial.eval_mul" -> "data", "zmod.prod_Ico_one_prime" -> "number_theory", "AddGroup.zero_apply" -> "algebra", "strict_mono.injective" -> "order", "has_fderiv_within_at.has_fderiv_at" -> "analysis", "finmap.mem_erase" -> "data", "fintype.bijective_bij_inv" -> "data", "hyperreal.not_infinite_iff_exist_lt_gt" -> "data", "nhds_left_sup_nhds_right'" -> "topology", "add_units.add_right_inj" -> "algebra", "measure_theory.lintegral_mono_ae" -> "analysis", "fderiv_within_inv" -> "analysis", "nat.primes.coe_pnat_inj" -> "data", "lower_bounds_mono_set" -> "order", "sum_card_order_of_eq_card_pow_eq_one" -> "algebra", "set.image2_image2_right" -> "data", "is_basis.mk_eq_dim" -> "algebra", "matrix.col_smul" -> "data", "category_theory.functor.op_hom_obj" -> "category_theory", "category_theory.equivalence.refl_inverse" -> "category_theory", "linear_recurrence.sol_space_dim" -> "algebra", "int.prime.dvd_nat_abs_of_coe_dvd_pow_two" -> "data", "finset.insert_union" -> "data", "polynomial.eval\:2082_pow" -> "data", "with_bot.none_eq_bot" -> "order", "nat.succ_add_sub_one" -> "data", "list.sum_repeat" -> "algebra", "ordinal.is_normal.le_self" -> "set_theory", "nat.div2_val" -> "init", "Cauchy.monotone_gen" -> "topology", "list.sum_of_fn" -> "data", "is_R_or_C.re_eq_add_conj" -> "data", "polynomial.coeff_map" -> "data", "is_local_min.max" -> "topology", "category_theory.nat_trans.ext" -> "category_theory", "cardinal.nat_cast_inj" -> "set_theory", "sup_bot_eq" -> "order", "cau_seq.completion.of_rat_mul" -> "data", "finset.prod_univ_sum" -> "data", "multiset.powerset_len_aux_eq_map_coe" -> "data", "int.coe_nat_succ" -> "init", "lucas_lehmer.\[Omega]_unit_coe" -> "number_theory", "differentiable_on_snd" -> "analysis", "polynomial.map_sub" -> "data", "cardinal.aleph'_succ" -> "set_theory", "category_theory.functor.id_comp" -> "category_theory", "vector.id_traverse" -> "data", "typevec.append_fun_id_id" -> "data", "circle_deg1_lift.translation_number_mul_of_commute" -> "dynamics", "measure_theory.tendsto_lintegral_filter_of_dominated_convergence" -> "analysis", "group.conjugates_of_set_mono" -> "algebra", "ring_hom.eq_of_eq_on_sdense" -> "algebra", "multiset.prod_add" -> "data", "int.sub_nonneg_of_le" -> "init", "basic_smooth_bundle_core.times_cont_mdiff_at_proj" -> "geometry", "mem_right_add_coset_iff" -> "algebra", "mv_polynomial.C_mul" -> "data", "nonempty_interior_of_Union_of_closed" -> "topology", "measure_theory.l1.norm_eq" -> "analysis", "one_div_neg_one_eq_neg_one" -> "algebra", "real.sqrt_pos" -> "data", "list.mem_inter_of_mem_of_mem" -> "data", "polynomial.eval_map" -> "data", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp_assoc" -> "category_theory", "Inf_range" -> "order", "list.keys_kerase" -> "data", "real.Sup_def" -> "data", "eventually_eq_nhds_within_iff" -> "topology", "measurable.smul" -> "analysis", "list.permutations_aux_nil" -> "data", "nat.pos_iff_ne_zero" -> "data", "matrix.cons_val'" -> "data", "int.coe_nat_eq_coe_nat_iff" -> "init", "ring_hom.map_pow" -> "algebra", "gcd_one_right" -> "algebra", "int.bodd_zero" -> "data", "set.finite_empty" -> "data", "list.kreplace_nodupkeys" -> "data", "finset.singleton_inter_of_not_mem" -> "data", "subring.prod_mem" -> "algebra", "category_theory.limits.colimit.post_desc" -> "category_theory", "list.map_lookup_eq_find" -> "data", "multiset.mem_range" -> "data", "times_cont_diff_within_at.differentiable_within_at'" -> "analysis", "complex.arg_neg_I" -> "analysis", "nat.one_succ_zero" -> "init", "metric.diam_union" -> "topology", "times_cont_mdiff_on.comp'" -> "geometry", "directed_of_sup" -> "order", "filter.gc_map_comap" -> "order", "int.neg_succ_of_nat_div" -> "data", "matrix.empty_mul" -> "data", "int.test_bit_lnot" -> "data", "wseq.equiv.refl" -> "data", "unique_diff_on_Icc" -> "analysis", "zsqrtd.neg_re" -> "data", "computation.map_ret" -> "data", "list.lex.imp" -> "data", "category_theory.over.post_obj" -> "category_theory", "category_theory.functor.sum_map_inr" -> "category_theory", "category_theory.limits.image.map_comp" -> "category_theory", "measurable_space.comap_mono" -> "analysis", "canonically_ordered_semiring.pow_le_one" -> "algebra", "computation.exists_of_lift_rel_right" -> "data", "list.foldl_argmax\:2082_eq_none" -> "data", "pow_sub" -> "algebra", "homeomorph.embedding" -> "topology", "has_deriv_at.lhopital_zero_at_bot_on_Iio" -> "analysis", "dif_eq_if" -> "init", "submodule.subtype_eq_val" -> "algebra", "ennreal.is_open_Ico_zero" -> "topology", "list.Ico.succ_singleton" -> "data", "finset.subset_union_elim" -> "data", "filter.tendsto_at_top_at_top_of_monotone'" -> "order", "category_theory.monoidal_category.tensor_right_tensor_inv_app" -> "category_theory", "commute.cast_nat_mul_right" -> "algebra", "add_right_neg" -> "algebra", "int.div_mul_le" -> "data", "hyperreal.infinitesimal_def" -> "data", "linear_equiv.map_add" -> "algebra", "polynomial.splits'" -> "algebra", "lcm_mul_right" -> "algebra", "option.is_some_none" -> "data", "pnat.xgcd_type.step_is_special" -> "data", "linear_equiv.ext" -> "algebra", "set.Iic_subset_Iic_union_Icc" -> "data", "add_subgroup.normal.comap" -> "algebra", "smooth_neg" -> "geometry", "list.argmin_nil" -> "data", "has_deriv_within_at_const" -> "analysis", "ennreal.top_ne_of_real" -> "data", "polynomial.degree_normalize" -> "data", "iff_iff_implies_and_implies" -> "init", "gaussian_int.to_complex_eq_zero" -> "data", "polynomial.div_by_monic_zero" -> "data", "continuous_multilinear_map.uncurry0_curry0" -> "analysis", "adjoin_root.algebra_map_eq" -> "algebra", "padic.coe_sub" -> "data", "finset.erase_ssubset" -> "data", "many_one_degree.add_le'" -> "computability", "list.perm.sum_eq'" -> "data", "continuous_within_at_Ico_iff_Ici" -> "topology", "equivariant_projection_condition" -> "algebra", "polynomial.dvd_iff_mod_by_monic_eq_zero" -> "data", "filter.eventually_le.is_local_min" -> "topology", "list.perm_of_mem_permutations_aux" -> "data", "set.finite_singleton" -> "data", "times_cont_diff_on.congr_mono" -> "analysis", "times_cont_diff.continuous_linear_map_comp" -> "analysis", "add_lt_of_lt_sub_right" -> "algebra", "category_theory.functor.to_cone_\[Pi]_app" -> "category_theory", "nat.sub_eq_of_eq_add" -> "data", "set.univ_pi_eq_empty" -> "data", "complex.sin_add_pi" -> "analysis", "quot.eqv_gen_sound" -> "init", "convex_on.add" -> "analysis", "mul_le_mul_right'" -> "algebra", "nat.mul_pow" -> "data", "dioph.xn_dioph" -> "number_theory", "affine.simplex.circumcenter_eq_affine_combination_of_points_with_circumcenter" -> "geometry", "complex.norm_sq_conj" -> "data", "fin.pred_one" -> "data", "norm_num.nat_cast_one" -> "tactic", "multiset.foldr_swap" -> "data", "padic_int.norm_sub_mod_part" -> "data", "lipschitz_with.of_dist_le'" -> "topology", "set.inter_compl_nonempty_iff" -> "data", "minimal_polynomial.dvd" -> "algebra", "dfinsupp.mk_zero" -> "data", "Inf_singleton" -> "order", "zmod.cast_one" -> "data", "omega.nat.holds_is_diff" -> "tactic", "multiset.card_eq_one" -> "data", "measure_theory.measure.measurable_map" -> "analysis", "filter.extraction_of_frequently_at_top'" -> "order", "function.comp_update" -> "logic", "metric.Hausdorff_dist_le_of_mem_dist" -> "topology", "complex.sub_conj" -> "data", "minimal_polynomial.zero" -> "algebra", "linear_independent.repr_eq_single" -> "algebra", "circle_deg1_lift.coe_pow" -> "dynamics", "commute.pow_pow" -> "algebra", "ideal.comap_le_iff_le_map" -> "algebra", "stream.cycle_singleton" -> "data", "ereal.neg_inj" -> "data", "emetric.diam_insert" -> "topology", "int.to_nat_le" -> "data", "measure_theory.measure.one_le_haar_outer_measure_self" -> "analysis", "nat.div_lt_self'" -> "data", "submodule.bot_coe" -> "algebra", "finset.filter_eq" -> "data", "multiset.fold_union_inter" -> "data", "quotient.fin_choice_eq" -> "data", "div_le_div_of_le_left" -> "algebra", "bdd_below.mono" -> "order", "dvd_mul_right" -> "algebra", "submonoid.localization_map.lift_eq" -> "algebra", "power_series.coeff_one" -> "algebra", "padic_norm_e.norm_int_lt_one_iff_dvd" -> "data", "roption.bind_defined" -> "data", "homological_complex.homology_obj" -> "algebra", "zsqrtd.norm_nonneg" -> "data", "finset.mono_of_fin_unique" -> "data", "functor.map_equiv_symm_apply" -> "data", "applicative.ext" -> "control", "complex.of_real_im" -> "data", "add_equiv.map_neg" -> "data", "zero_lt_mul_left" -> "algebra", "finsupp.monotone_to_fun" -> "data", "filter.tendsto_at_top" -> "order", "real.cos_neg_of_pi_div_two_lt_of_lt" -> "analysis", "holor.mul_right_distrib" -> "data", "set.left_inv_on.inj_on" -> "data", "set.preimage_add_const_Ico" -> "data", "nat.rfind_zero_none" -> "computability", "nat.one_ne_bit0" -> "init", "has_fderiv_at_iff_has_deriv_at" -> "analysis", "bilin_form.mem_is_pair_self_adjoint_submodule" -> "algebra", "continuous_norm" -> "analysis", "set.piecewise_compl" -> "data", "prod.snd_sub" -> "algebra", "filter.tendsto_at_bot_of_add_bdd_below_left" -> "order", "metric.continuous_iff'" -> "topology", "measure_theory.measure.join_eq_bind" -> "analysis", "set.univ_prod_univ" -> "data", "category_theory.over.mk_hom" -> "category_theory", "le_neg_iff_add_nonpos" -> "algebra", "nat.partrec.code.encode_code_eq" -> "computability", "linear_equiv.to_equiv_injective" -> "algebra", "measurable_dist" -> "analysis", "mvqpf.liftr_map" -> "data", "mv_power_series.constant_coeff_zero" -> "algebra", "mul_left_bound" -> "analysis", "hyperreal.is_st_trans_real" -> "data", "multiplicity.min_le_multiplicity_add" -> "algebra", "bdd_above.union" -> "order", "primorial_succ" -> "number_theory", "list.disjoint_comm" -> "data", "lipschitz_with.edist_iterate_succ_le_geometric" -> "topology", "real.Sup_empty" -> "data", "padic.coe_one" -> "data", "one_div_le_one_div_of_neg_of_le" -> "algebra", "nat.le_rec_on_injective" -> "data", "ultrafilter_extend_eq_iff" -> "topology", "lt_inv'" -> "algebra", "real.arcsin_nonpos" -> "analysis", "metric.bounded_ball" -> "topology", "is_R_or_C.of_real_inv" -> "data", "topological_space.compacts.equiv_to_fun_val" -> "topology", "list.sublists_aux\:2081_append" -> "data", "polynomial.nat_degree_X_sub_C" -> "data", "real.sin_pi_div_two_sub" -> "analysis", "pnat.xgcd_type.reduce_v" -> "data", "has_sum_iff_has_sum_of_ne_zero_bij" -> "topology", "eq_tt_of_not_eq_ff" -> "init", "cardinal.le_mk_iff_exists_subset" -> "set_theory", "cardinal.cantor_function_aux_succ" -> "data", "set.dual_Ioc" -> "data", "nnreal.coe_pos" -> "data", "list.index_of_argmin" -> "data", "polynomial.eisenstein_criterion_aux.is_unit_of_nat_degree_eq_zero_of_forall_dvd_is_unit" -> "algebra", "set.Iic_subset_Iio" -> "data", "category_theory.limits.colimit.desc_extend" -> "category_theory", "multiset.choose_spec" -> "data", "topological_space.mem_nhds_of_is_topological_basis" -> "topology", "complex.tan_neg" -> "data", "has_fderiv_at_filter.add" -> "analysis", "mv_power_series.constant_coeff_one" -> "algebra", "set.union_diff_distrib" -> "data", "ideal.mem_leading_coeff_nth_zero" -> "algebra", "isometry.ediam_range" -> "topology", "multiset.coe_fold_r" -> "data", "finset.fold_image" -> "data", "int.neg_of_nat_mul_neg_succ_of_nat" -> "init", "euclidean_geometry.exists_dist_eq_iff_exists_dist_orthogonal_projection_eq" -> "geometry", "nat.cast_add" -> "data", "linear_map.to_continuous_linear_map\:2081_coe" -> "analysis", "setoid.eqv_gen_le" -> "data", "free_add_semigroup.add_seq" -> "algebra", "string.str_ne_str_left" -> "init", "structure_groupoid.eq_on_source" -> "geometry", "hyperreal.eq_of_is_st_real" -> "data", "mul_left_surjective" -> "algebra", "multiset.powerset_cons" -> "data", "affine_subspace.vadd_mem_mk'" -> "algebra", "pnat.factor_multiset_le_iff'" -> "data", "submodule.span_mul_span" -> "algebra", "disjoint.mono" -> "order", "encodable.encodek2" -> "data", "set.surj_on.comap_nonempty" -> "data", "is_null_measurable.union_null" -> "analysis", "real.cos_nonneg_of_neg_pi_div_two_le_of_le_pi_div_two" -> "analysis", "generalized_continued_fraction.terminated_at_iff_part_denom_none" -> "algebra", "continuous_sigma" -> "topology", "gmultiples_subset" -> "algebra", "subgroup.list_prod_mem" -> "algebra", "polynomial.degree_mul'" -> "data", "div_lt_div_of_neg_of_lt" -> "algebra", "many_one_equiv.symm" -> "computability", "add_submonoid.coe_Inf" -> "algebra", "multiplicative.is_monoid_hom" -> "algebra", "asymptotics.is_O_with_const_mul_self" -> "analysis", "no_bot" -> "order", "cardinal.ord_eq" -> "set_theory", "measure_theory.integrable_neg_iff" -> "analysis", "add_submonoid.localization_map.lift_mk'" -> "algebra", "polynomial.map_expand_pow_char" -> "algebra", "eq_mul_of_inv_mul_eq" -> "algebra", "finset.prod_nonneg" -> "algebra", "free_monoid.lift_symm_apply" -> "algebra", "forall_not_of_not_exists" -> "init", "ordered_add_comm_group.lt_of_add_lt_add_left" -> "algebra", "dense_embedding.mk'" -> "topology", "filter.eventually.curry_nhds" -> "topology", "continuous_multilinear_map.unit_le_op_norm" -> "analysis", "dist_le_tsum_dist_of_tendsto" -> "topology", "measure_theory.measure.finite_at_filter.measure_mono" -> "analysis", "ring_hom.map_one" -> "algebra", "finsupp.subtype_domain_neg" -> "data", "asymptotics.is_o_comm" -> "analysis", "set.one_nonempty" -> "algebra", "has_strict_fderiv_at.image_mem_to_local_homeomorph_target" -> "analysis", "ideal.map_infi_comap_of_surjective" -> "algebra", "nat.bit_val" -> "init", "generalized_continued_fraction.numerators_stable_of_terminated" -> "algebra", "list.exists_of_mem_map" -> "data", "char_p.char_ne_one" -> "algebra", "list.lookup_all_eq_lookup" -> "data", "lucas_lehmer.residue_eq_zero_iff_s_mod_eq_zero" -> "number_theory", "category_theory.preimage_map" -> "category_theory", "filter.eventually_le.eventually_le_nhds" -> "topology", "list.foldr_reverse" -> "data", "fintype.exists_pair_of_one_lt_card" -> "data", "denumerable.of_equiv_of_nat" -> "data", "mjoin_map_mjoin" -> "control", "multiset.forall_of_pairwise" -> "data", "ordinal.is_normal.le_set" -> "set_theory", "has_strict_fderiv_at.implicit_to_local_homeomorph_fst" -> "analysis", "nat.mod_def_aux" -> "init", "ennreal.add_lt_top" -> "data", "multiset.le_cons_self" -> "data", "uniform_inducing.mk'" -> "topology", "nat.sub_le_left_of_le_add" -> "data", "ennreal.le_inv_iff_mul_le" -> "data", "subalgebra.pow_mem" -> "algebra", "well_founded.fix_F_eq" -> "init", "irrational.of_add_rat" -> "data", "finsupp.finite_le_nat" -> "data", "generalized_continued_fraction.terminated_at_iff_part_num_none" -> "algebra", "subring.comap_inf" -> "algebra", "localization_map.lift_surjective_iff" -> "algebra", "right_ord_continuous.map_cinfi" -> "order", "asymptotics.is_O_with.smul" -> "analysis", "and.rotate" -> "logic", "times_cont_diff_within_at.comp'" -> "analysis", "pi.inv_apply" -> "algebra", "list.sublist.append_right" -> "data", "le_of_inv_le_inv" -> "algebra", "measure_theory.simple_func.add_apply" -> "analysis", "int.add_pos_of_pos_of_nonneg" -> "init", "category_theory.limits.pushout_cocone.condition" -> "category_theory", "measure_theory.l1.norm_of_fun" -> "analysis", "roption.mem_some_iff" -> "data", "mvpfunctor.comp.get_mk" -> "data", "Top.sheaf_condition.fork_X" -> "topology", "seq_map_assoc" -> "control", "nhds_within_le_of_mem" -> "topology", "poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1" -> "algebra", "vector_span_eq_span_vsub_set_right_ne" -> "algebra", "bilin_form.sub_right" -> "algebra", "ennreal.coe_pow" -> "data", "times_cont_mdiff_at.times_cont_mdiff_within_at" -> "geometry", "ordinal.unbounded_range_of_sup_ge" -> "set_theory", "euclidean_geometry.dist_eq_iff_dist_orthogonal_projection_eq" -> "geometry", "submonoid.localization_map.mul_equiv_of_localizations_right_inv" -> "algebra", "gold_mul_gold_conj" -> "data", "has_deriv_at.rpow_of_one_le" -> "analysis", "add_equiv.apply_symm_apply" -> "data", "filter.lift_lift_same_eq_lift" -> "order", "or_not" -> "logic", "free_abelian_group.lift.add" -> "algebra", "int.coe_nat_abs_eq_normalize" -> "algebra", "category_theory.under.limit_\[Pi]_app" -> "category_theory", "set.singleton.is_mul_hom" -> "algebra", "submodule.inf_coe" -> "algebra", "polynomial.C_mul'" -> "data", "category_theory.functor.map_injective" -> "category_theory", "gronwall_bound_\[CurlyEpsilon]0_\[Delta]0" -> "analysis", "list.not_mem_of_not_mem_cons" -> "data", "ordinal.one_le_iff_pos" -> "set_theory", "alg_hom.injective_iff" -> "algebra", "is_R_or_C.abs_abs" -> "data", "filter.le_seq" -> "order", "computable.comp\:2082" -> "computability", "deriv_ccosh" -> "analysis", "add_monoid.mem_closure_union_iff" -> "algebra", "continuous_linear_map.coe_fst'" -> "topology", "with_zero.inv_zero" -> "algebra", "composition.monotone_size_up_to" -> "combinatorics", "mul_action.of_quotient_stabilizer_mem_orbit" -> "algebra", "submonoid.coe_copy" -> "algebra", "primrec.ulower_down" -> "computability", "dioph.dioph_fn_iff_pfun" -> "number_theory", "add_subgroup.mem_Sup_of_mem" -> "algebra", "subalgebra.mem_coe" -> "algebra", "pgame.add_le_add_left" -> "set_theory", "convex.linear_image" -> "analysis", "zsqrtd.le_trans" -> "data", "setoid.sup_eq_eqv_gen" -> "data", "differentiable_within_at.exp" -> "analysis", "abs_pos_of_pos" -> "algebra", "algebra.adjoin_union" -> "algebra", "except_t.run_bind" -> "init", "roption.eq_none_iff" -> "data", "dvd_mul_sub_mul" -> "algebra", "add_submonoid.map_le_of_le_comap" -> "algebra", "set.finite.union" -> "data", "monotone_and" -> "order", "infi_prod" -> "order", "eq_of_abs_sub_eq_zero" -> "algebra", "multiset.nodup_of_nodup_map" -> "data", "finset.filter_congr" -> "data", "ennreal.rpow_le_rpow" -> "analysis", "int.mul_mod_right" -> "data", "uniform_continuous_of_tendsto_zero" -> "topology", "simple_graph.neighbor_finset_eq_filter" -> "combinatorics", "constr_range" -> "algebra", "char_p.sum_two_squares" -> "algebra", "complex.arg_of_real_of_nonneg" -> "analysis", "with_one.some_eq_coe" -> "algebra", "nat.sub_lt_sub_add_sub" -> "data", "turing.partrec_to_TM2.succ_ok" -> "computability", "continuous_linear_map.lmul_left_right_is_bounded_bilinear" -> "analysis", "basic_smooth_bundle_core.smooth_proj" -> "geometry", "subsemiring.mem_top" -> "algebra", "category_theory.limits.span_map_fst" -> "category_theory", "is_lub_cSup" -> "order", "set.right_inv_on.congr_right" -> "data", "list.func.length_add" -> "data", "tsum_le_tsum" -> "topology", "finset.mem_sigma" -> "data", "tsum_eq_zero_of_not_summable" -> "topology", "nat.le_pred_of_lt" -> "data", "if_true_left_eq_or" -> "init", "semiconj_by.zero_left" -> "algebra", "lie_algebra.of_associative_algebra_hom_comp" -> "algebra", "lt_of_neg_lt_neg" -> "algebra", "list.alternating_sum_singleton" -> "data", "int.nat_abs_dvd_abs_iff" -> "data", "topological_space.is_open_generated_countable_inter" -> "topology", "is_seq_compact.subseq_of_frequently_in" -> "topology", "field.closure_subset_iff" -> "algebra", "card_lt_card_of_injective_of_not_mem" -> "data", "set.seq_singleton" -> "data", "rat.continuous_abs" -> "topology", "ring.fractional_ideal.mul_inv_cancel_iff" -> "algebra", "is_bounded_bilinear_map_smul_right" -> "analysis", "mvqpf.const.map_mk" -> "data", "finsupp.mem_frange" -> "data", "measure_theory.borel_le_lebesgue_measurable" -> "analysis", "norm_num.int_mod" -> "tactic", "sup_le_iff" -> "order", "ring.direct_limit.of_sub" -> "algebra", "mul_lt_one_of_nonneg_of_lt_one_left" -> "algebra", "filter.inf_principal_eq_bot" -> "order", "mul_ite" -> "algebra", "set.Union_subset_Union" -> "data", "ideal.comap_ne_bot_of_root_mem" -> "algebra", "measure_theory.l1.pos_part_to_fun" -> "analysis", "filter.ne_bot.ne" -> "order", "list.rotate'_eq_take_append_drop" -> "data", "measure_theory.simple_func.fin_meas_supp.integrable" -> "analysis", "filter.infi_sets_eq_finite'" -> "order", "dist_bdd_within_interval" -> "algebra", "list.count_erase_of_ne" -> "data", "t2_iff_ultrafilter" -> "topology", "disjoint.comm" -> "order", "filter.Liminf_principal" -> "order", "bdd_above_union" -> "order", "bounded_continuous_function.continuous_evalf" -> "topology", "subsemiring.sum_mem" -> "algebra", "min_sub" -> "algebra", "local_homeomorph.mdifferentiable.symm" -> "geometry", "matrix.vec_mul_vec_empty" -> "data", "iff.comm" -> "init", "compl_top" -> "order", "add_submonoid.le_def" -> "algebra", "finset.sum_powerset_insert" -> "algebra", "continuous_within_at_Ioi_iff_Ici" -> "topology", "onote.repr_add" -> "set_theory", "equiv.to_iso_inv" -> "category_theory", "set.mem_Iio" -> "data", "add_right_inj" -> "algebra", "is_local_max_on.comp_antimono" -> "topology", "mv_polynomial.is_noetherian_ring_fin_0" -> "algebra", "dist_triangle4" -> "topology", "finset.map_inter" -> "data", "mul_div_cancel" -> "algebra", "mul_equiv.to_CommMon_iso_hom" -> "algebra", "turing.partrec_to_TM2.K'.elim_update_aux" -> "computability", "inv_mul_cancel" -> "algebra", "filter.eventually_le.is_local_min_on" -> "topology", "piecewise_ae_eq_restrict" -> "analysis", "supr_le" -> "order", "pnat.coprime_one" -> "data", "mul_action.of_quotient_stabilizer_mk" -> "algebra", "list.count_repeat" -> "data", "measure_theory.l1.simple_func.norm_eq'" -> "analysis", "dfinsupp.sum_finset_sum_index" -> "data", "differentiable_on.sum" -> "analysis", "polynomial.coe_aeval_eq_eval" -> "data", "finset.eq_empty_iff_forall_not_mem" -> "data", "submonoid.localization_map.lift_surjective_iff" -> "algebra", "zorn.chain.image" -> "order", "formal_multilinear_series.bound_of_lt_radius" -> "analysis", "measure_theory.tendsto_integral_filter_of_dominated_convergence" -> "analysis", "zmod.cast_nat_cast" -> "data", "eq.congr_right" -> "logic", "fixed_points.f_le_inf_of_fixed_points" -> "order", "add_submonoid.closure_le" -> "algebra", "real.rpow_add" -> "analysis", "inner_sub_right" -> "analysis", "asymptotics.is_O_with_neg_right" -> "analysis", "finset.coe_inj" -> "data", "add_submonoid.exists_list_of_mem_closure" -> "algebra", "dist_sub_sub_le_of_le" -> "analysis", "list.perm.append_cons" -> "data", "tsum_geometric_two'" -> "analysis", "convex.inter" -> "analysis", "pgame.add_left_neg_le_zero" -> "set_theory", "Top.presheaf.germ_exist" -> "topology", "continuous_on_fst" -> "topology", "int.neg_add_lt_left_of_lt_add" -> "init", "mvpfunctor.W_map_W_mk" -> "data", "submodule.inner_left_of_mem_orthogonal" -> "analysis", "zsqrtd.sq_le_add_mixed" -> "data", "loc_path_connected_of_bases" -> "topology", "comp_comp_symm_mem_uniformity_sets" -> "topology", "measure_theory.ae_eq_fun.edist_eq_coe'" -> "analysis", "complex.inv_I" -> "data", "filter.has_basis_infi_principal_finite" -> "order", "subring.coe_to_submonoid" -> "algebra", "order_topology_of_nhds_abs" -> "topology", "is_add_unit.add_lift_right_neg" -> "algebra", "fintype.prod_unique" -> "data", "list.erase_dupkeys_cons" -> "data", "one_le_pow_of_one_le" -> "algebra", "bool.bxor_left_comm" -> "data", "Mon_.id_hom" -> "category_theory", "category_theory.arrow.hom_mk_left" -> "category_theory", "interior_univ" -> "topology", "bool.band_left_comm" -> "data", "finset.sum_union_inter" -> "algebra", "zsqrtd.nonneg_smul" -> "data", "multiset.mem_powerset_len_aux" -> "data", "is_measurable.subtype_image" -> "analysis", "filter.eventually_eq.is_local_max_iff" -> "topology", "finset.min'_lt_max'" -> "data", "matrix.transpose_transpose" -> "data", "with_top.one_eq_coe" -> "algebra", "equiv.perm.same_cycle_inv" -> "algebra", "mdifferentiable_at.mdifferentiable_within_at" -> "geometry", "closed_embedding.closed_iff_preimage_closed" -> "topology", "euclidean_geometry.angle_eq_left" -> "geometry", "local_homeomorph.of_set_to_local_equiv" -> "topology", "is_basis.equiv_fun_symm_apply" -> "algebra", "multiset.erase_dup_eq_self" -> "data", "is_compact.finite_measure" -> "analysis", "rel.core_mono" -> "data", "mv_polynomial.is_homogeneous_X" -> "algebra", "list.prod_join" -> "data", "filter.tendsto.mono_right" -> "order", "tactic.ring_exp.inverse_pf" -> "tactic", "filter.comap_sup" -> "order", "omega.sat_empty" -> "tactic", "differentiable_on.csin" -> "analysis", "pth_root_frobenius" -> "algebra", "nat.succ_pred_prime" -> "data", "subgroup.coe_one" -> "algebra", "orthogonal_projection_mem" -> "analysis", "tactic.ring_exp.mul_p_pf_zero" -> "tactic", "mem_non_zero_divisors_iff_ne_zero" -> "algebra", "mul_equiv.refl_apply" -> "data", "is_min_on.of_is_local_min_on_of_convex_on_Icc" -> "analysis", "category_theory.functor.right_adjoint_of_is_equivalence" -> "category_theory", "list.lookup_cons_ne" -> "data", "norm_add_mul_self" -> "analysis", "Class.mem_hom_right" -> "set_theory", "pfun.lift_eq_coe" -> "data", "is_local_min_on.is_local_min" -> "topology", "measure_theory.measure.haar.index_elim" -> "analysis", "submonoid.localization_map.exists_of_sec_mk'" -> "algebra", "summable_zero" -> "topology", "finset.exists_smaller_set" -> "data", "category_theory.comonad.coalgebra.EilenbergMoore_to_category_struct_comp" -> "category_theory", "real.one_rpow" -> "analysis", "complex.of_real_eq_zero" -> "data", "initial_seg.antisymm.aux" -> "set_theory", "real.log_mul" -> "analysis", "continuous_of_discrete_topology" -> "topology", "real.sin_nat_mul_pi" -> "analysis", "composition.of_fn_blocks_fun" -> "combinatorics", "is_adic_complete.subsingleton" -> "algebra", "is_min_on.of_is_local_min_of_convex_univ" -> "analysis", "is_R_or_C.of_real_to_complex" -> "data", "category_theory.functor.const.op_obj_unop_inv_app" -> "category_theory", "real.le_Sup" -> "data", "nnreal.sub_le_iff_le_add" -> "data", "nnreal.coe_mk" -> "data", "real.totally_bounded_Ico" -> "topology", "polynomial.expand_expand" -> "algebra", "multiset.mem_sort" -> "data", "filter.mem_mul" -> "order", "con.lift_mk'" -> "algebra", "set.prod_nonempty_iff" -> "data", "subgroup.mem_Sup_of_directed_on" -> "algebra", "is_measurable_inr_image" -> "analysis", "ennreal.sub_le_of_sub_le" -> "data", "quadratic_form.proj_apply" -> "algebra", "subgroup.map_le_iff_le_comap" -> "algebra", "free_group.to_group.mk" -> "algebra", "polynomial.eq_prod_roots_of_separable" -> "algebra", "zmod.inv_mul_of_unit" -> "data", "nat.sub_lt" -> "init", "half_le_harmonic_double_sub_harmonic" -> "analysis", "with_top.is_glb_Inf'" -> "order", "norm_num.bit1_succ" -> "tactic", "dioph.dioph_fn_compn" -> "number_theory", "measure_theory.simple_func.range_comp_subset_range" -> "analysis", "is_measurable.diff" -> "analysis", "differentiable_on.smul_const" -> "analysis", "measure_theory.outer_measure.of_content_preimage" -> "analysis", "has_mfderiv_within_at.mfderiv_within" -> "geometry", "continuous_of_rat" -> "topology", "is_compact.Inf_mem" -> "topology", "category_theory.limits.pushout.inl_desc" -> "category_theory", "category_theory.equivalence.cancel_counit_inv_right_assoc'" -> "category_theory", "bool.to_bool_or" -> "data", "rat.cast_sub" -> "data", "is_scalar_tower.smul_left_comm" -> "algebra", "linarith.eq_of_eq_of_eq" -> "tactic", "category_theory.monad_hom.id_comp" -> "category_theory", "category_theory.limits.pullback.lift_snd" -> "category_theory", "reader_t.ext" -> "init", "matrix.transpose_smul" -> "data", "has_deriv_within_at.csinh" -> "analysis", "nat.partrec.merge'" -> "computability", "times_cont_diff_on_fderiv_within_apply" -> "analysis", "set.preimage_const_sub_Ioi" -> "data", "tendsto_subseq_of_frequently_bounded" -> "topology", "nndist_eq_nnnorm" -> "analysis", "imp_true_iff" -> "logic", "reflect_lt" -> "order", "int.gcd_eq_zero_iff" -> "algebra", "affine_subspace.direction_top" -> "algebra", "multiset.rel_map_right" -> "data", "complex.abs_sub" -> "data", "submonoid.map_comap_eq_of_surjective" -> "algebra", "add_con.eq" -> "algebra", "set.Inter_subset_of_subset" -> "data", "antilipschitz_with.uniform_embedding" -> "topology", "infi_le_of_le" -> "order", "tendsto_prod_uniformity_fst" -> "topology", "linear_independent_smul" -> "algebra", "sup_idem" -> "order", "mul_equiv.map_inv" -> "data", "fin.update_snoc_last" -> "data", "circle_deg1_lift.tendsto_translation_number" -> "dynamics", "real.pi_lt_31416" -> "data", "list.nth_of_fn" -> "data", "submodule.closed_complemented.is_closed" -> "topology", "continuous_within_at_iff_ptendsto_res" -> "topology", "is_lub.unique" -> "order", "nhds_pi" -> "topology", "uniform_space.completion.uniform_continuous_map\:2082" -> "topology", "set.Icc_subset_Iic_iff" -> "data", "int.of_nat_eq_of_nat_iff" -> "init", "sub_add_eq_sub_sub" -> "algebra", "polynomial.eval_comp" -> "data", "cardinal.mk_range_eq" -> "set_theory", "ordinal.not_succ_is_limit" -> "set_theory", "category_theory.quotient.functor_obj_as" -> "category_theory", "complex.cos_int_mul_two_pi_add_pi" -> "analysis", "norm_num.min_fac_helper.n_pos" -> "tactic", "local_homeomorph.mdifferentiable.symm_comp_deriv" -> "geometry", "measure_theory.outer_measure.sup_apply" -> "analysis", "padic_seq.norm_eq_pow_val" -> "data", "fin.snoc_cast_succ" -> "data", "function.left_inverse.eq_right_inverse" -> "logic", "dfinsupp.sum_apply" -> "data", "real.tan_lt_tan_of_lt_of_lt_pi_div_two" -> "analysis", "is_local_min_on.inter" -> "topology", "continuous.I_extend" -> "topology", "add_subgroup.mem_gmultiples" -> "algebra", "finmap.disjoint_union_left" -> "data", "prime_spectrum.subset_zero_locus_iff_subset_vanishing_ideal" -> "algebraic_geometry", "tendsto_at_top_mul_left'" -> "analysis", "nnreal.rpow_mul" -> "analysis", "sylow.one_mem_vectors_prod_eq_one" -> "algebra", "has_fderiv_at_inv" -> "analysis", "set.empty_union" -> "data", "category_theory.monoidal_of_has_finite_coproducts.right_unitor_hom" -> "category_theory", "function.iterate_fixed" -> "logic", "equiv.perm.sign_eq_sign_of_equiv" -> "algebra", "localization.mk_eq_mk'" -> "algebra", "normed_field.exists_lt_norm" -> "analysis", "omega.coeffs.val_map_div" -> "tactic", "nhds_within_Ici_ne_bot" -> "topology", "category_theory.limits.limit.cone_morphism_hom" -> "category_theory", "lt_add_of_sub_left_lt" -> "algebra", "set.insert_pi" -> "data", "function.uncurry_bicompl" -> "logic", "with_top.nat_induction" -> "data", "omega.nat.preform.sat_or" -> "tactic", "ring_equiv.map_zero" -> "data", "unique.subsingleton_unique'" -> "logic", "matrix.ext" -> "data", "linarith.int.coe_nat_bit1" -> "tactic", "option.eq_none_of_is_none" -> "init", "category_theory.limits.cones.whiskering_equivalence_functor" -> "category_theory", "wseq.lift_rel.symm" -> "data", "multilinear_map.map_piecewise_smul" -> "algebra", "set.Ioo_eq_empty" -> "data", "mul_inv_cancel_right" -> "algebra", "semidirect_product.left_inl" -> "algebra", "finset.sum_subset_zero_on_sdiff" -> "algebra", "ordinal.univ_umax" -> "set_theory", "list.split_wrt_composition_join" -> "combinatorics", "to_mul_injective" -> "algebra", "ideal.is_maximal_iff_is_maximal_disjoint" -> "algebra", "UniformSpace.coe_id" -> "topology", "composition.ones_size_up_to" -> "combinatorics", "convex.neg" -> "analysis", "geom_series_def" -> "algebra", "smooth_on_fst" -> "geometry", "bounded_continuous_function.continuous_eval" -> "topology", "subgroup.gc_map_comap" -> "algebra", "category_theory.comma.iso_mk_inv_left" -> "category_theory", "filter.le_of_map_le_map_inj'" -> "order", "primrec.list_head'" -> "computability", "category_theory.limits.cokernel_cofork.app_zero" -> "category_theory", "bit1_lt_bit1" -> "algebra", "bounded_continuous_function.neg_apply" -> "topology", "matrix.to_lin_apply" -> "algebra", "computation.orelse_think" -> "data", "ring_hom.coe_range_restrict" -> "algebra", "distrib_mul_action_hom.map_add" -> "algebra", "nat.not_even_one" -> "data", "category_theory.limits.pair_obj_right" -> "category_theory", "category_theory.whiskering_right_obj_obj" -> "category_theory", "list.length_pmap" -> "data", "euclidean_geometry.orthogonal_projection_of_nonempty_of_complete_eq" -> "geometry", "list.minimum_concat" -> "data", "nonpos_of_mul_nonneg_right" -> "algebra", "inv_mul_eq_of_eq_mul" -> "algebra", "set.nmem_set_of_eq" -> "data", "zmod.val_min_abs_zero" -> "data", "free_ring.induction_on" -> "algebra", "simple_add_group_of_surjective" -> "algebra", "function.is_periodic_pt.eq_zero_of_lt_minimal_period" -> "dynamics", "nat.lt_add_of_sub_lt_right" -> "data", "if_eq_of_eq_true" -> "init", "normed_ring.inverse_add_nth_order" -> "analysis", "finite_field.expand_card" -> "algebra", "category_theory.discrete.equiv_of_equivalence_to_fun" -> "category_theory", "set.compl_Ici" -> "data", "nat.partrec.of_primrec" -> "computability", "continuous_linear_map.coe_fst" -> "topology", "iff_false" -> "init", "multiset.fold_erase_dup_idem" -> "data", "zsqrtd.not_sq_le_succ" -> "data", "category_theory.equivalence.unit_inverse" -> "category_theory", "of_add_zero" -> "algebra", "local_equiv.trans_target'" -> "data", "submodule.infi_colon_supr" -> "algebra", "pequiv.to_matrix_injective" -> "data", "derivation.map_add" -> "algebra", "continuous_multilinear_map.op_norm_neg" -> "analysis", "nat.sqrt_add_eq" -> "data", "interval_integral.deriv_integral_of_tendsto_ae_right" -> "analysis", "punit.one_eq" -> "algebra", "add_localization.add_equiv_of_quotient_symm_add_monoid_of" -> "algebra", "category_theory.abelian.pseudoelement.pseudo_surjective_of_epi" -> "category_theory", "multiset.coe_filter_map" -> "data", "algebraic_closure.adjoin_monic.algebra_map" -> "algebra", "classical.axiom_of_choice" -> "init", "tactic.group.gpow_trick" -> "tactic", "set.union_singleton" -> "data", "subsemiring.multiset_sum_mem" -> "algebra", "dense_inducing.extend_unique_at" -> "topology", "rel_embedding.is_total" -> "order", "list.chain.induction" -> "data", "measure_theory.simple_func.map_restrict_of_zero" -> "analysis", "measure_theory.compl_mem_ae_iff" -> "analysis", "dfinsupp.sub_apply" -> "data", "computable.vector_nth'" -> "computability", "linear_map.range_le_iff_comap" -> "algebra", "add_subgroup.closure_mono" -> "algebra", "metric.pos_of_mem_ball" -> "topology", "pow_zero" -> "algebra", "list.mem_insert_iff" -> "data", "submodule.prod_sup_prod" -> "algebra", "filter.at_bot_ne_bot" -> "order", "list.sublists'_nil" -> "data", "submodule.coe_to_add_subgroup" -> "algebra", "concave_on.translate_left" -> "analysis", "auto.not_or_eq" -> "tactic", "finset.center_mass_insert" -> "analysis", "polynomial.map_mul" -> "data", "int.even_neg" -> "data", "differentiable_on.rpow" -> "analysis", "turing.list_blank.tail_cons" -> "computability", "is_R_or_C.bit0_re" -> "data", "uniform_embedding_def'" -> "topology", "alist.mem_keys" -> "data", "ulift.neg_down" -> "algebra", "nat.partrec.code.exists_code" -> "computability", "bernoulli_two" -> "number_theory", "category_theory.limits.pullback.lift_fst" -> "category_theory", "int.lor_bit" -> "data", "add_con.ker_eq_lift_of_injective" -> "algebra", "semidirect_product.ext_iff" -> "algebra", "int.bodd_one" -> "data", "lipschitz_with.prod" -> "topology", "pfunctor.M.cases_on_mk" -> "data", "set.preimage_const_add_Ico" -> "data", "has_strict_fderiv_at.mem_implicit_to_local_homeomorph_source" -> "analysis", "riesz_extension" -> "analysis", "differentiable.sin" -> "analysis", "equiv.id_traverse" -> "control", "option_t.run_monad_lift" -> "init", "asymptotics.is_O.prod_left_fst" -> "analysis", "list.prefix_refl" -> "data", "lower_bounds_insert" -> "order", "matrix.mul_vec_diagonal" -> "data", "has_deriv_at.ccosh" -> "analysis", "Top.presheaf.stalk_pushforward.id" -> "topology", "eq_mul_of_mul_inv_eq" -> "algebra", "relation.eqv_gen_iff_of_equivalence" -> "logic", "with_top.coe_mul" -> "algebra", "sub_self" -> "algebra", "linear_map.map_le_map_iff'" -> "algebra", "nnreal.coe_nonneg" -> "data", "zero_vadd" -> "algebra", "left_neg_eq_right_neg" -> "algebra", "algebra.subset_adjoin" -> "algebra", "polynomial.monic_normalize" -> "data", "polynomial.div_def" -> "data", "inner_product_geometry.angle_sub_eq_angle_sub_rev_of_norm_eq" -> "geometry", "divp_eq_divp_iff" -> "algebra", "filter.sInter_mem_sets_of_finite" -> "order", "le_of_forall_sub_le" -> "algebra", "polynomial.eval_zero" -> "data", "category_theory.limits.pullback_cone.of_cone_X" -> "category_theory", "set.piecewise_range_comp" -> "data", "add_group.mclosure_subset" -> "algebra", "card_fiber_eq_of_mem_range" -> "algebra", "roption.assert_defined" -> "data", "seq_eq_bind_map" -> "control", "is_coprime.is_unit_of_dvd" -> "algebra", "filter.map_binfi_eq" -> "order", "category_theory.types_id_apply" -> "category_theory", "is_add_subgroup.add_mem_cancel_right" -> "algebra", "ring_hom.snd_comp_prod" -> "algebra", "category_theory.limits.prod.associator_naturality" -> "category_theory", "joined_in.refl" -> "topology", "affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty" -> "algebra", "finsupp.swap_mem_antidiagonal_support" -> "data", "turing.tape.mk'_left" -> "computability", "mem_nhds_within_insert" -> "topology", "iterated_deriv_within_eq_equiv_comp" -> "analysis", "function.support_infi" -> "data", "list.le_eq_not_gt" -> "init", "supr_neg" -> "order", "linear_map.ker_cod_restrict" -> "algebra", "add_monoid_hom.coprod_comp_inr" -> "algebra", "nat.cast_ne_zero" -> "algebra", "coe_coe" -> "logic", "subalgebra.list_prod_mem" -> "algebra", "set.dual_Iio" -> "data", "composition.to_composition_as_set_blocks" -> "combinatorics", "nat.pow_dvd_pow_iff_le_right'" -> "data", "metric.Hausdorff_dist_triangle" -> "topology", "filter.infi_sup_right" -> "order", "finset.finite_to_set" -> "data", "padic_val_nat_of_not_dvd" -> "data", "convex.segment_subset" -> "analysis", "is_basis.det_self" -> "algebra", "multiset.filter_add_filter" -> "data", "nonote.repr_power" -> "set_theory", "linear_map.span_singleton_eq_range" -> "algebra", "continuous_iff_sequentially_continuous" -> "topology", "int.add_mul_mod_self" -> "data", "measurable_subtype_coe" -> "analysis", "filter.eventually_ge_at_top" -> "order", "zsqrtd.conj_im" -> "data", "is_open_map.of_inverse" -> "topology", "multiset.sum_zero" -> "data", "lcm_one_left" -> "algebra", "filter.eventually_eq.is_local_extr_on_iff" -> "topology", "is_R_or_C.abs_add" -> "data", "nat.mul_sub_div" -> "init", "linear_action_act_smul" -> "algebra", "false_and" -> "init", "local_equiv.inv_fun_as_coe" -> "data", "category_theory.comma_morphism.ext_iff" -> "category_theory", "submodule.prod_map_fst" -> "algebra", "cardinal.mk_emptyc_iff" -> "set_theory", "filter.germ.const_le" -> "order", "complex.inv_zero" -> "data", "category_theory.limits.kernel_is_iso_comp_hom" -> "category_theory", "ordinal.cof_univ" -> "set_theory", "equiv.inv_fun_as_coe" -> "data", "add_submonoid.mrange_inr'" -> "algebra", "primrec.pair" -> "computability", "list.cons_sublist_cons" -> "data", "gcd_dvd_gcd" -> "algebra", "filter.frequently_at_bot" -> "order", "uniform_continuous_of_continuous" -> "topology", "list.keys_cons" -> "data", "asymptotics.is_o_neg_left" -> "analysis", "set.preimage_const_mul_Ico" -> "data", "pythagorean_triple.even_odd_of_coprime" -> "number_theory", "set.disjointed_subset" -> "data", "irrational_rat_sub_iff" -> "data", "pell.eq_of_xn_modeq_lem3" -> "number_theory", "ennreal.lt_sub_iff_add_lt" -> "data", "is_glb.lower_bounds_eq" -> "order", "sum.inr.inj_iff" -> "data", "nat.fact_inj" -> "data", "inducing.continuous" -> "topology", "exists_max_ideal_of_mem_nonunits" -> "algebra", "free_ring.coe_of" -> "algebra", "stream.mem_of_mem_odd" -> "data", "matrix.det_adjugate_of_is_unit" -> "algebra", "model_with_corners.unique_diff" -> "geometry", "pnat.coe_inj" -> "data", "infi_unit" -> "order", "real.exists_exp_eq_of_pos" -> "analysis", "list.sum_take_map_length_lt2" -> "data", "measure_theory.simple_func.ext" -> "analysis", "fract_zero" -> "algebra", "add_monoid_hom.eq_int_cast" -> "data", "cont_t.monad_lift_bind" -> "control", "nat.coprime.coprime_mul_left" -> "data", "cardinal.mul_eq_max_of_omega_le_left" -> "set_theory", "pgame.lt_of_mk_le" -> "set_theory", "add_group_with_zero_nhd.exists_Z_half" -> "topology", "add_sub_div_two_lt" -> "algebra", "nat.modeq.modeq_of_dvd_of_modeq" -> "data", "roption.bind_map" -> "data", "vsub_vadd_comm" -> "algebra", "pnat.mk_bit1" -> "data", "int.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul" -> "data", "padic_norm_z.le_one" -> "data", "wseq.head_terminates_iff" -> "data", "nat.le_mul_of_pos_right" -> "data", "submonoid.localization_map.lift_of_comp" -> "algebra", "filter.infi_ne_bot_of_directed'" -> "order", "sub_nonneg_of_le" -> "algebra", "pSet.equiv.ext" -> "set_theory", "multiset.antidiagonal_coe" -> "data", "set.disjoint_disjointed" -> "data", "bounded_continuous_function.ext" -> "topology", "palindrome.append_reverse" -> "data", "lt_of_pow_lt_pow" -> "algebra", "ceil_add_int" -> "algebra", "linear_map.comap_prod_prod" -> "algebra", "is_min_filter.sup" -> "order", "inner_product_geometry.norm_eq_of_angle_sub_eq_angle_sub_rev_of_angle_ne_pi" -> "geometry", "linear_map.is_linear_map_prod_iso" -> "algebra", "category_theory.functor.map_iso_hom" -> "category_theory", "set.Inter_pos" -> "data", "finset.coe_injective" -> "data", "le_mul_iff_one_le_left'" -> "algebra", "char_matrix_apply_nat_degree_le" -> "algebra", "is_open.unique_mdiff_within_at" -> "geometry", "function.injective.has_left_inverse" -> "logic", "category_theory.abelian.exact_iff'" -> "category_theory", "euclidean_domain.dvd_gcd" -> "algebra", "inner_product_geometry.angle_add_angle_sub_add_angle_sub_eq_pi" -> "geometry", "submodule.linear_proj_of_is_compl_comp_subtype" -> "algebra", "list.rel_of_sorted_cons" -> "data", "set.compl_univ_iff" -> "data", "matrix.transpose_col" -> "data", "has_deriv_within_at.log" -> "analysis", "principal_ideal_ring.factors_spec" -> "algebra", "real.is_conjugate_exponent_iff" -> "data", "measurable_from_nat" -> "analysis", "ennreal.mul_right_mono" -> "data", "abs_of_nonpos" -> "algebra", "AddCommGroup.free_obj_coe" -> "algebra", "finset.sum_range_succ'" -> "algebra", "hyperreal.is_st_inv" -> "data", "Sup_univ" -> "order", "set.image_add_right'" -> "algebra", "le_max_right_of_le" -> "algebra", "mv_polynomial.eq_zero_or_eq_zero_of_mul_eq_zero" -> "algebra", "linear_independent_iff'" -> "algebra", "metric.mem_nhds_iff" -> "topology", "choose_le_succ_of_lt_half_left" -> "data", "has_sum.mul_left" -> "topology", "list.sublists_len_zero" -> "data", "map_lift_comp_preserves_products_iso_hom_assoc" -> "category_theory", "finset.image_preimage" -> "data", "convex_segment" -> "analysis", "prod.fst_add_snd" -> "algebra", "lipschitz_with.comp" -> "topology", "add_con.ker_lift_injective" -> "algebra", "category_theory.limits.wide_pullback_shape.wide_cospan_map" -> "category_theory", "forall_or_distrib_right" -> "logic", "add_monoid_hom.map_int_module_smul" -> "algebra", "local_ring.is_unit_one_sub_self_of_mem_nonunits" -> "algebra", "asymptotics.is_O_norm_norm" -> "analysis", "has_deriv_within_at.liminf_right_slope_le" -> "analysis", "simple_group_of_surjective" -> "algebra", "ideal.comap_id" -> "algebra", "dim_submodule_le" -> "algebra", "metric.tendsto_locally_uniformly_iff" -> "topology", "has_deriv_at_filter.scomp" -> "analysis", "set.right_mem_Ico" -> "data", "module.direct_limit.of.zero_exact_aux" -> "algebra", "complex.equiv_real_prod_apply" -> "data", "ideal.zero_ne_one_of_proper" -> "algebra", "polynomial.multiplicity_X_sub_C_finite" -> "data", "filter.principal_le_iff" -> "order", "set.preimage_add_const_Ioc" -> "data", "computation.parallel_promises" -> "data", "has_deriv_at.log" -> "analysis", "finset.prod_const_one" -> "algebra", "Top.subsheaf_to_Types_presheaf" -> "topology", "erased.out_mk" -> "data", "is_max_on.of_is_local_max_on_of_concave_on" -> "analysis", "exists_associated_mem_of_dvd_prod" -> "algebra", "zmod.legendre_sym_eq_zero_iff" -> "number_theory", "tensor_product.tmul_neg" -> "algebra", "not_imp_of_and_not" -> "logic", "eq_of_linear_independent_of_span_subtype" -> "algebra", "lt_of_one_div_lt_one_div" -> "algebra", "eventually_eventually_eq_nhds" -> "topology", "continuous_on_of_locally_uniform_approx_of_continuous_on" -> "topology", "primrec.vector_nth'" -> "computability", "monoid_hom.inr_apply" -> "algebra", "with_bot.lattice_eq_DLO" -> "order", "list.mfoldr_append" -> "data", "complex.arg_le_pi" -> "analysis", "set.up_down" -> "algebra", "local_equiv.trans_source''" -> "data", "coe_int_of_digits" -> "data", "ennreal.tendsto_coe_nnreal_nhds_top" -> "topology", "cardinal.mk_pnat" -> "set_theory", "list.append_eq_cons_iff" -> "data", "buffer.append_list_mk_buffer" -> "data", "measurable_space.is_measurable_bot_iff" -> "analysis", "semiconj_by.inv_right'" -> "algebra", "is_extr_filter.neg" -> "order", "one_add_one_eq_two" -> "algebra", "fintype.card_punit" -> "data", "multiset.Ico.filter_le" -> "data", "function.is_periodic_pt_zero" -> "dynamics", "filter.map_lift_eq2" -> "order", "list.disjoint_of_disjoint_append_left_left" -> "data", "onote.NF_below_of_nat" -> "set_theory", "turing.list_blank.append_mk" -> "computability", "linear_independent_comp_subtype" -> "algebra", "domain_mvt" -> "analysis", "padic_norm.nonarchimedean" -> "data", "nat.fib_mono" -> "data", "real.Inf_empty" -> "data", "is_local_extr.fderiv_eq_zero" -> "analysis", "structure_groupoid.local_invariant_prop.lift_prop_within_at_indep_chart_aux" -> "geometry", "real.has_deriv_at_rpow" -> "analysis", "csupr_const" -> "order", "is_glb_univ" -> "order", "if_t_t" -> "init", "filter.tendsto.nnrpow" -> "analysis", "cardinal.le_powerlt" -> "set_theory", "equiv.cast_apply" -> "data", "set.nonempty_interval" -> "data", "nat.one_div_lt_one_div" -> "data", "nnreal.div_pow" -> "data", "mem_nhds_within_Ici_iff_exists_Ico_subset'" -> "topology", "list.smul_prod" -> "algebra", "has_deriv_within_at.ccos" -> "analysis", "category_theory.limits.id_zero_equiv_iso_zero_apply_hom" -> "category_theory", "list.foldl_eq_of_comm'" -> "data", "mv_power_series.constant_coeff_comp_C" -> "algebra", "pos_num.of_to_nat" -> "data", "dense_inducing.comap_nhds_ne_bot" -> "topology", "filter.eventually_eq.has_strict_fderiv_at_iff" -> "analysis", "tensor_product.tmul_smul" -> "algebra", "filter.tendsto.prod_map" -> "order", "continuous_linear_map.coe_equiv_prod_of_surjective_of_is_compl" -> "analysis", "category_theory.comma.map_left_obj_hom" -> "category_theory", "linear_pmap.map_smul" -> "algebra", "pnat.gcd_a'_coe" -> "data", "localization_map.mk'_mul_cancel_left" -> "algebra", "mv_polynomial.eval\:2097_apply" -> "algebra", "linear_map.sup_range_inl_inr" -> "algebra", "turing.TM1to1.tr_tape_mk'" -> "computability", "measure_theory.ae_eq_fun.pos_part_mk" -> "analysis", "list.scanr_aux_cons" -> "data", "is_bounded_linear_map.is_O_sub" -> "analysis", "measure_theory.measure.le_sum" -> "analysis", "mv_polynomial.sum_to_iter_Xl" -> "data", "complex.I_sq" -> "data", "list.alternating_sum_nil" -> "data", "finset.prod_comm" -> "algebra", "int.neg_add" -> "init", "set.union_diff_left" -> "data", "category_theory.limits.binary_bicone.to_cocone_\[Iota]_app_left" -> "category_theory", "turing.tape.write_move_right_n" -> "computability", "add_right_eq_self" -> "algebra", "complex.of_real_div" -> "data", "real.exp_list_sum" -> "data", "nat.primrec'.add" -> "computability", "int.lt_div_iff_mul_lt" -> "data", "totally_bounded_iff_filter" -> "topology", "monoid_hom.cancel_left" -> "algebra", "category_theory.limits.fork.condition" -> "category_theory", "is_open_map.continuous_on_image_of_left_inv_on" -> "topology", "ordinal.le_add_right" -> "set_theory", "has_sum_of_subseq_of_summable" -> "analysis", "path.continuous" -> "topology", "ordinal.cof_cof" -> "set_theory", "is_unit_of_mul_eq_one" -> "algebra", "set.update_preimage_pi" -> "data", "is_preconnected_sUnion" -> "topology", "nonempty_of_trunc" -> "data", "subring.map_supr" -> "algebra", "int.mul_le_of_le_div" -> "data", "padic_seq.lift_index_left_left" -> "data", "continuous_sum_rec" -> "topology", "filter.has_basis.le_iff" -> "order", "category_theory.evaluation_uncurried_map" -> "category_theory", "finset.Ico.filter_le_of_top_le" -> "data", "set.mk_preimage_prod_right" -> "data", "multiset.union_comm" -> "data", "add_subgroup.coe_smul" -> "algebra", "function.surj_inv_eq" -> "logic", "list.dvd_prod" -> "data", "filter.mem_seq_sets_def" -> "order", "finset.univ_map_embedding" -> "data", "minimal_polynomial.degree_pos" -> "algebra", "int.le_of_lt_add_one" -> "init", "continuous_linear_map.coprod_apply" -> "topology", "one_fpow" -> "algebra", "set.left_mem_interval" -> "data", "add_submonoid.map_comap_le" -> "algebra", "has_deriv_at_filter_neg" -> "analysis", "topological_space.opens.map_id_inv_app" -> "topology", "linear_map.proj_pi" -> "algebra", "add_commute.units_neg_right" -> "algebra", "pfunctor.M.dest_corec" -> "data", "add_group.mem_closure" -> "algebra", "rat.mul_one" -> "data", "measure_theory.simple_func.map_preimage" -> "analysis", "has_sum.has_sum_compl_iff" -> "topology", "semiconj_by.neg_one_left" -> "algebra", "stream.iterate_id" -> "data", "ring_hom.cancel_left" -> "algebra", "option_t.ext" -> "init", "subsemiring.range_snd" -> "algebra", "multiset.subset_ndunion_right" -> "data", "cau_seq.mul_equiv_zero'" -> "data", "add_monoid_hom.lift_of_surjective_comp_apply" -> "algebra", "fderiv_const_mul" -> "analysis", "supr_eq_top" -> "order", "initial_seg.lt_or_eq_apply_left" -> "set_theory", "is_measurable_insert" -> "analysis", "is_compact.exists_Inf_image_eq" -> "topology", "add_submonoid.localization_map.map_comp_map" -> "algebra", "unique_mdiff_within_at_iff" -> "geometry", "with_zero.coe_lt_coe" -> "algebra", "has_strict_fderiv_at.smul_algebra" -> "analysis", "disjoint.ne" -> "order", "localization_map.mk'_eq_iff_eq" -> "algebra", "presented_group.closure_rels_subset_ker" -> "algebra", "mvpfunctor.W_cases" -> "data", "primrec.of_equiv" -> "computability", "set.univ_subtype" -> "data", "singleton_charted_space_one_chart" -> "geometry", "pi.comp_zero" -> "algebra", "finset.countable_to_set" -> "data", "Pi.uniformity" -> "topology", "prod.id_prod" -> "data", "set.forall_not_of_sep_empty" -> "data", "mjoin_map_map" -> "control", "finset.sum_preimage_of_bij" -> "data", "stream.mem_of_mem_even" -> "data", "quotient.ind'" -> "data", "nat.partrec'.head" -> "computability", "category_theory.limits.pullback.condition" -> "category_theory", "set.indicator_zero'" -> "data", "alist.perm_union" -> "data", "polynomial.derivative_one" -> "data", "category_theory.limits.mono_factorisation_zero_m" -> "category_theory", "finite_dimensional.findim_of_field" -> "algebra", "pgame.neg_zero" -> "set_theory", "continuous_multilinear_curry_right_equiv_apply" -> "analysis", "ext_chart_at_coe_symm" -> "geometry", "add_submonoid.localization_map.lift_id" -> "algebra", "partrec.vector_m_of_fn" -> "computability", "measure_theory.measure.Inf_caratheodory" -> "analysis", "cauchy_of_totally_bounded_of_ultrafilter" -> "topology", "classical.by_contradiction" -> "init", "span_points_nonempty" -> "algebra", "subring.multiset_sum_mem" -> "algebra", "free_monoid.lift_apply" -> "algebra", "norm_eq_infi_iff_inner_eq_zero" -> "analysis", "ennreal.tendsto.const_mul" -> "topology", "add_con.rel_eq_coe" -> "algebra", "nat.partrec.code.rfind_prim" -> "computability", "fin.prod_univ_succ" -> "data", "tendsto_inv_nhds_within_Ioi" -> "topology", "typevec.drop_fun_comp" -> "data", "vector.map_nil" -> "data", "rat.nonneg_antisymm" -> "data", "nnreal.summable_of_le" -> "topology", "valuation.is_equiv.comap" -> "algebra", "polynomial.eval_X" -> "data", "setoid.eqv_gen_mono" -> "data", "circle_deg1_lift.inf_apply" -> "dynamics", "complex.continuous.inv" -> "topology", "real.arcsin_sin" -> "analysis", "finsupp.multiset_sum_sum_index" -> "data", "multiset.coe_foldl" -> "data", "set.Iio_def" -> "data", "ennreal.exists_inv_nat_lt" -> "data", "matrix.tail_val'" -> "data", "continuous_linear_equiv.map_add" -> "topology", "category_theory.limits.biprod.inr_fst" -> "category_theory", "differentiable_within_at_fst" -> "analysis", "real.Lp_add_le" -> "analysis", "complex.sin_pi_div_two" -> "analysis", "function.embedding.schroeder_bernstein" -> "set_theory", "div_pow_le" -> "algebra", "polynomial.root_or_root_of_root_mul" -> "data", "list.append_subset_of_subset_of_subset" -> "data", "is_complete.is_closed" -> "topology", "list.length_sublists_len" -> "data", "direct_sum.mk_add" -> "algebra", "deriv_inv" -> "analysis", "fpow_add" -> "algebra", "category_theory.limits.types.filtered_colimit.r_ge" -> "category_theory", "free_abelian_group.hom_equiv_symm_apply" -> "algebra", "category_theory.limits.cocones.precompose_equivalence_functor" -> "category_theory", "filter.le_Limsup_of_le" -> "order", "real.rpow_lt_one_of_one_lt_of_neg" -> "analysis", "free_abelian_group.lift.of" -> "algebra", "real.volume_singleton" -> "analysis", "continuous_linear_map.continuous" -> "topology", "mul_action_hom.ext_iff" -> "algebra", "open_add_subgroup.coe_add_subgroup_le" -> "topology", "semiconj_by.conj_mk" -> "algebra", "finsupp.on_finset_apply" -> "data", "seq.dropn_tail" -> "data", "pgame.impartial.le_zero_iff" -> "set_theory", "submodule.comap_smul" -> "algebra", "sym2.eq_swap" -> "data", "open_embedding.continuous_at_iff" -> "topology", "add_subgroup.normal_in_normalizer" -> "algebra", "category_theory.limits.pushout_cocone.is_colimit.hom_ext" -> "category_theory", "int.le_add_of_neg_le_sub_right" -> "init", "topological_space.opens.inter_eq" -> "topology", "relation.refl_trans_gen_lift" -> "logic", "le_mul_iff_one_le_right" -> "algebra", "roption.ext" -> "data", "function.surjective.infi_comp" -> "order", "max_lt_max" -> "algebra", "list.last_singleton" -> "data", "set.Ico_\:2124_card" -> "data", "typevec.append_fun_comp_id" -> "data", "polynomial.sum_C_mul_X_eq" -> "data", "alg_equiv.mk_apply" -> "algebra", "is_least.cInf_eq" -> "order", "mv_polynomial.algebra_map_eq" -> "data", "hyperreal.infinite_pos_iff_infinite_neg_neg" -> "data", "irrational.div_cases" -> "data", "list.disjoint_append_right" -> "data", "principal_ideal_ring.ne_zero_of_mem_factors" -> "algebra", "finset.sdiff_union_distrib" -> "data", "onote.sub_NF_below" -> "set_theory", "add_submonoid.localization_map.add_equiv_of_localizations_right_neg_apply" -> "algebra", "asymptotics.is_O.prod_left_snd" -> "analysis", "measure_theory.lintegral_infi" -> "analysis", "homeomorph.to_local_homeomorph_coe" -> "topology", "psigma.elim_val" -> "data", "norm_num.sub_nat_neg" -> "tactic", "partial_order.ext" -> "order", "nat.not_lt_zero" -> "init", "category_theory.cocones_map" -> "category_theory", "padic_norm.zero_of_padic_norm_eq_zero" -> "data", "exists_int_pow_near'" -> "algebra", "pequiv.single_mul_single" -> "data", "submodule.comap_inf" -> "algebra", "emetric.tendsto_locally_uniformly_iff" -> "topology", "poly.ext" -> "number_theory", "add_monoid_hom.map_gsmul" -> "algebra", "deriv_const_add" -> "analysis", "circle_deg1_lift.units_coe" -> "dynamics", "set.Ico_subset_Icc_self" -> "data", "deriv_id" -> "analysis", "equiv.subtype_equiv_codomain_symm_apply_ne" -> "data", "list.infix_of_prefix" -> "data", "normed_field.nnnorm_one" -> "analysis", "Set.eq_empty" -> "set_theory", "is_local_min_on.comp_continuous_on" -> "topology", "vadd_comm" -> "algebra", "set.mem_image2_iff" -> "data", "primrec.of_nat" -> "computability", "interior_closed_ball'" -> "analysis", "list.nth_le_append_right_aux" -> "data", "cauchy_iff'" -> "topology", "mul_action.mem_orbit" -> "algebra", "has_deriv_at_filter_iff_tendsto_slope" -> "analysis", "multiset.coe_map" -> "data", "is_closed_Icc" -> "topology", "primrec.list_concat" -> "computability", "and_eq_of_eq_true_left" -> "init", "image_sub_le_mul_sub_of_deriv_le" -> "analysis", "finset.card_sdiff" -> "data", "affine_subspace.mem_direction_iff_eq_vsub_left" -> "algebra", "category_theory.sum.inl__obj" -> "category_theory", "matrix.scalar_inj" -> "data", "convex.mul_sub_lt_image_sub_of_lt_deriv" -> "analysis", "category_theory.over.mk_right" -> "category_theory", "cardinal.add_le_add_right" -> "set_theory", "Gromov_Hausdorff.eq_to_GH_space" -> "topology", "principal_seg.lt_le_top" -> "set_theory", "fraction_map.mk'_num_denom" -> "algebra", "nnreal.div_div_eq_mul_div" -> "data", "is_min_filter.is_extr" -> "order", "nat.exists_mul_self" -> "data", "multiset.nodup_erase_dup" -> "data", "filter.univ_mem_sets'" -> "order", "left_ord_continuous.id" -> "order", "lucas_lehmer.\[Omega]_pow_eq_one" -> "number_theory", "function.semiconj.eq" -> "logic", "inducing.continuous_on_iff" -> "topology", "list.mem_lookup" -> "data", "isometric.coe_mul" -> "topology", "summable.summable_of_eq_zero_or_self" -> "topology", "measure_theory.simple_func.sup_apply" -> "analysis", "pgame.lt_mk_of_le" -> "set_theory", "le_rfl" -> "algebra", "abs_eq_zero" -> "algebra", "filter.frequently_top" -> "order", "measure_theory.lebesgue_length_Icc" -> "analysis", "bot_sup_eq" -> "order", "is_local_extr_on.congr" -> "topology", "nhds_list" -> "topology", "measurable.edist" -> "analysis", "turing.TM1to1.tr_tape'_move_left" -> "computability", "nnreal.le_inv_iff_mul_le" -> "data", "category_theory.abelian.pseudoelement.pseudo_apply_aux" -> "category_theory", "indicator_ae_eq_restrict" -> "analysis", "continuous_subtype_is_closed_cover" -> "topology", "dim_span_of_finset" -> "algebra", "pnat.xgcd_type.reduce_reduced" -> "data", "continuous_if'" -> "topology", "int.eq_zero_or_eq_zero_of_mul_eq_zero" -> "init", "inv_of_eq_inv" -> "algebra", "category_theory.Comonad.coassoc_func_app" -> "category_theory", "measure_theory.induced_outer_measure_eq_extend'" -> "analysis", "measure_theory.integral_div" -> "analysis", "nndist_triangle_right" -> "topology", "measure_theory.ae_all_iff" -> "analysis", "cauchy_seq.tendsto_lim" -> "topology", "ennreal.continuous_at_const_mul" -> "topology", "inv_inv'" -> "algebra", "cau_seq.complete" -> "data", "local_equiv.left_inv_on" -> "data", "unique_diff_on_Ici" -> "analysis", "continuous_linear_map.has_sum_of_summable" -> "analysis", "eq_of_nhds_eq_nhds" -> "topology", "exists_rat_btwn" -> "algebra", "ring.fractional_ideal.mul_generator_self_inv" -> "algebra", "stream.nth_inits" -> "data", "list.erase_eq_erasep" -> "data", "nat.pow_lt_pow_of_lt_right" -> "init", "ordinal.typein.principal_seg_coe" -> "set_theory", "bdd_above.inter_of_left" -> "order", "add_submonoid.localization_map.add_neg" -> "algebra", "list.perm.inter_right" -> "data", "convex_hull_singleton" -> "analysis", "tsum_comm'" -> "topology", "convex.linear_preimage" -> "analysis", "wseq.bind_congr" -> "data", "finset.attach_insert" -> "data", "rat.le_trans" -> "data", "implies_of_if_pos" -> "init", "submonoid.mem_closure_singleton" -> "algebra", "has_fderiv_at_const" -> "analysis", "finsupp.comap_domain_apply" -> "data", "submonoid.mrange_inr" -> "algebra", "fin.cases_zero" -> "data", "free_group.equivalence_join_red" -> "algebra", "mul_semiring_action_hom.comp_id" -> "algebra", "affine_subspace.direction_bot" -> "algebra", "nat.bodd_succ" -> "init", "nat.primrec'.idv" -> "computability", "real.log_lt_log" -> "analysis", "set.nonempty.image_const" -> "data", "units.mul_inv_eq_iff_eq_mul" -> "algebra", "associates.out_dvd_iff" -> "algebra", "finset.union_comm" -> "data", "category_theory.limits.biprod.total" -> "category_theory", "multiset.disjoint_of_subset_right" -> "data", "generalized_continued_fraction.zeroth_numerator_eq_h" -> "algebra", "free_add_monoid.closure_range_of" -> "algebra", "cardinal.add_def" -> "set_theory", "closure_union" -> "topology", "uniform_continuous_comap'" -> "topology", "ideal.map_eq_top_or_is_maximal_of_surjective" -> "algebra", "pgame.equiv_trans" -> "set_theory", "set.Icc_diff_Ioo_same" -> "data", "times_cont_mdiff_on.times_cont_mdiff_on_tangent_map_within" -> "geometry", "inv_fpow" -> "algebra", "real.sin_sq_add_cos_sq" -> "data", "wseq.bisim_o.imp" -> "data", "measure_theory.integrable.induction" -> "analysis", "category_theory.functor.equiv_inverse" -> "category_theory", "is_min_filter.filter_inf" -> "order", "category_theory.nat_trans.pi_app" -> "category_theory", "metric.tendsto_nhds" -> "topology", "associates.mk_eq_mk_iff_associated" -> "algebra", "gpow_one_add" -> "algebra", "list.nth_modify_nth_eq" -> "data", "polynomial.smul_C" -> "algebra", "pmf.has_sum_coe_one" -> "analysis", "filter.bind_def" -> "order", "has_deriv_within_at.sum" -> "analysis", "padic_int.val_eq_coe" -> "data", "perfect_closure.one_def" -> "algebra", "pequiv.trans_symm" -> "data", "isometric.point_reflection_dist_self_real" -> "analysis", "cardinal.le_one_iff_subsingleton" -> "set_theory", "submodule.eq_bot_iff" -> "algebra", "nat.mul_div_right" -> "init", "reader_t.run_map" -> "init", "normal_iff_eq_add_cosets" -> "algebra", "hash_map.find_insert_eq" -> "data", "int.mem_range_iff" -> "data", "is_R_or_C.norm_sq_eq_abs" -> "data", "seq.eq_or_mem_of_mem_cons" -> "data", "path.map_coe" -> "topology", "matrix.reindex_mul" -> "algebra", "multiset.coe_erase" -> "data", "linear_map.coprod_inl" -> "algebra", "nnreal.lt_of_real_iff_coe_lt" -> "data", "pnat.xgcd_type.reduce_a" -> "data", "principal_seg.coe_fn_mk" -> "set_theory", "simple_graph.dot_product_adj_matrix" -> "combinatorics", "cardinal.ord_injective" -> "set_theory", "non_contradictory_intro" -> "init", "CommRing.coe_of" -> "algebra", "ite_apply" -> "logic", "bucket_array.mem_as_list" -> "data", "distrib_mul_action_hom.comp_apply" -> "algebra", "subring.range_fst" -> "algebra", "int.le_to_nat" -> "data", "ordinal.typein_lt_typein" -> "set_theory", "filter.has_basis.mem_iff" -> "order", "Top.presheaf.pushforward_eq_eq" -> "topology", "list.mem_bag_inter" -> "data", "set.maps_to.union" -> "data", "set.mem_of_eq_of_mem" -> "data", "set.Union_subset" -> "data", "imp_congr_right" -> "init", "normal_of_eq_cosets" -> "algebra", "mv_polynomial.exists_degree_lt" -> "data", "is_open_lt'" -> "topology", "local_homeomorph.trans_of_set'" -> "topology", "rel_embedding.is_asymm" -> "order", "category_theory.limits.coprod.associator_naturality" -> "category_theory", "filter.limsup_le_limsup" -> "order", "mem_of_is_seq_closed" -> "topology", "galois_connection.le_u_l" -> "order", "rat.nonneg_add" -> "data", "times_cont_diff_at_fst" -> "analysis", "category_theory.limits.cofork.\[Pi]_eq_app_one" -> "category_theory", "free_add_magma.map_add" -> "algebra", "is_min_filter.min" -> "order", "mv_polynomial.C_injective" -> "data", "ordinal.mul_div_le" -> "set_theory", "mul_lt_mul_left" -> "algebra", "category_theory.iso.refl_hom" -> "category_theory", "fin.mod_def" -> "init", "set.Iic_diff_Iic" -> "data", "finite_dimensional.findim_fintype_fun_eq_card" -> "algebra", "real.mul_rpow" -> "analysis", "set.image_Inter_subset" -> "data", "matrix.row_mul_vec" -> "data", "asymptotics.is_O_fst_prod'" -> "analysis", "ordinal.one_add_omega" -> "set_theory", "ordered_cancel_comm_monoid.char_zero_of_inj_zero" -> "algebra", "gaussian_int.to_complex_im" -> "data", "list.perm.sum_eq" -> "data", "equiv.apply_eq_iff_eq" -> "data", "subgroup.gpowers_eq_closure" -> "algebra", "category_theory.limits.prod.map_snd_assoc" -> "category_theory", "is_group_hom.mul" -> "algebra", "ennreal.not_top_le_coe" -> "data", "hash_map.contains_aux_iff" -> "data", "measure_theory.integrable_at_filter.inf_of_right" -> "analysis", "norm_smul" -> "analysis", "finite_dimensional.findim_fin_fun" -> "algebra", "function.surjective.has_right_inverse" -> "logic", "list.pairwise_iff_nth_le" -> "data", "nhds_within_prod" -> "topology", "nat.cast_injective" -> "algebra", "concave_on_iff_div" -> "analysis", "fin.cast_lt_cast_succ" -> "data", "lie_algebra.equiv.trans_apply" -> "algebra", "measure_theory.l1.simple_func.dense_range" -> "analysis", "category_theory.limits.limit.id_pre" -> "category_theory", "add_equiv.map_add" -> "data", "monad_lift_refl" -> "init", "nonempty_inter" -> "topology", "binfi_le" -> "order", "initial_seg.unique_of_extensional" -> "set_theory", "mul_action.mem_fixed_points" -> "algebra", "strict_mono.top_preimage_top" -> "order", "formal_multilinear_series.comp_along_composition_apply" -> "analysis", "set.finite.exists_finset_coe" -> "data", "hash_map.find_iff" -> "data", "list.forall\:2082_cons_right_iff" -> "data", "topological_space.is_topological_basis_of_subbasis" -> "topology", "order_bot.ext_bot" -> "order", "cardinal.sum_const_eq_lift_mul" -> "set_theory", "category_theory.limits.equivalence_preserves_zero_morphisms" -> "category_theory", "continuous_linear_map.coe_mk" -> "topology", "cardinal.ne_zero_iff_nonempty" -> "set_theory", "continuous_linear_map.range_prod_le" -> "topology", "contracting_with.to_lipschitz_with" -> "topology", "linear_recurrence.geom_sol_iff_root_char_poly" -> "algebra", "ennreal.tendsto_coe_sub" -> "topology", "minimal_polynomial.degree_ne_zero" -> "algebra", "coeff_scale_roots" -> "algebra", "finsupp.erase_ne" -> "data", "category_theory.limits.cocones.precompose_equivalence_counit_iso" -> "category_theory", "iterated_fderiv_succ_apply_left" -> "analysis", "real.cos_eq_zero_iff" -> "analysis", "int.nat_abs_pos_of_ne_zero" -> "init", "local_equiv.eq_of_eq_on_source_univ" -> "data", "int.mod_add_cancel_right" -> "data", "left_add_coset_equiv_rel" -> "algebra", "add_monoid_hom.snd_comp_inl" -> "algebra", "has_strict_fderiv_at.restrict_scalars" -> "analysis", "edist_eq_coe_nnnorm_sub" -> "analysis", "num.cast_succ" -> "data", "has_strict_fderiv_at.iterate" -> "analysis", "ordinal.card_mul" -> "set_theory", "set.restrict_apply" -> "data", "swap_id_rel" -> "topology", "times_cont_diff_on.add" -> "analysis", "filter.comap_prod" -> "order", "is_unit.unit_spec" -> "algebra", "mul_semiring_action_hom.map_mul" -> "algebra", "ordinal.CNF_snd_lt" -> "set_theory", "opposite.unop_injective" -> "data", "nat.pow_eq_mul_pow_sub" -> "data", "nat.le_div_iff_mul_le'" -> "data", "differentiable.const_smul_algebra" -> "analysis", "set.left_inv_on.comp" -> "data", "list.filter_cons_of_neg" -> "init", "emetric.Hausdorff_edist_image" -> "topology", "continuous_linear_equiv.skew_prod_apply" -> "topology", "omega.coeffs.val_between_map_div" -> "tactic", "norm_num.min_fac_helper_4" -> "tactic", "submodule.comap_mono" -> "algebra", "compl_sup_eq_top" -> "order", "strict_mono_id" -> "order", "submodule.neg_mem" -> "algebra", "category_theory.over.creates_connected.raised_cone_lowers_to_original" -> "category_theory", "set.univ_neg" -> "algebra", "category_theory.limits.colimit.map_post" -> "category_theory", "vector_span_eq_span_vsub_set_left" -> "algebra", "free_monoid.lift_of_comp_eq_map" -> "algebra", "norm_num.adc_bit0_bit0" -> "tactic", "pgame.ne_of_lt" -> "set_theory", "matrix.is_unit_det_of_right_inverse" -> "algebra", "is_path_connected.joined_in" -> "topology", "set_coe.ext_iff" -> "data", "category_theory.equivalence.counit_functor" -> "category_theory", "set.countable_Union_Prop" -> "data", "set.seq_seq" -> "data", "ring_hom.map_int_cast" -> "data", "polynomial.coe_monomial" -> "algebra", "equiv.point_reflection_self" -> "data", "convex_on_pow" -> "analysis", "finset.sum_const_nat" -> "algebra", "lipschitz_with.of_le_add_mul'" -> "topology", "category_theory.limits.image.factor_map" -> "category_theory", "multiset.prod_ne_zero" -> "data", "real.exp_sum" -> "data", "set.image_add_const_Icc" -> "data", "nat.choose_zero_right" -> "data", "rel_embedding.eq_preimage" -> "order", "fintype.card_prod" -> "data", "list.sublists'_eq_sublists" -> "data", "multiset.to_finset_sum_count_eq" -> "algebra", "rat.coe_int_denom" -> "data", "finset.map_subtype_subset" -> "data", "pSet.resp.eval_val" -> "set_theory", "CommGroup.one_apply" -> "algebra", "set.pi_def" -> "data", "nnreal.coe_bit1" -> "data", "lists'.subset_def" -> "set_theory", "wseq.of_mem_append" -> "data", "max_mul_of_nonneg" -> "algebra", "abstract_completion.uniform_continuous_coe" -> "topology", "free_add_semigroup.pure_seq" -> "algebra", "wseq.lift_rel_o.swap" -> "data", "exists_forall_ge_and" -> "data", "units.map_id" -> "algebra", "continuous_linear_equiv.comp_differentiable_within_at_iff" -> "analysis", "Icc_mem_nhds_within_Ioi" -> "topology", "mv_polynomial.induction_on'" -> "data", "tactic.ring_exp.prod_to_sum_pf" -> "tactic", "filter.tendsto_at_top_principal" -> "order", "set.set_coe_eq_subtype" -> "data", "equiv.sum_empty_apply_inl" -> "data", "encodable.decode_zero" -> "data", "decidable.mul_le_mul_right" -> "algebra", "uniform_continuous.sub" -> "topology", "with_bot.coe_bit1" -> "algebra", "topological_space.is_open_Union_countable" -> "topology", "set.mem_univ_pi" -> "data", "cardinal.nat_cast_lt" -> "set_theory", "computation.length_bind" -> "data", "filter.eventually_eq_of_left_inv_of_right_inv" -> "order", "finset.length_sort" -> "data", "finset.sum_sum_elim" -> "algebra", "function.injective.of_comp" -> "logic", "matrix.special_linear_group.coe_to_GL" -> "algebra", "submodule.top_smul" -> "algebra", "nat.add_comm" -> "init", "set.Ioo_inter_Ioo" -> "data", "ideal.eq_radical_of_eq_jacobson" -> "algebra", "multiset.zero_sigma" -> "data", "nat.pos_of_bit0_pos" -> "data", "is_open_map.restrict" -> "topology", "polynomial.splitting_field_aux.exists_lift" -> "algebra", "nat.gcd_dvd_left" -> "data", "Class.of_Set.inj" -> "set_theory", "convex.mul_sub_le_image_sub_of_le_deriv" -> "analysis", "pow_mul_comm" -> "algebra", "pmf.ext" -> "analysis", "cardinal.powerlt_zero" -> "set_theory", "summable.has_sum_iff_tendsto_nat" -> "topology", "subring.ext'_iff" -> "algebra", "filter.order_top.at_top_eq" -> "order", "list.argmin_le_of_mem" -> "data", "submodule.mem_span_singleton" -> "algebra", "inner_add_sub_eq_zero_iff" -> "analysis", "bex_imp_distrib" -> "logic", "linear_map.trace_eq_matrix_trace" -> "algebra", "tendsto_neg_nhds_within_Ioi_neg" -> "topology", "norm_unit_eq_one" -> "algebra", "wseq.head_cons" -> "data", "direct_sum.of_neg" -> "algebra", "measure_theory.simple_func.integral_eq_sum_filter" -> "analysis", "linear_map.injective_iff_surjective" -> "algebra", "category_theory.quotient.lift.is_lift_hom" -> "category_theory", "prod_X_sub_smul.eval" -> "algebra", "primrec.nat_lt" -> "computability", "wseq.exists_of_lift_rel_left" -> "data", "topological_space.opens.op_map_comp_obj" -> "topology", "mv_polynomial.eval\:2082_assoc" -> "data", "le_inf_iff" -> "order", "holor.holor_index_cons_decomp" -> "data", "edist_le_of_edist_le_geometric_two_of_tendsto" -> "analysis", "is_local_min.fderiv_eq_zero" -> "analysis", "units.coe_mul_left" -> "data", "list.last_cons_cons" -> "data", "measure_theory.integral_union" -> "analysis", "encodable.decode_unit_succ" -> "data", "nat.mem_list_primes_of_dvd_prod" -> "data", "cardinal.add_eq_left_iff" -> "set_theory", "nat.lt_of_sub_lt_sub_right" -> "data", "partrec.bind_decode2_iff" -> "computability", "measure_theory.l1.integral_add" -> "analysis", "emetric.Hausdorff_edist_closure\:2082" -> "topology", "ring.fractional_ideal.coe_inv_of_nonzero" -> "algebra", "continuous_linear_map.prod_apply" -> "topology", "nat.lt_of_sub_eq_succ" -> "init", "inv_le_self" -> "algebra", "complex.abs_cast_nat" -> "data", "matrix.row_apply" -> "data", "semidirect_product.map_inl" -> "algebra", "add_submonoid.closure_eq_of_le" -> "algebra", "finsupp.map_range_multiset_sum" -> "data", "uniformly_extend_exists" -> "topology", "multiset.ndunion_le_union" -> "data", "algebra.subring_coe_algebra_map_hom" -> "algebra", "eq_zero_of_left_cancel_add_self" -> "algebra", "int.cast_bit1" -> "data", "to_bool_true_eq_tt" -> "init", "polynomial.div_X_C" -> "data", "fin.coe_coe_eq_self" -> "data", "nnreal.div_lt_one_of_lt" -> "data", "is_R_or_C.one_im" -> "data", "finset.piecewise_insert" -> "data", "list.map_fst_zip" -> "data", "equiv.perm.subtype_perm_one" -> "algebra", "list.reverse_cons'" -> "data", "mv_polynomial.dim_R" -> "algebra", "derivation.map_sub" -> "algebra", "isometry.antilipschitz" -> "topology", "emetric.diam_eq_zero_iff" -> "topology", "local_homeomorph.restr_coe_symm" -> "topology", "padic_int.cast_pow" -> "data", "is_compact.elim_finite_subcover_image" -> "topology", "lt_add_of_nonneg_of_lt" -> "algebra", "semidirect_product.mul_left" -> "algebra", "finsupp.filter_add" -> "data", "quotient.mk_out" -> "data", "subring.list_sum_mem" -> "algebra", "ordinal.pred_le" -> "set_theory", "is_Z_bilin.tendsto_zero_left" -> "topology", "padic_norm_z.one" -> "data", "subgroup.closure_empty" -> "algebra", "div_mul_left" -> "algebra", "linear_map.mk_continuous_of_exists_bound_coe" -> "analysis", "multiplicity.mul" -> "algebra", "submonoid.exists_list_of_mem_closure" -> "algebra", "filter.map_compose" -> "order", "ennreal.div_one" -> "data", "id_restr_groupoid_mem" -> "geometry", "ring_hom.map_pth_root" -> "algebra", "measure_theory.lebesgue_length_subadditive" -> "analysis", "category_theory.biprod.inl_of_components" -> "category_theory", "category_theory.limits.pushout.inl_desc_assoc" -> "category_theory", "uniform.continuous_iff'_left" -> "topology", "normalize_gcd" -> "algebra", "list.perm_ordered_insert" -> "data", "mv_polynomial.coeff_add" -> "data", "tensor_product.lcurry_apply" -> "algebra", "pfunctor.M.head_succ" -> "data", "Inf_sup_Inf" -> "order", "multiset.prod_eq_foldl" -> "data", "commute.mul_fpow" -> "algebra", "associated_one_of_mul_eq_one" -> "algebra", "nat.partrec.code.fixed_point\:2082" -> "computability", "int.cast_max" -> "data", "set.compl_bUnion" -> "data", "multiset.fold_cons_left" -> "data", "pos_num.add_one" -> "data", "category_theory.limits.types.jointly_surjective" -> "category_theory", "computation.lift_rel_think_right" -> "data", "multiset.length_ndinsert_of_not_mem" -> "data", "has_strict_deriv_at.has_deriv_at" -> "analysis", "with_top.top_ne_one" -> "algebra", "asymptotics.is_O.sub" -> "analysis", "closure_closure" -> "topology", "rat.mul_assoc" -> "data", "wseq.exists_of_mem_join" -> "data", "list.disjoint_iff_ne" -> "data", "complex.of_real_cpow" -> "analysis", "multiset.Ico.card" -> "data", "algebra.surjective_algbera_map_iff" -> "algebra", "set.indicator_compl" -> "data", "nat.partrec'.vec_iff" -> "computability", "sq_sub_sq" -> "algebra", "turing.blank_extends.above_of_le" -> "computability", "canonically_ordered_semiring.mul_le_mul" -> "algebra", "list.perm_insert_swap" -> "data", "bitvec.to_fin_le_to_fin_of_le" -> "data", "min_eq_left" -> "init", "nat.div_le_of_le_mul" -> "init", "category_theory.graded_object.comap_equiv_functor" -> "category_theory", "nat.min_fac_le_of_dvd" -> "data", "differentiable.prod" -> "analysis", "prod_mk_prod" -> "algebra", "real.cos_pi_div_thirty_two" -> "analysis", "real.sinh_eq" -> "data", "topological_space.open_nhds.map_id_obj'" -> "topology", "commute.cast_int_mul_self" -> "algebra", "Sup_apply" -> "order", "monoid.mem_closure_union_iff" -> "algebra", "category_theory.limits.cocone_morphism.ext_iff" -> "category_theory", "convex_cone.mem_mk" -> "analysis", "sub_lt_sub_iff_right" -> "algebra", "is_add_group_hom.neg_iff_ker" -> "algebra", "measure_theory.measure_mono_ae" -> "analysis", "stream.drop_append_stream" -> "data", "local_homeomorph.inv_image_trans_target" -> "topology", "filter.seq_assoc" -> "order", "polynomial.eval_eq_sum" -> "data", "matrix.smul_cons" -> "data", "multiset.map_id" -> "data", "category_theory.limits.image.map_hom_mk'_\[Iota]" -> "category_theory", "ideal.mem_span_insert'" -> "algebra", "polynomial.div_eq_zero_iff" -> "data", "le_mul_of_one_le_left" -> "algebra", "category_theory.uncurry_eq" -> "category_theory", "filter.comap_infi" -> "order", "deriv_within_const_mul" -> "analysis", "list.mem_append_right" -> "init", "set.maps_to.image_subset" -> "data", "subtype.coe_prop" -> "data", "uniform.continuous_within_at_iff'_left" -> "topology", "function.semiconj.inj_on_range" -> "data", "neg_neg_iff_pos" -> "algebra", "complex.cos_zero" -> "data", "perfect_closure.frobenius_mk" -> "algebra", "set.image_sub_const_Ico" -> "data", "equiv_equiv_iso_hom" -> "category_theory", "intermediate_value_univ\:2082" -> "topology", "derivation.coe_injective" -> "algebra", "formal_multilinear_series.congr" -> "analysis", "dfinsupp.support_map_range" -> "data", "one_div_one" -> "algebra", "list.map_id" -> "init", "irrational.of_rat_sub" -> "data", "hyperreal.infinite_neg_iff_infinitesimal_inv_neg" -> "data", "fpow_eq_zero" -> "algebra", "matrix.cons_val_zero'" -> "data", "rat.mk_num_ne_zero_of_ne_zero" -> "data", "finsupp.single_mem_supported" -> "algebra", "norm_num.one_succ" -> "tactic", "finset.image_bind_filter_eq" -> "data", "subring.range_subtype" -> "algebra", "lt_top_iff_ne_top" -> "order", "list.nth_le_take" -> "data", "nat.mod_le" -> "init", "ring_hom.map_ne_zero" -> "algebra", "finset.image_insert" -> "data", "transitive_many_one_reducible" -> "computability", "ordinal.card_lt_nat" -> "set_theory", "matrix.row_empty" -> "data", "set.disjoint_union_right" -> "data", "nat.add_le_add_right" -> "init", "submodule.le_div_iff" -> "algebra", "measure_theory.measure.haar.index_mono" -> "analysis", "typevec.cases_nil_append1" -> "data", "set.mem_Ioi" -> "data", "finset.map_eq_image" -> "data", "finset.bind_empty" -> "data", "category_theory.limits.prod_map_comp_id" -> "category_theory", "free_abelian_group.map_of" -> "algebra", "add_semiconj_by.map" -> "algebra", "set.mem_diff" -> "data", "is_integral_trans_aux" -> "algebra", "setoid.empty_not_mem_classes" -> "data", "equiv.prod_congr_symm" -> "data", "decidable.mul_le_mul_left" -> "algebra", "function.injective_of_partial_inv" -> "logic", "quadratic_form.lin_mul_lin_apply" -> "algebra", "submonoid.mem_powers" -> "algebra", "ennreal.add_sub_self'" -> "data", "ulift.rec.constant" -> "data", "pgame.le_def_lt" -> "set_theory", "finset.nat.mem_antidiagonal" -> "data", "encodable.Union_decode2" -> "data", "is_lub_singleton" -> "order", "set.range_ite_subset" -> "data", "pos_num.cast_one" -> "data", "con.con_gen_of_con" -> "algebra", "compl_le_of_compl_le" -> "order", "polynomial.zero_is_root_of_coeff_zero_eq_zero" -> "data", "filter.mem_zero" -> "order", "set.finite_range_const" -> "data", "category_theory.preadditive.sub_comp_assoc" -> "category_theory", "polynomial.map_nat_cast" -> "data", "joined_in.joined" -> "topology", "subalgebra.res_top" -> "algebra", "cInf_Ici" -> "order", "norm_add_square_eq_norm_square_add_norm_square_iff_inner_eq_zero" -> "analysis", "finset.sum_bind" -> "algebra", "metric.mem_ball_comm" -> "topology", "bilin_form.mem_self_adjoint_submodule" -> "algebra", "poly_equiv_tensor.to_fun_alg_hom_apply_tmul" -> "algebra", "is_compl.right_le_iff" -> "order", "add_con.sup_def" -> "algebra", "measurable_zero" -> "analysis", "subgroup.coe_inf" -> "algebra", "galois_coinsertion.l_injective" -> "order", "set.union_neg" -> "algebra", "continuous_linear_map.coe_prod_map" -> "topology", "ordinal.zero_CNF" -> "set_theory", "linear_map.ext_iff" -> "algebra", "set.indicator_le_self'" -> "data", "finset.Ico.filter_lt_of_top_le" -> "data", "mv_polynomial.coeff_neg" -> "data", "is_add_submonoid.finset_sum_mem" -> "algebra", "compl_infi" -> "order", "exists_eq_mul_right_of_dvd" -> "algebra", "continuous_multilinear_map.op_norm_smul_le" -> "analysis", "commute.one_right" -> "algebra", "set.nonempty.add" -> "algebra", "free_group.prod.unique" -> "algebra", "true_eq_false_of_false" -> "init", "differentiable_at_id'" -> "analysis", "norm'_def" -> "analysis", "eq_center_mass_card_le_dim_succ_of_mem_convex_hull" -> "analysis", "list.sublists_len_sublist_of_sublist" -> "data", "forall_of_ball" -> "logic", "complex.abs_re_div_abs_le_one" -> "data", "polynomial.degree_mul" -> "data", "generalized_continued_fraction.succ_succ_nth_convergent'_aux_eq_succ_nth_convergent'_aux_squash_seq" -> "algebra", "primrec.fst" -> "computability", "rat.sqrt_nonneg" -> "data", "free_semigroup.mul_bind" -> "algebra", "list.head_append" -> "data", "category_theory.as_iso_inv" -> "category_theory", "with_top.coe_lt_top" -> "order", "category_theory.prod_preserves_connected_limits.forget_cone_X" -> "category_theory", "relation.eq_comp" -> "logic", "topological_space.opens.comap_val" -> "topology", "category_theory.quotient.lift.is_lift_inv" -> "category_theory", "nat.pow_lt_iff_lt_left" -> "data", "cardinal.eq_of_add_eq_add_left" -> "set_theory", "category_theory.iso.eq_comp_inv" -> "category_theory", "ennreal.coe_add" -> "data", "asymptotics.is_O_with.mono" -> "analysis", "matrix.empty_eq" -> "data", "ennreal.coe_lt_top" -> "data", "bitraversable.tsnd_comp_tfst" -> "control", "ordinal.nat_cast_div" -> "set_theory", "ennreal.lt_iff_exists_rat_btwn" -> "data", "field.closure_mono" -> "algebra", "dfinsupp.filter_apply" -> "data", "finset.insert_singleton_comm" -> "data", "list.foldl_assoc_comm_cons" -> "data", "ordered_comm_group.lt_of_mul_lt_mul_left" -> "algebra", "finset.sum_range_one" -> "algebra", "mul_div_cancel_of_invertible" -> "algebra", "cardinal.card_typein_out_lt" -> "set_theory", "pythagorean_triple.coprime_of_coprime" -> "number_theory", "le_generate_from" -> "topology", "pfun.preimage_univ" -> "data", "with_top.none_lt_some" -> "order", "polynomial.derivative_add" -> "data", "finset.sum_range_id_mul_two" -> "algebra", "list.inter_cons_of_mem" -> "data", "pequiv.ext_iff" -> "data", "finset.add_sum_diff_singleton" -> "algebra", "pnat.coprime_coe" -> "data", "list.nth_le_of_fn'" -> "data", "multiset.sum_map_zero" -> "data", "relation.refl_trans_gen_mono" -> "logic", "ideal.comap_Inf" -> "algebra", "supr_exists" -> "order", "cardinal.lift_two_power" -> "set_theory", "infi_infi_eq_left" -> "order", "function.embedding.coe_sigma_mk" -> "logic", "pfun.ext" -> "data", "is_integral.is_algebraic" -> "algebra", "bilin_form.lin_mul_lin_comp_right" -> "algebra", "finset.range_mono_of_fin" -> "data", "onote.NF_below.oadd" -> "set_theory", "polynomial.C_eq_int_cast" -> "data", "measure_theory.outer_measure.of_content_opens" -> "analysis", "zsqrtd.norm_nat_cast" -> "data", "classical.skolem" -> "init", "ring_equiv.map_ne_one_iff" -> "data", "tactic.ring_exp.mul_p_pf_sum" -> "tactic", "ordinal.log_lt" -> "set_theory", "nat.coprime.gcd_mul" -> "data", "lucas_lehmer.two_lt_q" -> "number_theory", "polynomial.eval\:2082_zero" -> "data", "category_theory.types_comp_apply" -> "category_theory", "int.neg_le_sub_right_of_le_add" -> "init", "continuous_linear_equiv.coe_apply" -> "topology", "category_theory.limits.fork.app_zero_left_assoc" -> "category_theory", "mv_polynomial.aeval_def" -> "data", "category_theory.functor.comp_map" -> "category_theory", "array.read_map" -> "data", "with_top.coe_ne_top" -> "order", "zsqrtd.divides_sq_eq_zero_z" -> "data", "differentiable_within_at.continuous_within_at" -> "analysis", "seq.cons_append" -> "data", "times_cont_mdiff_within_at.mdifferentiable_within_at" -> "geometry", "function.inv_fun_surjective" -> "logic", "is_closed.cSup_mem" -> "topology", "nat.bit1_ne_bit0" -> "init", "prime_spectrum.subset_zero_locus_iff_le_vanishing_ideal" -> "algebraic_geometry", "category_theory.limits.biproduct.\[Iota]_\[Pi]_assoc" -> "category_theory", "add_units.neg_add_eq_iff_eq_add" -> "algebra", "cfilter.coe_mk" -> "data", "ordinal.le_omin" -> "set_theory", "measure_theory.measure.smul_to_outer_measure" -> "analysis", "list.ilast_eq_last'" -> "data", "set.mem_of_indicator_ne_zero" -> "data", "direct_sum.to_group_neg" -> "algebra", "ordinal.lift_lt" -> "set_theory", "add_monoid_hom.ext_nat" -> "data", "add_con.add_con_gen_mono" -> "algebra", "has_fderiv_within_at.restrict_scalars" -> "analysis", "filter.has_basis.inf_principal" -> "order", "list.mem_argmin_iff" -> "data", "dite_comp_equiv_update" -> "data", "pfun.preimage_subset_dom" -> "data", "max_le" -> "init", "list.modify_nth_eq_take_drop" -> "data", "game.add_zero" -> "set_theory", "ennreal.of_real_le_of_real_iff" -> "data", "zero_le_bit0" -> "algebra", "nat.exists_coprime'" -> "data", "list.chain'_singleton" -> "data", "measure_theory.lebesgue_to_outer_measure" -> "analysis", "units.ne_zero" -> "algebra", "cardinal.aleph'_nat" -> "set_theory", "equiv.arrow_congr_trans" -> "data", "set.monotone_inter" -> "data", "linear_equiv.eq_of_linear_map_eq" -> "algebra", "real.cos_two_pi" -> "analysis", "complex.abs_nonneg" -> "data", "monoid_hom.coe_prod_map" -> "algebra", "measure_theory.ae_eq_fun.is_add_subgroup" -> "analysis", "set.interval_of_not_ge" -> "data", "bilin_form.to_matrix_comp_left" -> "algebra", "multiset.mem_ndinsert_of_mem" -> "data", "eq_rec_compose" -> "init", "continuous_linear_equiv.comp_has_strict_fderiv_at_iff" -> "analysis", "galois_connection.u_Inf" -> "order", "commute.fpow_fpow" -> "algebra", "dfinsupp.mk_smul" -> "data", "euclidean_geometry.dist_orthogonal_projection_ne_zero_of_not_mem" -> "geometry", "ne.symm" -> "init", "sesq_form.add_right" -> "algebra", "pnat.xgcd_type.start_v" -> "data", "bounded_continuous_function.abs_diff_coe_le_dist" -> "topology", "complex.is_cau_seq_im" -> "data", "free_add_magma.lift_of" -> "algebra", "closed_embedding.is_closed_map" -> "topology", "multiset.coe_sum" -> "data", "uniformity_basis_edist_le'" -> "topology", "category_theory.comma.map_left_comp_hom_app_left" -> "category_theory", "ennreal.one_to_nnreal" -> "data", "category_theory.functor.inv_inv" -> "category_theory", "bilin_form.ortho_smul_left" -> "algebra", "int.eq_neg_of_eq_neg" -> "init", "ring_hom.map_multiset_prod" -> "algebra", "semidirect_product.inr_injective" -> "algebra", "add_monoid_hom.map_closure" -> "algebra", "measure_theory.simple_func.const_lintegral_restrict" -> "analysis", "filter.eventually_eq.trans" -> "order", "linear_map.map_eq_top_iff" -> "algebra", "filter.Sup_sets_eq" -> "order", "zsqrtd.coe_nat_val" -> "data", "asymptotics.is_o_zero" -> "analysis", "int.nat_abs_neg" -> "init", "set.Inter_univ" -> "data", "quadratic_form.polar_smul_right" -> "algebra", "opposite.unop_sub" -> "algebra", "powers_hom_apply" -> "algebra", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_apply_ker" -> "analysis", "equiv.sum_comm_apply" -> "data", "with_zero.div_one" -> "algebra", "fin.coe_of_nat_eq_mod" -> "data", "function.comp_apply" -> "logic", "inner_product_space.of_core.norm_eq_sqrt_inner" -> "analysis", "list.lookup_erase_dupkeys" -> "data", "list.reverse_append" -> "data", "set.nonempty_of_not_subset" -> "data", "int.add_one_le_iff" -> "data", "summable_iff_vanishing" -> "topology", "decidable.le_iff_lt_or_eq" -> "init", "emetric.inf_edist_le_inf_edist_of_subset" -> "topology", "multiset.induction_on" -> "data", "pnat.gcd_eq_right_iff_dvd" -> "data", "complex.cosh_zero" -> "data", "dioph.or_dioph" -> "number_theory", "times_cont_diff_at.prod_map'" -> "analysis", "emetric.Hausdorff_edist_zero_iff_closure_eq_closure" -> "topology", "fintype.sum_apply" -> "algebra", "structure_groupoid.lift_prop_within_at_univ" -> "geometry", "set.Ico_diff_left" -> "data", "is_cau_seq.cauchy\:2083" -> "data", "category_theory.monoidal_category.left_unitor_product_aux" -> "category_theory", "set.not_subset" -> "data", "lipschitz_with.nndist_le" -> "topology", "compact_Union" -> "topology", "filter.Limsup_principal" -> "order", "category_theory.coyoneda_map_app" -> "category_theory", "seq.of_stream_append" -> "data", "interval_integral.integral_neg" -> "analysis", "polynomial.degree_map'" -> "data", "linarith.mul_zero_eq" -> "tactic", "emetric.Hausdorff_edist_empty" -> "topology", "add_comm_group.is_Z_bilin.sub_right" -> "topology", "incomp_iff_eq" -> "init", "Lim_spec" -> "topology", "seq.coinduction2" -> "data", "pgame.nim.zero_first_loses" -> "set_theory", "list.join_join" -> "data", "polynomial.expand_inj" -> "algebra", "mv_polynomial.total_degree_le_degrees_card" -> "data", "subtype.irreducible_space" -> "topology", "finset.supr_union" -> "data", "semiconj_by.div_right" -> "algebra", "pow_unbounded_of_one_lt" -> "algebra", "matrix.special_linear_group.det_coe_fun" -> "algebra", "unique_factorization_domain.unique" -> "algebra", "nat.lxor_left_inj" -> "data", "abstract_completion.inverse_compare" -> "topology", "is_basis.repr_range" -> "algebra", "multiset.coe_le" -> "data", "list.forall_mem_append" -> "data", "to_bool_ff" -> "init", "pgame.relabel_move_right'" -> "set_theory", "Ico_mem_nhds_within_Ici" -> "topology", "submodule.smul_le_smul" -> "algebra", "simple_continued_fraction.coe_to_generalized_continued_fraction" -> "algebra", "add_units.coe_neg" -> "algebra", "option_t.run_bind" -> "init", "subgroup.closure_le" -> "algebra", "pgame.mk_lt_of_le" -> "set_theory", "nhds_within_Iio_self_ne_bot" -> "topology", "has_fpower_series_on_ball.tendsto_uniformly_on'" -> "analysis", "filter.tendsto_at_top_of_add_const_left" -> "order", "add_monoid_hom.flip_apply" -> "algebra", "finsupp.finite_lt_nat" -> "data", "AddCommGroup.free_map_coe" -> "algebra", "list.mem_product" -> "data", "is_R_or_C.I_to_real" -> "data", "relation.join_of_single" -> "logic", "filter.eventually_eq.mfderiv_within_eq" -> "geometry", "list.head'_map" -> "data", "finset.comp_inf_eq_inf_comp_of_is_total" -> "data", "euclidean_domain.dvd_mod_iff" -> "algebra", "ordinal.is_normal.trans" -> "set_theory", "gold_sq" -> "data", "measure_theory.measure.haar.echaar_sup_le" -> "analysis", "unique_diff_within_at.mono" -> "analysis", "filter.tendsto_pure_pure" -> "order", "equiv.psigma_equiv_sigma_apply" -> "data", "list.subperm.exists_of_length_lt" -> "data", "multiset.card_repeat" -> "data", "supr_eq_supr_finset'" -> "data", "set.finite.preimage" -> "data", "add_semiconj_by.zero_right" -> "algebra", "additive.is_add_hom" -> "algebra", "equiv.refl_trans" -> "data", "tensor_algebra.hom_ext" -> "algebra", "con.con_gen_eq" -> "algebra", "filter.frequently_iff_forall_eventually_exists_and" -> "order", "commute.inv_left_iff" -> "algebra", "category_theory.limits.binary_cofan.\[Iota]_app_left" -> "category_theory", "turing.tr_reaches_rev" -> "computability", "filter.principal_is_measurably_generated_iff" -> "analysis", "closure_subtype" -> "topology", "omega.nat.preterm.val_sub" -> "tactic", "category_theory.iso.trans_assoc" -> "category_theory", "is_noetherian_of_quotient_of_noetherian" -> "algebra", "ereal.coe_real_le" -> "data", "function.support_mul" -> "data", "category_theory.limits.coprod.desc_comp_comp_assoc" -> "category_theory", "polynomial.eval\:2082_add" -> "data", "vector.nth_cons_succ" -> "data", "linear_equiv.finite_dimensional" -> "algebra", "affine.simplex.eq_circumcenter_of_dist_eq" -> "geometry", "subset_tangent_cone_prod_right" -> "analysis", "prod_map" -> "data", "add_monoid_algebra.single_zero_mul_apply" -> "data", "complete_space_iff_is_complete_univ" -> "topology", "fin.cast_le_injective" -> "data", "polynomial.zero_le_degree_iff" -> "data", "znum.zero_add" -> "data", "int.cast_one" -> "data", "affine_combination_mem_affine_span" -> "algebra", "primrec\:2082.of_eq" -> "computability", "nat.modeq.modeq_of_modeq_mul_right" -> "data", "nat.test_bit_lxor" -> "init", "geom_sum_mul" -> "algebra", "is_R_or_C.norm_sq_add" -> "data", "finset.pi.cons_same" -> "data", "is_R_or_C.is_cau_seq_re" -> "data", "contracting_with.one_sub_K_ne_top" -> "topology", "finset.coe_inter" -> "data", "vector.nth_mem" -> "data", "measure_theory.simple_func.mem_range_of_measure_ne_zero" -> "analysis", "complex.exp_eq_exp_iff_exists_int" -> "analysis", "add_subgroup.normal.mem_comm" -> "algebra", "set.infinite_iff_frequently_cofinite" -> "order", "submodule.coe_is_compl_equiv_proj_symm_apply" -> "algebra", "list.drop_nil" -> "data", "finset.max_of_mem" -> "data", "complex.of_real_tan" -> "data", "nat.one_lt_pow'" -> "data", "linear_pmap.mk_span_singleton_apply" -> "algebra", "list.pairwise.imp\:2082" -> "data", "formal_multilinear_series.apply_composition_ones" -> "analysis", "Kuratowski_embedding.embedding_of_subset_isometry" -> "topology", "list.take_all_of_le" -> "data", "continuous_linear_map.has_deriv_within_at" -> "analysis", "set.mem_insert" -> "data", "category_theory.preadditive.sum_comp_assoc" -> "category_theory", "asymptotics.is_O_neg_right" -> "analysis", "set.indicator_range_comp" -> "data", "submodule.coe_injective" -> "algebra", "filter.extraction_of_eventually_at_top" -> "order", "exists_lt_of_lt_csupr" -> "order", "set.pairwise_on_eq_iff_exists_eq" -> "data", "complex.of_real_exp_of_real_re" -> "data", "equiv.perm.is_cycle_swap_mul" -> "algebra", "filter.tendsto_inf_right" -> "order", "category_theory.limits.types.coprod_desc" -> "category_theory", "is_greatest.cSup_eq" -> "order", "dfinsupp.mk_neg" -> "data", "padic_seq.add_eq_max_of_ne" -> "data", "is_bounded_linear_map.lim_zero_bounded_linear_map" -> "analysis", "category_theory.preimage_iso_hom" -> "category_theory", "matrix.from_blocks_to_blocks" -> "data", "dfinsupp.erase_apply" -> "data", "category_theory.iso.conj_pow" -> "category_theory", "list.range'_append" -> "data", "smooth_manifold_with_corners.mem_maximal_atlas_of_mem_atlas" -> "geometry", "stream.take_theorem" -> "data", "category_theory.under.post_map_right" -> "category_theory", "has_deriv_within_at.sqrt" -> "analysis", "rel_embedding.is_antisymm" -> "order", "one_div_mul_cancel" -> "algebra", "nnnorm_add_le" -> "analysis", "Inf_mem_closure" -> "topology", "Group.ext" -> "algebra", "cardinal.eq_of_add_eq_add_right" -> "set_theory", "set.preimage_neg_Ico" -> "data", "set.mem_image_iff_bex" -> "data", "ennreal.infi_ennreal" -> "data", "is_basis.constr_apply" -> "algebra", "category_theory.limits.cocone.of_pushout_cocone_\[Iota]" -> "category_theory", "pnat.gcd_mul_lcm" -> "data", "multiset.to_finset_inter" -> "data", "polynomial.map_pow" -> "data", "set.bUnion_mono" -> "data", "and_eq_of_eq_false_left" -> "init", "set.nonempty.image2" -> "data", "pequiv.symm_refl" -> "data", "pgame.turn_bound_of_left" -> "set_theory", "matrix.from_blocks_multiply" -> "data", "ordinal.dvd_add" -> "set_theory", "real.continuous_at_rpow_of_ne_zero" -> "analysis", "measure_theory.extend_Union_le_tsum_nat'" -> "analysis", "peirce" -> "logic", "with_top.is_lub_Sup" -> "order", "one_lt_mul_of_le_of_lt'" -> "algebra", "nat.dvd_gcd_iff" -> "data", "asymptotics.is_O_with.comp_tendsto" -> "analysis", "or_false" -> "init", "set.Iio_subset_Iio" -> "data", "mvqpf.Wequiv.refl" -> "data", "to_topological_space_subtype" -> "topology", "one_le_inv" -> "algebra", "category_theory.under.id_right" -> "category_theory", "computation.results_thinkN_ret" -> "data", "set.preimage_image_eq" -> "data", "alist.not_mem_empty" -> "data", "add_monoid_hom.gclosure_preimage_le" -> "algebra", "option.iget_mem" -> "data", "algebra.algebra_ext" -> "algebra", "iff_iff_and_or_not_and_not" -> "logic", "real.sin_sub" -> "data", "nat.choose_one_right" -> "data", "generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some" -> "algebra", "emetric.mem_ball" -> "topology", "le_mul_of_one_le_right'" -> "algebra", "nat.psub_eq_some" -> "data", "monotonicity.exists" -> "meta", "ennreal.zero_to_nnreal" -> "data", "matrix.from_blocks_smul" -> "data", "continuous.edist" -> "topology", "add_submonoid.localization_map.to_map_injective" -> "algebra", "category_theory.iso.cancel_iso_hom_right_assoc" -> "category_theory", "add_submonoid.mem_inf" -> "algebra", "affine_map.line_map_linear" -> "algebra", "finsupp.lmap_domain_id" -> "algebra", "padic_int.zmod_congr_of_sub_mem_max_ideal" -> "data", "category_theory.abelian.pseudoelement.zero_morphism_ext" -> "category_theory", "quot.lift_on\:2082_mk" -> "data", "polynomial.X_mul" -> "data", "exists_pos_bound_of_bound" -> "analysis", "set.left_inv_on.eq_on" -> "data", "affine_map.coe_homothety_hom" -> "algebra", "option.bind_eq_none" -> "data", "category_theory.limits.cocone.w" -> "category_theory", "mat_poly_equiv_coeff_apply_aux_2" -> "algebra", "ordinal.sub_le_self" -> "set_theory", "submonoid.localization_map.mk'_eq_iff_eq_mul" -> "algebra", "neg_le_sub_iff_le_add'" -> "algebra", "list.sublist_cons" -> "data", "has_sum.tendsto_sum_nat" -> "topology", "submonoid.coe_subtype" -> "algebra", "list.forall\:2082_take_append" -> "data", "set.image3_congr" -> "data", "ring_commutator.commutator" -> "algebra", "le_Inf_iff" -> "order", "pgame.add_move_right_inr" -> "set_theory", "category_theory.nat_trans.op_id" -> "category_theory", "set.preimage_const_mul_Ici" -> "data", "pgame.right_wins_of_equiv" -> "set_theory", "set.image_preimage_inter" -> "data", "complex.ext_abs_arg" -> "analysis", "midpoint_neg_neg" -> "algebra", "category_theory.equivalence.inv_fun_map" -> "category_theory", "linear_map.comap_cod_restrict" -> "algebra", "multiset.add_bind" -> "data", "category_theory.limits.cone.category_to_category_struct_id_hom" -> "category_theory", "compact_of_totally_bounded_is_closed" -> "topology", "has_strict_fderiv_at_snd" -> "analysis", "int.shiftr_eq_div_pow" -> "data", "set.Ici_inter_Ici" -> "data", "generalized_continued_fraction.part_denom_eq_s_b" -> "algebra", "open_embedding.open_target" -> "topology", "pow_two_nonneg" -> "algebra", "has_fderiv_within_at_const" -> "analysis", "add_con.lift_coe" -> "algebra", "is_local_max_on.sup" -> "topology", "lipschitz_with.prod_snd" -> "topology", "convex_cone.comap_comap" -> "analysis", "category_theory.limits.cokernel_is_iso_comp_inv" -> "category_theory", "pell.x_increasing" -> "number_theory", "set.countable_of_injective_of_countable_image" -> "data", "continuous_ulift_down" -> "topology", "ideal.map_top" -> "algebra", "int.sub_pos_of_lt" -> "init", "real.has_deriv_at_rpow_of_pos" -> "analysis", "continuous_linear_map.id_comp" -> "topology", "le_add_of_neg_add_le_left" -> "algebra", "has_deriv_at_filter.sub" -> "analysis", "with_zero.inv_one" -> "algebra", "exists_pos_rat_lt" -> "algebra", "filter.mem_generate_iff" -> "order", "affine_map.comp_id" -> "algebra", "real.sinh_zero" -> "data", "power_series.coeff_X_pow" -> "algebra", "polynomial.exists_separable_of_irreducible" -> "algebra", "times_cont_diff_zero_fun" -> "analysis", "is_extr_filter.congr" -> "order", "cardinal.lift_lt" -> "set_theory", "ordinal.has_succ_of_is_limit" -> "set_theory", "local_homeomorph.continuous_at_symm" -> "topology", "linear_map.has_deriv_within_at" -> "analysis", "subsemiring.coe_to_add_submonoid" -> "algebra", "generalized_continued_fraction.zeroth_convergent'_eq_h" -> "algebra", "category_theory.monad_hom.comp_id" -> "category_theory", "function.injective.eq_iff'" -> "logic", "ennreal.ne_top_of_mul_ne_top_right" -> "data", "dioph.dioph_fn_comp2" -> "number_theory", "div_eq_iff_mul_eq" -> "algebra", "rat.num_denom" -> "data", "ideal.map_mul" -> "algebra", "set.surj_on.mono" -> "data", "monoid_hom.normal_ker" -> "algebra", "is_strict_weak_order_of_is_order_connected" -> "order", "set.mem_sep" -> "data", "primrec.nat_mul" -> "computability", "list_all_iff_forall" -> "number_theory", "ennreal.inv_mul_cancel" -> "data", "add_right_comm" -> "algebra", "nat.sub_add_comm" -> "init", "units.inv_mul_of_eq" -> "algebra", "category_theory.monoidal_category.tensor_right_obj" -> "category_theory", "nnreal.tendsto_inverse_at_top_nhds_0_nat" -> "analysis", "is_closed_proj_of_compact" -> "topology", "set.sep_set_of" -> "data", "category_theory.monoidal.tensor_hom_app" -> "category_theory", "list.pairwise_sublists" -> "data", "measure_theory.simple_func.monotone_eapprox" -> "analysis", "has_fderiv_within_at.const_sub" -> "analysis", "list.mem_enum_from" -> "data", "list.Ico.filter_lt_of_ge" -> "data", "cardinal.mk_compl_eq_mk_compl_finite" -> "set_theory", "real.borel_eq_generate_from_Ioo_rat" -> "analysis", "category_theory.functor_to_types.naturality" -> "category_theory", "array.rev_list_foldr" -> "data", "measure_theory.ae_map_iff" -> "analysis", "omega.term.val_neg" -> "tactic", "semiconj_by.fpow_right" -> "algebra", "measure_theory.measure.regular.map" -> "analysis", "id_map'" -> "control", "affine_subspace.not_mem_bot" -> "algebra", "differentiable_within_at.neg" -> "analysis", "matrix.diagonal_neg" -> "data", "fintype.sum_pow_mul_eq_add_pow" -> "data", "linear_map.to_matrix_of_equiv" -> "algebra", "max.left_comm" -> "algebra", "submodule.mem_Sup_of_directed" -> "algebra", "multiset.countp_cons_of_neg" -> "data", "ennreal.two_ne_top" -> "data", "function.injective.iterate" -> "logic", "linear_independent_singleton" -> "algebra", "inducing.prod_mk" -> "topology", "filter.has_basis.comap" -> "order", "add_subgroup.coe_to_add_submonoid" -> "algebra", "ordinal.add_mul_limit_aux" -> "set_theory", "category_theory.action_as_functor_obj" -> "category_theory", "homological_complex.image_to_kernel_map_condition_assoc" -> "algebra", "category_theory.comonad.coalgebra.EilenbergMoore_to_category_struct_id" -> "category_theory", "continuous_multilinear_map.uncurry_right_apply" -> "analysis", "disjoint.eq_bot" -> "order", "finset.affine_combination_indicator_subset" -> "algebra", "ennreal.infi_mul_right" -> "topology", "real.tendsto_exp_at_top" -> "analysis", "approximates_linear_on.closed_ball_subset_target" -> "analysis", "derivation.commutator_apply" -> "algebra", "linear_map.supr_range_std_basis_le_infi_ker_proj" -> "algebra", "multiset.mem_erase_of_nodup" -> "data", "initial_seg.le_lt_apply" -> "set_theory", "subtype.eq" -> "init", "is_closed_map_smul_of_ne_zero" -> "topology", "relator.left_unique_of_rel_eq" -> "logic", "list.disjoint_singleton" -> "data", "units.dvd_mul_left" -> "algebra", "is_noetherian_span_of_finite" -> "algebra", "pi.one_apply" -> "algebra", "int.mod_eq_mod_iff_mod_sub_eq_zero" -> "data", "polynomial.eq_zero_of_eq_zero" -> "data", "free_group.red.step.diamond" -> "algebra", "category_theory.faithful.of_comp_eq" -> "category_theory", "category_theory.limits.limit.map_post" -> "category_theory", "circle_deg1_lift.lt_iterate_pos_iff" -> "dynamics", "classical.some_spec" -> "init", "nat.div_le_of_le_mul'" -> "data", "nat.mod_self" -> "init", "quotient_add_group.lift_mk'" -> "algebra", "uniform_space.separation_quotient.uniform_continuous_lift" -> "topology", "nat.shiftl_succ" -> "init", "nat.le_zero_iff" -> "data", "smul_neg" -> "algebra", "hyperreal.infinitesimal_add" -> "data", "Ico_mem_nhds_within_Ioi" -> "topology", "real.abs_cos_le_one" -> "data", "mem_closure_iff_frequently" -> "topology", "nat.size_bit0" -> "data", "surj_on_Ici_of_monotone_surjective" -> "data", "linear_independent.image" -> "algebra", "finset.prod_pow" -> "algebra", "top_unique" -> "order", "enorm.map_sub_le" -> "analysis", "isometric.to_equiv_inj" -> "topology", "continuous_linear_equiv.differentiable" -> "analysis", "real.sinh_sub" -> "data", "associated.trans" -> "algebra", "normed_ring.inverse_add_norm" -> "analysis", "uniform_space.separation_quotient.map_unique" -> "topology", "category_theory.monoidal_category.unitors_equal.cells_6'" -> "category_theory", "int.lcm_one_right" -> "algebra", "real.totally_bounded_Ioo" -> "topology", "times_cont_mdiff_id" -> "geometry", "list.singleton_perm" -> "data", "add_submonoid.top_prod" -> "algebra", "ite_mul_zero_right" -> "algebra", "int.modeq.modeq_mul" -> "data", "wseq.lift_rel_destruct_iff" -> "data", "neg_involutive" -> "algebra", "real.exp_sub" -> "data", "int.le_total" -> "init", "div_le_div" -> "algebra", "algebraic_geometry.structure_presheaf_in_CommRing_map_to_fun" -> "algebraic_geometry", "bdd_above.insert" -> "order", "mul_inv_eq_one" -> "algebra", "nat.add_mod_left" -> "init", "finset.val_le_iff" -> "data", "ring_hom.coe_srange_restrict" -> "algebra", "dfinsupp.support_filter" -> "data", "ordinal.dvd_antisymm" -> "set_theory", "category_theory.limits.eq_zero_of_mono_cokernel" -> "category_theory", "free_semigroup.traverse_pure'" -> "algebra", "subtype.forall" -> "data", "nnnorm_indicator_eq_indicator_nnnorm" -> "analysis", "list.perm_append_left_iff" -> "data", "list.forall_mem_cons'" -> "data", "submodule.orthogonal_disjoint" -> "analysis", "differentiable_on.congr" -> "analysis", "submodule.prod_equiv_of_is_compl_symm_apply_right" -> "algebra", "affine_map.line_map_apply" -> "algebra", "multiset.antidiagonal_map_fst" -> "data", "finset.Ico.pred_singleton" -> "data", "finset.sum_range_id" -> "algebra", "ennreal.coe_mono" -> "data", "finset.cons_val" -> "data", "finset.prod_nat_pow" -> "algebra", "add_submonoid.coe_subset_coe" -> "algebra", "category_theory.fork_\[Iota]_comp_cofork_\[Pi]" -> "algebra", "stream.interchange" -> "data", "nat.partrec.code.pair_prim" -> "computability", "is_local_extr.on" -> "topology", "linear_independent_inl_union_inr'" -> "algebra", "nat.div_mul_div_le_div" -> "data", "not_nontrivial_iff_subsingleton" -> "logic", "min_eq_neg_max_neg_neg" -> "algebra", "uniform_add_group.mk'" -> "topology", "generalized_tube_lemma" -> "topology", "mv_polynomial.is_homogeneous.mul" -> "algebra", "coe_not_mem_range_equiv_symm" -> "data", "measure_theory.inner_content_mono'" -> "analysis", "category_theory.limits.limit.cone_point_unique_up_to_iso_inv_comp" -> "category_theory", "dioph.add_dioph" -> "number_theory", "seq_bind_eq" -> "control", "equiv.forall\:2082_congr" -> "data", "image_norm_le_of_norm_deriv_right_lt_deriv_boundary" -> "analysis", "has_strict_fderiv_at.local_inverse_continuous_at" -> "analysis", "fraction_map.eq_zero_of_num_eq_zero" -> "algebra", "lt_add_of_pos_of_lt" -> "algebra", "finmap.erase_union_singleton" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence_inverse" -> "category_theory", "list.chain'.imp" -> "data", "semidirect_product.right_hom_comp_inr" -> "algebra", "list.mem_of_mem_filter" -> "data", "guard_true" -> "control", "continuous_linear_map.is_O_id" -> "analysis", "category_theory.non_preadditive_abelian.mono_of_zero_kernel" -> "category_theory", "quotient_add_group_saturate" -> "topology", "local_homeomorph.continuous_within_at_iff_continuous_within_at_comp_right" -> "topology", "unique_diff_on_Ico" -> "analysis", "affine_map.map_vadd" -> "algebra", "measurable_space.is_measurable_sup" -> "analysis", "infi_union" -> "order", "inner_sum_smul_sum_smul_of_sum_eq_zero" -> "analysis", "parallelogram_law" -> "analysis", "measure_theory.l1.simple_func.lintegral_edist_to_simple_func_lt_top" -> "analysis", "category_theory.reflective.comparison_ess_surj_aux" -> "category_theory", "prod_eq_generate_from" -> "topology", "eq_lim_at_left_extend_from_Ioo" -> "topology", "pnat.prime.ne_one" -> "data", "infi_comm" -> "order", "set.Union_union_distrib" -> "data", "matrix.det_update_column_add" -> "algebra", "omega.coeffs.val_except_add_eq" -> "tactic", "is_connected_connected_component" -> "topology", "mul_aut.mul_apply" -> "data", "omega.coeffs.val_except_update_set" -> "tactic", "complete_space_extension" -> "topology", "nat.not_prime_iff_min_fac_lt" -> "data", "filter.germ.coe_zero" -> "order", "real.arcsin_zero" -> "analysis", "summable.sub" -> "topology", "equiv.perm.sign_aux_eq_sign_aux2" -> "algebra", "continuous_within_at_Ioc_iff_Iic" -> "topology", "ring_equiv.map_eq_one_iff" -> "data", "char.eq_of_veq" -> "init", "group.closure_mono" -> "algebra", "free_group.reduce.not" -> "algebra", "int.neg_of_sign_eq_neg_one" -> "init", "infinite.exists_subset_card_eq" -> "data", "list.map_length_split_wrt_composition_aux" -> "combinatorics", "neg_add_rev" -> "algebra", "nat.pow_left_strict_mono" -> "data", "dif_neg" -> "init", "nat.decreasing_induction_trans" -> "data", "category_theory.arrow.has_lift.ext" -> "category_theory", "function.iterate_add" -> "logic", "subalgebra.srange_le" -> "algebra", "typevec.last_fun_split_fun" -> "data", "holor.cprank_max_mul" -> "data", "category_theory.non_preadditive_abelian.comp_sub" -> "category_theory", "set.mem_compl_iff" -> "data", "if_neg" -> "init", "asymptotics.is_O_const_mul_left_iff'" -> "analysis", "list.filter_true" -> "data", "ennreal.zero_rpow_def" -> "analysis", "complex.eta" -> "data", "free_monoid.map_of" -> "algebra", "is_connected_singleton" -> "topology", "category_theory.preadditive.comp_sub" -> "category_theory", "polynomial.sum_monomial_eq" -> "data", "primrec.of_eq" -> "computability", "monoid_hom.mem_range" -> "algebra", "int.of_nat_add_neg_succ_of_nat_of_lt" -> "data", "is_compact.measure_zero_of_nhds_within" -> "analysis", "inv_mul_self" -> "algebra", "mvpfunctor.liftp_iff" -> "data", "galois_connection.le_u" -> "order", "measurable.snd" -> "analysis", "deriv_rpow" -> "analysis", "polynomial.mem_degree_le" -> "algebra", "submonoid.closure_le" -> "algebra", "nat.bit0_le_bit" -> "data", "list.length_foldr_permutations_aux2'" -> "data", "category_theory.over.construct_products.cones_equiv_inverse_obj_2" -> "category_theory", "ennreal.coe_pos" -> "data", "dual_pair.is_basis" -> "algebra", "nat.sub_le_sub_right_iff" -> "init", "path.source" -> "topology", "znum.gcd_to_nat" -> "data", "is_cau_geo_series" -> "data", "mv_power_series.monomial_zero_eq_C_apply" -> "algebra", "computation.destruct_map" -> "data", "lie_algebra.equiv.symm_apply_apply" -> "algebra", "add_units.val_coe" -> "algebra", "power_series.X_prime" -> "algebra", "multiplicity.finite_of_finite_mul_right" -> "algebra", "continuous_linear_map.antilipschitz_of_uniform_embedding" -> "analysis", "zsqrtd.sqrtd_re" -> "data", "pfunctor.approx.approx_eta" -> "data", "formal_multilinear_series.change_origin_summable_aux1" -> "analysis", "function.is_fixed_pt.iterate" -> "dynamics", "fact_zero_lt_one" -> "geometry", "affine_subspace.coe_affine_span_singleton" -> "algebra", "ennreal.coe_lt_coe_nat" -> "data", "topological_space.is_topological_basis_of_open_of_nhds" -> "topology", "finite_dimensional.finset_card_le_findim_of_linear_independent" -> "algebra", "add_con.add_ker_mk_eq" -> "algebra", "tendsto_comp_of_locally_uniform_limit_within" -> "topology", "le_cInf" -> "order", "finset.union_insert" -> "data", "pfunctor.M.ext" -> "data", "add_le_add" -> "algebra", "matrix.std_basis_matrix_add" -> "data", "category_theory.limits.is_limit.cone_points_iso_of_equivalence_inv" -> "category_theory", "exists_eq_right'" -> "logic", "measure_theory.ae_eq_fun.coe_fn_add" -> "analysis", "category_theory.adjunction.hom_equiv_naturality_left_symm" -> "category_theory", "linear_map.to_affine_map_linear" -> "algebra", "real.exp_multiset_sum" -> "data", "linear_pmap.domain_sup" -> "algebra", "asymptotics.is_O.mul" -> "analysis", "induced_inf" -> "topology", "circle_deg1_lift.commute_int_add" -> "dynamics", "subgroup.one_mem" -> "algebra", "complex.zero_im" -> "data", "submodule.span_induction" -> "algebra", "mdifferentiable_within_at.congr_of_eventually_eq" -> "geometry", "subalgebra.to_submodule_inj" -> "algebra", "finset.disjoint_insert_right" -> "data", "constr_add" -> "algebra", "measure_theory.tendsto_measure_Inter" -> "analysis", "dist_triangle4_right" -> "topology", "lists'.of_to_list" -> "set_theory", "fderiv_within_inter" -> "analysis", "ext_chart_at_continuous_on_symm" -> "geometry", "prime_spectrum.vanishing_ideal_univ" -> "algebraic_geometry", "tendsto_nhds_within_congr" -> "topology", "multiset.card_pmap" -> "data", "ennreal.pow_lt_top" -> "data", "list.mem_erase_of_nodup" -> "data", "finset.card_pi" -> "data", "submodule.le_def'" -> "algebra", "submodule.add_eq_sup" -> "algebra", "option.lift_or_get_none_right" -> "data", "continuous_linear_equiv.norm_symm_pos" -> "analysis", "Set.singleton_inj" -> "set_theory", "list.pairwise_filter_map_of_pairwise" -> "data", "Module.monoidal_category.hom_apply" -> "algebra", "iterated_fderiv_within_apply_eq_iterated_deriv_within_mul_prod" -> "analysis", "mem_pair_self_adjoint_matrices_submodule" -> "algebra", "is_compact.union" -> "topology", "list.map_ret_sublist_sublists" -> "data", "infi_eq_infi_finset'" -> "data", "polynomial.nat_degree_restriction" -> "algebra", "nnreal.of_real_le_iff_le_coe" -> "data", "local_equiv.left_inv" -> "data", "has_fderiv_within_at.mul" -> "analysis", "polynomial.C_bit0" -> "data", "category_theory.coe_inv_hom_id" -> "category_theory", "complex.differentiable_sin" -> "analysis", "mul_div_cancel'" -> "algebra", "affine.simplex.monge_plane_def" -> "geometry", "typevec.last_append1" -> "data", "measurable_space.dynkin_system.generate_inter" -> "analysis", "finite_dimensional.findim_eq_card_basis'" -> "algebra", "equiv.const_vadd_zero" -> "algebra", "ordinal.mul_add_one" -> "set_theory", "turing.tape.mk'_head" -> "computability", "finset.inf_union" -> "data", "nonpos_of_neg_nonneg" -> "algebra", "affine_subspace.bot_coe" -> "algebra", "list.perm_lookmap" -> "data", "complex.sub_im" -> "data", "add_submonoid.comap_id" -> "algebra", "multiset.count_filter" -> "data", "finsupp.map_domain_id" -> "data", "equiv.comp_map" -> "control", "con.induction_on\:2082" -> "algebra", "cSup_intro'" -> "order", "category_theory.sum.swap_map_inr" -> "category_theory", "measure_theory.measure.haar.index_pos" -> "analysis", "lipschitz_with.uncurry" -> "topology", "fin_enum.mem_to_list" -> "data", "homological_complex.graded_homology_map" -> "algebra", "primrec.nat_cases'" -> "computability", "is_subgroup.mul_mem_cancel_left" -> "algebra", "primrec.vector_to_list" -> "computability", "nat.two_mul_odd_div_two" -> "data", "subspace.convex" -> "analysis", "int.nat_abs_of_nonneg" -> "init", "finset.superset.trans" -> "data", "local_homeomorph.trans_of_set" -> "topology", "mul_action_hom.comp_id" -> "algebra", "polynomial.coeff_comp_degree_mul_degree" -> "data", "cSup_mem_closure" -> "topology", "uniform_space.completion.uniform_continuous_extension\:2082" -> "topology", "wseq.drop.aux_none" -> "data", "subsemiring.top_prod" -> "algebra", "measure_theory.simple_func.restrict_empty" -> "analysis", "monoid_hom.map_iterate_frobenius" -> "algebra", "set.image_sub_const_Ioi" -> "data", "matrix.cons_eq_zero_iff" -> "data", "lt_one_div" -> "algebra", "wseq.mem_append_left" -> "data", "mfderiv_zero_of_not_mdifferentiable_at" -> "geometry", "le_supr'" -> "order", "dense_inducing.prod" -> "topology", "continuous_on_neg" -> "topology", "algebra.to_comap_apply" -> "algebra", "polynomial.degree_lt_eq_span_X_pow" -> "algebra", "neg_nsmul" -> "algebra", "d_array.ext" -> "init", "znum.cmp_to_int" -> "data", "mul_self_eq_mul_self_iff" -> "algebra", "finset.card_attach" -> "data", "finset.sum_pair" -> "algebra", "polynomial.monic_X_pow_add" -> "data", "rel.image_mono" -> "data", "category_theory.prod_comp_fst" -> "category_theory", "rat.cast_mul_of_ne_zero" -> "data", "finset.mem_singleton" -> "data", "times_cont_mdiff_within_at_iff" -> "geometry", "tactic.ring.horner_neg" -> "tactic", "category_theory.limits.\[Iota]_colim_map" -> "category_theory", "multiset.cons_inter_of_pos" -> "data", "pos_num.cast_le" -> "data", "category_theory.sum.associator_obj_inl_inr" -> "category_theory", "int.pred_self_lt" -> "data", "with_bot.inf_eq_min" -> "order", "localization_map.comap_map_of_is_prime_disjoint" -> "algebra", "lift_nhds_right" -> "topology", "interval_integral.integral_has_fderiv_at_of_tendsto_ae" -> "analysis", "continuous_linear_map.lipschitz" -> "analysis", "emetric.diam_ball" -> "topology", "complex.abs_ne_zero" -> "data", "add_monoid_hom.coe_mk'" -> "algebra", "metric.inductive_limit_dist_eq_dist" -> "topology", "tendsto_at_bot_add_tendsto_right" -> "topology", "category_theory.abelian.pseudoelement.apply_zero" -> "category_theory", "not_top_lt" -> "order", "adjoin_root.is_root_root" -> "algebra", "free_group.sum.mul" -> "algebra", "function.injective.sum_map" -> "data", "list.suffix_of_suffix_length_le" -> "data", "isometric.apply_symm_apply" -> "topology", "bilin_form.smul_apply" -> "algebra", "measurable.subtype_coe" -> "analysis", "real.sinh_surjective" -> "analysis", "mem_residual" -> "topology", "continuous_within_at_const" -> "topology", "is_local_max_on.on_subset" -> "topology", "finset.dvd_sum" -> "algebra", "compact_iff_totally_bounded_complete" -> "topology", "cau_seq.one_not_equiv_zero" -> "data", "znum.cast_le" -> "data", "add_submonoid.localization_map.lift_eq_iff" -> "algebra", "is_path_connected_iff_eq" -> "topology", "list.subperm_append_left" -> "data", "list.modify_nth_tail_modify_nth_tail_le" -> "data", "generalized_continued_fraction.part_denom_none_iff_s_none" -> "algebra", "is_open.preimage" -> "topology", "unique_factorization_domain.exists_mem_factors_of_dvd" -> "algebra", "wseq.cons_congr" -> "data", "list.nth_append" -> "data", "relation.transitive_join" -> "logic", "continuous_within_at.tendsto_nhds_within_image" -> "topology", "finset.mem_filter" -> "data", "list.nodup_nil" -> "data", "set.Ioo_def" -> "data", "is_submonoid_Union_of_directed" -> "algebra", "uniform_space.completion.coe_mul" -> "topology", "filter.le_Liminf_of_le" -> "order", "set.directed_on_Union" -> "data", "contracting_with.restrict" -> "topology", "mul_action.card_modeq_card_fixed_points" -> "algebra", "lie_add" -> "algebra", "stream.head_iterate" -> "data", "list.nth_le_of_sorted_of_le" -> "data", "sub_nonpos" -> "algebra", "primrec.not" -> "computability", "affine_map.decomp'" -> "algebra", "category_theory.limits.biproduct.\[Iota]_\[Pi]_self_assoc" -> "category_theory", "finsupp.single_sum" -> "data", "stream.tail_zip" -> "data", "convex.closure" -> "analysis", "finset.erase_insert" -> "data", "int.gcd_dvd_right" -> "algebra", "convex_on.convex_lt" -> "analysis", "set.coe_to_finset" -> "data", "nat.div_self" -> "init", "nat.sub_le_sub_right" -> "init", "pnat.xgcd_type.flip_z" -> "data", "dual_pair.eq_dual" -> "algebra", "dist_add_left" -> "analysis", "category_theory.functor.right_op_obj" -> "category_theory", "set.union_eq_self_of_subset_left" -> "data", "norm_num.lt_bit0_bit1" -> "tactic", "polynomial.ne_zero_of_degree_gt" -> "data", "add_submonoid.mem_top" -> "algebra", "affine_map.affine_comp_line_map" -> "algebra", "measure_theory.measure.restrict_union" -> "analysis", "stream.cons_append_stream" -> "data", "set.ssubset_iff_insert" -> "data", "metric.inf_dist_eq_closure" -> "topology", "list.nth_le_attach" -> "data", "commute.neg_left" -> "algebra", "subsingleton.eq_univ_of_nonempty" -> "data", "mem_upper_bounds" -> "order", "gold_conj_mul_gold" -> "data", "measure_theory.outer_measure.Union_finset" -> "analysis", "tendsto_uniformly.tendsto_locally_uniformly" -> "topology", "category_theory.map_functorial_obj" -> "category_theory", "deriv_cexp" -> "analysis", "add_group.image_closure" -> "algebra", "norm_num.rat_cast_ne" -> "tactic", "monoid_hom.map_inv" -> "algebra", "one_add_sub_mul_le_pow" -> "algebra", "padic_norm_e.zero_iff" -> "data", "convex_on.translate_right" -> "analysis", "is_submonoid.finset_prod_mem" -> "algebra", "nat.choose_mul_succ_eq" -> "data", "top_le_iff" -> "order", "galois_coinsertion.u_surjective" -> "order", "polynomial.monic_restriction" -> "algebra", "inv_le_inv_of_neg" -> "algebra", "ennreal.two_ne_zero" -> "data", "nat.dvd_div_of_mul_dvd" -> "data", "list.take_take" -> "data", "option.comp_traverse" -> "control", "inf_left_idem" -> "order", "linear_map.coe_to_affine_map" -> "algebra", "subsemiring.comap_top" -> "algebra", "nat.xgcd_aux_val" -> "data", "submonoid.localization_map.mul_mk'_eq_mk'_of_mul" -> "algebra", "set.card_range_of_injective" -> "data", "complex.sinh_of_real_re" -> "data", "measure_theory.measure.restrict_union_le" -> "analysis", "list.perm_merge" -> "data", "ring.direct_limit.lift_mul" -> "algebra", "cardinal.mk_Ici_real" -> "data", "le_sup_right'" -> "order", "multiset.foldl_cons" -> "data", "module.End.mem_eigenspace_iff" -> "algebra", "nat.partrec.code.evaln_sound" -> "computability", "set.Ioo_subset_Ioo_right" -> "data", "list.perm.diff_left" -> "data", "submonoid.localization_map.ext" -> "algebra", "inv_of_neg" -> "algebra", "multilinear_map.exists_bound_of_continuous" -> "analysis", "set.prod_range_univ_eq" -> "data", "pSet.mem_empty" -> "set_theory", "measure_theory.integrable_const_iff" -> "analysis", "continuous_on.congr_mono" -> "topology", "of_mul_one" -> "algebra", "pell.ysq_dvd_yy" -> "number_theory", "measure_theory.integrable.left_of_add_measure" -> "analysis", "finset.card_union_add_card_inter" -> "data", "nat.mul_dvd_mul_iff_right" -> "data", "measure_theory.l1.simple_func.integral_eq_integral" -> "analysis", "nnreal.of_real_add_le" -> "data", "lt_mul_of_one_lt_of_lt'" -> "algebra", "nat.prime.not_dvd_one" -> "data", "ring.fractional_ideal.map_add" -> "algebra", "filter.is_bounded_iff" -> "order", "zsqrtd.nonnegg_comm" -> "data", "one_div_add_one_div" -> "algebra", "linarith.int.coe_nat_zero_mul" -> "tactic", "padic_seq.lift_index_left" -> "data", "pnat.xgcd_type.reduce_special'" -> "data", "metric.uniformity_basis_dist_inv_nat_succ" -> "topology", "rat.coe_nat_num" -> "data", "measure_theory.ae_eq_fun.mul_to_germ" -> "analysis", "finset.sum_subset" -> "algebra", "category_theory.whisker_eq" -> "category_theory", "set.right_inv_on.eq" -> "data", "pos_num.le_to_nat" -> "data", "ulower.down_up" -> "data", "quadratic_form.associated_right_inverse" -> "algebra", "pgame.neg_add_le" -> "set_theory", "alg_hom.coe_fn_inj" -> "algebra", "gpow_sub_one" -> "algebra", "tendsto_at_bot_add_tendsto_left" -> "topology", "linear_map.deriv_within" -> "analysis", "linear_equiv.coe_to_equiv" -> "algebra", "smooth.prod_mk" -> "geometry", "measure_theory.outer_measure.le_add_caratheodory" -> "analysis", "int.test_bit_lor" -> "data", "finsupp.split_apply" -> "data", "linear_map.disjoint_ker" -> "algebra", "category_theory.monad.algebra.hom.ext_iff" -> "category_theory", "vector_span_range_eq_span_range_vsub_right" -> "algebra", "ordinal.add_right_cancel" -> "set_theory", "qpf.fix.ind" -> "data", "category_theory.op_id" -> "category_theory", "ordinal.power_dvd_power_iff" -> "set_theory", "lipschitz_with.prod_fst" -> "topology", "finset.pi_cons_injective" -> "data", "padic_int.coe_coe" -> "data", "differentiable_at.add_const" -> "analysis", "ring_equiv.trans_symm" -> "data", "is_ring_hom.map_sub" -> "algebra", "mul_left_embedding_apply" -> "logic", "add_con.lift_comp_mk'" -> "algebra", "ennreal.coe_to_nnreal" -> "data", "opposite.op_mul" -> "algebra", "continuous_linear_map.op_norm_add_le" -> "analysis", "finset.card_map" -> "data", "ring.fractional_ideal.span_singleton_eq_zero_iff" -> "algebra", "finset.sum_eq_multiset_sum" -> "algebra", "continuous.min" -> "topology", "open_embedding.continuous" -> "topology", "is_separated_def" -> "topology", "cauchy_prod" -> "topology", "ideal.jacobson_eq_top_iff" -> "algebra", "filter.bind_mono" -> "order", "rat.cast_le" -> "data", "linear_map.compl\:2082_apply" -> "algebra", "nat.primrec.of_eq" -> "computability", "multiset.dvd_sum" -> "data", "is_closed_fixed_points" -> "dynamics", "topological_space.opens.op_map_id_obj" -> "topology", "add_lt_of_neg_of_le" -> "algebra", "opposite.op_add" -> "algebra", "wseq.destruct_some_of_destruct_tail_some" -> "data", "pgame.add_move_left_inr" -> "set_theory", "quot.map\:2082_mk" -> "data", "list.range_concat" -> "data", "subgroup.map_bot" -> "algebra", "bilin_form.add_apply" -> "algebra", "nat.to_pnat'_coe" -> "data", "category_theory.limits.has_colimit.iso_of_equivalence_\[Pi]" -> "category_theory", "mvpfunctor.Wp_rec_eq" -> "data", "ordinal.div_one" -> "set_theory", "Class.insert_hom" -> "set_theory", "tendsto_subtype_rng" -> "topology", "finite_dimensional_vector_span_of_finite" -> "algebra", "measure_theory.measure.finite_at_nhds" -> "analysis", "quadratic_form.discr_comp" -> "algebra", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae'" -> "analysis", "ceil_coe" -> "algebra", "set.dual_Ioi" -> "data", "mem_gpowers" -> "algebra", "fintype.exists_max" -> "data", "category_theory.comonad.coalgebra.hom.id_f" -> "category_theory", "smooth_on_snd" -> "geometry", "filter.filter_eq_bot_of_not_nonempty" -> "order", "finset.Ico.filter_le" -> "data", "filter.eventually.self_of_nhds_within" -> "topology", "is_glb_empty" -> "order", "quadratic_form.polar_neg" -> "algebra", "rat.num_denom'" -> "data", "polynomial.nat_degree_eq_of_degree_eq_some" -> "data", "filter.eventually_le.refl" -> "order", "multiset.coe_sort" -> "data", "option.is_some_iff_exists" -> "data", "set.piecewise_eq_indicator" -> "data", "is_open_Ioo" -> "topology", "has_fderiv_within_at.differentiable_within_at" -> "analysis", "eq_lim_at_right_extend_from_Ioo" -> "topology", "onote.split_add_lt" -> "set_theory", "monoid_hom.map_inv'" -> "algebra", "nat.gcd_pos_of_pos_right" -> "data", "znum.of_to_int" -> "data", "int.lt_add_of_neg_lt_sub_right" -> "init", "differentiable_at.rpow_of_one_le" -> "analysis", "AddCommGroup.int_hom_ext" -> "algebra", "no_bot_order.lower_bounds_univ" -> "order", "ne_zero_and_ne_zero_of_mul" -> "algebra", "mul_zero" -> "algebra", "nat.le_rec_on_surjective" -> "data", "iff_of_false" -> "logic", "list.eq_nil_of_infix_nil" -> "data", "finset.disjoint_insert_left" -> "data", "interval_integral.integral_interval_add_interval_comm" -> "analysis", "pi.is_basis_fun" -> "algebra", "multiset.filter_filter_map" -> "data", "is_order_right_adjoint.right_mono" -> "order", "category_theory.as_iso_hom" -> "category_theory", "list.reverse_suffix" -> "data", "is_local_max_on.comp_continuous_on" -> "topology", "submodule.span_union" -> "algebra", "nonempty_prod" -> "logic", "discrete_valuation_ring.exists_irreducible" -> "algebra", "norm_num.min_fac_helper_1" -> "tactic", "fraction_map.mk'_eq_div" -> "algebra", "nat.lt_add_of_sub_lt_left" -> "data", "is_local_min.neg" -> "topology", "filter.frequently_bot" -> "order", "unique_factorization_domain.factors_irreducible" -> "algebra", "int.cast_sub" -> "data", "lipschitz_with.dist_iterate_succ_le_geometric" -> "topology", "finite_field.char_poly_pow_card" -> "algebra", "wseq.tail_congr" -> "data", "has_deriv_within_at.congr" -> "analysis", "set.preimage_neg_Icc" -> "data", "ring.direct_limit.lift_sub" -> "algebra", "list.mem_sigma" -> "data", "composition.single_blocks_fun" -> "combinatorics", "add_monoid_hom.map_zero" -> "algebra", "nat.bit0_ne_zero" -> "init", "is_cobounded_le_nhds" -> "topology", "euclidean_domain.lcm_zero_left" -> "algebra", "discrete_valuation_ring.associated_of_irreducible" -> "algebra", "model_with_corners.to_local_equiv_coe" -> "geometry", "int.neg_add_lt_of_lt_add" -> "init", "nat.prime.multiplicity_choose_prime_pow" -> "data", "real.dist_eq" -> "topology", "units.neg_eq_neg_one_mul" -> "algebra", "normalize_dvd_iff" -> "algebra", "linear_equiv.surjective" -> "algebra", "rel_embedding.is_linear_order" -> "order", "omega.int.clauses_sat_dnf_core" -> "tactic", "monotone_id" -> "order", "euclidean_domain.mod_eq_zero" -> "algebra", "is_integral_add" -> "algebra", "ulower.down_eq_down" -> "data", "multiset.eq_of_mem_repeat" -> "data", "ordinal.deriv_zero" -> "set_theory", "le_digits_len_le" -> "data", "category_theory.iso.hom_congr_refl" -> "category_theory", "path_connected_space_iff_zeroth_homotopy" -> "topology", "list.infix_append" -> "data", "semidirect_product.inl_inj" -> "algebra", "coinduced_id" -> "topology", "lt_of_le_of_lt" -> "init", "linear_map.to_fun_eq_coe" -> "algebra", "mdifferentiable_at.comp" -> "geometry", "category_theory.limits.cocone.functor_w" -> "category_theory", "continuous_within_at.mul" -> "topology", "simple_graph.complete_graph_degree" -> "combinatorics", "finset.inter_singleton_of_not_mem" -> "data", "convex_halfspace_gt" -> "analysis", "option.ne_none_iff_exists'" -> "data", "int.cast_neg_of_nat" -> "data", "local_homeomorph.symm_image_eq_source_inter_preimage" -> "topology", "with_zero.coe_one" -> "algebra", "differentiable_on_neg" -> "analysis", "lagrange.eval_basis_self" -> "algebra", "category_theory.limits.coequalizer.condition_assoc" -> "category_theory", "matrix.nonsing_inv_left_right" -> "algebra", "forall_pempty" -> "logic", "inv_of_one_lt_inv" -> "algebra", "equiv.perm.cycle_of_apply" -> "algebra", "pos_num.bit0_of_bit0" -> "data", "opposite.equiv_to_opposite_apply" -> "data", "list.kunion_kerase" -> "data", "add_lt_of_lt_of_neg" -> "algebra", "finset.subset_inter" -> "data", "set.sUnion_eq_compl_sInter_compl" -> "data", "tensor_product.smul_tmul'" -> "algebra", "one_lt_inv'" -> "algebra", "filter.comap_eq_lift'" -> "order", "antilipschitz_with.restrict" -> "topology", "group.conjugates_of_set_subset" -> "algebra", "polynomial.coeff_ne_zero_of_eq_degree" -> "data", "matrix.trace_diag" -> "algebra", "ennreal.div_def" -> "data", "num.min_fac_to_nat" -> "data", "set.Ico_inter_Iio" -> "data", "preorder_hom.comp_to_fun" -> "order", "times_cont_diff_on_fst" -> "analysis", "multiset.filter_map_eq_filter" -> "data", "dim_zero_iff_forall_zero" -> "algebra", "linear_map.fun_congr_left_comp" -> "algebra", "not_tendsto_nhds_of_tendsto_at_bot" -> "topology", "polynomial.expand_char" -> "algebra", "coe_tt" -> "init", "zsqrtd.norm_eq_mul_conj" -> "data", "finset.prod_subset_one_on_sdiff" -> "algebra", "category_theory.monad.algebra.EilenbergMoore_to_category_struct_id" -> "category_theory", "Set.map_unique" -> "set_theory", "smooth_at.smooth_within_at" -> "geometry", "semiquot.lift_on_of_mem" -> "data", "category_theory.limits.cone.of_fork_\[Pi]" -> "category_theory", "filter.germ.min_def" -> "order", "finsupp.emb_domain_map_range" -> "data", "matrix.cons_val_zero" -> "data", "pfun.mem_preimage" -> "data", "filter.eventually_eq.rw" -> "order", "free_group.eqv_gen_step_iff_join_red" -> "algebra", "seq.ge_stable" -> "data", "path_connected_space_iff_eq" -> "topology", "wseq.exists_nth_of_mem" -> "data", "eventually_nhds_nhds_within" -> "topology", "array.push_back_rev_list_aux" -> "data", "div_mul_div" -> "algebra", "function.cantor_injective" -> "logic", "module.End.eigenvectors_linear_independent" -> "algebra", "continuous_linear_map.bounds_nonempty" -> "analysis", "uniform_inducing.prod" -> "topology", "trunc.induction_on" -> "data", "finset.piecewise_eq_of_not_mem" -> "data", "rel_supr_sum" -> "topology", "measure_theory.integrable_add_measure" -> "analysis", "computation.not_mem_empty" -> "data", "ordinal.cof_succ" -> "set_theory", "nat.primrec'.encode" -> "computability", "nat.coprime.coprime_div_right" -> "data", "zmod.pow_card" -> "algebra", "pnat.prime.one_lt" -> "data", "padic_norm_e.defn" -> "data", "div_add_div" -> "algebra", "category_theory.limits.kernel.lift_\[Iota]_assoc" -> "category_theory", "category_theory.monoidal.left_unitor_inv_apply" -> "category_theory", "submodule.mem_prod" -> "algebra", "poly_equiv_tensor.to_fun_linear_algebra_map_tmul_one" -> "algebra", "le_of_sub_nonpos" -> "algebra", "local_homeomorph.subtype_restr_coe" -> "topology", "nat.shiftl'_tt_eq_mul_pow" -> "init", "finmap.insert_union" -> "data", "inv_le_inv'" -> "algebra", "filter.tendsto_at_top_add_nonneg_right" -> "order", "fixed_points.smul" -> "algebra", "function.bijective.comp" -> "init", "measure_theory.measure.haar_outer_measure_caratheodory" -> "analysis", "int.coe_nat_mul" -> "init", "category_theory.coev_ev" -> "category_theory", "discriminant_le_zero" -> "algebra", "ennreal.mul_rpow_of_ne_top" -> "analysis", "measure_theory.outer_measure.of_content_exists_compact" -> "analysis", "encodable.encode_star" -> "data", "rat.mul_denom" -> "data", "algebraic_closure.step.is_integral" -> "algebra", "dist_nonneg" -> "topology", "submonoid.localization_map.map_mk'" -> "algebra", "power_series.trunc_C" -> "algebra", "Inf_le_of_le" -> "order", "list.nth_le_drop" -> "data", "matrix.nonsing_inv_det" -> "algebra", "list.forall_mem_ne" -> "data", "real.rpow_neg_one" -> "analysis", "interval_integral.fderiv_integral_of_tendsto_ae" -> "analysis", "nat.rfind_spec" -> "computability", "asymptotics.is_O_with.prod_left_same" -> "analysis", "hash_map.find_erase_ne" -> "data", "convex.is_linear_image" -> "analysis", "fraction_map.num_mul_denom_eq_num_mul_denom_iff_eq" -> "algebra", "infi_le'" -> "order", "is_G\[Delta]_bInter" -> "topology", "has_deriv_within_at.differentiable_within_at" -> "analysis", "free_group.red.append_append_left_iff" -> "algebra", "fintype.card_of_finset" -> "data", "free_group.red.sublist" -> "algebra", "multiplicity.not_unit_of_finite" -> "algebra", "filter.frequently_of_forall" -> "order", "seq.tail_cons" -> "data", "comp_symm_of_uniformity" -> "topology", "set.pairwise_disjoint.range" -> "data", "mvfunctor.exists_iff_exists_of_mono" -> "control", "int.mod_one" -> "data", "gsmul_add" -> "algebra", "measure_theory.ae_of_all" -> "analysis", "add_con.mk'_ker" -> "algebra", "zsqrtd.coe_int_mul" -> "data", "is_bounded_linear_map.has_fderiv_at" -> "analysis", "roption.some_ne_none" -> "data", "pi.sub_apply" -> "algebra", "ordinal.is_limit.nat_lt" -> "set_theory", "filter.lift_ne_bot_iff" -> "order", "real.arccos_one" -> "analysis", "lt_nat_ceil" -> "algebra", "is_fixed_pt_of_tendsto_iterate" -> "dynamics", "contracting_with.fixed_point_unique'" -> "topology", "finset.sum_dite_eq'" -> "algebra", "is_open_prod_iff'" -> "topology", "measurable_add_left" -> "analysis", "function.injective.ne_iff'" -> "logic", "filter.realizer.map_F" -> "data", "zmod.nat_cast_val" -> "data", "list.nodup_fin_range" -> "data", "category_theory.fully_faithful_cancel_right_hom_app" -> "category_theory", "times_cont_diff.comp_times_cont_diff_within_at" -> "analysis", "computation.destruct_empty" -> "data", "has_deriv_within_at.exp" -> "analysis", "category_theory.limits.coprod.right_unitor_inv" -> "category_theory", "finset.pi_insert" -> "data", "mem_closure_iff_nhds'" -> "topology", "cancel_factors.cancel_factors_eq_div" -> "tactic", "map.is_add_monoid_hom" -> "order", "has_sum.compl_add" -> "topology", "category_theory.preadditive.comp_sub_assoc" -> "category_theory", "measure_theory.ae_eq_fun.lintegral_eq_zero_iff" -> "analysis", "add_monoid_hom.cancel_left" -> "algebra", "ideal.mem_Sup_of_mem" -> "algebra", "rat.cast_zero" -> "data", "hyperreal.st_inv" -> "data", "zsqrtd.nonneg_add" -> "data", "multiset.empty_eq_zero" -> "data", "times_cont_diff_on.mono" -> "analysis", "category_theory.limits.is_iso_zero_equiv_inv_fun_inv" -> "category_theory", "euclidean_geometry.reflection_eq_self_iff" -> "geometry", "digits_aux_zero" -> "data", "dioph.dioph_fn_vec_comp1" -> "number_theory", "matrix.neg_empty" -> "data", "category_theory.functor.map_arrow_obj_left" -> "category_theory", "measure_theory.simple_func.fin_meas_supp.add" -> "analysis", "supr_comp_le" -> "order", "list.of_fn_nth_le" -> "data", "is_open_and" -> "topology", "to_add_mul" -> "algebra", "submodule.linear_proj_of_is_compl_apply_left" -> "algebra", "measure_theory.l1.norm_le_norm_of_ae_le" -> "analysis", "ennreal.coe_mul" -> "data", "real.has_deriv_at_sinh" -> "analysis", "tangent_bundle_model_space_coe_chart_at" -> "geometry", "nhds_top" -> "topology", "ideal.mem_map_iff_of_surjective" -> "algebra", "add_sub_assoc" -> "algebra", "tactic.ring_exp.pow_pf_sum" -> "tactic", "nhds_basis_uniformity'" -> "topology", "set.preimage_const_mul_Ioo" -> "data", "mv_polynomial.eval\:2082_pow" -> "data", "filter.mem_rmap" -> "order", "real.volume_val" -> "analysis", "matrix.dot_product_zero" -> "data", "map_mem_non_zero_divisors" -> "algebra", "category_theory.discrete.equiv_of_equivalence_inv_fun" -> "category_theory", "int.cast_abs" -> "data", "compl_bot" -> "order", "submonoid.coe_Sup_of_directed_on" -> "algebra", "measure_theory.measure.count_apply_finset" -> "analysis", "is_R_or_C.of_real_rat_cast" -> "data", "nat.add_sub_add_left" -> "init", "turing.tape.write_mk'" -> "computability", "ennreal.to_real_of_real" -> "data", "nat.lcm_assoc" -> "data", "nat.mul_div_cancel" -> "init", "ordinal.nat_cast_sub" -> "set_theory", "is_absolute_value.abv_zero" -> "data", "cardinal.exists_aleph" -> "set_theory", "composition.ext" -> "combinatorics", "lt_iff_not_ge'" -> "algebra", "local_equiv.restr_source" -> "data", "subsemiring.coe_ssubset_coe" -> "algebra", "filter.frequently.and_eventually" -> "order", "alist.to_alist_cons" -> "data", "contracting_with.eq_or_edist_eq_top_of_fixed_points" -> "topology", "set.sInter_range" -> "data", "function.update_comp" -> "logic", "measure_theory.simple_func.is_measurable_cut" -> "analysis", "ge_of_tendsto" -> "topology", "galois_insertion.u_le_u_iff" -> "order", "setoid.refl'" -> "data", "sub_lt_zero" -> "algebra", "mul_self_le_mul_self_of_le_of_neg_le" -> "algebra", "monotone.comp" -> "order", "direct_sum.component.of" -> "algebra", "nat.dist_eq_zero" -> "data", "int.nat_abs_lcm" -> "algebra", "convex_halfspace_re_lt" -> "analysis", "sum_hom_units" -> "algebra", "finset.center_mass_singleton" -> "analysis", "category_theory.iso.cancel_iso_inv_right_assoc" -> "category_theory", "abs_add_le_abs_add_abs" -> "algebra", "mvqpf.fix.ind_rec" -> "data", "list.zip_map" -> "data", "circle_deg1_lift.sup_apply" -> "dynamics", "lie_algebra.equiv.of_subalgebras_symm_apply" -> "algebra", "Inf_eq_bot" -> "order", "alist.perm_replace" -> "data", "state_t.goto_mk_label" -> "control", "nat.pred_zero" -> "init", "metric.Hausdorff_dist_nonneg" -> "topology", "generalized_continued_fraction.continuants_aux_stable_of_terminated" -> "algebra", "asymptotics.is_O.comp_tendsto" -> "analysis", "tactic.abel.term_smul" -> "tactic", "circle_deg1_lift.le_map_of_map_zero" -> "dynamics", "composition.boundary_zero" -> "combinatorics", "nhds_within_Ici_self_ne_bot" -> "topology", "composition.mem_range_embedding_iff'" -> "combinatorics", "submodule.mem_colon" -> "algebra", "ennreal.rpow_mul" -> "analysis", "principal_seg.down'" -> "set_theory", "ennreal.coe_rpow_of_ne_zero" -> "analysis", "subring.mem_to_add_subgroup" -> "algebra", "dioph.dioph_fn_vec" -> "number_theory", "qpf.liftp_preservation_iff_uniform" -> "data", "wseq.lift_rel_dropn_destruct" -> "data", "matrix.smul_dot_product" -> "data", "equiv.perm.swap_mul_eq_iff" -> "algebra", "linear_independent.total_comp_repr" -> "algebra", "forall_le_or_exists_lt_inf" -> "order", "nat.div_mul_le_self'" -> "data", "differentiable_on.pow" -> "analysis", "mv_polynomial.map_rename" -> "data", "max_add_add_left" -> "algebra", "bool.coe_bool_iff" -> "data", "finite_field.trace_pow_card" -> "algebra", "valuation.map_pow" -> "algebra", "continuous_at_subtype_coe" -> "topology", "nat.mod_mod_of_dvd" -> "data", "erased.nonempty_iff" -> "data", "list.chain'_iff_pairwise" -> "data", "category_theory.iso.op_hom" -> "category_theory", "omega.nat.exists_clause_sat" -> "tactic", "complex.bit1_re" -> "data", "nat.coprime.symm" -> "data", "nat_ceil_coe" -> "algebra", "pgame.numeric_zero" -> "set_theory", "measure_theory.ae_ball_iff" -> "analysis", "cardinal.mk_plift_of_false" -> "set_theory", "list.sum_take_add_sum_drop" -> "data", "complex.sin_sub" -> "data", "commute.sub_right" -> "algebra", "add_lt_of_lt_of_nonpos" -> "algebra", "int.le.dest" -> "init", "list.sublists_len_sublist_sublists'" -> "data", "set.compl_compl_image" -> "data", "rel_iso.rel_symm_apply" -> "order", "finset.center_mass_pair" -> "analysis", "subring.closure_induction" -> "algebra", "ball_pi" -> "topology", "archimedean_iff_nat_le" -> "algebra", "one_div_nonneg" -> "algebra", "category_theory.limits.is_initial.hom_ext" -> "category_theory", "submonoid.top_prod" -> "algebra", "local_homeomorph.refl_trans" -> "topology", "category_theory.nat_trans.naturality_app" -> "category_theory", "nat.bitwise_zero" -> "init", "int.le_of_add_le_add_right" -> "init", "linear_map.fst_eq_coprod" -> "algebra", "list.Ico.filter_lt" -> "data", "uniform_space.separation_quotient.uniform_continuous_map" -> "topology", "exists_nhds_split4" -> "topology", "associates.one_le" -> "algebra", "matrix.vec_mul_zero" -> "data", "semiconj_by.inv_right_iff'" -> "algebra", "and_imp" -> "logic", "topological_space.opens.map_id_obj" -> "topology", "valuation.comap_supp" -> "algebra", "encodable.encode_list_nil" -> "data", "category_theory.nat_iso.cancel_nat_iso_inv_right" -> "category_theory", "real.Inf_le" -> "data", "finset.insert_sdiff_of_not_mem" -> "data", "prod.snd_vsub" -> "algebra", "filter.liminf_eq" -> "order", "nat.partrec'.part_iff\:2082" -> "computability", "measure_theory.ae_smul_measure" -> "analysis", "linear_map.has_deriv_at" -> "analysis", "rat.sqrt_eq" -> "data", "linear_map.mk_continuous_of_exists_bound_apply" -> "analysis", "alg_equiv.inv_fun_apply" -> "algebra", "partrec.of_eq" -> "computability", "vector3.append_nil" -> "number_theory", "pythagorean_triple.mul" -> "number_theory", "neg_le_neg_iff" -> "algebra", "computation.lift_rel.imp" -> "data", "nat.coprime_of_dvd'" -> "data", "list.erasep_cons_of_pos" -> "data", "pequiv.refl_trans" -> "data", "bernoulli_one" -> "number_theory", "metric.compact_iff_closed_bounded" -> "topology", "equiv.set.sum_diff_subset_symm_apply_of_mem" -> "data", "list.map_injective_iff" -> "data", "or_and_distrib_right" -> "logic", "bit1_gsmul" -> "algebra", "rel_embedding.well_founded" -> "order", "add_submonoid.localization_map.of_add_equiv_of_localizations_id" -> "algebra", "category_theory.limits.fan.mk_\[Pi]_app" -> "category_theory", "filter.mem_prod_self_iff" -> "order", "fpow_one" -> "algebra", "function.commute.id_right" -> "logic", "fderiv_inverse" -> "analysis", "set.ord_connected_Ioo" -> "data", "div_sub_div" -> "algebra", "filter.is_countably_generated.has_antimono_basis" -> "order", "disjoint_sup_left" -> "order", "cardinal.aleph_idx.rel_iso_coe" -> "set_theory", "local_homeomorph.restr_target" -> "topology", "set.subset_preimage_image" -> "data", "turing.to_partrec.code.pred_eval" -> "computability", "quotient_ring_saturate" -> "topology", "measure_theory.ae_eq_symm" -> "analysis", "set.finite.bdd_below_bUnion" -> "data", "dioph.const_dioph" -> "number_theory", "pfunctor.fst_map" -> "data", "linear_map.snd_prod" -> "algebra", "function.embedding.equiv_of_fintype_self_embedding_to_embedding" -> "data", "submodule.annihilator_eq_top_iff" -> "algebra", "metric.bounded.ediam_ne_top" -> "topology", "prime_multiset.coe_nat_injective" -> "data", "set.Iic_inter_Iic" -> "data", "subsemiring.closure_empty" -> "algebra", "dist_add_right" -> "analysis", "submodule.coe_smul" -> "algebra", "interval_integral.integral_of_le" -> "analysis", "matrix.map_sub" -> "data", "set.mk_mem_prod" -> "data", "polynomial.map_mod_by_monic" -> "data", "add_assoc" -> "algebra", "function.commute.left_bij_on_fixed_pts_comp" -> "dynamics", "dense_inducing.extend_unique" -> "topology", "two_mul" -> "algebra", "local_homeomorph.trans_refl" -> "topology", "measure_theory.extend_mono" -> "analysis", "norm_algebra_map_eq" -> "analysis", "mv_polynomial.total_degree_zero" -> "data", "state_t.run_bind" -> "init", "category_theory.iso.symm_inv" -> "category_theory", "measure_theory.measure.finite_at_nhds_within" -> "analysis", "polynomial.nat_degree_pos_of_aeval_root" -> "data", "smul_prod" -> "algebra", "set.not_mem_of_not_mem_sUnion" -> "data", "filter.ext'" -> "order", "real.range_sin" -> "analysis", "real.rpow_def_of_nonneg" -> "analysis", "nat.lt_asymm" -> "init", "category_theory.abelian.coimages.coimage_strong_epi_mono_factorisation_to_mono_factorisation_I" -> "category_theory", "pequiv.mem_iff_mem" -> "data", "filter.lift'_inf_powerset" -> "order", "add_subgroup.add_mem" -> "algebra", "metric.uniformity_eq_comap_nhds_zero" -> "topology", "measurable_sum" -> "analysis", "submodule.smul_induction_on" -> "algebra", "tendsto_inv_nhds_within_Ioi_inv" -> "topology", "summable.mul_left" -> "topology", "norm_indicator_eq_indicator_norm" -> "analysis", "subring.Inf_to_submonoid" -> "algebra", "module.End.eigenspace_eval\:2082_polynomial_degree_1" -> "algebra", "function.commute.iterate_left" -> "logic", "subsemiring.mem_to_submonoid" -> "algebra", "norm_num.lt_one_bit0" -> "tactic", "finset.filter_true" -> "data", "filter.tendsto_at_bot_of_add_const_left" -> "order", "pnat.coprime.gcd_mul_right_cancel" -> "data", "path.extend_one" -> "topology", "times_cont_diff_within_at.continuous_within_at'" -> "analysis", "primrec.list_index_of" -> "computability", "set.bInter_eq_Inter" -> "data", "emetric.mem_iff_ind_edist_zero_of_closed" -> "topology", "dvd_add_right" -> "algebra", "polynomial.prime_X_sub_C" -> "data", "measurable.min" -> "analysis", "nonempty_empty" -> "logic", "abs_sub_le" -> "algebra", "set.countable_iff_exists_injective" -> "data", "filter.germ.lift_rel_const_iff" -> "order", "wseq.mem_cons_of_mem" -> "data", "finset.inf_le" -> "data", "polynomial.div_mod_by_monic_unique" -> "data", "list.rotate'_length" -> "data", "list.take_nil" -> "data", "set.bij_on.inter" -> "data", "omega.term.val_div" -> "tactic", "mul_right_eq_self" -> "algebra", "matrix.transpose_mul" -> "data", "add_units.lift_right_neg_add" -> "algebra", "le_iff_exists_add" -> "algebra", "inv_lt_inv" -> "algebra", "free_add_monoid.lift_eval_of" -> "algebra", "ennreal.inv_lt_top" -> "data", "tactic.ring_exp.pow_p_pf_one" -> "tactic", "pos_of_mul_neg_left" -> "algebra", "units.one_sub_coe" -> "analysis", "ring_hom.injective_iff_ker_eq_bot" -> "algebra", "finset.prod_add_prod_le" -> "algebra", "deriv_add_const" -> "analysis", "linear_map.findim_range_add_findim_ker" -> "algebra", "opposite.op_zero" -> "algebra", "primrec.sum_inr" -> "computability", "int.zero_ne_neg_of_ne" -> "init", "set.preimage_const_mul_Ioo_of_neg" -> "data", "algebra.adjoin_eq_span" -> "algebra", "pgame.impartial.not_first_loses" -> "set_theory", "polynomial.exists_irreducible_of_nat_degree_ne_zero" -> "algebra", "le_max_left_of_le" -> "algebra", "supr_of_empty" -> "order", "category_theory.bifunctor.map_comp_id" -> "category_theory", "finsupp.emb_domain_apply" -> "data", "convex_ball" -> "analysis", "linear_map.range_comp_le_range" -> "algebra", "set.Ioc_subset_Ioc_left" -> "data", "exists_ne" -> "logic", "category_theory.types_hom" -> "category_theory", "ge_mem_nhds" -> "topology", "real.Sup_le" -> "data", "polynomial.coeff_smul" -> "data", "norm_num.div_eq" -> "tactic", "primrec.fin_val" -> "computability", "rat.coe_nat_eq_mk" -> "data", "primrec.fin_app" -> "computability", "zmod.sum_two_squares" -> "algebra", "computation.head_empty" -> "data", "nat.exists_prime_and_dvd" -> "data", "nat.zero_lxor" -> "data", "has_strict_fderiv_at.comp" -> "analysis", "function.update_eq_self" -> "logic", "equiv.perm.ne_and_ne_of_swap_mul_apply_ne_self" -> "algebra", "has_ftaylor_series_up_to_on.has_fderiv_within_at" -> "analysis", "free_group.red.step.cons" -> "algebra", "zorn.chain_closure_empty" -> "order", "topological_fiber_bundle_core.local_triv_at_symm_fst" -> "topology", "inv_lt_one_iff_one_lt" -> "algebra", "complex.neg_im" -> "data", "metric.Hausdorff_dist_closure" -> "topology", "list.pw_filter_nil" -> "data", "norm_snd_le" -> "analysis", "category_theory.differential_object.zero_f" -> "category_theory", "matrix.col_mul_vec" -> "data", "composition.one_le_blocks" -> "combinatorics", "real.tan_inj_of_lt_of_lt_pi_div_two" -> "analysis", "multiset.eq_repeat_of_mem" -> "data", "ideal.is_prime.radical" -> "algebra", "equiv.perm.cycle_of_apply_self" -> "algebra", "multiset.sub_le_self" -> "data", "induced_infi" -> "topology", "turing.list_blank.append_assoc" -> "computability", "topological_space.open_nhds.map_obj" -> "topology", "affine_map.coe_mul" -> "algebra", "except_t.goto_mk_label" -> "control", "is_greatest_singleton" -> "order", "wseq.map_think" -> "data", "ordinal.is_limit_iff_omega_dvd" -> "set_theory", "list.chain_lt_range'" -> "data", "punit.zero_eq" -> "algebra", "set.disjoint_iff" -> "data", "eq_of_sub_eq_zero" -> "algebra", "is_R_or_C.of_real_nat_cast" -> "data", "list.nil_infix" -> "data", "euclidean_domain.dvd_lcm_right" -> "algebra", "emetric.diam_le_iff_forall_edist_le" -> "topology", "add_subgroup.add_mem_cancel_right" -> "algebra", "continuous_linear_equiv.symm_symm_apply" -> "topology", "linear_map.sub_mem_ker_iff" -> "algebra", "nat.partrec'.tail" -> "computability", "ctop.realizer.of_equiv_\[Sigma]" -> "data", "CommRing.colimits.quot_mul" -> "algebra", "list.perm_nil" -> "data", "nat.dvd_add_self_left" -> "data", "encodable.Union_decode2_disjoint_on" -> "data", "int.mul_def" -> "data", "omega.coeffs.val_between_sub" -> "tactic", "sequentially_complete.set_seq_sub_aux" -> "topology", "nat.bodd_add_div2" -> "init", "complex.dist_eq" -> "topology", "dense_inducing.extend_eq" -> "topology", "measure_theory.outer_measure.zero_caratheodory" -> "analysis", "nat.partrec.code.eval_curry" -> "computability", "eq_of_zero_eq_one" -> "algebra", "denumerable.raise_lower" -> "data", "nat.add_mul_div_right" -> "init", "real.arctan_one" -> "analysis", "eq.congr_left" -> "logic", "pSet.equiv_iff_mem" -> "set_theory", "has_strict_fderiv_at.map_implicit_function_of_complemented_eq" -> "analysis", "compact_open_separated_add" -> "topology", "finsupp.hom_ext" -> "data", "num_is_root_scale_roots_of_aeval_eq_zero" -> "algebra", "list.mem_diff_iff_of_nodup" -> "data", "lucas_lehmer.X.\[Omega]_mul_\[Omega]b" -> "number_theory", "exists_int_lt" -> "algebra", "filter.map_congr" -> "order", "holor.slice_add" -> "data", "category_theory.limits.equalizer.iso_source_of_self_inv" -> "category_theory", "is_noetherian_ring.well_founded_dvd_not_unit" -> "algebra", "localization_map.mem_coe_submodule" -> "algebra", "set.maps_to.iterate" -> "data", "equiv.sigma_preimage_equiv_symm_apply_fst" -> "data", "real.sqrt_eq_rpow" -> "analysis", "differentiable.csinh" -> "analysis", "pequiv.trans_assoc" -> "data", "primrec.option_bind" -> "computability", "set_of_is_preconnected_eq_of_ordered" -> "topology", "measure_theory.lintegral_map" -> "analysis", "category_theory.adjunction.left_triangle" -> "category_theory", "prime_spectrum.gc_set" -> "algebraic_geometry", "stream.zip_eq" -> "data", "dfinsupp.subtype_domain_neg" -> "data", "polynomial.is_unit_C" -> "data", "finset.Ico.eq_empty_of_le" -> "data", "times_cont_diff_on_const" -> "analysis", "subgroup.mem_sup_right" -> "algebra", "true_iff_false" -> "init", "set.indicator_nonneg" -> "data", "tfae_mem_nhds_within_Iic" -> "topology", "stream.all_def" -> "data", "principal_seg.coe_coe_fn" -> "set_theory", "equiv.nontrivial" -> "data", "cauchy_nhds" -> "topology", "qpf.Wequiv.abs'" -> "data", "measurable_inv_iff" -> "analysis", "finset.disjoint_of_subset_left" -> "data", "set.Ico_subset_Ico_union_Ico" -> "data", "set.image_mul_right_Icc" -> "data", "sum.elim_injective" -> "data", "lists.to_of_list" -> "set_theory", "ennreal.tsum_supr_eq" -> "topology", "option.orelse_none" -> "data", "relation.equivalence_join_refl_trans_gen" -> "logic", "smooth_left_mul" -> "geometry", "measure_theory.outer_measure.of_content_caratheodory" -> "analysis", "list.count_eq_zero_of_not_mem" -> "data", "emetric.inf_edist_le_inf_edist_add_edist" -> "topology", "nat.test_bit_lor" -> "init", "sub_eq_zero_of_eq" -> "algebra", "is_path_connected_iff" -> "topology", "prod.fst_mul" -> "algebra", "polynomial.continuous" -> "analysis", "ennreal.coe_nat_ne_top" -> "data", "dfinsupp.mk_add" -> "data", "edist_mem_uniformity" -> "topology", "polynomial.is_root_of_aeval_algebra_map_eq_zero" -> "data", "pell.is_pell_mul" -> "number_theory", "dvd_of_mul_left_dvd" -> "algebra", "polynomial.ne_zero_of_ne_zero_of_monic" -> "data", "add_subgroup.prod_mono_left" -> "algebra", "metric.sum.one_dist_le" -> "topology", "category_theory.limits.zero_of_source_iso_zero" -> "category_theory", "int.modeq.modeq_mul_left'" -> "data", "ideal.eq_jacobson_iff_not_mem" -> "algebra", "mdifferentiable_within_at.congr" -> "geometry", "exists_unique.exists2" -> "logic", "measure_theory.l1.simple_func.coe_neg" -> "analysis", "computable.succ" -> "computability", "neg_concave_on_iff" -> "analysis", "simple_graph.mem_neighbor_finset" -> "combinatorics", "computation.results_thinkN" -> "data", "ideal.comap_radical" -> "algebra", "ext_chart_preimage_mem_nhds_within" -> "geometry", "closure_Ioc" -> "topology", "measure_theory.outer_measure.is_caratheodory_inter" -> "analysis", "ring.fractional_ideal.mul_right_mono" -> "algebra", "measure_theory.integrable_on_of_bounded" -> "analysis", "imp_eq_of_eq_false_left" -> "init", "exists_add_lt_and_pos_of_lt" -> "algebra", "and_assoc" -> "init", "powers.one_mem" -> "algebra", "lucas_lehmer_sufficiency" -> "number_theory", "subring.closure_univ" -> "algebra", "isometric.coe_to_affine_map" -> "analysis", "linear_equiv.map_eq_zero_iff" -> "algebra", "sesq_form.sub_right" -> "algebra", "filter.frequently_imp_distrib" -> "order", "setoid.nonempty_of_mem_partition" -> "data", "mul_eq_one_iff'" -> "algebra", "homological_complex.kernel_map_comp" -> "algebra", "continuous_subtype_val" -> "topology", "set.singleton_one" -> "algebra", "add_commute.refl" -> "algebra", "zmod.units_pow_card_sub_one_eq_one" -> "algebra", "ideal.mul_assoc" -> "algebra", "free_abelian_group.of_mul" -> "algebra", "one_le_div_of_neg" -> "algebra", "multiset.singleton_disjoint" -> "data", "nat.bit1_lt" -> "init", "imp_self" -> "logic", "uniform_space.has_basis_nhds_prod" -> "topology", "list.all_iff_forall" -> "data", "norm_num.zero_succ" -> "tactic", "category_theory.limits.epi_image_of_epi" -> "category_theory", "max_lt" -> "init", "is_local_max.on" -> "topology", "ptendsto_nhds" -> "topology", "filter.tendsto_snd" -> "order", "is_extr_on.inter" -> "order", "free_group.prod_mk" -> "algebra", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_inv" -> "category_theory", "list.any_iff_exists_prop" -> "data", "circle_equiv_symm_apply" -> "number_theory", "set.disjoint_diff" -> "data", "category_theory.fully_faithful_cancel_right_inv_app" -> "category_theory", "stream.tail_map" -> "data", "ideal.quotient.zero_ne_one_iff" -> "algebra", "int.add_lt_add" -> "init", "ideal.mul_le_inf" -> "algebra", "add_semiconj_by.neg_neg_symm" -> "algebra", "int.distrib_right" -> "init", "cardinal.mk_image_eq_of_inj_on_lift" -> "set_theory", "measurable.mono" -> "analysis", "emetric.exists_edist_lt_of_inf_edist_lt" -> "topology", "list.nodup.sublist_ext" -> "data", "is_bounded_linear_map.comp" -> "analysis", "ordinal.is_normal.nfp_le_fp" -> "set_theory", "ennreal.exists_pos_sum_of_encodable" -> "analysis", "has_fpower_series_on_ball.tendsto_locally_uniformly_on" -> "analysis", "add_subgroup.bot_normal" -> "algebra", "int.sub_nat_nat_add_add" -> "init", "fintype.card_ulift" -> "data", "nonneg_of_mul_nonpos_right" -> "algebra", "divp_left_inj" -> "algebra", "submodule.smul_mono_right" -> "algebra", "real.mk_lt" -> "data", "associates.is_unit_iff_eq_one" -> "algebra", "is_lub_Icc" -> "order", "rat.zero_mk" -> "data", "group.conj_mem_conjugates_of_set" -> "algebra", "real.differentiable_cosh" -> "analysis", "category_theory.limits.cocones.ext_inv_hom" -> "category_theory", "algebra.id.smul_eq_mul" -> "algebra", "fin.snoc_update" -> "data", "div_nonneg" -> "algebra", "turing.partrec_to_TM2.tr_ret_respects" -> "computability", "strict_mono.order_dual" -> "order", "ring_invo.map_eq_zero_iff" -> "algebra", "add_comm_group.direct_limit.of_sub" -> "algebra", "set.seq_subset" -> "data", "circle_deg1_lift.translation_number_map_id" -> "dynamics", "submonoid.localization_map.lift_mk'" -> "algebra", "norm_num.rat_cast_div" -> "tactic", "function.commute.inv_on_fixed_pts_comp" -> "dynamics", "int.le_of_neg_le_neg" -> "init", "nat.modeq.mod_modeq" -> "data", "finset.weighted_vsub_of_point_apply" -> "algebra", "polynomial.coeff_mul" -> "data", "finmap.replace_to_finmap" -> "data", "omega.int.preform.sat_of_implies_of_sat" -> "tactic", "strict_mono.monotone" -> "order", "complex.abs_I" -> "data", "tactic.ring_exp.div_pf" -> "tactic", "quotient_map.continuous_iff" -> "topology", "affine_map.coe_zero" -> "algebra", "nat.add_pos_right" -> "data", "cardinal.zero_lt_bit0" -> "set_theory", "mvpfunctor.W_dest'_W_mk" -> "data", "pgame.lt_of_le_of_lt" -> "set_theory", "int.neg_succ_of_nat_add_neg_succ_of_nat" -> "init", "set.singleton_def" -> "data", "multiset.pi.cons_same" -> "data", "wseq.ret_bind" -> "data", "function.bij_on_pts_of_period" -> "dynamics", "subgroup.coe_coe" -> "algebra", "int.nat_abs_add_le" -> "data", "multiples.self_mem" -> "algebra", "has_fpower_series_on_ball.coeff_zero" -> "analysis", "list.le_argmax_of_mem" -> "data", "measure_theory.measure.regular_haar_measure" -> "analysis", "measure_theory.le_infi_lintegral" -> "analysis", "con.coe_eq" -> "algebra", "turing.list_blank.exists_cons" -> "computability", "mdifferentiable_within_at.comp" -> "geometry", "tactic.ring.horner_mul_horner" -> "tactic", "free_group.join_red_of_step" -> "algebra", "is_local_extr_on_const" -> "topology", "measure_theory.simple_func.sup_eq_map\:2082" -> "analysis", "equiv.symm_trans_apply" -> "data", "Class.powerset_hom" -> "set_theory", "circle_deg1_lift.iterate_pos_eq_iff" -> "dynamics", "prod.map_fst'" -> "data", "cardinal.mul_le_mul_right" -> "set_theory", "multiset.powerset_len_aux_cons" -> "data", "function.left_inverse.surjective" -> "logic", "monoid_hom.coe_of" -> "algebra", "nhds_within_Ioc_eq_nhds_within_Iic" -> "topology", "multiset.card_pos" -> "data", "finite_dimensional.complete" -> "analysis", "typevec.typevec_cases_cons\:2082_append_fun" -> "data", "hyperreal.infinitesimal_neg_iff_infinite_neg_inv" -> "data", "eq_of_forall_dist_le" -> "topology", "mem_groupoid_of_pregroupoid" -> "geometry", "con.le_def" -> "algebra", "mvqpf.corecF_eq" -> "data", "is_closed.preimage" -> "topology", "sym2.other_is_mem_other" -> "data", "equiv.perm.disjoint_mul_comm" -> "algebra", "category_theory.limits.image.map_id" -> "category_theory", "list.mem_singleton_self" -> "data", "add_le_of_le_of_nonpos'" -> "algebra", "ideal.coeff_zero_mem_comap_of_root_mem" -> "algebra", "set.maps_to_empty" -> "data", "nat.mod_two_of_bodd" -> "init", "list.perm_insertion_sort" -> "data", "set.nonempty.inr" -> "data", "alist.keys_insert" -> "data", "right_mem_segment" -> "analysis", "vector_allp_nil" -> "number_theory", "Module.Mon_Module_equivalence_Algebra.functor_map_to_fun" -> "category_theory", "matrix.transpose_nonsing_inv" -> "algebra", "tactic.abel.subst_into_smulg" -> "tactic", "symmetric_symmetrize_rel" -> "topology", "zsqrtd.divides_sq_eq_zero" -> "data", "false_ne_true" -> "logic", "finset.inj_on_of_surj_on_of_card_le" -> "data", "category_theory.limits.cones.whiskering_equivalence_counit_iso" -> "category_theory", "real.sqrt_le_left" -> "data", "holor.cast_type" -> "data", "generalized_continued_fraction.convergents'_aux_stable_of_terminated" -> "algebra", "has_strict_fderiv_at.sub_const" -> "analysis", "ordinal.sub_le" -> "set_theory", "finset.sum_Ico_eq_sum_range" -> "algebra", "multiset.prod_repeat" -> "data", "power_series.coeff_inv_aux" -> "algebra", "ideal.map_mono" -> "algebra", "forall_congr_eq" -> "init", "derivation.smul_to_linear_map_coe" -> "algebra", "int.sign_one" -> "init", "matrix.alg_hom.map_det" -> "algebra", "nat.dist.triangle_inequality" -> "data", "int.neg_lt_neg" -> "init", "irrational.rat_sub" -> "data", "real.inner_le_Lp_mul_Lq" -> "analysis", "list.find_some" -> "data", "closed_under_restriction_iff_id_le" -> "geometry", "circle_deg1_lift.translation_number_eq_of_semiconj" -> "dynamics", "associates.factor_set.sup_add_inf_eq_add" -> "algebra", "seq.join_cons_nil" -> "data", "isometric.preimage_symm" -> "topology", "comp.seq_mk" -> "control", "category_theory.adjunction.right_triangle" -> "category_theory", "int.div_lt_iff_lt_mul" -> "data", "filter.has_basis.exists_iff" -> "order", "semiquot.mem_map" -> "data", "pos_num.min_fac_aux_to_nat" -> "data", "of_digits_eq_foldr" -> "data", "list.bind_singleton" -> "data", "ereal.neg_def" -> "data", "set.bUnion_union" -> "data", "is_least_Icc" -> "order", "padic_norm_z.norm_p" -> "data", "mem_nhds_iff_exists_Ioo_subset'" -> "topology", "set.singleton_union" -> "data", "wseq.cons_append" -> "data", "add_monoid_hom.cancel_right" -> "algebra", "mvqpf.const.mk_get" -> "data", "has_strict_fderiv_at.smul_const" -> "analysis", "lie_algebra.orthogonal.Pso_inv" -> "algebra", "has_fderiv_at.comp" -> "analysis", "continuous_linear_equiv.continuous_on" -> "topology", "measure_theory.eventually_eq_dirac'" -> "analysis", "is_R_or_C.norm_sq_mul" -> "data", "ordinal.sub_eq_zero_iff_le" -> "set_theory", "gt_of_ge_of_gt" -> "init", "ennreal.rpow_one" -> "analysis", "abstract_completion.compare_coe" -> "topology", "multiset.rel_zero_left" -> "data", "list.is_nil_iff_eq_nil" -> "data", "list.chain'.cons'" -> "data", "set.subset_pi_eval_image" -> "data", "int.nat_abs_mul_self'" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_within_at_of_lift_prop_at" -> "geometry", "multiset.sup_zero" -> "data", "pSet.resp.refl" -> "set_theory", "ennreal.not_lt_zero" -> "data", "add_magma.free_add_semigroup.induction_on" -> "algebra", "nat.sub_mul_mod" -> "init", "tendsto_pow_at_top_nhds_0_of_lt_1" -> "analysis", "ring.subset_closure" -> "algebra", "polynomial.eval_unique" -> "data", "mul_div_cancel_left" -> "algebra", "mv_polynomial.degrees_monomial_eq" -> "data", "nat.fact_ne_zero" -> "data", "stream.nth_unfolds_head_tail" -> "data", "category_theory.limits.bicone.to_cone_X" -> "category_theory", "add_submonoid.localization_map.of_add_equiv_of_localizations_apply" -> "algebra", "pnat.coprime.symm" -> "data", "int.not_even_one" -> "data", "topological_space.nhds_mk_of_nhds" -> "topology", "set.Icc_subset_Icc_union_Icc" -> "data", "add_submonoid.map_inl" -> "algebra", "ordinal.le_total" -> "set_theory", "cardinal.bit1_eq_self_iff" -> "set_theory", "cancel_factors.cancel_factors_eq" -> "tactic", "category_theory.comma.comp_right" -> "category_theory", "supr_subtype" -> "order", "nat.bit0_inj" -> "init", "measure_theory.measure.haar.mem_prehaar_empty" -> "analysis", "affine.triangle.altitude_eq_monge_plane" -> "geometry", "complex.cos_pi_div_two_sub" -> "analysis", "int.sub_lt_sub_left" -> "init", "finset.image_eq_empty" -> "data", "Module.Mon_Module_equivalence_Algebra.inverse_map_hom" -> "category_theory", "set.nonempty_iff_univ_nonempty" -> "data", "matrix.transpose_apply" -> "data", "poly.proj_eval" -> "number_theory", "mv_polynomial.sum_to_iter_Xr" -> "data", "local_homeomorph.tendsto_symm" -> "topology", "list.nth_update_nth_ne" -> "data", "finset.mem_univ" -> "data", "subtype.val_injective" -> "data", "category_theory.limits.biproduct.map_eq_map'" -> "category_theory", "roption.bind_dom" -> "data", "set.Ioc_subset_Ioo_right" -> "data", "nat.min_fac_eq_one_iff" -> "data", "option.some_bind" -> "data", "emetric.diam_empty" -> "topology", "is_coprime.of_mul_add_right_right" -> "algebra", "ideal.mul_eq_bot" -> "algebra", "nat.lt_iff_add_one_le" -> "data", "algebra.adjoin_le" -> "algebra", "list.map_of_fn" -> "data", "cardinal.powerlt_omega_le" -> "set_theory", "continuous_linear_equiv.map_sub" -> "topology", "set.Icc_subset_Ico_iff" -> "data", "zsqrtd.le_antisymm" -> "data", "category_theory.limits.biprod.inr_map_assoc" -> "category_theory", "nat.mul_self_le_mul_self_iff" -> "data", "metric.is_open_ball" -> "topology", "finset.union_sdiff_distrib" -> "data", "times_cont_diff.comp" -> "analysis", "filter.tendsto_at_bot_add_nonpos_left" -> "order", "nat.sub_lt_right_iff_lt_add" -> "data", "add_magma.free_add_semigroup.map_add" -> "algebra", "subtype.equiv_iff" -> "data", "gronwall_bound_x0" -> "analysis", "mv_polynomial.C_add" -> "data", "category_theory.quotient.lift_obj" -> "category_theory", "with_top.add_lt_add_iff_right" -> "algebra", "finite_field.forall_pow_eq_one_iff" -> "algebra", "set.Icc_union_Ioc_eq_Icc" -> "data", "dense_inducing.extend_eq_at" -> "topology", "tendsto_at_top_mul_left" -> "analysis", "valuation.map_neg" -> "algebra", "finset.bind_singleton_eq_self" -> "data", "eq_true_of_not_eq_false" -> "init", "category_theory.Monad.Monad_Mon_equiv_functor" -> "category_theory", "Icc_mem_nhds_within_Iic" -> "topology", "set.inter_singleton_nonempty" -> "data", "monoid_hom.coe_range" -> "algebra", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_self" -> "analysis", "function.commute.iterate_pos_lt_of_map_lt" -> "order", "continuous_multilinear_map.op_norm_zero_iff" -> "analysis", "nat.coprime.gcd_mul_left_cancel" -> "data", "fin_enum.mem_pi" -> "data", "add_monoid_hom.coprod_unique" -> "algebra", "is_local_min.min" -> "topology", "measure_theory.simple_func.map_coe_ennreal_restrict" -> "analysis", "primrec.nat_div_mod" -> "computability", "zmod.nat_coe_zmod_eq_zero_iff_dvd" -> "data", "differentiable_on_inv" -> "analysis", "nat.choose_eq_fact_div_fact" -> "data", "circle_deg1_lift.lt_map_map_zero" -> "dynamics", "finset.prod_range_reflect" -> "algebra", "linear_action_add_act" -> "algebra", "function.equiv.is_equivalence" -> "init", "add_submonoid.le_comap_map" -> "algebra", "adjoin_root.lift_of" -> "algebra", "contracting_with.apriori_edist_iterate_efixed_point_le" -> "topology", "add_monoid_hom.coe_mul_left" -> "algebra", "list.filter_map_nil" -> "data", "unique_factorization_domain.induction_on_prime" -> "algebra", "ordinal.le_add_left" -> "set_theory", "is_min_filter.max" -> "order", "tsum_prod'" -> "topology", "nat.shiftl'_sub" -> "init", "set.sUnion_subset_sUnion" -> "data", "times_cont_diff_on.differentiable_on_iterated_fderiv_within" -> "analysis", "lie_algebra.endo_algebra_bracket" -> "algebra", "imp_iff_right" -> "logic", "free_group.reduce.red" -> "algebra", "measurable_nnnorm" -> "analysis", "category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso_hom" -> "category_theory", "linear_equiv.prod_apply" -> "algebra", "continuous_linear_map.uniform_embedding_of_bound" -> "analysis", "skew_adjoint_matrices_lie_subalgebra_equiv_apply" -> "algebra", "int.sign_mul" -> "data", "free_add_semigroup.traverse_pure" -> "algebra", "poly.add_eval" -> "number_theory", "zmod.cast_int_cast'" -> "data", "unit_of_invertible_val" -> "algebra", "span_le_span_iff" -> "algebra", "local_homeomorph.eq_on_source.trans'" -> "topology", "equiv.arrow_congr_symm" -> "data", "zmod.neg_val" -> "data", "ideal.eq_top_of_unit_mem" -> "algebra", "complex.norm_real" -> "analysis", "fin_enum.finset.mem_enum" -> "data", "wseq.destruct_tail" -> "data", "nat.totient_pos" -> "data", "set.bUnion_univ" -> "data", "ennreal.tendsto_to_real" -> "topology", "category_theory.faithful_reflects_epi" -> "category_theory", "inv_le_iff_one_le_mul" -> "algebra", "zmod.val_zero" -> "data", "fin.val_eq_coe" -> "data", "emetric.closeds.edist_eq" -> "topology", "filter.lift_infi'" -> "order", "gaussian_int.to_complex_div_im" -> "data", "uniform_continuous\:2082_def" -> "topology", "infi_image" -> "order", "measure_theory.ae_eq_fun.comp\:2082_mk_mk" -> "analysis", "geom_sum_Ico" -> "algebra", "padic_int.ext" -> "data", "direct_sum.mk_zero" -> "algebra", "category_theory.limits.cones.postcompose_obj_X" -> "category_theory", "tactic.ring_exp.pow_pp_pf_prod" -> "tactic", "matrix.minor_cons_row" -> "data", "pnat.xgcd_type.reduce_special" -> "data", "filter.tendsto_principal_principal" -> "order", "formal_multilinear_series.min_radius_le_radius_add" -> "analysis", "abs_sub_round" -> "algebra", "nat.lt_size_self" -> "data", "is_R_or_C.inv_re" -> "data", "finsupp.single_eq_zero" -> "data", "linear_pmap.to_fun_eq_coe" -> "algebra", "sym2.rel_bool_spec" -> "data", "measure_theory.l1.simple_func.dense_inducing" -> "analysis", "semidirect_product.lift_inl" -> "algebra", "rat.add_comm" -> "data", "commute.self_cast_nat_mul" -> "algebra", "complex.conj_im" -> "data", "ordinal.power_is_limit_left" -> "set_theory", "well_founded.lt_succ_iff" -> "order", "real.inv_rpow" -> "analysis", "finset.coe_preimage" -> "data", "cardinal.lift_max" -> "set_theory", "multiset.bind_add" -> "data", "set.card_singleton" -> "data", "category_theory.eq_of_comp_right_eq" -> "category_theory", "uniform_embedding_subtype_val" -> "topology", "divp_eq_one_iff_eq" -> "algebra", "category_theory.sum_comp_inl" -> "category_theory", "topological_fiber_bundle_core.local_triv'_inv_fst" -> "topology", "false_or" -> "init", "pgame.left_moves_mk" -> "set_theory", "deriv.lhopital_zero_nhds_left" -> "analysis", "list.append_subset_iff" -> "data", "sup_inf_le" -> "order", "list_all_cons" -> "number_theory", "smul_comm" -> "algebra", "matrix.subsingleton_of_empty_right" -> "data", "finsupp.induction\:2082" -> "data", "add_con.ker_lift_range_eq" -> "algebra", "tactic.ring_exp.pow_pf_c_c" -> "tactic", "int.coe_nat_zero" -> "init", "finset.mem_of_mem_erase" -> "data", "exists_or_distrib" -> "logic", "typevec.comp_id" -> "data", "list.rel_foldr" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_id" -> "geometry", "right_ord_continuous.map_infi" -> "order", "measure_theory.measure.haar.prehaar_self" -> "analysis", "cardinal.aleph_idx_le" -> "set_theory", "of_digits_append" -> "data", "algebra.adjoin_le_iff" -> "algebra", "primrec.encode_iff" -> "computability", "finset.erase_eq_of_not_mem" -> "data", "Mod.comap_obj_X" -> "category_theory", "function.const_comp" -> "logic", "list.nth_range" -> "data", "setoid.inf_iff_and" -> "data", "fin.nat_find_mem_find" -> "data", "units.unit_of_nearby_coe" -> "analysis", "mv_polynomial.coeff_X'" -> "data", "nhds_within_ext_chart_target_eq" -> "geometry", "ring.fractional_ideal.span_singleton_fractional" -> "algebra", "finset.eq_one_of_prod_eq_one" -> "algebra", "galois_coinsertion.strict_mono_l" -> "order", "finset.sum_subtype_of_mem" -> "algebra", "filter.tendsto_map" -> "order", "function.right_inverse_surj_inv" -> "logic", "ball_subset_of_comp_subset" -> "topology", "add_div_eq_mul_add_div" -> "algebra", "set.abs_sub_left_of_mem_interval" -> "data", "primrec.list_inth" -> "computability", "bool.dichotomy" -> "data", "list.map_add_range'" -> "data", "category_theory.equivalence.cancel_unit_right_assoc" -> "category_theory", "set.inter_subset_inter_right" -> "data", "real.cos_sq_le_one" -> "data", "prod.inv_mk" -> "algebra", "power_series.order_monomial_of_ne_zero" -> "algebra", "category_theory.monoidal_category.right_unitor_inv_naturality" -> "category_theory", "algebraic_geometry.PresheafedSpace.ext" -> "algebraic_geometry", "mem_path_component_self" -> "topology", "measure_theory.extend_union" -> "analysis", "commute.fpow_self" -> "algebra", "category_theory.non_preadditive_abelian.neg_sub'" -> "category_theory", "padic_norm_e.zero" -> "data", "ennreal.to_real_add" -> "data", "euclidean_geometry.dist_set_eq_iff_dist_orthogonal_projection_eq" -> "geometry", "list.cons_append" -> "init", "monotone_comp_rel" -> "topology", "has_fderiv_within_at.prod" -> "analysis", "list.erase_sublist" -> "data", "relation.trans_gen.head" -> "logic", "nat.bodd_zero" -> "init", "filter.mem_Sup_sets" -> "order", "real.continuous_sin" -> "analysis", "inner_product_geometry.angle_neg_right" -> "geometry", "composition_card" -> "combinatorics", "set.finite.of_fintype" -> "data", "complex.abs_eq_zero" -> "data", "real.of_rat_sub" -> "data", "set.inter_diff_self" -> "data", "times_cont_diff_at.add" -> "analysis", "list.insert_of_not_mem" -> "data", "open_subgroup.ext_iff" -> "topology", "turing.tape.mk'_right" -> "computability", "linear_independent.inl_union_inr" -> "algebra", "asymptotics.is_o.congr_of_sub" -> "analysis", "string.iterator.zero_lt_length_next_to_string_of_has_next" -> "init", "multiset.zero_add" -> "data", "multiset.sections_cons" -> "data", "Ioo_mem_nhds_within_Ioi" -> "topology", "is_coprime.mul_dvd" -> "algebra", "zsqrtd.le_of_add_le_add_left" -> "data", "multiset.mem_attach" -> "data", "compact_univ" -> "topology", "measure_theory.l1.simple_func.dense_embedding" -> "analysis", "monotonicity.const" -> "meta", "continuous_subtype_nhds_cover" -> "topology", "ordinal.CNF_foldr" -> "set_theory", "complex.exp_sub" -> "data", "times_cont_diff_on.continuous_on_iterated_fderiv_within" -> "analysis", "lucas_lehmer.s_mod_mod" -> "number_theory", "filter.push_pull" -> "order", "uniformity_le_symm" -> "topology", "asymptotics.is_o_const_smul_right" -> "analysis", "ideal.eval\:2082_C_mk_eq_zero" -> "algebra", "set.inj_on.inv_fun_on_image" -> "data", "list.join_repeat_nil" -> "data", "set.univ_nonempty" -> "data", "omega.coeffs.val_between_nil" -> "tactic", "finset.prod_sum" -> "algebra", "multiset.fold_add" -> "data", "continuous_iff_ultrafilter" -> "topology", "filter.frequently_iff" -> "order", "add_monoid_hom.fst_comp_prod" -> "algebra", "list.sum_take_of_fn" -> "data", "Set.mem_inter" -> "set_theory", "ideal.sup_mul_left_self" -> "algebra", "polynomial.splits_id_iff_splits" -> "algebra", "finite_dimensional.of_finite_basis" -> "algebra", "reflexive_one_one_reducible" -> "computability", "filter.add_zero" -> "order", "mv_polynomial.iter_to_sum_C_C" -> "data", "real.has_deriv_at_log_of_pos" -> "analysis", "mdifferentiable_id" -> "geometry", "nat.primrec'.sub" -> "computability", "compl_inf" -> "order", "mul_left_eq_self" -> "algebra", "multiset.to_finset_subset" -> "data", "category_theory.limits.binary_bicone.to_cone_X" -> "category_theory", "finset.mem_image_of_mem" -> "data", "nat.cast_id" -> "data", "nnreal.geom_mean_le_arith_mean3_weighted" -> "analysis", "state_t.run_monad_lift" -> "init", "has_ftaylor_series_up_to_on.congr" -> "analysis", "equiv.psigma_equiv_sigma_symm_apply" -> "data", "CommRing.free_obj_coe" -> "algebra", "gronwall_bound_K0" -> "analysis", "affine_map.coe_one" -> "algebra", "is_local_extr.comp_continuous" -> "topology", "decidable.not_ball" -> "logic", "measurable_space.gc_comap_map" -> "analysis", "with_one.coe_ne_one" -> "algebra", "euclidean_geometry.orthogonal_projection_eq_self_iff" -> "geometry", "group.closure_subset_iff" -> "algebra", "power_series.coeff_succ_mul_X" -> "algebra", "dense_inter_of_open_right" -> "topology", "add_subgroup.map_bot" -> "algebra", "ordinal.mul_lt_mul_iff_left" -> "set_theory", "implicit_function_data.left_map_implicit_function" -> "analysis", "complex.abs_div" -> "data", "fin.le_iff_coe_le_coe" -> "data", "fpow_le_iff_le" -> "algebra", "function.support_sub" -> "data", "polynomial.mod_by_monic_X" -> "data", "category_theory.limits.prod.map_fst_assoc" -> "category_theory", "int.add_le_of_le_sub_right" -> "init", "typevec.diag_sub_val" -> "data", "pell.n_lt_a_pow" -> "number_theory", "nat.coprime_one_left_iff" -> "data", "category_theory.limits.zero_of_epi_comp" -> "category_theory", "equiv.has_sum_iff_of_support" -> "topology", "algebra.comap_top" -> "algebra", "measurable_space.is_measurable_generate_from" -> "analysis", "is_min_filter.sub" -> "order", "pgame.lt_zero" -> "set_theory", "or_iff_left_of_imp" -> "init", "complex.sin_pi" -> "analysis", "cau_seq.abv_pos_of_not_lim_zero" -> "data", "pgame.le_of_equiv_of_le" -> "set_theory", "pnat.one_coe" -> "data", "map_cInf_of_continuous_at_of_monotone" -> "topology", "complex.log_I" -> "analysis", "module.gsmul_eq_smul" -> "algebra", "dense_inducing.extend_Z_bilin" -> "topology", "multiset.filter_eq_nil" -> "data", "free_abelian_group.mul_def" -> "algebra", "generalized_continued_fraction.of_h_eq_floor" -> "algebra", "set.bij_on_Union" -> "data", "dioph.dioph_comp2" -> "number_theory", "wseq.to_list'_map" -> "data", "measure_theory.ae_eq_fun.quotient_out'_eq_coe_fn" -> "analysis", "deriv_within_mul" -> "analysis", "measure_theory.measure.dirac_apply" -> "analysis", "is_least_union_iff" -> "order", "geom_series\:2082_self" -> "algebra", "neg_add_le_right_of_le_add" -> "algebra", "complex.sin_neg" -> "data", "inner_product_space.of_core.inner_smul_right" -> "analysis", "rel.preimage_univ" -> "data", "bool.ff_eq_to_bool_iff" -> "data", "nat.coprime.gcd_right" -> "data", "filter.mem_sets_of_eq_bot" -> "order", "real.nnnorm_coe_nat" -> "analysis", "open_embedding_inl" -> "topology", "padic.coe_mul" -> "data", "norm_num.add_bit1_bit1" -> "tactic", "equiv.coe_mul_left" -> "data", "differentiable_within_at.pow" -> "analysis", "list.tfae_cons_of_mem" -> "data", "finset.sup_empty" -> "data", "polynomial.degree_eq_degree_of_associated" -> "data", "le_of_forall_ge_of_dense" -> "order", "has_sum_subtype_iff_indicator" -> "topology", "set.preimage_coe_coe_diagonal" -> "data", "finset.sum_product'" -> "algebra", "uniform_continuous\:2082_curry" -> "topology", "isometry.right_inv" -> "topology", "complex.re_add_im" -> "data", "fin.find_min'" -> "data", "ordinal.mul_pos" -> "set_theory", "is_coprime.mul_right" -> "algebra", "one_le_two" -> "algebra", "add_submonoid.mem_infi" -> "algebra", "set.Ioc_diff_right" -> "data", "multiset.cons_subset" -> "data", "dist_le_of_le_geometric_two_of_tendsto" -> "analysis", "ennreal.of_real_one" -> "data", "compact_compact_separated" -> "topology", "filter.image_coe_mem_sets" -> "order", "is_local_max_on.fderiv_within_nonpos" -> "analysis", "continuous_inf_dom_left" -> "topology", "zero_eq_dist" -> "topology", "local_equiv.maps_to" -> "data", "is_cyclic.exists_monoid_generator" -> "algebra", "category_theory.limits.biprod.braiding_map_braiding_assoc" -> "category_theory", "closure_Ioi" -> "topology", "finsupp.mem_supported" -> "algebra", "add_submonoid.comap_infi" -> "algebra", "infi_and" -> "order", "set.finite.coe_to_finset" -> "data", "submonoid.localization_map.sec_spec'" -> "algebra", "list.nth_le_drop'" -> "data", "finset.mem_bind" -> "data", "nat.succ_le_iff" -> "data", "pos_num.cast_add" -> "data", "measure_theory.simple_func.fin_meas_supp.pair" -> "analysis", "smooth_right_mul" -> "geometry", "list.erase_cons_tail" -> "data", "times_cont_mdiff_within_at.mono" -> "geometry", "complex.sinh_conj" -> "data", "smooth.prod_map" -> "geometry", "is_greatest.bdd_above" -> "order", "mfderiv_within_inter" -> "geometry", "continuous_linear_equiv.times_cont_diff_within_at_comp_iff" -> "analysis", "continuous_within_at.tendsto" -> "topology", "cardinal.univ_umax" -> "set_theory", "list.length_lookmap" -> "data", "category_theory.monoidal_of_has_finite_coproducts.tensor_obj" -> "category_theory", "ennreal.le_inv_iff_le_inv" -> "data", "module.direct_limit.induction_on" -> "algebra", "multiset.sup_cons" -> "data", "category_theory.limits.prod.hom_ext" -> "category_theory", "neg_add_le_left_of_le_add" -> "algebra", "category_theory.under.comp_right" -> "category_theory", "list.sum_hom_rel" -> "data", "equiv.symm_trans_swap_trans" -> "data", "div_ne_zero" -> "algebra", "cardinal.add_eq_right_iff" -> "set_theory", "add_submonoid.coe_supr_of_directed" -> "algebra", "list.append_eq_has_append" -> "data", "finite_field.card'" -> "algebra", "linear_pmap.left_le_sup" -> "algebra", "rel.core_id" -> "data", "cau_seq.zero_lim_zero" -> "data", "nat.prime_two" -> "data", "circle_deg1_lift.translation_number_translate" -> "dynamics", "int.to_nat_lt_to_nat" -> "data", "set.insert_diff_of_mem" -> "data", "localization.induction_on\:2082" -> "algebra", "matrix.from_blocks_add" -> "data", "nat.le_of_succ_le" -> "init", "pgame.move_right_mk" -> "set_theory", "linear_independent_monoid_hom" -> "algebra", "subgroup.prod_mono_left" -> "algebra", "function.is_periodic_pt.sub" -> "dynamics", "vsub_left_injective" -> "algebra", "cauchy_pure" -> "topology", "cardinal.lt_omega" -> "set_theory", "is_bounded_linear_map.differentiable_at" -> "analysis", "nhds_def" -> "topology", "compl_le_compl_iff_le" -> "order", "is_bounded_bilinear_map_mul" -> "analysis", "omega.coeffs.val_between_eq_of_le" -> "tactic", "submonoid.prod_bot_sup_bot_prod" -> "algebra", "onote.NF.below_of_lt'" -> "set_theory", "is_measurable.compl_iff" -> "analysis", "filter.const_eventually_eq'" -> "order", "list.pairwise_filter" -> "data", "tendsto.max" -> "topology", "zsqrtd.one_im" -> "data", "nhds_basis_opens" -> "topology", "submodule.eta" -> "algebra", "lt_max_iff" -> "algebra", "con.ext'_iff" -> "algebra", "nat.primrec'.comp\:2082" -> "computability", "infi_pos" -> "order", "category_theory.limits.coprod_desc_inl_inr" -> "category_theory", "fin.succ_le_succ_iff" -> "data", "pow_two_pos_of_ne_zero" -> "algebra", "algebra.restrict_scalars_equiv_apply" -> "algebra", "metric.tendsto_nhds_within_nhds_within" -> "topology", "category_theory.iso.hom_eq_inv" -> "category_theory", "set.range_comp_subset_range" -> "data", "ennreal.ne_top_of_mul_ne_top_left" -> "data", "finset.prod_preimage" -> "data", "bdd_above_Ico" -> "order", "or.comm" -> "init", "one_one_equiv.le_congr_left" -> "computability", "stream.even_interleave" -> "data", "filter.map.is_monoid_hom" -> "order", "ideal.eq_bot_or_top" -> "algebra", "submodule.mem_span_insert'" -> "algebra", "mul_geom_sum" -> "algebra", "structure_groupoid.compatible" -> "geometry", "alist.insert_singleton_eq" -> "data", "cardinal.mk_bounded_set_le" -> "set_theory", "sum.traverse_map" -> "control", "convex_empty" -> "analysis", "finset.coe_mem" -> "data", "finset.fold_map" -> "data", "affine_subspace.affine_span_coe" -> "algebra", "add_subgroup.mem_comap" -> "algebra", "localization_map.ring_equiv_of_ring_equiv_eq_map" -> "algebra", "measurable.nnnorm" -> "analysis", "is_coprime.mul_add_left_right_iff" -> "algebra", "prod.fst_mul_snd" -> "algebra", "CommRing.free_map_coe" -> "algebra", "finset.inf_def" -> "data", "coe_not_mem_range_equiv" -> "data", "linear_map.quotient_inf_equiv_sup_quotient_symm_apply_left" -> "algebra", "exists_eq_left" -> "logic", "omega.int.valid_of_unsat_not" -> "tactic", "Sup_insert" -> "order", "padic.of_rat_one" -> "data", "list.count_append" -> "data", "list.ne_nil_of_mem" -> "data", "real.add_lt_add_iff_left" -> "data", "dioph.lt_dioph" -> "number_theory", "real.exp_ne_zero" -> "data", "add_submonoid.localization_map.eq_of_eq" -> "algebra", "tensor_product.smul_tmul" -> "algebra", "tendsto_uniformly.continuous" -> "topology", "is_linear_map.map_neg" -> "algebra", "differentiable_on.mul_const" -> "analysis", "matrix.scalar.commute" -> "data", "galois_connection.l_u_le" -> "order", "bdd_below_iff_subset_Ici" -> "order", "emetric.mem_closure_iff_inf_edist_zero" -> "topology", "concave_on.le_on_segment'" -> "analysis", "set.inj_on.comp" -> "data", "complex.lim_re" -> "data", "galois_connection.l_sup" -> "order", "euclidean_geometry.angle_eq_angle_of_angle_eq_pi" -> "geometry", "wseq.mem_think" -> "data", "list.mem_union_right" -> "data", "pSet.lift_mem_embed" -> "set_theory", "measure_theory.integrable_zero" -> "analysis", "convex.mem_Icc" -> "analysis", "add_submonoid.comap_map_comap" -> "algebra", "category_theory.functor_to_types.hom_inv_id_app_apply" -> "category_theory", "continuous_linear_map.differentiable" -> "analysis", "metric.bounded.subset" -> "topology", "mvpfunctor.W_mk_eq" -> "data", "traversable.mfoldl_map" -> "control", "polynomial.next_coeff_of_pos_nat_degree" -> "data", "pfunctor.iget_map" -> "data", "ennreal.lt_iff_exists_real_btwn" -> "data", "finset.subset_range_sup_succ" -> "data", "zsqrtd.le_total" -> "data", "subgroup.gpowers_subset" -> "algebra", "mul_le_mul_of_nonneg_left" -> "algebra", "Module.Mon_Module_equivalence_Algebra.inverse_obj_mul" -> "category_theory", "convex_on_univ_of_deriv2_nonneg" -> "analysis", "filter.prod_map_map_eq" -> "order", "real.sqr_sqrt" -> "data", "ordinal.power_le_power_left" -> "set_theory", "cau_seq.lim_mul" -> "data", "antilipschitz_with.of_subsingleton" -> "topology", "mul_lt_mul''''" -> "algebra", "metric.nonempty_closed_ball" -> "topology", "is_min_filter.bicomp_mono" -> "order", "int.gcd_dvd_left" -> "algebra", "fintype.left_inverse_bij_inv" -> "data", "list.index_of_inj" -> "data", "smul_eq_zero" -> "algebra", "cau_seq.exists_lt" -> "data", "contracting_with.dist_le_of_fixed_point" -> "topology", "list.foldl_eq_foldr" -> "data", "divp_mul_cancel" -> "algebra", "free_group.one_bind" -> "algebra", "order_bot.lower_bounds_univ" -> "order", "has_deriv_at.smul_const" -> "analysis", "ennreal.one_lt_two" -> "data", "neg_add_lt_iff_lt_add_right" -> "algebra", "continuous_linear_equiv.injective" -> "topology", "ordinal.add_omega_power" -> "set_theory", "submodule.coe_mk" -> "algebra", "subtype.map_comp" -> "data", "filter.tendsto_comap" -> "order", "finset.inf_empty" -> "data", "bool.cond_ff" -> "data", "times_cont_diff_on_succ_iff_has_fderiv_within_at" -> "analysis", "pell.xz_succ_succ" -> "number_theory", "submonoid.localization_map.eq_mk'_iff_mul_eq" -> "algebra", "univ_unique" -> "data", "eq_top_iff" -> "order", "submodule.prod_map_snd" -> "algebra", "isometric.mul_apply" -> "topology", "is_noetherian_ring.exists_irreducible_factor" -> "algebra", "linear_map.range_prod_le" -> "algebra", "semidirect_product.mul_right" -> "algebra", "associated_normalize" -> "algebra", "holor.mul_assoc0" -> "data", "nat.prime.pow_not_prime" -> "data", "polynomial.prod_X_sub_C_next_coeff" -> "algebra", "coe_I_zero" -> "topology", "has_sum_le" -> "topology", "category_theory.biproduct.column_nonzero_of_iso'" -> "category_theory", "int.mul_mod" -> "data", "finset.singleton_subset_set_iff" -> "data", "hyperreal.infinite_pos_iff_infinite_of_pos" -> "data", "interval_integral.integral_has_fderiv_within_at" -> "analysis", "cardinal.aleph_is_normal" -> "set_theory", "set.inter_subset_right" -> "data", "le_of_tendsto'" -> "topology", "measure_theory.to_measure_apply" -> "analysis", "nnreal.zero_rpow" -> "analysis", "matrix.dot_product_diagonal'" -> "data", "ring.fractional_ideal.sup_eq_add" -> "algebra", "bool.to_nat_le_to_nat" -> "data", "multiset.sub_eq_fold_erase" -> "data", "add_con.map_of_surjective_eq_map_gen" -> "algebra", "padic_seq.norm_eq" -> "data", "multiset.erase_dup_singleton" -> "data", "of_not_imp" -> "logic", "finset.prod_range_one" -> "algebra", "enat.with_top_equiv_lt" -> "data", "list.length_injective" -> "data", "div_le_iff_of_nonneg_of_le" -> "algebra", "turing.partrec_to_TM2.tr_normal_respects" -> "computability", "list.map_filter_map_of_inv" -> "data", "submodule.sup_orthogonal_of_is_complete" -> "analysis", "list.lex.append_right" -> "data", "set.ext_iff" -> "data", "hyperreal.coe_bit0" -> "data", "quadratic_form.to_matrix_smul" -> "algebra", "finset.card_bind_le" -> "algebra", "circle_deg1_lift.map_nat_add" -> "dynamics", "cardinal.add_le_add_left" -> "set_theory", "asymptotics.is_O_with.sub_is_o" -> "analysis", "convex_hull_to_cone_is_least" -> "analysis", "int.zero_add" -> "init", "lie_algebra.direct_sum.bracket_apply" -> "algebra", "multiset.nat.mem_antidiagonal" -> "data", "measure_theory.outer_measure.mono'" -> "analysis", "pmf.tsum_coe" -> "analysis", "finset.comp_sup_eq_sup_comp_of_is_total" -> "data", "submonoid.prod_mono" -> "algebra", "list.erase_cons_subperm_cons_erase" -> "data", "category_theory.limits.fork.of_\[Iota]_app_zero" -> "category_theory", "has_fderiv_within_at.add_const" -> "analysis", "has_mfderiv_within_at_inter" -> "geometry", "equiv.apply_symm_apply" -> "data", "measure_theory.measure.regular.smul" -> "analysis", "finset.card_erase_of_mem" -> "data", "finset.sum_centroid_weights_eq_one_of_nonempty" -> "algebra", "nat.land_assoc" -> "data", "mvqpf.fix.mk_dest" -> "data", "pow_gcd_card_eq_one_iff" -> "algebra", "tsum_eq_sum" -> "topology", "finset.mem_map_of_mem" -> "data", "lie_zero" -> "algebra", "derivation.coe_fn_coe" -> "algebra", "multiset.fold_singleton" -> "data", "is_local_extr_on.inter" -> "topology", "push_neg.not_implies_eq" -> "tactic", "wseq.lift_rel_flatten" -> "data", "exists_mem_ne_zero_of_ne_bot" -> "algebra", "int.to_nat_zero_of_neg" -> "data", "has_strict_fderiv_at.to_local_homeomorph_coe" -> "analysis", "with_top.le_coe" -> "order", "local_homeomorph.restr_open_source" -> "topology", "multiset.rel.add" -> "data", "padic_int.mk_units_eq" -> "data", "Cauchy.pure_cauchy_dense" -> "topology", "cardinal.mk_range_le" -> "set_theory", "associates.prod_le_prod" -> "algebra", "has_deriv_at.cos" -> "analysis", "bit0_pos" -> "algebra", "stream.mem_cons_of_mem" -> "data", "nat.lt_of_lt_pred" -> "data", "qpf.fix.ind_rec" -> "data", "ring.direct_limit.of_one" -> "algebra", "list.exists_le_of_sum_le" -> "data", "nat.mul_dvd_mul_iff_left" -> "data", "continuous_dist" -> "topology", "polynomial.continuous_on" -> "analysis", "smul_inv" -> "algebra", "category_theory.biprod.of_components_fst" -> "category_theory", "set.lt_eq_ssubset" -> "data", "pow_le_one_of_le_one" -> "algebra", "lipschitz_with.edist_lt_top" -> "topology", "set.nonempty_Ico_sdiff" -> "data", "free_ring.lift_comp_of" -> "algebra", "filter.tendsto.comp" -> "order", "filter.lift'_mono" -> "order", "order.sequence_of_cofinals.monotone" -> "order", "irrational_add_rat_iff" -> "data", "exists_lt_mul_self" -> "algebra", "nat.mul_lt_mul_of_pos_right" -> "init", "irrational.of_mul_rat" -> "data", "valuation.map_neg_one" -> "algebra", "category_theory.limits.biprod.inr_snd_assoc" -> "category_theory", "opposite.op_neg" -> "algebra", "prime_spectrum.zero_locus_empty_of_one_mem" -> "algebraic_geometry", "mul_self_lt_mul_self" -> "algebra", "measurable_space.is_measurable_Inf" -> "analysis", "div_self_of_invertible" -> "algebra", "uniform_continuous_subtype_mk" -> "topology", "category_theory.limits.types.terminal_from" -> "category_theory", "quadratic_form.polar_smul_left" -> "algebra", "ideal.le_comap_mul" -> "algebra", "set.image2_empty_right" -> "data", "div_mul_right" -> "algebra", "mv_polynomial.mem_restrict_degree" -> "algebra", "half_add_self" -> "algebra", "zorn.zorn_subset" -> "order", "submonoid.map_bot" -> "algebra", "not_forall_of_exists_not" -> "logic", "set.preimage_id'" -> "data", "multiset.mem_cons_self" -> "data", "lie_algebra.equiv.of_subalgebra_apply" -> "algebra", "polynomial.differentiable_at" -> "analysis", "eq_of_nhds_ne_bot" -> "topology", "finset.sup_lt_iff" -> "data", "polynomial.eq_X_add_C_of_degree_eq_one" -> "data", "char.vne_of_ne" -> "init", "sequential_closure_subset_closure" -> "topology", "pow_succ'" -> "algebra", "cardinal.one_le_bit0" -> "set_theory", "compact_open_separated_mul" -> "topology", "fin.lt_def" -> "init", "nat.coprime.gcd_left" -> "data", "int.coe_nat_lt_coe_nat_of_lt" -> "init", "measure_theory.simple_func.fin_meas_supp.of_lintegral_lt_top" -> "analysis", "fderiv_within_sum" -> "analysis", "nat.mul_succ" -> "init", "real.continuous_rpow_aux1" -> "analysis", "nnnorm_eq_zero" -> "analysis", "category_theory.comma.id_left" -> "category_theory", "upper_bounds_Ioc" -> "order", "bilin_form.is_adjoint_pair.mul" -> "algebra", "convex_cone.salient_of_blunt" -> "analysis", "bilin_form.is_adjoint_pair.smul" -> "algebra", "powers_hom_symm_apply" -> "algebra", "equiv.set.sum_compl_symm_apply_of_mem" -> "data", "finset.fold_insert_idem" -> "data", "uniform_space.completion.continuous_extension" -> "topology", "measure_theory.ae_eq_fun.neg_mk" -> "analysis", "lt_irrefl" -> "init", "finset.subtype_map_of_mem" -> "data", "add_commute.left_comm" -> "algebra", "gsmul_one" -> "algebra", "zmod.legendre_sym_eq_one_or_neg_one" -> "number_theory", "finset.fold_union_empty_singleton" -> "data", "measure_theory.integrable_of_dominated_convergence" -> "analysis", "dist_partial_sum_le_of_le_geometric" -> "analysis", "set.ball_insert_iff" -> "data", "list.length_enum" -> "data", "dense_inducing.mk'" -> "topology", "char_poly_degree_eq_dim" -> "algebra", "list.Ico.pred_singleton" -> "data", "units.zero_lt" -> "algebra", "zorn.super_of_not_max" -> "order", "subtype.range_coe_subtype" -> "data", "filter.lift'_pure" -> "order", "prod.snd_one" -> "algebra", "set.diff_subset_comm" -> "data", "nat.rfind_opt_spec" -> "computability", "lcm_units_coe_right" -> "algebra", "upper_bounds_insert" -> "order", "holor.cprank_max_upper_bound" -> "data", "integral_domain.to_is_integral_domain" -> "algebra", "num.add_to_nat" -> "data", "norm_eq_infi_iff_inner_le_zero" -> "analysis", "complex.nat_cast_im" -> "data", "principal_seg.of_element_top" -> "set_theory", "hyperreal.infinite_of_infinitesimal_inv" -> "data", "category_theory.arrow.lift_mk'_right_assoc" -> "category_theory", "set.image_add_const_Ico" -> "data", "is_max_on.inf" -> "order", "matrix.det_zero_of_column_eq" -> "algebra", "semiquot.mem_blur'" -> "data", "functor.map_equiv_apply" -> "data", "pos_num.pred_to_nat" -> "data", "set.eq_on.image_eq" -> "data", "digits_lt_base'" -> "data", "eq_add_cosets_of_normal" -> "algebra", "is_preconnected_closed_iff" -> "topology", "field.subset_closure" -> "algebra", "smooth_mul" -> "geometry", "computation.terminates_of_mem" -> "data", "pgame.nim.sum_first_wins_iff_neq" -> "set_theory", "category_theory.discrete.nat_iso_inv_app" -> "category_theory", "filter.ne_bot.nonempty_of_mem" -> "order", "is_order_right_adjoint_Sup" -> "order", "list.perm_repeat" -> "data", "nat.bit0_succ_eq" -> "init", "game.le_antisymm" -> "set_theory", "quotient.exists_rep" -> "init", "lucas_lehmer.X.coe_nat" -> "number_theory", "structure_groupoid.local_invariant_prop.lift_prop_within_at_congr_iff_of_eventually_eq" -> "geometry", "inf_sup_self" -> "order", "onote.zero_mul" -> "set_theory", "int.neg_mul_comm" -> "init", "category_theory.limits.biprod.braiding_map_braiding" -> "category_theory", "ordinal.succ_inj" -> "set_theory", "filter.comap_eq_of_inverse" -> "order", "add_units.is_add_unit_add_add_units" -> "algebra", "inv_involutive" -> "algebra", "differentiable_at.neg" -> "analysis", "ring_equiv.map_eq_zero_iff" -> "data", "linarith.int.coe_nat_mul_one" -> "tactic", "int.neg_neg_of_nat_succ" -> "init", "set.inter_right_comm" -> "data", "wseq.exists_of_lift_rel_right" -> "data", "option.bind_assoc" -> "data", "localization_map.ring_equiv_of_ring_equiv_eq" -> "algebra", "category_theory.zero_mul_inv" -> "category_theory", "vector.to_list_injective" -> "data", "is_greatest_Ioc" -> "order", "fin.cons_succ" -> "data", "measure_theory.integral_nonneg_of_ae" -> "analysis", "fin.cast_succ_injective" -> "data", "equiv.bijective" -> "data", "nonneg_add_comm_group.nonneg_total_iff" -> "algebra", "convex.norm_image_sub_le_of_norm_fderiv_le" -> "analysis", "category_theory.limits.walking_pair.swap_symm_apply_ff" -> "category_theory", "measure_theory.measure.conj_conj" -> "analysis", "abs_inv" -> "algebra", "norm_num.adc_one_one" -> "tactic", "mdifferentiable_at_atlas_symm" -> "geometry", "category_theory.functor.map_iso_trans" -> "category_theory", "primrec\:2082.right" -> "computability", "measure_theory.integrable_on.mono" -> "analysis", "is_measurable.sUnion" -> "analysis", "polynomial.eval\:2082_eq_sum" -> "data", "iff_false_left" -> "logic", "joined_in.mono" -> "topology", "times_cont_mdiff_at.prod_map'" -> "geometry", "circle_deg1_lift.lt_map_of_nat_lt_translation_number" -> "dynamics", "lt_supr_iff" -> "order", "one_div_lt_one_div_of_lt" -> "algebra", "ennreal.to_real_rpow" -> "analysis", "ordinal.type_eq_zero_iff_empty" -> "set_theory", "set.preimage_const_add_Iio" -> "data", "imp_not_comm" -> "logic", "filter.map_sub_at_top_eq_nat" -> "order", "int.mul_lt_mul_of_neg_right" -> "init", "quotient_add_group.coe_zero" -> "algebra", "nsmul_add_comm'" -> "algebra", "real.exp_neg" -> "data", "measure_theory.simple_func.mem_range" -> "analysis", "filter.germ.const_top" -> "order", "with_top.some_le_some" -> "order", "opposite.unop_eq_zero_iff" -> "algebra", "finmap.keys_singleton" -> "data", "generalized_continued_fraction.continuants_aux_stable_step_of_terminated" -> "algebra", "has_fderiv_at.sub" -> "analysis", "nat.pred_lt" -> "init", "set.Union_neg" -> "data", "finmap.keys_replace" -> "data", "submodule.linear_proj_of_is_compl_idempotent" -> "algebra", "subgroup.le_normalizer_of_normal" -> "algebra", "category_theory.comma.fst_map" -> "category_theory", "list.nil_kunion" -> "data", "has_deriv_at_filter.is_O_sub" -> "analysis", "hyperreal.is_st_st_of_is_st" -> "data", "abs_pos_of_neg" -> "algebra", "zsqrtd.muld_val" -> "data", "category_theory.prod_id_snd" -> "category_theory", "continuous_within_at.congr" -> "topology", "is_local_min_on.comp_mono" -> "topology", "approximates_linear_on.surj_on_closed_ball" -> "analysis", "Mod.assoc_flip" -> "category_theory", "complex.cosh_of_real_re" -> "data", "filter.map_inf'" -> "order", "finmap.lift_on_to_finmap" -> "data", "homological_complex.d_squared" -> "algebra", "real.sin_nonpos_of_nonnpos_of_neg_pi_le" -> "analysis", "computation.terminates_congr" -> "data", "supr_eq_of_tendsto" -> "topology", "category_theory.limits.cofork.is_colimit.hom_ext" -> "category_theory", "frontier_le_subset_eq" -> "topology", "continuous_linear_map.coe_coprod" -> "topology", "list.take'_nil" -> "data", "int.mod_sub_cancel_right" -> "data", "set.sigma_to_Union_surjective" -> "data", "modeq_digits_sum" -> "data", "with_top.add_eq_top" -> "algebra", "subgroup.multiset_prod_mem" -> "algebra", "int.neg_succ_of_nat_mod" -> "data", "tangent_map_chart_symm" -> "geometry", "generalized_continued_fraction.of_correctness_at_top_of_terminates" -> "algebra", "nat.choose_succ_right_eq" -> "data", "directed.rel_sequence" -> "data", "measure_theory.measure.restrict_Union" -> "analysis", "con.mul_ker_mk_eq" -> "algebra", "ring_hom.coe_add_monoid_hom_injective" -> "algebra", "multiset.coe_foldr" -> "data", "ennreal.to_nnreal_sum" -> "data", "nnreal.coe_ne_zero" -> "data", "finsupp.sum_neg" -> "data", "linear_independent.mono" -> "algebra", "real.rpow_eq_zero_iff_of_nonneg" -> "analysis", "add_subgroup.coe_bot" -> "algebra", "equiv.set.union_apply_right" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_at_of_mem_maximal_atlas" -> "geometry", "linear_map.std_basis_apply" -> "algebra", "mv_polynomial.smul_eval" -> "data", "finsupp.prod_single_index" -> "data", "pgame.add_congr" -> "set_theory", "bernoulli_four" -> "number_theory", "ennreal.mul_Sup" -> "topology", "qpf.liftp_iff'" -> "data", "times_cont_diff_on_succ_iff_fderiv_within" -> "analysis", "equiv.perm.sign_inv" -> "algebra", "cardinal.sup_le" -> "set_theory", "filter.tendsto.basis_both" -> "order", "subsemiring.coe_bot" -> "algebra", "nat.lt_of_le_and_ne" -> "init", "vsub_sub_vsub_cancel_right" -> "algebra", "cau_seq.lim_zero_sub_rev" -> "data", "polynomial.coe_eval\:2082_ring_hom" -> "data", "premetric.metric_quot_dist_eq" -> "topology", "function.embedding.refl_apply" -> "logic", "measurable_space.map_infi" -> "analysis", "equiv.subtype_congr_right_mk" -> "data", "set.mem_interval_of_le" -> "data", "filter.frequently.exists" -> "order", "nnreal.coe_div" -> "data", "ereal.le_neg_of_le_neg" -> "data", "gcd_assoc" -> "algebra", "local_homeomorph.continuous_on_iff_continuous_on_comp_right" -> "topology", "lt_of_le_not_le" -> "init", "nat.bit1_inj" -> "init", "zero_smul" -> "algebra", "multiset.disjoint_of_nodup_add" -> "data", "div_lt_div_iff" -> "algebra", "fin.is_some_find_iff" -> "data", "le_top" -> "order", "times_cont_mdiff.prod_mk" -> "geometry", "nat.cast_two" -> "data", "associates.prod_mono" -> "algebra", "zorn.chain_succ" -> "order", "ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem" -> "algebra", "cmp_compares" -> "algebra", "free_add_magma.map_of" -> "algebra", "is_min_on.sub" -> "order", "nat.partrec'.of_prim" -> "computability", "euclidean_domain.gcd_eq_gcd_ab" -> "algebra", "or_eq_of_eq_false_right" -> "init", "nat.partrec.code.evaln_mono" -> "computability", "min_le_min" -> "algebra", "euclidean_domain.div_zero" -> "algebra", "equiv.mul_left_symm" -> "data", "comp_le_comp_left_of_monotone" -> "order", "euclidean_geometry.reflection_reflection" -> "geometry", "function.semiconj\:2082.id_left" -> "logic", "nsmul_sub" -> "algebra", "eq_zero_of_mul_self_add_mul_self_eq_zero" -> "algebra", "is_measurable_Ici" -> "analysis", "asymptotics.is_O.congr_right" -> "analysis", "convex_halfspace_im_lt" -> "analysis", "free_magma.traverse_pure" -> "algebra", "real.sin_pi_div_four" -> "analysis", "sum.elim_inr" -> "data", "mv_polynomial.total_degree_rename_le" -> "data", "mv_polynomial.pderivative_eq_zero_of_not_mem_vars" -> "data", "differentiable_on.sin" -> "analysis", "interval_integral.norm_integral_eq_norm_integral_Ioc" -> "analysis", "computation.think_mem" -> "data", "is_unit_iff_forall_dvd" -> "algebra", "list.kreplace_self" -> "data", "ne.def" -> "init", "multiset.to_list_zero" -> "data", "num.cast_bit0" -> "data", "affine_map.coe_homothety_affine" -> "algebra", "nat.sub_zero" -> "init", "fin.update_cons_zero" -> "data", "neg_inj" -> "algebra", "subtype.tag_irrelevant" -> "init", "of_iff_true" -> "init", "zsqrtd.add_def" -> "data", "deriv_zero_of_not_differentiable_at" -> "analysis", "antilipschitz_with.to_right_inv_on'" -> "topology", "omega.nat.holds_nonneg_consts" -> "tactic", "list.traverse_eq_map_id" -> "control", "cardinal.mk_image_eq_lift" -> "set_theory", "is_R_or_C.norm_sq_eq_def'" -> "data", "pnat.prime.not_dvd_one" -> "data", "list.subperm_cons_diff" -> "data", "is_compl.to_order_dual" -> "order", "finset.sum_add_distrib" -> "algebra", "affine_subspace.mem_inf_iff" -> "algebra", "measure_theory.simple_func.integral_eq_integral" -> "analysis", "category_theory.abelian.pseudoelement.pseudo_injective_of_mono" -> "category_theory", "holor.cprank_max_nil" -> "data", "continuous_linear_map.differentiable_within_at" -> "analysis", "cardinal.aleph_idx.init" -> "set_theory", "list.map_concat" -> "data", "filter.map_eq_bot_iff" -> "order", "set.image_add_left'" -> "algebra", "polynomial.degree_mul_le" -> "data", "finset.surj_on_of_inj_on_of_card_le" -> "data", "hyperreal.infinite_pos_of_tendsto_top" -> "data", "multiset.count_le_of_le" -> "data", "ultrafilter_is_open_basic" -> "topology", "has_fderiv_within_at.const_add" -> "analysis", "array.mem_rev_list_aux" -> "data", "zorn.chain_closure_closure" -> "order", "num.shiftr_to_nat" -> "data", "ring_hom.eq_lift_of_surjective" -> "algebra", "is_compl.antimono" -> "order", "category_theory.limits.cokernel_comp_is_iso_inv" -> "category_theory", "category_theory.cokernel_zero_of_nonzero_to_simple" -> "category_theory", "finset.piecewise_univ" -> "data", "complex.abs_im_div_abs_le_one" -> "data", "padic_seq.ne_zero_iff_nequiv_zero" -> "data", "asymptotics.is_O.prod_left" -> "analysis", "lt_or_le" -> "algebra", "or_true" -> "init", "qpf.supp_eq_of_is_uniform" -> "data", "normalize_coe_units" -> "algebra", "ennreal.lt_iff_exists_nnreal_btwn" -> "data", "add_subgroup.coe_inf" -> "algebra", "turing.tape.nth_zero" -> "computability", "polynomial.X_sub_C_mul_remove_factor" -> "algebra", "list.forall\:2082_drop" -> "data", "nat.cast_eq_zero" -> "algebra", "computation.lift_rel_congr" -> "data", "nat.multiplicity_eq_card_pow_dvd" -> "data", "sum.swap_swap_eq" -> "data", "measurable.is_glb" -> "analysis", "list.nth_range'" -> "data", "turing.pointed_map.map_pt" -> "computability", "neg_add_cancel_left" -> "algebra", "not_imp_not" -> "logic", "add_lt_add_right" -> "algebra", "cardinal.zero_power" -> "set_theory", "int.eq_mul_div_of_mul_eq_mul_of_dvd_left" -> "data", "subring.closure_eq_of_le" -> "algebra", "continuous_linear_map.op_norm_comp_le" -> "analysis", "int.mod_nonneg" -> "data", "continuous_linear_map.coe_cod_restrict" -> "topology", "set.image_image" -> "data", "pnat.gcd_eq" -> "data", "add_submonoid.localization_map.map_comp" -> "algebra", "subgroup.coe_inv" -> "algebra", "lcm_one_right" -> "algebra", "list.map_filter_eq_foldr" -> "data", "le_total" -> "init", "complex.linear_map.coe_re" -> "data", "locally_finite_iff_exists_realizer" -> "data", "multiset.bind_assoc" -> "data", "dfinsupp.mem_support_to_fun" -> "data", "sub_lt_of_sub_lt" -> "algebra", "topological_space.opens.supr_s" -> "topology", "complex.of_real_sin_of_real_re" -> "data", "list.rel_perm_imp" -> "data", "multiset.ndunion_le_add" -> "data", "category_theory.limits.is_equivalence_preserves_zero_morphisms" -> "category_theory", "filter.Limsup_le_Limsup_of_le" -> "order", "mv_polynomial.monic_monomial_eq" -> "data", "nat.coprime.gcd_mul_left_cancel_right" -> "data", "set.insert_nonempty" -> "data", "continuous_on_inv" -> "topology", "roption.ret_eq_some" -> "data", "matrix.special_linear_group.ext" -> "algebra", "measure_theory.ae_eq_fun.induction_on\:2083" -> "analysis", "wseq.of_list_cons" -> "data", "localization_map.mk'_mul_cancel_right" -> "algebra", "nnreal.add_halves" -> "data", "monotone.const_mul" -> "algebra", "ring.direct_limit.of_neg" -> "algebra", "add_monoid_algebra.coe_algebra_map" -> "data", "complex.norm_rat" -> "analysis", "inner_mul_inner_self_le" -> "analysis", "exists_lt_of_cinfi_lt" -> "order", "category_theory.limits.pushout_cocone.mk_X" -> "category_theory", "bilin_form.coe_fn_congr" -> "algebra", "ideal.is_maximal.is_prime" -> "algebra", "subtype.coe_eta" -> "data", "has_fderiv_at.neg" -> "analysis", "cardinal.sup_lt_ord_of_is_regular" -> "set_theory", "multiset.bind_bind" -> "data", "uniform_space.uniform_continuous_quotient_mk" -> "topology", "submodule.sum_smul_mem" -> "algebra", "vsub_left_cancel_iff" -> "algebra", "finset.card_le_one_of_subsingleton" -> "data", "list.tendsto_insert_nth" -> "topology", "rel_iso.apply_symm_apply" -> "order", "finset.sdiff_subset_sdiff" -> "data", "generalized_continued_fraction.ext_iff" -> "algebra", "traversable.foldr_map" -> "control", "submonoid.mem_sup" -> "algebra", "cardinal.lift_eq_nat_iff" -> "set_theory", "ordinal.type_out" -> "set_theory", "ordinal.cof_le_card" -> "set_theory", "is_local_extr.comp_antimono" -> "topology", "units.mul_left_eq_zero" -> "algebra", "measure_theory.simple_func.lintegral_sum" -> "analysis", "inv_div_left" -> "algebra", "set.univ_inv" -> "algebra", "normal_of_compact_t2" -> "topology", "list.prod_hom" -> "data", "continuous.continuous_at" -> "topology", "int.lt_sub_right_of_add_lt" -> "init", "list.subperm.countp_le" -> "data", "has_strict_deriv_at_neg" -> "analysis", "fintype.univ_bool" -> "data", "fderiv_smul_algebra_const" -> "analysis", "set.image_preimage_subset" -> "data", "category_theory.monoidal_functor.comp_\[CurlyEpsilon]_is_iso" -> "category_theory", "set.surj_on.inter" -> "data", "measurable_space.le_map_comap" -> "analysis", "nat.modeq.modeq_mul_right'" -> "data", "measure_theory.simple_func.bind_apply" -> "analysis", "category_theory.limits.pushout_cocone.mk_inl" -> "category_theory", "roption.ext'" -> "data", "set.indicator_finset_sum" -> "data", "nat.div_div_div_eq_div" -> "data", "finsupp.smul_single" -> "data", "add_submonoid.localization_map.ext" -> "algebra", "order.mem_ideal_of_cofinals" -> "order", "wseq.lift_rel_destruct" -> "data", "associates.prod_top" -> "algebra", "nat.dvd_of_pow_dvd" -> "data", "Set.ext" -> "set_theory", "measure_theory.integral_add_compl" -> "analysis", "computation.equiv.equivalence" -> "data", "add_submonoid.forall" -> "algebra", "real.exp_pos" -> "data", "zmod.pow_div_two_eq_neg_one_or_one" -> "number_theory", "polynomial.derivative_eval\:2082_C" -> "data", "free_group.red.exact" -> "algebra", "continuous_quotient_mk" -> "topology", "mul_div_mul_right" -> "algebra", "nat.partrec.code.evaln_complete" -> "computability", "measurable_space.generate_from_sup_generate_from" -> "analysis", "nat.prime.multiplicity_one" -> "data", "add_submonoid.coe_prod" -> "algebra", "has_fderiv_within_at.continuous_within_at" -> "analysis", "has_deriv_at_filter.const_add" -> "analysis", "list.chain_singleton" -> "data", "list.map_erase" -> "data", "filter.tendsto_iff_rtendsto'" -> "order", "category_theory.equivalence.pow_one" -> "category_theory", "continuous_extend_from" -> "topology", "interior_mem_uniformity" -> "topology", "finset.filter_union_right" -> "data", "uniform_continuous_uniformly_extend" -> "topology", "list.mem_insert_nth" -> "data", "digits_zero_succ" -> "data", "sym_sesq_form.ortho_sym" -> "algebra", "polynomial.coeff_nat_degree_eq_zero_of_degree_lt" -> "data", "polynomial.fderiv_within" -> "analysis", "interval_integral.integral_smul" -> "analysis", "digits_len_le_digits_len_succ" -> "data", "with_zero.coe_mul" -> "algebra", "mvqpf.const.get_map" -> "data", "int.eq_of_mul_eq_mul_right" -> "init", "functor.comp.applicative_comp_id" -> "control", "Set.mem_insert" -> "set_theory", "submodule.mem_sup'" -> "algebra", "filter.ptendsto_iff_rtendsto" -> "order", "turing.partrec_to_TM2.head_main_ok" -> "computability", "ennreal.add_ne_top" -> "data", "has_fderiv_within_at.nhds_within" -> "analysis", "game.add_assoc" -> "set_theory", "filter.rcomap'_compose" -> "order", "wseq.lift_rel_think_left" -> "data", "dfinsupp.prod_map_range_index" -> "data", "cardinal.mul_lt_omega" -> "set_theory", "subsemiring.map_le_iff_le_comap" -> "algebra", "bounded_continuous_function.norm_eq" -> "topology", "quotient_group.eq" -> "algebra", "and_not_self" -> "init", "path.of_line_mem" -> "topology", "continuous_linear_map.has_strict_fderiv_at" -> "analysis", "mul_equiv.to_equiv_symm" -> "data", "znum.cast_inj" -> "data", "alt_sesq_form.self_eq_zero" -> "algebra", "int.zero_shiftl" -> "data", "Set.mem_Union" -> "set_theory", "int.units_pow_two" -> "algebra", "category_theory.adjunction.cones_iso_component_hom_app" -> "category_theory", "preorder_hom.ext" -> "order", "joined_in.target_mem" -> "topology", "add_submonoid.localization_map.mk'_eq_iff_mk'_eq" -> "algebra", "is_compact.exists_is_lub" -> "topology", "set.bUnion_empty" -> "data", "ennreal.coe_nonneg" -> "data", "commute.units_inv_right_iff" -> "algebra", "submonoid.mem_inf" -> "algebra", "int.nat_abs_of_neg_succ_of_nat" -> "init", "finset.Ico.subset" -> "data", "add_lt_add_iff_right" -> "algebra", "omega.nat.sub_subst_equiv" -> "tactic", "nhds_within_Iic_self_ne_bot" -> "topology", "norm_norm" -> "analysis", "list.update_nth_length" -> "data", "category_theory.limits.biproduct.\[Iota]_\[Pi]_ne" -> "category_theory", "measure_theory.simple_func.restrict_preimage_singleton" -> "analysis", "is_group_hom.comp" -> "algebra", "mul_equiv.coe_symm_mk" -> "data", "ennreal.le_div_iff_mul_le" -> "data", "pgame.winner_cases" -> "set_theory", "add_submonoid.coe_comap" -> "algebra", "nat.add_div_eq_of_add_mod_lt" -> "data", "typevec.cases_cons_append1" -> "data", "complex.sin_add" -> "data", "category_theory.arrow.lift.fac_left" -> "category_theory", "computation.think_equiv" -> "data", "times_cont_mdiff_on_id" -> "geometry", "equiv.neg_symm" -> "data", "finmap.keys_union" -> "data", "tendsto_finset_prod" -> "topology", "measure_theory.regular_conj_iff" -> "analysis", "pos_num.mul_to_nat" -> "data", "uliftable.up_down" -> "control", "nat.zero_of_test_bit_eq_ff" -> "data", "with_zero.zero_le" -> "algebra", "subgroup.map_map" -> "algebra", "ideal.quotient.eq_zero_iff_mem" -> "algebra", "set.down_up" -> "algebra", "irrational.rat_add" -> "data", "filter.mem_or_compl_mem_of_ultrafilter" -> "order", "denumerable.denumerable_list_aux" -> "data", "monotone_gfp" -> "order", "sub_sub_sub_cancel_right" -> "algebra", "padic_norm_z.padic_norm_z_of_int" -> "data", "char.zero_lt_d800" -> "init", "rat.denom_neg_eq_denom" -> "data", "function.injective.nontrivial" -> "logic", "decidable.forall_or_distrib_left" -> "logic", "polynomial.splitting_field_aux.succ" -> "algebra", "multiset.ndinsert_of_mem" -> "data", "Lim_nhds" -> "topology", "finset.not_mem_sdiff_of_mem_right" -> "data", "continuous_linear_map.range_prod_eq" -> "topology", "associates.out_top" -> "algebra", "real.cos_int_mul_two_pi_add_pi" -> "analysis", "finset.center_mass_subset" -> "analysis", "tangent_bundle.smooth_at_proj" -> "geometry", "cardinal.mk_compl_eq_mk_compl_finite_lift" -> "set_theory", "inner_product_geometry.angle_zero_right" -> "geometry", "free_group.red.to_append_iff" -> "algebra", "mul_self_eq_zero" -> "algebra", "list.range'_sublist_right" -> "data", "equiv.tsum_eq_tsum_of_support" -> "topology", "nat.cast_dvd_char_zero" -> "algebra", "polynomial.has_strict_deriv_at" -> "analysis", "multiset.disjoint_left" -> "data", "list.maximum_eq_none" -> "data", "algebra_map_isometry" -> "topology", "associates.eq_of_factors_eq_factors" -> "algebra", "cluster_pt_iff" -> "topology", "bot_inf_eq" -> "order", "complex.smul_re" -> "data", "abelianization.commutator_subset_ker" -> "algebra", "le_div_iff_of_neg" -> "algebra", "le_sup_left" -> "order", "hyperreal.is_st_neg" -> "data", "div_lt_one" -> "algebra", "finset.inter_eq_inter_of_sdiff_eq_sdiff" -> "data", "measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto" -> "analysis", "Mod.id_hom'" -> "category_theory", "nat.modeq.modeq_add_cancel_right" -> "data", "fderiv_within_const_add" -> "analysis", "lt_mul_of_one_lt_right'" -> "algebra", "finset.weighted_vsub_empty" -> "algebra", "free_group.pure_bind" -> "algebra", "list.sublists'_aux_eq_sublists'" -> "data", "function.semiconj.inverses_right" -> "logic", "inner_product_geometry.angle_neg_left" -> "geometry", "pred_ne_self" -> "algebra", "omega.coeffs.val_between_set" -> "tactic", "padic_seq.not_equiv_zero_const_of_nonzero" -> "data", "circle_deg1_lift.translation_number_eq_of_tendsto\:2080" -> "dynamics", "subring.in_closure.rec_on" -> "algebra", "equiv.coe_fn_injective" -> "data", "lucas_lehmer.X.nat_coe_snd" -> "number_theory", "ext_chart_at_source" -> "geometry", "ordinal.power_pos" -> "set_theory", "nat.dvd_add_right" -> "data", "measure_theory.lintegral_const_mul" -> "analysis", "affine_subspace.le_def'" -> "algebra", "finsupp.range_restrict_dom" -> "algebra", "alist.lookup_insert" -> "data", "tendsto_indicator_of_monotone" -> "order", "filter.eventually_le.trans_eq" -> "order", "finset.powerset_len_mono" -> "data", "bool.coe_to_bool" -> "data", "is_local_min.has_deriv_at_eq_zero" -> "analysis", "convex.mem_Ioo" -> "analysis", "associates.quotient_mk_eq_mk" -> "algebra", "nat.mul_dvd_of_dvd_div" -> "data", "typevec.eq_of_drop_last_eq" -> "data", "measurable_space.comap_generate_from" -> "analysis", "has_fderiv_at.comp_has_deriv_within_at" -> "analysis", "topological_space.compacts.ext" -> "topology", "polynomial.coeff_C_mul" -> "data", "finsupp.prod_subtype_domain_index" -> "data", "measure_theory.measure.restrict_empty" -> "analysis", "list.insert_nth_remove_nth_of_ge" -> "data", "fintype.card_le_one_iff" -> "data", "pfunctor.M.bisim" -> "data", "times_cont_diff_on_zero" -> "analysis", "ideal.map_id" -> "algebra", "computable.sum_inl" -> "computability", "list.append_left_inj" -> "data", "prime_multiset.coe_nat_prime" -> "data", "rat.denom_div_eq_of_coprime" -> "data", "monoid_algebra.single_one_comm" -> "data", "polynomial.is_unit_or_eq_zero_of_separable_expand" -> "algebra", "and.imp_right" -> "logic", "bounded_std_simplex" -> "analysis", "int.div_pos_of_pos_of_dvd" -> "data", "mul_left_cancel_iff" -> "algebra", "cardinal.lift_lift" -> "set_theory", "metric.ediam_le_of_forall_dist_le" -> "topology", "pfunctor.comp_map" -> "data", "smooth.neg" -> "geometry", "is_scalar_tower.algebra_map_apply" -> "algebra", "filter.germ.coe_coe_ring_hom" -> "order", "measure_theory.measure.le_iff'" -> "analysis", "path.cast_coe" -> "topology", "set.mem_Inter_of_mem" -> "data", "enorm.ext" -> "analysis", "set.inter_assoc" -> "data", "nat.prime.multiplicity_fact" -> "data", "le_generate_from_iff_subset_is_open" -> "topology", "category_theory.eq_whisker" -> "category_theory", "is_R_or_C.int_cast_im" -> "data", "nat.gcd_rec" -> "init", "finset.image_empty" -> "data", "filter.Liminf_le_Liminf" -> "order", "list.maximum_concat" -> "data", "computable.of_option" -> "computability", "set.bijective_iff_bij_on_univ" -> "data", "metric.to_inductive_limit_commute" -> "topology", "category_theory.whisker_left_id" -> "category_theory", "submonoid.closure_univ" -> "algebra", "list.alternating_prod_eq_finset_prod" -> "data", "matrix.head_zero" -> "data", "monoid_algebra.single_one_mul_apply" -> "data", "monotone.iterate_le_of_le" -> "order", "continuous_linear_map.op_norm_smul_le" -> "analysis", "ring_equiv.coe_add_equiv" -> "data", "nat.primrec.cases" -> "computability", "mv_polynomial.as_sum" -> "data", "directed_of_inf" -> "order", "filter.mem_pure_sets" -> "order", "nnreal.div_add_div_same" -> "data", "finset.sup_insert" -> "data", "sub_left_inj" -> "algebra", "max_le_add_of_nonneg" -> "algebra", "submonoid.prod_mem" -> "algebra", "associates.factors_mono" -> "algebra", "inf_eq_bot_iff_le_compl" -> "order", "int.eq_mul_of_div_eq_right" -> "data", "padic_val_nat_one" -> "data", "multiset.map_add" -> "data", "is_max_filter.congr" -> "order", "associates.mk_mul_mk" -> "algebra", "linear_equiv.dim_eq" -> "algebra", "multiset.eq_union_right" -> "data", "metric.diam_ball" -> "topology", "polynomial.degree_le_mul_left" -> "data", "category_theory.of_type_functor_obj" -> "category_theory", "continuous_linear_map.curry_uncurry_left" -> "analysis", "bitraversable.tfst_tsnd" -> "control", "finset.bdd_below" -> "data", "fintype.card_fun" -> "data", "isometric.coe_neg" -> "topology", "is_coprime.prod_right" -> "algebra", "ordinal.type_le" -> "set_theory", "alg_hom.coe_mk" -> "algebra", "nat.bit1_succ_eq" -> "init", "category_theory.eq_of_comp_left_eq" -> "category_theory", "submodule.fg_bot" -> "algebra", "tensor_product.comm_tmul" -> "algebra", "csupr_le_csupr" -> "order", "subgroup.mem_comap" -> "algebra", "differentiable_at_inv" -> "analysis", "hyperreal.zero_iff_infinitesimal_real" -> "data", "pell.yz_succ_succ" -> "number_theory", "eventually_nhds_within_of_eventually_nhds" -> "topology", "int.add_mul_div_right" -> "data", "continuous_mul_left" -> "topology", "nnreal.div_def" -> "data", "ordinal.mul_sub" -> "set_theory", "is_measurable.insert" -> "analysis", "times_cont_diff_within_at.times_cont_diff_on" -> "analysis", "category_theory.iso.to_equiv_comp" -> "category_theory", "multiset.coe_sigma" -> "data", "nat.sub_one" -> "init", "polynomial.degree_derivative_lt" -> "data", "list.nodup_erase_of_nodup" -> "data", "real.cos_nonpos_of_pi_div_two_le_of_le" -> "analysis", "is_compact.exists_forall_ge" -> "topology", "is_local_min.comp_continuous" -> "topology", "map_bind" -> "control", "filter.join_le" -> "order", "mv_power_series.coeff_inv_of_unit" -> "algebra", "circle_deg1_lift.dist_map_zero_lt_of_semiconj" -> "dynamics", "list.foldr_join" -> "data", "mv_polynomial.homogeneous_component_is_homogeneous" -> "algebra", "fin_enum.pi.mem_enum" -> "data", "equiv.sigma_equiv_prod_symm_apply" -> "data", "ennreal.le_of_forall_epsilon_le" -> "data", "set.Ico_disjoint_Ico" -> "data", "real.arctan_tan" -> "analysis", "isometric.const_vadd_zero" -> "analysis", "list.nth_le_update_nth_eq" -> "data", "list.reverse_revzip" -> "data", "submodule.map_smul'" -> "algebra", "ite_cast" -> "tactic", "pequiv.single_apply_of_ne" -> "data", "filter.has_basis.uniform_continuous_iff" -> "topology", "cluster_pt_principal_iff" -> "topology", "ennreal.zero_rpow_of_neg" -> "analysis", "computation.lift_rel.symm" -> "data", "ennreal.pow_pos" -> "data", "local_equiv.refl_coe" -> "data", "mem_of_is_glb_of_is_closed" -> "topology", "affine.simplex.ext" -> "algebra", "euclidean_geometry.orthogonal_projection_fn_eq" -> "geometry", "list.prod_singleton" -> "data", "list.mfoldl_eq_foldl" -> "data", "is_unit.mul_right_eq_zero" -> "algebra", "convex_convex_hull" -> "analysis", "cardinal.lift_univ" -> "set_theory", "list.cons_head_tail" -> "data", "filter.tendsto_lift'_powerset_mono" -> "order", "nat.lt_two_pow" -> "data", "mem_interior" -> "topology", "ctop.coe_mk" -> "data", "tendsto_pow_at_top_at_top_of_one_lt" -> "analysis", "multiset.zero_ndinter" -> "data", "has_deriv_at_real_of_complex" -> "analysis", "has_deriv_within_at.add" -> "analysis", "local_of_surjective" -> "algebra", "card_order_of_eq_totient_aux\:2082" -> "algebra", "abs_le_abs" -> "algebra", "is_R_or_C.abs_re_div_abs_le_one" -> "data", "eq_false" -> "init", "filter.ptendsto'_def" -> "order", "hash_map.valid.find_aux_iff" -> "data", "list.sublists'_aux_append" -> "data", "not.imp" -> "logic", "category_theory.sum.associator_map_inl_inl" -> "category_theory", "set.union_inter_distrib_left" -> "data", "differentiable.rpow_of_one_le" -> "analysis", "category_theory.limits.prod.triangle" -> "category_theory", "continuous_linear_map.coe_apply" -> "topology", "add_submonoid.localization_map.sec_spec'" -> "algebra", "padic_seq.norm_nonneg" -> "data", "prime_multiset.prod_smul" -> "data", "add_submonoid.map_bot" -> "algebra", "fin.succ_pos" -> "data", "ordinal.card_succ" -> "set_theory", "nat.add_sub_of_le" -> "init", "category_theory.comonad.coalgebra.hom.ext" -> "category_theory", "category_theory.monad.forget_creates_colimits.commuting" -> "category_theory", "inv_eq_iff_mul_eq_one" -> "algebra", "Inf_pair" -> "order", "category_theory.limits.pullback_cone.mk_snd" -> "category_theory", "quotient_add_group.open_coe" -> "topology", "is_closed_Union_of_locally_finite" -> "topology", "continuous_smul" -> "topology", "half_lt_self" -> "algebra", "mvqpf.cofix.bisim'" -> "data", "vector.traverse_eq_map_id" -> "data", "is_preirreducible.image" -> "topology", "zsqrtd.smul_val" -> "data", "multilinear_map.restr_norm_le" -> "analysis", "filter.map_add" -> "order", "add_monoid_hom.inr_apply" -> "algebra", "polynomial.coeff_nat_degree_succ_eq_zero" -> "data", "polynomial.degree_X_pow" -> "data", "polynomial.leading_coeff_add_of_degree_eq" -> "data", "deriv_cosh" -> "analysis", "subgroup.conjugates_of_set_subset_normal_closure" -> "algebra", "mv_polynomial.induction_on" -> "data", "cau_seq.bounded'" -> "data", "hyperreal.infinite_neg_add_not_infinite_pos" -> "data", "equiv.perm.disjoint_comm" -> "algebra", "function.commute.iterate_pos_eq_iff_map_eq" -> "order", "inv_lt'" -> "algebra", "cardinal.mk_Iio_real" -> "data", "ordinal.type_add" -> "set_theory", "pi.single_eq_same" -> "algebra", "int.mul_div_mul_of_pos_left" -> "data", "is_min_filter.inf" -> "order", "inner_product_geometry.angle_nonneg" -> "geometry", "ennreal.inv_top" -> "data", "uniform_space.completion.continuous_coe" -> "topology", "finset.bUnion_union" -> "data", "polynomial.eval\:2082_list_prod_noncomm" -> "data", "finsupp.supported_comap_lmap_domain" -> "algebra", "measure_theory.to_outer_measure_apply" -> "analysis", "has_strict_fderiv_at.approximates_deriv_on_open_nhds" -> "analysis", "max_eq_right_of_lt" -> "init", "multiplicity.finite_pow" -> "algebra", "continuous_linear_map.has_deriv_at_filter" -> "analysis", "nat.gcd_mul_left_left" -> "data", "is_max_filter.inf" -> "order", "list.eq_of_mem_map_const" -> "data", "bounded_continuous_function.norm_of_normed_group_le" -> "topology", "local_equiv.trans_assoc" -> "data", "dim_eq_zero" -> "algebra", "matrix.row_add" -> "data", "char_p.char_is_prime_or_zero" -> "algebra", "set.powerset_nonempty" -> "data", "measure_theory.inner_content_mono" -> "analysis", "measure_theory.measure.of_measurable_apply" -> "analysis", "monoid_hom.iterate_map_pow" -> "algebra", "subset_closure" -> "topology", "add_subgroup.mem_normalizer_iff" -> "algebra", "affine_subspace.exists_of_lt" -> "algebra", "norm_mul_le" -> "analysis", "set.image_sub_const_Icc" -> "data", "exists_open_singleton_of_fintype" -> "topology", "zmod.euler_criterion_units" -> "number_theory", "set.ssubset_iff_subset_ne" -> "data", "roption.of_option_dom" -> "data", "continuous_within_at_Ioo_iff_Ioi" -> "topology", "multiples.add_mem" -> "algebra", "equiv.punit_prod_apply" -> "data", "alist.to_finmap_entries" -> "data", "free_group.reduce.step.eq" -> "algebra", "pgame.equiv_iff_grundy_value_eq" -> "set_theory", "is_local_min_on.sup" -> "topology", "cauchy_seq_of_summable_dist" -> "topology", "primrec.ite" -> "computability", "univ_separated_iff" -> "topology", "filter.eventually.exists_mem" -> "order", "filter.hyperfilter_ne_bot" -> "order", "lie_algebra.equiv.refl_apply" -> "algebra", "tendsto_const_div_at_top_nhds_0_nat" -> "analysis", "matrix.is_unit_iff_is_unit_det" -> "algebra", "polynomial.coeff_expand" -> "algebra", "finset.insert.comm" -> "data", "measure_theory.ae_eq_fun.edist_mk_mk'" -> "analysis", "filter.eventually.prod_inr" -> "order", "algebraic_closure.to_splitting_field_eval_X_self" -> "algebra", "category_theory.over.construct_products.cones_equiv_inverse_obj_X" -> "category_theory", "mul_lt_mul_left_of_neg" -> "algebra", "differentiable_neg" -> "analysis", "continuous_finset_sum" -> "topology", "finset.insert_union_distrib" -> "data", "nnreal.rpow_sub" -> "analysis", "list.rotate_length" -> "data", "monotonicity.imp" -> "meta", "formal_multilinear_series.change_origin_summable_aux2" -> "analysis", "tactic.ring_exp.add_overlap_pf" -> "tactic", "inf_uniformity" -> "topology", "norm_num.add_bit0_bit1" -> "tactic", "ideal.mk_ker" -> "algebra", "submodule.liftq_mkq" -> "algebra", "finset.prod_Ico_id_eq_fact" -> "algebra", "pequiv.to_matrix_trans" -> "data", "seq1.join_map_ret" -> "data", "num.zneg_to_znum_neg" -> "data", "algebraic_geometry.PresheafedSpace.restrict_presheaf" -> "algebraic_geometry", "set.preimage_sub_const_Iic" -> "data", "euclidean_domain.lcm_dvd_iff" -> "algebra", "gaussian_int.to_complex_neg" -> "data", "convex.subset_to_cone" -> "analysis", "category_theory.limits.limit.hom_iso_hom" -> "category_theory", "category_theory.nat_iso.naturality_2" -> "category_theory", "is_open_interior" -> "topology", "units.max_coe" -> "algebra", "times_cont_diff.neg" -> "analysis", "set.sUnion_singleton" -> "data", "mv_polynomial.coeff_C_mul" -> "data", "not_imp_comm" -> "logic", "ball_mono" -> "topology", "strict_weak_order.not_lt_of_equiv" -> "init", "units.coe_pow" -> "algebra", "real.coe_fib_eq'" -> "data", "primrec.fin_succ" -> "computability", "matrix.col_empty" -> "data", "function.bijective_iff_has_inverse" -> "logic", "finset.Ico_\:2124.mem" -> "data", "computable.sum_cases" -> "computability", "int.modeq.modeq_add" -> "data", "is_bounded_bilinear_map.is_O_comp" -> "analysis", "pell.x_sub_y_dvd_pow" -> "number_theory", "to_mul_of_mul" -> "algebra", "tactic.ring_exp.mul_pf_prod_c" -> "tactic", "polynomial.coeff_mul_C" -> "data", "exists_int_gt" -> "algebra", "wseq.equiv.equivalence" -> "data", "subsingleton_of_zero_eq_one" -> "algebra", "list.foldr_with_index_aux_eq_foldr_with_index_aux_spec" -> "data", "computation.lift_rel_aux.ret_right" -> "data", "dist_sub_sub_le" -> "analysis", "is_least.nonempty" -> "order", "continuous_linear_map.coe_injective" -> "topology", "mem_nhds_within_Ici_iff_exists_Icc_subset" -> "topology", "measure_theory.outer_measure.is_caratheodory_sum" -> "analysis", "geom_gold_conj_is_sol_fib_rec" -> "data", "qpf.cofix.dest_corec" -> "data", "complex.arg_eq_arg_iff" -> "analysis", "nat.cond_to_bool_mod_two" -> "init", "function.involutive_iff_iter_2_eq_id" -> "logic", "cardinal.mul_def" -> "set_theory", "of_digits_zmodeq'" -> "data", "disjoint_nested_nhds" -> "topology", "stream.corec_eq" -> "data", "alg_hom.coe_monoid_hom_injective" -> "algebra", "nnreal.pow_arith_mean_le_arith_mean_pow" -> "analysis", "filter.map_inf" -> "order", "matrix.nonsing_inv_mul" -> "algebra", "is_coprime.of_prod_left" -> "algebra", "ring.fractional_ideal.eq_zero_iff" -> "algebra", "nnreal.coe_pow" -> "data", "measurable_const_smul_iff" -> "analysis", "primrec\:2082.unpaired" -> "computability", "nat.pow_dvd_pow_iff_le_right" -> "data", "metric.finite_approx_of_totally_bounded" -> "topology", "ring.fractional_ideal.map_mul" -> "algebra", "add_monoid_hom.map_nsmul" -> "algebra", "onote.mul_zero" -> "set_theory", "mv_power_series.trunc_one" -> "algebra", "algebra.subring_algebra_map_apply" -> "algebra", "linear_map.std_basis_ne" -> "algebra", "list.perm_iff_count" -> "data", "fraction_map.lift_mk'" -> "algebra", "wseq.nth_mem" -> "data", "free_group.prod.of" -> "algebra", "nat.add_lt_of_lt_sub_left" -> "data", "list.pairwise.imp_of_mem" -> "data", "Mod.comp_hom" -> "category_theory", "multiset.ndunion_eq_union" -> "data", "add_subgroup.closure_induction" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_within_at_congr" -> "geometry", "list.countp_filter" -> "data", "lcm_eq_left_iff" -> "algebra", "set.image_sInter_subset" -> "data", "linear_equiv.prod_symm" -> "algebra", "implicit_function_data.implicit_function_apply_image" -> "analysis", "localization.mul_equiv_of_quotient_mk'" -> "algebra", "set.eq_univ_of_forall" -> "data", "int.mod_def" -> "data", "linear_map.is_compl_of_proj" -> "algebra", "nndist_add_add_le" -> "analysis", "set.image_inter_preimage" -> "data", "set.Union_eq_Union_finset'" -> "data", "subsemiring.subset_closure" -> "algebra", "submonoid.coe_prod" -> "algebra", "cSup_empty" -> "order", "sum_inner" -> "analysis", "polynomial.eq_C_of_degree_le_zero" -> "data", "multiset.countp_eq_card_filter" -> "data", "forall_true_iff" -> "logic", "category_theory.has_hom.hom.unop_inj" -> "category_theory", "set.mem_union.elim" -> "data", "nat.dvd_gcd" -> "data", "quotient_group.coe_inv" -> "algebra", "finset.nonempty.image" -> "data", "filter.eventually_pure" -> "order", "stream.tails_eq" -> "data", "measure_theory.measure.ext_iff" -> "analysis", "uniform_continuous_def" -> "topology", "has_fpower_series_at.add" -> "analysis", "ordering.ite_eq_lt_distrib" -> "init", "imp_imp_imp" -> "logic", "filter.lift'_mono'" -> "order", "metric.emetric_closed_ball" -> "topology", "add_lt_of_lt_sub_left" -> "algebra", "polynomial.separable.of_mul_right" -> "algebra", "zsqrtd.sq_le_cancel" -> "data", "function.right_inverse.left_inverse" -> "logic", "set.surjective_iff_surj_on_univ" -> "data", "affine_subspace.span_empty" -> "algebra", "is_compl.le_left_iff" -> "order", "category_theory.monoidal_category.right_unitor_product_aux" -> "category_theory", "nonneg_of_mul_nonpos_left" -> "algebra", "continuous_linear_map.neg_apply" -> "topology", "int.sqrt_nonneg" -> "data", "norm_num.dvd_eq_int" -> "tactic", "subgroup.center_normal" -> "algebra", "matrix.special_linear_group.mul_val" -> "algebra", "is_unit.dvd_mul_right" -> "algebra", "multiset.erase_le_iff_le_cons" -> "data", "measure_theory.lebesgue_length_mono" -> "analysis", "mv_polynomial.vars_monomial" -> "data", "multiset.card_pi" -> "data", "nat.gcd_dvd_gcd_mul_left" -> "data", "open_add_subgroup.coe_subset" -> "topology", "topological_fiber_bundle_core.local_triv_symm_fst" -> "topology", "continuous_of_locally_uniform_approx_of_continuous" -> "topology", "finset.sum_subtype" -> "data", "nat.add_assoc" -> "init", "category_theory.over.construct_products.cones_equiv_inverse_map_hom" -> "category_theory", "principal_seg.coe_coe_fn'" -> "set_theory", "is_complete.complete_space_coe" -> "topology", "int.mul_neg_eq_neg_mul_symm" -> "init", "gpow_coe_nat" -> "algebra", "set.inf_eq_inter" -> "data", "category_theory.limits.cone_of_cocone_left_op_\[Pi]_app" -> "category_theory", "submonoid.comap_injective_of_surjective" -> "algebra", "is_add_subgroup.subset_add_normalizer" -> "algebra", "algebraic_geometry.SheafedSpace.comp_c_app" -> "algebraic_geometry", "complex.continuous_sinh" -> "analysis", "polynomial.nat_degree_le_nat_degree" -> "data", "holor.mul_zero" -> "data", "category_theory.equivalence.cancel_unit_inv_right" -> "category_theory", "subring.closure_Union" -> "algebra", "supr_pair" -> "order", "set.pairwise_on.on_injective" -> "data", "localization_map.mk'_spec" -> "algebra", "ring.fractional_ideal.fractional_of_subset_one" -> "algebra", "multiset.range_subset" -> "data", "multiset.count_sup" -> "data", "set.finite_mem_finset" -> "data", "eq_iff_true_of_subsingleton" -> "logic", "times_cont_diff.comp_times_cont_diff_at" -> "analysis", "nat.dist_self" -> "data", "list.modify_nth_tail_modify_nth_tail" -> "data", "norm_num.le_bit1_bit0" -> "tactic", "iff_not_comm" -> "logic", "nat.one_div_pos_of_nat" -> "data", "finset.sum_range_sub" -> "algebra", "iff.refl" -> "init", "deriv_sub_const" -> "analysis", "set.ord_connected_bInter" -> "data", "has_strict_fderiv_at.sum" -> "analysis", "turing.to_partrec.step_normal_then" -> "computability", "set.zero_subset" -> "algebra", "UniformSpace.extension_hom_val" -> "topology", "ring.direct_limit.of.zero_exact" -> "algebra", "finsupp.span_single_image" -> "algebra", "nat.modeq.modeq_mul" -> "data", "wseq.join_append" -> "data", "finsupp.map_range_single" -> "data", "neg_eq_iff_neg_eq" -> "algebra", "bernoulli_def" -> "number_theory", "dioph.ne_dioph" -> "number_theory", "category_theory.non_preadditive_abelian.lift_map" -> "category_theory", "enorm.map_zero" -> "analysis", "hyperreal.inv_epsilon_eq_omega" -> "data", "ring_hom.coe_monoid_hom_injective" -> "algebra", "category_theory.limits.prod_map_id_comp" -> "category_theory", "direct_sum.to_group.unique" -> "algebra", "add_equiv.to_AddMon_iso_hom" -> "algebra", "multiset.singleton_eq_singleton" -> "data", "pgame.lt_congr" -> "set_theory", "deriv_div_const" -> "analysis", "filter.eventually_eq.eq_of_nhds" -> "topology", "alg_equiv_iso_Algebra_iso_hom" -> "algebra", "rel.dom_inv" -> "data", "quot.induction_on\:2082" -> "data", "computation.lift_eq_iff_equiv" -> "data", "monotone.mul_const" -> "algebra", "decidable.imp_iff_not_or" -> "logic", "finset.filter_subset" -> "data", "pfun.core_mono" -> "data", "con.ker_lift_mk" -> "algebra", "con.Sup_eq_con_gen" -> "algebra", "directed.mono_comp" -> "order", "multiset.inf_cons" -> "data", "is_seq_compact.is_compact" -> "topology", "cau_seq.completion.of_rat_one" -> "data", "finset.mono_of_fin_injective" -> "data", "pythagorean_triple.gcd_dvd" -> "number_theory", "measure_theory.integrable_on_finset_union" -> "analysis", "inner_product_geometry.norm_sub_square_eq_norm_square_add_norm_square'" -> "geometry", "exists_nhds_square" -> "topology", "finset.prod_sigma" -> "algebra", "category_theory.limits.is_terminal.mono_from" -> "category_theory", "finsupp.lmap_domain_disjoint_ker" -> "algebra", "smooth_right_add" -> "geometry", "ite_eq_mem_std_simplex" -> "analysis", "is_bounded_linear_map.times_cont_diff" -> "analysis", "uniform_space.completion.extension_unique" -> "topology", "measure_theory.outer_measure.supr_apply" -> "analysis", "finset.image_to_finset" -> "data", "cardinal.denumerable_iff" -> "set_theory", "Cauchy.uniform_embedding_pure_cauchy" -> "topology", "nat.prime.multiplicity_mul" -> "data", "has_fderiv_at.of_local_left_inverse" -> "analysis", "times_cont_mdiff_on.prod_map" -> "geometry", "poly.one_eval" -> "number_theory", "char_poly_monic_of_nontrivial" -> "algebra", "is_add_submonoid_Union_of_directed" -> "algebra", "deriv.comp" -> "analysis", "category_theory.limits.coprod.hom_ext" -> "category_theory", "convex_cone.mem_top" -> "analysis", "tactic.abel.term_add_term" -> "tactic", "continuous_multilinear_map.norm_map_init_le" -> "analysis", "measure_theory.measure_ne_top" -> "analysis", "opposite.op_sub" -> "algebra", "padic_int.zmod_repr_lt_p" -> "data", "add_subgroup.comap_comap" -> "algebra", "generalized_continued_fraction.squash_seq_nth_of_lt" -> "algebra", "vector.nth_map" -> "data", "continuous_multilinear_map.uncurry_curry_left" -> "analysis", "emetric.ball_eq_empty_iff" -> "topology", "mvfunctor.liftr_def" -> "control", "le_refl" -> "init", "pequiv.single_mul_single_of_ne" -> "data", "euclidean_domain.xgcd_val" -> "algebra", "list.sublists_len_aux_eq" -> "data", "list.nodup_of_fn" -> "data", "list.subset_cons_of_subset" -> "init", "of_digits_digits_append_digits" -> "data", "set.set_of_exists" -> "data", "dfinsupp.ext" -> "data", "list.repeat_subset_singleton" -> "data", "le_csupr" -> "order", "tt_band" -> "init", "continuous_linear_map.coe_snd" -> "topology", "filter.has_basis.sup" -> "order", "primrec.unpair" -> "computability", "finset.singleton_iff_unique_mem" -> "data", "add_eq_of_eq_sub'" -> "algebra", "ennreal.sub_zero" -> "data", "setoid.Sup_def" -> "data", "strict_mono.mul_const" -> "algebra", "normed_space.norm_le_dual_bound" -> "analysis", "le_trans" -> "init", "gaussian_int.norm_nonneg" -> "data", "decidable.of_not_not" -> "init", "multiset.foldr_zero" -> "data", "le_of_eq" -> "init", "nat.choose_zero_succ" -> "data", "continuous_stone_cech_extend" -> "topology", "eqv_lt_iff_eq" -> "init", "finsupp.filter_apply_pos" -> "data", "int.lt.intro" -> "init", "supr_le_iff" -> "order", "nhds_basis_uniformity" -> "topology", "disjoint_sup_right" -> "order", "category_theory.discrete.functor_map" -> "category_theory", "nat.gcd_gcd_self_left_right" -> "data", "list.perm.subset" -> "data", "is_measurable.bUnion" -> "analysis", "zsqrtd.norm_int_cast" -> "data", "has_deriv_at.has_deriv_within_at" -> "analysis", "nnreal.add_sub_cancel'" -> "data", "linear_map.one_app" -> "algebra", "is_noetherian_of_surjective" -> "algebra", "metric.Hausdorff_dist_le_of_inf_dist" -> "topology", "mul_lt_of_le_one_of_lt" -> "algebra", "linear_independent_le_dim" -> "algebra", "dvd.intro" -> "algebra", "finmap.lookup_empty" -> "data", "subgroup.comap_infi" -> "algebra", "is_closed_frontier" -> "topology", "mul_action.eq_inv_smul_iff" -> "algebra", "sub_lt" -> "algebra", "measurable.piecewise" -> "analysis", "mvfunctor.id_map'" -> "control", "measure_theory.l1.simple_func.add_to_simple_func" -> "analysis", "list.pairwise_join" -> "data", "div_eq_of_eq_mul" -> "algebra", "add_con.comp_mk'_apply" -> "algebra", "num.dvd_to_nat" -> "data", "finset.sum_smul" -> "algebra", "interval_integrable.symm" -> "analysis", "uniform_space.completion.continuous_map" -> "topology", "ring.direct_limit.exists_of" -> "algebra", "localization_map.eq_iff_exists" -> "algebra", "interior_Ico" -> "topology", "nat.lt_sub_left_iff_add_lt" -> "data", "int.neg_mul_eq_neg_mul" -> "init", "is_bounded_linear_map.continuous" -> "analysis", "finmap.induction_on\:2083" -> "data", "semilattice_inf.ext_inf" -> "order", "has_fderiv_at.sum" -> "analysis", "is_min_on.is_local_min" -> "topology", "cau_seq.ext" -> "data", "local_homeomorph.source_preimage_target" -> "topology", "add_submonoid.localization_map.eq_mk'_iff_add_eq" -> "algebra", "list.nat.antidiagonal_zero" -> "data", "category_theory.limits.limit.map_\[Pi]_assoc" -> "category_theory", "open_subgroup.coe_inf" -> "topology", "ordinal.one_add_of_omega_le" -> "set_theory", "not_imp" -> "logic", "finset.mem_sup" -> "data", "computable.snd" -> "computability", "monoid_hom.prod_apply" -> "algebra", "filter.limsup_eq_infi_supr" -> "order", "list.nth_le_update_nth_of_ne" -> "data", "composition_as_set.mem_boundaries_iff_exists_blocks_sum_take_eq" -> "combinatorics", "affine_map.coe_comp" -> "algebra", "one_div_le_one_div" -> "algebra", "set.inter_distrib_left" -> "data", "frontier_Ioi" -> "topology", "simple_graph.edge_other_ne" -> "combinatorics", "set.image_neg_Iic" -> "data", "ring.fractional_ideal.coe_add" -> "algebra", "is_closed.mem_of_frequently_of_tendsto" -> "topology", "int.div_nonneg" -> "data", "mv_polynomial.eval\:2082_one" -> "data", "compact_iff_compact_space" -> "topology", "has_deriv_at.mul_const" -> "analysis", "nat.sqrt_le_self" -> "data", "matrix.dot_product_punit" -> "data", "polynomial.root_mul" -> "data", "submodule.to_add_submonoid_injective" -> "algebra", "is_coprime.of_mul_left_right" -> "algebra", "category_theory.comma.iso_mk_inv_right" -> "category_theory", "category_theory.non_preadditive_abelian.neg_add" -> "category_theory", "abelianization.hom_ext" -> "algebra", "primrec.sum_cases" -> "computability", "fpow_ne_zero" -> "algebra", "category_theory.monoidal_category.tensor_left_map" -> "category_theory", "with_zero.coe_le_coe" -> "algebra", "complex.cosh_add_sinh" -> "data", "nat.add_succ_sub_one" -> "data", "gt_mem_sets_of_Liminf_gt" -> "topology", "differentiable_within_at.rpow_of_one_le" -> "analysis", "set.preimage_compl" -> "data", "nat.factors_prime" -> "data", "cmp_using_eq_lt" -> "init", "norm_num.rat_cast_bit0" -> "tactic", "multiset.erase_dup_map_erase_dup_eq" -> "data", "circle_deg1_lift.floor_sub_le_translation_number" -> "dynamics", "ceil_zero" -> "algebra", "eq_mul_inv_iff_mul_eq" -> "algebra", "dioph.modeq_dioph" -> "number_theory", "metric.sphere_subset_closed_ball" -> "topology", "quadratic_eq_zero_iff_discrim_eq_square" -> "algebra", "mvqpf.Wequiv_map" -> "data", "tactic.ring2.horner_expr.cseval_atom" -> "tactic", "list.sublists_aux_eq_foldr" -> "data", "fin.forall_iff" -> "data", "ennreal.sub_le_iff_le_add'" -> "data", "function.involutive.surjective" -> "logic", "times_cont_mdiff.continuous_tangent_map" -> "geometry", "mul_eq_mul_prime_prod" -> "algebra", "pell.yn_add" -> "number_theory", "eq_rec_constant" -> "logic", "submonoid.localization_map.lift_mul_right" -> "algebra", "dense_iff_inter_open" -> "topology", "differentiable_within_at.congr" -> "analysis", "infi_inf_eq" -> "order", "measure_theory.ae_eq_fun.comp\:2082_eq_pair" -> "analysis", "computation.map_ret'" -> "data", "ring_hom.fst_comp_prod" -> "algebra", "finset.Ico.subset_iff" -> "data", "dfinsupp.support_smul" -> "data", "mk_of_closure_sets" -> "topology", "polynomial.nat_degree_comp" -> "data", "finite_dimensional.dim_lt_omega" -> "algebra", "category_theory.whisker_left_id'" -> "category_theory", "mem_nhds_within" -> "topology", "multiset.traverse_map" -> "data", "list.update_nth_eq_take_cons_drop" -> "data", "function.inv_fun_on_neg" -> "logic", "times_cont_diff_at_inverse" -> "analysis", "monoid_algebra.equivariant_of_linear_of_comm_apply" -> "data", "list.mem_tails" -> "data", "filter.tendsto.lim_eq" -> "topology", "znum.cast_zero'" -> "data", "qpf.liftp_iff" -> "data", "is_open_map.id" -> "topology", "finset.le_min'" -> "data", "tactic.ring_exp.mul_pp_pf_prod_gt" -> "tactic", "dist_triangle_left" -> "topology", "computation.map_parallel" -> "data", "matrix.nonsing_inv_right_left" -> "algebra", "mem_span_insert_exchange" -> "algebra", "is_connected_range" -> "topology", "real.exp_log_eq_abs" -> "analysis", "normed_ring.inverse_add" -> "analysis", "tendsto_order" -> "topology", "nat.zero_test_bit" -> "data", "add_comm_group.is_Z_bilin.neg_right" -> "topology", "prod_mk_mem_comp_rel" -> "topology", "left_inverse_pth_root_frobenius" -> "algebra", "wseq.bind_ret" -> "data", "tendsto_comp_of_locally_uniform_limit" -> "topology", "affine_map.homothety_apply" -> "algebra", "ideal.le_map_of_comap_le_of_surjective" -> "algebra", "principal_seg.equiv_lt_apply" -> "set_theory", "continuous_on.preimage_closed_of_closed" -> "topology", "edist_le_range_sum_edist" -> "topology", "many_one_equiv.congr_right" -> "computability", "set.image_eq_range" -> "data", "tsum_geometric_nnreal" -> "analysis", "is_add_subgroup.eq_trivial_iff" -> "algebra", "list.subperm.count_le" -> "data", "is_local_min.sub" -> "topology", "list.length_merge_sort" -> "data", "set.preimage_const_mul_Ioi_of_neg" -> "data", "pnat.one_le" -> "data", "list.disjoint_right" -> "data", "category_theory.limits.pullback_cone.of_cone_\[Pi]" -> "category_theory", "Ioc_mem_nhds_within_Iic" -> "topology", "sub_add_add_cancel" -> "algebra", "is_glb_singleton" -> "order", "Set.mem_map" -> "set_theory", "has_fderiv_within_at.iterate" -> "analysis", "finset.card_empty" -> "data", "alist.mem_replace" -> "data", "monotone_of_monotone_nat" -> "order", "typevec.drop_fun_of_subtype" -> "data", "adic_completion.range_eval" -> "algebra", "nat.gcd_succ" -> "init", "zmod.wilsons_lemma" -> "number_theory", "differentiable_at.smul_algebra_const" -> "analysis", "set.finite.summable" -> "topology", "monotone.map_inf_le" -> "order", "eq_of_uniformity_inf_nhds_of_is_separated" -> "topology", "is_mul_hom.mul" -> "algebra", "neg_of_mul_pos_left" -> "algebra", "is_linear_map.is_linear_map_smul" -> "algebra", "is_max_on_iff" -> "order", "measure_theory.measure.to_outer_measure_le" -> "analysis", "dvd_iff_dvd_of_dvd_sub" -> "algebra", "computation.terminates_parallel.aux" -> "data", "is_local_min_on.add" -> "topology", "list.left_unique_forall\:2082" -> "data", "with_top.lt_iff_exists_coe_btwn" -> "order", "int.nonneg_of_neg_nonpos" -> "init", "neg_one_lt_gold_conj" -> "data", "metric.continuous_iff" -> "topology", "equiv.arrow_congr'_refl" -> "data", "eq_zero_of_add_self_right_cancel" -> "algebra", "of_digits_singleton" -> "data", "polynomial.derivative_map" -> "data", "mv_polynomial.homogeneous_component_eq_zero'" -> "algebra", "nat.pow_lt_pow_succ" -> "data", "complex.continuous_im" -> "topology", "topological_space.mem_basis_subset_of_mem_open" -> "topology", "topological_space.opens.le_def" -> "topology", "add_zero" -> "algebra", "list.sublists_cons_perm_append" -> "data", "has_strict_deriv_at_pow" -> "analysis", "inner_product_space.of_core.inner_add_right" -> "analysis", "category_theory.monoidal_category.tensoring_right_obj" -> "category_theory", "free_group.mul_bind" -> "algebra", "associated.refl" -> "algebra", "filter.infi_sets_induct" -> "order", "metric.mem_uniformity_dist" -> "topology", "convex_iff_segment_subset" -> "analysis", "ordinal.CNF_rec_ne_zero" -> "set_theory", "int.cast_two" -> "data", "asymptotics.is_O_with.prod_left_fst" -> "analysis", "nnreal.coe_min" -> "data", "int.zero_mod" -> "data", "frontier_Ico" -> "topology", "nat.pow_dvd_of_le_of_pow_dvd" -> "data", "mul_equiv.to_fun_apply" -> "data", "finset.bind_mono" -> "data", "category_theory.limits.kernel_fork.condition" -> "category_theory", "submonoid.localization_map.mul_inv_right" -> "algebra", "category_theory.comma.map_right_comp_hom_app_left" -> "category_theory", "initial_seg.eq" -> "set_theory", "poly_equiv_tensor_symm_apply_tmul" -> "algebra", "directed.sequence_mono" -> "data", "dfinsupp.subtype_domain_apply" -> "data", "pi_Lp.add_apply" -> "topology", "dlist.to_list_cons" -> "data", "list.zip_nil_right" -> "data", "multiset.count_smul" -> "data", "omega.coeffs.forall_val_dvd_of_forall_mem_dvd" -> "tactic", "has_lt.lt.gt" -> "algebra", "fin.val_zero'" -> "data", "ordinal.one_power" -> "set_theory", "set.bInter_pair" -> "data", "closed_embedding_of_continuous_injective_closed" -> "topology", "ctop.realizer.of_equiv_F" -> "data", "not_lt_bot" -> "order", "nat.div2_bit0" -> "data", "string.iterator.length_next_to_string_next" -> "init", "linear_map.range_range_restrict" -> "algebra", "alist.mem_of_perm" -> "data", "order_top.ext_top" -> "order", "zsqrtd.nonnegg_cases_right" -> "data", "multiset.add_inter_distrib" -> "data", "if_congr" -> "init", "continuous_linear_equiv.has_fderiv_within_at" -> "analysis", "semiconj_by.cast_nat_mul_right" -> "algebra", "is_extr_on.elim" -> "order", "lucas_lehmer.\[Omega]_pow_formula" -> "number_theory", "forall_elim_eq_right" -> "tactic", "roption.mem_bind" -> "data", "pgame.domineering.move_right_smaller" -> "set_theory", "free_ring.lift_of" -> "algebra", "asymptotics.is_O.const_mul_right'" -> "analysis", "rat.eq_iff_mul_eq_mul" -> "data", "unique_factorization_domain.integrally_closed" -> "algebra", "polynomial.roots_mul" -> "data", "finsupp.map_domain_injective" -> "data", "pell.x_sub_y_dvd_pow_lem" -> "number_theory", "differentiable_at.inv" -> "analysis", "measure_theory.l1.simple_func.neg_part_to_simple_func" -> "analysis", "joined_in.source_mem" -> "topology", "rat.denom_div_cast_eq_one_iff" -> "data", "has_deriv_within_at.neg" -> "analysis", "polynomial.map_monic_ne_zero" -> "data", "list.nodup_repeat" -> "data", "computation.lift_rel_rec.lem" -> "data", "field.mem_closure" -> "algebra", "filter.mem_lift'" -> "order", "nat.zero_lt_one_add" -> "init", "alg_equiv.to_Algebra_iso_hom" -> "algebra", "setoid.Inf_def" -> "data", "galois_connection.upper_bounds_l_image_subset" -> "order", "is_submonoid.coe_mul" -> "algebra", "submonoid.map_le_map_iff_of_injective" -> "algebra", "not_lt_of_le" -> "algebra", "category_theory.limits.is_colimit.unique_up_to_iso_hom" -> "category_theory", "mul_aut.conj_apply" -> "data", "real.sqrt_two_add_series_zero_nonneg" -> "analysis", "has_fderiv_at.fst" -> "analysis", "set.inter_eq_Inter" -> "data", "le_mul_of_inv_mul_le_left" -> "algebra", "con.ker_eq_lift_of_injective" -> "algebra", "finset.univ_inter" -> "data", "mul_one" -> "algebra", "asymptotics.is_o_norm_norm" -> "analysis", "category_theory.non_preadditive_abelian.sub_zero" -> "category_theory", "list.choose_mem" -> "data", "infinite.exists_not_mem_finset" -> "data", "multiset.coe_add" -> "data", "monotone.order_dual" -> "order", "unique_mdiff_within_at.eq" -> "geometry", "filter.ultrafilter_of_ultrafilter" -> "order", "equiv.perm.gpow_apply_eq_self_of_apply_eq_self" -> "algebra", "metric.mk_uniformity_basis_le" -> "topology", "well_founded.has_min" -> "order", "convex.norm_image_sub_le_of_norm_deriv_le" -> "analysis", "linear_independent.insert" -> "algebra", "nat.le_mul_self" -> "data", "set.nonempty.fst" -> "data", "normal.exists_is_splitting_field" -> "algebra", "matrix.one_map" -> "data", "array.read_write_of_ne" -> "init", "composition.size_up_to_length" -> "combinatorics", "is_local_extr.elim" -> "topology", "metric.closed_ball_diff_ball" -> "topology", "compact_empty" -> "topology", "computation.get_thinkN" -> "data", "equiv.point_reflection_symm" -> "data", "composition.single_length" -> "combinatorics", "finset.sum_sub_distrib" -> "algebra", "nat.nsmul_eq_mul" -> "algebra", "set.indicator_of_not_mem" -> "data", "with_bot.bot_lt_some" -> "order", "list.map_append" -> "init", "add_monoid_hom.eq_on_closure" -> "algebra", "ennreal.div_lt_iff" -> "data", "zorn.chain.total_of_refl" -> "order", "has_deriv_at.neg" -> "analysis", "real.cosh_eq" -> "data", "int.gcd_div_gcd_div_gcd" -> "algebra", "list.sublist.reverse" -> "data", "add_monoid_hom.iterate_map_sub" -> "algebra", "gaussian_int.to_complex_def'" -> "data", "category_theory.comma.map_right_map_left" -> "category_theory", "measure_theory.outer_measure.of_function_caratheodory" -> "analysis", "int.succ_neg_succ" -> "data", "emetric.continuous_inf_edist" -> "topology", "traversable.traverse_id" -> "control", "set.nonempty_Iio" -> "data", "sub_le_sub_iff" -> "algebra", "filter.tendsto.dist" -> "topology", "bot_unique" -> "order", "fpow_inj" -> "algebra", "pgame.mk_add_move_right_inr" -> "set_theory", "nat.neg_one_pow_eq_one_iff_even" -> "data", "dvd_add_left" -> "algebra", "add_localization.add_equiv_of_quotient_add_monoid_of" -> "algebra", "multiset.attach_cons" -> "data", "quadratic_form.ext" -> "algebra", "category_theory.over.construct_products.cones_equiv_functor_map_hom" -> "category_theory", "measure_theory.integral_zero" -> "analysis", "add_lt_of_nonpos_of_lt" -> "algebra", "padic_int.irreducible_p" -> "data", "dfinsupp.erase_def" -> "data", "pgame.impartial.first_wins_symm" -> "set_theory", "true_ne_false" -> "init", "set.image2_singleton_right" -> "data", "polynomial.mem_roots" -> "data", "homeomorph.is_O_congr" -> "analysis", "module_ext" -> "algebra", "semidirect_product.inv_left" -> "algebra", "continuous.prod_mk" -> "topology", "nat.eq_zero_or_pos" -> "init", "ennreal.rpow_eq_pow" -> "analysis", "nat.pred_lt_pred" -> "init", "nat.bit1_lt_bit0_iff" -> "data", "int.bitwise_diff" -> "data", "Limsup_eq_of_le_nhds" -> "topology", "complex.of_real_tan_of_real_re" -> "data", "mul_semiring_action_hom.coe_polynomial" -> "algebra", "complex.conj_eq_zero" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_on_of_lift_prop" -> "geometry", "add_submonoid.exists" -> "algebra", "polynomial.is_coprime_map" -> "data", "ennreal.bit0_eq_zero_iff" -> "data", "function.injective_of_partial_inv_right" -> "logic", "continuous_multilinear_map.cons_smul" -> "topology", "dim_fun'" -> "algebra", "category_theory.functor.cones_map_app" -> "category_theory", "real.sqrt_eq_iff_sqr_eq" -> "data", "ring.fractional_ideal.inv_nonzero" -> "algebra", "tsum_fintype" -> "topology", "linear_independent.repr_eq" -> "algebra", "polynomial.degree_one" -> "data", "mfderiv_const" -> "geometry", "nat.choose_symm_half" -> "data", "quadratic_form.map_neg" -> "algebra", "group.mclosure_subset" -> "algebra", "filter.is_ultrafilter.eventually_imp" -> "order", "nat.coprime_mul_iff_right" -> "data", "measure_theory.integrable.integrable_on" -> "analysis", "finite_of_linear_independent" -> "algebra", "irreducible_component_subset_connected_component" -> "topology", "mul_semiring_action_hom.ext_iff" -> "algebra", "list.mem_fin_range" -> "data", "roption.bind_eq_bind" -> "data", "category_theory.limits.bicone.to_cone_\[Pi]_app" -> "category_theory", "has_sum_geometric_of_lt_1" -> "analysis", "le_of_tendsto_of_tendsto'" -> "topology", "continuous_linear_equiv.units_equiv_aut_apply" -> "topology", "submodule.le_orthogonal_orthogonal" -> "analysis", "continuous_linear_map.bounds_bdd_below" -> "analysis", "eq_of_incomp" -> "init", "measure_theory.ae_eq_fun.coe_fn_zero" -> "analysis", "monoid_algebra.coe_algebra_map" -> "data", "uniform_embedding_of_rat" -> "topology", "alist.empty_entries" -> "data", "polynomial.separable.is_coprime" -> "algebra", "is_subring_Union_of_directed" -> "algebra", "measure_theory.lintegral_rw\:2082" -> "analysis", "equiv.perm.swap_mul_eq_mul_swap" -> "algebra", "is_R_or_C.abs_inv" -> "data", "lucas_lehmer.X.X_card" -> "number_theory", "measure_theory.measure_diff" -> "analysis", "submonoid.le_comap_map" -> "algebra", "sylow.exists_prime_order_of_dvd_card" -> "algebra", "ennreal.to_nnreal_pos_iff" -> "data", "cardinal.mk_image_le_lift" -> "set_theory", "set.finite.summable_compl_iff" -> "topology", "if_pos" -> "init", "equiv.perm.support_swap_mul_eq" -> "algebra", "prod.fst_sum" -> "algebra", "is_subring.coe_subtype" -> "algebra", "multiset.sub_zero" -> "data", "measure_theory.is_left_invariant_inner_content" -> "analysis", "mul_neg_geom_sum" -> "algebra", "continuous_generated_from" -> "topology", "finmap.disjoint_empty" -> "data", "ennreal.one_to_real" -> "data", "set.image_inter_subset" -> "data", "is_measurable.empty" -> "analysis", "category_theory.reassoc_of" -> "tactic", "complex.inv_re" -> "data", "monoid_algebra.single_pow" -> "data", "complex.exp_log" -> "analysis", "linear_equiv.is_unit_det" -> "algebra", "is_compl.sup_inf" -> "order", "set.powerset_mono" -> "data", "sym2.mem_iff" -> "data", "set.subset_compl_singleton_iff" -> "data", "fract_fract" -> "algebra", "to_lin_to_matrix" -> "algebra", "is_integral_alg_hom" -> "algebra", "continuous_linear_map.ext" -> "topology", "mvqpf.liftp_iff" -> "data", "fin.le_coe_last" -> "data", "set.mem_sep_iff" -> "data", "filter.germ.coe_le" -> "order", "mv_polynomial.homogeneous_component_eq_zero" -> "algebra", "tangent_map_within_congr" -> "geometry", "list.ne_nil_of_length_eq_succ" -> "init", "is_separated_of_separated_space" -> "topology", "set.nonempty.right" -> "data", "int.bitwise_and" -> "data", "rat.uniform_space_eq" -> "topology", "nat.lt_succ_iff" -> "data", "cauchy.comap" -> "topology", "asymptotics.is_O_with.congr_left" -> "analysis", "is_extr_on.on_subset" -> "order", "matrix.is_unit_det_transpose" -> "algebra", "cardinal.mk_set_le" -> "set_theory", "measurable_mul" -> "analysis", "bilin_form.is_adjoint_pair_id" -> "algebra", "tangent_map_within_proj" -> "geometry", "quadratic_form.lin_mul_lin_self_pos_def" -> "algebra", "set.Ioi_subset_Ioc_union_Ici" -> "data", "mvqpf.liftr_iff" -> "data", "local_homeomorph.trans_self_symm" -> "topology", "int.div_nonpos" -> "data", "differentiable_within_at.cosh" -> "analysis", "category_theory.non_preadditive_abelian.comp_add" -> "category_theory", "cardinal.omega_is_regular" -> "set_theory", "ennreal.exists_nat_gt" -> "data", "cardinal.mk_list_eq_sum_pow" -> "set_theory", "submodule.mem_map" -> "algebra", "ennreal.to_real_eq_to_real" -> "data", "lt_min" -> "init", "filter.at_top_ne_bot" -> "order", "emetric.tendsto_nhds" -> "topology", "differentiable_on.ccosh" -> "analysis", "digits_zero_zero" -> "data", "dioph.dom_dioph" -> "number_theory", "real.is_lub_Sup" -> "data", "decidable.not_and_distrib" -> "logic", "add_neg_of_neg_of_nonpos'" -> "algebra", "well_founded.eq_iff_not_lt_of_le" -> "order", "UniformSpace.extension_comp_coe" -> "topology", "is_add_unit.lift_right_neg_add" -> "algebra", "monoid_hom.ext_iff" -> "algebra", "nat.bodd_one" -> "init", "normed_algebra.norm_one" -> "analysis", "multiset.inf_zero" -> "data", "metric.completion.eq_of_dist_eq_zero" -> "topology", "pi.algebra_map_apply" -> "algebra", "turing.list_blank.nth_mk" -> "computability", "finset.empty_sdiff" -> "data", "dfinsupp.single_eq_of_ne" -> "data", "mv_power_series.coeff_X" -> "algebra", "tangent_map_chart" -> "geometry", "homeomorph.is_closed_map" -> "topology", "padic_int.zmod_congr_of_sub_mem_span" -> "data", "qpf.supp_map" -> "data", "bex.imp_right" -> "logic", "left_inverse_neg_add_add_right" -> "algebra", "add_semiconj_by.neg_right" -> "algebra", "int.add_le_add_three" -> "init", "complex.tan_eq_sin_div_cos" -> "data", "omega.coeffs.val_between_add" -> "tactic", "tendsto_nhds" -> "topology", "measure_theory.lebesgue_outer_Icc" -> "analysis", "multiset.powerset_aux'_nil" -> "data", "finsupp.prod_comm" -> "data", "continuous_nndist" -> "topology", "complex.abs_cpow_inv_nat" -> "analysis", "asymptotics.is_o_const_mul_left_iff" -> "analysis", "linear_independent_of_finite" -> "algebra", "AddCommGroup.colimits.quot_neg" -> "algebra", "finsupp.supported_univ" -> "algebra", "subgroup.mul_mem" -> "algebra", "category_theory.functor.op_inv_map" -> "category_theory", "filter.tendsto.sup" -> "order", "lt_add_of_lt_of_pos'" -> "algebra", "vsub_mem_vsub_set" -> "algebra", "nnreal.coe_sum" -> "data", "add_units.mk_semiconj_by" -> "algebra", "is_R_or_C.rat_cast_im" -> "data", "convex_cone.coe_inf" -> "analysis", "complex.is_cau_seq_re" -> "data", "associates.prod_coe" -> "algebra", "induced_compose" -> "topology", "submodule.map_sup" -> "algebra", "ring_hom.codomain_trivial_iff_range_eq_singleton_zero" -> "algebra", "finmap.disjoint.symm" -> "data", "function.inv_fun_on_eq'" -> "logic", "erased.pure_def" -> "data", "is_bounded_linear_map.differentiable_within_at" -> "analysis", "composition.sigma_eq_iff_blocks_eq" -> "combinatorics", "nat.dist_add_add_right" -> "data", "times_cont_mdiff_on_iff" -> "geometry", "int.eq_coe_or_neg" -> "init", "hash_map.find_erase" -> "data", "complex.cosh_sub" -> "data", "hyperreal.epsilon_eq_inv_omega" -> "data", "category_theory.preadditive.neg_comp_assoc" -> "category_theory", "metric.cauchy_iff" -> "topology", "continuous_within_at_iff_continuous_at_restrict" -> "topology", "is_closed.closed_embedding_subtype_coe" -> "topology", "filter.eventually.eventually_nhds" -> "topology", "finmap.union_empty" -> "data", "local_homeomorph.eventually_right_inverse'" -> "topology", "nhds_within_empty" -> "topology", "lt_iff_le_not_le" -> "init", "category_theory.monoidal.associator_inv_apply" -> "category_theory", "polynomial.div_by_monic_eq_of_not_monic" -> "data", "filter.frequently_sup" -> "order", "num.mem_of_znum'" -> "data", "nat.coprime.gcd_mul_right_cancel_right" -> "data", "set.ord_connected_interval" -> "data", "bit1_nsmul" -> "algebra", "multiset.erase_dup_eq_zero" -> "data", "int.gcd_comm" -> "algebra", "function.inv_fun_on_pos" -> "logic", "monoid_hom.fst_comp_inl" -> "algebra", "measure_theory.measure.haar_outer_measure_of_is_open" -> "analysis", "stream.map_map" -> "data", "embedding.prod_mk" -> "topology", "submonoid.localization_map.of_mul_equiv_of_mul_equiv_apply" -> "algebra", "set.mem_inter_eq" -> "data", "div_le_iff_of_neg" -> "algebra", "equiv.sigma_congr_right_apply" -> "data", "list.mfoldl_with_index_eq_mfoldl_enum" -> "data", "multiset.sup_union" -> "data", "pnat.factor_multiset_one" -> "data", "nonempty_psigma" -> "logic", "composition.index_exists" -> "combinatorics", "is_compact.tendsto_subseq'" -> "topology", "ordinal.lift.principal_seg_top'" -> "set_theory", "measure_theory.l1.edist_eq" -> "analysis", "exists_eq" -> "logic", "local_homeomorph.of_set_coe" -> "topology", "set.preimage_sub_const_Ico" -> "data", "real.div_sqrt_one_add_lt_one" -> "analysis", "of_to_bool_ff" -> "init", "free_group.red.step.cons_left_iff" -> "algebra", "asymptotics.is_o.def'" -> "analysis", "times_cont_mdiff_on_symm_of_mem_maximal_atlas" -> "geometry", "finite_dimensional.span_of_finite" -> "algebra", "finset.Ico.filter_Ico_bot" -> "data", "and_self_left" -> "logic", "measure_theory.l1.simple_func.eq_iff'" -> "analysis", "is_open_map_add_left" -> "topology", "set.right_mem_Ioc" -> "data", "tendsto_inv_nhds_within_Iio" -> "topology", "finmap.keys_erase" -> "data", "fin.pred_inj" -> "data", "ge_of_eq" -> "algebra", "subsemiring.zero_mem" -> "algebra", "dfinsupp.prod_zero_index" -> "data", "monad_map_refl" -> "init", "function.Sup_div_semiconj" -> "order", "list.mem_filter_map" -> "data", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_apply" -> "analysis", "mem_gmultiples" -> "algebra", "multiset.repeat_succ" -> "data", "matrix.induction_on" -> "data", "monotone_Inf_of_monotone" -> "order", "cardinal.mk_preimage_of_subset_range" -> "set_theory", "polynomial.nat_degree_X_sub_C_le" -> "data", "dfinsupp.mk_apply" -> "data", "has_mfderiv_at.mdifferentiable_at" -> "geometry", "nat.le_lt_antisymm" -> "init", "category_theory.nat_trans.vcomp_eq_comp" -> "category_theory", "is_glb.infi_eq" -> "order", "function.commute.id_left" -> "logic", "category_theory.limits.cone.whisker_\[Pi]" -> "category_theory", "has_deriv_within_at.const_smul" -> "analysis", "finset.empty_union" -> "data", "polynomial.coe_add" -> "algebra", "top_inf_eq" -> "order", "real.geom_mean_le_arith_mean2_weighted" -> "analysis", "nat.lt_succ_sqrt" -> "data", "submonoid.localization_map.of_mul_equiv_of_mul_equiv" -> "algebra", "filter.le_pure_iff" -> "order", "isometric.to_real_linear_equiv_symm_apply" -> "analysis", "is_measurable.inter" -> "analysis", "category_theory.limits.cone.w" -> "category_theory", "exists_eq_mul_left_of_dvd" -> "algebra", "seq.join_append" -> "data", "submodule.mem_map_of_mem" -> "algebra", "emetric.uniform_embedding_iff" -> "topology", "equiv.perm.is_cycle_cycle_of" -> "algebra", "continuous_linear_equiv.to_span_nonzero_singleton_homothety" -> "analysis", "padic_norm.mul" -> "data", "circle_deg1_lift.translation_number_le_of_le_add_nat" -> "dynamics", "multiset.powerset_coe'" -> "data", "measure_theory.l1.lintegral_edist_to_fun_lt_top" -> "analysis", "set.piecewise_eq_of_mem" -> "data", "int.sub_mul" -> "init", "function.is_periodic_pt.minimal_period_dvd" -> "dynamics", "monoid_algebra.single_mul_apply_aux" -> "data", "free_add_semigroup.traverse_add'" -> "algebra", "category_theory.cones_obj" -> "category_theory", "localization_map.lift_of_comp" -> "algebra", "lagrange.interpolate_sub" -> "algebra", "lie_algebra.orthogonal.is_unit_PD" -> "algebra", "composition_as_set.boundary_length" -> "combinatorics", "uniform_space.completion.dense_inducing_coe" -> "topology", "is_conj_refl" -> "algebra", "computation.lift_rel_rec" -> "data", "int.mul_lt_mul'" -> "init", "set.countable.insert" -> "data", "uniform.tendsto_nhds_left" -> "topology", "bounded_continuous_function.norm_const_le" -> "topology", "floor_eq_iff" -> "algebra", "distrib_mul_action_hom.comp_id" -> "algebra", "equiv.one_def" -> "data", "measure_theory.lintegral_liminf_le" -> "analysis", "bool.to_bool_true" -> "data", "measurable.ennreal_of_real" -> "analysis", "Set.regularity" -> "set_theory", "emetric.mk_uniformity_basis_le" -> "topology", "ennreal.tsum_mul_right" -> "topology", "multiset.card_erase_lt_of_mem" -> "data", "finset.sdiff_empty" -> "data", "subtype.restrict_injective" -> "data", "lt_add_iff_pos_right" -> "algebra", "matrix.diagonal_mul_diagonal" -> "data", "pgame.numeric.lt_move_right" -> "set_theory", "emetric.empty_or_nonempty_of_Hausdorff_edist_ne_top" -> "topology", "emetric.uniform_embedding_iff'" -> "topology", "nat.partrec.ppred" -> "computability", "cardinal.mk_bounded_set_le_of_omega_le" -> "set_theory", "computation.map_id" -> "data", "set.surj_on_Union" -> "data", "traversable.comp_sequence" -> "control", "real.two_pi_pos" -> "analysis", "filter.ne_bot.map" -> "order", "matrix.smul_empty" -> "data", "int.ne_neg_of_ne" -> "init", "padic_norm_z.padic_norm_z_eq_padic_norm_e" -> "data", "add_units.eq_neg_add_iff_add_eq" -> "algebra", "set.mem_powerset_iff" -> "data", "is_R_or_C.eq_conj_iff_re" -> "data", "convex_hyperplane" -> "analysis", "pfunctor.M.cases_mk" -> "data", "mv_polynomial.map_eval\:2082" -> "data", "category_theory.eq_to_iso_refl" -> "category_theory", "set.image_mul_prod" -> "algebra", "set.disjointed_induct" -> "data", "seq.mem_rec_on" -> "data", "complex.div_I" -> "data", "is_add_hom.add" -> "algebra", "list.perm_append_singleton" -> "data", "mv_polynomial.rename_C" -> "data", "set.Union_image_left" -> "data", "is_min_on.comp_antimono" -> "order", "complex.linear_map.coe_of_real" -> "data", "filter.tendsto_at_bot_at_bot_of_monotone" -> "order", "pythagorean_triple.classification" -> "number_theory", "tactic.ring.horner_mul_const" -> "tactic", "unique_factorization_domain.irreducible_factors" -> "algebra", "mul_eq_one_iff_eq_inv" -> "algebra", "of_real_norm_eq_coe_nnnorm" -> "analysis", "category_theory.pi.comap_id_inv_app" -> "category_theory", "real.continuous_at_rpow" -> "analysis", "hyperreal.st_eq_Sup" -> "data", "list.forall_mem_inter_of_forall_right" -> "data", "fract_add_floor" -> "algebra", "mv_power_series.mul_inv_of_unit" -> "algebra", "filter.forall_sets_nonempty_iff_ne_bot" -> "order", "linear_map.continuous_of_finite_dimensional" -> "analysis", "real.le_Inf" -> "data", "bit1_pos" -> "algebra", "pell.is_pell_conj" -> "number_theory", "decidable.lt_or_eq_of_le" -> "init", "lucas_lehmer.\[Omega]_pow_eq_neg_one" -> "number_theory", "set.mem_univ" -> "data", "is_glb.Inf_eq" -> "order", "list.prefix_iff_eq_take" -> "data", "list.func.get_nil" -> "data", "relation.refl_trans_gen.head_induction_on" -> "logic", "list.to_finset_card_le" -> "data", "int.mod_lt" -> "data", "turing.TM1to1.tr_supports" -> "computability", "has_strict_fderiv_at_id" -> "analysis", "matrix.empty_val'" -> "data", "add_pow" -> "data", "measure_theory.ae_eq_fun.integrable_mk" -> "analysis", "bilin_form.lin_mul_lin_apply" -> "algebra", "real.continuous_sinh" -> "analysis", "function.sometimes_eq" -> "logic", "localization_map.lift_injective_iff" -> "algebra", "complex.is_cau_abs_exp" -> "data", "char_p.exists" -> "algebra", "set.sInter_union_sInter" -> "data", "rel.preimage_inter" -> "data", "localization_map.sec_spec'" -> "algebra", "le_one_div" -> "algebra", "list.nth_le_map" -> "data", "is_min_filter_const" -> "order", "nat.add_sub_eq_max" -> "data", "is_compact.finite_compact_cover" -> "topology", "AddCommGroup.colimits.quot_zero" -> "algebra", "nat.succ_sub_succ" -> "init", "trans" -> "init", "list.mem_sublists" -> "data", "int.mul_mod_mul_of_pos" -> "data", "add_comm_group.is_Z_bilin.comp_hom" -> "topology", "eq_tt_eq_not_eq_ff" -> "init", "ring_hom.eq_on_sclosure" -> "algebra", "subgroup.mul_mem_cancel_left" -> "algebra", "list.le_count_iff_repeat_sublist" -> "data", "except_t.run_map" -> "init", "semimodule.nsmul_eq_smul" -> "algebra", "rat.exists_mul_self" -> "data", "measure_theory.outer_measure.is_caratheodory_Union_nat" -> "analysis", "galois_coinsertion.u_supr_l" -> "order", "relation.refl_trans_gen.trans" -> "logic", "int.mul_div_mul_of_pos" -> "data", "order_embedding.acc" -> "order", "equiv.option_equiv_sum_punit_none" -> "data", "monoid_hom.map_units_inv" -> "algebra", "uniformly_extend_of_ind" -> "topology", "algebra.is_algebraic_trans" -> "algebra", "list.length_pos_of_ne_nil" -> "data", "rat.coe_int_eq_mk" -> "data", "multilinear_map.curry_right_apply" -> "algebra", "set.bInter_mono'" -> "data", "real.differentiable_cos" -> "analysis", "fderiv_within_univ" -> "analysis", "Sup_union" -> "order", "is_add_subgroup.mem_trivial" -> "algebra", "cardinal.mk_Ico_real" -> "data", "ctop.realizer.is_open" -> "data", "multiset.pmap_eq_map_attach" -> "data", "algebraic_closure.exists_of_step" -> "algebra", "convex.norm_image_sub_le_of_norm_has_fderiv_within_le" -> "analysis", "continuous_linear_map.uncurry_left_norm" -> "analysis", "set.ord_connected_sInter" -> "data", "tangent_bundle_model_space_coe_chart_at_symm" -> "geometry", "has_strict_fderiv_at.approximates_deriv_on_nhds" -> "analysis", "le_ceil" -> "algebra", "mem_closure_iff_cluster_pt" -> "topology", "bsupr_le_supr" -> "order", "set.diff_inter_self" -> "data", "bitraversable.id_tfst" -> "control", "add_right_iterate" -> "algebra", "has_ftaylor_series_up_to.zero_eq'" -> "analysis", "real.cos_bound" -> "data", "neg_le_neg" -> "algebra", "turing.TM2to1.add_bottom_nth_succ_fst" -> "computability", "monoid_algebra.zero_mul" -> "data", "dfinsupp.single_eq_same" -> "data", "list.func.mem_get_of_ne_zero" -> "data", "hyperreal.is_st_st_of_exists_st" -> "data", "set.union_eq_self_of_subset_right" -> "data", "list.sublists_aux_ne_nil" -> "data", "turing.TM2to1.tr_stmts\:2081_run" -> "computability", "complex.continuous_linear_map.of_real_isometry" -> "analysis", "ring.direct_limit.lift_neg" -> "algebra", "gold_conj_irrational" -> "data", "convex_halfspace_re_lge" -> "analysis", "pSet.mem.congr_right" -> "set_theory", "supr_true" -> "order", "continuous_multilinear_map.curry_right_norm" -> "analysis", "category_theory.monad.forget_creates_limits.lifted_cone_X" -> "category_theory", "padic_seq.stationary" -> "data", "zero_le_mul_left" -> "algebra", "div_add'" -> "algebra", "prime.div_or_div" -> "algebra", "submodule.map_subtype_top" -> "algebra", "nnreal.zero_le_coe" -> "data", "pnat.xgcd_type.flip_a" -> "data", "circle_deg1_lift.le_iterate_of_add_int_le_map" -> "dynamics", "eq_Icc_cInf_cSup_of_connected_bdd_closed" -> "topology", "submodule.mem_annihilator'" -> "algebra", "category_theory.abelian.images.image_strong_epi_mono_factorisation_to_mono_factorisation_e" -> "category_theory", "function.semiconj.maps_to_periodic_pts" -> "dynamics", "nhds_within_eq" -> "topology", "is_group_hom.one_ker_inv'" -> "algebra", "euclidean_geometry.angle_eq_zero_of_angle_eq_pi_left" -> "geometry", "set.ord_connected_Ico" -> "data", "div_sub'" -> "algebra", "list.qsort_cons" -> "init", "category_theory.forget_obj_eq_coe" -> "category_theory", "commute.units_gpow_left" -> "algebra", "is_R_or_C.abs_eq_zero" -> "data", "nat.sub_le_self" -> "data", "affine.simplex.sum_monge_point_weights_with_circumcenter" -> "geometry", "mem_right_add_coset" -> "algebra", "commute.pow_self" -> "algebra", "simple_graph.irrefl" -> "combinatorics", "complex.exp_inj_of_neg_pi_lt_of_le_pi" -> "analysis", "finset.image_filter" -> "data", "pfun.ext'" -> "data", "category_theory.monoidal_category.unitors_equal.cells_14" -> "category_theory", "category_theory.monoidal_category.tensor_left_tensor_hom_app" -> "category_theory", "category_theory.limits.is_initial.epi_to" -> "category_theory", "set.finite.is_compact" -> "topology", "geom_sum_Ico_mul_neg" -> "algebra", "nat.dvd_prime" -> "data", "list.lex.to_ne" -> "data", "generalized_continued_fraction.zeroth_denominator_eq_one" -> "algebra", "equiv.subtype_preimage_apply" -> "data", "linear_pmap.snd_apply" -> "algebra", "finsupp.map_domain_finset_sum" -> "data", "real.exp_log_of_neg" -> "analysis", "set.ssubset_def" -> "data", "submodule.inner_right_of_mem_orthogonal" -> "analysis", "nsmul_le_nsmul_of_le_right" -> "algebra", "div_le_iff'" -> "algebra", "asymptotics.is_O_of_le" -> "analysis", "tensor_product.smul_zero" -> "algebra", "basic_smooth_bundle_core.mem_chart_source_iff" -> "geometry", "order_of_eq_prime" -> "algebra", "differentiable.comp_differentiable_on" -> "analysis", "multiset.sub_inter" -> "data", "real.rpow_int_cast" -> "analysis", "vector_span_range_eq_span_range_vsub_left" -> "algebra", "function.involutive.injective" -> "logic", "emetric.countable_closure_of_compact" -> "topology", "map_Inf_of_continuous_at_of_monotone'" -> "topology", "except_t.run_monad_lift" -> "init", "turing.tape.move_left_right" -> "computability", "list.eq_of_sum_take_eq" -> "data", "measure_theory.simple_func.supr_approx_apply" -> "analysis", "set.maps_to_bInter_bInter" -> "data", "category_theory.eq_of_comp_left_eq'" -> "category_theory", "semiquot.is_pure_of_subsingleton" -> "data", "set.subset_sUnion_of_mem" -> "data", "equiv.symm_apply_apply" -> "data", "num.cast_bit1" -> "data", "nat.gcd_one_left" -> "init", "polynomial.derivative_pow_succ" -> "data", "cInf_le_cInf" -> "order", "Module.of_self_iso_hom" -> "algebra", "polynomial.one_comp" -> "data", "nat.eq_zero_of_le_zero" -> "init", "finset.mono_of_fin_strict_mono" -> "data", "category_theory.iso.self_symm_id_assoc" -> "category_theory", "category_theory.limits.binary_fan.is_limit.hom_ext" -> "category_theory", "lie_mem_right" -> "algebra", "measure_theory.simple_func.finite_range" -> "analysis", "add_submonoid.localization_map.of_add_equiv_of_dom_comp_symm" -> "algebra", "list.mem_reverse" -> "data", "fin.veq_of_eq" -> "init", "finset.min_empty" -> "data", "finsupp.sum_add_index" -> "data", "unique_diff_within_at.inter'" -> "analysis", "ennreal.of_real_to_real" -> "data", "function.embedding.antisymm" -> "set_theory", "rat.cast_ne_zero" -> "data", "add_monoid_hom.apply_apply" -> "algebra", "add_equiv.coe_symm_mk" -> "data", "Mon.colimits.cocone_naturality" -> "algebra", "min_add_add_right" -> "algebra", "complex.continuous_linear_map.re_apply" -> "analysis", "category_theory.monoidal_category.right_unitor_nat_iso_inv_app" -> "category_theory", "option.some_get" -> "data", "int.coe_nat_eq" -> "init", "wseq.map_comp" -> "data", "turing.tape.mk'_right\:2080" -> "computability", "nat.mem_factors" -> "data", "AddCommGroup.colimits.cocone_naturality_components" -> "algebra", "auto.classical.implies_iff_not_or" -> "tactic", "is_cyclic.image_range_order_of" -> "algebra", "set.image_mul_left_Icc" -> "data", "finsupp.sup_apply" -> "data", "add_units.neg_add_cancel_right" -> "algebra", "real.cos_sub_pi_div_two" -> "analysis", "circle_deg1_lift.mul_floor_map_zero_le_floor_iterate_zero" -> "dynamics", "set.image_preimage_eq_iff" -> "data", "multiset.filter_filter" -> "data", "polynomial.monomial_eq_smul_X" -> "data", "int.mod_add_mod" -> "data", "fderiv_const_smul" -> "analysis", "ring.direct_limit.lift_zero" -> "algebra", "set.preimage_Inter" -> "data", "option.map_id" -> "init", "filter.has_basis.forall_iff" -> "order", "list.forall_of_forall_of_pairwise" -> "data", "nat.gcd_eq_left" -> "data", "differentiable_at.div_const" -> "analysis", "int.units_pow_eq_pow_mod_two" -> "algebra", "category_theory.monoidal_category.tensor_id_comp_id_tensor" -> "category_theory", "matrix.smul_mat_cons" -> "data", "set.range_subset_singleton" -> "data", "ennreal.measurable_of_real" -> "analysis", "nat.dvd_add_iff_right" -> "init", "is_R_or_C.norm_sq_eq_zero" -> "data", "int.prime.dvd_mul'" -> "algebra", "has_strict_fderiv_at.is_O_sub" -> "analysis", "list.prefix_of_prefix_length_le" -> "data", "dioph.le_dioph" -> "number_theory", "nnreal.pow_nat_rpow_nat_inv" -> "analysis", "matrix.is_add_monoid_hom_mul_right" -> "data", "set.coe_cod_restrict_apply" -> "data", "nat.lt_size" -> "data", "classical.prop_complete" -> "init", "pure_le_nhds_within" -> "topology", "fintype.injective_iff_surjective_of_equiv" -> "data", "set.forall_range_iff" -> "data", "norm_num.adc_bit1_bit1" -> "tactic", "nat.dvd_mod_iff" -> "init", "convex.is_const_of_fderiv_within_eq_zero" -> "analysis", "stream.any_def" -> "data", "one_div_ne_zero" -> "algebra", "continuous_map.continuous_coev" -> "topology", "times_cont_diff_within_at.add" -> "analysis", "padic_int.valuation_p" -> "data", "tendsto_uniformly.tendsto_uniformly_on" -> "topology", "concave_on.subset" -> "analysis", "submonoid.localization_map.of_mul_equiv_of_dom_apply" -> "algebra", "mvqpf.fix.dest_mk" -> "data", "ideal.mul_mem_right" -> "algebra", "set.preimage_mul_const_Iio_of_neg" -> "data", "pgame.le_def" -> "set_theory", "polynomial.eval_pow" -> "data", "to_topological_space_Inf" -> "topology", "filter.prod_eq" -> "order", "function.update_idem" -> "logic", "continuous_multilinear_map.uncurry0_apply" -> "analysis", "real.tendsto_log_at_top" -> "analysis", "set.inclusion_right" -> "data", "times_cont_mdiff_at_id" -> "geometry", "is_basis.repr_self_apply" -> "algebra", "pSet.arity.equiv_const" -> "set_theory", "ring_hom.codomain_trivial_iff_map_one_eq_zero" -> "algebra", "finset.prod_nat_cast" -> "algebra", "list.argmin_cons" -> "data", "push_neg.not_forall_eq" -> "tactic", "alist.entries_to_alist" -> "data", "pcontinuous_iff'" -> "topology", "finset.comp_inf_eq_inf_comp" -> "data", "with_zero.zero_ne_coe" -> "algebra", "multiset.card_product" -> "data", "polynomial.monic_of_degree_le" -> "data", "Set.mem_image" -> "set_theory", "pow_le_one" -> "algebra", "metric.closed_ball_eq_empty_iff_neg" -> "topology", "inner_product_geometry.angle_smul_left_of_neg" -> "geometry", "neg_unique" -> "algebra", "set.indicator_add_eq_left" -> "data", "subalgebra.algebra_map_mem" -> "algebra", "swap_dist" -> "topology", "measure_theory.l1.of_fun_neg" -> "analysis", "typevec.id_comp" -> "data", "tendsto_coe_int_real_at_top_at_top" -> "topology", "times_cont_mdiff.mdifferentiable" -> "geometry", "supr_split" -> "order", "ideal.le_comap_map" -> "algebra", "list.forall\:2082_same" -> "data", "mul_le_mul_of_nonpos_left" -> "algebra", "implies_true_iff" -> "init", "mul_inv_self" -> "algebra", "filter.map_ne_bot_iff" -> "order", "localization_map.is_prime_iff_is_prime_disjoint" -> "algebra", "finset.prod_image'" -> "algebra", "real.sqrt_eq_zero'" -> "data", "turing.TM2to1.tr_cfg_init" -> "computability", "measure_theory.measure.to_outer_measure_injective" -> "analysis", "hyperreal.coe_one" -> "data", "list.exists_perm_sublist" -> "data", "ring_hom.iterate_map_sub" -> "algebra", "abs_sub_lt_one_of_floor_eq_floor" -> "algebra", "polynomial.restriction_zero" -> "algebra", "multiset.filter_add_not" -> "data", "mul_lt_of_le_of_lt_one" -> "algebra", "zsqrtd.nonnegg_neg_pos" -> "data", "homeomorph.is_O_with_congr" -> "analysis", "asymptotics.is_o.sum" -> "analysis", "nat.primrec.swap" -> "computability", "with_bot.cSup_empty" -> "order", "polynomial.coe_one" -> "algebra", "set.pairwise_on_disjoint_fiber" -> "data", "multiset.filter_map_le_filter_map" -> "data", "many_one_degree.le_antisymm" -> "computability", "ennreal.tendsto_nhds" -> "topology", "asymptotics.is_O.exists_nonneg" -> "analysis", "list.mem_inter" -> "data", "list.modify_nth_tail_eq_take_drop" -> "data", "turing.reaches_eval" -> "computability", "relator.rel_iff" -> "logic", "is_local_extr_on.on_subset" -> "topology", "neg_dvd_iff_dvd" -> "algebra", "mv_polynomial.total_degree_add" -> "data", "linear_map.map_zero\:2082" -> "algebra", "int.lt_succ_self" -> "data", "set.range_piecewise" -> "data", "cardinal.bit1_le_bit1" -> "set_theory", "measure_theory.measure.restrict_union_apply" -> "analysis", "submonoid.map_le_of_le_comap" -> "algebra", "function.bUnion_pts_of_period" -> "dynamics", "set.seq_mono" -> "data", "nat.mkpair_unpair" -> "data", "category_theory.discrete.functor_obj" -> "category_theory", "pmf.bind_pure_comp" -> "analysis", "multiset.card_attach" -> "data", "reader_t.run_monad_lift" -> "init", "multilinear_map.snoc_smul" -> "algebra", "is_group_hom.inv" -> "algebra", "add_subgroup.mem_coe" -> "algebra", "padic_norm_e.norm_rat_le_one" -> "data", "omega.nat.implies_neg_elim_core" -> "tactic", "hash_map.entries_empty" -> "data", "has_deriv_within_at.div" -> "analysis", "list.perm_singleton" -> "data", "measure_theory.simple_func.neg_part_map_norm" -> "analysis", "cau_seq.pos_add_lim_zero" -> "data", "nat.le_add_of_sub_le_right" -> "data", "add_subgroup.coe_subtype" -> "algebra", "decidable_linear_ordered_add_comm_group.add_lt_add_left" -> "algebra", "submodule.mem_div_iff_forall_mul_mem" -> "algebra", "continuous_linear_equiv.symm_symm" -> "topology", "matrix.transpose_zero" -> "data", "measure_theory.simple_func.coe_sub" -> "analysis", "localization_map.map_eq" -> "algebra", "ordinal.zero_sub" -> "set_theory", "submodule.mapq_apply" -> "algebra", "bilin_form.is_adjoint_pair.comp" -> "algebra", "ordinal.lift.initial_seg_coe" -> "set_theory", "list.pairwise_sublists'" -> "data", "deriv_inv'" -> "analysis", "with_bot.some_eq_coe" -> "order", "free_add_magma.add_seq" -> "algebra", "list.map_eq_append_split" -> "data", "set.indicator_union_of_not_mem_inter" -> "data", "eval_det" -> "algebra", "submodule.exists_is_compl" -> "algebra", "add_pos_of_nonneg_of_pos" -> "algebra", "real.cos_pi_sub" -> "analysis", "is_compact.elim_finite_subcover" -> "topology", "int.sign_zero" -> "init", "Ioo_mem_nhds_within_Iic" -> "topology", "finset.bind_inter" -> "data", "times_cont_mdiff_on.of_le" -> "geometry", "computation.lift_rel.equiv" -> "data", "le_of_le_mul_right" -> "algebra", "con.le_iff" -> "algebra", "units.add_coe" -> "analysis", "multiset.inf_add" -> "data", "contracting_with.efixed_point_mem'" -> "topology", "exists_local_extr_Ioo" -> "analysis", "matrix.to_lin_add" -> "algebra", "cardinal.add_eq_left" -> "set_theory", "submonoid.localization_map.map_map" -> "algebra", "category_theory.limits.prod.braiding_hom" -> "category_theory", "closure_empty" -> "topology", "path.continuous_extend" -> "topology", "set.Ioo_subset_Icc_self" -> "data", "differentiable_at.continuous_at" -> "analysis", "measure_theory.measure.haar_outer_measure_le_chaar" -> "analysis", "list.append_concat" -> "data", "finset.card_le_of_subset" -> "data", "mfderiv_id" -> "geometry", "rat.nonneg_iff_zero_le" -> "data", "strict_mono.compares" -> "order", "distrib_mul_action_hom.map_sub" -> "algebra", "set.finite.prod" -> "data", "polynomial.gcd_map" -> "data", "add_con.add_con_gen_le" -> "algebra", "category_theory.limits.biprod.map_fst" -> "category_theory", "int.nat_abs_lt_nat_abs_of_nonneg_of_lt" -> "data", "le_sup_inf" -> "order", "localization_map.is_prime_of_is_prime_disjoint" -> "algebra", "nat.succ_ne_zero" -> "init", "finite_field.card" -> "algebra", "Inf_eq_top" -> "order", "bitvec.to_fin_of_fin" -> "data", "list.pw_filter_cons_of_pos" -> "data", "holor.slice_sum" -> "data", "ring.direct_limit.lift_add" -> "algebra", "finsupp.mem_supported'" -> "algebra", "category_theory.comma.iso_mk_hom_left" -> "category_theory", "list.scanr_nil" -> "data", "add_monoid_hom.map_sub" -> "algebra", "cardinal.bit0_le_bit0" -> "set_theory", "euclidean_domain.lt_one" -> "algebra", "function.eval_apply" -> "logic", "lt_or_ge" -> "init", "dvd_mul_of_dvd_right" -> "algebra", "pairwise_on_bool" -> "data", "set.left_inv_on.congr_right" -> "data", "int.dvd_gcd" -> "algebra", "generalized_continued_fraction.num_eq_conts_a" -> "algebra", "category_theory.limits.biprod.inl_snd" -> "category_theory", "differentiable.sinh" -> "analysis", "nat.add_div_right" -> "init", "ideal.le_comap_of_map_le" -> "algebra", "list.rel_prod" -> "data", "enat.cases_on" -> "data", "list.forall\:2082_cons_left_iff" -> "data", "irrefl" -> "init", "ring_equiv.to_add_monoid_hom_refl" -> "data", "complex.abs_cpow_real" -> "analysis", "finset.sup_coe" -> "data", "with_top.le_coe_iff" -> "order", "differentiable_within_at.mono" -> "analysis", "filter.tendsto_at_top'" -> "order", "multiset.coe_ndinsert" -> "data", "normed_field.norm_fpow" -> "analysis", "nat.le_fib_self" -> "data", "has_strict_fderiv_at.mul_const" -> "analysis", "exists_has_deriv_at_eq_slope" -> "analysis", "div_eq_mul_one_div" -> "algebra", "equiv.zero_def" -> "data", "valuation.map_units_inv" -> "algebra", "additive.is_add_submonoid" -> "algebra", "multiplicity.le_multiplicity_of_pow_dvd" -> "algebra", "padic_int.zmod_repr_spec" -> "data", "has_fderiv_at.smul_algebra_const" -> "analysis", "normed_field.norm_pow" -> "analysis", "add_subgroup.add_mem_cancel_left" -> "algebra", "is_open_discrete" -> "topology", "complete_space_iff_is_complete_range" -> "topology", "set.injective_iff_inj_on_univ" -> "data", "mv_power_series.coeff_zero_one" -> "algebra", "filter.is_bounded_under_of" -> "order", "norm_num.sub_nat_pos" -> "tactic", "mul_nsmul'" -> "algebra", "finset.card_product" -> "data", "list.split_at_eq_take_drop" -> "data", "continuous_multilinear_map.norm_image_sub_le_of_bound'" -> "analysis", "strict_mono_of_le_iff_le" -> "order", "mv_polynomial.hom_eq_hom" -> "data", "polynomial.coeff_mul_X_sub_C" -> "data", "dfinsupp.induction" -> "data", "emetric.diam_union" -> "topology", "monotone_app" -> "order", "monotone.const_mul'" -> "algebra", "add_equiv.ext" -> "data", "category_theory.limits.cocone_of_split_epi_\[Iota]_app_one" -> "category_theory", "topological_fiber_bundle_core.mem_local_triv_target" -> "topology", "bor_tt" -> "init", "complex.log_im" -> "analysis", "finsupp.mem_split_support_iff_nonzero" -> "data", "metric.to_glue_l_isometry" -> "topology", "add_monoid_hom.eq_int_cast_hom" -> "data", "list.foldl_ext" -> "data", "measure_theory.measure.haar.mul_left_index_le" -> "analysis", "not_tendsto_at_bot_of_tendsto_nhds" -> "topology", "category_theory.preadditive.mono_iff_cancel_zero" -> "category_theory", "presented_group.to_group_eq_one_of_mem_closure" -> "algebra", "irrational.of_rat_div" -> "data", "set.subset_def" -> "data", "charted_space_core.open_source'" -> "geometry", "generalized_continued_fraction.zeroth_continuant_aux_eq_one_zero" -> "algebra", "list.nth_le_append" -> "data", "category_theory.preadditive.comp_sum" -> "category_theory", "is_open_map_sigma" -> "topology", "galois_connection.l_supr" -> "order", "deriv_cos" -> "analysis", "ordinal.card_type" -> "set_theory", "sigma.eta" -> "data", "list.kerase_comm" -> "data", "div_self_mul_self" -> "algebra", "mv_polynomial.aeval_C" -> "data", "filter.realizer.le_iff" -> "data", "list.lookup_eq_none" -> "data", "ennreal.le_of_forall_lt_one_mul_lt" -> "data", "linear_map.snd_apply" -> "algebra", "con.ker_lift_range_eq" -> "algebra", "free_magma.lift_of" -> "algebra", "con.eq" -> "algebra", "nhds_comap_dist" -> "topology", "le_cInf_inter" -> "order", "quotient_ring.is_open_map_coe" -> "topology", "add_eq_of_eq_add_neg" -> "algebra", "frontier_Iio" -> "topology", "finsupp.total_on_finset" -> "algebra", "computable.option_cases" -> "computability", "affine.simplex.dist_circumcenter_eq_circumradius" -> "geometry", "lie_submodule.quotient.lie_quotient_action_apply" -> "algebra", "has_ftaylor_series_up_to_on.zero_eq'" -> "analysis", "exists_open_singleton_of_open_finset" -> "topology", "list.map_const" -> "data", "int.gcd_pos_of_non_zero_left" -> "algebra", "one_div_neg_eq_neg_one_div" -> "algebra", "tendsto_add" -> "topology", "is_max_on.sub" -> "order", "complex.of_real_sinh" -> "data", "is_preconnected.image" -> "topology", "mv_power_series.inv_eq_zero" -> "algebra", "submonoid.mem_prod" -> "algebra", "is_closed_Inter" -> "topology", "subalgebra.multiset_prod_mem" -> "algebra", "bool.bnot_false" -> "data", "complex.deriv_sinh" -> "analysis", "ODE_solution_unique" -> "analysis", "tactic.ring2.horner_expr.cseval_horner'" -> "tactic", "filter.frequently_map" -> "order", "real.deriv_cosh" -> "analysis", "category_theory.cancel_epi_id" -> "category_theory", "hyperreal.lt_of_tendsto_zero_of_pos" -> "data", "finset.self_mem_range_succ" -> "data", "separated_def" -> "topology", "measure_theory.l1.simple_func.dist_eq" -> "analysis", "measure_theory.integrable_map_measure" -> "analysis", "omega.nat.is_nnf_nnf" -> "tactic", "direct_sum.to_module.ext" -> "algebra", "list.Ico.filter_lt_of_top_le" -> "data", "option.is_some_some" -> "data", "eq_zero_of_zero_eq_one" -> "algebra", "list.filter_map_map" -> "data", "smooth_on.inv" -> "geometry", "mul_bit0" -> "algebra", "lt_of_mul_lt_mul_left" -> "algebra", "embedding_inl" -> "topology", "exists_preimage_norm_le" -> "analysis", "multiset.forall_mem_cons" -> "data", "real.neg_pi_div_two_lt_arctan" -> "analysis", "setoid.map_of_surjective_eq_map" -> "data", "sum.lex_inr_inr" -> "data", "enat.to_with_top_le" -> "data", "alg_equiv.commutes" -> "algebra", "bitvec.bits_to_nat_to_list" -> "data", "mul_right_embedding_apply" -> "logic", "to_mul_neg" -> "algebra", "eq_neg_add_of_add_eq" -> "algebra", "finsupp.sum_curry_index" -> "data", "cardinal.le_lift_iff" -> "set_theory", "set.mem_Inter" -> "data", "function.is_fixed_pt.comp" -> "dynamics", "continuous_within_at_Ioo_iff_Iio" -> "topology", "measure_theory.measure.add_to_outer_measure" -> "analysis", "local_homeomorph.left_inv" -> "topology", "list.perm_lookup_all" -> "data", "function.is_periodic_pt.gcd" -> "dynamics", "finset.lt_wf" -> "data", "bilin_form.polar_to_quadratic_form" -> "algebra", "fderiv_within_id" -> "analysis", "tsum_ite_eq" -> "topology", "vector_space.card_fintype" -> "algebra", "nat.bodd_bit" -> "init", "set.compl_subset_compl" -> "data", "list.sublists_singleton" -> "data", "add_monoid_hom.coe_of_map_midpoint" -> "algebra", "set.surj_on.subset_range" -> "data", "free_group.reduce.exact" -> "algebra", "real.Sup_univ" -> "data", "nat.sub_mul_div" -> "init", "measure_theory.l1.simple_func.integral_smul" -> "analysis", "computation.exists_of_lift_rel_left" -> "data", "list.unzip_swap" -> "data", "function.injective_iff_has_left_inverse" -> "logic", "homeomorph.preimage_symm" -> "topology", "uniformly_extend_unique" -> "topology", "fin.sub_def" -> "init", "multiset.map_map" -> "data", "measure_theory.integrable_on_add_measure" -> "analysis", "polynomial.map_restriction" -> "algebra", "algebra.lmul_left_right_apply" -> "algebra", "finset.sum_product" -> "algebra", "commute.units_coe" -> "algebra", "iterated_fderiv_within_succ_eq_comp_left" -> "analysis", "supr_sum" -> "order", "monotone.le_map_supr" -> "order", "int.succ_neg_nat_succ" -> "data", "measurable.supr_Prop" -> "analysis", "lt_mul_of_lt_of_one_le'" -> "algebra", "iterated_fderiv_within_congr" -> "analysis", "set.subsingleton_univ" -> "data", "adjoin_root.induction_on" -> "algebra", "joined_in_univ" -> "topology", "multiset.nodup_ndunion" -> "data", "measure_theory.integral_univ" -> "analysis", "Mon_.comp_hom" -> "category_theory", "pnat.coe_lt_coe" -> "data", "nnreal.coe_to_real_hom" -> "data", "equiv.perm.subtype_perm_of_subtype" -> "algebra", "category_theory.Monad.Monad_to_Mon_map_hom" -> "category_theory", "computable.pair" -> "computability", "pgame.numeric.move_right" -> "set_theory", "local_homeomorph.refl_symm" -> "topology", "set.sep_subset" -> "data", "list.nodupkeys_nil" -> "data", "submodule.prod_equiv_of_is_compl_symm_apply_snd_eq_zero" -> "algebra", "polynomial.degree_X_sub_C" -> "data", "complex.cpow_zero" -> "analysis", "mem_uniform_prod" -> "topology", "symm" -> "init", "lie_algebra.orthogonal.PB_inv" -> "algebra", "quotient.mk_out'" -> "data", "mem_nhds_within_Iic_iff_exists_Ioc_subset" -> "topology", "right_coset_one" -> "algebra", "measure_theory.measure_Union_eq_supr_nat" -> "analysis", "mv_polynomial.pderivative.add_monoid_hom_apply" -> "data", "category_theory.abelian.pseudoelement.over_coe_def" -> "category_theory", "list.subperm.refl" -> "data", "ordering.ite_eq_eq_distrib" -> "init", "set.support_indicator" -> "data", "int.add_def" -> "data", "category_theory.equivalence.functor_inv" -> "category_theory", "circle_deg1_lift.le_translation_number_of_add_int_le" -> "dynamics", "category_theory.abelian.images.image_strong_epi_mono_factorisation_to_mono_factorisation_m" -> "category_theory", "int.sign_eq_zero_iff_zero" -> "init", "convex_Iio" -> "analysis", "finite_dimensional.findim_eq_card_finset_basis" -> "algebra", "measure_theory.measure_union_le" -> "analysis", "list.chain_iff_pairwise" -> "data", "centroid_mem_affine_span_of_card_ne_zero" -> "algebra", "is_coprime_of_dvd" -> "algebra", "multiset.nodup_ndinter" -> "data", "nnreal.rpow_eq_pow" -> "analysis", "filter.is_bounded_under_sup" -> "order", "norm_num.inv_div" -> "tactic", "polynomial.map_one" -> "data", "ennreal.has_sum_iff_tendsto_nat" -> "topology", "semidirect_product.map_left" -> "algebra", "semiconj_by.neg_one_right" -> "algebra", "set.insert_inter" -> "data", "rat.cast_max" -> "data", "mul_left_injective" -> "algebra", "matrix.det_update_row_smul" -> "algebra", "complex.tan_zero" -> "data", "one_one_equiv.of_equiv" -> "computability", "deriv.lhopital_zero_at_top_on_Ioi" -> "analysis", "polynomial.degree_neg" -> "data", "supr_Prop_eq" -> "order", "real.angle.coe_nat_mul_eq_nsmul" -> "analysis", "complex.arg_of_real_of_neg" -> "analysis", "padic_norm.dvd_iff_norm_le" -> "data", "alg_hom.map_one" -> "algebra", "is_closed.complete_space_coe" -> "topology", "pow_inv_comm'" -> "algebra", "Icc_mem_nhds_within_Iio" -> "topology", "set.nonempty.not_subset_empty" -> "data", "mv_polynomial.support_sum_monomial_coeff" -> "data", "continuous_linear_map.coe_mk'" -> "topology", "equiv.sigma_equiv_prod_apply" -> "data", "deriv_within_inv'" -> "analysis", "set.mem_neg" -> "algebra", "primrec.map_decode_iff" -> "computability", "num.cmp_eq" -> "data", "mv_power_series.coeff_comp_monomial" -> "algebra", "is_R_or_C.of_real_div" -> "data", "list.remove_nth_insert_nth" -> "data", "add_neg_of_nonpos_of_neg'" -> "algebra", "generalized_continued_fraction.continuants_aux_eq_continuants_aux_squash_gcf_of_le" -> "algebra", "filter.bot_ne_hyperfilter" -> "order", "equiv.to_pequiv_apply" -> "data", "ideal.mul_bot" -> "algebra", "local_homeomorph.prod_source" -> "topology", "turing.to_partrec.code.head_eval" -> "computability", "units.neg_mul_neg" -> "algebra", "polynomial.coeff_mul_X_pow" -> "data", "ordering.or_else_eq_lt" -> "algebra", "mul_dvd_mul_right" -> "algebra", "deriv_fderiv" -> "analysis", "subgroup.coe_bot" -> "algebra", "smooth_within_at.smooth_at" -> "geometry", "nat.sub_sub" -> "init", "add_eq_zero_iff" -> "algebra", "nat.div2_bit" -> "init", "affine_subspace.inter_eq_singleton_of_nonempty_of_is_compl" -> "algebra", "bex.imp_left" -> "logic", "nat.coprime_zero_right" -> "data", "ordinal.cof_zero" -> "set_theory", "structure_groupoid.le_iff" -> "geometry", "Top.presheaf_to_Type_map" -> "topology", "fact.bit0.pos" -> "data", "set.inv_on.bij_on" -> "data", "computation.map_think'" -> "data", "onote.NF_repr_split" -> "set_theory", "measurable_unit" -> "analysis", "of_add_injective" -> "algebra", "one_div_pos" -> "algebra", "polynomial.coeff_X_mul_zero" -> "data", "set.interval_swap" -> "data", "monoid_hom.to_range_ker" -> "algebra", "finset.sup_congr" -> "data", "complex.sin_two_mul" -> "data", "cardinal.mk_preimage_of_subset_range_lift" -> "set_theory", "cau_seq.lim_inv" -> "data", "set.Ici_bot" -> "data", "cluster_point_of_compact" -> "topology", "nat.div_le_self'" -> "data", "basic_smooth_bundle_core.smooth_on_proj" -> "geometry", "ennreal.tendsto_inv_nat_nhds_zero" -> "topology", "one_div_div" -> "algebra", "equiv.computable.symm" -> "computability", "category_theory.functor.pi_map" -> "category_theory", "primrec.list_length" -> "computability", "mv_polynomial.degrees_monomial" -> "data", "finset.sum_fiberwise" -> "data", "list.length_sublists" -> "data", "category_theory.comp_eq_zero_of_exact" -> "algebra", "preorder.ext" -> "order", "matrix.reindex_alg_equiv_apply" -> "algebra", "function.is_fixed_pt.to_left_inverse" -> "dynamics", "filter.tendsto.div_const" -> "analysis", "partrec.const'" -> "computability", "finset.lt_iff_ssubset" -> "data", "set.prod_mk_mem_set_prod_eq" -> "data", "free_monoid.of_def" -> "algebra", "free_semigroup.map_mul'" -> "algebra", "submonoid.subset_closure" -> "algebra", "measure_theory.ae_eq_fun.integrable_coe_fn" -> "analysis", "is_basis_empty" -> "algebra", "list.mem_attach" -> "data", "add_equiv.to_AddCommMon_iso_inv" -> "algebra", "add_units.coe_zero" -> "algebra", "gpow_mul" -> "algebra", "set.range_nonempty_iff_nonempty" -> "data", "mdifferentiable_within_at_iff" -> "geometry", "function.semiconj.maps_to_pts_of_period" -> "dynamics", "matrix.std_basis_matrix_zero" -> "data", "not_tendsto_nhds_of_tendsto_at_top" -> "topology", "set.Ici_singleton_of_top" -> "data", "list.mem_bind_of_mem" -> "data", "affine.simplex.monge_point_eq_smul_vsub_vadd_circumcenter" -> "geometry", "polynomial.monic_X_sub_C" -> "data", "induced_order_topology" -> "topology", "fderiv_within_const_smul_algebra" -> "analysis", "set.mem_bInter" -> "data", "circle_deg1_lift.forall_map_sub_of_Icc" -> "dynamics", "finset.pi_subset" -> "data", "measure_theory.ae_eq_fun.edist_add_right" -> "analysis", "list.filter_subset" -> "data", "is_local_min_on.has_fderiv_within_at_nonneg" -> "analysis", "finset.sum_apply_dite" -> "algebra", "asymptotics.is_O_with.const_mul_right" -> "analysis", "span_int_eq" -> "algebra", "list.mem_erasep_of_neg" -> "data", "metric.ball_subset_interior_closed_ball" -> "topology", "add_monoid_hom.map_mclosure" -> "algebra", "monoid_hom.coe_to_hom_units" -> "algebra", "polynomial.derivative_eval" -> "data", "submodule.map_mono" -> "algebra", "iff.elim_left" -> "init", "neg_eq_iff_add_eq_zero" -> "algebra", "mul_max_of_nonneg" -> "algebra", "has_sum.sigma" -> "topology", "differentiable_within_at_univ" -> "analysis", "qpf.corecF_eq" -> "data", "nat.mul_left_eq_self_iff" -> "data", "composition.embedding_injective" -> "combinatorics", "is_open.is_G\[Delta]" -> "topology", "gaussian_int.norm_sq_div_sub_div_lt_one" -> "data", "list.map_sublists'_aux" -> "data", "pfunctor.M.iselect_eq_default" -> "data", "directed_comp" -> "order", "times_cont_mdiff_on_congr" -> "geometry", "category_theory.comma.iso_mk_hom_right" -> "category_theory", "cau_seq.neg_lim_zero" -> "data", "enorm.max_map" -> "analysis", "polynomial.nat_degree_zero" -> "data", "matrix.update_row_apply" -> "data", "multiset.filter_map_cons_none" -> "data", "add_submonoid.coe_copy" -> "algebra", "add_left_cancel_iff" -> "algebra", "function.left_inverse.iterate" -> "logic", "linear_map.lsmul_apply" -> "algebra", "Sup_le_Sup" -> "order", "filter.has_antimono_basis.tendsto" -> "order", "finset.mem_univ_val" -> "data", "measure_theory.tsum_measure_preimage_singleton" -> "analysis", "differentiable_at.sqrt" -> "analysis", "nat.add_eq_one_iff" -> "data", "subgroup.normal_closure_mono" -> "algebra", "list.suffix_insert" -> "data", "homeomorph.comp_continuous_iff" -> "topology", "right_coset_assoc" -> "algebra", "measure_theory.measure.count_apply_infinite" -> "analysis", "list.join_split_wrt_composition_aux" -> "combinatorics", "int.neg_nonneg_of_nonpos" -> "init", "function.comp.left_id" -> "init", "proof_irrel" -> "init", "differentiable_on.log" -> "analysis", "nnreal.of_real_add" -> "data", "uniformity_eq_symm" -> "topology", "convex_cone.mem_coe" -> "analysis", "hyperreal.lt_of_pos_of_infinitesimal" -> "data", "mvpfunctor.M.bisim\:2080" -> "data", "measure_theory.simple_func.supr_eapprox_apply" -> "analysis", "complex.inv_def" -> "data", "list.Ico.eq_cons" -> "data", "submonoid.localization_map.symm_comp_of_mul_equiv_of_localizations_apply" -> "algebra", "polynomial.leading_coeff_prod'" -> "algebra", "add_units.eq_iff" -> "algebra", "is_R_or_C.abs_two" -> "data", "mv_polynomial.mem_restrict_degree_iff_sup" -> "algebra", "linear_recurrence.mk_sol_eq_init" -> "algebra", "filter.low_scores" -> "order", "category_theory.limits.cone_morphism.ext_iff" -> "category_theory", "norm_num.adc_one_bit0" -> "tactic", "finset.sdiff_inter_self" -> "data", "category_theory.limits.prod.lift_map" -> "category_theory", "filter.prod_inf_prod" -> "order", "fin.succ_inj" -> "data", "denumerable.lower_raise" -> "data", "polynomial.continuous_at" -> "analysis", "polynomial.unique_separable_of_irreducible" -> "algebra", "nonempty.congr" -> "logic", "add_self_eq_zero" -> "algebra", "generalized_continued_fraction.continuants_stable_of_terminated" -> "algebra", "linarith.int.coe_nat_mul_zero" -> "tactic", "decidable.not_and_iff_or_not" -> "init", "matrix.vec_mul_diagonal" -> "data", "nat.div2_bit1" -> "data", "set.preimage_surjective" -> "data", "list.sublist_or_mem_of_sublist" -> "data", "multiplicity.eq_some_iff" -> "algebra", "ball_and_distrib" -> "logic", "formal_multilinear_series.id_apply_ne_one" -> "analysis", "category_theory.limits.equalizer.lift_\[Iota]" -> "category_theory", "set.image2_right" -> "data", "complex.int_cast_im" -> "data", "pSet.mem_image" -> "set_theory", "submodule.inf_comap_le_comap_add" -> "algebra", "lt_div_iff_of_neg'" -> "algebra", "finsupp.span_eq_map_total" -> "algebra", "subring.le_def" -> "algebra", "nat.le_find_greatest" -> "data", "finset.prod_insert_one" -> "algebra", "hash_map.valid.erase" -> "data", "abstract_completion.continuous_coe" -> "topology", "con.mk'_ker" -> "algebra", "measure_theory.measure.haar.chaar_sup_le" -> "analysis", "filter.frequently_supr" -> "order", "local_equiv.image_inter_source_eq" -> "data", "ring_hom.comp_assoc" -> "algebra", "enat.with_top_equiv_symm_top" -> "data", "nat.test_bit_land" -> "init", "free_group.sum.of" -> "algebra", "image.is_add_submonoid" -> "algebra", "derive_fintype.finset_in.mem_mk" -> "tactic", "submonoid.map_surjective_of_surjective" -> "algebra", "has_deriv_within_at.const_sub" -> "analysis", "span_gcd" -> "algebra", "polynomial.degree_ne_of_nat_degree_ne" -> "data", "array.rev_list_length" -> "data", "disjoint.mono_left" -> "order", "finmap.ext_iff" -> "data", "complex.sin_pi_sub" -> "analysis", "category_theory.iso.refl_conj" -> "category_theory", "function.is_partial_inv_left" -> "logic", "differentiable_on.cexp" -> "analysis", "lucas_lehmer.s_mod_nonneg" -> "number_theory", "multiset.coe_eq_coe" -> "data", "filter.is_bounded_bot" -> "order", "fin.val_two" -> "data", "rel.image_id" -> "data", "measure_theory.l1.of_fun_smul" -> "analysis", "finset.union_sdiff_self" -> "data", "nat.primrec'.mkpair" -> "computability", "finset.Ico.self_eq_empty" -> "data", "set.bUnion_range_preimage_singleton" -> "data", "polynomial.separable_prod_X_sub_C_iff" -> "algebra", "submodule.ker_liftq_eq_bot" -> "algebra", "padic.valuation_zero" -> "data", "fin.succ_above_zero" -> "data", "le_add_iff_nonneg_left" -> "algebra", "ordinal.cof_bsup_le_lift" -> "set_theory", "list.disjoint_cons_left" -> "data", "times_cont_diff_within_at.continuous_within_at" -> "analysis", "pythagorean_triple.mul_is_classified" -> "number_theory", "norm_le_zero_iff" -> "analysis", "multiset.eq_zero_iff_forall_not_mem" -> "data", "continuous_on.continuous_at" -> "topology", "coinduced_bot" -> "topology", "neg_add_eq_zero" -> "algebra", "has_sum_nat_add_iff" -> "topology", "cau_seq.lim_mul_lim" -> "data", "mat_poly_equiv_coeff_apply_aux_1" -> "algebra", "galois_coinsertion.u_inf_l" -> "order", "measure_theory.measure.haar_measure_pos_of_is_open" -> "analysis", "topological_space.opens.comap_comp" -> "topology", "finset.prod_Ico_eq_prod_range" -> "algebra", "is_R_or_C.int_cast_re" -> "data", "zorn.chain.mono" -> "order", "commute.div_left" -> "algebra", "multiset.le_zero" -> "data", "nnreal.inv_pow" -> "data", "nat.cast_mul" -> "data", "quotient_add_group.ker_lift_mk'" -> "algebra", "open_embedding.to_local_equiv_coe" -> "topology", "circle_deg1_lift.map_fract_sub_fract_eq" -> "dynamics", "abs_inner_div_norm_mul_norm_eq_one_iff" -> "analysis", "int.exists_mul_self" -> "data", "mv_polynomial.degrees_prod" -> "data", "pfunctor.M.dest_mk" -> "data", "mem_connected_component" -> "topology", "cardinal.bit1_le_bit0" -> "set_theory", "one_le_of_inv_le_one" -> "algebra", "list.lookup_cons_eq" -> "data", "measurable_pi_apply" -> "analysis", "cardinal.succ_le" -> "set_theory", "finset.prod_ite_eq" -> "algebra", "ordinal.lift_umax" -> "set_theory", "ordinal.card_le_card" -> "set_theory", "has_sum_geometric_of_abs_lt_1" -> "analysis", "continuous_linear_equiv.units_equiv_to_continuous_linear_map" -> "analysis", "convergent_eqv_pure" -> "topology", "metric.emetric_closed_ball_nnreal" -> "topology", "polynomial.eval_sub" -> "data", "add_submonoid.closure_univ" -> "algebra", "lim_nhds_within_id" -> "topology", "quadratic_form.associated_apply" -> "algebra", "continuous_linear_equiv.symm_apply_eq" -> "topology", "function.injective.prod_map" -> "data", "add_con.ext'_iff" -> "algebra", "is_preconnected_empty" -> "topology", "pgame.neg_neg" -> "set_theory", "sub_nonpos_of_le" -> "algebra", "topological_group.regular_space" -> "topology", "turing.tape.map_mk'" -> "computability", "le_floor" -> "algebra", "or.imp_left" -> "init", "measure_theory.outer_measure.trim_eq" -> "analysis", "exp_neg_inv_glue.smooth" -> "analysis", "equiv.ring_equiv_apply" -> "data", "finsupp.of_multiset_apply" -> "data", "finset.eq_empty_of_not_nonempty" -> "data", "linarith.lt_of_eq_of_lt" -> "tactic", "rat.coe_nat_denom" -> "data", "subalgebra.val_apply" -> "algebra", "units.mul_inv'" -> "algebra", "set.singleton.is_add_hom" -> "algebra", "free_monoid.lift_comp_of" -> "algebra", "monoid_hom.comp_to_functor" -> "category_theory", "nat.le_of_add_le_add_left" -> "init", "ring_invo.to_fun_eq_coe" -> "algebra", "dfinsupp.support_erase" -> "data", "set.bUnion_range" -> "data", "is_ring_hom.map_zero" -> "algebra", "int.div_lt_of_lt_mul" -> "data", "ordinal.div_eq_zero_of_lt" -> "set_theory", "free_add_magma.traverse_eq" -> "algebra", "CpltSepUniformSpace.coe_of" -> "topology", "is_unit_of_mul_is_unit_right" -> "algebra", "set.univ_mul_univ" -> "algebra", "set.maps_to.inter_inter" -> "data", "finset.disjoint_iff_disjoint_coe" -> "data", "equiv.perm.inv_def" -> "data", "multiset.disjoint_ndinsert_right" -> "data", "quot.lift_indep_pr1" -> "init", "submonoid.localization_map.mul_equiv_of_mul_equiv_mk'" -> "algebra", "finset.inter_insert_of_not_mem" -> "data", "principal_seg.coe_fn_to_rel_embedding" -> "set_theory", "exists_swap" -> "logic", "order_of_dvd_card_univ" -> "algebra", "cau_seq.completion.mk_neg" -> "data", "category_theory.comma.map_left_id_hom_app_right" -> "category_theory", "eq_zero_of_ne_zero_of_mul_eq_zero" -> "algebra", "traversable.fold_map_hom_free" -> "control", "finset.mem_of_mem_insert_of_ne" -> "data", "div_mul_eq_mul_div_comm" -> "algebra", "set.inj_on_Union_of_directed" -> "data", "finset.centroid_weights_apply" -> "algebra", "inv_mul_lt_iff_lt_mul" -> "algebra", "multiset.coe_attach" -> "data", "dist_eq_norm_vsub" -> "analysis", "has_strict_fderiv_at.neg" -> "analysis", "complex.tan_of_real_im" -> "data", "semiconj_by.inv_symm_left'" -> "algebra", "free_abelian_group.one_def" -> "algebra", "computation.get_mem" -> "data", "local_homeomorph.restr_to_local_equiv" -> "topology", "int.abs_div_le_abs" -> "data", "category_theory.mono_of_mono" -> "category_theory", "has_ftaylor_series_up_to_on.prod" -> "analysis", "nat.bit1_ne_one" -> "init", "convex_on_exp" -> "analysis", "pgame.equiv_nim_grundy_value" -> "set_theory", "linear_map.mk\:2082_apply" -> "algebra", "affine_map.linear_map_vsub" -> "algebra", "deriv.lhopital_zero_nhds_right" -> "analysis", "add_localization.induction_on\:2082" -> "algebra", "int.le_sub_right_of_add_le" -> "init", "ordinal.card_univ" -> "set_theory", "function.mem_support" -> "data", "zorn.exists_maximal_of_chains_bounded" -> "order", "differentiable_at.prod_map" -> "analysis", "localization_map.is_integer_mul" -> "algebra", "list.nodup_map_iff" -> "data", "complex.exp_multiset_sum" -> "data", "pmf.coe_bind_apply" -> "analysis", "stream.tail_cons" -> "data", "real.exp_injective" -> "data", "complex.norm_sq_one" -> "data", "is_open_induced" -> "topology", "cauchy_seq_of_edist_le_geometric" -> "analysis", "int.coe_nat_ne_coe_nat_iff" -> "tactic", "ordinal.lift_le" -> "set_theory", "enat.coe_inj" -> "data", "times_cont_diff_on.continuous_on_iterated_deriv_within" -> "analysis", "sub_lt_sub_right" -> "algebra", "constr_smul" -> "algebra", "ordinal.add_lt_add_iff_left" -> "set_theory", "structure_groupoid.local_invariant_prop.lift_prop_on_chart_symm" -> "geometry", "list.count_cons" -> "data", "exists_true_iff_nonempty" -> "logic", "monotone_mul_right_of_nonneg" -> "algebra", "category_theory.limits.parallel_pair_map_right" -> "category_theory", "setoid.mk_classes_classes" -> "data", "submonoid.powers_eq_closure" -> "algebra", "midpoint_sub_right" -> "algebra", "list.indexes_values_eq_filter_enum" -> "data", "generalized_continued_fraction.exists_s_b_of_part_denom" -> "algebra", "em" -> "logic", "turing.list_blank.map_mk" -> "computability", "supr_const" -> "order", "filter.frequently_at_top" -> "order", "multiset.powerset_len_mono" -> "data", "list.nth_concat_length" -> "data", "equiv.perm.eq_inv_iff_eq" -> "algebra", "bilin_form.is_skew_adjoint_iff_neg_self_adjoint" -> "algebra", "matrix.reindex_lie_equiv_symm_apply" -> "algebra", "is_cau_series_of_abv_cau" -> "data", "direct_sum.to_group_zero" -> "algebra", "complex.uniform_continuous_of_real" -> "topology", "roption.bind_none" -> "data", "list.chain'_map" -> "data", "ennreal.coe_max" -> "data", "list.nth_le_mem" -> "data", "min_eq_right" -> "init", "omega.coeffs.val_nil" -> "tactic", "computation.eq_of_ret_mem" -> "data", "vector.traverse_def" -> "data", "finset.inter_val" -> "data", "finset.nonempty_of_prod_ne_one" -> "algebra", "ordinal.is_normal.lt_nfp" -> "set_theory", "subring.coe_Sup_of_directed_on" -> "algebra", "convex_on.exists_ge_of_center_mass" -> "analysis", "list.sublist_append_of_sublist_right" -> "data", "monoid_hom.map_range" -> "algebra", "free_magma.mul_seq" -> "algebra", "subtype.range_val_subtype" -> "data", "Set.Union_singleton" -> "set_theory", "fin.div_def" -> "init", "uniform_space.completion.uniform_continuous_completion_separation_quotient_equiv_symm" -> "topology", "category_theory.limits.is_limit.lift_cone_morphism_hom" -> "category_theory", "measure_theory.integrable.mono'" -> "analysis", "abs_lt_of_lt_of_neg_lt" -> "algebra", "nat.add_mul_mod_self_left" -> "init", "monoid_hom.map_exists_left_inv" -> "algebra", "int.coe_nat_dvd_left" -> "data", "has_deriv_at.comp" -> "analysis", "ring_equiv.to_monoid_hom_refl" -> "data", "padic_norm.triangle_ineq" -> "data", "nat.coprime.gcd_mul_right_cancel" -> "data", "lists.of_to_list" -> "set_theory", "list.split_wrt_composition_aux_cons" -> "combinatorics", "partrec.sum_cases" -> "computability", "submodule.ext'_iff" -> "algebra", "is_add_unit.map" -> "algebra", "submodule.smul_mem_iff" -> "algebra", "mdifferentiable_within_at.mfderiv_within" -> "geometry", "nnreal.is_greatest_Lp" -> "analysis", "ring.fractional_ideal.one_mem_one" -> "algebra", "filter.eq_binfi_of_mem_sets_iff_exists_mem" -> "order", "is_conj_one_right" -> "algebra", "list.exists_mem_cons_iff" -> "data", "set_of_is_preconnected_subset_of_ordered" -> "topology", "mul_action.mem_fixed_points_iff_card_orbit_eq_one" -> "algebra", "continuous_linear_equiv.one_le_norm_mul_norm_symm" -> "analysis", "list.mem_lookup_kunion" -> "data", "wseq.mem_of_mem_dropn" -> "data", "cardinal.infinite_iff" -> "set_theory", "multiplicity.get_one_right" -> "algebra", "metric.ball_union_sphere" -> "topology", "inner_product_geometry.sin_angle_sub_add_angle_sub_rev_eq_sin_angle" -> "geometry", "local_equiv.symm_image_inter_target_eq" -> "data", "encodable.mem_decode2'" -> "data", "sym2.map_id" -> "data", "uniform_space.separation_quotient.lift_mk" -> "topology", "uniform_space.completion.coe_add" -> "topology", "category_theory.limits.limit_iso_limit_curry_comp_lim_hom_\[Pi]_\[Pi]" -> "category_theory", "ideal.comap_comap" -> "algebra", "linear_map.comp_smul" -> "algebra", "times_cont_diff_iff_iterated_deriv" -> "analysis", "list.sublist.append" -> "data", "has_fderiv_within_at.comp" -> "analysis", "add_units.coe_add" -> "algebra", "add_submonoid.localization_map.lift_of_comp" -> "algebra", "power_series.coeff_monomial'" -> "algebra", "int.le_add_of_nonneg_right" -> "init", "finset.union_inter_cancel_right" -> "data", "filter.range_mem_map" -> "order", "set.Icc_inter_Icc" -> "data", "lt_add_of_lt_of_nonneg" -> "algebra", "wseq.dropn_cons" -> "data", "norm_num.add_bit1_bit0" -> "tactic", "totally_bounded_preimage" -> "topology", "exists_imp_distrib" -> "logic", "multiset.map_mk_eq_map_mk_of_rel" -> "data", "commute.left_comm" -> "algebra", "encodable.length_sorted_univ" -> "data", "complex.abs_abs" -> "data", "measure_theory.ae_eq_fun.inv_mk" -> "analysis", "tendsto_nhds_within_iff_subtype" -> "topology", "associated_zero_iff_eq_zero" -> "algebra", "bitvec.add_lsb_eq_twice_add_one" -> "data", "linear_map.cod_restrict_apply" -> "algebra", "filter.is_countably_generated.filter_basis_filter" -> "order", "measure_theory.measure.count_apply_lt_top" -> "analysis", "subring.mem_bot" -> "algebra", "min_le_max" -> "algebra", "sum_range_choose" -> "data", "fintype.coe_image_univ" -> "data", "algebraic_geometry.LocallyRingedSpace.id_val" -> "algebraic_geometry", "list.argmax_singleton" -> "data", "nat.add_left_comm" -> "init", "free_group.map.one" -> "algebra", "semidirect_product.hom_ext" -> "algebra", "finset.prod_induction" -> "algebra", "polynomial.eval_int_cast" -> "data", "category_theory.limits.coequalizer.iso_target_of_self_hom" -> "category_theory", "rel_embedding.collapse_F.lt" -> "set_theory", "bilin_form.to_matrix_comp" -> "algebra", "measure_theory.integrable_zero_measure" -> "analysis", "local_of_nonunits_ideal" -> "algebra", "one_div_lt_one_div_of_neg_of_lt" -> "algebra", "list.kunion_cons" -> "data", "mul_action_hom.id_apply" -> "algebra", "measure_theory.l1.simple_func.zero_to_simple_func" -> "analysis", "nat.add_sub_cancel_right" -> "data", "disjoint_nhds_at_top" -> "topology", "set.Inter_subset_Inter2" -> "data", "differentiable_within_at.smul_algebra_const" -> "analysis", "nat.modeq.symm" -> "data", "cancel_factors.cancel_factors_le" -> "tactic", "lt_of_lt_of_incomp" -> "init", "nonempty_psum" -> "logic", "prime_spectrum.zero_locus_bot" -> "algebraic_geometry", "is_group_hom.inv_ker_one'" -> "algebra", "convex.mono_of_deriv_nonneg" -> "analysis", "matrix.mul_neg" -> "data", "equiv.add_equiv_apply" -> "data", "not_nonempty_iff_imp_false" -> "logic", "measure_theory.integrable_on.right_of_union" -> "analysis", "measure_theory.coe_to_outer_measure" -> "analysis", "decidable_eq_inr_neg" -> "init", "linear_map.disjoint_ker'" -> "algebra", "measure_theory.lintegral_congr_ae" -> "analysis", "bot_lt_iff_ne_bot" -> "order", "has_strict_fderiv_at.eventually_left_inverse" -> "analysis", "has_mfderiv_at.continuous_at" -> "geometry", "list.nodup_join" -> "data", "linear_map.zero_apply" -> "algebra", "contracting_with.tendsto_iterate_efixed_point" -> "topology", "category_theory.limits.is_image.fac_lift_assoc" -> "category_theory", "tensor_product.map_tmul" -> "algebra", "gcd_zero_left" -> "algebra", "rel_embedding.is_trichotomous" -> "order", "le_of_sup_eq" -> "order", "enat.get_le_get" -> "data", "traversable.to_list_map" -> "control", "dvd_add_iff_left" -> "algebra", "padic_val_rat.defn" -> "data", "nat.mod_def" -> "init", "tactic.ring2.horner_expr.cseval_of_csexpr" -> "tactic", "tangent_bundle_model_space_topology_eq_prod" -> "geometry", "pnat.gcd_rel_left" -> "data", "is_group_hom.map_one" -> "algebra", "is_measurable.diff_null" -> "analysis", "list.forall_mem_of_forall_mem_union_right" -> "data", "int.eq_of_mod_eq_of_nat_abs_sub_lt_nat_abs" -> "data", "trunc.induction_on\:2082" -> "data", "exists_eq_left'" -> "logic", "onote.zero_add" -> "set_theory", "topological_space.opens.gi_choice_val" -> "topology", "free_semigroup.map_of" -> "algebra", "measure_theory.tendsto_lintegral_norm_of_dominated_convergence" -> "analysis", "category_theory.monoidal_category.unitors_equal.cells_6" -> "category_theory", "pi.smul_apply'" -> "algebra", "eventually_norm_pow_le" -> "analysis", "gaussian_int.norm_pos" -> "data", "is_G\[Delta]_univ" -> "topology", "multiset.sum_add" -> "data", "is_unit_of_dvd_unit" -> "algebra", "finsupp.support_subtype_domain" -> "data", "tactic.ring_exp.add_pf_sum_overlap_zero" -> "tactic", "ordinal.one_eq_type_unit" -> "set_theory", "computable.of_eq" -> "computability", "int.lt_div_add_one_mul_self" -> "data", "polynomial.splitting_field_aux.algebra_map_succ" -> "algebra", "measure_theory.measure.restrict_apply_eq_zero" -> "analysis", "is_open_sUnion" -> "topology", "add_submonoid.closure_eq" -> "algebra", "is_bounded_bilinear_map.continuous_right" -> "analysis", "powers_eq_gpowers" -> "algebra", "seq.mem_cons_of_mem" -> "data", "finset.sum_nonneg" -> "algebra", "homeomorph.to_local_homeomorph_coe_symm" -> "topology", "ennreal.tendsto.mul_const" -> "topology", "category_theory.limits.zero_of_to_zero" -> "category_theory", "filter.is_basis.filter_eq_generate" -> "order", "joined_in.symm" -> "topology", "Set.map_fval" -> "set_theory", "strict_mono.mul" -> "algebra", "linear_map.findim_le_findim_of_injective" -> "algebra", "has_deriv_at.lhopital_zero_right_on_Ico" -> "analysis", "omega.nat.val_canonize" -> "tactic", "finset.attach_eq_univ" -> "data", "add_submonoid.map_map" -> "algebra", "pgame.mk_le_mk" -> "set_theory", "function.left_inverse.comp" -> "logic", "measure_theory.ae_eq_fun.coe_fn_le" -> "analysis", "list.perm.subperm" -> "data", "sub_mul_add_eq_of_mul_add_eq_mul_add" -> "algebra", "Group.one_apply" -> "algebra", "nat.add_le_to_le_sub" -> "init", "euclidean_domain.lcm_zero_right" -> "algebra", "le_sup_right" -> "order", "set.preimage_neg_Ioi" -> "data", "padic_val_rat_of_nat" -> "data", "irrational_sqrt_two" -> "data", "finset.prod_union_inter" -> "algebra", "homological_complex.comm" -> "algebra", "matrix.to_bilin_form_apply" -> "algebra", "subsemiring.mk'_to_submonoid" -> "algebra", "Sup_le_Sup_of_subset_instert_bot" -> "order", "linear_equiv.lie_conj_apply" -> "algebra", "computation.think_bind" -> "data", "multiset.sub_le_sub_right" -> "data", "rat.denom_one" -> "data", "turing.TM2to1.supports_run" -> "computability", "bounded_continuous_function.arzela_ascoli" -> "topology", "category_theory.limits.prod_comparison_inv_natural" -> "category_theory", "sylow.mem_fixed_points_mul_left_cosets_iff_mem_normalizer" -> "algebra", "strict_mono.mul_monotone" -> "algebra", "times_cont_mdiff.times_cont_mdiff_at" -> "geometry", "uniform_continuous\:2082.uniform_continuous" -> "topology", "rel_iso.coe_one" -> "order", "abs_max_sub_max_le_abs" -> "algebra", "nat.sub_lt_succ" -> "init", "measure_theory.lintegral_supr" -> "analysis", "filter.germ.induction_on" -> "order", "rank_finset_sum_le" -> "algebra", "bitvec.bits_to_nat_to_bool" -> "data", "measure_theory.le_inner_content" -> "analysis", "list.reverse_foldl" -> "data", "continuous_linear_map.smul_right_one_eq_iff" -> "topology", "measure_theory.simple_func.lintegral_map" -> "analysis", "mv_polynomial.map_monomial" -> "data", "list.mem_split" -> "data", "function.support_div" -> "data", "mv_polynomial.pderivative_mul" -> "data", "lower_bounds_union" -> "order", "subring.mem_map" -> "algebra", "finsupp.to_multiset_strict_mono" -> "data", "implies_of_if_neg" -> "init", "equiv.arrow_congr_refl" -> "data", "int.div_eq_zero_of_lt" -> "data", "enorm.finite_norm_eq" -> "analysis", "list.extractp_eq_find_erasep" -> "data", "lie_self" -> "algebra", "submodule.span_eq_of_le" -> "algebra", "measure_theory.norm_set_integral_le_of_norm_le_const" -> "analysis", "dim_fin_fun" -> "algebra", "measure_theory.simple_func.lintegral_eq_lintegral" -> "analysis", "mem_closure_iff_seq_limit" -> "topology", "deriv_sqrt" -> "analysis", "finsupp.to_finset_to_multiset" -> "data", "quotient_map_quotient_mk" -> "topology", "set.finite_range_ite" -> "data", "bernoulli_three" -> "number_theory", "deriv_const_mul" -> "analysis", "prime_spectrum.comap_as_ideal" -> "algebraic_geometry", "category_theory.limits.image.iso_strong_epi_mono_inv_comp_mono" -> "category_theory", "is_local_max.inf" -> "topology", "free_comm_ring.map_subtype_val_restriction" -> "algebra", "list.length_pos_iff_ne_nil" -> "data", "polynomial.aeval_alg_hom" -> "data", "equiv.nonempty_iff_nonempty" -> "data", "int.add_mod_self" -> "data", "matrix.diag_apply" -> "algebra", "pfunctor.M.nth_of_bisim" -> "data", "is_noetherian_submodule_left" -> "algebra", "filter.eventually_eq.prod_mk" -> "order", "omega.clauses.unsat_nil" -> "tactic", "padic_polynomial_dist" -> "data", "set.preimage_const_sub_Ico" -> "data", "nat.cases_succ" -> "computability", "linear_map.continuous_on_pi" -> "analysis", "padic_int.appr_spec" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_obj_X_map" -> "category_theory", "category_theory.abelian.pseudoelement.pseudo_apply_mk" -> "category_theory", "magma.free_semigroup.map_mul" -> "algebra", "polynomial.is_noetherian_ring" -> "algebra", "is_bounded_bilinear_map.is_O" -> "analysis", "equiv.swap_core_swap_core" -> "data", "filter.eventually.congr" -> "order", "nat.div_zero" -> "init", "matrix_equiv_tensor.left_inv" -> "algebra", "nat.choose_two_right" -> "data", "equiv.prod_sum_distrib_apply_left" -> "data", "unique_diff_on.inter" -> "analysis", "is_irrefl.swap" -> "order", "typevec.subtype_val_nil" -> "data", "int.shiftl_eq_mul_pow" -> "data", "finset.mem_powerset_len" -> "data", "polynomial.nat_degree_eq_zero_iff_degree_le_zero" -> "data", "submodule.map_inl" -> "algebra", "real.cos_sub_cos" -> "analysis", "equiv.sum_pempty_apply_inl" -> "data", "polynomial.integral_normalization_coeff_degree" -> "data", "semiconj_by.units_coe_iff" -> "algebra", "ennreal.div_add_div_same" -> "data", "iff_not_self" -> "init", "equiv.perm.sign_aux_mul" -> "algebra", "AddCommGroup.kernel_iso_ker_hom_comp_subtype" -> "algebra", "field.direct_limit.mul_inv_cancel" -> "algebra", "nat.cast_pred" -> "data", "mv_polynomial.coe_one" -> "algebra", "matrix.adjugate_mul" -> "algebra", "category_theory.monoidal_of_has_finite_products.tensor_obj" -> "category_theory", "pfunctor.liftp_iff'" -> "data", "submonoid.le_def" -> "algebra", "localization_map.ring_equiv_of_ring_equiv_eq_map_apply" -> "algebra", "has_ftaylor_series_up_to_on.continuous_on" -> "analysis", "encodable.decode_prod_val" -> "data", "continuous_within_at_of_locally_uniform_approx_of_continuous_within_at" -> "topology", "nat.gcd_gcd_self_right_left" -> "data", "div_lt_div_left" -> "algebra", "function.is_periodic_pt.const_mul" -> "dynamics", "measure_theory.ae_eq_fun.lift_rel_mk_mk" -> "analysis", "category_theory.limits.types.prod" -> "category_theory", "list.foldr_append" -> "data", "mod_mem_iff" -> "algebra", "ordinal.min_eq" -> "set_theory", "set.Inter_inter_distrib" -> "data", "polynomial.coeff_monomial" -> "data", "list.any_cons" -> "data", "set.preimage_const_mul_Ioc" -> "data", "abs_mul_self" -> "algebra", "valuation.comap_comp" -> "algebra", "char_p.char_is_prime_of_pos" -> "algebra", "measure_theory.measure.map_mul_right_eq_self" -> "analysis", "affine_subspace.direction_inf" -> "algebra", "generalized_continued_fraction.ext" -> "algebra", "le_cSup_of_le" -> "order", "sub_neg_eq_add" -> "algebra", "commute.pow_right" -> "algebra", "set.bInter_range" -> "data", "pos_num.cast_to_znum" -> "data", "filter.image_mem_map" -> "order", "nat.prime.one_lt" -> "data", "is_subgroup.mem_center" -> "algebra", "set.set_of_mem_eq" -> "data", "category_theory.le_of_hom" -> "category_theory", "le_binfi" -> "order", "equiv.eq_symm_apply" -> "data", "finsupp.smul_sum" -> "algebra", "category_theory.limits.biproduct.map_eq" -> "category_theory", "partrec.fix" -> "computability", "uniform_space.uniformity_quotient" -> "topology", "polynomial.degree_pos_of_irreducible" -> "data", "list.pairwise_lt_range" -> "data", "zmod.card" -> "data", "set.singleton_seq" -> "data", "list.find_indexes_eq_map_indexes_values" -> "data", "hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg" -> "data", "list.head_add_tail_sum'" -> "data", "partrec.nat_cases_right" -> "computability", "stream.tail_iterate" -> "data", "traversable.traverse_eq_map_id'" -> "control", "pfunctor.M.children_mk" -> "data", "ordinal.type_ne_zero_iff_nonempty" -> "set_theory", "filter.map_inj" -> "order", "list.perm.swap'" -> "data", "prime_multiset.prod_zero" -> "data", "category_theory.iso.cancel_iso_inv_right" -> "category_theory", "isometric.symm_apply_apply" -> "topology", "structure_groupoid.local_invariant_prop.lift_prop_within_at_indep_chart" -> "geometry", "quotient_add_group.range_ker_lift_injective" -> "algebra", "set.inter_univ" -> "data", "pnat.factor_multiset_le_iff" -> "data", "inducing_of_inducing_compose" -> "topology", "monotone.iterate_ge_of_ge" -> "order", "category_theory.limits.types.sigma" -> "category_theory", "subgroup.comap_comap" -> "algebra", "znum.cast_succ" -> "data", "inner_self_eq_zero" -> "analysis", "is_measurable_Ioc" -> "analysis", "measurable_space.comap_bot" -> "analysis", "list.reverse_nil" -> "data", "multiset.zero_disjoint" -> "data", "filter.lift_inf" -> "order", "lists.is_list_of_mem" -> "set_theory", "seq.of_list_cons" -> "data", "forall_lt_iff_le'" -> "algebra", "neg_neg_of_pos" -> "algebra", "inner_product_space.of_core.inner_comm" -> "analysis", "nat.even_add" -> "data", "category_theory.functor.map_arrow_obj_right" -> "category_theory", "lim_nhds_id" -> "topology", "is_preconnected.intermediate_value" -> "topology", "power_series.inv_of_unit_eq'" -> "algebra", "partrec\:2082.comp" -> "computability", "category_theory.limits.cocones.ext_hom_hom" -> "category_theory", "circle_deg1_lift.pow_mono" -> "dynamics", "ring_hom.eq_of_eq_on_set_top" -> "algebra", "finset.card_sigma" -> "algebra", "ordinal.pred_eq_iff_not_succ" -> "set_theory", "concave_on.le_on_segment" -> "analysis", "finset.ne_insert_of_not_mem" -> "data", "linear_equiv.conj_comp" -> "algebra", "primrec.const" -> "computability", "local_equiv.refl_restr_target" -> "data", "ordinal.zero_power'" -> "set_theory", "primrec.list_reverse" -> "computability", "continuous_linear_map.lmul_right_apply" -> "analysis", "mfderiv_within_subset" -> "geometry", "cardinal.prop_eq_two" -> "set_theory", "category_theory.concrete_category.mono_of_injective" -> "category_theory", "filter.add_mem_add" -> "order", "submonoid.forall" -> "algebra", "primrec.list_append" -> "computability", "ordinal.succ_pred_iff_is_succ" -> "set_theory", "rel_iso.map_sup" -> "order", "turing.TM2to1.add_bottom_head_fst" -> "computability", "set.disjoint_right" -> "data", "category_theory.limits.prod_map_id_comp_assoc" -> "category_theory", "semiquot.is_pure_iff" -> "data", "one_div_le_neg_one" -> "algebra", "linear_map.proj_apply" -> "algebra", "euclidean_geometry.dist_affine_combination" -> "geometry", "exists_integral_multiple" -> "algebra", "semiquot.is_pure.mono" -> "data", "order_of_dvd_iff_pow_eq_one" -> "algebra", "padic_val_rat.min_le_padic_val_rat_add" -> "data", "set.pairwise_disjoint.subset" -> "data", "eq_univ_of_nonempty_clopen" -> "topology", "nat.pow_one" -> "init", "neg_nonneg" -> "algebra", "real.tanh_zero" -> "data", "subgroup.prod_mem" -> "algebra", "pos_num.one_sub'" -> "data", "finset.nat.card_antidiagonal" -> "data", "exists_mem_ne_zero_of_dim_pos" -> "algebra", "polynomial.separable_X_sub_C" -> "algebra", "nat.le_antisymm" -> "init", "one_div_pow" -> "algebra", "times_cont_diff_within_at_univ" -> "analysis", "quot.induction_on" -> "init", "normed_field.norm_inv" -> "analysis", "smooth_iff" -> "geometry", "filter.inf_ne_bot_iff" -> "order", "galois_connection.is_glb_l" -> "order", "filter.tendsto.prod_mk" -> "order", "category_theory.monad.forget_map" -> "category_theory", "ordering.ite_eq_gt_distrib" -> "init", "has_deriv_within_at.mono" -> "analysis", "pSet.mem.ext" -> "set_theory", "real.le_of_forall_epsilon_le" -> "data", "adjoin_root.lift_root" -> "algebra", "multiset.fold_eq_foldr" -> "data", "false_of_a_eq_not_a" -> "init", "basic_smooth_bundle_core.times_cont_mdiff_on_proj" -> "geometry", "complex.sin_zero" -> "data", "valuation.comap_on_quot_eq" -> "algebra", "add_submonoid.comap_top" -> "algebra", "pgame.first_wins_of_equiv_iff" -> "set_theory", "finsupp.to_multiset_single" -> "data", "local_equiv.source_inter_preimage_inv_preimage" -> "data", "bdd_above_Icc" -> "order", "sub_lt_sub_of_lt_of_le" -> "algebra", "multiset.nodup_pmap" -> "data", "category_theory.limits.biprod.lift_desc" -> "category_theory", "multiset.nodup_of_nodup_cons" -> "data", "nat.sub_mono_right_strict" -> "tactic", "asymptotics.is_O_with.const_mul_left" -> "analysis", "prod.mk_sub_mk" -> "algebra", "localization_map.lift_eq_iff" -> "algebra", "pi_Lp.aux_uniformity_eq" -> "topology", "seq.map_append" -> "data", "ideal.is_maximal.exists_inv" -> "algebra", "with_zero.mul_left_inv" -> "algebra", "circle_deg1_lift.map_sub_int" -> "dynamics", "real.mul_pos" -> "data", "multiset.ndinsert_of_not_mem" -> "data", "equiv.perm.pow_apply_eq_self_of_apply_eq_self" -> "algebra", "bool.bor_inl" -> "data", "cont_t.run_with_cont_t" -> "control", "list.sublist_of_cons_sublist" -> "data", "matrix.special_linear_group.ext_iff" -> "algebra", "multiset.of_mem_filter" -> "data", "qpf.id_map" -> "data", "edist_le_Ico_sum_edist" -> "topology", "turing.TM2to1.tr_supports" -> "computability", "list.mem_range" -> "data", "upper_bounds_Ioo" -> "order", "list.insert_nth_remove_nth_of_le" -> "data", "differentiable_on.cosh" -> "analysis", "isometry_emetric_iff_metric" -> "topology", "differentiable_within_at.iterate" -> "analysis", "le_nhds_of_Limsup_eq_Liminf" -> "topology", "pgame.nim_add_nim_equiv" -> "set_theory", "set.finite.compact_bUnion" -> "topology", "isometric.range_coe" -> "topology", "fpow_zero" -> "algebra", "submodule.orthogonal_gc" -> "analysis", "circle_deg1_lift.tendsto_translation_number\:2080" -> "dynamics", "num.add_zero" -> "data", "set.ord_connected_Ioc" -> "data", "set.disjoint.union_left" -> "data", "eq_add_neg_iff_add_eq" -> "algebra", "ideal.is_jacobson_localization" -> "algebra", "linear_map.ker_id" -> "algebra", "units.mul_left_dvd" -> "algebra", "pow_eq_mod_order_of" -> "algebra", "linear_action_smul_act" -> "algebra", "set.preimage_kern_image" -> "data", "with_top.coe_Sup" -> "order", "semiconj_by.sub_right" -> "algebra", "set.range_inclusion" -> "data", "finsupp.sum_smul_index" -> "data", "list.filter_map_filter_map" -> "data", "category_theory.non_preadditive_abelian.image.fac_assoc" -> "category_theory", "int.lt_of_add_lt_add_right" -> "init", "category_theory.graded_object.comap_eq_hom_app" -> "category_theory", "is_integral_mul" -> "algebra", "measure_theory.outer_measure.Inf_gen_nonempty2" -> "analysis", "category_theory.limits.coequalizer.\[Pi]_desc" -> "category_theory", "metric.mem_ball'" -> "topology", "finset.monotone_preimage" -> "data", "is_basis.dual_lin_independent" -> "algebra", "continuous_at.prod" -> "topology", "has_deriv_at.const_mul" -> "analysis", "linear_equiv.to_Module_iso_hom" -> "algebra", "bounded_continuous_function.dist_set_exists" -> "topology", "ennreal.to_nnreal_add" -> "data", "ordinal.le_power_self" -> "set_theory", "associated_mul_left_cancel" -> "algebra", "inf_sup_left" -> "order", "asymptotics.is_o.tendsto_0" -> "analysis", "fintype.card_sigma" -> "data", "has_fderiv_at_filter_id" -> "analysis", "power_series.trunc_add" -> "algebra", "znum.bit1_of_bit1" -> "data", "complex.cos_two_pi" -> "analysis", "affine_independent_iff_linear_independent_vsub" -> "algebra", "ctop.realizer.nhds_F" -> "data", "asymptotics.is_o.comp_tendsto" -> "analysis", "ordinal.is_normal.deriv_fp" -> "set_theory", "category_theory.ev_coev_assoc" -> "category_theory", "monotone.map_infi2_le" -> "order", "is_add_group_hom.sub" -> "algebra", "list.length_erasep_of_mem" -> "data", "not_and_of_not_left" -> "logic", "equiv.forall_congr_left'" -> "data", "list.func.get_pointwise" -> "data", "tendsto_at_top_add_tendsto_left" -> "topology", "set.not_disjoint_iff" -> "data", "is_local_min.comp_continuous_on" -> "topology", "complex.continuous_sin" -> "analysis", "filter.liminf_eq_supr_infi" -> "order", "has_fderiv_at.snd" -> "analysis", "int.lt_of_neg_lt_neg" -> "init", "rat.zero_ne_one" -> "data", "fract_coe" -> "algebra", "is_complete_of_complete_image" -> "topology", "continuous_linear_map.is_bounded_linear_map" -> "analysis", "affine_subspace.ext_of_direction_eq" -> "algebra", "pfunctor.supp_eq" -> "data", "has_strict_fderiv_at.differentiable_at" -> "analysis", "category_theory.limits.pushout_cocone.of_cocone_\[Iota]" -> "category_theory", "nat.lxor_bit" -> "init", "category_theory.curry_id_eq_coev" -> "category_theory", "field.direct_limit.exists_inv" -> "algebra", "linarith.le_of_eq_of_le" -> "tactic", "polynomial.exists_finset_roots" -> "data", "set.Icc_subset_Ici_self" -> "data", "finset.union_distrib_left" -> "data", "nat.lt_of_sub_pos" -> "data", "nat.primrec.mul" -> "computability", "pfun.compl_dom_subset_core" -> "data", "primrec.ulower_up" -> "computability", "ordinal.lift_is_limit" -> "set_theory", "free_ring.coe_add" -> "algebra", "filter.eventually_eq.is_max_filter_iff" -> "order", "category_theory.limits.cone_left_op_of_cocone_\[Pi]_app" -> "category_theory", "nonempty_sigma" -> "logic", "abstract_completion.extend_def" -> "topology", "finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype" -> "algebra", "homeomorph.quotient_map" -> "topology", "affine_subspace.direction_eq_vector_span" -> "algebra", "function.support_add" -> "data", "category_theory.functor.left_adjoint_of_is_equivalence" -> "category_theory", "ordinal.cof_eq" -> "set_theory", "vector3.cons_head_tail" -> "number_theory", "category_theory.comma.map_right_id_inv_app_left" -> "category_theory", "list.erase_dup_eq_self" -> "data", "nhds_left_sup_nhds_right" -> "topology", "measure_theory.integrable.neg" -> "analysis", "abs_of_pos" -> "algebra", "ideal.is_prime.comap" -> "algebra", "rel_iso.inv_apply_self" -> "order", "vector.eq_nil" -> "data", "affine_map.add_linear" -> "algebra", "subring.coe_mul" -> "algebra", "cardinal.lift_ord" -> "set_theory", "is_add_group_hom.injective_iff_trivial_ker" -> "algebra", "circle_deg1_lift.transnum_aux_seq_zero" -> "dynamics", "measure_theory.norm_set_integral_le_of_norm_le_const'" -> "analysis", "finset.subset_union_left" -> "data", "category_theory.non_preadditive_abelian.lift_sub_lift" -> "category_theory", "finsupp.single_left_inj" -> "data", "finset.card_eq_one" -> "data", "filter.tendsto_at_top_of_add_bdd_above_right" -> "order", "turing.TM2to1.tr_eval" -> "computability", "eq_affine_combination_of_mem_affine_span" -> "algebra", "eq.symm" -> "init", "add_comm_group.direct_limit.lift_of" -> "algebra", "mv_polynomial.total_degree_finset_prod" -> "data", "times_cont_diff_at_snd" -> "analysis", "tactic.abel.zero_smul" -> "tactic", "applicative_transformation.preserves_map" -> "control", "category_theory.monad.algebra.hom.ext" -> "category_theory", "ctop.realizer.mem_interior_iff" -> "data", "set.image_diff_preimage" -> "data", "ideal.is_maximal_of_is_integral_of_is_maximal_comap" -> "algebra", "mul_nonneg_of_nonpos_of_nonpos" -> "algebra", "mul_lt_of_lt_one_of_lt'" -> "algebra", "complex.one_cpow" -> "analysis", "rat.num_nonneg_iff_zero_le" -> "data", "cardinal.mul_eq_left" -> "set_theory", "pnat.bit0_le_bit0" -> "data", "category_theory.currying_inverse_map_app_app" -> "category_theory", "list.sublist.trans" -> "data", "topological_group.t2_space" -> "topology", "matrix.det_transpose" -> "algebra", "submonoid.localization_map.of_mul_equiv_of_dom_id" -> "algebra", "convex_cone.salient_iff_not_flat" -> "analysis", "mul_le_mul_of_nonneg_right" -> "algebra", "real.arccos_nonneg" -> "analysis", "strict_mono.add_const" -> "algebra", "nhds_eq_uniformity" -> "topology", "filter.exists_lt_of_tendsto_at_top" -> "order", "set.image_univ" -> "data", "infi_false" -> "order", "finset.fold_op_rel_iff_or" -> "data", "has_groupoid_of_pregroupoid" -> "geometry", "category_theory.limits.cones.ext_inv_hom" -> "category_theory", "div_right_comm" -> "algebra", "fixed_points.minpoly.irreducible" -> "algebra", "finsupp.prod_zero_index" -> "data", "int.even_coe_nat" -> "data", "multiset.Ico.filter_lt" -> "data", "is_separated_iff_induced" -> "topology", "norm_sub_square_eq_norm_square_add_norm_square" -> "analysis", "polynomial.roots_multiset_prod" -> "data", "metric.continuous_within_at_iff'" -> "topology", "extend_from_extends" -> "topology", "submodule.convex" -> "analysis", "affine_subspace.vsub_right_mem_direction_iff_mem" -> "algebra", "measure_theory.measure_empty" -> "analysis", "int.to_nat_coe_nat_add_one" -> "data", "complex.abs_two" -> "data", "ennreal.forall_ennreal" -> "data", "hensels_lemma" -> "data", "galois_coinsertion.l_le_l_iff" -> "order", "ring.exists_list_of_mem_closure" -> "algebra", "or_of_or_of_imp_right" -> "logic", "coinduced_mono" -> "topology", "ennreal.of_real_ne_top" -> "data", "continuous_linear_equiv.symm_equiv_of_inverse" -> "topology", "category_theory.limits.map_pair_right" -> "category_theory", "differentiable_at.log" -> "analysis", "submodule.coe_neg" -> "algebra", "nat.lt_or_ge" -> "init", "nat.sqrt_lt_self" -> "data", "ring.image_closure" -> "algebra", "real.has_deriv_at_rpow_of_neg" -> "analysis", "add_group_with_zero_nhd.add_Z" -> "topology", "finsupp.subtype_domain_add" -> "data", "category_theory.comonad.forget_obj" -> "category_theory", "gsmul_eq_mul'" -> "algebra", "finset.sum_comm" -> "algebra", "zsqrtd.decompose" -> "data", "int.mod_self" -> "data", "nonempty_ulift" -> "logic", "linear_independent_Union_of_directed" -> "algebra", "real.one_lt_exp_iff" -> "data", "has_deriv_at.sin" -> "analysis", "magma.free_semigroup.lift_mul" -> "algebra", "differentiable_within_at.add_const" -> "analysis", "tactic.ring_exp.add_pf_sum_lt" -> "tactic", "hyperreal.infinite_iff_infinite_neg" -> "data", "euclidean_geometry.orthogonal_projection_def" -> "geometry", "interior_subset_closure" -> "topology", "dvd_mul_left" -> "algebra", "pgame.turn_bound_of_right" -> "set_theory", "lie_algebra.morphism.range_bracket" -> "algebra", "ordinal.is_normal.refl" -> "set_theory", "finset.card_image_of_inj_on" -> "data", "option.get_or_else_some" -> "data", "max_self" -> "init", "convex_cone.ext" -> "analysis", "vadd_vsub_vadd_cancel_left" -> "algebra", "int.not_even_bit1" -> "data", "polynomial.nat_degree_one" -> "data", "equiv.sum_compl_apply_symm_of_pos" -> "data", "pythagorean_triple.eq" -> "number_theory", "list.mem_keys_kinsert" -> "data", "monotone.map_sup" -> "order", "linear_equiv.arrow_congr_trans" -> "algebra", "alist.insert_entries_of_neg" -> "data", "ordinal.cof_add" -> "set_theory", "submonoid.comap_inf" -> "algebra", "finset.image_bind" -> "data", "dfinsupp.prod_neg_index" -> "data", "turing.list_blank.tail_mk" -> "computability", "metric.diam_closed_ball" -> "topology", "smooth_iff_proj_smooth" -> "geometry", "list.mem_permutations_aux2" -> "data", "int.div_one" -> "data", "prod.snd_add" -> "algebra", "neg_le_abs_self" -> "algebra", "continuous_linear_map.differentiable_on" -> "analysis", "finset.disjoint_bind_left" -> "data", "free_group.sum.inv" -> "algebra", "add_subgroup.mem_center_iff" -> "algebra", "abs_one_div" -> "algebra", "nat.lt_sub_right_of_add_lt" -> "data", "list.erasep_append_right" -> "data", "times_cont_mdiff_within_at.congr_of_eventually_eq" -> "geometry", "set.disjoint_of_subset" -> "data", "eq_orthogonal_projection_fn_of_mem_of_inner_eq_zero" -> "analysis", "filter.eventually.and" -> "order", "finset.bUnion_finset_image" -> "data", "filter.supr_join" -> "order", "times_cont_diff_on.ftaylor_series_within" -> "analysis", "ring_equiv.is_integral_domain" -> "data", "subsemiring.coe_subset_coe" -> "algebra", "convex.combo_self" -> "analysis", "znum.le_to_int" -> "data", "free_ring.coe_neg" -> "algebra", "iter_deriv_pow" -> "analysis", "category_theory.sum.inr__obj" -> "category_theory", "computation.terminates_of_lift_rel" -> "data", "buffer.to_list_append_list" -> "data", "subsemiring.comap_inf" -> "algebra", "padic_seq.val_eq_iff_norm_eq" -> "data", "finset.map_map" -> "data", "add_monoid_algebra.zero_mul" -> "data", "free_add_magma.traverse_pure'" -> "algebra", "ennreal.tsum_eq_supr_sum" -> "topology", "algebra.adjoin_algebra_map'" -> "algebra", "finset.mono_of_fin_singleton" -> "data", "add_monoid_hom.coe_fst" -> "algebra", "local_ring.is_unit_or_is_unit_one_sub_self" -> "algebra", "set.fmap_eq_image" -> "data", "partrec.nat_elim" -> "computability", "generalized_continued_fraction.squash_seq_succ_n_tail_eq_squash_seq_tail_n" -> "algebra", "primrec.option_get" -> "computability", "is_lub_of_mem_nhds" -> "topology", "function.right_inverse_iff_comp" -> "logic", "measure_theory.ae_eq_fun.coe_fn_pair" -> "analysis", "matrix.transpose_empty_rows" -> "data", "sum.swap_right_inverse" -> "data", "is_add_monoid_hom.comp" -> "algebra", "is_coprime.mul_right_iff" -> "algebra", "hyperreal.is_st_add" -> "data", "real.sqrt_two_add_series_two" -> "analysis", "multiset.rel_cons_left" -> "data", "wseq.nil_append" -> "data", "exists_extension_norm_eq" -> "analysis", "finmap.mem_insert" -> "data", "nat.not_pos_pow_dvd" -> "data", "nat.lor_comm" -> "data", "has_fpower_series_on_ball.neg" -> "analysis", "interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right" -> "analysis", "set.Iic_def" -> "data", "not_iff_not" -> "logic", "set.set_compr_eq_eq_singleton" -> "data", "norm_num.min_fac_helper_2" -> "tactic", "category_theory.id_of_comp_left_id" -> "category_theory", "asymptotics.is_o.prod_left" -> "analysis", "category_theory.evaluation_map_app" -> "category_theory", "direct_sum.of_sub" -> "algebra", "finset.max_eq_none" -> "data", "ring_hom.ker_eq_comap_bot" -> "algebra", "fintype.card_equiv" -> "data", "nonote.repr_mul" -> "set_theory", "ring_hom.ext_int" -> "data", "int.neg_ne_zero_of_ne" -> "init", "set.diff_singleton_eq_self" -> "data", "num.of_znum_to_nat" -> "data", "polynomial.separable.injective_of_prod_X_sub_C" -> "algebra", "add_pow_char_pow" -> "algebra", "cardinal.finset_card" -> "set_theory", "measure_theory.measure.sum_bool" -> "analysis", "ennreal.pow_eq_top" -> "data", "fin.pred_above_succ_above" -> "data", "finsupp.prod_fintype" -> "data", "linear_independent_Union_finite_subtype" -> "algebra", "filter.tendsto.sub" -> "topology", "interval_integral.integral_has_deriv_at_left" -> "analysis", "inv_nonneg" -> "algebra", "int.test_bit_zero" -> "data", "nat.coprime.pow_left" -> "data", "differentiable_at.fst" -> "analysis", "emetric.Hausdorff_edist_self" -> "topology", "ordinal.lt_power_succ_log" -> "set_theory", "adjoin_root.adjoin_root_eq_top" -> "algebra", "Top.presheaf_to_Top_obj" -> "topology", "measurable.indicator" -> "analysis", "cauchy.map" -> "topology", "bounded_continuous_function.smul_apply" -> "topology", "primrec.list_head" -> "computability", "equiv.sum_compl_apply_inl" -> "data", "sym2.eq_iff" -> "data", "zsqrtd.eq_zero_or_eq_zero_of_mul_eq_zero" -> "data", "category_theory.functor.map_inv" -> "category_theory", "category_theory.non_preadditive_abelian.lift_map_assoc" -> "category_theory", "span_nat_eq_add_group_closure" -> "algebra", "category_theory.limits.cospan_right" -> "category_theory", "turing.list_blank.tail_map" -> "computability", "is_bounded_linear_map_prod_iso" -> "analysis", "is_glb.mono" -> "order", "list.map_eq_foldr" -> "data", "filter.is_bounded_principal" -> "order", "matrix.diagonal_dot_product" -> "data", "is_R_or_C.abs_abs_sub_le_abs_sub" -> "data", "category_theory.adjunction.functoriality_unit'_app_hom" -> "category_theory", "alist.lookup_union_right" -> "data", "quotient.choice_eq" -> "data", "fin.cast_succ_lt_succ" -> "data", "div_lt_div_of_lt" -> "algebra", "free_group.map_mul" -> "algebra", "mdifferentiable_at_id" -> "geometry", "is_open_mul_right" -> "topology", "add_submonoid.localization_map.add_mk'_zero_eq_mk'" -> "algebra", "direct_sum.to_module_lof" -> "algebra", "units_eq_one" -> "algebra", "poly_equiv_tensor.right_inv" -> "algebra", "measure_theory.measure.eventually_cofinite" -> "analysis", "linear_map.is_unit_iff" -> "algebra", "finset.singleton_inter_of_mem" -> "data", "direct_sum.mk_smul" -> "algebra", "mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset" -> "topology", "zmod.cast_mul'" -> "data", "list.Ico.map_sub" -> "data", "cardinal.mk_le_of_surjective" -> "set_theory", "submodule.mem_annihilator" -> "algebra", "category_theory.prod.snd_obj" -> "category_theory", "set.union_distrib_Inter_left" -> "data", "set.mem_Iic" -> "data", "inv_mul_le_of_le_mul" -> "algebra", "cardinal.ord_omega" -> "set_theory", "multiplicity.pow_dvd_of_le_multiplicity" -> "algebra", "set.maps_to_univ" -> "data", "linear_independent.image_subtype" -> "algebra", "complex.cos_add_pi" -> "analysis", "int.mul_div_cancel" -> "data", "typevec.last_fun_from_append1_drop_last" -> "data", "Sup_le" -> "order", "list.forall\:2082.mp" -> "data", "subring.mem_mk'" -> "algebra", "measure_theory.measure.count_apply_finite" -> "analysis", "has_strict_fderiv_at.mul" -> "analysis", "submodule.add_mem_iff_right" -> "algebra", "is_measurable_closed_ball" -> "analysis", "pSet.equiv.trans" -> "set_theory", "roption.mem_map" -> "data", "eventually_ne_of_tendsto_norm_at_top" -> "analysis", "function.commute.iterate_iterate" -> "logic", "nat.one_le_of_lt" -> "data", "list.lex.ne_iff" -> "data", "category_theory.under.hom_mk_left" -> "category_theory", "is_glb_lt_iff" -> "order", "units.mul_left_inj" -> "algebra", "ennreal.supr_mul" -> "topology", "complex.norm_sq_nonneg" -> "data", "le_of_mul_le_mul_left'" -> "algebra", "is_R_or_C.of_real_pow" -> "data", "one_div_lt_neg_one" -> "algebra", "is_open.frontier_eq" -> "topology", "znum.cast_neg" -> "data", "wseq.tail_of_seq" -> "data", "linear_equiv_matrix_apply" -> "algebra", "nat.size_pos" -> "data", "preorder_hom.coe_id" -> "order", "tfae_mem_nhds_within_Ici" -> "topology", "set.univ_pi_eq_empty_iff" -> "data", "category_theory.limits.wide_pullback_shape.wide_cospan_obj" -> "category_theory", "circle_deg1_lift.dist_map_zero_lt_of_semiconj_by" -> "dynamics", "polynomial.leading_coeff_X_pow" -> "data", "num.to_nat_inj" -> "data", "convex_hull_subset_union" -> "analysis", "finset.fold_union_inter" -> "data", "mv_polynomial.pderivative_zero" -> "data", "int.pred_succ" -> "data", "is_measurable.disjointed" -> "analysis", "mv_polynomial.smul_eq_C_mul" -> "data", "set.forall_of_forall_insert" -> "data", "ordinal.mul_add_div" -> "set_theory", "add_comm_group.direct_limit.lift_unique" -> "algebra", "zsqrtd.norm_mul" -> "data", "int.nat_abs_add_neg" -> "init", "convex_cone.smul_mem" -> "analysis", "nat.gcd_eq_left_iff_dvd" -> "data", "gsmul_int_int" -> "algebra", "cau_seq.is_cau" -> "data", "dfinsupp.erase_add_single" -> "data", "is_const_of_fderiv_eq_zero" -> "analysis", "midpoint_zero_add" -> "algebra", "enorm.eq_zero_iff" -> "analysis", "ne_of_gt" -> "init", "set.Ioo_union_Ici_eq_Ioi" -> "data", "associates.unique'" -> "algebra", "is_local_extr_on.neg" -> "topology", "complex.equiv_real_prod_symm_im" -> "data", "poly.zero_eval" -> "number_theory", "set.countable_empty" -> "data", "prime_spectrum.comap_comp" -> "algebraic_geometry", "nat.coprime_one_right" -> "data", "set.bij_on.maps_to" -> "data", "list.nodup_middle" -> "data", "not_non_contradictory_iff_absurd" -> "init", "lower_bounds_mono_mem" -> "order", "affine_independent_embedding_of_affine_independent" -> "algebra", "list.not_nodup_cons_of_mem" -> "data", "dist_le_of_approx_trajectories_ODE" -> "analysis", "generalized_continued_fraction.int_fract_pair.nth_stream_fr_lt_one" -> "algebra", "minimal_polynomial.root" -> "algebra", "associated_one_iff_is_unit" -> "algebra", "linear_map.has_deriv_at_filter" -> "analysis", "pow_two" -> "algebra", "ring_hom.map_rat_cast" -> "data", "polynomial.root_multiplicity_eq_multiplicity" -> "data", "category_theory.image_to_kernel_map_zero_right" -> "algebra", "typevec.drop_fun_rel_last" -> "data", "algebra.eq_top_iff" -> "algebra", "continuous_linear_map.infi_ker_proj" -> "topology", "monoid_hom.mem_mrange" -> "algebra", "dist_smul" -> "analysis", "option_t.goto_mk_label" -> "control", "is_integral_of_surjective" -> "algebra", "emetric.Hausdorff_edist_self_closure" -> "topology", "polynomial.nat_degree_prod'" -> "algebra", "has_sum.has_sum_iff_compl" -> "topology", "two_nsmul" -> "algebra", "setoid.Sup_eq_eqv_gen" -> "data", "polynomial.degree_pos_of_aeval_root" -> "data", "add_comm_group.direct_limit.lift_neg" -> "algebra", "vadd_assoc" -> "algebra", "composition.index_embedding" -> "combinatorics", "topological_space.opens.inclusion_open_embedding" -> "topology", "category_theory.monoidal_category.tensoring_right_map_app" -> "category_theory", "dite_apply" -> "logic", "finset.disjoint_union_left" -> "data", "measure_theory.integrable_congr'" -> "analysis", "pell.pell_val" -> "number_theory", "nhds_basis_opens'" -> "topology", "submonoid.coe_infi" -> "algebra", "list.perm.subperm_right" -> "data", "ordinal.nat_cast_pos" -> "set_theory", "linear_map.range_eq_top_of_cancel" -> "algebra", "list.index_of_cons_ne" -> "data", "stream.nth_interleave_left" -> "data", "multiplicative.normal_subgroup_iff" -> "algebra", "set.univ_inter" -> "data", "multiplicity.neg" -> "algebra", "linear_map.lflip_apply" -> "algebra", "category_theory.adjunction.counit_naturality_assoc" -> "category_theory", "set.to_finset_empty" -> "data", "edist_le_of_edist_le_geometric_of_tendsto\:2080" -> "analysis", "finset.map_inj" -> "data", "local_equiv.restr_eq_of_source_subset" -> "data", "nat.add_self_ne_one" -> "init", "set.Icc_diff_Ico_same" -> "data", "metric.sphere_disjoint_ball" -> "topology", "set.sUnion_empty" -> "data", "set.image_const_add_Iic" -> "data", "multiplicity.finite_mul_iff" -> "algebra", "is_R_or_C.smul_im" -> "data", "category_theory.curry.obj_map_app" -> "category_theory", "category_theory.lax_monoidal_functor.comp_to_functor" -> "category_theory", "fintype.card_eq" -> "data", "trunc.lift_beta" -> "data", "function.equiv.trans" -> "init", "submodule.one_le" -> "algebra", "mem_closure_of_is_lub" -> "topology", "abs_dist" -> "topology", "antilipschitz_with.injective" -> "topology", "equiv.perm.disjoint_one_right" -> "algebra", "and_true" -> "init", "or.imp" -> "init", "add_con.Inf_def" -> "algebra", "continuous_linear_map.coe_zero'" -> "topology", "nat.pow_le_pow_of_le_right" -> "init", "cardinal.add_eq_self" -> "set_theory", "enat.lt_add_one_iff_lt" -> "data", "decidable.not_and_not_right" -> "logic", "composition_as_set.lt_length" -> "combinatorics", "ennreal.lt_of_real_iff_to_real_lt" -> "data", "linear_map.range_mkq_comp" -> "algebra", "linear_equiv.of_bijective_apply" -> "algebra", "submodule.coe_prod_equiv_of_is_compl" -> "algebra", "local_equiv.prod_symm" -> "data", "compare_reals.compare_uc_symm" -> "topology", "is_measurable_le'" -> "analysis", "uniform_space.completion.coe_one" -> "topology", "list.maximum_nil" -> "data", "category_theory.non_preadditive_abelian.\[CapitalDelta]_\[Sigma]_assoc" -> "category_theory", "multiplicity.multiplicity_eq_zero_of_not_dvd" -> "algebra", "multiset.prod_singleton" -> "data", "affine.simplex.eq_monge_point_of_forall_mem_monge_plane" -> "geometry", "list.bind_append" -> "data", "finset.fold_max_le" -> "data", "euclidean_geometry.orthogonal_projection_orthogonal_projection" -> "geometry", "ring_hom.map_frobenius" -> "algebra", "category_theory.limits.walking_pair.equiv_bool_apply_right" -> "category_theory", "category_theory.curry_uncurry" -> "category_theory", "tendsto_inv_nhds_within_Iio_inv" -> "topology", "topological_space.nhds_generate_from" -> "topology", "local_homeomorph.trans_source'" -> "topology", "function.semiconj.comp_left" -> "logic", "fderiv_within_smul_algebra_const" -> "analysis", "real.sin_lt_sin_of_le_of_le_pi_div_two" -> "analysis", "real.differentiable_at_sinh" -> "analysis", "category_theory.pi.comap_eval_iso_eval_hom_app" -> "category_theory", "linear_map.to_matrix_id" -> "algebra", "omega.nat.holds_nonneg_consts_core" -> "tactic", "filter.ne_bot.mul" -> "order", "sup_inf_self" -> "order", "ennreal.supr_add_supr" -> "topology", "cardinal.mk_prod" -> "set_theory", "finset.filter_ssubset" -> "data", "measurable_space.comap_sup" -> "analysis", "dioph.reindex_dioph" -> "number_theory", "list.func.nil_pointwise" -> "data", "with_zero.lift_unique" -> "algebra", "category_theory.monoidal_category.unitors_equal.cells_1_2" -> "category_theory", "rel_embedding.is_symm" -> "order", "is_subgroup.subset_normalizer" -> "algebra", "polynomial.nat_degree_pos_iff_degree_pos" -> "data", "euclidean_geometry.exists_unique_dist_eq_of_insert" -> "geometry", "one_not_mem_nonunits" -> "algebra", "ring_hom.ker_eq" -> "algebra", "equiv.swap_self" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_on_mono" -> "geometry", "category_theory.limits.types.filtered_colimit.is_colimit_eq_iff" -> "category_theory", "exists_approx_preimage_norm_le" -> "analysis", "real.sin_le_sin_of_le_of_le_pi_div_two" -> "analysis", "int.dvd_sub_of_mod_eq" -> "data", "cardinal.extend_function" -> "set_theory", "compact_space_of_finite_subfamily_closed" -> "topology", "equiv.to_local_equiv_symm_coe" -> "data", "equiv.neg_def" -> "data", "matrix.mul_assoc" -> "data", "nat.mem_factors_iff_dvd" -> "data", "continuous.nndist" -> "topology", "decidable.lt_or_le" -> "init", "null_is_null_measurable" -> "analysis", "set.disjoint_compl" -> "data", "pell.pell_zd_sub" -> "number_theory", "real.cos_add_pi_div_two" -> "analysis", "relation.refl_trans_gen.cases_head_iff" -> "logic", "magma.free_semigroup.of_mul" -> "algebra", "polynomial.nat_degree_pow'" -> "data", "abstract_completion.dense'" -> "topology", "add_monoid_hom.eq_nat_cast" -> "data", "left_inverse_add_right_neg_add" -> "algebra", "equiv.has_sum_iff" -> "topology", "pnat.coprime.factor_eq_gcd_right_right" -> "data", "filter.tendsto_at_bot_at_top" -> "order", "prod.mk_vsub_mk" -> "algebra", "free_group.quot_lift_mk" -> "algebra", "ideal.is_open_of_open_subideal" -> "topology", "is_closed.cInf_mem" -> "topology", "add_neg_of_nonpos_of_neg" -> "algebra", "constr_basis" -> "algebra", "differentiable_on.smul_algebra_const" -> "analysis", "metric.sphere_union_ball" -> "topology", "finite_dimensional.findim_eq_card_basis" -> "algebra", "multiset.erase_cons_head" -> "data", "category_theory.abelian.pseudoelement.zero_eq_zero" -> "category_theory", "closure_singleton" -> "topology", "disjoint_span_singleton" -> "algebra", "supr_le_supr2" -> "order", "int.shiftr_coe_nat" -> "data", "subgroup.coe_gpow" -> "algebra", "set.preimage_neg_Ioo" -> "data", "pequiv.trans_refl" -> "data", "closure_eq_interior_union_frontier" -> "topology", "topological_space.opens.map_iso_refl" -> "topology", "set.Icc_union_Ioo_eq_Ico" -> "data", "category_theory.curry_eq" -> "category_theory", "composition.to_composition_as_set_boundaries" -> "combinatorics", "multiset.foldr_add" -> "data", "tendsto_zero_iff_norm_tendsto_zero" -> "analysis", "con.ext" -> "algebra", "dfinsupp.subtype_domain_add" -> "data", "padic.mk_eq" -> "data", "list.rel_append" -> "data", "set.mem_compl_singleton_iff" -> "data", "linear_equiv.symm_trans" -> "algebra", "ideal.comap_ne_bot_of_integral_mem" -> "algebra", "bilin_form.ext" -> "algebra", "asymptotics.is_o.smul_is_O" -> "analysis", "interval_integral.integral_const'" -> "analysis", "multiset.Ico.filter_le_of_bot" -> "data", "psigma.ext" -> "data", "inner_add_add_self" -> "analysis", "ideal.is_maximal_iff" -> "algebra", "complex.uniform_continuous_abs" -> "topology", "hash_map.insert_lemma" -> "data", "hyperreal.infinitesimal_zero" -> "data", "quotient.lift_on_beta" -> "data", "int.cast_nonneg" -> "data", "measure_theory.simple_func.forall_range_iff" -> "analysis", "set.nonempty_Ici" -> "data", "list.forall\:2082.flip" -> "data", "set.univ_subset_iff" -> "data", "set.bot_eq_empty" -> "data", "ennreal.rpow_le_one" -> "analysis", "setoid.rel_iff_exists_classes" -> "data", "option.get_some" -> "data", "category_theory.comonad.coalgebra.hom.ext_iff" -> "category_theory", "linear_map.quotient_inf_equiv_sup_quotient_apply_mk" -> "algebra", "measurable_norm" -> "analysis", "rat.inv_def" -> "data", "linear_independent.repr_range" -> "algebra", "rank_comp_le1" -> "algebra", "measure_theory.measure.le_lift_linear_apply" -> "analysis", "turing.partrec_to_TM2.split_at_pred_eq" -> "computability", "polynomial.degree_derivative_eq" -> "data", "measure_theory.outer_measure.of_content_interior_compacts" -> "analysis", "real.one_le_rpow_of_pos_of_le_one_of_nonpos" -> "analysis", "wseq.head_nil" -> "data", "category_theory.iso.conj_Aut_gpow" -> "category_theory", "has_sum.mul_right" -> "topology", "submodule.bot_smul" -> "algebra", "ordering.compares.inj" -> "algebra", "is_basis.to_matrix_apply" -> "algebra", "mul_lt_of_lt_of_lt_one'" -> "algebra", "submodule.add_mem_iff_left" -> "algebra", "or_imp_distrib" -> "logic", "bilin_form.neg_left" -> "algebra", "category_theory.limits.types.coprod_inl" -> "category_theory", "fintype.card_option" -> "data", "list.foldl_append" -> "data", "units.coe_inv'" -> "algebra", "matrix.from_blocks_diagonal" -> "data", "nnreal.summable_comp_injective" -> "topology", "int.bit0_val" -> "data", "finset.prod_pos" -> "algebra", "pos_num.div'_to_nat" -> "data", "set.prod_inter_prod" -> "data", "int.gcd_dvd_gcd_mul_right_right" -> "algebra", "continuous_linear_equiv.differentiable_on" -> "analysis", "ennreal.div_le_iff_le_mul" -> "data", "cardinal.powerlt_omega" -> "set_theory", "group.mclosure_inv_subset" -> "algebra", "measure_theory.measure.finite_at_filter.mono" -> "analysis", "prod_charted_space_chart_at" -> "geometry", "le_one_div_of_neg" -> "algebra", "normalize_eq_zero" -> "algebra", "prime_two_or_dvd_of_dvd_two_mul_pow_self_two" -> "algebra", "add_commute.map" -> "algebra", "list.mem_or_eq_of_mem_update_nth" -> "data", "and.left_comm" -> "init", "linarith.lt_of_lt_of_eq" -> "tactic", "has_deriv_at.deriv" -> "analysis", "cau_seq.lim_zero_congr" -> "data", "norm_num.ne_zero_neg" -> "tactic", "singleton_has_groupoid" -> "geometry", "differentiable_on_of_locally_differentiable_on" -> "analysis", "exists_extension_of_le_sublinear" -> "analysis", "algebra.adjoin_int" -> "algebra", "units.mul_inv" -> "algebra", "ideal.radical_pow" -> "algebra", "int.coe_nat_pow" -> "algebra", "initial_seg.trans_apply" -> "set_theory", "convex.smul_preimage" -> "analysis", "measure_theory.inner_content_Sup_nat" -> "analysis", "free_add_semigroup_free_add_magma_add" -> "algebra", "monoid_hom.map_mul_eq_one" -> "algebra", "tactic.ring_exp.add_pf_sum_z" -> "tactic", "list.drop_take_succ_eq_cons_nth_le" -> "data", "t2_iff_nhds" -> "topology", "real.rpow_nonneg_of_nonneg" -> "analysis", "complex.of_real_bit0" -> "data", "list.unzip_zip_left" -> "data", "subgroup.subset_closure" -> "algebra", "ordinal.sub_zero" -> "set_theory", "filter.map_div_at_top_eq_nat" -> "order", "typevec.nil_fun_comp" -> "data", "stream.mem_append_stream_right" -> "data", "finmap.mem_to_finmap" -> "data", "finite_dimensional.exists_nontrivial_relation_of_dim_lt_card" -> "algebra", "subring.one_mem" -> "algebra", "is_min_on.min" -> "order", "znum.dvd_to_int" -> "data", "complex.mul_inv_cancel" -> "data", "topological_space.tendsto_nhds_generate_from" -> "topology", "free_group.red.church_rosser" -> "algebra", "nat.div2_zero" -> "init", "set.indicator_compl_add_self" -> "data", "zmod.cast_id" -> "data", "nat.mul_ne_zero" -> "data", "continuous.pow" -> "topology", "set.union_empty" -> "data", "nat.partrec'.map" -> "computability", "edist_nndist" -> "topology", "nat.sqrt_le_add" -> "data", "filter.lift_principal2" -> "order", "measure_theory.simple_func.piecewise_compl" -> "analysis", "matrix.cons_val_succ'" -> "data", "sum.lex_wf" -> "data", "edist_add_add_le" -> "analysis", "finset.sum_range_zero" -> "algebra", "mv_polynomial.C_neg" -> "data", "cSup_insert" -> "order", "ennreal.coe_Sup" -> "data", "complex.is_cau_seq_conj" -> "data", "id.map_eq" -> "init", "padic_int.inv_mul" -> "data", "id.def" -> "init", "zmod.cast_sub'" -> "data", "polynomial.eval_smul'" -> "algebra", "matrix.special_linear_group.to_GL_mul" -> "algebra", "nat.eq_zero_of_mul_eq_zero" -> "init", "nonpos_of_mul_nonneg_left" -> "algebra", "linear_map.fun_congr_left_id" -> "algebra", "tendsto_uniformly_on.continuous_on" -> "topology", "real.sin_le_one" -> "data", "cauchy_seq_of_le_geometric" -> "analysis", "derive_fintype.finset_above.mem_cons_self" -> "tactic", "category_theory.limits.cone_of_cone_uncurry_X" -> "category_theory", "enat.get_zero" -> "data", "finsupp.support_eq_empty" -> "data", "traversable.map_eq_traverse_id" -> "control", "nat.pos_of_dvd_of_pos" -> "init", "pell.yn_ge_n" -> "number_theory", "complex.cos_add_pi_div_two" -> "analysis", "finset.sup_eq_supr" -> "data", "nat.le_mkpair_left" -> "data", "ring_hom.to_fun_eq_coe" -> "algebra", "bounded_continuous_function.coe_le_coe_add_dist" -> "topology", "list.map_cons" -> "init", "nat.add_mod_of_add_mod_lt" -> "data", "convex_on.le_on_segment" -> "analysis", "mul_one_div_cancel" -> "algebra", "function.is_periodic_pt.minimal_period_pos" -> "dynamics", "finmap.union_assoc" -> "data", "local_homeomorph.of_set_trans_of_set" -> "topology", "affine_map.id_linear" -> "algebra", "quotient_group.ker_mk" -> "algebra", "real.convex_iff_is_preconnected" -> "analysis", "left_ord_continuous.comp" -> "order", "pos_num.one_add" -> "data", "finsupp.card_to_multiset" -> "data", "wseq.destruct_nil" -> "data", "set.image_diff" -> "data", "metric.mem_closed_ball_self" -> "topology", "partrec.of_eq_tot" -> "computability", "list.eq_nil_of_subset_nil" -> "data", "finmap.extract_eq_lookup_erase" -> "data", "list.erase_dup_append" -> "data", "continuous_multilinear_map.sub_apply" -> "topology", "cardinal.le_add_right" -> "set_theory", "commute.geom_sum\:2082_mul_add" -> "algebra", "is_asymm.is_irrefl" -> "order", "homological_complex.image_to_kernel_map_comp_kernel_map" -> "algebra", "finset.max_of_nonempty" -> "data", "option.bind_eq_some" -> "data", "pythagorean_triple.classified" -> "number_theory", "set.image_inv" -> "algebra", "nnreal.of_real_one" -> "data", "filter.is_cobounded.mk" -> "order", "measure_theory.to_measure_to_outer_measure" -> "analysis", "filter.eventually_le.antisymm" -> "order", "add_subgroup.map_sup" -> "algebra", "is_bounded_bilinear_map_comp" -> "analysis", "linear_map.map_add\:2082" -> "algebra", "has_ftaylor_series_up_to_on.of_le" -> "analysis", "times_cont_diff_on.prod" -> "analysis", "multilinear_map.ext" -> "algebra", "free_magma.map_mul" -> "algebra", "cluster_pt.of_nhds_le" -> "topology", "Module.monoidal_category.left_unitor_naturality" -> "algebra", "filter.is_countably_generated.exists_antimono_seq'" -> "order", "subgroup.pow_mem" -> "algebra", "continuous_multilinear_map.curry_right_apply" -> "analysis", "num.bitwise_to_nat" -> "data", "affine.simplex.monge_point_mem_affine_span" -> "geometry", "local_equiv.trans_target''" -> "data", "topological_space.opens.coe_comap" -> "topology", "add_submonoid.closure_union" -> "algebra", "filter.mul_mem_mul" -> "order", "polynomial.mod_by_monic_eq_sub_mul_div" -> "data", "nat.modeq.modeq_mul_right" -> "data", "lists'.to_list_cons" -> "set_theory", "matrix.mul_vec_mul_vec" -> "data", "set.preimage_add_right_zero'" -> "algebra", "comp_mem_uniformity_sets" -> "topology", "array.mem_to_list" -> "data", "is_basis.to_matrix_self" -> "algebra", "closure_of_rat_image_lt" -> "topology", "nnreal.eq" -> "data", "finsupp.lt_wf" -> "data", "add_aut.one_apply" -> "data", "set.snd_image_prod_subset" -> "data", "left_distrib" -> "algebra", "exists.elim" -> "init", "t2_iff_is_closed_diagonal" -> "topology", "setoid.sup_def" -> "data", "cauchy_iff" -> "topology", "pgame.lt_of_le_mk" -> "set_theory", "filter.monotone_mem_sets" -> "order", "set.image_inter_on" -> "data", "has_ftaylor_series_up_to_succ_iff_right" -> "analysis", "measure_theory.l1.simple_func.coe_zero" -> "analysis", "polynomial.monic_integral_normalization" -> "data", "list.countp_le_of_sublist" -> "data", "list.rel_filter" -> "data", "multiset.antidiagonal_zero" -> "data", "gaussian_int.norm_mod_lt" -> "data", "multiset.Ico.self_eq_zero" -> "data", "ennreal.mem_Ioo_self_sub_add" -> "data", "int.bit1_nonneg" -> "init", "compact_pi_infinite" -> "topology", "ring_equiv.to_Ring_iso_hom" -> "algebra", "and_eq_of_eq_false_right" -> "init", "bool.coe_sort_tt" -> "data", "finsupp.supported_mono" -> "algebra", "enat.coe_add_get" -> "data", "pi.neg_apply" -> "algebra", "one_gsmul" -> "algebra", "rat.floor_def" -> "data", "subrel_val" -> "order", "function.equiv.symm" -> "init", "ordinal.omega_le_of_is_limit" -> "set_theory", "filter.tendsto_finset_range" -> "order", "to_bool_true" -> "init", "finset.product_eq_bind" -> "data", "nhds_within_mono" -> "topology", "set.image_neg_Ioc" -> "data", "list.take_cons" -> "data", "is_path_connected.image" -> "topology", "set.Icc_union_Ioi_eq_Ici" -> "data", "dfinsupp.sum_add" -> "data", "semidirect_product.right_hom_eq_right" -> "algebra", "power_series.order_monomial" -> "algebra", "convex_hull_exists_dist_ge2" -> "analysis", "has_fderiv_at_filter.tendsto_nhds" -> "analysis", "not_of_not_not_not" -> "init", "norm_num.mul_bit0_bit0" -> "tactic", "isometry_subsingleton" -> "topology", "complex.div_re" -> "data", "cardinal.ord_univ" -> "set_theory", "filter.tendsto_at_bot_add_nonpos_right'" -> "order", "filter.tendsto_if" -> "order", "list.count_cons_self" -> "data", "filter.tendsto.mul" -> "topology", "set.Ioc_subset_Ioo_union_Icc" -> "data", "finset.min'_singleton" -> "data", "nat.dist_succ_succ" -> "data", "set.nmem_singleton_empty" -> "data", "nat.add_mod" -> "data", "bool.forall_bool" -> "data", "ideal.map_le_iff_le_comap" -> "algebra", "option.eq_some_of_is_some" -> "init", "measure_theory.simple_func.le_sup_lintegral" -> "analysis", "mv_polynomial.eval_C" -> "data", "complex.arg_cos_add_sin_mul_I" -> "analysis", "linear_map.coe_equiv_prod_of_surjective_of_is_compl" -> "algebra", "inv_eq_zero" -> "algebra", "pythagorean_triple.is_classified_of_normalize_is_primitive_classified" -> "number_theory", "measure_theory.measure.add_apply" -> "analysis", "generalized_continued_fraction.succ_nth_convergent_eq_squash_gcf_nth_convergent" -> "algebra", "matrix.mul_sum" -> "data", "generalized_continued_fraction.int_fract_pair.succ_nth_stream_eq_none_iff" -> "algebra", "add_semiconj_by.units_neg_right_iff" -> "algebra", "category_theory.limits.zero_of_target_iso_zero" -> "category_theory", "pell.xn_modeq_x2n_add" -> "number_theory", "matrix.transpose_sub" -> "data", "padic_seq.norm_zero_iff" -> "data", "finsupp.prod_sum_index" -> "data", "associated_of_dvd_dvd" -> "algebra", "units.mul_neg" -> "algebra", "monoid_hom.range_top_of_surjective" -> "algebra", "charted_space_core.open_target" -> "geometry", "times_cont_mdiff_top" -> "geometry", "uniform_continuous.continuous" -> "topology", "mvqpf.comp.mk_get" -> "data", "multiset.to_finset_zero" -> "data", "pythagorean_triple.is_primitive_classified_of_coprime_of_odd_of_pos" -> "number_theory", "multiset.join_cons" -> "data", "nat.prime_iff_prime" -> "algebra", "add_units.coe_add_left" -> "data", "infi_split_single" -> "order", "order_of_le_of_pow_eq_one" -> "algebra", "int.coe_nat_add" -> "init", "continuous_linear_equiv.map_smul" -> "topology", "has_deriv_at_gronwall_bound" -> "analysis", "nndist_eq_zero" -> "topology", "complex.sin_conj" -> "data", "cardinal.mk_union_le" -> "set_theory", "edist_eq_coe_nnnorm" -> "analysis", "set.countable_set_of_finite_subset" -> "data", "Cauchy.uniform_continuous_extend" -> "topology", "equiv.sum_compl_apply_symm_of_neg" -> "data", "fpow_pos_of_pos" -> "algebra", "tactic.abel.term_add_const" -> "tactic", "set.empty_def" -> "data", "buffer.write_eq_write'" -> "data", "int.ne_zero_of_gcd" -> "algebra", "ennreal.coe_one" -> "data", "fderiv_const_sub" -> "analysis", "real.angle.coe_add" -> "analysis", "multiset.inter_le_left" -> "data", "list.mfoldr_nil" -> "data", "continuous.continuous_on" -> "topology", "convex.strict_mono_of_deriv_pos" -> "analysis", "fixed_points.minpoly.monic" -> "algebra", "has_sum_geometric_of_norm_lt_1" -> "analysis", "set.preimage_const" -> "data", "alg_hom.comp_apply" -> "algebra", "pgame.one_right_moves" -> "set_theory", "direct_sum.of_zero" -> "algebra", "category_theory.functor.right_unitor_hom_app" -> "category_theory", "is_add_monoid_hom.map_add" -> "algebra", "polynomial.units_coeff_zero_smul" -> "data", "computation.head_think" -> "data", "int.coe_nat_inj'" -> "data", "polynomial.C_1" -> "data", "differentiable_at.const_smul" -> "analysis", "submonoid.coe_eq_coe" -> "algebra", "nat.bitwise_bit" -> "init", "int.add_lt_add_of_lt_of_le" -> "init", "sub_sub_assoc_swap" -> "algebra", "list.nth_len_le" -> "data", "finset.card_image_of_injective" -> "data", "asymptotics.is_O_with.triangle" -> "analysis", "lt_div_iff'" -> "algebra", "subgroup.mem_map" -> "algebra", "finset.nonempty_iff_ne_empty" -> "data", "continuous_linear_map.differentiable_at" -> "analysis", "I_symm_zero" -> "topology", "bifunctor.id_snd" -> "control", "ge_iff_le" -> "algebra", "finset.bind_image" -> "data", "associates.factors_mk" -> "algebra", "non_contradictory_em" -> "init", "finset.sdiff_subset" -> "data", "int.one_shiftl" -> "data", "rat.cast_nonpos" -> "data", "zorn.chain.directed_on" -> "order", "filter.has_basis_self" -> "order", "hyperreal.zero_of_infinitesimal_real" -> "data", "measure_theory.tsum_measure_le_measure_univ" -> "analysis", "char_matrix_apply_ne" -> "algebra", "is_R_or_C.of_real_bit0" -> "data", "equiv.injective" -> "data", "differentiable.add" -> "analysis", "filter.mem_at_bot" -> "order", "category_theory.limits.wide_pushout_shape.wide_span_obj" -> "category_theory", "eq_equivalence" -> "logic", "dfinsupp.sum_subtype_domain_index" -> "data", "magma.free_semigroup.of_mul_assoc" -> "algebra", "affine.simplex.face_eq_mk_of_point" -> "algebra", "filter.tendsto_at_bot_at_bot_of_monotone'" -> "order", "is_bounded_bilinear_map.continuous_left" -> "analysis", "module.gsmul_eq_smul_cast" -> "algebra", "ideal.quotient.lift_mk" -> "algebra", "ennreal.top_to_real" -> "data", "measure_theory.outer_measure.is_caratheodory_empty" -> "analysis", "fin.mk_coe" -> "data", "lagrange.nat_degree_basis" -> "algebra", "polynomial.is_unit_iff_degree_eq_zero" -> "data", "complex.equiv_real_prod_symm_re" -> "data", "is_lub_of_is_lub_of_tendsto" -> "topology", "borel_eq_top_of_encodable" -> "analysis", "Icc_zero_one_symm" -> "topology", "int.bit_coe_nat" -> "data", "smooth_at_fst" -> "geometry", "pfunctor.M.cases_on_mk'" -> "data", "mdifferentiable_within_at.has_mfderiv_within_at" -> "geometry", "int.mod_mod" -> "data", "measure_theory.simple_func.coe_piecewise" -> "analysis", "measure_theory.outer_measure.le_sum_caratheodory" -> "analysis", "linear_map.coe_quotient_inf_to_sup_quotient" -> "algebra", "pfun.preimage_def" -> "data", "polynomial.prime_X" -> "data", "dif_ctx_congr" -> "init", "linear_map.zero_comp" -> "algebra", "emetric.exists_ball_subset_ball" -> "topology", "matrix.linear_equiv_matrix_comp" -> "algebra", "function.surjective.exists\:2082" -> "logic", "nat.bitwise_bit_aux" -> "init", "list.rotate_mod" -> "data", "padic_seq.norm_mul" -> "data", "primrec.nat_strong_rec" -> "computability", "nnreal.rpow_le_rpow_of_exponent_le" -> "analysis", "ball_of_forall" -> "logic", "prime_spectrum.zero_locus_univ" -> "algebraic_geometry", "not_iff_comm" -> "logic", "mv_polynomial.pderivative_C_mul" -> "data", "differentiable.inv" -> "analysis", "polynomial.leading_coeff_map" -> "data", "is_preconnected_Iio" -> "topology", "nat.le_induction" -> "data", "int.abs_eq_nat_abs" -> "data", "differentiable_at.div" -> "analysis", "sub_sub_self" -> "algebra", "finset.prod_subtype_eq_prod_filter" -> "algebra", "implicit_function_data.to_local_homeomorph_apply" -> "analysis", "ball_0_eq" -> "analysis", "hyperreal.infinite_neg_add_not_infinite" -> "data", "linear_independent.unique" -> "algebra", "unique_diff_on_Icc_zero_one" -> "analysis", "Module.Mon_Module_equivalence_Algebra.ring_neg" -> "category_theory", "int.mul_zero" -> "init", "set.Ico_subset_Ioo_left" -> "data", "nnreal.mul_div_cancel" -> "data", "multiplicity.multiplicity_sub_of_gt" -> "algebra", "category_theory.comonad_hom.assoc" -> "category_theory", "forall_and_distrib" -> "logic", "add_units.add_neg_of_eq" -> "algebra", "quadratic_form.isometry.map_app" -> "algebra", "coinduced_supr" -> "topology", "computation.mem_map" -> "data", "list.mem_sections" -> "data", "decidable.not_or_of_imp" -> "logic", "measure_theory.integrable.integrable_on'" -> "analysis", "continuous_linear_map.pi_zero" -> "topology", "pnat.prime_two" -> "data", "true_or" -> "init", "matrix.neg_mul_vec" -> "data", "filter.mem_cofinite" -> "order", "int.sub_nat_nat_add" -> "init", "finset.coe_singleton" -> "data", "real.cos_add" -> "data", "is_basis_of_span_eq_top_of_card_eq_findim" -> "algebra", "finset.prod_eq_prod_Ico_succ_bot" -> "algebra", "continuous.max" -> "topology", "cardinal.le_add_left" -> "set_theory", "multiplicity.finite_int_iff" -> "algebra", "structure_groupoid.lift_prop_on_univ" -> "geometry", "polynomial.degree_le_eq_span_X_pow" -> "algebra", "measure_theory.ae_eq_fun.inv_to_germ" -> "analysis", "has_strict_deriv_at.to_local_left_inverse" -> "analysis", "lucas_lehmer.X.units_card" -> "number_theory", "ultrafilter_extend_extends" -> "topology", "edist_ne_top" -> "topology", "basic_smooth_bundle_core.coe_chart_at_symm_fst" -> "geometry", "mul_self_inj_of_nonneg" -> "algebra", "localization.r_of_eq" -> "algebra", "game.not_le" -> "set_theory", "nat.prime.dvd_choose_add" -> "data", "finset.mul_prod_diff_singleton" -> "algebra", "simple_graph.adj_matrix_mul_self_apply_self" -> "combinatorics", "abstract_completion.funext" -> "topology", "real.young_inequality_of_nonneg" -> "analysis", "finset.sup_def" -> "data", "filter.eventually.exists" -> "order", "is_mul_hom.inv" -> "algebra", "int.to_add_pow" -> "algebra", "list.pairwise_append_comm" -> "data", "exists_false" -> "logic", "real.Sup_le_ub" -> "data", "sub_le_iff_le_add" -> "algebra", "rat.div_num_denom" -> "data", "pgame.impartial.lt_zero_iff" -> "set_theory", "times_cont_mdiff_within_at_top" -> "geometry", "denumerable.decode_eq_of_nat" -> "data", "fintype.card_subtype_lt" -> "data", "algebra.adjoin_empty" -> "algebra", "Set.subset_iff" -> "set_theory", "finmap.lookup_eq_none" -> "data", "continuous_within_at.prod_map" -> "topology", "is_R_or_C.im_to_real" -> "data", "lfp_lfp" -> "order", "monoid_hom.coe_snd" -> "algebra", "Top.subpresheaf_to_Types_map_val" -> "topology", "zmod.inv_zero" -> "data", "prod.neg_mk" -> "algebra", "fin.exists_iff" -> "data", "infi_subtype" -> "order", "multiset.pmap_congr" -> "data", "principal_seg.irrefl" -> "set_theory", "isometric.coe_const_vadd" -> "analysis", "padic_val_rat.le_padic_val_rat_add_of_le" -> "data", "fintype.eq_of_subsingleton_of_prod_eq" -> "data", "multiplicity.unique" -> "algebra", "associates.le_mul_left" -> "algebra", "has_fderiv_at_filter.const_add" -> "analysis", "category_theory.limits.bicone.to_binary_bicone_snd" -> "category_theory", "set.image_zero" -> "algebra", "sub_lt_of_abs_sub_lt_left" -> "algebra", "uniform_inducing.inducing" -> "topology", "list.nodupkeys.eq_of_mk_mem" -> "data", "mv_power_series.mul_assoc" -> "algebra", "ennreal.sub_eq_of_add_eq" -> "data", "nat.eq_of_lt_succ_of_not_lt" -> "data", "filter.realizer.of_equiv_\[Sigma]" -> "data", "category_theory.functor.op_inv_obj" -> "category_theory", "push_neg.classical.implies_iff_not_or" -> "tactic", "real.differentiable_at_cosh" -> "analysis", "mv_polynomial.exists_finset_rename" -> "data", "relation.refl_trans_gen_of_equivalence" -> "logic", "pgame.lt_of_equiv_of_lt" -> "set_theory", "ennreal.of_real_lt_top" -> "data", "commute.add_right" -> "algebra", "one_smul" -> "algebra", "is_extr_filter.comp_mono" -> "order", "add_submonoid.copy_eq" -> "algebra", "poly.mul_eval" -> "number_theory", "hyperreal.infinite_iff_infinite_abs" -> "data", "mvqpf.fix.rec_eq" -> "data", "int.neg_succ_of_nat_add_of_nat" -> "init", "Mon.coe_of" -> "algebra", "cauchy_seq_of_edist_le_geometric_two" -> "analysis", "finset.summable_compl_iff" -> "topology", "list.find_nil" -> "data", "pgame.zero_add_equiv" -> "set_theory", "finset.card_le_univ" -> "data", "list.func.eq_get_of_mem" -> "data", "list.index_of_le_length" -> "data", "semiconj_by.map" -> "algebra", "ennreal.ne_top_of_tsum_ne_top" -> "topology", "matrix.neg_mul" -> "data", "prime_multiset.factor_multiset_prod" -> "data", "finset.fin_range_card" -> "data", "edist_triangle_right" -> "topology", "category_theory.limits.is_image.iso_ext_hom" -> "category_theory", "mem_map_sets_iff'" -> "topology", "set.Ici_inter_Iio" -> "data", "continuous_multilinear_curry_right_equiv_symm_apply" -> "analysis", "add_subgroup.comap_infi" -> "algebra", "has_deriv_at.sqrt" -> "analysis", "relator.rel_forall_of_right_total" -> "logic", "list.kreplace_of_forall_not" -> "data", "list.nil_append" -> "init", "infi_subtype'" -> "order", "isometric.add_right_to_equiv" -> "topology", "real.arccos_zero" -> "analysis", "not_bounded_iff" -> "order", "quotient_group.coe_one" -> "algebra", "enat.lt_wf" -> "data", "ring_hom.mul_def" -> "algebra", "category_theory.limits.cocones.precompose_obj_X" -> "category_theory", "multiplicity.get_multiplicity_self" -> "algebra", "free_add_monoid.lift_symm_apply" -> "algebra", "category_theory.action_category.\[Pi]_map" -> "category_theory", "order_of_le_card_univ" -> "algebra", "polynomial.degree_coe_units" -> "data", "model_with_corners_prod_coe_symm" -> "geometry", "nonpos_of_mul_nonpos_left" -> "algebra", "list.take_zero" -> "data", "nat.fact_mul_pow_le_fact" -> "data", "list.alternating_prod_singleton" -> "data", "set.mul_subset_mul" -> "algebra", "complex.tanh_of_real_re" -> "data", "ennreal.coe_nat_lt_coe_nat" -> "data", "rat.cast_coe_int" -> "data", "measure_theory.simple_func.coe_add" -> "analysis", "nat.mul_mod_right" -> "init", "multiset.erase_dup_subset" -> "data", "category_theory.over.creates_connected.raise_cone_\[Pi]_app" -> "category_theory", "set.Icc_eq_empty" -> "data", "abs_zero" -> "algebra", "category_theory.limits.cones.functoriality_map_hom" -> "category_theory", "tactic.ring_exp.sum_congr" -> "tactic", "complex.abs_conj" -> "data", "add_submonoid.nsmul_mem" -> "algebra", "multiset.nodup_bind" -> "data", "ordinal.one_ne_zero" -> "set_theory", "mul_inv'" -> "algebra", "continuous_on.comp'" -> "topology", "finsupp.disjoint_lsingle_lsingle" -> "algebra", "stream.drop_map" -> "data", "padic_val_nat.div'" -> "data", "category_theory.comma.snd_map" -> "category_theory", "measure_theory.integrable_at_filter.inf_ae_iff" -> "analysis", "deriv.lhopital_zero_right_on_Ioo" -> "analysis", "is_coprime.add_mul_left_right" -> "algebra", "cardinal.power_le_power_left" -> "set_theory", "category_theory.sum.inr__map" -> "category_theory", "bdd_below.union" -> "order", "free_group.map_pure" -> "algebra", "le_implies_le_of_le_of_le" -> "algebra", "algebra_compatible_smul" -> "algebra", "function.support_binop_subset" -> "data", "measure_theory.measure.restrict_compl_add_restrict" -> "analysis", "matrix.vec_mul_vec_eq" -> "data", "stream.drop_const" -> "data", "euclidean_domain.gcd_zero_left" -> "algebra", "nat.eq_sqrt" -> "data", "linear_equiv.map_neg" -> "algebra", "well_founded.induction" -> "init", "nat.modeq.trans" -> "data", "AddCommGroup.as_hom_injective" -> "algebra", "mul_eq_mul_prime_pow" -> "algebra", "function.is_periodic_pt.is_fixed_pt" -> "dynamics", "real.uniform_continuous_add" -> "topology", "opposite.unop_add" -> "algebra", "add_subgroup.neg_mem" -> "algebra", "circle_deg1_lift.map_le_of_map_zero" -> "dynamics", "is_closed.Icc_subset_of_forall_exists_gt" -> "topology", "add_monoid_hom.ext" -> "algebra", "normalize_eq_normalize" -> "algebra", "with_top.coe_one" -> "algebra", "add_pow_char_of_commute" -> "algebra", "real.tendsto_exp_div_pow_at_top" -> "analysis", "list.bex_cons" -> "init", "continuous_multilinear_curry_fin1_apply" -> "analysis", "category_theory.arrow.w" -> "category_theory", "ne_zero_iff_of_associated" -> "algebra", "ennreal.one_half_lt_one" -> "data", "real.differentiable_sinh" -> "analysis", "lcm_dvd_lcm_mul_right_right" -> "algebra", "is_R_or_C.of_real_to_real" -> "data", "pell.y_increasing" -> "number_theory", "affine_subspace.self_mem_mk'" -> "algebra", "quotient_group.card_preimage_mk" -> "algebra", "measure_theory.measure.restrict_Union_apply" -> "analysis", "category_theory.limits.colimit.\[Iota]_cocone_morphism" -> "category_theory", "add_submonoid.localization_map.mk'_self" -> "algebra", "polynomial.degree_map_eq_of_injective" -> "data", "ideal.span_singleton_one" -> "algebra", "measure_theory.measure.haar_outer_measure_exists_compact" -> "analysis", "category_theory.curry_injective" -> "category_theory", "wseq.flatten_think" -> "data", "set.mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset" -> "data", "tendsto_coe_nat_real_at_top_iff" -> "topology", "set.maps_to_Union" -> "data", "monoid_algebra.mul_def" -> "data", "differentiable.cosh" -> "analysis", "polynomial.monic_X_add_C" -> "data", "strict_mono.bot_preimage_bot" -> "order", "set.image3_congr'" -> "data", "relation.iff_comp" -> "logic", "list.unzip_right" -> "data", "is_add_group_hom.mem_ker" -> "algebra", "of_eq_true" -> "init", "associates.exists_mem_multiset_le_of_prime" -> "algebra", "finset.empty_inter" -> "data", "semiquot.mem_univ" -> "data", "associates.mk_le_mk_iff_dvd_iff" -> "algebra", "set.preimage_eq_core" -> "data", "set.mem_Iic_Iio_of_subset_of_subset" -> "data", "polynomial.coeff_to_subring" -> "algebra", "computable_pred.rice\:2082" -> "computability", "hash_map.mem_erase" -> "data", "free_abelian_group.induction_on" -> "algebra", "one_one_reducible.disjoin_right" -> "computability", "list.Ico.filter_lt_of_le_bot" -> "data", "nat.coprime_mul_iff_left" -> "data", "galois_connection.u_l_u_eq_u" -> "order", "add_submonoid.monotone_comap" -> "algebra", "finset.sum_insert_zero" -> "algebra", "multiset.rec_on_0" -> "data", "list.perm.erase" -> "data", "int.add_nonpos" -> "init", "category_theory.adjunction.cones_iso_component_inv_app" -> "category_theory", "add_submonoid.localization_map.mk'_spec" -> "algebra", "ideal.mul_mono" -> "algebra", "hyperreal.lt_of_st_lt" -> "data", "category_theory.monoidal.tensor_obj_obj" -> "category_theory", "contracting_with.edist_efixed_point_le'" -> "topology", "connected_space_iff_connected_component" -> "topology", "category_theory.monad.forget_creates_colimits.\[Gamma]_app" -> "category_theory", "eq.trans_le" -> "algebra", "has_deriv_at.differentiable_at" -> "analysis", "finset.empty_val" -> "data", "category_theory.non_preadditive_abelian.neg_def" -> "category_theory", "list.kunion_nodupkeys" -> "data", "with_zero.lift_zero" -> "algebra", "wseq.tail_nil" -> "data", "ordinal.sub_is_limit" -> "set_theory", "add_submonoid.localization_map.add_neg_right" -> "algebra", "is_strict_order.swap" -> "order", "computation.map_think" -> "data", "polynomial.degree_C_mul_X_pow_le" -> "data", "set.finite_image_iff" -> "data", "cardinal.omega_le_bit0" -> "set_theory", "filter.le_map_comap_of_surjective'" -> "order", "ring_hom.range_top_iff_surjective" -> "algebra", "add_pos" -> "algebra", "div_eq_iff" -> "algebra", "matrix.special_linear_group.inv_apply" -> "algebra", "mvqpf.liftp_preservation_iff_uniform" -> "data", "submodule.span_singleton_eq_range" -> "algebra", "set.to_finset_card" -> "data", "has_strict_deriv_at.of_local_left_inverse" -> "analysis", "mv_polynomial.is_homogeneous_monomial" -> "algebra", "filter.principal_singleton" -> "order", "summable.sigma'" -> "topology", "enat.add_lt_add_iff_left" -> "data", "rel.comp_left_id" -> "data", "add_subgroup.normal.mem_comm_iff" -> "algebra", "pfunctor.M.truncate_approx" -> "data", "ite_mul_zero_left" -> "algebra", "rat.zero_add" -> "data", "algebra.tensor_product.congr_symm_apply" -> "algebra", "filter.comap_lift_eq2" -> "order", "one_le_bit1" -> "algebra", "sum_range_sub_sum_range" -> "data", "ordinal.power_is_normal" -> "set_theory", "filter.tendsto.is_cobounded_under_ge" -> "topology", "category_theory.limits.equalizer.condition" -> "category_theory", "pgame.mk_add_move_left_inr" -> "set_theory", "inv_eq_iff" -> "algebra", "finset.sum_image" -> "algebra", "set.Ioi_subset_Ici" -> "data", "polynomial.derivative_C" -> "data", "is_irreducible_iff_sInter" -> "topology", "rel_iso.cof.aux" -> "set_theory", "nat.one_lt_bit0_iff" -> "data", "free_group.reduce.min" -> "algebra", "le_add_right" -> "algebra", "lt_mul_iff_one_lt_right" -> "algebra", "deriv_within_csinh" -> "analysis", "add_submonoid.localization_map.add_equiv_of_localizations_symm_eq_add_equiv_of_localizations" -> "algebra", "subring.closure_empty" -> "algebra", "ideal.jacobson_top" -> "algebra", "free_group.red.refl" -> "algebra", "matrix.from_blocks_apply\:2081\:2081" -> "data", "orthogonal_projection_def" -> "analysis", "set.right_inv_on.eq_on" -> "data", "measure_theory.ae_eq_fun.pair_eq_mk" -> "analysis", "measure_theory.outer_measure.le_trim_iff" -> "analysis", "strict_weak_order.esymm" -> "init", "matrix.to_linear_equiv_apply" -> "algebra", "set.mem_image2" -> "data", "set.diff_eq_empty" -> "data", "multiset.add_sub_cancel_left" -> "data", "sub_div'" -> "algebra", "primrec.vector_to_list_iff" -> "computability", "category_theory.limits.limit.cone_point_unique_up_to_iso_inv_comp_assoc" -> "category_theory", "measure_theory.all_ae_of_real_f_le_bound" -> "analysis", "category_theory.sum.inverse_associator_map_inr_inl" -> "category_theory", "polynomial.degree_div_by_monic_lt" -> "data", "is_R_or_C.smul_re'" -> "data", "wseq.equiv.symm" -> "data", "nat.shiftl'_ne_zero_left" -> "data", "list.perm.foldr_eq" -> "data", "eq_iff_le_not_lt" -> "algebra", "forall_le_or_exists_lt_sup" -> "order", "is_order_connected.neg_trans" -> "order", "con.lift_funext" -> "algebra", "int.mul_nonneg_of_nonpos_of_nonpos" -> "init", "zmod.card_units_eq_totient" -> "data", "map_ne_zero_of_mem_non_zero_divisors" -> "algebra", "polynomial.nat_degree_remove_factor" -> "algebra", "computable.pred" -> "computability", "of_digits_modeq" -> "data", "add_monoid_hom.normal_ker" -> "algebra", "equiv.coe_vadd_const_symm" -> "algebra", "except_t.run_monad_map" -> "init", "submonoid.map_inl" -> "algebra", "sesq_form.ext" -> "algebra", "category_theory.limits.is_limit.hom_iso_hom" -> "category_theory", "padic_norm.padic_norm_p_lt_one_of_prime" -> "data", "pell.y_dvd_iff" -> "number_theory", "set.maps_to.iterate_restrict" -> "data", "free_add_magma.traverse_add" -> "algebra", "real.cosh_add" -> "data", "has_deriv_within_at.prod" -> "analysis", "div_le_div_right" -> "algebra", "dense_inducing.nhds_eq_comap" -> "topology", "cardinal.power_le_max_power_one" -> "set_theory", "local_homeomorph.trans_source" -> "topology", "ideal.mem_span_insert" -> "algebra", "multiset.cons_eq_cons" -> "data", "enat.with_top_equiv_symm_le" -> "data", "multiset.to_finset_eq_empty" -> "data", "dfinsupp.sum_zero_index" -> "data", "padic_norm_z.nonarchimedean" -> "data", "sub_le_of_abs_sub_le_right" -> "algebra", "mv_polynomial.eval\:2082_add" -> "data", "nnreal.tendsto.sub" -> "topology", "inner_product_space.of_core.inner_add_add_self" -> "analysis", "int.coe_nat_lt" -> "data", "ring_hom.map_srange" -> "algebra", "finset.prod_eq_multiset_prod" -> "algebra", "le_of_forall_le" -> "algebra", "zmod.int_coe_zmod_eq_zero_iff_dvd" -> "data", "set.mul_comm" -> "algebra", "le_sub_right_of_add_le" -> "algebra", "real.log_pos_iff" -> "analysis", "mdifferentiable_at.continuous_at" -> "geometry", "real.sqrt_one" -> "data", "is_compact.adherence_nhdset" -> "topology", "has_strict_deriv_at.scomp" -> "analysis", "mv_polynomial.eval\:2082_C" -> "data", "hyperreal.exists_st_iff_not_infinite" -> "data", "localization_map.lift_id" -> "algebra", "circle_deg1_lift.translate_pow" -> "dynamics", "category_theory.functor.map_iso_symm" -> "category_theory", "submodule.linear_proj_of_is_compl_range" -> "algebra", "real.rpow_eq_pow" -> "analysis", "filter.map_inf_le" -> "order", "list.perm.erase_dup" -> "data", "cardinal.mk_range_eq_of_injective" -> "set_theory", "exists_rat_near" -> "algebra", "nat.eq_zero_of_dvd_of_lt" -> "data", "subspace.closed_complemented_iff_has_closed_compl" -> "analysis", "list.pairwise_pw_filter" -> "data", "times_cont_diff_id" -> "analysis", "nat.not_succ_le_self" -> "init", "pequiv.of_set_symm" -> "data", "real.arccos_neg_one" -> "analysis", "exists_nhds_split_inv" -> "topology", "turing.list_blank.ext" -> "computability", "category_theory.uncurry_natural_left" -> "category_theory", "eq_mul_inv_of_mul_eq" -> "algebra", "multiplicity.multiplicity_add_of_gt" -> "algebra", "multiset.le_ndunion_left" -> "data", "submonoid.map_supr" -> "algebra", "int.gcd_self" -> "algebra", "set.sUnion_pair" -> "data", "category_theory.abelian.image_eq_image" -> "category_theory", "add_lt_add_of_le_of_lt" -> "algebra", "equiv.perm.sign_bij_aux_mem" -> "algebra", "wseq.nth_tail" -> "data", "measure_theory.outer_measure.diff_null" -> "analysis", "set.maps_to_bUnion_bUnion" -> "data", "submodule.map_top" -> "algebra", "set.Ioo_union_Icc_eq_Ioc" -> "data", "times_cont_diff_on_top_iff_fderiv_within" -> "analysis", "list.lookmap_cons_some" -> "data", "ring_hom.iterate_map_one" -> "algebra", "vsub_set_finite_of_finite" -> "algebra", "nat.commute_cast" -> "data", "finset.disjoint_sdiff_inter" -> "data", "has_fderiv_at_filter.congr_of_eventually_eq" -> "analysis", "add_submonoid.localization_map.of_add_equiv_of_localizations_comp" -> "algebra", "measure_theory.measure.finite_at_filter.inf_ae_iff" -> "analysis", "sup_compl_eq_top" -> "order", "monoid_hom.mrange_top_of_surjective" -> "algebra", "cau_seq.of_near" -> "data", "set.Inter_lt_succ" -> "data", "topological_space.Union_basis_of_is_open" -> "topology", "mv_power_series.coeff_zero_X" -> "algebra", "inv_mul_lt_of_lt_mul" -> "algebra", "category_theory.is_iso.iso.inv_inv" -> "category_theory", "cau_seq.cauchy_seq" -> "topology", "finset.card_image_le" -> "data", "ennreal.to_real_pos_iff" -> "data", "equiv.perm.of_subtype_subtype_perm" -> "algebra", "int.modeq.mod_coprime" -> "data", "mv_polynomial.eval\:2082_cast_comp" -> "data", "hyperreal.infinite_pos_def" -> "data", "nat.add_pos_iff_pos_or_pos" -> "data", "sum.exists" -> "data", "ennreal.one_ne_top" -> "data", "hyperreal.coe_le_coe" -> "data", "Sup_eq_top" -> "order", "homeomorph.is_open_preimage" -> "topology", "filter.tendsto_comap'_iff" -> "order", "list.disjoint_nil_left" -> "data", "Top.coe_of" -> "topology", "ordinal.le_succ_of_is_limit" -> "set_theory", "left_inverse_sub_add_left" -> "algebra", "buffer.lt_aux_1" -> "data", "decidable.not_iff" -> "logic", "nat.gcd_zero_right" -> "init", "submodule.le_comap_mkq" -> "algebra", "irrational.inv" -> "data", "measure_theory.ae_eq_fun.smul_to_germ" -> "analysis", "finset.Ico.image_const_sub" -> "data", "invertible_unique" -> "algebra", "semiconj_by.units_inv_symm_left" -> "algebra", "mvpfunctor.M.dest_eq_dest'" -> "data", "list.enum_map_fst" -> "data", "category_theory.functor.pentagon" -> "category_theory", "set.Icc_subset_Ico_union_Icc" -> "data", "pfun.preimage_as_subtype" -> "data", "ordinal.log_le_log" -> "set_theory", "polynomial.div_wf_lemma" -> "data", "padic_int.mk_zero" -> "data", "free_group.to_group.unique" -> "algebra", "hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos" -> "data", "of_irreducible_map" -> "algebra", "circle_deg1_lift.map_add_int" -> "dynamics", "local_equiv.image_source_eq_target" -> "data", "mvpfunctor.const.mk_get" -> "data", "category_theory.adjunction.hom_equiv_naturality_left" -> "category_theory", "findim_eq_zero_of_dim_eq_zero" -> "algebra", "nnreal.coe_Inf" -> "data", "omega.unsat_of_unsat_eq_elim" -> "tactic", "list.perm.nodup_iff" -> "data", "set.sUnion_insert" -> "data", "submodule.closed_complemented_bot" -> "topology", "isometric.coe_eq_to_equiv" -> "topology", "sub_add_eq_add_sub" -> "algebra", "nat.dist_pos_of_ne" -> "data", "set.sInter_pair" -> "data", "list.take_append_drop" -> "data", "free_semigroup.traverse_mul'" -> "algebra", "nat.bit1_eq_succ_bit0" -> "init", "computation.terminates_parallel" -> "data", "primrec.list_rec" -> "computability", "eq_bot_mono" -> "order", "classical.nonempty_pi" -> "logic", "continuous_multilinear_map.curry0_apply" -> "analysis", "metric.Hausdorff_edist_ne_top_of_nonempty_of_bounded" -> "topology", "norm_num.one_add" -> "tactic", "closure_eq_inter_uniformity" -> "topology", "set.prod_singleton" -> "data", "continuous_linear_equiv.fderiv" -> "analysis", "mvpfunctor.M.bisim_lemma" -> "data", "closure_Iio'" -> "topology", "vector.nth_zero" -> "data", "real.deriv_cos" -> "analysis", "finset.inter_subset_inter_right" -> "data", "int.shiftr_add" -> "data", "nat.prime.ne_zero" -> "data", "ordinal.wf" -> "set_theory", "cardinal.mk_union_add_mk_inter" -> "set_theory", "filter.eventually.exists_forall_of_at_top" -> "order", "real.is_conjugate_exponent.pos" -> "data", "geom_sum" -> "algebra", "equiv.set.union_apply_left" -> "data", "complex.of_real_tanh" -> "data", "int.exists_eq_neg_of_nat" -> "init", "id_rel_subset" -> "topology", "submodule.comap_bot" -> "algebra", "matrix.update_column_ne" -> "data", "category_theory.functor.const_comp_hom_app" -> "category_theory", "set.finite_lt_nat" -> "data", "fderiv_within_sub" -> "analysis", "circle_deg1_lift.translation_number_eq_of_tendsto\:2080'" -> "dynamics", "category_theory.arrow.has_lift.ext_iff" -> "category_theory", "has_deriv_within_at.smul" -> "analysis", "category_theory.limits.equalizer.lift_\[Iota]_assoc" -> "category_theory", "abs_one" -> "algebra", "add_halves'" -> "algebra", "list.all_iff_forall_prop" -> "data", "omega.coeffs.val_between_neg" -> "tactic", "category_theory.limits.cokernel_zero_iso_target_hom" -> "category_theory", "discrete_valuation_ring.has_unit_mul_pow_irreducible_factorization.of_ufd_of_unique_irreducible" -> "algebra", "category_theory.discrete.equivalence_inverse" -> "category_theory", "int.nat_abs_dvd" -> "data", "filter.realizer.bot_\[Sigma]" -> "data", "not_injective_infinite_fintype" -> "data", "abs_norm_sub_norm_le" -> "analysis", "set.inj_on.congr" -> "data", "quadratic_form.coe_fn_add" -> "algebra", "convex.to_cone_is_least" -> "analysis", "is_basis.repr_ker" -> "algebra", "list.mem_cons_of_mem" -> "init", "eq_sub_iff_add_eq" -> "algebra", "subsemiring.prod_bot_sup_bot_prod" -> "algebra", "rat.mk_eq" -> "data", "matrix.diag_one" -> "algebra", "summable.indicator" -> "topology", "measure_theory.simple_func.map_integral" -> "analysis", "function.semiconj.maps_to_preimage" -> "data", "primrec_rel.comp\:2082" -> "computability", "is_monoid_hom.of_mul" -> "algebra", "with_top.zero_lt_top" -> "algebra", "rat.mk_eq_zero" -> "data", "composition.sigma_pi_composition_eq_iff" -> "analysis", "submonoid.mem_top" -> "algebra", "matrix.from_blocks_apply\:2081\:2082" -> "data", "normed_ring.tsum_geometric_of_norm_lt_1" -> "analysis", "int.neg_add_cancel_right" -> "init", "denumerable.prod_nat_of_nat" -> "data", "ennreal.mul_lt_top" -> "data", "list.map_tail" -> "data", "finset.disj_union_eq_union" -> "data", "dist_nndist" -> "topology", "nnreal.of_real_pos" -> "data", "has_fderiv_within_at.sum" -> "analysis", "turing.to_partrec.step_normal.is_ret" -> "computability", "le_infi" -> "order", "turing.pointed_map.head_map" -> "computability", "mv_power_series.mul_inv" -> "algebra", "num.cast_lt" -> "data", "has_strict_deriv_at.has_strict_fderiv_at_equiv" -> "analysis", "category_theory.limits.mono_factorisation_zero_e" -> "category_theory", "nat.dvd_of_mul_dvd_mul_left" -> "init", "mv_polynomial.is_homogeneous.total_degree" -> "algebra", "lower_bounds_Ioo" -> "order", "list.map_join" -> "data", "add_con.trans" -> "algebra", "computation.map_congr" -> "data", "fpow_sub" -> "algebra", "euclidean_geometry.angle_le_pi" -> "geometry", "has_deriv_at_iff_is_o_nhds_zero" -> "analysis", "bool.bnot_true" -> "data", "int.mul_nonneg" -> "init", "linear_map.ker_le_range_iff" -> "algebra", "category_theory.non_preadditive_abelian.sub_add" -> "category_theory", "prime_multiset.coe_pnat_prime" -> "data", "continuous_Sup_dom" -> "topology", "eq_Icc_of_connected_compact" -> "topology", "int.le.elim" -> "init", "finsupp.filter_apply_neg" -> "data", "hash_map.valid.as_list_nodup" -> "data", "abstract_completion.continuous_map\:2082" -> "topology", "mem_of_mem_perms_of_list" -> "data", "measure_theory.simple_func.map_coe_nnreal_restrict" -> "analysis", "nhds_within_Icc_eq_nhds_within_Iic" -> "topology", "filter.const_eventually_eq" -> "order", "real.abs_sin_le_one" -> "data", "asymptotics.is_O.sum" -> "analysis", "affine.simplex.sum_centroid_weights_with_circumcenter" -> "geometry", "zmod.nat_cast_surjective" -> "data", "quot.eq" -> "data", "list.argmax_eq_some_iff" -> "data", "finset.sum_const_zero" -> "algebra", "finset.inter_distrib_left" -> "data", "category_theory.limits.types.prod_snd" -> "category_theory", "ennreal.coe_inv" -> "data", "semidirect_product.right_hom_comp_map" -> "algebra", "list.is_prefix.trans" -> "data", "pos_of_neg_neg" -> "algebra", "submonoid.mem_map" -> "algebra", "function.commute.iterate_pos_le_iff_map_le'" -> "order", "con.map_of_surjective_eq_map_gen" -> "algebra", "set.image_add_right" -> "algebra", "pgame.one_move_left" -> "set_theory", "bilin_form.ortho_smul_right" -> "algebra", "with_zero.mul_comm" -> "algebra", "category_theory.limits.functor_category_colimit_cocone_X" -> "category_theory", "finset.min_of_nonempty" -> "data", "filter.tendsto_at_bot_add_nonpos_left'" -> "order", "finset.inter_comm" -> "data", "alg_equiv.coe_ring_equiv" -> "algebra", "finsupp_lequiv_direct_sum_symm_lof" -> "algebra", "fin.tail_init_eq_init_tail" -> "data", "category_theory.monoidal_functor.map_left_unitor" -> "category_theory", "nat.cast_nonneg" -> "data", "num.sub_to_nat" -> "data", "pequiv.mem_of_set_self_iff" -> "data", "module.direct_limit.totalize_apply" -> "algebra", "mdifferentiable_chart" -> "geometry", "matrix.one_apply" -> "data", "list.cons_subset" -> "data", "structure_groupoid.chart_mem_maximal_atlas" -> "geometry", "ordinal.succ_zero" -> "set_theory", "set.Iic_union_Ico_eq_Iio" -> "data", "mul_nonpos_of_nonneg_of_nonpos" -> "algebra", "filter.principal_univ" -> "order", "ff_bxor" -> "init", "list.range_sublist" -> "data", "neg_smul" -> "algebra", "int.sub_nat_nat_of_sub_eq_succ" -> "init", "has_strict_fderiv_at.local_inverse_apply_image" -> "analysis", "modeq_mersenne" -> "number_theory", "set.interval_of_not_le" -> "data", "category_theory.simple.ext" -> "category_theory", "set.ssubset_insert" -> "data", "real.rpow_sub" -> "analysis", "znum.cast_mul" -> "data", "continuous_within_at.neg" -> "topology", "complex.exp_neg" -> "data", "interior_compl" -> "topology", "filter.tendsto.nnnorm" -> "analysis", "lie_algebra.equiv.symm_trans_apply" -> "algebra", "set.univ_prod" -> "data", "fintype.sum_extend_by_zero" -> "data", "padic_int.unit_coeff_spec" -> "data", "subsingleton.measurable" -> "analysis", "lagrange.interpolate_neg" -> "algebra", "decidable.ne_iff_lt_or_gt" -> "init", "add_con.lift_mk'" -> "algebra", "set.bex_insert_iff" -> "data", "submodule.coe_is_compl_equiv_proj_apply" -> "algebra", "list.length_map_accumr\:2082" -> "init", "lt_of_sub_neg" -> "algebra", "differentiable_on.iterate" -> "analysis", "int.gcd_dvd_gcd_mul_left" -> "algebra", "cardinal.aleph_idx_aleph'" -> "set_theory", "has_strict_deriv_at.to_local_inverse" -> "analysis", "finset.nonempty.mono" -> "data", "has_fderiv_at_iff_tendsto" -> "analysis", "measure_theory.measure_bUnion_le" -> "analysis", "list.subset.refl" -> "init", "computable_pred.to_re" -> "computability", "is_closed_le" -> "topology", "turing.TM2.stmts\:2081_supports_stmt_mono" -> "computability", "multiset.inter_add_distrib" -> "data", "set.pure_def" -> "data", "differentiable_within_at.fst" -> "analysis", "set.subset_inter" -> "data", "real.zero_lt_one" -> "data", "int.lcm_zero_right" -> "algebra", "int.of_nat_succ" -> "init", "set.zero_mem_zero" -> "algebra", "category_theory.iso.trans_hom" -> "category_theory", "category_theory.nat_trans.ext_iff" -> "category_theory", "typevec.last_fun_of_subtype" -> "data", "left_inv_eq_right_inv" -> "algebra", "finset.range_one" -> "data", "function.is_periodic_pt.map" -> "dynamics", "mv_polynomial.is_homogeneous.coeff_eq_zero" -> "algebra", "semiquot.mem_pure_self" -> "data", "filter.eventually_le.is_min_filter" -> "order", "dioph.mul_dioph" -> "number_theory", "finset.mem_range" -> "data", "nat.prime.multiplicity_pow" -> "data", "list.Ico.succ_top" -> "data", "category_theory.monad.forget_creates_limits.cone_point_A" -> "category_theory", "bitvec.to_bool_add_lsb_mod_two" -> "data", "nat.le_of_dvd" -> "init", "computable.nat_div2" -> "computability", "is_submonoid.pow_mem" -> "algebra", "affine_subspace.span_points_subset_coe_of_subset_coe" -> "algebra", "list.to_finset_nil" -> "data", "option.none_orelse" -> "data", "is_group_hom.injective_iff_trivial_ker" -> "algebra", "measure_theory.simple_func.mul_apply" -> "analysis", "tensor_product.lift.unique" -> "algebra", "int.le_of_sub_nonneg" -> "init", "ball_eq_of_symmetry" -> "topology", "filter.tendsto_infi'" -> "order", "vector.mmap_nil" -> "data", "forall_3_true_iff" -> "logic", "Set.omega_succ" -> "set_theory", "cau_seq.const_inv" -> "data", "heq.trans" -> "init", "finset.filter_or" -> "data", "quotient_add_group.injective_ker_lift" -> "algebra", "set.inclusion_self" -> "data", "fderiv_add" -> "analysis", "power_series.constant_coeff_inv" -> "algebra", "units.eq_mul_inv_iff_mul_eq" -> "algebra", "floor_one" -> "algebra", "times_cont_mdiff_on.mdifferentiable_on" -> "geometry", "mv_power_series.coeff_mul_C" -> "algebra", "computation.terminates_map_iff" -> "data", "nat.with_bot.add_eq_zero_iff" -> "data", "metric.closed_ball_mem_nhds" -> "topology", "category_theory.limits.kernel_fork.app_one" -> "category_theory", "rel.preimage_comp" -> "data", "finset.sum_nat_cast" -> "algebra", "complex.of_real_sub" -> "data", "ennreal.one_lt_coe_iff" -> "data", "local_homeomorph.mdifferentiable.trans" -> "geometry", "multiset.disjoint_iff_ne" -> "data", "nhds_within_Ioo_eq_nhds_within_Ioi" -> "topology", "pell.pell_zd_im" -> "number_theory", "fin.eq_mk_iff_coe_eq" -> "data", "nat.bodd_bit1" -> "data", "is_min_on.on_subset" -> "order", "add_commute.symm_iff" -> "algebra", "metric.completion.dist_comm" -> "topology", "homological_complex.homology_map_id" -> "algebra", "finset.Ico.image_sub" -> "data", "push_neg.not_exists_eq" -> "tactic", "submonoid.comap_map_eq_of_injective" -> "algebra", "mersenne_pos" -> "number_theory", "local_equiv.eq_on_source_refl" -> "data", "enat.to_with_top_zero" -> "data", "set.prod_mono" -> "data", "polynomial.degree_pow_le" -> "data", "function.injective.comap_subsingleton" -> "logic", "category_theory.functor.congr_hom" -> "category_theory", "list.ball_cons" -> "init", "abs_sub" -> "algebra", "continuous_linear_map.coe_mul" -> "topology", "continuous_pi" -> "topology", "mvpfunctor.W_path_cases_on_eta" -> "data", "free_group.red.step.cons_bnot" -> "algebra", "push_neg.not_or_eq" -> "tactic", "add_aut.mul_def" -> "data", "prod.fst_one" -> "algebra", "differentiable.rpow" -> "analysis", "subgroup.mul_mem_cancel_right" -> "algebra", "measure_theory.integrable_smul_iff" -> "analysis", "roption.map_bind" -> "data", "finset.insert_ne_empty" -> "data", "set.image_const_add_Ico" -> "data", "ennreal.zero_eq_coe" -> "data", "finset.union_sdiff_of_subset" -> "data", "set.add_image_prod" -> "algebra", "category_theory.forget_map_eq_coe" -> "category_theory", "bdd_below_Ioi" -> "order", "nat.div_mul_div" -> "data", "primrec_rel.comp" -> "computability", "submodule.mem_orthogonal" -> "analysis", "quotient.out_eq" -> "data", "list.foldl_hom" -> "data", "enat.coe_zero" -> "data", "list.qsort_nil" -> "init", "polynomial.monomial_mul_monomial" -> "data", "measure_theory.ae_eq_fun.mk_sub" -> "analysis", "set.range_eq_Union" -> "data", "ge_of_tendsto'" -> "topology", "set.Inter_const" -> "data", "int.sum_two_squares_of_two_mul_sum_two_squares" -> "number_theory", "polynomial.map_map" -> "data", "lie_add_group_core.to_lie_add_group" -> "geometry", "neg_mul_eq_mul_neg" -> "algebra", "band_ff" -> "init", "nat.lt_add_right" -> "init", "filter.frequently_at_top'" -> "order", "seq.map_comp" -> "data", "homeomorph.range_coe" -> "topology", "ideal.disjoint_closure_singleton_iff_not_mem" -> "algebra", "measure_theory.outer_measure.trim_sum_ge" -> "analysis", "set.neg_mem_neg" -> "algebra", "int.div_dvd_div" -> "data", "mvqpf.cofix.ext" -> "data", "complex.cos_add" -> "data", "add_monoid_hom.comp_apply" -> "algebra", "set.Icc_subset_Ioo" -> "data", "topological_fiber_bundle_core.is_topological_fiber_bundle" -> "topology", "equiv.right_inverse_symm" -> "data", "list.cons_ne_nil" -> "data", "list.all_nil" -> "data", "pow_lt_pow" -> "algebra", "has_fderiv_at.sub_const" -> "analysis", "supr_eq_if" -> "order", "le_of_nat_ceil_le" -> "algebra", "set.prod_subset_prod_iff" -> "data", "multiset.map_zero" -> "data", "interior_Icc" -> "topology", "submodule.disjoint_span_singleton" -> "algebra", "ennreal.add_left_inj" -> "data", "finset.subset.antisymm_iff" -> "data", "localization_map.integer_normalization_coeff" -> "algebra", "rat.inv_mul_cancel" -> "data", "mul_action.mem_stabilizer_iff" -> "algebra", "bifunctor.comp_fst" -> "control", "is_subgroup.coe_inv" -> "algebra", "measure_theory.integrable_on_zero" -> "analysis", "category_theory.comonad_hom.comp_id" -> "category_theory", "add_submonoid.mrange_inl" -> "algebra", "finsupp.sigma_support" -> "data", "category_theory.limits.pullback_cone.mk_\[Pi]_app" -> "category_theory", "list.perm.fold_op_eq" -> "data", "functor.comp.pure_seq_eq_map" -> "control", "if_false_right_eq_and" -> "init", "power_series.coeff_mul_C" -> "algebra", "category_theory.ev_coev" -> "category_theory", "model_with_corners.mdifferentiable" -> "geometry", "complex.re_sq_le_norm_sq" -> "data", "measure_theory.simple_func.lintegral_mono" -> "analysis", "list.pw_filter_subset" -> "data", "filter.comap_Sup" -> "order", "times_cont_mdiff_on.congr" -> "geometry", "open_embedding.comp" -> "topology", "set.bInter_subset_bInter_left" -> "data", "category_theory.eq_to_hom_trans" -> "category_theory", "cardinal.succ_zero" -> "set_theory", "emetric.Hausdorff_edist_zero_iff_eq_of_closed" -> "topology", "submonoid.localization_map.mul_equiv_of_localizations_symm_apply" -> "algebra", "computable.vector_cons" -> "computability", "complex.log_re" -> "analysis", "mv_polynomial.rename_id" -> "data", "complex.differentiable_at_exp" -> "analysis", "continuous_inr" -> "topology", "real.ball_eq_Ioo" -> "topology", "has_fderiv_at_filter.neg" -> "analysis", "category_theory.limits.kernel_comp_is_iso_hom_comp_kernel_\[Iota]" -> "category_theory", "infi_le_infi_const" -> "order", "is_R_or_C.abs_one" -> "data", "sub_eq_neg_add" -> "algebra", "poly_equiv_tensor.to_fun_linear_mul_tmul_mul" -> "algebra", "pnat.gcd_dvd_left" -> "data", "is_unit.mul_right_dvd" -> "algebra", "mvpfunctor.W_dest'_W_mk'" -> "data", "complex.cosh_sub_sinh" -> "data", "filter.ne_bot.add" -> "order", "hyperreal.infinite_pos_neg_of_infinite_neg" -> "data", "filter.tendsto_inf_left" -> "order", "linear_map.range_le_bot_iff" -> "algebra", "is_local_extr_on.comp_antimono" -> "topology", "finset.mem_erase" -> "data", "computation.mem_of_promises" -> "data", "free_ring.coe_eq" -> "algebra", "abs_dist_sub_le" -> "topology", "metric.uniform_continuous_inf_dist_pt" -> "topology", "computation.le_stable" -> "data", "category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv" -> "category_theory", "set.preimage_const_add_Ioo" -> "data", "turing.tr_eval_rev" -> "computability", "order_separated" -> "topology", "measure_theory.ae_eq_fun.integrable_zero" -> "analysis", "asymptotics.is_o.add_is_O_with" -> "analysis", "int.dvd_of_pow_dvd" -> "data", "set.subset_empty_iff" -> "data", "exists_Ico_subset_of_mem_nhds" -> "topology", "dense_inter_of_open_left" -> "topology", "norm_sub_pow_two" -> "analysis", "continuous_linear_map.pi_apply" -> "topology", "category_theory.single_obj.map_hom_comp" -> "category_theory", "cau_seq.le_of_le_of_eq" -> "data", "times_cont_diff_on_univ" -> "analysis", "is_basis.iff_det" -> "algebra", "int.coe_nat_bit1" -> "data", "fin.one_pos" -> "data", "pequiv.trans_eq_none" -> "data", "measure_theory.simple_func.coe_neg" -> "analysis", "fin.mk_bit0" -> "data", "free_semigroup.lift_of_mul" -> "algebra", "principal_seg.init_iff" -> "set_theory", "nat.exists_eq_add_of_le" -> "data", "polynomial.coeff_one_zero" -> "data", "function.surjective.nontrivial" -> "logic", "div_le_iff_of_neg'" -> "algebra", "complex.norm_sq_neg" -> "data", "set.comp_piecewise" -> "data", "iterated_deriv_eq_iterate" -> "analysis", "lt_iff_lt_of_le_iff_le'" -> "algebra", "category_theory.monoidal.right_unitor_hom_apply" -> "category_theory", "pnat.coe_nat_factor_multiset" -> "data", "dfinsupp.subtype_domain_sub" -> "data", "pequiv.single_mul_single_right" -> "data", "prod.fst_injective" -> "data", "set.prod_union" -> "data", "tendsto_const_nhds" -> "topology", "multiset.fold_zero" -> "data", "uniformity_basis_edist_le" -> "topology", "fintype.card_le_one_iff_subsingleton" -> "data", "category_theory.over.iterated_slice_equiv_functor" -> "category_theory", "mv_polynomial.pderivative_monomial_mul" -> "data", "ordinal.power_lt_omega" -> "set_theory", "pfunctor.liftp_iff" -> "data", "le_inv_iff_mul_le_one" -> "algebra", "is_coprime.mul_add_left_left_iff" -> "algebra", "category_theory.monad.forget_creates_limits.new_cone_X" -> "category_theory", "mvqpf.liftr_map_last" -> "data", "category_theory.eq_to_iso_trans" -> "category_theory", "mul_equiv.map_prod" -> "algebra", "submodule.linear_proj_of_is_compl_ker" -> "algebra", "list.kerase_kerase" -> "data", "subsemiring.mul_mem" -> "algebra", "topological_space.opens.open_embedding_of_le" -> "topology", "smul_zero" -> "algebra", "localization.mul_equiv_of_quotient_mk" -> "algebra", "subgroup.normal_closure_le_normal" -> "algebra", "nonote.repr_sub" -> "set_theory", "matrix.diagonal_mul" -> "data", "mv_polynomial.degrees_neg" -> "data", "complex.arg_eq_arg_neg_sub_pi_of_im_neg_of_re_neg" -> "analysis", "filter.has_basis.cauchy_seq_iff" -> "topology", "composition_as_set.ext" -> "combinatorics", "set.range_id" -> "data", "exists_lt_of_lt_cSup" -> "order", "times_cont_diff_iff_continuous_differentiable" -> "analysis", "mem_skew_adjoint_matrices_lie_subalgebra" -> "algebra", "nhds_within_Iio_ne_bot'" -> "topology", "cInf_le" -> "order", "continuous_multilinear_map.op_norm_le_bound" -> "analysis", "category_theory.nat_iso.of_components.app" -> "category_theory", "linear_equiv.symm_apply_apply" -> "algebra", "is_compact.exists_is_greatest" -> "topology", "homeomorph.coinduced_eq" -> "topology", "gaussian_int.to_complex_div_re" -> "data", "free_abelian_group.sub_bind" -> "algebra", "is_linear_map.is_linear_map_add" -> "algebra", "dual_pair.coeffs_lc" -> "algebra", "has_deriv_within_at.limsup_slope_norm_le" -> "analysis", "nat.fact_succ" -> "data", "add_left_cancel" -> "algebra", "hofer" -> "analysis", "list.traverse_nil" -> "control", "is_lub_le_iff" -> "order", "or_iff_not_imp_left" -> "logic", "int.dvd_nat_abs" -> "data", "multiset.erase_add_left_pos" -> "data", "exists_unique_iff_exists" -> "logic", "set.preimage_inter_range" -> "data", "group.conjugates_of_set_subset_normal_closure" -> "algebra", "add_lt_of_lt_of_neg'" -> "algebra", "filter.eventually_supr" -> "order", "filter.has_basis.ex_mem" -> "order", "category_theory.limits.kernel_iso_of_eq_refl" -> "category_theory", "finset.sdiff_inter_distrib_right" -> "data", "differentiable_at.add" -> "analysis", "hyperreal.st_neg" -> "data", "measure_theory.integrable.congr'" -> "analysis", "linear_map.range_smul'" -> "algebra", "plift.rec.constant" -> "data", "submodule.mem_infi" -> "algebra", "ennreal.rpow_lt_rpow_of_exponent_lt" -> "analysis", "is_local_extr_on.is_local_extr" -> "topology", "ring_equiv.map_mul" -> "data", "filter.at_top_countable_basis" -> "order", "complex.norm_sq_sub" -> "data", "is_R_or_C.conj_to_complex" -> "data", "ordinal.zero_eq_lift_type_empty" -> "set_theory", "finite_dimensional.exists_relation_sum_zero_pos_coefficient_of_dim_succ_lt_card" -> "algebra", "associates.one_eq_mk_one" -> "algebra", "subgroup.prod_top" -> "algebra", "subsemiring.closure_union" -> "algebra", "filter.map_swap_eq_comap_swap" -> "order", "category_theory.curry_eq_iff" -> "category_theory", "asymptotics.is_O_with_norm_norm" -> "analysis", "mv_polynomial.coeff_map" -> "data", "ennreal.sub_supr" -> "topology", "add_monoid_hom.lift_of_surjective_comp" -> "algebra", "filter.has_basis.cauchy_iff" -> "topology", "turing.TM2to1.stk_nth_val" -> "computability", "category_theory.abelian.pseudoelement.mono_of_zero_of_map_zero" -> "category_theory", "mv_polynomial.coeff_mul_X'" -> "data", "free_group.red.step.to_group" -> "algebra", "units.inv_unique" -> "algebra", "nat.gcd_mul_right" -> "data", "exists_pempty" -> "logic", "concave_on.comp_affine_map" -> "analysis", "inducing.nhds_eq_comap" -> "topology", "bxor_coe_iff" -> "init", "int.eq_zero_of_nat_abs_eq_zero" -> "init", "alg_equiv.map_sum" -> "algebra", "is_open.unique_diff_on" -> "analysis", "algebraic_closure.span_eval_ne_top" -> "algebra", "ring_equiv.to_CommRing_iso_inv" -> "algebra", "multiset.le_induction_on" -> "data", "not_lt_zero'" -> "algebra", "is_add_group_hom.injective_iff" -> "algebra", "matrix.map_add" -> "data", "deriv_within_sub_const" -> "analysis", "digits_zero" -> "data", "category_theory.core.comp_hom" -> "category_theory", "lucas_lehmer.X.mul_fst" -> "number_theory", "nat.sqrt_le" -> "data", "quotient.induction_on\:2083'" -> "data", "real.cos_arcsin_nonneg" -> "analysis", "differentiable.mul" -> "analysis", "category_theory.Monad.to_Mon_X" -> "category_theory", "uniformity_basis_edist" -> "topology", "order_bot.bdd_below" -> "order", "add_submonoid.localization_map.mk'_spec'" -> "algebra", "nnreal.rpow_zero" -> "analysis", "differentiable_on.sqrt" -> "analysis", "has_deriv_at.add" -> "analysis", "heq_of_eq" -> "init", "lt_mem_sets_of_Limsup_lt" -> "topology", "max_neg_neg" -> "algebra", "mul_div_cancel_of_imp" -> "algebra", "multilinear_map.mk_continuous_norm_le" -> "analysis", "zsqrtd.add_re" -> "data", "filter.eventually_lift'_powerset_forall" -> "order", "add_semiconj_by.units_neg_symm_left_iff" -> "algebra", "list.pairwise_of_pairwise_cons" -> "data", "multiset.sub_le_iff_le_add" -> "data", "submodule.comap_subtype_eq_top" -> "algebra", "subtype.restrict_apply" -> "data", "continuous_at.iterate" -> "topology", "multiset.pmap_zero" -> "data", "equiv_of_is_basis_comp" -> "algebra", "measure_theory.measure.haar.is_left_invariant_index" -> "analysis", "set.surj_on.image_eq_of_maps_to" -> "data", "filter.inf_ne_bot_iff_frequently_left" -> "order", "finset.mem_mk" -> "data", "is_measurable.univ" -> "analysis", "set.sep_mem_eq" -> "data", "free_abelian_group.map_add" -> "algebra", "initial_seg.init'" -> "set_theory", "metric.bounded_union" -> "topology", "is_least_Ico" -> "order", "submodule.linear_proj_of_is_compl_apply_right'" -> "algebra", "times_cont_diff.has_strict_fderiv_at" -> "analysis", "eq_bot_iff_dim_eq_zero" -> "algebra", "times_cont_diff_at.continuous_linear_map_comp" -> "analysis", "has_fderiv_at_filter.snd" -> "analysis", "matrix.update_column_transpose" -> "data", "list.map_eq_map_iff" -> "data", "ideal.comap_ne_bot_of_algebraic_mem" -> "algebra", "has_fpower_series_on_ball.sum" -> "analysis", "list.concat_eq_append" -> "data", "set.preimage_range_inter" -> "data", "nhds_is_closed" -> "topology", "set.prod_insert" -> "data", "monoid_hom.eq_of_eq_on_mdense" -> "algebra", "linear_equiv_matrix_apply'" -> "algebra", "lipschitz_with.uniform_continuous" -> "topology", "multiset.sum_eq_foldl" -> "data", "circle_deg1_lift.coe_one" -> "dynamics", "list.countp_cons_of_pos" -> "data", "zmod.legendre_sym_two" -> "number_theory", "category_theory.functor.triangle" -> "category_theory", "list.chain'_map_of_chain'" -> "data", "prod.mk_mul_mk" -> "algebra", "dim_of_field" -> "algebra", "submonoid.prod_top" -> "algebra", "category_theory.equivalence.cancel_counit_inv_right_assoc" -> "category_theory", "cauchy_map_iff_exists_tendsto" -> "topology", "category_theory.discrete.id_def" -> "category_theory", "set.eq_sep_of_subset" -> "data", "list.perm.bag_inter" -> "data", "affine_subspace.vsub_left_mem_direction_iff_mem" -> "algebra", "set.mul_singleton" -> "algebra", "linear_map.comp_apply" -> "algebra", "polynomial.expand_eq_map_domain" -> "algebra", "sum_le_has_sum" -> "topology", "max_eq_left_of_lt" -> "init", "subgroup.coe_subset_coe" -> "algebra", "mfderiv_eq_fderiv" -> "geometry", "supr_bot" -> "order", "pfunctor.M.head_eq_head'" -> "data", "multiset.subset_iff" -> "data", "nhds_within_eq_map_subtype_coe" -> "topology", "wseq.think_congr" -> "data", "holor.sum_unit_vec_mul_slice" -> "data", "wseq.dropn_add" -> "data", "filter.mul_assoc" -> "order", "denumerable.sigma_of_nat_val" -> "data", "finmap.lookup_list_to_finmap" -> "data", "computation.results_think" -> "data", "category_theory.uncurry_natural_right" -> "category_theory", "not_bex" -> "logic", "real.abs_exp" -> "data", "deriv_const_sub" -> "analysis", "free_group.to_group.of_eq" -> "algebra", "nat.dist_mul_right" -> "data", "ideal.bot_mul" -> "algebra", "complex.continuous_of_real" -> "topology", "int.induction_on" -> "data", "set.exists_finite_iff_finset" -> "data", "euclidean_geometry.reflection_involutive" -> "geometry", "le_gronwall_bound_of_liminf_deriv_right_le" -> "analysis", "category_theory.yoneda_obj_map" -> "category_theory", "exists_const" -> "logic", "homological_complex.comm_at" -> "algebra", "cInf_lt_of_lt" -> "order", "polynomial.coeff_inv_units" -> "data", "concave_on.convex_lt" -> "analysis", "finset.inf_insert" -> "data", "list.eq_of_mem_repeat" -> "data", "turing.partrec_to_TM2.pred_ok" -> "computability", "function.surjective.range_eq" -> "data", "mv_power_series.mul_zero" -> "algebra", "category_theory.preimage_id" -> "category_theory", "real.sin_arccos" -> "analysis", "ulift.add_down" -> "algebra", "multiset.map_le_map" -> "data", "linear_equiv.symm_conj_apply" -> "algebra", "continuous_linear_map.subtype_val_apply" -> "topology", "set.Ico_\:2115_card" -> "data", "pfun.dom_eq" -> "data", "semidirect_product.left_inr" -> "algebra", "zero_smul_set" -> "algebra", "rel_iso.cof" -> "set_theory", "finset.attach_val" -> "data", "algebra.subring_coe_algebra_map" -> "algebra", "set.mem_image_iff_of_inverse" -> "data", "iterated_fderiv_within_zero_apply" -> "analysis", "set.dual_Ioo" -> "data", "multiset.zero_bind" -> "data", "mv_polynomial.monomial_zero" -> "data", "multiset.inf_mono" -> "data", "tendsto_multiset_sum" -> "topology", "sum.map_inr" -> "data", "padic.coe_div" -> "data", "eq_inv_smul_iff" -> "algebra", "fixed_points.f_le_Inf_of_fixed_points" -> "order", "add_localization.add_equiv_of_quotient_mk'" -> "algebra", "list.to_finset_val" -> "data", "asymptotics.is_O.trans_is_o" -> "analysis", "linear_independent_subtype_disjoint" -> "algebra", "mem_Icc_of_mem_std_simplex" -> "analysis", "subring.coe_map" -> "algebra", "category_theory.functor.right_unitor_inv_app" -> "category_theory", "real.le_sqrt'" -> "data", "has_fderiv_within_at.const_smul_algebra" -> "analysis", "polynomial.monic.degree_eq_zero_iff_eq_one" -> "data", "list.reverse_prefix" -> "data", "continuous_on.add" -> "topology", "add_submonoid.dense_induction" -> "algebra", "matrix.to_lin_zero" -> "algebra", "znum.zneg_bit1" -> "data", "finset.bind_insert" -> "data", "real.rpow_add'" -> "analysis", "one_lt_mul" -> "algebra", "list.nth_le_nth" -> "data", "complex.conj_neg_I" -> "data", "with_zero.mul_le_mul_left" -> "algebra", "nat.dist_comm" -> "data", "is_add_group_hom.map_sub" -> "algebra", "set.bInter_image" -> "data", "neg_one_pow_eq_or" -> "algebra", "has_deriv_at_real_of_complex_aux" -> "analysis", "finset.card_singleton_inter" -> "data", "affine_independent_subtype_of_affine_independent" -> "algebra", "set.mul_union" -> "algebra", "nat.sub_succ" -> "init", "finset.mem_attach_fin" -> "data", "submodule.is_principal.mem_iff_generator_dvd" -> "algebra", "smodeq.top" -> "algebra", "category_theory.quotient.sound" -> "category_theory", "int.sub_neg_of_lt" -> "init", "is_open_map.nhds_le" -> "topology", "measure_theory.inner_content_empty" -> "analysis", "finset.inf_singleton" -> "data", "semiconj_by.cast_int_mul_cast_int_mul" -> "algebra", "exists_has_deriv_within_at_eq_of_lt_of_gt" -> "analysis", "inf_of_le_right" -> "order", "circle_deg1_lift.tendsto_translation_number\:2080'" -> "dynamics", "int.coe_nat_ne_zero" -> "data", "char_p.char_is_prime" -> "algebra", "measure_theory.integrable_norm_iff" -> "analysis", "polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map" -> "data", "seq.dropn_add" -> "data", "turing.partrec_to_TM2.move_ok" -> "computability", "emetric.second_countable_of_separable" -> "topology", "tensor_product.curry_apply" -> "algebra", "nat.eq_zero_or_eq_succ_pred" -> "init", "category_theory.monoidal_category.left_unitor_product_aux_square" -> "category_theory", "punit.inf_eq" -> "algebra", "is_add_group_hom.zero_iff_ker_neg" -> "algebra", "set.left_mem_Ioo" -> "data", "list.prefix_cons_inj" -> "data", "asymptotics.is_O_with.add_is_o" -> "analysis", "continuous_linear_map.comp_zero" -> "topology", "int.le_neg_of_le_neg" -> "init", "category_theory.category_of_elements.from_comma_map" -> "category_theory", "ulower.ext" -> "data", "deriv_within_const_smul" -> "analysis", "isometry.dist_eq" -> "topology", "abs_mul_abs_self" -> "algebra", "set.countable_iff_exists_inj_on" -> "data", "lucas_lehmer.X.ext" -> "number_theory", "irreducible_of_associated" -> "algebra", "typevec.fst_diag" -> "data", "add_submonoid.localization_map.mk'_eq_of_eq" -> "algebra", "open_embedding.open_iff_image_open" -> "topology", "localization.mk_eq_mk'_apply" -> "algebra", "ext_chart_at_source_mem_nhds" -> "geometry", "roption.mem_eq" -> "data", "category_theory.limits.cofork.of_cocone_\[Iota]" -> "category_theory", "localization_map.integer_normalization_aeval_eq_zero" -> "algebra", "function.surjective.of_comp" -> "logic", "setoid.injective_iff_ker_bot" -> "data", "circle_deg1_lift.translation_number_pow" -> "dynamics", "set.monotone_image" -> "data", "algebraic_geometry.structure_sheaf.is_locally_fraction_pred" -> "algebraic_geometry", "ennreal.inv_lt_iff_inv_lt" -> "data", "category_theory.monad.free_obj_A" -> "category_theory", "pow_eq_one_iff" -> "algebra", "filter.eventually_eq.comp\:2082" -> "order", "circle_deg1_lift.le_translation_number_of_add_le" -> "dynamics", "times_cont_diff.comp_times_cont_diff_on" -> "analysis", "lie_algebra.matrix_trace_commutator_zero" -> "algebra", "premetric.dist_nonneg" -> "topology", "filter.mem_comap_sets" -> "order", "has_deriv_at.add_const" -> "analysis", "ordinal.cof_omega" -> "set_theory", "emetric.ball_subset" -> "topology", "fin.cons_update" -> "data", "category_theory.abelian.pseudoelement.pseudo_zero_iff" -> "category_theory", "category_theory.limits.pushout.inr_desc_assoc" -> "category_theory", "finset.bInter_insert_update" -> "data", "polynomial.support_map_subset" -> "data", "wseq.to_list_nil" -> "data", "is_preconnected_Ioc" -> "topology", "free_comm_ring.is_supported_int" -> "algebra", "is_preconnected.closure" -> "topology", "int.cast_coe_nat" -> "data", "is_closed.Icc_subset_of_forall_mem_nhds_within" -> "topology", "add_group.char_zero_of_inj_zero" -> "algebra", "ennreal.coe_div" -> "data", "nat.gcd_le_left" -> "data", "ring_equiv.refl_apply" -> "data", "galois_insertion.l_surjective" -> "order", "differentiable_on.const_sub" -> "analysis", "finset.filter_singleton" -> "data", "complex.mul_self_abs" -> "data", "ordinal.lift_nat_cast" -> "set_theory", "continuous_map.continuous" -> "topology", "with_bot.coe_eq_coe" -> "order", "nat.partrec.code.rec_prim" -> "computability", "submodule.eq_top_of_nonempty_interior'" -> "topology", "is_compact.nonempty_Inter_of_sequence_nonempty_compact_closed" -> "topology", "smodeq.zero" -> "algebra", "real.arcsin_inj" -> "analysis", "multiset.count_cons_of_ne" -> "data", "constr_zero" -> "algebra", "category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso_inv" -> "category_theory", "finsupp.sum_id_lt_of_lt" -> "data", "measurable_generate_from" -> "analysis", "cardinal.mul_le_mul" -> "set_theory", "computable_pred.computable_iff" -> "computability", "hyperreal.coe_bit1" -> "data", "model_with_corners.mdifferentiable_on_symm" -> "geometry", "formal_multilinear_series.comp_partial_sum" -> "analysis", "imp_congr_ctx_eq" -> "init", "compact_diff" -> "topology", "gpow_add" -> "algebra", "set.bInter_univ" -> "data", "int.test_bit_lxor" -> "data", "generalized_continued_fraction.convergents'_aux_stable_step_of_terminated" -> "algebra", "Set.mem_empty" -> "set_theory", "complex.exp_eq_exp_re_mul_sin_add_cos" -> "data", "scale_roots_aeval_eq_zero" -> "algebra", "real.arccos_neg" -> "analysis", "commute.units_gpow_right" -> "algebra", "min_le_add_of_nonneg_left" -> "algebra", "submodule.quotient.mk'_eq_mk" -> "algebra", "asymptotics.is_O.add_is_o" -> "analysis", "formal_multilinear_series.comp_coeff_zero'" -> "analysis", "ordinal.card_eq_nat" -> "set_theory", "category_theory.limits.alternative_cone_\[Pi]" -> "category_theory", "enat.add_left_cancel_iff" -> "data", "has_strict_fderiv_at.sub" -> "analysis", "measure_theory.ae_eq_fun.coe_fn_inv" -> "analysis", "filter.lift_infi" -> "order", "le_add_of_sub_left_le" -> "algebra", "measurable_to_nat" -> "analysis", "set.maps_to_preimage" -> "data", "monoid_hom.map_ne_zero" -> "algebra", "pfunctor.W.mk_dest" -> "data", "interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right" -> "analysis", "pgame.impartial_def" -> "set_theory", "nat.not_succ_le_zero" -> "init", "multiset.nat.antidiagonal_zero" -> "data", "is_integral_trans" -> "algebra", "polynomial.degree_add_div" -> "data", "polynomial.eq_X_add_C_of_degree_le_one" -> "data", "set.insert_eq" -> "data", "set.infinite_coe_iff" -> "data", "finsupp.map_domain_zero" -> "data", "polynomial.expand_pow" -> "algebra", "localization_map.to_map_ne_zero_of_mem_non_zero_divisors" -> "algebra", "mv_polynomial.eval\:2082_rename_prodmk" -> "data", "nat.succ_eq_add_one" -> "init", "continuous_linear_map.closed_complemented_ker_of_right_inverse" -> "topology", "continuous_on_Ico_extend_from_Ioo" -> "topology", "pfun.mem_fix_iff" -> "data", "measurable_edist" -> "analysis", "category_theory.nat_trans.hcomp_id_app" -> "category_theory", "multiset.coe_sections" -> "data", "multiset.sup_ndunion" -> "data", "set.subsingleton_empty" -> "data", "measure_theory.measure.haar.prehaar_le_index" -> "analysis", "finset.prod_update_of_not_mem" -> "algebra", "subgroup.mem_center_iff" -> "algebra", "nonote.cmp_compares" -> "set_theory", "add_submonoid.localization_map.eq'" -> "algebra", "semidirect_product.mk_eq_inl_mul_inr" -> "algebra", "finset.prod_le_prod" -> "algebra", "int.eq_of_mul_eq_mul_left" -> "init", "neg_add_lt_of_lt_add" -> "algebra", "wseq.destruct_of_seq" -> "data", "fpow_mul" -> "algebra", "neg_one_pow_eq_pow_mod_two" -> "algebra", "primrec.nat_max" -> "computability", "linear_map.lcomp_apply" -> "algebra", "pgame.numeric.move_left_le" -> "set_theory", "Class.subset_hom" -> "set_theory", "submodule.fg_map" -> "algebra", "set.image_add_left" -> "algebra", "filter.comap_bot" -> "order", "prod.dist_eq" -> "topology", "filter.le_principal_iff" -> "order", "wseq.join_congr" -> "data", "zsqrtd.le_arch" -> "data", "local_equiv.symm_image_eq_source_inter_preimage" -> "data", "alg_equiv.ext" -> "algebra", "omega.coeffs.val_add" -> "tactic", "is_clopen_compl" -> "topology", "qpf.supp_preservation_iff_uniform" -> "data", "multiset.le_iff_count" -> "data", "cardinal.mk_def" -> "set_theory", "polynomial.degree_erase_le" -> "data", "antilipschitz_with.id" -> "topology", "category_theory.limits.equalizer.fork_\[Pi]_app_zero" -> "category_theory", "lipschitz_with.subtype_val" -> "topology", "subring.mem_supr_of_directed" -> "algebra", "prod.mk.eta" -> "init", "refl_le_uniformity" -> "topology", "monoid_algebra.lift_symm_apply" -> "data", "finset.union_distrib_right" -> "data", "by_contra" -> "logic", "supr_le_supr_const" -> "order", "continuous_linear_map.map_neg" -> "topology", "add_commute.units_coe_iff" -> "algebra", "category_theory.adjunction.equiv_homset_right_of_nat_iso_apply" -> "category_theory", "semidirect_product.right_hom_surjective" -> "algebra", "filter.le_map" -> "order", "equiv.coe_subtype_equiv_codomain_symm" -> "data", "set.bUnion_of_singleton" -> "data", "nat.pow_left_injective" -> "data", "int.even_zero" -> "data", "free_add_semigroup.map_add'" -> "algebra", "galois_insertion.l_supr_u" -> "order", "category_theory.any_functor_const_on_obj" -> "category_theory", "mv_power_series.monomial_zero_eq_C" -> "algebra", "multiplicity.multiplicity_unit" -> "algebra", "function.involutive.left_inverse" -> "logic", "ennreal.tendsto.div" -> "topology", "category_theory.sum.inverse_associator_obj_inr_inr" -> "category_theory", "complex.conj_I" -> "data", "with_top.top_ne_coe" -> "order", "finset.Ico.image_add" -> "data", "nhds_swap" -> "topology", "equiv.trans_symm" -> "data", "units.coe_eq_one" -> "algebra", "znum.cast_bit1" -> "data", "set.image_const_sub_Icc" -> "data", "int.test_bit_land" -> "data", "snum.bit_zero" -> "data", "function.inv_fun_eq" -> "logic", "nnreal.mul_inv" -> "data", "nat.primrec'.prim_iff\:2082" -> "computability", "continuous_multilinear_map.neg_apply" -> "topology", "functor.comp.ext" -> "control", "inv_inv_of_one_lt" -> "algebra", "list.mfoldl_append" -> "data", "measure_theory.outer_measure.top_caratheodory" -> "analysis", "int.le.dest_sub" -> "init", "differentiable_within_at.mul_const" -> "analysis", "is_lub.nhds_within_ne_bot" -> "topology", "bool.bxor_ff_left" -> "data", "let_body_eq" -> "init", "list.nth_le_repeat" -> "data", "list.tfae_cons_cons" -> "data", "ordinal.lift_id'" -> "set_theory", "nat.sub_mod_eq_zero_of_mod_eq" -> "data", "piecewise_ae_eq_restrict_compl" -> "analysis", "real.differentiable_at_sin" -> "analysis", "nat.pred_le" -> "init", "list.modify_nth_eq_update_nth" -> "data", "list.disjoint_of_disjoint_cons_left" -> "data", "continuous_linear_map.deriv_within" -> "analysis", "ordinal.power_is_limit" -> "set_theory", "nat.dist_zero_left" -> "data", "rel_iso.to_rel_embedding_eq_coe" -> "order", "nat.subtype.lt_succ_iff_le" -> "data", "zmod.cast_pow" -> "data", "real.sin_neg_of_neg_of_neg_pi_lt" -> "analysis", "dlist.to_list_concat" -> "data", "asymptotics.is_O_const_mul_right_iff" -> "analysis", "principal_ideal_ring.is_maximal_of_irreducible" -> "algebra", "structure_groupoid.mem_maximal_atlas_of_mem_atlas" -> "geometry", "mv_polynomial.ker_eval\:2097" -> "algebra", "measure_theory.measure.haar.is_left_invariant_prehaar" -> "analysis", "add_sub_cancel'" -> "algebra", "continuous_linear_equiv.differentiable_within_at" -> "analysis", "int.ne_of_nat_ne_nonneg_case" -> "init", "neg_preimage_closure" -> "topology", "monotone.map_is_greatest" -> "order", "is_add_subgroup.add_mem_cancel_left" -> "algebra", "linear_equiv.eq_bot_of_equiv" -> "algebra", "differentiable_within_at.smul_const" -> "analysis", "tactic.ring_exp.simple_pf_prod_neg_one" -> "tactic", "lists'.mem_def" -> "set_theory", "matrix.trace_transpose" -> "algebra", "alist.mem_union" -> "data", "ordinal.one_dvd" -> "set_theory", "differentiable_within_at.ccos" -> "analysis", "linear_map.sum_apply" -> "algebra", "power_series.X_pow_dvd_iff" -> "algebra", "measure_theory.l1.add_to_fun" -> "analysis", "set.indicator_le" -> "data", "homeomorph.coe_eq_to_equiv" -> "topology", "nat.decreasing_induction_succ" -> "data", "free_magma.lift_mul" -> "algebra", "omega.nat.preterm.val_var" -> "tactic", "frobenius_nat_cast" -> "algebra", "category_theory.biprod.unipotent_lower_inv" -> "category_theory", "category_theory.limits.cokernel.condition" -> "category_theory", "polynomial.eval\:2082_bit1" -> "data", "mem_of_nhds" -> "topology", "right_ord_continuous.map_Inf" -> "order", "ennreal.to_real_mul_to_real" -> "data", "hyperreal.is_st_symm_real" -> "data", "smul_le_smul_of_nonneg" -> "algebra", "finset.eq_empty_or_nonempty" -> "data", "tactic.ring_exp.exp_congr" -> "tactic", "multiset.filter_map_eq_map" -> "data", "asymptotics.is_O_self_const_mul'" -> "analysis", "cardinal.prod_mk" -> "set_theory", "list.mem_sections_length" -> "data", "local_equiv.to_fun_as_coe" -> "data", "int.lnot_bit" -> "data", "list.erase_dup_nil" -> "data", "zorn.max_chain_spec" -> "order", "cau_seq.const_add" -> "data", "dvd_add_iff_right" -> "algebra", "real.sin_eq_zero_iff_cos_eq" -> "analysis", "is_compact.induction_on" -> "topology", "algebra.id.map_eq_self" -> "algebra", "ring_equiv.to_Ring_iso_inv" -> "algebra", "cau_seq.le_of_exists" -> "data", "category_theory.iso.inv_comp_eq" -> "category_theory", "function.surjective.range_comp" -> "data", "measure_theory.outer_measure.ext" -> "analysis", "topological_space.opens.empty_eq" -> "topology", "if_false_left_eq_and" -> "init", "chart_at_self_eq" -> "geometry", "continuous_linear_map.has_strict_deriv_at" -> "analysis", "mul_semiring_action_hom.coe_fn_coe" -> "algebra", "units.mk0_coe" -> "algebra", "zmod.euler_criterion" -> "number_theory", "imp_eq_of_eq_false_right" -> "init", "norm_num.mul_neg_pos" -> "tactic", "multiset.map_cons" -> "data", "tendsto_iff_norm_tendsto_zero" -> "analysis", "homeomorph.comp_continuous_on_iff" -> "topology", "linear_map.finite_dimensional_of_surjective" -> "algebra", "ideal.is_prime.mem_or_mem_of_mul_eq_zero" -> "algebra", "polynomial.comp_zero" -> "data", "category_theory.currying_inverse_obj_map_app" -> "category_theory", "list.repeat_succ" -> "data", "category_theory.limits.cocone.category_to_category_struct_comp_hom" -> "category_theory", "ordinal.mul_le_mul_left" -> "set_theory", "onote.repr_one" -> "set_theory", "znum.neg_zero" -> "data", "linear_map.is_linear" -> "algebra", "finsupp.prod_neg_index" -> "data", "measure_theory.measure.ext" -> "analysis", "finset.singleton_val" -> "data", "subring.coe_one" -> "algebra", "dim_mul_dim" -> "algebra", "finset.prod_range_induction" -> "algebra", "free_group.reduce.sound" -> "algebra", "formal_multilinear_series.radius_neg" -> "analysis", "interval_integral.integral_add" -> "analysis", "submodule.eq_zero_of_bot_submodule" -> "algebra", "list.pw_filter_sublist" -> "data", "stream.interleave_eq" -> "data", "multiset.inter_le_ndinter" -> "data", "is_open_sInter" -> "topology", "differentiable_at.smul_algebra" -> "analysis", "int.coe_nat_le_coe_nat_iff" -> "init", "tactic.ring_exp.mul_coeff_pf_mul_one" -> "tactic", "finmap.lookup_erase" -> "data", "convex.center_mass_mem" -> "analysis", "inf_le_right'" -> "order", "has_sum.prod_fiberwise" -> "topology", "set.Ioc_subset_Ioi_self" -> "data", "differentiable_at_const" -> "analysis", "is_local_extr.comp_continuous_on" -> "topology", "ennreal.add_eq_top" -> "data", "linear_map.pi_zero" -> "algebra", "turing.TM2.step_supports" -> "computability", "add_neg_eq_of_eq_add" -> "algebra", "filter.tendsto.not_tendsto" -> "order", "real.cos_neg" -> "data", "has_strict_deriv_at.neg" -> "analysis", "multiset.product_add" -> "data", "finset.sum_apply" -> "algebra", "pSet.subset.congr_left" -> "set_theory", "continuous_iff_continuous_at" -> "topology", "measure_theory.ae_eq_fun.comp\:2082_eq_mk" -> "analysis", "continuous_quot_mk" -> "topology", "add_submonoid.mem_carrier" -> "algebra", "functor.const.ext" -> "control", "int.to_nat_sub_of_le" -> "data", "fintype.prod_dvd_of_coprime" -> "algebra", "measure_theory.simple_func.coe_smul" -> "analysis", "dioph.dioph_list_all" -> "number_theory", "list.last_cons" -> "data", "nonempty.map2" -> "logic", "set.prod_empty" -> "data", "nat.lt_irrefl" -> "init", "is_total.swap" -> "order", "compl_compl'" -> "order", "filter.frequently_false" -> "order", "set.ball_image_of_ball" -> "data", "decidable.not_imp_comm" -> "logic", "continuous_linear_equiv.comp_fderiv" -> "analysis", "measure_theory.outer_measure.coe_fn_injective" -> "analysis", "edist_le_of_edist_le_geometric_of_tendsto" -> "analysis", "affine_span_disjoint_of_disjoint_of_affine_independent" -> "algebra", "measurable_space.is_measurable_top" -> "analysis", "set.enumerate_mem" -> "data", "nnreal.one_le_rpow" -> "analysis", "differentiable.const_smul" -> "analysis", "equiv.forall_congr_left" -> "data", "generalized_continued_fraction.int_fract_pair.nth_seq1_eq_succ_nth_stream" -> "algebra", "nnreal.of_real_le_of_real" -> "data", "one_div_mul_one_div" -> "algebra", "measure_theory.measure.lt_iff" -> "analysis", "prod.map_snd'" -> "data", "deriv_neg" -> "analysis", "homological_complex.image_to_kernel_map_condition" -> "algebra", "filter.eventually_eq.le" -> "order", "list.choose_spec" -> "data", "matrix.cons_head_tail" -> "data", "tfae_mem_nhds_within_Iio" -> "topology", "computation.think_empty" -> "data", "bit1_le_bit1" -> "algebra", "filter.lift'_inf" -> "order", "multiplicity.is_greatest'" -> "algebra", "multiset.nodup_of_le" -> "data", "functor.comp.comp_map" -> "control", "set.image_add_const_Iic" -> "data", "is_topological_fiber_bundle.continuous_proj" -> "topology", "linear_equiv.findim_eq" -> "algebra", "function.embedding.coe_subtype" -> "logic", "filter.tendsto_congr'" -> "order", "fin.coe_zero" -> "data", "mv_polynomial.degrees_sum" -> "data", "finset.inter_bind" -> "data", "times_cont_mdiff_within_at.prod_map" -> "geometry", "asymptotics.is_O_refl_left" -> "analysis", "cardinal.lt_succ_self" -> "set_theory", "subsemiring.mem_comap" -> "algebra", "category_theory.comma.map_right_id_hom_app_left" -> "category_theory", "matrix.zero_dot_product'" -> "data", "local_equiv.eq_on_source.symm_eq_on" -> "data", "monotonicity.true" -> "meta", "vector_space.dual_dim_eq" -> "algebra", "dfinsupp.prod_single_index" -> "data", "ideal.comap_is_prime" -> "algebra", "tangent_cone_mono_nhds" -> "analysis", "nat.partrec'.bind" -> "computability", "pnat.mk_le_mk" -> "data", "asymptotics.is_O_zero_right_iff" -> "analysis", "subgroup.coe_subtype" -> "algebra", "pow_le_pow_of_le_one" -> "algebra", "category_theory.faithful.of_iso" -> "category_theory", "list.chain'.tail" -> "data", "dif_pos" -> "init", "list.count_cons'" -> "data", "pgame.one_left_moves" -> "set_theory", "rel.mem_core" -> "data", "decidable.not_not" -> "logic", "set.Icc_subset_Ico_right" -> "data", "continuous_at_fst" -> "topology", "finmap.lookup_to_finmap" -> "data", "set.set_of_forall" -> "data", "is_R_or_C.I_re" -> "data", "int.mul_neg_succ_of_nat_neg_succ_of_nat" -> "init", "units.neg_neg" -> "algebra", "has_deriv_within_at.deriv_within" -> "analysis", "mem_perms_of_list_iff" -> "data", "gaussian_int.mod_four_eq_three_of_nat_prime_of_prime" -> "data", "category_theory.is_equivalence.fun_inv_map" -> "category_theory", "finset.univ_sigma_univ" -> "data", "turing.to_partrec.code.nil_eval" -> "computability", "monoid_hom.ext" -> "algebra", "lt_one_div_of_neg" -> "algebra", "list.scanr_cons" -> "data", "measure_theory.l1.simple_func.of_simple_func_add" -> "analysis", "is_add_subgroup.mem_norm_comm_iff" -> "algebra", "filter.limsup_congr" -> "order", "iff_false_right" -> "logic", "set.subset_image_compl" -> "data", "is_lub.cSup_eq" -> "order", "subsemiring.comap_infi" -> "algebra", "coe_I_one" -> "topology", "finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero" -> "algebra", "complex.exists_extension_norm_eq" -> "analysis", "image_le_of_liminf_slope_right_lt_deriv_boundary" -> "analysis", "category_theory.limits.diagram_of_cones.cone_points_map" -> "category_theory", "set.indicator_congr" -> "data", "pnat.coprime.gcd_mul_right_cancel_right" -> "data", "submonoid.mem_infi" -> "algebra", "category_theory.limits.has_limit.iso_of_nat_iso_hom_\[Pi]_assoc" -> "category_theory", "ennreal.mul_sub" -> "data", "cardinal.mk_Ioc_real" -> "data", "set.Ico_eq_Ico_iff" -> "data", "list.pairwise.iff_of_mem" -> "data", "equiv.set.sum_compl_symm_apply_of_not_mem" -> "data", "subring.coe_neg" -> "algebra", "times_cont_diff_at.has_strict_fderiv_at" -> "analysis", "real.continuous_log'" -> "analysis", "set.union_distrib_left" -> "data", "span_eq_top_of_linear_independent_of_card_eq_findim" -> "algebra", "dioph.dioph_pfun_vec" -> "number_theory", "affine_map.line_map_continuous" -> "topology", "computation.lift_rel.refl" -> "data", "continuous_linear_map.to_span_singleton_homothety" -> "analysis", "category_theory.iso.to_linear_equiv_to_fun" -> "algebra", "rel_embedding.coe_fn_mk" -> "order", "power_series.le_order" -> "algebra", "neg_le_sub_iff_le_add" -> "algebra", "times_cont_diff_zero" -> "analysis", "functor.comp.map_mk" -> "control", "measure_theory.supr2_lintegral_le" -> "analysis", "has_deriv_within_at.continuous_within_at" -> "analysis", "cardinal.bit1_lt_omega" -> "set_theory", "filter.tendsto_at_bot_add_const_right" -> "order", "set.image_empty" -> "data", "submonoid.map_map" -> "algebra", "times_cont_mdiff_within_at.smooth_within_at" -> "geometry", "asymptotics.is_O_zero" -> "analysis", "monoid_hom.map_div" -> "algebra", "times_cont_mdiff_within_at.continuous_within_at" -> "geometry", "times_cont_mdiff_within_at_univ" -> "geometry", "cardinal.increasing_cantor_function" -> "data", "cau_seq.completion.mk_eq_mk" -> "data", "real.exists_sin_eq" -> "analysis", "multiplicity.finite_mul" -> "algebra", "and.swap" -> "init", "strict_mono_of_deriv_pos" -> "analysis", "is_noetherian_ring_of_ring_equiv" -> "algebra", "polynomial.degree_map" -> "data", "has_fderiv_within_at.mono" -> "analysis", "conj_mul" -> "algebra", "has_fderiv_at_filter_snd" -> "analysis", "list.append_right_inj" -> "data", "open_add_subgroup.is_open" -> "topology", "iff_true_intro" -> "init", "measure_theory.ae_eq_fun.coe_fn_sub" -> "analysis", "nat.strong_rec_on_beta'" -> "data", "is_glb.union" -> "order", "composition.sum_blocks_fun" -> "combinatorics", "linear_independent_comp_subtype_disjoint" -> "algebra", "computation.ret_mem" -> "data", "is_greatest.upper_bounds_eq" -> "order", "multiset.eq_repeat" -> "data", "is_Hausdorff.subsingleton" -> "algebra", "list.nodup_attach" -> "data", "equiv.swap_apply_right" -> "data", "approximates_linear_on.inverse_approx_map_contracts_on" -> "analysis", "is_total_preorder.swap" -> "order", "wseq.destruct_join" -> "data", "equiv.subtype_preimage_symm_apply_coe_neg" -> "data", "int.lt_of_add_lt_add_left" -> "init", "set.maps_to.comp" -> "data", "valuation.mem_supp_iff" -> "algebra", "is_closed_eq" -> "topology", "linarith.int.coe_nat_bit0" -> "tactic", "finite_dimensional.cardinal_mk_le_findim_of_linear_independent" -> "algebra", "category_theory.Monad.to_Mon_mul" -> "category_theory", "set.image_subset_range" -> "data", "measure_theory.outer_measure.empty'" -> "analysis", "is_local_extr_on.comp_mono" -> "topology", "list.take_while_append_drop" -> "data", "fderiv_smul_algebra" -> "analysis", "set.indicator_compl_add_self_apply" -> "data", "measure_theory.outer_measure.of_content_eq_infi" -> "analysis", "multiset.to_finset_val" -> "data", "computation.map_comp" -> "data", "submodule.span_smul" -> "algebra", "add_con.lift_apply_mk'" -> "algebra", "multiset.map_eq_map_of_bij_of_nodup" -> "data", "circle_deg1_lift.translate_inv_apply" -> "dynamics", "nat.zero_mul" -> "init", "finset.coe_map_subset_range" -> "data", "cardinal.mk_univ" -> "set_theory", "ideal.span_singleton_eq_span_singleton" -> "algebra", "has_strict_fderiv_at.eq_implicit_function" -> "analysis", "upper_bounds_mono_set" -> "order", "det_of_card_zero" -> "algebra", "monoid_hom.coprod_comp_inr" -> "algebra", "ideal.mem_span_singleton" -> "algebra", "filter.not_frequently" -> "order", "finset.univ_sum_single" -> "algebra", "lfp_le" -> "order", "pgame.le_zero" -> "set_theory", "associates.is_unit_mk" -> "algebra", "ring_equiv.map_neg" -> "data", "int.sub_le_sub" -> "init", "nnreal.sub_add_cancel_of_le" -> "data", "nnreal.rpow_lt_rpow" -> "analysis", "with_zero.lift_coe" -> "algebra", "finset.sdiff_eq_self_of_disjoint" -> "data", "submodule.mul_bot" -> "algebra", "pgame.add_move_left_inl" -> "set_theory", "mdifferentiable_at.congr_of_eventually_eq" -> "geometry", "asymptotics.is_o.const_mul_left" -> "analysis", "uniform_space.comap_quotient_eq_uniformity" -> "topology", "lie_algebra.orthogonal.PD_inv" -> "algebra", "function.iterate_pred_comp_of_pos" -> "logic", "mul_self_lt_mul_self_iff" -> "algebra", "polynomial.eval\:2082_sum" -> "data", "category_theory.limits.fork.\[Iota]_eq_app_zero" -> "category_theory", "localization.ring_equiv_of_quotient_symm_mk'" -> "algebra", "Top.presheaf.stalk_functor_obj" -> "topology", "list.Ico.filter_lt_of_succ_bot" -> "data", "ideal.mul_mono_right" -> "algebra", "ordinal.lift_type_le" -> "set_theory", "isometric.add_right_symm" -> "topology", "filter.eventually_or_distrib_left" -> "order", "nat.add_succ" -> "init", "list.nth_le_append_right" -> "data", "sub_pow_char_pow" -> "algebra", "power_series.monomial_eq_mk" -> "algebra", "submodule.closed_complemented_top" -> "topology", "category_theory.over.construct_products.cones_equiv_counit_iso_2" -> "category_theory", "submodule.map_subtype_embedding_eq" -> "algebra", "set.bUnion_subset_bUnion_left" -> "data", "category_theory.prod.symmetry_hom_app" -> "category_theory", "multiset.to_finsupp_support" -> "data", "infi_eq_bot" -> "order", "multiset.count_add" -> "data", "metric.uniformity_basis_dist_inv_nat_pos" -> "topology", "ring.fractional_ideal.ext" -> "algebra", "stream.nth_const" -> "data", "alg_equiv.coe_alg_hom" -> "algebra", "fib_rec_char_poly_eq" -> "data", "filter.liminf_le_limsup" -> "order", "tendsto_right_nhds_uniformity" -> "topology", "ideal.comap_eq_top_iff" -> "algebra", "with_zero.zero_mul" -> "algebra", "primrec.bnot" -> "computability", "floor_lt" -> "algebra", "real.arcsin_one" -> "analysis", "int.to_add_gpow" -> "algebra", "composition.size_up_to_le" -> "combinatorics", "nat.le_mul_of_pos_left" -> "data", "add_subgroup.ext'" -> "algebra", "abstract_completion.uniform_continuous_extend" -> "topology", "eventually_eventually_nhds" -> "topology", "polynomial.mem_nth_roots" -> "data", "formal_multilinear_series.le_radius_of_bound" -> "analysis", "infi_inf" -> "order", "turing.blank_extends.trans" -> "computability", "equiv.coe_add_right" -> "data", "ideal.exists_sub_mem" -> "algebra", "nat_ceil_mono" -> "algebra", "polynomial.derivative_mul" -> "data", "multiset.revzip_powerset_aux_lemma" -> "data", "free_abelian_group.of_mul_of" -> "algebra", "category_theory.monad.free_map_f" -> "category_theory", "int.of_nat_nat_abs_of_nonpos" -> "init", "free_abelian_group.neg_seq" -> "algebra", "measurable.subtype_mk" -> "analysis", "category_theory.discrete.functor_map_id" -> "category_theory", "filter.rmap_sets" -> "order", "continuous_within_at.image_closure" -> "topology", "nat.size_le_size" -> "data", "add_le_add_right" -> "algebra", "int.mul_lt_mul_of_pos_right" -> "init", "nat.le_mod_add_mod_of_dvd_add_of_not_dvd" -> "data", "category_theory.unop_id_op" -> "category_theory", "decidable.iff_iff_and_or_not_and_not" -> "logic", "mul_lt_mul" -> "algebra", "mvqpf.has_good_supp_iff" -> "data", "norm_num.min_fac_helper_5" -> "tactic", "units.inv_smul_smul" -> "algebra", "semidirect_product.map_inr" -> "algebra", "mul_semiring_action_hom.map_zero" -> "algebra", "category_theory.sum.swap_obj_inl" -> "category_theory", "list.erase_append_left" -> "data", "smooth_on.mul" -> "geometry", "finset.sum_extend_by_zero" -> "algebra", "polynomial.is_unit_iff" -> "data", "category_theory.iso.inv_eq_inv" -> "category_theory", "monoid_hom.coe_inj" -> "algebra", "relation.reflexive_refl_trans_gen" -> "logic", "add_submonoid.localization_map.add_neg_left" -> "algebra", "category_theory.cones_map" -> "category_theory", "mv_polynomial.exists_fin_rename" -> "data", "dim_top" -> "algebra", "set.bij_on_Union_of_directed" -> "data", "int.div_neg'" -> "data", "eq_mpr_rfl" -> "logic", "ennreal.coe_Inf" -> "data", "filter.eventually_le_bind" -> "order", "finset.filter_mem_eq_inter" -> "data", "is_closed.compact" -> "topology", "measure_theory.l1.norm_eq_nnnorm_to_fun" -> "analysis", "set.compl_subset_comm" -> "data", "is_add_group_hom.neg" -> "algebra", "real.exists_cos_eq" -> "analysis", "fintype.exists_ne_of_one_lt_card" -> "data", "complex.continuous_exp" -> "analysis", "quot.lift_beta" -> "init", "inv_smul_smul'" -> "algebra", "add_commute.neg_neg_iff" -> "algebra", "int.mul_neg_of_neg_of_pos" -> "init", "vector.cons_tail" -> "data", "typevec.const_append1" -> "data", "uniform_continuous_iff" -> "topology", "emetric.diam_pos_iff" -> "topology", "finset.coe_subset" -> "data", "ennreal.lt_inv_iff_lt_inv" -> "data", "pairwise.pairwise_on" -> "data", "mv_power_series.ext" -> "algebra", "finsupp.support_filter" -> "data", "onote.mul_nat_eq_mul" -> "set_theory", "filter.prod_def" -> "order", "affine_map.coe_add" -> "algebra", "trans_rel_right" -> "init", "has_strict_fderiv_at.mem_to_local_homeomorph_source" -> "analysis", "subring.coe_subset_coe" -> "algebra", "free_semigroup.traverse_pure" -> "algebra", "differentiable_on.csinh" -> "analysis", "hyperreal.infinitesimal_pos_iff_infinite_pos_inv" -> "data", "injective_of_lt_imp_ne" -> "order", "int.sub_lt_sub_of_le_of_lt" -> "init", "ordinal.lt_mul_succ_div" -> "set_theory", "category_theory.uncurry_injective" -> "category_theory", "finite_field.card_image_polynomial_eval" -> "algebra", "nat.le_of_pred_lt" -> "data", "floor_nonneg" -> "algebra", "pfun.dom_iff_graph" -> "data", "measure_theory.l1.simple_func.coe_pos_part" -> "analysis", "filter.realizer.principal_F" -> "data", "list.ordered_insert_nil" -> "data", "local_homeomorph.of_set_trans" -> "topology", "filter.infi_principal_finset" -> "order", "ennreal.top_ne_coe" -> "data", "ennreal.inv_inv" -> "data", "category_theory.limits.pair_obj_left" -> "category_theory", "concave_on_real_of_slope_mono_adjacent" -> "analysis", "with_top.none_le" -> "order", "is_local_min_on.min" -> "topology", "add_units.coe_hom_apply" -> "algebra", "setoid.inf_def" -> "data", "pmf.summable_coe" -> "analysis", "ultrafilter_converges_iff" -> "topology", "fin.init_update_cast_succ" -> "data", "is_max_filter.comp_tendsto" -> "order", "fin.one_val" -> "data", "nat.dvd_sub_mod" -> "data", "fintype.prod_sum_type" -> "data", "option.some_orelse'" -> "data", "list.head_mem_head'" -> "data", "filter.Limsup_eq_infi_Sup" -> "order", "bounded_continuous_function.norm_le" -> "topology", "le_antisymm'" -> "order", "nat.min_fac_has_prop" -> "data", "finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype" -> "algebra", "linear_independent_iff" -> "algebra", "add_lt_of_nonpos_of_lt'" -> "algebra", "contracting_with.one_sub_K_pos'" -> "topology", "filter.tendsto.liminf_eq" -> "topology", "multiset.add_sigma" -> "data", "ordinal.is_normal.le_set'" -> "set_theory", "local_equiv.refl_symm" -> "data", "lucas_lehmer.X.bit0_fst" -> "number_theory", "category_theory.limits.biprod.map_fst_assoc" -> "category_theory", "multiset.to_finsupp_add" -> "data", "local_equiv.eq_on_source.source_inter_preimage_eq" -> "data", "add_units.add_neg_eq_iff_eq_add" -> "algebra", "gpowers_subset" -> "algebra", "bool.of_to_bool_iff" -> "data", "multiset.add_left_cancel" -> "data", "padic_int.p_dvd_of_norm_lt_one" -> "data", "ideal.quotient.nontrivial" -> "algebra", "ennreal.zero_sub" -> "data", "is_local_extr.neg" -> "topology", "stream.tail_drop" -> "data", "encodable.subtype.encode_eq" -> "data", "geom_sum_inv" -> "algebra", "free_add_semigroup.traverse_pure'" -> "algebra", "set.Ioc_union_Icc_eq_Ioc" -> "data", "denumerable.of_nat_nat" -> "data", "times_cont_diff_at.sub" -> "analysis", "iff_of_true" -> "logic", "one_div_mul_one_div_rev" -> "algebra", "set.image_const_add_Ioi" -> "data", "mdifferentiable_at_const" -> "geometry", "dvd_or_coprime" -> "algebra", "computation.bind_assoc" -> "data", "option.bex_ne_none" -> "data", "int.bit1_pos" -> "init", "polynomial.degree_div_by_monic_le" -> "data", "ordinal.enum_lt" -> "set_theory", "measure_theory.measure.lintegral_join" -> "analysis", "order_embedding.map_lt_iff" -> "order", "set.countable_prod" -> "data", "category_theory.limits.fork.of_cone_\[Pi]" -> "category_theory", "mv_power_series.X_dvd_iff" -> "algebra", "uniformity_prod_eq_prod" -> "topology", "dfinsupp.single_add" -> "data", "finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one" -> "algebra", "galois_connection.monotone_u" -> "order", "set.Ioo_subset_Iio_self" -> "data", "with_bot.coe_nsmul" -> "algebra", "is_open_map_mul_right" -> "topology", "set.inter_singleton_eq_empty" -> "data", "lagrange.interpolate_zero" -> "algebra", "continuous_ultrafilter_extend" -> "topology", "complex.cpow_nat_inv_pow" -> "analysis", "valuation.map_zero" -> "algebra", "lt_add_of_neg_lt_sub_left" -> "algebra", "approximates_linear_on.inverse_approx_map_maps_to" -> "analysis", "is_add_subgroup.sub_mem" -> "algebra", "power_series.monomial_zero_eq_C" -> "algebra", "partrec.sum_cases_left" -> "computability", "ring_hom.coe_mul" -> "algebra", "free_magma.lift_unique" -> "algebra", "differentiable_within_at.has_fderiv_within_at" -> "analysis", "equiv.perm.sign_refl" -> "algebra", "algebra.mul_smul_comm" -> "algebra", "deriv_sinh" -> "analysis", "has_deriv_at.lhopital_zero_nhds" -> "analysis", "finset.not_mem_union" -> "data", "category_theory.limits.prod.symmetry" -> "category_theory", "tendsto_at_top_of_geom_lt" -> "analysis", "polynomial.nat_degree_pos_of_eval\:2082_root" -> "data", "add_units.coe_mk_of_add_eq_zero" -> "algebra", "category_theory.limits.image.map_\[Iota]" -> "category_theory", "emetric.Hausdorff_edist_triangle" -> "topology", "list.erase_dup_subset" -> "data", "filter.tendsto_at_bot_add_left_of_ge'" -> "order", "turing.TM2.stmts\:2081_self" -> "computability", "asymptotics.is_O_iff" -> "analysis", "galois_connection.is_glb_u_image" -> "order", "semiconj_by.add_right" -> "algebra", "pow_add" -> "algebra", "category_theory.monoidal_of_has_finite_coproducts.right_unitor_inv" -> "category_theory", "CommGroup.ext" -> "algebra", "list.pairwise_pair" -> "data", "category_theory.nat_trans.hcomp_app" -> "category_theory", "real.is_cau_seq_iff_lift" -> "data", "finset.sdiff_eq_filter" -> "data", "cardinal.mk_preimage_of_injective_of_subset_range_lift" -> "set_theory", "div_ne_zero_iff" -> "algebra", "filter.generate_eq_generate_inter" -> "order", "valuation.map_eq_of_sub_lt" -> "algebra", "category_theory.limits.coprod.braiding_inv" -> "category_theory", "list.perm_merge_sort" -> "data", "embedding_of_embedding_compose" -> "topology", "int.neg_lt_sub_right_of_lt_add" -> "init", "tactic.ring_exp.mul_pp_pf_prod_lt" -> "tactic", "measure_theory.outer_measure.coe_supr" -> "analysis", "decidable.of_not_imp" -> "logic", "ordinal.mul_omega" -> "set_theory", "bit1_pos'" -> "algebra", "fract_lt_one" -> "algebra", "open_add_subgroup.coe_inf" -> "topology", "rtendsto_nhds" -> "topology", "times_cont_diff.differentiable_iterated_deriv" -> "analysis", "set.Inter_subset_Inter" -> "data", "category_theory.sum.associator_map_inr" -> "category_theory", "ennreal.max_mul" -> "data", "rat.mul_def" -> "data", "list.tail_subset" -> "data", "is_coprime.mul_add_right_left_iff" -> "algebra", "ring_invo.coe_ring_equiv" -> "algebra", "string.str_ne_str_right" -> "init", "has_deriv_at.scomp_has_deriv_within_at" -> "analysis", "set.indicator_apply" -> "data", "ordinal.succ_pos" -> "set_theory", "category_theory.iso.to_equiv_symm_fun" -> "category_theory", "deriv_sub" -> "analysis", "Top.stalk_to_fiber_germ" -> "topology", "mv_polynomial.is_integral_domain_fin_zero" -> "algebra", "subsemiring.mem_Sup_of_directed_on" -> "algebra", "pell.yz_sub" -> "number_theory", "pythagorean_triple.symm" -> "number_theory", "polynomial.root_mul_right_of_is_root" -> "data", "fin.cast_succ_fin_succ" -> "data", "metric.mem_nhds_within_iff" -> "topology", "finset.Ico.diff_left" -> "data", "int.test_bit_succ" -> "data", "continuous_linear_map.norm_id_field'" -> "analysis", "finset.coe_map" -> "data", "equiv.sum_assoc_apply_in2" -> "data", "interval_integral.integral_const_of_cdf" -> "analysis", "matrix.det_eq_one_of_card_eq_zero" -> "algebra", "continuous_within_at.prod" -> "topology", "ring.in_closure.rec_on" -> "algebra", "times_cont_mdiff_at_snd" -> "geometry", "filter.rcomap_compose" -> "order", "fraction_map.comap_is_algebraic_iff" -> "algebra", "list.sublists_concat" -> "data", "asymptotics.is_O.congr_of_sub" -> "analysis", "complex.cpow_def" -> "analysis", "fract_floor" -> "algebra", "free_group.red.append_append" -> "algebra", "roption.dom_iff_mem" -> "data", "min_le_add_of_nonneg_right" -> "algebra", "add_submonoid.multiset_sum_mem" -> "algebra", "list.reverse_sublist_iff" -> "data", "complex.cos_sub" -> "data", "auto.not_and_eq" -> "tactic", "function.embedding.equiv_symm_to_embedding_trans_to_embedding" -> "logic", "list.erase_subperm" -> "data", "int.shiftl_sub" -> "data", "unique_uniformity_of_compact_t2" -> "topology", "sub_smul" -> "algebra", "monoid_hom.cancel_right" -> "algebra", "mem_uniformity_edist" -> "topology", "equiv.perm.cycle_of_inv" -> "algebra", "list.foldr_map" -> "data", "uniform_continuous\:2082.comp" -> "topology", "set.add_empty" -> "algebra", "emetric.tendsto_uniformly_on_iff" -> "topology", "function.left_inverse_iff_comp" -> "logic", "nat.primrec'.mul" -> "computability", "sub_add_cancel" -> "algebra", "dvd_neg" -> "algebra", "submodule.restrict_scalars_bot" -> "algebra", "set.mem_singleton_iff" -> "data", "homeomorph.symm_to_local_homeomorph" -> "topology", "canonically_ordered_semiring.pow_pos" -> "algebra", "int.div_sign" -> "data", "stream.interleave_tail_tail" -> "data", "set.range_const_subset" -> "data", "with_bot.bot_add" -> "algebra", "list.range_core_range'" -> "data", "category_theory.unop_unop_obj" -> "category_theory", "filter.eventually_principal" -> "order", "nat.partrec.code.eval_part" -> "computability", "affine_map.homothety_def" -> "algebra", "ideal.mul_mono_left" -> "algebra", "partrec.nat_iff" -> "computability", "padic_norm_e.is_rat" -> "data", "nat.add_mod_right" -> "init", "rat.denom_ne_zero" -> "data", "set.mem_inter" -> "data", "measurable_space.map_inf" -> "analysis", "eq.subst" -> "init", "add_equiv.map_ne_zero_iff" -> "data", "free_magma.mul_bind" -> "algebra", "is_closed_of_closure_subset" -> "topology", "submodule.subset_span" -> "algebra", "measure_theory.lintegral_mono" -> "analysis", "neg_le_sub_left_of_le_add" -> "algebra", "set.card_image_of_injective" -> "data", "is_local_extr_on.elim" -> "topology", "eq_one_of_right_cancel_mul_self" -> "algebra", "padic_norm_e.neg" -> "data", "complex.of_real_fpow" -> "data", "nat.le_of_add_le_add_right" -> "init", "add_subgroup.mem_Inf" -> "algebra", "dioph.div_dioph" -> "number_theory", "finset.sum_const" -> "algebra", "is_add_unit_zero" -> "algebra", "euclidean_geometry.orthogonal_projection_fn_vsub_mem_direction_orthogonal" -> "geometry", "nat.partrec.code.rec_prim'" -> "computability", "int.one_nonneg" -> "init", "le_one_of_one_le_inv" -> "algebra", "list.keys_kreplace" -> "data", "matrix.mul_one" -> "data", "mul_lt_right'" -> "algebra", "free_group.prod.mul" -> "algebra", "tactic.ring2.horner_expr.cseval_mul_const" -> "tactic", "bilin_form.comp_right_comp_left" -> "algebra", "perfect_closure.nat_cast" -> "algebra", "finset.prod_ne_zero_iff" -> "algebra", "smul_assoc" -> "algebra", "set.finite.sUnion" -> "data", "nonempty.elim_to_inhabited" -> "logic", "is_compact.elim_finite_subfamily_closed" -> "topology", "set.prod_preimage_eq" -> "data", "pi.const_one" -> "algebra", "con.lift_coe" -> "algebra", "affine_map.coe_mk'" -> "algebra", "category_theory.limits.colimit.map_desc" -> "category_theory", "nhds_within_has_basis" -> "topology", "setoid.classes_mk_classes" -> "data", "differentiable_within_at_inter'" -> "analysis", "dfinsupp.support_subtype_domain" -> "data", "finset.filter_not" -> "data", "set.sUnion_subset" -> "data", "affine.simplex.face_points" -> "algebra", "add_monoid_hom.map_sum" -> "algebra", "lt_mul_of_one_lt_right" -> "algebra", "num.to_of_nat" -> "data", "filter.germ.coe_coe_add_hom" -> "order", "add_submonoid.coe_Sup_of_directed_on" -> "algebra", "Mod.id_hom" -> "category_theory", "fin.of_nat_eq_coe" -> "data", "category_theory.limits.colimit.\[Iota]_map_assoc" -> "category_theory", "pell.matiyasevic" -> "number_theory", "fin.coe_pred" -> "data", "filter.at_bot_basis'" -> "order", "multiset.smul_sum" -> "algebra", "rat.num_ne_zero_of_ne_zero" -> "data", "differentiable_on.div" -> "analysis", "set.inj_on.image_Inter_eq" -> "data", "has_sum_of_bounded_monoid_hom_of_summable" -> "analysis", "set.range_comp" -> "data", "mul_aut.coe_one" -> "data", "continuous_multilinear_curry_fin0_apply" -> "analysis", "polynomial.nat_degree_separable_eq_card_roots" -> "algebra", "deriv_within_div_const" -> "analysis", "nhds_within_Iic_ne_bot" -> "topology", "measure_theory.outer_measure.smul_dirac_apply" -> "analysis", "int.to_nat_of_nonneg" -> "data", "list.length_split_lt" -> "data", "enorm.finite_edist_eq" -> "analysis", "sub_right_le_of_le_add" -> "algebra", "local_equiv.target_inter_inv_preimage_preimage" -> "data", "ennreal.tsum_coe_ne_top_iff_summable" -> "topology", "unique_diff_on_Iio" -> "analysis", "Algebra.coe_of" -> "algebra", "omega.int.univ_close_of_unsat_clausify" -> "tactic", "emetric.cauchy_seq_iff_nnreal" -> "topology", "Top.presheaf.pushforward.id_inv_app'" -> "topology", "nhds_infi" -> "topology", "is_compl.disjoint_right_iff" -> "order", "exp_neg_inv_glue.pos_of_pos" -> "analysis", "classical.epsilon_spec_aux" -> "init", "dense_Union_interior_of_closed" -> "topology", "self_le_inv" -> "algebra", "subring.coe_Inf" -> "algebra", "is_max_filter.bicomp_mono" -> "order", "add_le_add_iff_left" -> "algebra", "category_theory.iso.op_inv" -> "category_theory", "category_theory.functor.map_arrow_map_right" -> "category_theory", "exp_neg_inv_glue.f_aux_deriv_pos" -> "analysis", "continuous_linear_map.lmul_left_right_apply" -> "analysis", "nat.primes.coe_nat_inj" -> "data", "zsqrtd.coe_nat_re" -> "data", "derivation.leibniz" -> "algebra", "mem_closure2" -> "topology", "exists_norm_eq_infi_of_complete_convex" -> "analysis", "set.diff_subset_diff_left" -> "data", "valuation.map_add_of_distinct_val" -> "algebra", "with_top.op_sum" -> "algebra", "measure_theory.l1.simple_func.coe_neg_part" -> "analysis", "fin.forall_fin_succ" -> "data", "submonoid.localization_map.mul_mk'_one_eq_mk'" -> "algebra", "int.ne_of_lt" -> "init", "smooth_within_at.times_cont_mdiff_within_at" -> "geometry", "category_theory.limits.coprod.inl_desc" -> "category_theory", "finset.prod_Ico_consecutive" -> "algebra", "norm_num.int_cast_ne" -> "tactic", "stream.inits_eq" -> "data", "submodule.liftq_apply" -> "algebra", "category_theory.limits.inv_prod_comparison_map_fst" -> "category_theory", "subring.coe_mk'" -> "algebra", "prime_spectrum.zero_locus_empty" -> "algebraic_geometry", "list.length_reverse" -> "data", "submonoid.localization_map.inv_inj" -> "algebra", "differentiable.div" -> "analysis", "monoid_hom.range_top_iff_surjective" -> "algebra", "set.union_preimage_subset" -> "data", "generalized_continued_fraction.int_fract_pair.stream_is_seq" -> "algebra", "monotone_lam" -> "order", "perfect_closure.induction_on" -> "algebra", "left_ord_continuous.order_dual" -> "order", "set.finite.map" -> "data", "filter.tendsto.mul_mul" -> "order", "monoid_hom.inv_apply" -> "algebra", "mul_semiring_action_hom.map_add" -> "algebra", "cardinal.le_mul_right" -> "set_theory", "category_theory.over.map_obj_hom" -> "category_theory", "category_theory.functor.associator_hom_app" -> "category_theory", "composition.single_embedding" -> "combinatorics", "gpow_neg_succ_of_nat" -> "algebra", "pell.xn_one" -> "number_theory", "znum.to_of_int" -> "data", "ennreal.continuous_coe" -> "topology", "measure_theory.l1.eq_iff" -> "analysis", "direct_sum.mk_injective" -> "algebra", "sub_eq_of_eq_add" -> "algebra", "generalized_continued_fraction.first_numerator_eq" -> "algebra", "frontier_closed_ball" -> "analysis", "array.rev_list_reverse_aux" -> "data", "not_bdd_above_iff'" -> "order", "int.div2_bit" -> "data", "multiplicity.multiplicity_add_eq_min" -> "algebra", "filter.map_at_bot_eq_of_gc" -> "order", "parallelogram_law_with_norm" -> "analysis", "nat.pred_eq_ppred" -> "data", "upper_bounds_empty" -> "order", "dense_Inter_of_open" -> "topology", "set.Ico_disjoint_Ico_same" -> "data", "ordinal.div_def" -> "set_theory", "hyperreal.infinitesimal_of_tendsto_zero" -> "data", "category_theory.iso.hom_congr_trans" -> "category_theory", "category_theory.limits.prod_right_unitor_hom_naturality" -> "category_theory", "nhds_within_Ioi_ne_bot" -> "topology", "roption.mem_map_iff" -> "data", "ordinal.is_limit_add_iff" -> "set_theory", "int.add_nonneg" -> "init", "finset.prod_eq_zero" -> "algebra", "submodule.disjoint_iff_comap_eq_bot" -> "algebra", "filter.inf_principal" -> "order", "tendsto_nhds_within_mono_left" -> "topology", "multiset.to_finset_map" -> "data", "set.preimage_const_mul_Iio" -> "data", "deriv_pow" -> "analysis", "list.join_split_wrt_composition" -> "combinatorics", "set.set_of_true" -> "data", "multiset.powerset_len_aux_perm" -> "data", "category_theory.limits.cones.whiskering_equivalence_inverse" -> "category_theory", "primrec.nat_iterate" -> "computability", "function.support_max" -> "data", "is_linear_map.is_linear_map_sub" -> "algebra", "nhds_within_basis_open" -> "topology", "multiset.coe_nil_eq_zero" -> "data", "znum.abs_to_nat" -> "data", "cardinal.mk_subtype_mono" -> "set_theory", "real.cos_eq_one_iff" -> "analysis", "submonoid.closure_eq_of_le" -> "algebra", "nat.sub_eq_psub" -> "data", "list.Ico.chain'_succ" -> "data", "pgame.add_right_neg_le_zero" -> "set_theory", "quadratic_form.add_apply" -> "algebra", "zorn.succ_increasing" -> "order", "filter.le_of_ultrafilter" -> "order", "set.singleton_smul" -> "algebra", "stream.nth_drop" -> "data", "dense_Inter_of_open_nat" -> "topology", "inv_mul_lt_iff_lt_mul_right" -> "algebra", "linear_map.smul_right\:2097_apply" -> "algebra", "rat.div_mk_div_cancel_left" -> "data", "metric.bounded_of_finite" -> "topology", "measure_theory.integrable_on.add_measure" -> "analysis", "linear_pmap.map_neg" -> "algebra", "pell.xy_coprime" -> "number_theory", "list.of_fn_zero" -> "data", "generalized_continued_fraction.of_correctness_of_terminates" -> "algebra", "dense_range.closure_range" -> "topology", "measure_theory.simple_func.bind_const" -> "analysis", "pgame.subsequent.right_move" -> "set_theory", "complex.of_real_inv" -> "data", "is_open_uniformity" -> "topology", "equiv.perm.same_cycle.symm" -> "algebra", "submonoid.localization_map.symm_comp_of_mul_equiv_of_localizations_apply'" -> "algebra", "ordinal.mul_zero" -> "set_theory", "submodule.findim_lt" -> "algebra", "free_abelian_group.add_seq" -> "algebra", "multiset.powerset_aux'_perm" -> "data", "padic_seq.norm_neg" -> "data", "category_theory.has_hom.hom.op_unop" -> "category_theory", "times_cont_diff_groupoid_prod" -> "geometry", "composition.blocks_length" -> "combinatorics", "set.inv_mem_inv" -> "algebra", "list.lookmap_id'" -> "data", "multiset.nodup_powerset_len" -> "data", "con.Inf_def" -> "algebra", "continuous_linear_equiv.symm_apply_apply" -> "topology", "ennreal.add_halves" -> "data", "bdd_above_Iio" -> "order", "alg_equiv.apply_symm_apply" -> "algebra", "list.iota_eq_reverse_range'" -> "data", "add_localization.r_eq_r'" -> "algebra", "interior_union_is_closed_of_interior_empty" -> "topology", "fin.prod_univ_cast_succ" -> "data", "complex.mul_conj" -> "data", "submodule.linear_proj_of_is_compl_apply_eq_zero_iff" -> "algebra", "measure_theory.lintegral_dirac" -> "analysis", "with_top.coe_bit1" -> "algebra", "cardinal.sup_lt_of_is_regular" -> "set_theory", "deriv_within.scomp" -> "analysis", "quotient.eq'" -> "data", "category_theory.exp_comparison_natural_right" -> "category_theory", "list.perm_cons_append_cons" -> "data", "is_extr_filter.filter_mono" -> "order", "has_deriv_within_at.mul_const" -> "analysis", "nat.sub_lt_left_iff_lt_add" -> "data", "int.add_left_cancel" -> "init", "function.inv_fun_neg" -> "logic", "monotone_lfp" -> "order", "card_trivial" -> "algebra", "add_units.neg_add_of_eq" -> "algebra", "exists_Ico_subset_of_mem_nhds'" -> "topology", "polynomial.eval_smul" -> "data", "filter.germ.abs_def" -> "order", "computable.list_reverse" -> "computability", "finsupp.sub_single_one_add" -> "data", "equiv.perm.swap_induction_on" -> "algebra", "ennreal.sub_right_inj" -> "data", "cau_seq.const_neg" -> "data", "measure_theory.outer_measure.comap_apply" -> "analysis", "borel_eq_top_of_discrete" -> "analysis", "dvd_trans" -> "algebra", "has_fderiv_at.has_deriv_at" -> "analysis", "nonzero_of_invertible" -> "algebra", "category_theory.equivalence.equivalence_mk'_unit" -> "category_theory", "abs_abs_sub_le_abs_sub" -> "algebra", "is_least_univ" -> "order", "ceil_lt_add_one" -> "algebra", "metric.continuous_at_iff" -> "topology", "neg_vsub_eq_vsub_rev" -> "algebra", "sym_bilin_form.is_refl" -> "algebra", "floor_add_int" -> "algebra", "commute.mul_right" -> "algebra", "matrix.det_adjugate_of_cancel" -> "algebra", "stream.mem_cycle" -> "data", "formal_multilinear_series.change_origin_summable_aux_j_injective" -> "analysis", "model_with_corners.unique_diff_preimage_source" -> "geometry", "set.surj_on_Inter_Inter" -> "data", "nat.zero_min" -> "init", "is_measurable_Iio" -> "analysis", "padic_int.coe_one" -> "data", "coe_sort_tt" -> "init", "pos_num.succ'_pred'" -> "data", "add_submonoid.mrange_fst" -> "algebra", "valuation.ext" -> "algebra", "set.dual_Ico" -> "data", "ordinal.succ_le_succ" -> "set_theory", "finsupp.support_map_range" -> "data", "category_theory.iso.symm_mk" -> "category_theory", "continuous_linear_map.uniform_continuous" -> "analysis", "monotone.div_const" -> "algebra", "not_congr" -> "init", "add_comm_group.direct_limit.lift_add" -> "algebra", "valuation.comap_id" -> "algebra", "category_theory.limits.colimit.pre_id" -> "category_theory", "submodule.lt_def" -> "algebra", "multiplicity.multiplicity_le_multiplicity_iff" -> "algebra", "polynomial.to_subring_one" -> "algebra", "dense_embedding.to_embedding" -> "topology", "fixed_points.minpoly.eval\:2082" -> "algebra", "neg_eq_neg_one_mul" -> "algebra", "times_cont_mdiff_within_at_iff_times_cont_mdiff_on_nhds" -> "geometry", "onote.oadd_lt_oadd_1" -> "set_theory", "infi_le_infi_of_subset" -> "order", "series_ratio_test" -> "data", "continued_fraction.convergents_eq_convergents'" -> "algebra", "Ioo_mem_nhds" -> "topology", "tendsto_abs_at_top_at_top" -> "topology", "list.foldl_reverse" -> "data", "ideal.mul_comm" -> "algebra", "subsemiring.le_def" -> "algebra", "zorn.zorn_partial_order\:2080" -> "order", "uniform.tendsto_congr" -> "topology", "ordered_ring.mul_nonneg" -> "algebra", "interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae" -> "analysis", "bot_le" -> "order", "imp_iff_not_or" -> "logic", "irrational.of_rat_mul" -> "data", "cardinal.mk_finset_eq_mk" -> "set_theory", "emetric.exists_edist_lt_of_Hausdorff_edist_lt" -> "topology", "pos_num.cast_mul" -> "data", "finset.sum_univ_pi" -> "data", "rel.image_univ" -> "data", "units.coe_gpow'" -> "algebra", "fin.heq_ext_iff" -> "data", "lie_algebra.special_linear.E_trace_zero" -> "algebra", "list.drop_suffix" -> "data", "polynomial.monic_map_iff" -> "data", "real.cos_arcsin" -> "analysis", "list.length_tail" -> "init", "znum.cast_pos" -> "data", "functor.comp.map_pure" -> "control", "linear_equiv.coe_uncurry" -> "algebra", "affine_subspace.direction_inf_of_mem_inf" -> "algebra", "ennreal.mul_div_cancel" -> "data", "matrix.one_apply_eq" -> "data", "turing.TM2to1.tr_respects_aux\:2081" -> "computability", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp" -> "category_theory", "inv_zero" -> "algebra", "euclidean_domain.gcd_eq_left" -> "algebra", "equiv.perm.disjoint.symm" -> "algebra", "vector3.insert_fs" -> "number_theory", "one_one_reducible.of_equiv" -> "computability", "polynomial.comp_one" -> "data", "pgame.not_le_lt" -> "set_theory", "vector_span_eq_span_vsub_set_left_ne" -> "algebra", "complex.differentiable_cos" -> "analysis", "list.sublist.erase" -> "data", "is_open_iff_nhds" -> "topology", "bilin_form.to_matrix_apply" -> "algebra", "submodule.mkq_apply" -> "algebra", "infi_eq_dif" -> "order", "continuous_linear_map.smul_comp" -> "topology", "finset.mem_of_subset" -> "data", "ordinal.is_normal.le_iff" -> "set_theory", "category_theory.unop_unop_map" -> "category_theory", "isometric.eq_symm_apply" -> "topology", "set.right_mem_Ioo" -> "data", "power_series.order_eq" -> "algebra", "linear_map.quotient_inf_equiv_sup_quotient_symm_apply_eq_zero_iff" -> "algebra", "filter.is_countably_generated_iff_exists_antimono_basis" -> "order", "function.surjective.iterate" -> "logic", "min_max_distrib_right" -> "algebra", "monoid_hom.comp_assoc" -> "algebra", "pell.pell_eqz" -> "number_theory", "nhds_cons" -> "topology", "multiset.cons_product" -> "data", "ideal.neg_mem_iff" -> "algebra", "rat.coe_cast_hom" -> "data", "add_monoid_hom.map_exists_right_neg" -> "algebra", "pell.xn_modeq_x4n_sub" -> "number_theory", "measure_theory.l1.coe_smul" -> "analysis", "ulift.down_up" -> "init", "complex.of_real_sin" -> "data", "set.subset.rfl" -> "data", "prod.smul_fst" -> "algebra", "polynomial.eval\:2082_mul_noncomm" -> "data", "complex.continuous_mul" -> "topology", "list.not_mem_keys_kerase" -> "data", "emetric.totally_bounded_iff" -> "topology", "is_compl.disjoint_left_iff" -> "order", "ring_hom.sclosure_preimage_le" -> "algebra", "pow_two_sub_pow_two" -> "algebra", "continuous_at.inv" -> "topology", "category_theory.limits.biprod.map_snd_assoc" -> "category_theory", "finsupp.sum_smul_index'" -> "data", "exists_elim_eq_right" -> "tactic", "inner_sub_left" -> "analysis", "ennreal.coe_eq_zero" -> "data", "filter.frequently_const" -> "order", "primrec.decode" -> "computability", "measure_theory.measure_zero_iff_ae_nmem" -> "analysis", "bdd_below_empty" -> "order", "int.mul_assoc" -> "init", "free_magma.mul_map_seq" -> "algebra", "list.reverse_singleton" -> "data", "finset.subset_insert" -> "data", "real.volume_interval" -> "analysis", "smodeq.symm" -> "algebra", "padic_val_nat_eq_factors_count" -> "data", "measure_theory.lebesgue_length_Ioo" -> "analysis", "subtype.mem" -> "data", "ideal.top_mul" -> "algebra", "of_digits_lt_base_pow_length'" -> "data", "list.erasep_subset" -> "data", "mul_neg_geom_series" -> "analysis", "base_pow_length_digits_le" -> "data", "finset.sort_sorted_lt" -> "data", "Top.sheaf_condition.w" -> "topology", "is_coprime.of_mul_add_left_left" -> "algebra", "set.image2_subset" -> "data", "mv_power_series.ext_iff" -> "algebra", "field.ring_closure_subset" -> "algebra", "one_div_lt" -> "algebra", "asymptotics.is_O_const_one" -> "analysis", "finsupp.supported_eq_span_single" -> "algebra", "add_sub_cancel" -> "algebra", "free_group.red.cons_nil_iff_singleton" -> "algebra", "int.coe_nat_sub" -> "init", "local_homeomorph.image_inter_source_eq" -> "topology", "ennreal.of_real_eq_coe_nnreal" -> "data", "is_unit_of_dvd_one" -> "algebra", "onote.oadd_mul_NF_below" -> "set_theory", "ereal.neg_le" -> "data", "real.has_deriv_at_sin" -> "analysis", "function.left_inverse.comp_eq_id" -> "logic", "finset.singleton_inj" -> "data", "finset.weighted_vsub_of_point_erase" -> "algebra", "polynomial.degree_add_C" -> "data", "category_theory.monoidal_functor.id_\[Mu]_is_iso" -> "category_theory", "filter.has_basis.tendsto_right_iff" -> "order", "matrix.mul_add" -> "data", "fin.coe_cast_le" -> "data", "measure_theory.ae_eq_fun.induction_on" -> "analysis", "vector.nth_of_fn" -> "data", "directed_of_chain" -> "order", "set.Union_subset_Union_const" -> "data", "asymptotics.is_o_zero_right_iff" -> "analysis", "local_homeomorph.mdifferentiable.comp_symm_deriv" -> "geometry", "subalgebra.zero_mem" -> "algebra", "pow_card_eq_one" -> "algebra", "submonoid.map_id" -> "algebra", "has_fderiv_within_at_fst" -> "analysis", "finset.piecewise_empty" -> "data", "bitraversable.comp_tfst" -> "control", "complex.abs_inv" -> "data", "real.cos_two_neg" -> "data", "finset.card_eq_sum_ones" -> "algebra", "list.ordered_insert_count" -> "data", "set.preimage_const_of_mem" -> "data", "polynomial.mod_eq_self_iff" -> "data", "submodule.annihilator_mono" -> "algebra", "multiset.rel_map_left" -> "data", "ring.direct_limit.lift_one" -> "algebra", "filter.tendsto.congr_uniformity" -> "topology", "add_subgroup.prod_top" -> "algebra", "abstract_completion.map_comp" -> "topology", "znum.cast_zneg" -> "data", "finmap.union_comm_of_disjoint" -> "data", "heq.symm" -> "init", "metric.diam_union'" -> "topology", "filter.not_ne_bot" -> "order", "bilin_form.is_adjoint_pair_zero" -> "algebra", "is_unit_of_mul_is_unit_left" -> "algebra", "enat.add_lt_add_right" -> "data", "prime_spectrum.zero_locus_singleton_zero" -> "algebraic_geometry", "polynomial.has_fderiv_within_at" -> "analysis", "ctop.realizer.tendsto_nhds_iff" -> "data", "interval_integral.integral_has_deriv_at_of_tendsto_ae_right" -> "analysis", "category_theory.monoidal_category.unitors_equal.cells_8" -> "category_theory", "nnreal.dist_eq" -> "topology", "finset.exists_le_of_sum_le" -> "algebra", "category_theory.limits.coprod.inl_desc_assoc" -> "category_theory", "submonoid.coe_one" -> "algebra", "prod.snd_surjective" -> "data", "ordinal.rel_iso_enum'" -> "set_theory", "linear_equiv.range" -> "algebra", "fderiv_within_neg" -> "analysis", "normal_add_subgroup_of_add_comm_group" -> "algebra", "add_monoid_hom.comp_id" -> "algebra", "polynomial.monic_prod_of_monic" -> "data", "continuous_list_sum" -> "topology", "enat.add_one_le_iff_lt" -> "data", "filter.has_basis.tendsto_left_iff" -> "order", "affine.simplex.point_eq_affine_combination_of_points_with_circumcenter" -> "geometry", "exists_prop_of_true" -> "logic", "local_homeomorph.symm_to_local_equiv" -> "topology", "filter.frequently_low_scores" -> "order", "zsqrtd.sq_le_smul" -> "data", "finset.nonempty.bex" -> "data", "nat.primrec'.head" -> "computability", "category_theory.lax_monoidal_functor.comp_\[Mu]" -> "category_theory", "linear_equiv_matrix_id" -> "algebra", "add_submonoid.closure_induction" -> "algebra", "function.is_periodic_pt.eq_of_apply_eq_same" -> "dynamics", "is_absolute_value.sub_abv_le_abv_sub" -> "data", "nat.left_distrib" -> "init", "inf_right_idem" -> "order", "measure_theory.measure.comap_apply" -> "analysis", "basic_smooth_bundle_core.times_cont_mdiff_proj" -> "geometry", "metric.closure_ball_subset_closed_ball" -> "topology", "times_cont_mdiff_within_at.prod_map'" -> "geometry", "nat.cast_succ" -> "data", "abstract_completion.map_unique" -> "topology", "measure_theory.ae_eq_fun.induction_on\:2082" -> "analysis", "nat.mul_le_mul_of_nonneg_right" -> "init", "uniform_inducing.uniform_continuous" -> "topology", "add_monoid_algebra.single_mul_apply_aux" -> "data", "set.mem_one" -> "algebra", "semiquot.pure_le" -> "data", "free_abelian_group.lift.unique" -> "algebra", "filter.tendsto.norm" -> "analysis", "affine.simplex.dist_circumcenter_eq_circumradius'" -> "geometry", "encodable.encode_sigma_val" -> "data", "with_top.add_lt_add_iff_left" -> "algebra", "eq_mp_rfl" -> "logic", "simple_graph.complete_graph_is_regular" -> "combinatorics", "subtype.dist_eq" -> "topology", "closure_Iic" -> "topology", "ordinal.power_le_of_limit" -> "set_theory", "set.restrict_eq" -> "data", "gaussian_int.to_complex_inj" -> "data", "list.perm_comp_forall\:2082" -> "data", "infi_sigma" -> "order", "num.lt_iff_cmp" -> "data", "int.sign_mul_nat_abs" -> "init", "polynomial.nat_degree_pow" -> "data", "classical.indefinite_description" -> "init", "add_submonoid.localization_map.ext_iff" -> "algebra", "ideal.quotient.is_integral_domain_iff_prime" -> "algebra", "add_monoid_hom.coe_of" -> "algebra", "nat.odd_mul_odd" -> "data", "digits_of_lt" -> "data", "polynomial.C_eq_nat_cast" -> "data", "add_submonoid.closure_eq_mrange" -> "algebra", "alg_hom.map_prod" -> "algebra", "ennreal.coe_lt_one_iff" -> "data", "add_magma.free_add_semigroup.lift_of" -> "algebra", "power_series.trunc_one" -> "algebra", "list.cons_union" -> "data", "smooth_on_const" -> "geometry", "polynomial.degree_lt_degree_mul_X" -> "data", "dfinsupp.map_range_apply" -> "data", "submonoid.mem_closure" -> "algebra", "direct_sum.component.lof_self" -> "algebra", "isometric.point_reflection_dist_self'" -> "analysis", "category_theory.limits.colimit.\[Iota]_pre" -> "category_theory", "measure_theory.measure.finite_at_filter.filter_mono" -> "analysis", "eckmann_hilton.one" -> "algebra", "bxor_tt" -> "init", "ordinal.cof_eq'" -> "set_theory", "set.diff_diff_right" -> "data", "fderiv_const_smul_algebra" -> "analysis", "sesq_form.neg_right" -> "algebra", "min_left_comm" -> "init", "filter.frequently_cofinite_iff_infinite" -> "order", "commute.sub_left" -> "algebra", "traversable.foldr_to_list" -> "control", "uniform_continuous_snd" -> "topology", "real.arcsin_nonneg" -> "analysis", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_is_iso_comp_inv" -> "category_theory", "list.bag_inter_nil_iff_inter_nil" -> "data", "uniform_space.complete_of_cauchy_seq_tendsto" -> "topology", "is_local_max_on.congr" -> "topology", "computation.equiv.trans" -> "data", "measure_theory.finite_at_filter_of_finite" -> "analysis", "units.coe_mul_right" -> "data", "computation.equiv.refl" -> "data", "semiconj_by.inv_inv_symm_iff" -> "algebra", "bdd_below_union" -> "order", "finset.insert_erase" -> "data", "tactic.ring_exp.add_pf_z_sum" -> "tactic", "lie_algebra.orthogonal.is_unit_Pso" -> "algebra", "nnreal.add_sub_cancel" -> "data", "set.mem_to_finset_val" -> "data", "homeomorph.homeomorph_mk_coe" -> "topology", "has_strict_fderiv_at.to_implicit_function_of_complemented" -> "analysis", "geom_gold_is_sol_fib_rec" -> "data", "equiv.perm.sign_surjective" -> "algebra", "if_false" -> "init", "bifunctor.fst_comp_fst" -> "control", "continuous_multilinear_map.uncurry_curry_right" -> "analysis", "mul_lt_mul_right'" -> "algebra", "filter.tendsto_iff_comap" -> "order", "int.modeq.gcd_a_modeq" -> "data", "measurable.const_smul" -> "analysis", "max_choice" -> "algebra", "polynomial.expand_eq_C" -> "algebra", "category_theory.functor.prod_obj" -> "category_theory", "submodule.restrict_scalars_carrier" -> "algebra", "nndist_edist" -> "topology", "list.revzip_map_snd" -> "data", "continuous_map.coe_continuous" -> "topology", "nhds_within_Icc_eq_nhds_within_Ici" -> "topology", "lt_ceil" -> "algebra", "filter.sets_iff_generate" -> "order", "infi_empty" -> "order", "uniform_space.completion.dense\:2082" -> "topology", "not_iff_self" -> "init", "localization_map.map_smul" -> "algebra", "add_monoid_hom.map_nat_cast_smul" -> "algebra", "fintype.sum_bool" -> "data", "mem_closure_iff" -> "topology", "inner_product_geometry.norm_sub_square_eq_norm_square_add_norm_square_sub_two_mul_norm_mul_norm_mul_cos_angle" -> "geometry", "linear_independent.injective" -> "algebra", "continuous_inv" -> "topology", "list.kerase_nodupkeys" -> "data", "set.zero_nonempty" -> "algebra", "abs_by_cases" -> "algebra", "ring.fractional_ideal.coe_map" -> "algebra", "nat.mkpair_unpair'" -> "data", "and_iff_left_iff_imp" -> "logic", "ordinal.is_normal.limit_le" -> "set_theory", "continuous_linear_equiv.of_bijective_apply_symm_apply" -> "analysis", "frobenius_mul" -> "algebra", "palindrome.of_reverse_eq" -> "data", "finset.nonempty_of_sum_ne_zero" -> "algebra", "fin.coe_one'" -> "data", "set.preimage_add_const_Ici" -> "data", "measure_theory.outer_measure.is_left_invariant_of_content" -> "analysis", "turing.to_partrec.code.exists_code.comp" -> "computability", "iff_eq_eq" -> "init", "filter.Ioi_mem_at_top" -> "order", "card_eq_card_quotient_mul_card_subgroup" -> "algebra", "div_eq_one_iff_eq" -> "algebra", "complex.rat_cast_im" -> "data", "rat.cast_commute" -> "data", "times_cont_diff.prod" -> "analysis", "polynomial.roots_list_prod" -> "data", "metric.diam_pair" -> "topology", "category_theory.iso_whisker_left_inv" -> "category_theory", "vector.mmap_cons" -> "data", "infi_const" -> "order", "has_deriv_at.comp_has_deriv_within_at" -> "analysis", "equiv.swap_inv" -> "data", "euclidean_geometry.dist_square_eq_dist_square_add_dist_square_iff_angle_eq_pi_div_two" -> "geometry", "pnat.add_coe" -> "data", "monotone_Sup_of_monotone" -> "order", "rel_embedding.map_inf_le" -> "order", "game.le_trans" -> "set_theory", "free_monoid.hom_map_lift" -> "algebra", "supr_sigma" -> "order", "submonoid.localization_map.inv_unique" -> "algebra", "alist.to_finmap_eq" -> "data", "padic_int.coe_neg" -> "data", "char_p.eq" -> "algebra", "norm_sum_le" -> "analysis", "omega.coeffs_reduce_correct" -> "tactic", "nat.pow_lt_pow_of_lt_left" -> "init", "category_theory.limits.image_mono_iso_source_hom_self" -> "category_theory", "monoid_hom.coprod_apply" -> "algebra", "topological_space.opens.local_homeomorph_subtype_coe_source" -> "topology", "ordinal.le_div" -> "set_theory", "omega.nat.implies_neg_elim" -> "tactic", "ordinal.mul_succ" -> "set_theory", "lucas_lehmer.s_mod_lt" -> "number_theory", "int.div_mul_cancel" -> "data", "filter.ne_bot.comap_of_image_mem" -> "order", "AddGroup.ext" -> "algebra", "local_homeomorph.continuous_at_iff_continuous_at_comp_right" -> "topology", "subtype.preconnected_space" -> "topology", "is_unit.smul_eq_zero" -> "algebra", "pow_bit0" -> "algebra", "nat.fact_pos" -> "data", "linear_map.supr_range_std_basis_eq_infi_ker_proj" -> "algebra", "dist_edist" -> "topology", "list.chain'_cons'" -> "data", "nnreal.of_real_of_nonpos" -> "data", "category_theory.limits.cofork.right_app_one_assoc" -> "category_theory", "finset.exists_max_image" -> "data", "ordinal.le_of_mul_le_mul_left" -> "set_theory", "lt_of_mul_lt_mul_right'" -> "algebra", "dif_ctx_simp_congr" -> "init", "smul_add_hom_apply" -> "algebra", "list.modify_nth_tail_modify_nth_tail_same" -> "data", "free_semigroup.mul_map_seq" -> "algebra", "ring_hom.coe_comp" -> "algebra", "mul_comm" -> "algebra", "measure_theory.measure.restrict_add_restrict_compl" -> "analysis", "span_nat_eq" -> "algebra", "nat.shiftl_add" -> "init", "multiset.rec_on_cons" -> "data", "category_theory.limits.prod.map_snd" -> "category_theory", "list.mem_keys_kunion" -> "data", "pythagorean_triple.is_primitive_classified_of_coprime_of_zero_left" -> "number_theory", "add_submonoid.list_sum_mem" -> "algebra", "multiset.erase_subset" -> "data", "rel_iso.bijective" -> "order", "cardinal.pow_cast_right" -> "set_theory", "subalgebra.ext_iff" -> "algebra", "int.gcd_eq_right" -> "algebra", "list.mem_map_of_mem" -> "data", "isometry.diam_range" -> "topology", "finset.supr_singleton" -> "data", "edist_triangle_left" -> "topology", "lie_algebra.orthogonal.is_unit_PB" -> "algebra", "equiv.swap_comp_apply" -> "data", "times_cont_mdiff_iff" -> "geometry", "ordinal.mul_lt_mul_of_pos_left" -> "set_theory", "free_group.red.length" -> "algebra", "forall_or_of_or_forall" -> "logic", "polynomial.not_is_unit_X" -> "data", "set.not_mem_of_mem_compl" -> "data", "measurable_space.dynkin_system.has_compl_iff" -> "analysis", "padic.cast_eq_of_rat_of_int" -> "data", "equiv.arrow_congr'_trans" -> "data", "finset.center_mass_filter_ne_zero" -> "analysis", "nat.cast_one" -> "data", "pequiv.eq_some_iff" -> "data", "finset.prod_bij_ne_one" -> "algebra", "pell.pell_zd_succ" -> "number_theory", "set.interval_subset_interval_iff_le" -> "data", "polynomial.card_roots" -> "data", "pgame.impartial.add_self" -> "set_theory", "nnreal.geom_mean_le_arith_mean_weighted" -> "analysis", "zsqrtd.coe_int_add" -> "data", "circle_deg1_lift.tendsto_translation_number_aux" -> "dynamics", "zmod.val_one_eq_one_mod" -> "data", "finset.singleton_disjoint" -> "data", "has_strict_fderiv_at.of_local_left_inverse" -> "analysis", "sub_self_div_two" -> "algebra", "le_of_not_lt" -> "algebra", "polynomial.finset_sum_coeff" -> "data", "list.nil_suffix" -> "data", "le_neg" -> "algebra", "filter.tendsto.neg" -> "topology", "complex.cpow_eq_pow" -> "analysis", "category_theory.iso.symm_self_id" -> "category_theory", "tendsto_inf_principal_nhds_iff_of_forall_eq" -> "topology", "subgroup.coe_mul" -> "algebra", "add_commute.units_of_coe" -> "algebra", "ordinal.deriv_is_normal" -> "set_theory", "continuous_within_at.mem_closure_image" -> "topology", "real.sqrt_le_sqrt" -> "data", "is_compl.of_eq" -> "order", "inv_mul_cancel_right'" -> "algebra", "matrix.to_lin_neg" -> "algebra", "is_extr_filter.comp_antimono" -> "order", "finset.singleton_ne_empty" -> "data", "function.mem_pts_of_period" -> "dynamics", "pth_root_eq_iff" -> "algebra", "euclidean_domain.xgcd_aux_P" -> "algebra", "list.length_erase_of_mem" -> "data", "omega.symmod_eq" -> "tactic", "finset.eq_of_subset_of_card_le" -> "data", "zero_scale_roots" -> "algebra", "nat.sqrt_aux_2" -> "data", "finset.image_id" -> "data", "continuous_multilinear_map.add_apply" -> "topology", "list.take'_left" -> "data", "finsupp.sum_sub" -> "data", "list.lookup_kunion_left" -> "data", "list.Ico.self_empty" -> "data", "list.subperm.length_le" -> "data", "euclidean_domain.zero_mod" -> "algebra", "has_fderiv_at_filter.const_sub" -> "analysis", "le_gfp" -> "order", "polynomial.coeff_zero" -> "data", "continuous_linear_map.range_coe" -> "topology", "polynomial.coeff_zero_eq_eval_zero" -> "data", "ennreal.bit1_ne_zero" -> "data", "category_theory.functor.hom_pairing_map" -> "category_theory", "bool.bxor_ff_right" -> "data", "zero_open_separated_add" -> "topology", "real.lb_le_Inf" -> "data", "nnreal.rpow_lt_rpow_iff" -> "analysis", "category_theory.prod_preserves_connected_limits.\[Gamma]\:2082_app" -> "category_theory", "turing.TM2to1.add_bottom_nth_snd" -> "computability", "ennreal.tsum_coe_eq" -> "topology", "list.mem_insert_self" -> "data", "category_theory.iso.hom_congr_comp" -> "category_theory", "rel_embedding.coe_fn_to_embedding" -> "order", "uniform_continuous.comp" -> "topology", "category_theory.currying_unit_iso_inv_app_app_app" -> "category_theory", "multiset.map_pmap" -> "data", "cau_seq.completion.cau_seq_zero_ne_one" -> "data", "mv_polynomial.degrees_one" -> "data", "is_connected.image" -> "topology", "rel_embedding.well_founded_iff_no_descending_seq" -> "order", "polynomial.separable.of_pow'" -> "algebra", "gaussian_int.to_complex_def\:2082" -> "data", "has_fderiv_at.has_fderiv_within_at" -> "analysis", "category_theory.monoidal.right_unitor_inv_app" -> "category_theory", "with_bot.bot_lt_coe" -> "order", "filter.comap_lift'_eq" -> "order", "direct_sum.ext_iff" -> "algebra", "emetric.mk_uniformity_basis" -> "topology", "ennreal.top_ne_zero" -> "data", "add_monoid_algebra.of_apply" -> "data", "filter.mem_map_seq_iff" -> "order", "monoid.subset_closure" -> "algebra", "matrix.vec_mul_cons" -> "data", "multiset.singleton_inj" -> "data", "int.of_add_mul" -> "algebra", "eq_inv_of_mul_eq_one" -> "algebra", "infinite.of_surjective" -> "data", "set.image_eq" -> "data", "pos_num.mod'_to_nat" -> "data", "nat.fib_pos" -> "data", "function.injective.summable_iff" -> "topology", "is_local_min.has_fderiv_at_eq_zero" -> "analysis", "list.nth_le_map'" -> "data", "matrix.transpose_one" -> "data", "asymptotics.is_o_pow_pow" -> "analysis", "linear_equiv.to_Module_iso'_hom" -> "algebra", "finsupp.emb_domain_zero" -> "data", "add_submonoid.multiples_subset" -> "algebra", "centroid_mem_affine_span_of_cast_card_ne_zero" -> "algebra", "set.singleton_zero" -> "algebra", "set.preimage_mul_left_one" -> "algebra", "is_glb_le_is_lub" -> "order", "option.some_injective" -> "data", "ideal.map_quotient_self" -> "algebra", "multiset.rel_flip" -> "data", "pgame.impartial.no_good_right_moves_iff_first_loses" -> "set_theory", "multiset.subset_zero" -> "data", "is_closed_map_sigma_mk" -> "topology", "continuous_linear_map.smul_right_norm" -> "analysis", "decidable.not_not_iff" -> "init", "list.mem_ext" -> "data", "dfinsupp.support_zip_with" -> "data", "measure_theory.ae_eq_trans" -> "analysis", "add_subgroup.ext'_iff" -> "algebra", "category_theory.functor.comp_obj" -> "category_theory", "subspace.coe_prod_equiv_of_closed_compl" -> "analysis", "with_zero.some_eq_coe" -> "algebra", "set.Union_subset_Union2" -> "data", "finset.coe_sdiff" -> "data", "measure_theory.measure.lt_iff'" -> "analysis", "set.image_inv_Ioo_0_left" -> "data", "submodule.forall" -> "algebra", "finset.some_mem_insert_none" -> "data", "mul_semiring_action_hom.coe_fn_coe'" -> "algebra", "int.units_eq_one_or" -> "data", "total_of" -> "init", "vector_span_image_eq_span_vsub_set_left_ne" -> "algebra", "free_group.closure_subset" -> "algebra", "list.nodup_iff_nth_le_inj" -> "data", "div_pos" -> "algebra", "metric.Hausdorff_dist_closure\:2082" -> "topology", "list.minimum_cons" -> "data", "continuous_inv_of_strict_mono_equiv" -> "topology", "finset.exists_intermediate_set" -> "data", "power_series.map_id" -> "algebra", "is_basis_span" -> "algebra", "function.support_comp_eq" -> "data", "real.differentiable_at_exp" -> "analysis", "Mod.regular_X" -> "category_theory", "to_bool_tt" -> "init", "div_mul_le_div_mul_of_div_le_div" -> "algebra", "function.support_supr" -> "data", "wseq.dropn_of_seq" -> "data", "set.Ioo_subset_Ioo_left" -> "data", "measure_theory.integral_empty" -> "analysis", "ennreal.summable" -> "topology", "set.union_insert" -> "data", "composition.eq_ones_iff" -> "combinatorics", "inner_zero_right" -> "analysis", "turing.TM2to1.tr_respects" -> "computability", "measure_theory.l1.simple_func.integral_eq_lintegral" -> "analysis", "le_supr" -> "order", "int.neg_of_nat_mul_of_nat" -> "init", "zmod.coe_to_nat" -> "data", "finmap.lookup_union_left_of_not_in" -> "data", "category_theory.preimage_iso_inv" -> "category_theory", "finsupp.map_range_apply" -> "data", "option.guard_eq_some" -> "data", "zero_eq_mul" -> "algebra", "ennreal.coe_nat" -> "data", "equiv.to_pequiv_trans" -> "data", "le_of_sub_nonneg" -> "algebra", "norm_num.int_cast_bit0" -> "tactic", "category_theory.limits.image.\[Iota]_zero'" -> "category_theory", "generalized_continued_fraction.squash_seq_eq_self_of_terminated" -> "algebra", "continuous_multilinear_map.map_piecewise_smul" -> "topology", "turing.tape.mk'_left_right\:2080" -> "computability", "circle_deg1_lift.iterate_mono" -> "dynamics", "lower_bounds_singleton" -> "order", "add_monoid_algebra.mul_single_zero_apply" -> "data", "comp_le_uniformity" -> "topology", "multiset.subset_erase_dup" -> "data", "zsqrtd.mul_conj" -> "data", "subset_comp_self" -> "topology", "free_add_magma.map_add'" -> "algebra", "list.index_of_nil" -> "data", "eq_rec_heq" -> "init", "power_series.le_order_add" -> "algebra", "approximates_linear_on.inj_on" -> "analysis", "pnat.lcm_dvd" -> "data", "is_basis.det_apply" -> "algebra", "set.maps_to.coe_restrict_apply" -> "data", "multiset.subset_of_le" -> "data", "int.modeq.modeq_and_modeq_iff_modeq_mul" -> "data", "prod.snd_neg" -> "algebra", "linear_equiv.trans_refl" -> "algebra", "seq.not_mem_nil" -> "data", "vector_all_iff_forall" -> "number_theory", "associated_mul_right_cancel" -> "algebra", "multiplicity.finset.prod" -> "algebra", "list.nth_of_fn_aux" -> "data", "set.interval_subset_interval_left" -> "data", "set.compl_empty_iff" -> "data", "znum.zneg_zneg" -> "data", "add_monoid_hom.mclosure_preimage_le" -> "algebra", "measure_theory.measure.map_dirac" -> "analysis", "category_theory.limits.walking_pair.equiv_bool_apply_left" -> "category_theory", "nat.prime_def_min_fac" -> "data", "int.lt.dest" -> "init", "padic.of_rat_add" -> "data", "real.rpow_le_one_of_one_le_of_nonpos" -> "analysis", "polynomial.splits_of_splits_id" -> "algebra", "polynomial.eval_div_by_monic_pow_root_multiplicity_ne_zero" -> "data", "turing.list_blank.nth_zero" -> "computability", "nat.add_le_add" -> "init", "linear_map.continuous_iff_is_closed_ker" -> "analysis", "category_theory.tensoring_right_monoidal_to_lax_monoidal_functor_\[Mu]_app" -> "category_theory", "bucket_array.foldl_eq" -> "data", "cast_heq" -> "init", "matrix.cons_transpose" -> "data", "measure_theory.exists_is_measurable_superset_iff_measure_eq_zero" -> "analysis", "finset.sdiff_disjoint" -> "data", "ordinal.typein_enum" -> "set_theory", "measurable.sub_nnreal" -> "analysis", "metric.ball_disjoint_same" -> "topology", "list.map_map" -> "init", "metric.ball_subset_ball" -> "topology", "set.union_inter_distrib_right" -> "data", "ideal.map_map" -> "algebra", "category_theory.monoidal_category.triangle_assoc_comp_right_inv" -> "category_theory", "is_extr_filter.filter_inf" -> "order", "finset.sum_fin_eq_sum_range" -> "data", "polynomial.nat_degree_C" -> "data", "nnreal.coe_prod" -> "data", "list.diff_eq_foldl" -> "data", "linear_map.fun_left_id" -> "algebra", "inv_smul_eq_iff" -> "algebra", "mvpfunctor.liftp_iff'" -> "data", "add_submonoid.localization_map.map_add_right" -> "algebra", "times_cont_diff_add" -> "analysis", "multiset.revzip_powerset_aux_perm" -> "data", "zsqrtd.norm_eq_one_iff" -> "data", "nat.add_mod_eq_add_mod_left" -> "data", "is_subgroup.mem_norm_comm" -> "algebra", "map_Sup_of_continuous_at_of_monotone" -> "topology", "category_theory.functor_to_types.map_inv_map_hom_apply" -> "category_theory", "int.div_eq_iff_eq_mul_right" -> "data", "vsub_eq_zero_iff_eq" -> "algebra", "list_all_map" -> "number_theory", "ordinal.fintype_card" -> "set_theory", "primrec.vector_cons" -> "computability", "list.perm.kunion" -> "data", "rat.le_refl" -> "data", "linear_map.comap_le_comap_iff" -> "algebra", "computable.option_map" -> "computability", "is_local_min.inf" -> "topology", "real.cos_one_le" -> "data", "ennreal.inv_pos" -> "data", "set.image_id'" -> "data", "submodule.infi_orthogonal" -> "analysis", "finmap.disjoint_union_right" -> "data", "list.forall\:2082_map_left_iff" -> "data", "set.Ico_inter_Ico" -> "data", "set.subset_Union" -> "data", "multiset.count_zero" -> "data", "lie_act" -> "algebra", "set.union_def" -> "data", "roption.mem_some" -> "data", "polynomial.X_pow_sub_C_ne_zero" -> "data", "stream.mem_interleave_right" -> "data", "multiset.ndinter_eq_inter" -> "data", "int.to_nat_zero" -> "data", "int.coe_nat_succ_pos" -> "data", "category_theory.eq_curry_iff" -> "category_theory", "measure_theory.outer_measure.trim_add" -> "analysis", "finset.sum_range_reflect" -> "algebra", "continuous_within_at_univ" -> "topology", "set.Ioc_union_Ioc_right" -> "data", "mul_lt_mul_of_pos_right" -> "algebra", "real.sqrt_two_add_series_succ" -> "analysis", "norm_num.from_nat_pow" -> "tactic", "mem_perms_of_finset_iff" -> "data", "tactic.ring.horner_horner" -> "tactic", "function.semiconj.commute" -> "logic", "if_congr_prop" -> "init", "eq_false_of_or_eq_false_left" -> "init", "polynomial.support_zero" -> "data", "nonneg_le_nonneg_of_squares_le" -> "algebra", "dist_sub_left" -> "analysis", "add_monoid_hom.coe_to_real_linear_map" -> "topology", "mul_le_iff_le_one_right'" -> "algebra", "set.surj_on.left_inv_on_of_right_inv_on" -> "data", "list.mem_erase_iff_of_nodup" -> "data", "subtype.preimage_coe_eq_preimage_coe_iff" -> "data", "subring.mem_comap" -> "algebra", "forall_swap" -> "logic", "filter.mem_map_sets_iff" -> "order", "is_preirreducible.closure" -> "topology", "int.lt_iff_add_one_le" -> "init", "has_fderiv_at_filter.sum" -> "analysis", "mul_eq_zero_comm" -> "algebra", "filter.bind_inf_principal" -> "order", "finset.Ico.union_consecutive" -> "data", "equiv.coe_ulift_symm" -> "data", "primrec.option_get_or_else" -> "computability", "ring_equiv.local_ring" -> "data", "computation.results.mem" -> "data", "valuation.supp_quot" -> "algebra", "int.nat_abs_gcd" -> "algebra", "set.pi_if" -> "data", "equiv.trans_refl" -> "data", "list.prod_eq_foldr" -> "data", "add_units.coe_mk" -> "algebra", "nat.one_mul" -> "init", "filter.prod_infi_left" -> "order", "con.lift_range" -> "algebra", "ennreal.mul_lt_of_lt_div" -> "data", "function.is_periodic_pt.add" -> "dynamics", "tendsto_indicator_of_antimono" -> "order", "typevec.repeat_eq_append1" -> "data", "mul_action.smul_inv_smul" -> "algebra", "filter.realizer.ne_bot_iff" -> "data", "abs_inner_le_norm" -> "analysis", "real.rpow_le_one" -> "analysis", "local_equiv.image_eq_target_inter_inv_preimage" -> "data", "finset.disjoint_left" -> "data", "free_abelian_group.lift.sub" -> "algebra", "is_local_min_on.has_fderiv_within_at_eq_zero" -> "analysis", "ideal.ker_le_comap" -> "algebra", "category_theory.equivalence.symm_unit_iso" -> "category_theory", "ordinal.div_le_of_le_mul" -> "set_theory", "matrix.is_unit_det_of_left_inverse" -> "algebra", "subsemiring.closure_sUnion" -> "algebra", "nat.coprime.gcd_eq_one" -> "data", "finset.filter_union_filter_neg_eq" -> "data", "cardinal.zero_lt_bit1" -> "set_theory", "mul_lt_mul_left'" -> "algebra", "category_theory.limits.kernel.\[Iota]_of_mono" -> "category_theory", "category_theory.is_iso.hom_inv_id" -> "category_theory", "nat.primrec'.if_lt" -> "computability", "filter.lift'_bot" -> "order", "cardinal.mul_eq_left_iff" -> "set_theory", "Top.stalk_to_fiber_surjective" -> "topology", "metric.mem_closure_range_iff_nat" -> "topology", "subsemiring.closure_le" -> "algebra", "measure_theory.lintegral_sub" -> "analysis", "ordinal.mul_lt_omega" -> "set_theory", "finset.prod_eq_one" -> "algebra", "Module.monoidal_category.triangle" -> "algebra", "separated_iff_t2" -> "topology", "list.mfoldr_with_index_eq_mfoldr_enum" -> "data", "set.preimage_image_preimage" -> "data", "set.union_subset_union" -> "data", "semiquot.map_def" -> "data", "int.cast_commute" -> "data", "algebra.mem_top" -> "algebra", "real.rpow_def_of_neg" -> "analysis", "list.tendsto_cons_iff" -> "topology", "turing.TM2to1.tr_respects_aux\:2082" -> "computability", "nat.exists_most_significant_bit" -> "data", "cardinal.mk_Union_eq_sum_mk" -> "set_theory", "quadratic_form.associated_left_inverse" -> "algebra", "sym2.rel.symm" -> "data", "generalized_continued_fraction.squash_seq_nth_of_not_terminated" -> "algebra", "times_cont_mdiff_on.continuous_on" -> "geometry", "metric.ball_eq_empty_iff_nonpos" -> "topology", "nat.eq_zero_of_mul_le" -> "data", "differentiable.neg" -> "analysis", "is_open_ne" -> "topology", "uniformity_basis_edist_inv_nat" -> "topology", "list.naturality" -> "control", "monoid_hom.map_closure" -> "algebra", "affine.simplex.points_with_circumcenter_eq_circumcenter" -> "geometry", "bilin_form.smul_left" -> "algebra", "finset.sdiff_sdiff_self_left" -> "data", "asymptotics.is_o.const_mul_right'" -> "analysis", "pow_dvd_pow" -> "algebra", "lcm_units_coe_left" -> "algebra", "finset.prod_piecewise" -> "algebra", "inner_smul_self_left" -> "analysis", "linear_pmap.map_add" -> "algebra", "strict_mono.mul_const'" -> "algebra", "finsupp.filter_sum" -> "data", "nat.is_unit_iff" -> "data", "mv_polynomial.map_map" -> "data", "list.exists_lt_of_sum_lt" -> "data", "complex.cos_pi" -> "analysis", "list.func.get_eq_default_of_le" -> "data", "smooth_left_add" -> "geometry", "pgame.impartial.neg_equiv_self" -> "set_theory", "emetric.nonempty_compacts.is_closed_in_closeds" -> "topology", "multiset.cons_inj_right" -> "data", "asymptotics.is_O_with_congr" -> "analysis", "is_R_or_C.conj_bit1" -> "data", "inv_mul_le_left_of_le_mul" -> "algebra", "num.add_of_nat" -> "data", "list.mem_permutations_of_perm_lemma" -> "data", "multiset.card_add" -> "data", "wseq.tail_cons" -> "data", "int.even_sub" -> "data", "metric.diam_triple" -> "topology", "mul_neg_one" -> "algebra", "pnat.xgcd_type.flip_y" -> "data", "norm_image_sub_le_of_norm_deriv_le_segment'" -> "analysis", "irrational.mul_cases" -> "data", "int.normalize_coe_nat" -> "algebra", "ennreal.mul_supr" -> "topology", "list.perm.union" -> "data", "surreal.not_le" -> "set_theory", "midpoint_def" -> "algebra", "continued_fraction.coe_to_simple_continued_fraction" -> "algebra", "set.left_inv_on.congr_left" -> "data", "ordinal.dvd_zero" -> "set_theory", "snum.bit_one" -> "data", "has_le.le.ge" -> "algebra", "submodule.mem_supr_of_directed" -> "algebra", "set.subset_preimage_univ" -> "data", "list.lex.not_nil_right" -> "data", "multiset.mem_filter" -> "data", "cardinal.mk_int" -> "set_theory", "mdifferentiable_on_of_locally_mdifferentiable_on" -> "geometry", "num.lt_to_nat" -> "data", "finsupp.nat_sub_apply" -> "data", "add_monoid_hom.map_range" -> "algebra", "cardinal.one_power" -> "set_theory", "padic_val_rat.finite_int_prime_iff" -> "data", "emetric.uniformity_has_countable_basis" -> "topology", "normed_field.continuous_on_inv" -> "analysis", "category_theory.non_preadditive_abelian.neg_neg" -> "category_theory", "finset.fold_insert" -> "data", "polynomial.alg_hom_eval\:2082_algebra_map" -> "data", "finset.weighted_vsub_apply" -> "algebra", "list.rel_foldl" -> "data", "complex.uniform_continuous_mul" -> "topology", "list.length_permutations_aux2" -> "data", "finset.prod_image" -> "algebra", "rat.mul_comm" -> "data", "list.take'_length" -> "data", "list.func.length_sub" -> "data", "add_con.refl" -> "algebra", "turing.TM2to1.tr_normal_run" -> "computability", "units.coe_lt_coe" -> "algebra", "group_separation_rel" -> "topology", "rat.mul_add" -> "data", "real.arccos_le_pi" -> "analysis", "monoid_hom.map_eq_zero" -> "algebra", "prime_spectrum.zero_locus_Union" -> "algebraic_geometry", "seq.of_list_nil" -> "data", "writer_t.goto_mk_label" -> "control", "finsupp.prod_map_domain_index" -> "data", "measure_theory.simple_func.mem_range_self" -> "analysis", "list.disjoint_of_subset_left" -> "data", "padic_val_rat.one" -> "data", "computable.comp" -> "computability", "lucas_lehmer.X.add_snd" -> "number_theory", "ideal.bot_prime" -> "algebra", "hash_map.valid.replace_aux" -> "data", "linear_equiv.refl_trans" -> "algebra", "monotone.is_lub_image_le" -> "order", "localization_map.eq_iff_eq" -> "algebra", "filter.is_countably_generated_binfi_principal" -> "order", "option.none_bind" -> "data", "dvd_zero" -> "algebra", "deriv_within_cosh" -> "analysis", "submodule.quot_hom_ext" -> "algebra", "subring.Inf_to_add_subgroup" -> "algebra", "continuous_sub" -> "topology", "direction_affine_span" -> "algebra", "emetric.mem_ball_comm" -> "topology", "list.countp_cons_of_neg" -> "data", "int.bodd_neg_of_nat" -> "data", "neg_le_iff_add_nonneg" -> "algebra", "le_add_of_nonneg_left" -> "algebra", "is_scalar_tower.to_alg_hom_apply" -> "algebra", "div_eq_div_iff" -> "algebra", "finite_dimensional.eq_top_of_findim_eq" -> "algebra", "nhds_eq_nhds_iff" -> "topology", "list.func.get_neg" -> "data", "Class.inter_hom" -> "set_theory", "cardinal.mk_list_eq_mk" -> "set_theory", "multiset.filter_union" -> "data", "computable_pred.halting_problem" -> "computability", "tactic.ring_exp.exp_to_prod_pf" -> "tactic", "nnreal.mul_div_cancel'" -> "data", "ideal.mem_image_of_mem_map_of_surjective" -> "algebra", "nat.gcd_gcd_self_left_left" -> "data", "alist.ext" -> "data", "int.to_nat_add_one" -> "data", "category_theory.functor.equiv_functor_obj" -> "category_theory", "linear_map.dom_restrict_apply" -> "algebra", "ring_hom.map_sclosure" -> "algebra", "cardinal.le_mk_iff_exists_set" -> "set_theory", "mem_affine_span_iff_mem_of_affine_independent" -> "algebra", "cluster_pt.of_inf_left" -> "topology", "measure_theory.l1.simple_func.norm_to_simple_func" -> "analysis", "matrix.map_mul" -> "data", "is_compl.le_right_iff" -> "order", "nat.psub_eq_none" -> "data", "ordinal.add_left_cancel" -> "set_theory", "list.inter_subset_left" -> "data", "equiv.trans_to_embedding" -> "logic", "linear_map.map_coe_ker" -> "algebra", "ring.direct_limit.of.zero_exact_aux" -> "algebra", "continuous_linear_map.op_norm_nonneg" -> "analysis", "function.support_prod_subset" -> "data", "set.image_compl_subset" -> "data", "set.inter_union_distrib_left" -> "data", "is_bounded_bilinear_map.differentiable" -> "analysis", "nat.mul_eq_one_iff" -> "data", "polynomial.separable_one" -> "algebra", "composition.ones_blocks" -> "combinatorics", "is_basis.equiv_fun_total" -> "algebra", "Module.Mon_Module_equivalence_Algebra.inverse_obj_X" -> "category_theory", "finset.fold_sup_bot_singleton" -> "data", "is_basis.injective" -> "algebra", "category_theory.quotient.comp_left" -> "category_theory", "finset.prod_bij'" -> "algebra", "equiv.set.image_apply" -> "data", "generalized_continued_fraction.convergents_stable_of_terminated" -> "algebra", "setoid.eqv_classes_of_disjoint_union" -> "data", "polynomial.of_irreducible_expand_pow" -> "algebra", "polynomial.coeff_mul_monomial_zero" -> "data", "setoid.eq_iff_classes_eq" -> "data", "category_theory.limits.biprod.inl_fst_assoc" -> "category_theory", "finsupp.support_sup" -> "data", "cau_seq.bounded" -> "data", "Ico_mem_nhds_within_Iic" -> "topology", "category_theory.is_iso.inv_hom_id_assoc" -> "category_theory", "encodable.mem_decode2" -> "data", "module.End.eigenspace_div" -> "algebra", "option.ball_ne_none" -> "data", "is_glb_of_is_lub_of_tendsto" -> "topology", "int.modeq.modeq_add_fac" -> "data", "finset.sum_comp" -> "algebra", "measure_theory.l1.integral_sub" -> "analysis", "list.sublists_aux_cons_append" -> "data", "category_theory.limits.types.prod_lift" -> "category_theory", "set.countable_iff_exists_surjective_to_subtype" -> "data", "set.Ioo_self" -> "data", "category_theory.monoidal.associator_hom_app" -> "category_theory", "max_le_max" -> "algebra", "add_subgroup.normal_of_comm" -> "algebra", "measure_theory.l1.simple_func.smul_to_simple_func" -> "analysis", "fin.coe_add_nat" -> "data", "finsupp.total_comp" -> "algebra", "primrec_pred.of_eq" -> "computability", "category_theory.limits.is_image.iso_ext_inv" -> "category_theory", "matrix.diagonal_one" -> "data", "isometric.point_reflection_dist_self" -> "analysis", "list.nth_eq_some" -> "data", "measure_theory.simple_func.coe_const" -> "analysis", "nat.factors_lemma" -> "data", "nat.partrec'.nil" -> "computability", "bool.not_ff" -> "data", "uniform_space.completion.coe_zero" -> "topology", "measure_theory.measure.restrict\:2097_apply" -> "analysis", "dvd_sub_pow_of_dvd_sub" -> "number_theory", "linear_map.curry_uncurry_left" -> "algebra", "primrec.list_foldl" -> "computability", "list.count_singleton" -> "data", "metric.closed_ball_diff_sphere" -> "topology", "lt_mul_of_inv_mul_lt" -> "algebra", "mvqpf.fix.ind_aux" -> "data", "approximates_linear_on.continuous_on" -> "analysis", "ideal.span_singleton_eq_top" -> "algebra", "mv_polynomial.pderivative_add" -> "data", "neg_one_lt_zero" -> "algebra", "matrix.cons_vec_mul" -> "data", "deriv.neg" -> "analysis", "filter.tendsto.is_bounded_under_le" -> "topology", "nnreal.le_of_forall_epsilon_le" -> "data", "metric.to_glue_commute" -> "topology", "linear_equiv.mk_apply" -> "algebra", "ceil_pos" -> "algebra", "has_deriv_at.of_local_left_inverse" -> "analysis", "measure_theory.outer_measure.add_apply" -> "analysis", "polynomial.X_dvd_iff" -> "data", "category_theory.limits.biproduct.\[Iota]_\[Pi]_ne_assoc" -> "category_theory", "category_theory.comonad_hom.id_comp" -> "category_theory", "isometric.add_left_symm" -> "topology", "add_localization.r_of_eq" -> "algebra", "list.sum_range_succ'" -> "data", "associates.prod_le" -> "algebra", "neg_le_of_neg_le" -> "algebra", "polynomial.coeff_coe" -> "algebra", "embedding.map_nhds_eq" -> "topology", "lcm_assoc" -> "algebra", "stream.mem_cons" -> "data", "measure_theory.measure.regular.inner_regular_eq" -> "analysis", "category_theory.limits.limit.lift_map" -> "category_theory", "uniform_inducing.dense_inducing" -> "topology", "tendsto_locally_uniformly_on.mono" -> "topology", "category_theory.functor.pi_obj" -> "category_theory", "alg_equiv.trans_apply" -> "algebra", "int.bitwise_or" -> "data", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_inv_assoc" -> "category_theory", "is_clopen_diff" -> "topology", "heq.elim" -> "init", "subsemiring.coe_comap" -> "algebra", "homological_complex.homology_map_comp" -> "algebra", "complex.equiv_lim_aux" -> "data", "mul_inv_rev'" -> "algebra", "finsupp.smul_apply'" -> "data", "tendsto_iff_edist_tendsto_0" -> "topology", "differentiable_on.const_smul_algebra" -> "analysis", "measure_theory.measure.join_map_map" -> "analysis", "measure_theory.outer_measure.Inf_gen_nonempty1" -> "analysis", "nat.le_total" -> "init", "finset.Ico.succ_singleton" -> "data", "summable.has_sum" -> "topology", "measure_theory.integral_const" -> "analysis", "finsupp_lequiv_direct_sum_single" -> "algebra", "multiset.le_count_iff_repeat_le" -> "data", "times_cont_diff_within_at.differentiable_within_at" -> "analysis", "filter.germ.quot_mk_eq_coe" -> "order", "real.cos_nat_mul_two_pi" -> "analysis", "metric.inf_edist_ne_top" -> "topology", "pos_num.lt_to_nat" -> "data", "metric.proper_image_of_proper" -> "topology", "summable.prod_symm" -> "topology", "local_homeomorph.refl_source" -> "topology", "measurable_space.generate_from_le" -> "analysis", "category_theory.comma.map_right_id_hom_app_right" -> "category_theory", "with_bot.well_founded_lt" -> "order", "true_and" -> "init", "list.perm_cons_erase" -> "data", "int.lt_of_add_one_le" -> "init", "category_theory.types_comp" -> "category_theory", "uniform_space.completion.map_id" -> "topology", "topological_space.open_nhds.op_map_id_obj" -> "topology", "bool.bxor_comm" -> "data", "filter.mem_prod_same_iff" -> "order", "summable_geometric_of_lt_1" -> "analysis", "algebraic_geometry.SheafedSpace.comp_base" -> "algebraic_geometry", "set.finite_univ" -> "data", "subsemiring.map_map" -> "algebra", "filter.is_bounded_le_of_top" -> "order", "is_open.unique_mdiff_on" -> "geometry", "finset.disjoint_empty_left" -> "data", "multiset.add_product" -> "data", "has_fpower_series_on_ball.sub" -> "analysis", "ideal.map_sup" -> "algebra", "semiquot.pure_is_pure" -> "data", "emetric.tendsto_uniformly_iff" -> "topology", "filter.prod_bot" -> "order", "preorder_hom.coe_inj" -> "order", "local_ring.eq_maximal_ideal" -> "algebra", "has_fderiv_at_filter.sub" -> "analysis", "contracting_with.apriori_edist_iterate_efixed_point_le'" -> "topology", "ennreal.mul_lt_mul_left" -> "data", "nat.lcm_dvd" -> "data", "pell.is_pell_pell_zd" -> "number_theory", "nat.prime.ne_one" -> "data", "eq_bot_iff" -> "order", "multiset.Ico.nodup" -> "data", "option.bind_eq_none'" -> "data", "measurable.dist" -> "analysis", "int.coe_cast_ring_hom" -> "data", "dvd_add_self_left" -> "algebra", "one_div_fpow" -> "algebra", "finset.insert_val'" -> "data", "complex.deriv_cos'" -> "analysis", "zsqrtd.nonnegg_pos_neg" -> "data", "set.bUnion_singleton" -> "data", "polynomial.degree_to_subring" -> "algebra", "fintype.card_pempty" -> "data", "polynomial.irreducible_of_degree_eq_one_of_monic" -> "data", "set.maps_to_image" -> "data", "tsum_eq_zero_add" -> "topology", "filter.eventually_eq.exists_mem" -> "order", "omega.int.univ_close_of_valid" -> "tactic", "map_eq_bind_pure_comp" -> "control", "is_add_group_hom.zero_ker_neg'" -> "algebra", "padic_norm_z.norm_p_pow" -> "data", "asymptotics.is_O_norm_left" -> "analysis", "multiset.mem_union" -> "data", "nat.lt_le_antisymm" -> "init", "nhds_translation_add_neg" -> "topology", "many_one_degree.of_le_of" -> "computability", "int.sub_right_le_of_le_add" -> "init", "algebraic_geometry.LocallyRingedSpace.comp_val" -> "algebraic_geometry", "computable\:2082.part" -> "computability", "filter.is_bounded.is_bounded_under" -> "order", "eq.ge" -> "algebra", "nat.exists_dvd_of_not_prime" -> "data", "differentiable_within_at.add" -> "analysis", "times_cont_diff_fst" -> "analysis", "has_fderiv_at_boundary_of_tendsto_fderiv" -> "analysis", "znum.of_nat_cast" -> "data", "padic.coe_inj" -> "data", "int.mul_le_mul_of_nonneg_right" -> "init", "padic_norm_z.norm_one" -> "data", "int.of_nat_div" -> "data", "category_theory.monoidal_category.right_assoc_tensor_obj" -> "category_theory", "int.dist_eq" -> "topology", "zmod.cast_nat_cast'" -> "data", "free_abelian_group.pure_seq" -> "algebra", "metric.glue_dist_glued_points" -> "topology", "int.add_mul_mod_self_left" -> "data", "multiset.exists_mem_of_ne_zero" -> "data", "znum.to_int_inj" -> "data", "forall_prop_of_true" -> "logic", "abs_nonpos_iff" -> "algebra", "exists_ratio_has_deriv_at_eq_ratio_slope'" -> "analysis", "pgame.zero_le" -> "set_theory", "half_pos" -> "algebra", "interval_integral.integral_sub_linear_is_o_of_tendsto_ae" -> "analysis", "linear_map.mk_continuous_norm_le" -> "analysis", "finset.Ico.zero_bot" -> "data", "ordinal.log_def" -> "set_theory", "list.reverse_cons" -> "data", "tactic.ring.horner_mul_horner_zero" -> "tactic", "multiset.sum_map_mul_left" -> "data", "measure_theory.measure.coe_zero" -> "analysis", "asymptotics.is_O_with.add" -> "analysis", "pow_ne_zero'" -> "algebra", "div_pos_of_neg_of_neg" -> "algebra", "prod.smul_mk" -> "algebra", "is_min_filter.comp_mono" -> "order", "measure_theory.integrable.smul" -> "analysis", "equiv.subtype_equiv_codomain_apply" -> "data", "bounded_continuous_function.uniform_continuous_comp" -> "topology", "mul_nonpos_of_nonpos_of_nonneg" -> "algebra", "category_theory.limits.mono_factorisation.ext" -> "category_theory", "ordinal.nat_cast_succ" -> "set_theory", "alg_hom.map_add" -> "algebra", "ordinal.mul_ne_zero" -> "set_theory", "ordinal.add_succ" -> "set_theory", "primrec\:2082.uncurry" -> "computability", "padic_int.coe_sub" -> "data", "submodule.mem_span_insert" -> "algebra", "category_theory.over.map_map_left" -> "category_theory", "is_max_on.add" -> "order", "summable_iff_cauchy_seq_finset" -> "topology", "is_basis.smul" -> "algebra", "measure_theory.tendsto_integral_of_dominated_convergence" -> "analysis", "sum.lex_acc_inr" -> "data", "bounded_continuous_function.sub_apply" -> "topology", "is_coprime.add_mul_left_right_iff" -> "algebra", "commute.gpow_gpow_self" -> "algebra", "sylow.one_mem_fixed_points_rotate" -> "algebra", "ennreal.is_open_ne_top" -> "topology", "prime_spectrum.mem_vanishing_ideal" -> "algebraic_geometry", "differentiable_within_at.has_deriv_within_at" -> "analysis", "wseq.lift_rel.swap_lem" -> "data", "algebra.lmul'_apply" -> "algebra", "num.le_iff_cmp" -> "data", "fin.succ_above_below" -> "data", "measure_theory.measure.measurable_of_measurable_coe" -> "analysis", "zsqrtd.of_int_re" -> "data", "lie_algebra.equiv.one_apply" -> "algebra", "cardinal.prod_ne_zero" -> "set_theory", "nat.max_succ_succ" -> "data", "rat.lt_one_iff_num_lt_denom" -> "data", "real.uniform_continuous_neg" -> "topology", "complex.of_real_inj" -> "data", "cInf_mem_closure" -> "topology", "filter.mem_bind_sets" -> "order", "vadd_vsub_vadd_cancel_right" -> "algebra", "dist_neg_neg" -> "analysis", "finset.bind_singleton" -> "data", "filter.eventually_eq.deriv_within_eq" -> "analysis", "finset.compl_eq_univ_sdiff" -> "data", "list.drop_sum_join" -> "data", "rat.cast_sub_of_ne_zero" -> "data", "le_sup_left_of_le" -> "order", "commute.units_inv_left" -> "algebra", "equiv.forall_congr'" -> "data", "is_R_or_C.im_le_abs" -> "data", "gt_mem_nhds" -> "topology", "is_subgroup.coe_gpow" -> "algebra", "multiset.sub_add_inter" -> "data", "quot.exact" -> "init", "inf_infi" -> "order", "nnreal.rpow_add" -> "analysis", "finset.sdiff_subset_self" -> "data", "num.succ_to_nat" -> "data", "is_compl.sup_eq_top" -> "order", "metric.ball_half_subset" -> "topology", "multiset.count_eq_one_of_mem" -> "data", "galois_insertion.l_infi_of_ul_eq_self" -> "order", "ge.le" -> "algebra", "finset.min_insert" -> "data", "category_theory.differential_object.comp_f" -> "category_theory", "num.cast_zero" -> "data", "filter.map_eq_of_inverse" -> "order", "finset.sum_subtype_map_embedding" -> "algebra", "wseq.dropn_nil" -> "data", "multiset.inter_eq_zero_iff_disjoint" -> "data", "multiset.attach_map_val" -> "data", "computation.get_eq_of_promises" -> "data", "cardinal.aleph'_zero" -> "set_theory", "fin.mem_find_iff" -> "data", "asymptotics.is_o.const_mul_right" -> "analysis", "int.add_assoc" -> "init", "set.pairwise_on.mono" -> "data", "list.not_mem_keys" -> "data", "discrete_valuation_ring.aux_pid_of_ufd_of_unique_irreducible" -> "algebra", "ordinal.sup_le" -> "set_theory", "linear_map.ker_eq_bot_iff_range_eq_top" -> "algebra", "free_ring.coe_one" -> "algebra", "zero_fpow" -> "algebra", "typevec.append_fun_comp" -> "data", "nhds_translation_mul_inv" -> "topology", "stream.nth_even" -> "data", "has_sum_geometric_two" -> "analysis", "filter.comap_add_comap_le" -> "order", "pmf.map_id" -> "analysis", "times_cont_diff_on.of_le" -> "analysis", "is_valid_char_range_2" -> "init", "free_abelian_group.lift.zero" -> "algebra", "measure_theory.lintegral_smul_measure" -> "analysis", "ennreal.tsum_sigma" -> "topology", "abs_inner_div_norm_mul_norm_le_one" -> "analysis", "set.preimage_mul_const_Ico" -> "data", "submodule.quotient_equiv_of_is_compl_apply_mk_coe" -> "algebra", "congr_arg2" -> "logic", "filter.has_basis.le_basis_iff" -> "order", "multiset.coe_bind" -> "data", "measure_theory.measure_eq_infi" -> "analysis", "zsqrtd.nonneg_mul_lem" -> "data", "semidirect_product.inl_injective" -> "algebra", "matrix.special_linear_group.mul_apply" -> "algebra", "affine_independent_iff_indicator_eq_of_affine_combination_eq" -> "algebra", "finset.sum_div" -> "algebra", "sylow.mem_vectors_prod_eq_one" -> "algebra", "geom_lt" -> "analysis", "filter.comap_inf_principal_ne_bot_of_image_mem" -> "order", "filter.germ.coe_neg" -> "order", "multiset.join_zero" -> "data", "category_theory.limits.prod_comparison_natural_assoc" -> "category_theory", "wseq.exists_of_mem_bind" -> "data", "ideal.span_mono" -> "algebra", "matrix.std_basis_eq_basis_mul_basis" -> "data", "subtype.image_preimage_val" -> "data", "category_theory.limits.limit.cone_morphism_\[Pi]" -> "category_theory", "function.is_fixed_pt.eq" -> "dynamics", "nat.mul_div_cancel_left'" -> "data", "pos_num.cast_to_int" -> "data", "measure_theory.simple_func.fin_meas_supp.lintegral_lt_top" -> "analysis", "multiplicative.is_group_hom" -> "algebra", "add_submonoid.localization_map.of_add_equiv_of_dom_apply" -> "algebra", "unique.forall_iff" -> "logic", "linear_map.bound_of_continuous" -> "analysis", "int.lt_add_one_iff" -> "data", "emetric.ball_zero" -> "topology", "category_theory.limits.as_factor_thru_image" -> "category_theory", "multiset.disjoint_cons_right" -> "data", "bex_congr" -> "logic", "encodable.axiom_of_choice" -> "data", "vector.ext" -> "data", "auto.not_not_eq" -> "tactic", "local_homeomorph.symm_target" -> "topology", "set.mem_bInter_iff" -> "data", "rel.image_subset_iff" -> "data", "tendsto_one_div_add_at_top_nhds_0_nat" -> "analysis", "ennreal.Ico_eq_Iio" -> "data", "is_conj_symm" -> "algebra", "semiconj_by.units_coe" -> "algebra", "times_cont_diff_top" -> "analysis", "set.preimage_const_mul_Ioi" -> "data", "polynomial.coe_norm_unit" -> "data", "category_theory.adjunction.eq_hom_equiv_apply" -> "category_theory", "nnreal.inv_inv" -> "data", "set.diff_empty" -> "data", "units.inv_mul" -> "algebra", "complex.continuous_linear_map.of_real_norm" -> "analysis", "set.nonempty.inl" -> "data", "topological_space.opens.map_comp_obj_unop" -> "topology", "array.read_map\:2082" -> "data", "continuous_linear_map.norm_map_tail_le" -> "analysis", "set.mem_Ioo" -> "data", "differentiable_at.comp" -> "analysis", "gaussian_int.nat_cast_real_norm" -> "data", "set.finite.image2" -> "data", "submodule.add_mem" -> "algebra", "sesq_form.smul_right" -> "algebra", "subsemiring.top_prod_top" -> "algebra", "nat.lor_assoc" -> "data", "int.le_of_sub_nonpos" -> "init", "ennreal.coe_le_one_iff" -> "data", "list.nth_le_index_of" -> "data", "set.singleton_add" -> "algebra", "set.pairwise_on_univ" -> "data", "frobenius_sub" -> "algebra", "left_coset_mem_left_coset" -> "algebra", "le_sub" -> "algebra", "fpow_le_one_of_nonpos" -> "algebra", "has_deriv_within_at.pow" -> "analysis", "reader_t.run_read" -> "init", "metric.ball_disjoint" -> "topology", "rat.cast_inv_of_ne_zero" -> "data", "fpow_neg_one" -> "algebra", "category_theory.limits.nonzero_image_of_nonzero" -> "category_theory", "finsupp.supr_lsingle_range" -> "algebra", "polynomial.roots_map" -> "algebra", "smul_mul'" -> "algebra", "ennreal.rpow_eq_top_iff" -> "analysis", "enat.coe_one" -> "data", "list.subset_append_of_subset_right" -> "data", "primrec.of_nat_iff" -> "computability", "real.log_lt_log_iff" -> "analysis", "local_equiv.restr_coe_symm" -> "data", "dense_Inter_of_G\[Delta]" -> "topology", "smooth_at_snd" -> "geometry", "punit.mul_eq" -> "algebra", "is_coprime.pow" -> "algebra", "set.card_fintype_insert'" -> "data", "units.mul_left_symm" -> "data", "ennreal.coe_nnreal_eq" -> "data", "sub_left_le_of_le_add" -> "algebra", "int.exists_gcd_one'" -> "algebra", "is_bounded_bilinear_map.is_bounded_linear_map_right" -> "analysis", "holor_index.cast_type" -> "data", "padic_seq.norm_one" -> "data", "measure_theory.integrable_on.mono_set_ae" -> "analysis", "nat.fact_eq_one" -> "data", "multiset.erase_le_erase" -> "data", "nnreal.one_div_div" -> "data", "real.arcsin_neg_one" -> "analysis", "multiset.fold_cons'_left" -> "data", "set.image_insert_eq" -> "data", "category_theory.limits.cocones.functoriality_map_hom" -> "category_theory", "finset.sigma_mono" -> "data", "ring.direct_limit.lift_unique" -> "algebra", "category_theory.monad.forget_creates_limits.lifted_cone_is_limit_lift_f" -> "category_theory", "max_comm" -> "init", "mul_semiring_action_hom.ext" -> "algebra", "nat.div_pos" -> "data", "filter.disjoint_iff" -> "order", "compact_range" -> "topology", "bdd_above_insert" -> "order", "mv_power_series.coeff_trunc" -> "algebra", "category_theory.limits.cocones.precompose_equivalence_inverse" -> "category_theory", "filter.liminf_le_liminf" -> "order", "quadratic_form.map_smul" -> "algebra", "linear_map.ker_eq_bot" -> "algebra", "fpow_lt_iff_lt" -> "algebra", "list.nodup_map_on" -> "data", "nat.bit0_val" -> "init", "seq.mem_cons" -> "data", "has_ftaylor_series_up_to_on.comp_continuous_linear_map" -> "analysis", "is_local_max_on.has_fderiv_within_at_eq_zero" -> "analysis", "pgame.equiv_symm" -> "set_theory", "generalized_continued_fraction.zeroth_convergent'_aux_eq_zero" -> "algebra", "associates.prod_factors" -> "algebra", "primrec.nat_bit0" -> "computability", "int.div_neg" -> "data", "pequiv.is_some_symm_get" -> "data", "affine_map.coe_id" -> "algebra", "to_topological_space_prod" -> "topology", "ennreal.mul_lt_mul_right" -> "data", "cSup_le_cSup" -> "order", "set.smul_mem_smul_set" -> "algebra", "category_theory.limits.cocone.naturality_concrete" -> "category_theory", "measurable_space.is_measurable_inf" -> "analysis", "finset.prod_le_prod'" -> "algebra", "category_theory.yoneda_map_app" -> "category_theory", "set.image_subset_iff" -> "data", "convex_Ioo" -> "analysis", "stream.eq_or_mem_of_mem_cons" -> "data", "turing.partrec_to_TM2.tr_nat_nat_end" -> "computability", "int.lt.elim" -> "init", "one_le_one_div" -> "algebra", "times_cont_mdiff_within_at.congr" -> "geometry", "int.mul_pos_of_neg_of_neg" -> "init", "has_mfderiv_within_at_id" -> "geometry", "list.forall\:2082_cons" -> "data", "ring_equiv.map_add" -> "data", "add_monoid_hom.eq_on_neg" -> "algebra", "alist.keys_singleton" -> "data", "filter.rmap_compose" -> "order", "algebra.commutes" -> "algebra", "set.image_preimage_eq" -> "data", "lt_iff_not_ge" -> "init", "cardinal.mk_cardinal" -> "set_theory", "continuous_linear_map.coe_sub" -> "topology", "dist_triangle4_left" -> "topology", "list.drop_add" -> "data", "filter.has_basis_binfi_principal" -> "order", "add_le_of_le_neg_add" -> "algebra", "ideal.mul_left_self_sup" -> "algebra", "finset.range_succ" -> "data", "nat.find_greatest_eq_zero" -> "data", "category_theory.limits.cocone.extend_\[Iota]" -> "category_theory", "tendsto_add_one_pow_at_top_at_top_of_pos" -> "analysis", "pgame.numeric_neg" -> "set_theory", "equiv.add_right_symm" -> "data", "inv_mul_cancel_of_invertible" -> "algebra", "is_add_group_hom.mk'" -> "algebra", "cau_seq.const_inj" -> "data", "lucas_lehmer.int.coe_nat_pow_pred" -> "number_theory", "Set.mem_prod" -> "set_theory", "list.nth_le_range" -> "data", "nontrivial_iff" -> "logic", "enorm.map_sub_rev" -> "analysis", "wseq.lift_rel_cons" -> "data", "submonoid.localization_map.lift_left_inverse" -> "algebra", "nat.find_min'" -> "init", "ordinal.not_zero_is_limit" -> "set_theory", "cardinal.powerlt_le" -> "set_theory", "con.ker_rel" -> "algebra", "pfunctor.id_map" -> "data", "lie_algebra.special_linear.E_diag_zero" -> "algebra", "rel_iso.coe_coe_fn" -> "order", "category_theory.monoidal.tensor_apply" -> "category_theory", "lipschitz_with.ediam_image_le" -> "topology", "real.neg_pi_div_two_le_arcsin" -> "analysis", "finset.eq_zero_of_sum_eq_zero" -> "algebra", "continuous_linear_map.ker_prod" -> "topology", "measurable.inv'" -> "analysis", "polynomial.mem_roots_sub_C" -> "data", "pell.pell_eq" -> "number_theory", "category_theory.lax_monoidal_functor.comp_\[CurlyEpsilon]" -> "category_theory", "emetric.continuous_inf_edist_Hausdorff_edist" -> "topology", "deriv_ccos" -> "analysis", "category_theory.limits.types.pi_\[Pi]" -> "category_theory", "int.cast_add" -> "data", "multiset.mem_map_of_mem" -> "data", "add_subgroup.map_le_iff_le_comap" -> "algebra", "finset.Ico.not_mem_top" -> "data", "mul_right_cancel'" -> "algebra", "filter.hyperfilter_le_cofinite" -> "order", "power_series.ext" -> "algebra", "linear_map.quot_ker_equiv_range_apply_mk" -> "algebra", "dist_eq_norm" -> "analysis", "measure_theory.measure.haar_measure_self" -> "analysis", "multiset.mem_filter_of_mem" -> "data", "dfinsupp.support_zero" -> "data", "set.preimage_const_add_Ioc" -> "data", "bilin_form.to_matrix_mul" -> "algebra", "list.forall\:2082_nil_left_iff" -> "data", "subring.closure_preimage_le" -> "algebra", "polynomial.map_dvd_map'" -> "data", "is_monoid_hom.map_pow" -> "algebra", "finset.mem_insert_none" -> "data", "array.to_list_foldl" -> "data", "ennreal.measurable_coe" -> "analysis", "filter.germ.coe_smul" -> "order", "pow_sub'" -> "algebra", "nat.with_bot.add_eq_one_iff" -> "data", "polynomial.nat_degree_derivative_lt" -> "data", "supr_or" -> "order", "fin.coe_eq_val" -> "data", "category_theory.monoidal_category.tensor_left_obj" -> "category_theory", "asymptotics.is_o_const_mul_left_iff'" -> "analysis", "cauchy_seq_iff_tendsto_dist_at_top_0" -> "topology", "measure_theory.l1.simple_func.pos_part_to_simple_func" -> "analysis", "classical.some_spec2" -> "logic", "pos_num.to_nat_inj" -> "data", "mem_affine_span" -> "algebra", "fintype.card_eq_zero_iff" -> "data", "inner_self_nonpos" -> "analysis", "real.log_one" -> "analysis", "asymptotics.is_O.trans_tendsto" -> "analysis", "hyperreal.infinite_neg_of_tendsto_bot" -> "data", "finsupp.linear_independent_single" -> "algebra", "constr_self" -> "algebra", "submodule.coe_of_le" -> "algebra", "category_theory.comma_morphism.ext" -> "category_theory", "is_max_filter.comp_antimono" -> "order", "tangent_map_within_subset" -> "geometry", "is_basis_of_linear_independent_of_card_eq_findim" -> "algebra", "multiset.repeat_subset_singleton" -> "data", "multiset.nodup_iff_pairwise" -> "data", "algebraic_geometry.SheafedSpace.as_coe" -> "algebraic_geometry", "basic_smooth_bundle_core.times_cont_mdiff_within_at_proj" -> "geometry", "order_eq_card_gpowers" -> "algebra", "has_strict_fderiv_at.const_smul_algebra" -> "analysis", "nnreal.le_div_iff_mul_le" -> "data", "metric.diam_singleton" -> "topology", "decidable.iff_not_comm" -> "logic", "Top.presheaf.germ_res_apply" -> "topology", "measure_theory.simple_func.restrict_lintegral_eq_lintegral_restrict" -> "analysis", "one_gpow" -> "algebra", "right_comm" -> "init", "smodeq.map" -> "algebra", "function.injective.eq_iff" -> "logic", "is_integral_tower_top_of_is_integral" -> "algebra", "multiset.count_singleton" -> "data", "category_theory.limits.pushout.condition" -> "category_theory", "mem_own_right_coset" -> "algebra", "multilinear_map.map_coord_zero" -> "algebra", "nnreal.mul_inv_cancel" -> "data", "le_max_left" -> "init", "Inf_le_Sup" -> "order", "filter.unbounded_of_tendsto_at_bot" -> "order", "set.range_find_greatest_subset" -> "data", "tendsto_smul" -> "topology", "multiset.fold_cons_right" -> "data", "algebra.tensor_product.one_mul" -> "algebra", "int.add_neg_of_nonpos_of_neg" -> "init", "normed_field.norm_prod" -> "analysis", "basic_smooth_bundle_core.chart_target" -> "geometry", "well_founded.well_founded_iff_has_min'" -> "order", "polynomial.monic_to_subring" -> "algebra", "pell.xz_succ" -> "number_theory", "measure_theory.outer_measure.trim_eq_infi" -> "analysis", "surj_on_Ioi_of_monotone_surjective" -> "data", "complex.norm_int_of_nonneg" -> "analysis", "is_add_group_hom.trivial_ker_iff_eq_zero" -> "algebra", "topological_space.opens.coe_inf" -> "topology", "category_theory.limits.types.terminal" -> "category_theory", "mul_inv" -> "algebra", "is_open.is_open_map_subtype_coe" -> "topology", "differentiable_at.sinh" -> "analysis", "finset.inf_congr" -> "data", "submonoid.localization_map.surj" -> "algebra", "derivation.add_apply" -> "algebra", "is_compact.is_greatest_Sup" -> "topology", "continuous_on.mul" -> "topology", "is_lub.of_image" -> "order", "category_theory.comma.map_left_comp_inv_app_right" -> "category_theory", "list.lookmap_map_eq" -> "data", "gold_conj_sq" -> "data", "subsemiring.closure_mono" -> "algebra", "linear_map.ker_eq_bot'" -> "algebra", "finset.not_mem_singleton" -> "data", "list.exists_of_mem_bind" -> "data", "multiset.inter_zero" -> "data", "real.sin_pos_of_pos_of_lt_pi" -> "analysis", "prime_spectrum.sup_vanishing_ideal_le" -> "algebraic_geometry", "div_neg_of_pos_of_neg" -> "algebra", "roption.some_get" -> "data", "measure_theory.lebesgue_outer_Ioc" -> "analysis", "nat.cases_zero" -> "computability", "alist.insert_entries" -> "data", "vector.to_list_take" -> "data", "finset.le_sum_of_subadditive" -> "algebra", "semimodule.smul_eq_smul" -> "algebra", "formal_multilinear_series.comp_along_composition_multilinear_bound" -> "analysis", "rat.nonneg_total" -> "data", "supr_unit" -> "order", "filter.has_basis.is_basis" -> "order", "bit0_nsmul" -> "algebra", "fintype.preorder.well_founded" -> "data", "list.nodup_singleton" -> "data", "principal_ideal_ring.ring_hom_mem_submonoid_of_factors_subset_of_units_subset" -> "algebra", "emetric.cauchy_seq_iff" -> "topology", "le_of_tendsto" -> "topology", "ennreal.add_sub_self" -> "data", "punit.ext" -> "tactic", "zmod.coe_mul_inv_eq_one" -> "data", "real.cos_int_mul_two_pi" -> "analysis", "zorn.chain_closure_succ_fixpoint" -> "order", "int.mul_div_cancel'" -> "data", "category_theory.nat_trans.prod_app" -> "category_theory", "computation.of_thinkN_terminates" -> "data", "algebra.lmul_apply" -> "algebra", "le_mul_inv_of_mul_le" -> "algebra", "monoid_algebra.support_mul" -> "data", "is_bounded_linear_map.is_O_id" -> "analysis", "linear_map.range_zero" -> "algebra", "add_semiconj_by.add_right" -> "algebra", "subspace.closed_complemented_of_closed_compl" -> "analysis", "category_theory.differential_object.id_f" -> "category_theory", "is_local_max_on.bicomp_mono" -> "topology", "convex.add" -> "analysis", "nat.rfind_dom'" -> "computability", "metric.nhds_basis_ball_inv_nat_succ" -> "topology", "cardinal.lift_id'" -> "set_theory", "category_theory.non_preadditive_abelian.lift_\[Sigma]_assoc" -> "category_theory", "mul_le_of_le_one_of_le'" -> "algebra", "circle_deg1_lift.le_translation_number_of_add_nat_le" -> "dynamics", "nat.le_of_eq" -> "init", "is_min_on.inf" -> "order", "sum_range_choose_halfway" -> "data", "forall_iff_forall_surj" -> "logic", "finset.map_union" -> "data", "category_theory.limits.map_pair_iso_hom" -> "category_theory", "continuous_on.sub" -> "topology", "nat.zero_lt_succ" -> "init", "set.Icc_subset_Icc_union_Ioc" -> "data", "differentiable_within_at.const_sub" -> "analysis", "subring.mem_coe" -> "algebra", "padic.exi_rat_seq_conv" -> "data", "has_deriv_at_filter_id" -> "analysis", "circle_deg1_lift.translation_number_conj_eq" -> "dynamics", "antimono_of_deriv_nonpos" -> "analysis", "category_theory.limits.cocones.whiskering_equivalence_unit_iso" -> "category_theory", "dfinsupp.single_add_erase" -> "data", "local_homeomorph.refl_coe" -> "topology", "ideal.mem_sup_left" -> "algebra", "hash_map.valid.replace" -> "data", "list.bag_inter_nil" -> "data", "is_lub.mono" -> "order", "nat.sqrt_aux_dec" -> "data", "max_sub_min_eq_abs'" -> "algebra", "nat.gcd_gcd_self_right_right" -> "data", "add_monoid_hom.mul_right_apply" -> "algebra", "sdiff_eq_left" -> "order", "finset.inter_sdiff_self" -> "data", "free_group.reduce.self" -> "algebra", "category_theory.comma.map_right_comp_inv_app_left" -> "category_theory", "int.pow_dvd_pow_iff" -> "algebra", "set.diff_diff_cancel_left" -> "data", "mv_power_series.add_mul" -> "algebra", "sub_le_of_sub_le" -> "algebra", "finset.sdiff_singleton_eq_erase" -> "data", "neg_lt_neg" -> "algebra", "finset.sum_flip" -> "algebra", "matrix.scalar_apply_eq" -> "data", "simple_graph.adj_matrix_mul_vec_const_apply_of_regular" -> "combinatorics", "fintype.injective_iff_bijective" -> "data", "nat.not_even_iff" -> "data", "nat.dvd_one" -> "data", "div_div_self" -> "algebra", "prod.norm_def" -> "analysis", "measure_theory.outer_measure.is_caratheodory_union" -> "analysis", "real.continuous_at_log" -> "analysis", "nat.coprime.dvd_of_dvd_mul_left" -> "data", "tactic.ring.pow_succ" -> "tactic", "localization_map.mk'_eq_of_eq" -> "algebra", "ring.fractional_ideal.coe_one" -> "algebra", "filter.not_eventually" -> "order", "composition.mem_range_embedding_iff" -> "combinatorics", "measure_theory.outer_measure.union" -> "analysis", "function.surjective.sum_map" -> "data", "multiset.to_finset_card_le" -> "data", "denumerable.lower_raise'" -> "data", "set.Ioc_union_Ico_eq_Ioo" -> "data", "units.inv_eq_self_iff" -> "algebra", "units.lift_right_inv_mul" -> "algebra", "has_deriv_at.lhopital_zero_nhds'" -> "analysis", "binfi_le_binfi" -> "order", "enat.lt_add_iff_pos_right" -> "data", "eq_zero_of_mul_self_eq_zero" -> "algebra", "function.semiconj.inj_on_preimage" -> "data", "squeeze_zero" -> "topology", "associates.mk_le_mk_of_dvd" -> "algebra", "int.lt_of_coe_nat_lt_coe_nat" -> "init", "finsupp.prod_ite_eq" -> "data", "is_subfield_Union_of_directed" -> "algebra", "localization_map.map_units" -> "algebra", "polynomial.degree_zero" -> "data", "filter.is_ultrafilter_hyperfilter" -> "order", "finite_field.pow_card" -> "algebra", "is_min_on.comp_mono" -> "order", "affine_subspace.mem_top" -> "algebra", "category_theory.limits.bicone_\[Iota]_\[Pi]_ne" -> "category_theory", "fin.coe_one" -> "data", "sequentially_complete.set_seq_prod_subset" -> "topology", "direct_sum.mk_sub" -> "algebra", "multiset.induction_on_multiset_quot" -> "data", "set.range_sigma_eq_Union_range" -> "data", "units.coe_map'" -> "algebra", "pos_num.size_to_nat" -> "data", "fpow_one_add" -> "algebra", "nat.size_le" -> "data", "category_theory.functor.map_cone_\[Pi]" -> "category_theory", "list.erasep_nil" -> "data", "lt_mul_of_one_le_of_lt" -> "algebra", "category_theory.limits.limit.lift_extend" -> "category_theory", "gaussian_int.prime_iff_mod_four_eq_three_of_nat_prime" -> "data", "category_theory.limits.cokernel.desc_zero" -> "category_theory", "stream.map_cons" -> "data", "monoid_algebra.single_mul_apply" -> "data", "csupr_le" -> "order", "totally_bounded_iff_ultrafilter" -> "topology", "category_theory.limits.types.prod_fst" -> "category_theory", "add_comm_group.is_Z_bilin.neg_left" -> "topology", "setoid.classes_inj" -> "data", "formal_multilinear_series.mem_comp_partial_sum_target_iff" -> "analysis", "mono_harmonic" -> "analysis", "measure_theory.measure.haar.chaar_mono" -> "analysis", "ring.inverse_unit" -> "algebra", "many_one_degree.le_comap_left" -> "computability", "list.subset_cons" -> "init", "category_theory.abelian.coimages.coimage_strong_epi_mono_factorisation_to_mono_factorisation_e" -> "category_theory", "category_theory.nat_iso.unop_inv" -> "category_theory", "prime_spectrum.is_closed_iff_zero_locus" -> "algebraic_geometry", "path.extend_zero" -> "topology", "localization_map.mk'_mul_mk'_eq_one'" -> "algebra", "list.sum_reverse" -> "data", "alg_equiv.coe_fun_injective" -> "algebra", "bor_coe_iff" -> "init", "sup_inf_left" -> "order", "asymptotics.is_o.congr'" -> "analysis", "inf_eq_left" -> "order", "norm_num.nonneg_pos" -> "tactic", "free_add_semigroup.pure_bind" -> "algebra", "padic_norm_e.image'" -> "data", "equiv.comp_traverse" -> "control", "composition.to_composition_as_set_length" -> "combinatorics", "multiset.sup_eq_union" -> "data", "ring_equiv.coe_mul_equiv_refl" -> "data", "differentiable_id'" -> "analysis", "classical.dec_rel" -> "logic", "filter.filter_eq" -> "order", "category_theory.limits.mono_factorisation_zero_I" -> "category_theory", "list.mem_sublists'" -> "data", "powers.mul_mem" -> "algebra", "list.nodup_erase_dup" -> "data", "continuous_induced_rng" -> "topology", "dioph.eq_dioph" -> "number_theory", "add_submonoid.coe_zero" -> "algebra", "mul_lt_of_lt_of_lt_one" -> "algebra", "linear_map.fst_apply" -> "algebra", "measure_theory.measure.map_map" -> "analysis", "equiv.subtype_preimage_symm_apply_coe" -> "data", "list.length_le_sum_of_one_le" -> "data", "qpf.fix.dest_mk" -> "data", "uniform_continuous_subtype_val" -> "topology", "is_lub_Iio" -> "order", "cardinal.aleph'.rel_iso_coe" -> "set_theory", "set.indicator_union_of_disjoint" -> "data", "tactic.ring.horner_const_mul" -> "tactic", "category_theory.limits.cokernel_comp_is_iso_hom" -> "category_theory", "localization_map.mk'_sec" -> "algebra", "set.indicator_nonpos" -> "data", "norm_num.lt_neg_pos" -> "tactic", "nnreal.rpow_neg_one" -> "analysis", "mem_closure_iff_comap_ne_bot" -> "topology", "associates.out_one" -> "algebra", "free_monoid.comp_lift" -> "algebra", "fintype.surjective_iff_bijective" -> "data", "continuous_multilinear_map.coe_continuous" -> "topology", "semidirect_product.inl_left_mul_inr_right" -> "algebra", "fin.coe_clamp" -> "data", "norm_num.subst_into_neg" -> "tactic", "continuous_at_iff_continuous_left'_right'" -> "topology", "ext_chart_at_target_mem_nhds_within" -> "geometry", "le_of_mul_le_of_one_le" -> "algebra", "pos_num.cmp_to_nat" -> "data", "multiset.inter_comm" -> "data", "finset.mem_inter_of_mem" -> "data", "pnat.add_one_le_iff" -> "data", "deriv_within_univ" -> "analysis", "linear_equiv.is_basis" -> "algebra", "lucas_lehmer.X.int_coe_fst" -> "number_theory", "generalized_continued_fraction.denominators_stable_of_terminated" -> "algebra", "category_theory.monoidal_category.unitors_equal.cells_5_6" -> "category_theory", "filter.has_basis.filter_eq" -> "order", "complex.cpow_mul" -> "analysis", "padic_int.p_nonnunit" -> "data", "cauchy.mono" -> "topology", "nat.add_sub_cancel" -> "init", "mem_right_coset_iff" -> "algebra", "complex.abs_of_nonneg" -> "data", "turing.fun_respects" -> "computability", "Pi.uniform_continuous_proj" -> "topology", "measure_theory.exists_nonempty_inter_of_measure_univ_lt_sum_measure" -> "analysis", "category_theory.limits.colimit.\[Iota]_map" -> "category_theory", "list.nodup_of_nodupkeys" -> "data", "list.foldl_eq_foldr'" -> "data", "set.Icc_subset_Iic_self" -> "data", "filter.eventually_imp_distrib_right" -> "order", "interior_subset" -> "topology", "is_monoid_hom.map_mul" -> "algebra", "nat.fib_succ_succ" -> "data", "submodule.comap_map_mkq" -> "algebra", "int.cast_min" -> "data", "category_theory.limits.colimit.pre_desc" -> "category_theory", "equiv.fun_unique_apply" -> "data", "enat.ne_top_iff" -> "data", "nat.mul_le_mul_of_nonneg_left" -> "init", "category_theory.monoidal_category.comp_tensor_id" -> "category_theory", "nat.sqrt_pos" -> "data", "category_theory.single_obj.map_hom_id" -> "category_theory", "category_theory.limits.kernel_comp_is_iso_inv_comp_kernel_\[Iota]" -> "category_theory", "sum.id_traverse" -> "control", "finset.supr_coe" -> "data", "alg_hom.coe_to_add_monoid_hom" -> "algebra", "continuous.to_sequentially_continuous" -> "topology", "quadratic_form.neg_apply" -> "algebra", "affine_subspace.direction_lt_of_nonempty" -> "algebra", "div_le_div_of_le_of_nonneg" -> "algebra", "polynomial.eval\:2082_X" -> "data", "inv_injective" -> "algebra", "emetric.Hausdorff_edist_le_ediam" -> "topology", "gpow_bit1" -> "algebra", "category_theory.monad_hom.assoc" -> "category_theory", "fin.mk_bit1" -> "data", "category_theory.is_iso.inv_eq_inv" -> "category_theory", "subsemiring.coe_subtype" -> "algebra", "supr_eq_bot" -> "order", "zsqrtd.of_int_eq_coe" -> "data", "submodule.Inf_orthogonal" -> "analysis", "not_le_of_lt" -> "algebra", "int.nonneg.elim" -> "init", "nat.sub_pos_of_lt" -> "init", "finset.powerset_mono" -> "data", "finset.sum_centroid_weights_eq_one_of_card_eq_add_one" -> "algebra", "category_theory.epi_of_epi_fac" -> "category_theory", "joined.refl" -> "topology", "topological_space_eq" -> "topology", "category_theory.tensoring_right_monoidal_to_lax_monoidal_functor_to_functor" -> "category_theory", "le_of_inf_eq" -> "order", "zmod.legendre_sym_eq_pow" -> "number_theory", "power_series.order_X_pow" -> "algebra", "poly_equiv_tensor_apply" -> "algebra", "has_fderiv_within_at.fst" -> "analysis", "real.cos_sub" -> "data", "times_cont_mdiff.of_succ" -> "geometry", "category_theory.monoidal_category.left_unitor_inv_naturality" -> "category_theory", "antilipschitz_with.comp" -> "topology", "add_monoid_hom.coe_mk" -> "algebra", "galois_connection.l_le" -> "order", "category_theory.limits.bicone.to_binary_bicone_X" -> "category_theory", "right_ne_zero_of_mul_eq_one" -> "algebra", "ordinal.mul_le_mul_iff_left" -> "set_theory", "is_max_on.comp_mono" -> "order", "localization_map.is_integer_smul" -> "algebra", "quot.ind_beta" -> "init", "ring_equiv.ext" -> "data", "irrational.add_rat" -> "data", "category_theory.limits.types.lift_\[Pi]_apply" -> "category_theory", "dim_pi" -> "algebra", "finmap.lookup_insert_of_ne" -> "data", "is_least.mono" -> "order", "category_theory.equivalence.inverse_counit_inv_comp" -> "category_theory", "add_monoid_hom.snd_comp_inr" -> "algebra", "equiv.coe_fn_symm_mk" -> "data", "list.length_split_le" -> "data", "set.prod_eq_empty_iff" -> "data", "filter.map_comap" -> "order", "asymptotics.is_O_with.mul" -> "analysis", "metric.Hausdorff_dist_zero_iff_eq_of_closed" -> "topology", "inf_sup_right" -> "order", "multiset.coe_reverse" -> "data", "category_theory.limits.prod_comparison_natural" -> "category_theory", "list.sum_erase" -> "data", "is_R_or_C.norm_sq_nonneg" -> "data", "digits_add_two_add_one" -> "data", "list.nth_le_reverse" -> "data", "continuous_linear_equiv.unique_diff_on_preimage_iff" -> "analysis", "fderiv_sub_const" -> "analysis", "finset.prod_multiset_count" -> "algebra", "neg_add_cancel_right" -> "algebra", "filter.Liminf_le_of_le" -> "order", "int.modeq.mod_modeq" -> "data", "algebra.adjoin_mono" -> "algebra", "stream.mem_append_stream_left" -> "data", "polynomial.degree_eq_bot" -> "data", "ordinal.lift_inj" -> "set_theory", "convex.norm_image_sub_le_of_norm_fderiv_within_le" -> "analysis", "support_scale_roots_le" -> "algebra", "times_cont_diff.continuous_iterated_deriv" -> "analysis", "generalized_continued_fraction.exists_conts_b_of_denom" -> "algebra", "orthogonal_projection_fn_eq" -> "analysis", "finset.inf_mono_fun" -> "data", "free_add_magma.add_bind" -> "algebra", "measure_theory.ae_eq_fun.mk_add_mk" -> "analysis", "vsub_vadd_eq_vsub_sub" -> "algebra", "multiset.card_join" -> "data", "nnnorm_norm" -> "analysis", "category_theory.limits.functor_category_colimit_cocone_\[Iota]_app_app" -> "category_theory", "subgroup.normal_closure_subset_iff" -> "algebra", "circle_deg1_lift.commute_sub_nat" -> "dynamics", "convex.norm_image_sub_le_of_norm_fderiv_within_le'" -> "analysis", "finset.not_mem_range_self" -> "data", "presented_group.to_group.one" -> "algebra", "with_top.coe_nat" -> "data", "infinite.of_injective" -> "data", "ennreal.div_eq_top" -> "data", "free_ring.coe_sub" -> "algebra", "multiset.Ico.succ_top" -> "data", "multiset.disjoint_of_le_left" -> "data", "finset.le_inf" -> "data", "times_cont_mdiff_on.times_cont_mdiff_on_tangent_map_within_aux" -> "geometry", "int.coe_nat_add_one_out" -> "init", "tangent_map_proj" -> "geometry", "polynomial.map_to_subring" -> "algebra", "filter.tendsto.congr_dist" -> "topology", "bdd_below_Ici" -> "order", "tendsto_at_top_mul_right'" -> "analysis", "incomp_trans" -> "init", "category_theory.whiskering_right_obj_map" -> "category_theory", "rat.cast_neg" -> "data", "metric.inf_dist_image" -> "topology", "submonoid.map_inr" -> "algebra", "filter.frequently.mp" -> "order", "prod_mem_nhds_sets" -> "topology", "num.cast_add" -> "data", "option.traverse_eq_map_id" -> "control", "mv_polynomial.coeff_zero" -> "data", "has_deriv_at_filter.congr_of_eventually_eq" -> "analysis", "times_cont_diff_on.comp" -> "analysis", "category_theory.monoidal_category.unitors_equal.cells_7" -> "category_theory", "has_deriv_at_filter.comp" -> "analysis", "dist_pi_lt_iff" -> "topology", "hyperreal.neg_lt_of_tendsto_zero_of_pos" -> "data", "inv_involutive'" -> "algebra", "rat.cast_mk_of_ne_zero" -> "data", "submodule.smul_mono" -> "algebra", "wseq.of_list_nil" -> "data", "nnreal.tsum_comp_le_tsum_of_inj" -> "topology", "is_connected_iff_connected_space" -> "topology", "pell.eq_of_xn_modeq_le" -> "number_theory", "set.union_diff_right" -> "data", "algebraic_geometry.PresheafedSpace.stalk_map.comp" -> "algebraic_geometry", "complex.cos_neg" -> "data", "set.set_of_subset_set_of" -> "data", "cardinal.univ_inaccessible" -> "set_theory", "free_group.map_eq_to_group" -> "algebra", "zsqrtd.le_refl" -> "data", "subsemiring.prod_top" -> "algebra", "bool.band_elim_left" -> "data", "asymptotics.is_O_snd_prod" -> "analysis", "cau_seq.cauchy\:2082" -> "data", "multiset.map_comp_coe" -> "data", "list.disjoint_nil_right" -> "data", "nhds_subtype_eq_comap" -> "topology", "list.sublists_aux_cons_cons" -> "data", "uniform.continuous_within_at_iff'_right" -> "topology", "div_le_iff" -> "algebra", "tactic.abel.term_smulg" -> "tactic", "add_submonoid.closure_empty" -> "algebra", "measurable_space.comap_supr" -> "analysis", "asymptotics.is_O_with_zero'" -> "analysis", "local_equiv.inv_image_target_eq_source" -> "data", "semiconj_by.inv_symm_left" -> "algebra", "set.image_const_add_Iio" -> "data", "onote.NF.oadd" -> "set_theory", "dvd_symm_iff_of_irreducible" -> "algebra", "wseq.lift_rel.trans" -> "data", "pow_lt_pow_of_lt_left" -> "algebra", "zero_ne_one_or_forall_eq_0" -> "algebra", "iterate_frobenius" -> "algebra", "dense_bInter_of_open" -> "topology", "le_of_inf_le_sup_le" -> "order", "turing.TM2to1.tr_respects_aux\:2083" -> "computability", "dist_le_tsum_of_dist_le_of_tendsto" -> "topology", "array.rev_list_length_aux" -> "data", "associates.dvd_of_mk_le_mk" -> "algebra", "div_nonpos_of_nonneg_of_nonpos" -> "algebra", "add_monoid_hom.iterate_map_neg" -> "algebra", "filter.subtype_coe_map_comap_prod" -> "order", "list.disjoint_of_disjoint_append_right_right" -> "data", "equiv.perm.mul_swap_eq_swap_mul" -> "algebra", "order_of_one" -> "algebra", "matrix.from_blocks_transpose" -> "data", "nat.sub_min" -> "data", "Module.Mon_Module_equivalence_Algebra.ring_zero" -> "category_theory", "finset.mem_pi" -> "data", "asymptotics.is_O_one_of_tendsto" -> "analysis", "quadratic_form.associated_is_sym" -> "algebra", "asymptotics.is_O_with_self_const_mul" -> "analysis", "local_homeomorph.mdifferentiable.mdifferentiable_at_symm" -> "geometry", "algebra.adjoin_eq_ring_closure" -> "algebra", "finsupp.total_comap_domain" -> "algebra", "nat.le_rec_on_self" -> "data", "category_theory.epi_from_simple_zero_of_not_iso" -> "category_theory", "submonoid.ext'_iff" -> "algebra", "dim_add_dim_split" -> "algebra", "Hausdorffification.lift_comp_of" -> "algebra", "monoid_hom.map_list_prod" -> "data", "submonoid.localization_map.ext_iff" -> "algebra", "fderiv_smul_const" -> "analysis", "add_subgroup.gmultiples_eq_closure" -> "algebra", "list.enum_map_snd" -> "data", "set.preimage_bUnion" -> "data", "emetric.complete_of_cauchy_seq_tendsto" -> "topology", "with_top.coe_inf" -> "order", "set.image_pair" -> "data", "mv_polynomial.ne_zero_iff" -> "data", "measure_theory.lintegral_nnnorm_zero" -> "analysis", "matrix.mul_vec_empty" -> "data", "set.monotone_prod" -> "data", "infi_and'" -> "order", "local_homeomorph.is_o_congr" -> "analysis", "list.minimum_eq_coe_iff" -> "data", "sub_sub" -> "algebra", "irrational.rat_mul" -> "data", "list.forall\:2082.imp" -> "data", "polynomial.degree_sub_lt" -> "data", "ne_zero_of_eq_one" -> "algebra", "simple_graph.adj_matrix_dot_product" -> "combinatorics", "finset.eq_of_mem_of_not_mem_erase" -> "data", "mfderiv_within_eq_fderiv_within" -> "geometry", "sub_pos" -> "algebra", "polynomial.X_ne_zero" -> "data", "or.swap" -> "init", "has_fderiv_within_at.smul" -> "analysis", "list.or_exists_of_exists_mem_cons" -> "data", "list.forall\:2082_drop_append" -> "data", "subring.comap_top" -> "algebra", "int.le.intro" -> "init", "is_greatest_univ" -> "order", "rel.core_subset" -> "data", "equiv.mul_equiv_apply" -> "data", "irreducible_or_factor" -> "algebra", "power_series.mul_inv_of_unit" -> "algebra", "enorm.ext_iff" -> "analysis", "mdifferentiable_iff_differentiable" -> "geometry", "add_con.le_iff" -> "algebra", "finset.le_max'" -> "data", "linear_ordered_ring.eq_zero_or_eq_zero_of_mul_eq_zero" -> "algebra", "cardinal.le_mul_left" -> "set_theory", "alist.insert_insert" -> "data", "structure_groupoid.local_invariant_prop.lift_prop_at_chart_symm" -> "geometry", "category_theory.has_hom.hom.op_inj" -> "category_theory", "convex_hull_mono" -> "analysis", "linear_equiv.to_span_nonzero_singleton_one" -> "algebra", "polynomial.eval\:2082_algebra_map_X" -> "data", "with_top.mul_eq_top_iff" -> "algebra", "cau_seq.const_apply" -> "data", "finsupp.smul_single_one" -> "data", "computation.of_think_terminates" -> "data", "set.union_comm" -> "data", "continuous_linear_map.equiv_prod_of_surjective_of_is_compl_to_linear_equiv" -> "analysis", "decidable.le_imp_le_of_lt_imp_lt" -> "init", "turing.partrec_to_TM2.tr_list_ne_Cons" -> "computability", "set.Icc_subset_interval'" -> "data", "is_add_monoid_hom.map_nsmul" -> "algebra", "set.Inter_neg" -> "data", "ideal.mem_comap" -> "algebra", "times_cont_mdiff_at.of_succ" -> "geometry", "eq_true_intro" -> "init", "interval_integral.integral_has_fderiv_at" -> "analysis", "free_add_semigroup.add_map_seq" -> "algebra", "gpow_zero" -> "algebra", "alist.union_entries" -> "data", "multiset.not_nodup_pair" -> "data", "generalized_continued_fraction.nth_of_eq_some_of_succ_nth_int_fract_pair_stream" -> "algebra", "finset.erase_subset_erase" -> "data", "list.mem_erase_dup" -> "data", "list.subperm_cons" -> "data", "is_irreducible_singleton" -> "topology", "int.shiftr_neg" -> "data", "turing.TM1.stmts\:2081_self" -> "computability", "bitraversable.tsnd_tfst" -> "control", "bitvec.of_fin_le_of_fin_of_le" -> "data", "gsmul_mul'" -> "algebra", "set.preimage_neg_Iio" -> "data", "list.reverse_inj" -> "data", "continuous_linear_map.mul_apply" -> "topology", "turing.reaches\:2081.to\:2080" -> "computability", "list.lookmap_none" -> "data", "ordinal.is_normal.lt_iff" -> "set_theory", "simple_graph.mul_adj_matrix_apply" -> "combinatorics", "subsemiring.coe_Inf" -> "algebra", "category_theory.prod.fst_map" -> "category_theory", "monoid_algebra.lift_apply" -> "data", "int.one_mul" -> "init", "mul_left_cancel" -> "algebra", "complex.abs_zero" -> "data", "int.sub_le_of_sub_le" -> "init", "affine.simplex.circumcenter_circumradius_unique_dist_eq" -> "geometry", "real.pi_upper_bound_start" -> "data", "measure_theory.is_right_invariant_conj" -> "analysis", "set.ord_connected.dual" -> "data", "polynomial.pow_root_multiplicity_dvd" -> "data", "function.cSup_div_semiconj" -> "order", "real.has_deriv_at_log" -> "analysis", "dec_em" -> "logic", "infi_Prop_eq" -> "order", "subring.coe_comap" -> "algebra", "set.inter_subset" -> "data", "nine_dvd_iff" -> "data", "continuous_finset_prod" -> "topology", "deriv_within_id" -> "analysis", "ring.mem_closure" -> "algebra", "nat.eq_of_dist_eq_zero" -> "data", "subset_comp_self_of_mem_uniformity" -> "topology", "filter.ultrafilter.eq_iff_val_le_val" -> "order", "finmap.lookup_erase_ne" -> "data", "eq_one_of_mul_self_right_cancel" -> "algebra", "power_series.order_zero" -> "algebra", "emetric.nhds_basis_closed_eball" -> "topology", "omega.nat.univ_close_of_unsat_neg_elim_not" -> "tactic", "implicit_function_data.prod_fun_apply" -> "analysis", "unique_diff_within_at_inter" -> "analysis", "convex_on_const" -> "analysis", "subring.subset_closure" -> "algebra", "differentiable_within_at.restrict_scalars" -> "analysis", "punit.le" -> "algebra", "cardinal.nat_cast_pow" -> "set_theory", "edist_le_zero" -> "topology", "ring.fractional_ideal.map_id" -> "algebra", "submodule.quotient.mk_eq_zero" -> "algebra", "ring_equiv.map_neg_one" -> "data", "computable.vector_of_fn'" -> "computability", "decidable.not_forall_not" -> "logic", "measurable_of_measurable_union_cover" -> "analysis", "enat.with_top_equiv_zero" -> "data", "category_theory.kernel_zero_of_nonzero_from_simple" -> "category_theory", "Top.id_app" -> "topology", "mul_aut.one_def" -> "data", "times_cont_diff_within_at.sum" -> "analysis", "nat.lcm_zero_right" -> "data", "omega.pred_mono_2" -> "tactic", "category_theory.mono_to_simple_zero_of_not_iso" -> "category_theory", "measurable.comp" -> "analysis", "list.sublist_append_of_sublist_left" -> "data", "multiset.induction" -> "data", "uniform_embedding_translate" -> "topology", "ring.is_noetherian_of_zero_eq_one" -> "algebra", "filter.tendsto_add_at_top_iff_nat" -> "order", "has_deriv_at.sinh" -> "analysis", "of_digits_zmod" -> "data", "cardinal.zero_le" -> "set_theory", "multiset.add_sub_cancel" -> "data", "rat.mul_denom_eq_num" -> "data", "differentiable_within_at.log" -> "analysis", "punit.Inf_eq" -> "algebra", "multiplicity.finite_nat_iff" -> "algebra", "function.update_comm" -> "logic", "nhds_bot" -> "topology", "dense_inducing.self_sub_closure_image_preimage_of_open" -> "topology", "list.perm_nodupkeys" -> "data", "pell.xn_succ_succ" -> "number_theory", "tangent_map_within_id" -> "geometry", "real.uniform_continuous_abs" -> "topology", "category_theory.action_category.\[Pi]_obj" -> "category_theory", "category_theory.equivalence.pow_minus_one" -> "category_theory", "nat.dvd_add" -> "init", "multiset.sum_eq_foldr" -> "data", "fintype.exists_univ_list" -> "data", "finset.abs_sum_le_sum_abs" -> "algebra", "list.length_rotate" -> "data", "subsingleton.is_measurable" -> "analysis", "subsemiring.ext'" -> "algebra", "not_not" -> "logic", "wseq.nth_of_seq" -> "data", "linear_map.fst_prod" -> "algebra", "local_homeomorph.trans_to_local_equiv" -> "topology", "category_theory.sum.swap_obj_inr" -> "category_theory", "uniform_space.separation_quotient.map_mk" -> "topology", "category_theory.limits.coprod.braiding_hom" -> "category_theory", "finset.singleton_nonempty" -> "data", "int.sub_eq_zero_iff_eq" -> "init", "multiset.count_bind" -> "data", "subsemiring.coe_top" -> "algebra", "category_theory.limits.lim_map_\[Pi]" -> "category_theory", "int.land_bit" -> "data", "add_subgroup.coe_comap" -> "algebra", "disjoint_nhds_at_bot" -> "topology", "set.sInter_empty" -> "data", "ring.direct_limit.polynomial.exists_of" -> "algebra", "int.sign_eq_div_abs" -> "data", "add_submonoid.localization_map.map_left_cancel" -> "algebra", "euclidean_geometry.dist_orthogonal_projection_eq_zero_iff" -> "geometry", "submodule.eq_top_iff'" -> "algebra", "tactic.ring_exp.negate_pf" -> "tactic", "ring_hom.not_one_mem_ker" -> "algebra", "is_unit_zero_iff" -> "algebra", "multiset.rel_eq_refl" -> "data", "stream.map_const" -> "data", "disjoin_le" -> "computability", "set.image_Union" -> "data", "submodule.quotient.mk_add" -> "algebra", "measure_theory.l1.simple_func.norm_eq" -> "analysis", "discrete_valuation_ring.not_a_field" -> "algebra", "pgame.relabel_move_right" -> "set_theory", "nonneg_of_mul_nonneg_right" -> "algebra", "multilinear_map.map_add_univ" -> "algebra", "approximates_linear_on.lipschitz" -> "analysis", "sub_eq_of_eq_add'" -> "algebra", "real.continuous_at_rpow_of_pos" -> "analysis", "units.coe_mk0" -> "algebra", "equiv.prod_comm_symm" -> "data", "pos_of_mul_neg_right" -> "algebra", "matrix.one_apply_ne" -> "data", "is_unit.dvd_mul_left" -> "algebra", "continued_fraction.coe_to_generalized_continued_fraction" -> "algebra", "num.cast_succ'" -> "data", "dist_le_of_le_geometric_of_tendsto" -> "analysis", "mdifferentiable_on_atlas" -> "geometry", "divp_eq_iff_mul_eq" -> "algebra", "geom_sum_mul_add" -> "algebra", "iff_of_eq" -> "logic", "set.preimage_mul_preimage_subset" -> "algebra", "distrib_mul_action_hom.coe_fn_coe'" -> "algebra", "mv_polynomial.degrees_pow" -> "data", "convex_iff_forall_pos" -> "analysis", "nat.gcd_dvd_right" -> "data", "tactic.ring2.correctness" -> "tactic", "stream.append_approx_drop" -> "data", "list.eq_nil_of_map_eq_nil" -> "data", "pos_num.pred'_succ'" -> "data", "pfunctor.M.corec_unique" -> "data", "real.exp_eq_one_iff" -> "data", "measure_theory.ae_eq_fun.comp_to_germ" -> "analysis", "polynomial.degree_map_eq_of_leading_coeff_ne_zero" -> "data", "category_theory.monoidal_category.id_tensor_comp" -> "category_theory", "eq_inv_of_eq_inv" -> "algebra", "direct_sum.to_group_of" -> "algebra", "zsqrtd.conj_mul" -> "data", "fin.mk.inj_iff" -> "data", "list.cons_perm_iff_perm_erase" -> "data", "filter.has_basis.lift'" -> "order", "measure_theory.measure.haar.prehaar_nonneg" -> "analysis", "sym2.is_diag_iff_proj_eq" -> "data", "alg_hom.coe_to_ring_hom" -> "algebra", "filter.mem_join_sets" -> "order", "is_extr_on_dual_iff" -> "order", "nat.discriminate" -> "init", "padic_norm_e.zero_def" -> "data", "continuous_linear_map.comp_assoc" -> "topology", "list.repeat_count_eq_of_count_eq_length" -> "data", "topological_space.is_open_of_is_topological_basis" -> "topology", "add_submonoid.range_subtype" -> "algebra", "inner_product_geometry.angle_eq_zero_iff" -> "geometry", "nat.eq_zero_of_double_le" -> "data", "mem_tangent_cone_of_segment_subset" -> "analysis", "div_lt_iff_of_neg'" -> "algebra", "contracting_with.dist_fixed_point_le" -> "topology", "mv_polynomial.total_degree_mul" -> "data", "finset.inf_coe" -> "data", "fpow_neg_mul_fpow_self" -> "algebra", "list.mem_of_mem_inter_left" -> "data", "ordinal.lift_omega" -> "set_theory", "nat.bit0_le" -> "data", "continuous_linear_equiv.coe_coe" -> "topology", "well_founded.recursion" -> "init", "euclidean_geometry.inner_weighted_vsub" -> "geometry", "has_fderiv_within_at_inter'" -> "analysis", "euclidean_geometry.dist_reflection_eq_of_mem" -> "geometry", "is_add_submonoid.multiple_subset" -> "algebra", "category_theory.functor.comp_id" -> "category_theory", "map_supr_of_continuous_at_of_monotone'" -> "topology", "set.pi_eq_empty" -> "data", "free_add_magma.lift_unique" -> "algebra", "list.permutations_aux2_snd_cons" -> "data", "mul_inv_cancel" -> "algebra", "set.finite.bdd_below" -> "data", "submodule.one_eq_map_top" -> "algebra", "is_connected.union" -> "topology", "linear_map.mk_continuous_coe" -> "analysis", "nat.add_lt_add_right" -> "init", "measure_theory.integral_congr_ae" -> "analysis", "nat.size_shiftl'" -> "data", "int.nat_abs_of_nat_core" -> "init", "submodule.bot_mul" -> "algebra", "digits_aux_def" -> "data", "add_submonoid.localization_map.of_add_equiv_of_localizations_eq_iff_eq" -> "algebra", "dist_vadd_cancel_left" -> "analysis", "is_subgroup.mem_norm_comm_iff" -> "algebra", "filter.liminf_const" -> "order", "is_irreducible.is_connected" -> "topology", "finsupp.erase_same" -> "data", "multiset.cons_inj_left" -> "data", "ordinal.succ_ne_zero" -> "set_theory", "category_theory.functor.map_inv_hom" -> "category_theory", "Set.mem_diff" -> "set_theory", "filter.infi_principal_fintype" -> "order", "hyperreal.infinite_pos_add_not_infinite_neg" -> "data", "uniform_space.completion.coe_eq" -> "topology", "inner_product_geometry.angle_smul_left_of_pos" -> "geometry", "set.coe_embedding_of_subset_apply" -> "logic", "list.pairwise_lt_range'" -> "data", "finsupp.le_iff" -> "data", "ring_equiv.symm_to_ring_hom_apply_to_ring_hom_apply" -> "data", "free_group.map.mk" -> "algebra", "generalized_continued_fraction.squash_gcf_nth_of_lt" -> "algebra", "is_max_filter.sup" -> "order", "multiplicity.unique'" -> "algebra", "category_theory.limits.cocone_left_op_of_cone_\[Iota]_app" -> "category_theory", "cardinal.aleph'_lt" -> "set_theory", "le_lfp" -> "order", "localization_map.lift_comp" -> "algebra", "free_abelian_group.map_sub" -> "algebra", "continuous_linear_equiv.comp_has_fderiv_within_at_iff" -> "analysis", "implicit_function_data.to_local_homeomorph_coe" -> "analysis", "polynomial.irreducible_of_degree_eq_one" -> "data", "nnreal.coe_inv" -> "data", "magma.free_semigroup.induction_on" -> "algebra", "filter.tendsto_at_top_of_monotone_of_filter" -> "order", "units.mul_right_eq_zero" -> "algebra", "bool.bor_assoc" -> "data", "holor.slice_unit_vec_mul" -> "data", "measure_theory.integrable.max_zero" -> "analysis", "hyperreal.infinite_pos_mul_infinite_pos" -> "data", "typevec.const_iff_true" -> "data", "complex.sinh_add" -> "data", "padic_seq.equiv_zero_of_val_eq_of_equiv_zero" -> "data", "band_self" -> "init", "linear_map.uniform_continuous_of_bound" -> "analysis", "nnreal.arith_mean_le_rpow_mean" -> "analysis", "nat.mul_mod_left" -> "init", "dfinsupp.smul_apply" -> "data", "or_eq_of_eq_false_left" -> "init", "wseq.lift_rel.equiv" -> "data", "finsupp.erase_single_ne" -> "data", "nat.prime.multiplicity_le_multiplicity_choose_add" -> "data", "continuous_at_iff_ultrafilter" -> "topology", "inv_eq_one" -> "algebra", "continuous_linear_equiv.antilipschitz" -> "analysis", "vsub_right_injective" -> "algebra", "alg_equiv.map_sub" -> "algebra", "Set.ext_iff" -> "set_theory", "is_preorder.swap" -> "order", "measure_theory.integrable_on.indicator" -> "analysis", "set.preimage_const_mul_Icc" -> "data", "stream.head_even" -> "data", "mv_polynomial.eval_assoc" -> "data", "lie_group_core.to_topological_group" -> "geometry", "times_cont_mdiff_at_iff_times_cont_diff_at" -> "geometry", "polynomial.eval\:2082_one" -> "data", "multiset.to_finset_add" -> "data", "int.nonpos_of_neg_nonneg" -> "init", "polynomial.degree_div_X_lt" -> "data", "category_theory.limits.prod_map_id_id" -> "category_theory", "lcm_dvd_iff" -> "algebra", "matrix_equiv_tensor.right_inv" -> "algebra", "exists_exists_and_eq_and" -> "logic", "rat.mk_denom_ne_zero_of_ne_zero" -> "data", "measure_theory.simple_func.lintegral_add" -> "analysis", "polynomial.coe_X" -> "algebra", "const_smul_hom_apply" -> "algebra", "is_unit_of_map_unit" -> "algebra", "local_equiv.trans_self_symm" -> "data", "measure_theory.simple_func.approx_comp" -> "analysis", "ennreal.tendsto.div_const" -> "topology", "list.func.length_set" -> "data", "padic_norm_z.eq_of_norm_add_lt_right" -> "data", "embedding.continuous" -> "topology", "int.cast_coe_nat'" -> "data", "is_closed_map_smul_of_unit" -> "topology", "category_theory.limits.cones.whiskering_equivalence_unit_iso" -> "category_theory", "measurable_one" -> "analysis", "nat.coe_cast_add_monoid_hom" -> "data", "right_ord_continuous.map_inf" -> "order", "multiplicative.is_submonoid" -> "algebra", "nat.pow_mul" -> "data", "ennreal.pow_le_pow" -> "data", "int.coe_nat_inj" -> "init", "pequiv.bot_apply" -> "data", "complex.abs_neg" -> "data", "enat.sup_eq_max" -> "data", "circle_deg1_lift.translation_number_of_map_pow_eq_add_int" -> "dynamics", "filter.tendsto_at_top_embedding" -> "order", "structure_groupoid.id_mem_maximal_atlas" -> "geometry", "filter.map_supr" -> "order", "linear_map.smul_right_apply" -> "algebra", "fderiv_within_smul_algebra" -> "analysis", "list.disjoint_of_disjoint_cons_right" -> "data", "list.mem_filter_of_mem" -> "data", "nat.cast_inj" -> "algebra", "lt_add_of_neg_add_lt" -> "algebra", "is_compact.bdd_above" -> "topology", "matrix.from_blocks_one" -> "data", "finset.prod_bind" -> "algebra", "category_theory.limits.image.fac_lift_assoc" -> "category_theory", "mul_div_comm" -> "algebra", "continuous_linear_map.comp_smul" -> "topology", "pgame.zero_le_add_left_neg" -> "set_theory", "prod.snd_zero" -> "algebra", "zero_mem_nonunits" -> "algebra", "antilipschitz_with.add_lipschitz_with" -> "analysis", "differentiable_on_id" -> "analysis", "computable.list_of_fn" -> "computability", "asymptotics.is_O_with.trans_le" -> "analysis", "mem_nhds_within_iff_exists_mem_nhds_inter" -> "topology", "filter.eventually_eq.is_local_max_on_iff" -> "topology", "function.left_inverse_of_surjective_of_right_inverse" -> "init", "list.subperm.trans" -> "data", "pfun.mem_core" -> "data", "asymptotics.is_O.mono" -> "analysis", "neg_sub" -> "algebra", "int.nat_abs_bit1_nonneg" -> "init", "onote.NF_below.mono" -> "set_theory", "nat.le.dest" -> "init", "measurable_from_top" -> "analysis", "normalize_eq_normalize_iff" -> "algebra", "add_submonoid.localization_map.map_eq" -> "algebra", "submonoid.localization_map.map_right_cancel" -> "algebra", "function.support_subset_iff" -> "data", "dist_zero_right" -> "analysis", "wseq.dropn_think" -> "data", "measure_theory.extend_Union" -> "analysis", "nndist_self" -> "topology", "traversable.length_to_list" -> "control", "bundle_trivialization.coe_fst" -> "topology", "nat.pow_right_injective" -> "data", "measure_theory.simple_func.induction" -> "analysis", "cauchy_seq_of_controlled" -> "topology", "nat.eq_or_lt_of_le" -> "init", "finset.sum_erase" -> "algebra", "cardinal.lift_inj" -> "set_theory", "nonempty_subtype" -> "logic", "set.mem_prod" -> "data", "multiset.prod_map_one" -> "data", "interval_integral.integral_has_deriv_within_at_of_tendsto_ae_right" -> "analysis", "polynomial.coeff_neg" -> "data", "list.nth_le_singleton" -> "data", "category_theory.limits.image.fac_assoc" -> "category_theory", "topological_fiber_bundle_core.mem_local_triv_source" -> "topology", "nat.even_div" -> "data", "category_theory.concrete_category.hom_ext" -> "category_theory", "set.sum_indicator_subset" -> "data", "finite_dimensional.findim_mul_findim" -> "algebra", "ring_hom.srange_top_iff_surjective" -> "algebra", "con.mul" -> "algebra", "tendsto_if_nhds_within" -> "topology", "int.eq_nat_abs_of_zero_le" -> "init", "finset.prod_empty" -> "algebra", "ordinal.card_one" -> "set_theory", "le_mul_of_le_of_one_le" -> "algebra", "rat.cast_round" -> "algebra", "measure_theory.simple_func.coe_zero" -> "analysis", "pgame.one_left_wins" -> "set_theory", "nat.gcd_comm" -> "data", "dense_inducing.continuous_extend" -> "topology", "fixed_points.sup_le_f_of_fixed_points" -> "order", "finset.exists_pos_of_sum_zero_of_exists_nonzero" -> "algebra", "is_unit.ne_zero" -> "algebra", "nat.mul_right_inj" -> "data", "set.mem_Ici" -> "data", "set.nonempty_Ioc" -> "data", "zmod.pow_totient" -> "algebra", "nat.xgcd_aux_fst" -> "data", "unique_factorization_domain.irreducible_iff_prime" -> "algebra", "list.nodup_range" -> "data", "nat.dvd_lcm_left" -> "data", "linear_pmap.Sup_le" -> "algebra", "finsupp.mem_support_iff" -> "data", "list.alternating_prod_nil" -> "data", "is_unit.mul" -> "algebra", "cardinal.bit1_ne_zero" -> "set_theory", "has_deriv_at_pow" -> "analysis", "poly_equiv_tensor.left_inv" -> "algebra", "times_cont_diff_groupoid_zero_eq" -> "geometry", "generalized_continued_fraction.coe_to_generalized_continued_fraction" -> "algebra", "polynomial.eval\:2082_nat_cast" -> "data", "and_iff_right" -> "init", "commute.neg_one_left" -> "algebra", "continuous_linear_equiv.symm_comp_self" -> "topology", "category_theory.graded_object.comap_equiv_counit_iso" -> "category_theory", "finset.mem_sdiff" -> "data", "set.surj_on_Inter" -> "data", "category_theory.sum.inverse_associator_map_inr_inr" -> "category_theory", "is_linear_map.map_zero" -> "algebra", "stream.mem_map" -> "data", "finsupp.zero_apply" -> "data", "measurable_space.map_top" -> "analysis", "local_equiv.symm_source" -> "data", "set.preimage_mul_const_Icc" -> "data", "is_measurable.const" -> "analysis", "ideal.map_comap_of_surjective" -> "algebra", "differentiable_pow" -> "analysis", "mul_le_of_le_of_le_one'" -> "algebra", "filter.eventually_of_forall" -> "order", "ideal.mem_radical_of_pow_mem" -> "algebra", "has_fderiv_within_at.sub" -> "analysis", "affine_map.coe_mk" -> "algebra", "set.Ioo_union_Ico_eq_Ioo" -> "data", "metric.nhds_basis_closed_ball" -> "topology", "list.perm_of_mem_permutations" -> "data", "semilattice_sup.ext_sup" -> "order", "nat.gcd_mul_left_right" -> "data", "category_theory.limits.coprod.desc_comp_comp" -> "category_theory", "setoid.eqv_gen_idem" -> "data", "associates.eq_of_mul_eq_mul_left" -> "algebra", "linear_equiv.of_submodules_apply" -> "algebra", "pos_div_pow_pos" -> "algebra", "lipschitz_with.mk_one" -> "topology", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_obj_one_app" -> "category_theory", "pfun.preimage_inter" -> "data", "ennreal.mem_Iio_self_add" -> "data", "multiplicity.finite_def" -> "algebra", "nnreal.coe_eq_zero" -> "data", "differentiable_on_congr" -> "analysis", "add_monoid_hom.mrange_top_iff_surjective" -> "algebra", "nat.exists_dvd_of_not_prime2" -> "data", "sum_le_tsum" -> "topology", "set.ord_connected_empty" -> "data", "category_theory.prod_id" -> "category_theory", "function.injective.ne_iff" -> "logic", "nat.le_sqrt" -> "data", "complex.sinh_mul_I" -> "data", "complex.abs_abs_sub_le_abs_sub" -> "data", "composition_as_set.blocks_sum" -> "combinatorics", "ideal.pow_le_pow" -> "algebra", "list.filter_sublist" -> "init", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_obj_X_obj" -> "category_theory", "algebra.gc" -> "algebra", "add_localization.add_equiv_of_quotient_symm_mk" -> "algebra", "local_equiv.symm_symm" -> "data", "finsupp.sum_finset_sum_index" -> "data", "measure_theory.integrable_at_filter.eventually" -> "analysis", "filter.binfi_sup_left" -> "order", "neg_of_mul_neg_left" -> "algebra", "basic_smooth_bundle_core.chart_source" -> "geometry", "category_theory.arrow.lift.fac_right" -> "category_theory", "finset.case_strong_induction_on" -> "data", "tensor_product.lid_tmul" -> "algebra", "abs_of_nonneg" -> "algebra", "measure_theory.l1.integrable" -> "analysis", "ordinal.zero_div" -> "set_theory", "gfp_le" -> "order", "uniform_embedding_set_inclusion" -> "topology", "local_homeomorph.right_inv" -> "topology", "seq.mem_map" -> "data", "is_connected.Icc_subset" -> "topology", "continuous_multilinear_map.ratio_le_op_norm" -> "analysis", "lucas_lehmer.X.bit1_fst" -> "number_theory", "uniform_space.uniform_continuous_quotient" -> "topology", "nat.gcd_dvd_gcd_of_dvd_right" -> "data", "list.tfae_singleton" -> "data", "filter.tendsto_at_bot_of_monotone_of_subseq" -> "order", "subgroup.coe_pow" -> "algebra", "category_theory.limits.cocone_left_op_of_cone_X" -> "category_theory", "measurable_space.generate_from_le_iff" -> "analysis", "turing.TM0to1.tr_respects" -> "computability", "free_group.red.step.bnot_rev" -> "algebra", "Kuratowski_embedding.isometry" -> "topology", "subsemiring.map_bot" -> "algebra", "multiset.union_le_iff" -> "data", "multiset.lt_iff_cons_le" -> "data", "complex.continuous_cosh" -> "analysis", "free_semigroup.lift_unique" -> "algebra", "finset.fold_empty" -> "data", "linear_map.llcomp_apply" -> "algebra", "ultrafilter_pure_injective" -> "topology", "ordinal.div_aux" -> "set_theory", "rat.continuous_mul" -> "topology", "primrec.sum_inl" -> "computability", "list.perm.diff_right" -> "data", "smooth_on.add" -> "geometry", "multiset.filter_map_zero" -> "data", "list.insert_nth_nil" -> "data", "category_theory.Monad.to_of_mon_end_iso_hom_app_to_nat_trans_app" -> "category_theory", "one_le_div" -> "algebra", "real.sqrt_eq_zero" -> "data", "filter.tendsto_iff_eventually" -> "order", "nndist_nnnorm_nnnorm_le" -> "analysis", "computation.lift_rel_mem_cases" -> "data", "add_subgroup.center_normal" -> "algebra", "perfect_closure.eq_iff" -> "algebra", "is_lub.insert" -> "order", "partrec.option_cases_right" -> "computability", "affine_map.coe_smul" -> "algebra", "int.lt_add_of_sub_right_lt" -> "init", "set.sUnion_union" -> "data", "pnat.le_of_dvd" -> "data", "multiplicity.eq_top_iff_not_finite" -> "algebra", "differentiable_within_at.snd" -> "analysis", "measure_theory.is_right_invariant_conj'" -> "analysis", "is_partial_order.swap" -> "order", "le_supr_iff" -> "order", "mul_lt_iff_lt_one_right'" -> "algebra", "finset.card_range" -> "data", "times_cont_diff_on_iff_continuous_on_differentiable_on" -> "analysis", "differentiable_at.pow" -> "analysis", "finset.card_le_one_iff" -> "data", "fact.pow.pos" -> "data", "set.mem_zero" -> "algebra", "category_theory.whiskering_left_map_app_app" -> "category_theory", "finset.sum_Ico_add" -> "algebra", "real.one_le_rpow" -> "analysis", "pgame.impartial.winner_cases" -> "set_theory", "finsupp.lsum_single" -> "algebra", "list.append_assoc" -> "init", "nat.land_comm" -> "data", "stream.tail_eq_drop" -> "data", "category_theory.limits.cokernel_iso_of_eq_refl" -> "category_theory", "finsupp.total_emb_domain" -> "algebra", "submodule.fg_mul" -> "algebra", "set.indicator_comp_of_zero" -> "data", "nat.succ_ne_self" -> "init", "norm_le_gronwall_bound_of_norm_deriv_right_le" -> "analysis", "nsmul_neg_comm" -> "algebra", "implicit_function_data.implicit_function_has_strict_fderiv_at" -> "analysis", "set.enumerate_inj" -> "data", "uniformity_lift_le_swap" -> "topology", "ring_hom.map_sum" -> "algebra", "measure_theory.outer_measure.f_Union" -> "analysis", "pgame.nonmoves_nonempty" -> "set_theory", "rel_iso.mul_apply" -> "order", "frobenius_one" -> "algebra", "seq.map_cons" -> "data", "image_norm_le_of_norm_deriv_right_lt_deriv_boundary'" -> "analysis", "neg_square" -> "algebra", "add_monoid_hom.map_exists_left_neg" -> "algebra", "list.of_fn_succ" -> "data", "unique_diff_on_Ioo" -> "analysis", "local_homeomorph.of_set_target" -> "topology", "map_lift_comp_preserves_products_iso_hom" -> "category_theory", "local_equiv.eq_on_source.eq_on" -> "data", "measurable.nnreal_of_real" -> "analysis", "bitraversable.tsnd_eq_snd_id" -> "control", "matrix.adjugate_apply" -> "algebra", "mv_polynomial.eval_prod" -> "data", "neg_inv" -> "algebra", "is_scalar_tower.restrict_base_apply" -> "algebra", "is_Z_bilin.tendsto_zero_right" -> "topology", "complex.abs_exp_sub_one_sub_id_le" -> "data", "sesq_form.ortho_zero" -> "algebra", "function.commute.iterate_iterate_self" -> "logic", "omega.int.unsat_of_clauses_unsat" -> "tactic", "norm_nonneg" -> "analysis", "power_series.coeff_zero_X" -> "algebra", "category_theory.abelian.app_hom" -> "category_theory", "fderiv_within_const_apply" -> "analysis", "ordinal.mul_lt_omega_power" -> "set_theory", "local_equiv.symm_target" -> "data", "real.continuous.inv" -> "topology", "has_deriv_within_at.iterate" -> "analysis", "metric.mem_closure_iff_inf_dist_zero" -> "topology", "lt_inf_iff" -> "order", "function.involutive.bijective" -> "logic", "cardinal.mk_union_of_disjoint" -> "set_theory", "ordinal.pred_lt_iff_is_succ" -> "set_theory", "category_theory.comonad_hom.ext" -> "category_theory", "subring.list_prod_mem" -> "algebra", "isometric.symm_symm" -> "topology", "list.reverse_concat" -> "data", "linear_map.comp_der_apply" -> "algebra", "adjoin_root.lift_comp_of" -> "algebra", "segment_translate_preimage" -> "analysis", "not_not_intro" -> "init", "int.le_of_add_le_add_left" -> "init", "nat.mod_two_ne_one" -> "data", "isometric.point_reflection_apply" -> "analysis", "neg_lt_neg_iff" -> "algebra", "not_iff_not_of_iff" -> "init", "list.maximum_cons" -> "data", "module.End.ker_eval\:2082_ring_hom_noncomm_unit_polynomial" -> "algebra", "fixed_points.Sup_le_f_of_fixed_points" -> "order", "category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom" -> "category_theory", "free_abelian_group.of_one" -> "algebra", "convex_on_real_of_slope_mono_adjacent" -> "analysis", "category_theory.functor_to_types.comp" -> "category_theory", "linear_pmap.sup_apply" -> "algebra", "subsemiring.coe_one" -> "algebra", "set.image_sub_const_Ioo" -> "data", "finset.Ico.filter_le_of_le_bot" -> "data", "list.rel_join" -> "data", "category_theory.monoidal.functor_category.tensor_hom_app" -> "category_theory", "num.of_nat'_eq" -> "data", "set.image_sub_const_Iio" -> "data", "pequiv.symm_symm" -> "data", "real.rpow_lt_rpow_of_exponent_lt" -> "analysis", "submodule.smul_mem_span_smul_of_mem" -> "algebra", "real.bounded_iff_bdd_below_bdd_above" -> "topology", "submodule.span_univ" -> "algebra", "convex_cone.salient_of_positive_cone" -> "analysis", "list.perm.mem_iff" -> "data", "continuous_linear_map.coe_coe" -> "topology", "neg_ne_zero" -> "algebra", "decidable.em" -> "init", "monoid_hom.comp_apply" -> "algebra", "galois_connection.u_infi" -> "order", "set.image2_congr'" -> "data", "decidable.not_forall" -> "logic", "inner_product_geometry.angle_neg_self_of_nonzero" -> "geometry", "category_theory.currying_functor_map_app" -> "category_theory", "measure_theory.l1.simple_func.integral_eq_norm_pos_part_sub" -> "analysis", "set.inter_def" -> "data", "pnat.gcd_det_eq" -> "data", "filter.has_basis.prod'" -> "order", "filter.limsup_eq" -> "order", "is_closed_sigma_iff" -> "topology", "formal_multilinear_series.id_apply_one" -> "analysis", "subring.coe_inf" -> "algebra", "asymptotics.is_O.mul_is_o" -> "analysis", "polynomial.C_neg" -> "data", "complex.norm_nat" -> "analysis", "pfunctor.approx.truncate_eq_of_agree" -> "data", "cardinal.bit0_lt_bit0" -> "set_theory", "nat.subtype.succ_le_of_lt" -> "data", "measure_theory.measure.conj_apply" -> "analysis", "list.not_nodup_pair" -> "data", "composition_as_set.length_lt_card_boundaries" -> "combinatorics", "list.perm_append_comm" -> "data", "exists_dual_vector'" -> "analysis", "submonoid.localization_map.mul_equiv_of_localizations_symm_eq_mul_equiv_of_localizations" -> "algebra", "punit_eq" -> "init", "lagrange.eq_of_eval_eq" -> "algebra", "dist_le_of_approx_trajectories_ODE_of_mem_set" -> "analysis", "fin.comp_init" -> "data", "semiconj_by.inv_symm_left_iff" -> "algebra", "set.image2_left" -> "data", "inv_lt_zero" -> "algebra", "linear_map.comp_coe" -> "algebra", "encodable.encode_prod_val" -> "data", "has_deriv_within_at_fpow" -> "analysis", "mv_power_series.X_def" -> "algebra", "nat.choose_succ_succ" -> "data", "finsupp.map_domain_comap_domain" -> "data", "int.mod_zero" -> "data", "continuous.add" -> "topology", "set.interval_subset_interval" -> "data", "circle_deg1_lift.map_add_nat" -> "dynamics", "list.pmap_eq_map_attach" -> "data", "power_series.X_eq" -> "algebra", "sym2.map_comp" -> "data", "preserves_products_iso_hom_\[Pi]_assoc" -> "category_theory", "int.bit_neg_succ" -> "data", "subring.gsmul_mem" -> "algebra", "polynomial.monic_one" -> "data", "add_subgroup.forall" -> "algebra", "set.quot_mk_range_eq" -> "data", "list.argmin_eq_some_iff" -> "data", "ennreal.Lp_add_le" -> "analysis", "add_subgroup.coe_zero" -> "algebra", "list.prod_range_succ'" -> "data", "subspace.coe_continuous_linear_proj_of_closed_compl" -> "analysis", "category_theory.pi.comap_comp_inv_app" -> "category_theory", "is_closed_ge'" -> "topology", "differentiable_at.sub_const" -> "analysis", "add_monoid_hom.inl_apply" -> "algebra", "category_theory.limits.coprod.associator_inv" -> "category_theory", "semiconj_by.neg_left" -> "algebra", "ordinal.one_le_iff_ne_zero" -> "set_theory", "matrix.det_mul" -> "algebra", "polynomial.C_eq_algebra_map" -> "data", "nat.modeq.pow_totient" -> "algebra", "not_bdd_below_iff'" -> "order", "asymptotics.is_O_with.congr'" -> "analysis", "category_theory.limits.biprod.braiding'_hom" -> "category_theory", "wseq.not_mem_nil" -> "data", "tensor_product.lift_mk_compr\:2082" -> "algebra", "category_theory.limits.cocones.functoriality_obj_X" -> "category_theory", "seq.zip_with_nth_none" -> "data", "tensor_product.assoc_tmul" -> "algebra", "real.log_neg_eq_log" -> "analysis", "pequiv.of_set_eq_some_self_iff" -> "data", "mul_lt_of_lt_of_le_one" -> "algebra", "filter.Limsup_bot" -> "order", "set.Ioi_diff_Ici" -> "data", "cardinal.mul_le_max_of_omega_le_left" -> "set_theory", "isometry.uniform_embedding" -> "topology", "finset.infi_singleton" -> "data", "free_group.red.red_iff_irreducible" -> "algebra", "finset.mono_of_fin_zero" -> "data", "polynomial.coeff_coe_units_zero_ne_zero" -> "data", "finsupp.map_domain_sum" -> "data", "nat.add_pos_left" -> "data", "segment_eq_interval" -> "analysis", "ring.fractional_ideal.mem_singleton_mul" -> "algebra", "algebra.is_integral_trans" -> "algebra", "nat.modeq.modeq_mul_left" -> "data", "zsqrtd.mul_re" -> "data", "is_open_diff" -> "topology", "turing.to_partrec.cont.then_eval" -> "computability", "measure_theory.measure.haar_outer_measure_lt_top_of_is_compact" -> "analysis", "pi.single_eq_of_ne" -> "algebra", "category_theory.epi_of_epi" -> "category_theory", "poly.neg_eval" -> "number_theory", "imp_eq_of_eq_true_right" -> "init", "nnreal.one_rpow" -> "analysis", "mdifferentiable_on.congr_mono" -> "geometry", "is_open_map.prod" -> "topology", "setoid.eqv_gen_of_setoid" -> "data", "category_theory.sum.inverse_associator_obj_inl" -> "category_theory", "ring_hom.lift_of_surjective_comp_apply" -> "algebra", "continuous_within_at_id" -> "topology", "int.cast_neg" -> "data", "pfunctor.M.approx_mk" -> "data", "polynomial.X_pow_mul" -> "data", "ideal.quotient.exists_inv" -> "algebra", "list.index_of_lt_length" -> "data", "rel_supr_tsum" -> "topology", "asymptotics.is_o.prod_left_fst" -> "analysis", "subtype.exists" -> "data", "differentiable.restrict_scalars" -> "analysis", "ring_hom.map_geom_series" -> "algebra", "eq_of_div_eq_one" -> "algebra", "pnat.bit1_le_bit0" -> "data", "algebra.map_top" -> "algebra", "list.zip_nil_left" -> "data", "free_group.red.step.append_right" -> "algebra", "mv_polynomial.coe_add" -> "algebra", "ring.fractional_ideal.span_fractional_iff" -> "algebra", "cmp_using_eq_eq" -> "init", "neg_neg" -> "algebra", "real.Inf_of_not_bdd_below" -> "data", "ordinal.power_add" -> "set_theory", "real.cosh_zero" -> "data", "submodule.prod_comap_inl" -> "algebra", "ennreal.sum_eq_top_iff" -> "data", "finset.union_self" -> "data", "finsupp.support_zero" -> "data", "has_deriv_at.continuous_at" -> "analysis", "multiset.zero_subset" -> "data", "pgame.le_iff_neg_ge" -> "set_theory", "add_con.inf_def" -> "algebra", "set.subset.trans" -> "data", "isometry.diam_image" -> "topology", "intermediate_value_Icc" -> "topology", "locally_compact_of_compact_nhds" -> "topology", "equiv.const_vadd_add" -> "algebra", "category_theory.graded_object.comap_equiv_unit_iso" -> "category_theory", "right_ord_continuous.map_is_least" -> "order", "list.length_sublists'" -> "data", "lt_add_of_lt_of_pos" -> "algebra", "inv_of_inv_of" -> "algebra", "zmod.nat_coe_eq_nat_coe_iff" -> "data", "measure_theory.simple_func.range_zero" -> "analysis", "matrix.mul_zero" -> "data", "finset.Ico.insert_succ_bot" -> "data", "cSup_lower_bounds_eq_cInf" -> "order", "add_semiconj_by.units_neg_right" -> "algebra", "add_subgroup.is_open_of_mem_nhds" -> "topology", "unique_mdiff_within_at.inter'" -> "geometry", "filter.tendsto.is_bounded_under_ge" -> "topology", "dfinsupp.induction\:2082" -> "data", "nat.find_spec" -> "init", "eq_neg_of_add_eq_zero" -> "algebra", "is_closed_singleton" -> "topology", "convex_on.le_on_segment'" -> "analysis", "monoid_hom.coprod_comp_inl" -> "algebra", "exists_unique.elim2" -> "logic", "topological_space.opens.map_comp_obj'" -> "topology", "closed_embedding_of_embedding_closed" -> "topology", "setoid.is_partition_classes" -> "data", "list.modify_nth_length" -> "data", "primrec\:2082.option_some_iff" -> "computability", "valuation.on_quot_comap_eq" -> "algebra", "finsupp.order_embedding_to_fun_apply" -> "data", "is_R_or_C.norm_sq_to_complex" -> "data", "submonoid.coe_inf" -> "algebra", "uniformity_basis_edist'" -> "topology", "option.mem_def" -> "data", "exists_Ioc_subset_of_mem_nhds" -> "topology", "polynomial.separable.of_mul_left" -> "algebra", "add_subgroup.le_normalizer_of_normal" -> "algebra", "category_theory.nat_iso.cancel_nat_iso_hom_left" -> "category_theory", "linear_map.map_sum" -> "algebra", "euclidean_geometry.orthogonal_projection_fn_mem" -> "geometry", "finset.disjoint_filter_filter" -> "data", "submodule.ker_subtype" -> "algebra", "monotone.map_infi_le" -> "order", "set.Ici_diff_Ioi" -> "data", "lt_iff_le_and_ne" -> "algebra", "normalize_eq" -> "algebra", "has_fderiv_at.comp_has_fderiv_within_at" -> "analysis", "nat.dvd_add_self_right" -> "data", "list.func.get_set_eq_of_ne" -> "data", "nat.pow_zero" -> "init", "dense_range.equalizer" -> "topology", "generalized_continued_fraction.continuants_recurrence_aux" -> "algebra", "category_theory.category_of_elements.\[Pi]_obj" -> "category_theory", "set.countable_pi" -> "data", "zero_eq_inv" -> "algebra", "category_theory.equivalence.inverse_counit" -> "category_theory", "pfunctor.W.dest_mk" -> "data", "real.pi_lt_sqrt_two_add_series" -> "data", "list.chain_of_pairwise" -> "data", "nat.partrec.none" -> "computability", "bool.bor_left_comm" -> "data", "list.sublist.antisymm" -> "data", "nat.sqrt_eq_zero" -> "data", "ideal.factors_decreasing" -> "algebra", "metric.uniform_continuous_on_iff" -> "topology", "set.bij_on.inj_on" -> "data", "cardinal.cantor_function_le" -> "data", "is_basis.coord_fun_eq_repr" -> "algebra", "has_fderiv_at.mul" -> "analysis", "localization_map.lift_eq" -> "algebra", "associates.eq_of_mul_eq_mul_right" -> "algebra", "has_mfderiv_at.comp_has_mfderiv_within_at" -> "geometry", "squeeze_zero'" -> "topology", "mv_polynomial.coeff_mul" -> "data", "submodule.sup_mul" -> "algebra", "category_theory.iso.hom_congr_symm" -> "category_theory", "pnat.gcd_a_eq" -> "data", "is_min_on.neg" -> "order", "cardinal.cantor'" -> "set_theory", "measure_theory.ae_eq_fun.integrable.add" -> "analysis", "metric.cauchy_seq_iff'" -> "topology", "equiv.set.univ_apply" -> "data", "free_magma.traverse_mul" -> "algebra", "cau_seq.completion.mk_add" -> "data", "local_ring.is_unit_of_mem_nonunits_one_sub_self" -> "algebra", "local_homeomorph.to_fun_eq_coe" -> "topology", "uniform.continuous_on_iff'_left" -> "topology", "nat.mod_two_eq_zero_or_one" -> "init", "is_closed_connected_component" -> "topology", "list.chain'_cons" -> "data", "is_glb.bdd_below" -> "order", "mv_polynomial.eq_zero_of_eval_eq_zero" -> "algebra", "cardinal_lift_le_dim_of_linear_independent" -> "algebra", "uniform_space.has_seq_basis" -> "topology", "polynomial.degree_X" -> "data", "tendsto_pow_at_top_nhds_0_of_abs_lt_1" -> "analysis", "dense_inducing.closure_range" -> "topology", "cardinal.le_min" -> "set_theory", "pfunctor.M.is_path_cons'" -> "data", "commute.neg_right" -> "algebra", "real.rpow_def_of_nonpos" -> "analysis", "add_subgroup.coe_subset_coe" -> "algebra", "add_monoid_hom.id_apply" -> "algebra", "direct_sum.lof_apply" -> "algebra", "alg_hom.map_sub" -> "algebra", "is_add_group_hom.zero_iff_ker_neg'" -> "algebra", "category_theory.limits.biprod.hom_ext" -> "category_theory", "is_closed_sInter" -> "topology", "category_theory.adjunction.functoriality_unit_app_hom" -> "category_theory", "iff_def'" -> "logic", "finset.image_subset_image" -> "data", "ordinal.zero_dvd" -> "set_theory", "nat.succ_inj'" -> "data", "measure_theory.simple_func.coe_restrict" -> "analysis", "category_theory.limits.biproduct.desc_eq" -> "category_theory", "nat.prime.dvd_of_dvd_pow" -> "data", "dual_pair.dual_lc" -> "algebra", "real.sqrt_inv" -> "data", "wseq.lift_rel_nil" -> "data", "and.right_comm" -> "logic", "filter.germ.coe_sub" -> "order", "nat.pred_inj" -> "init", "continuous_linear_equiv.comp_continuous_on_iff" -> "topology", "finset.sum_ite" -> "algebra", "generalized_continued_fraction.int_fract_pair.exists_succ_nth_stream_of_fr_zero" -> "algebra", "nonempty.exists" -> "logic", "nat.primrec'.cons" -> "computability", "continuous.iterate" -> "topology", "has_strict_fderiv_at.const_mul" -> "analysis", "measure_theory.simple_func.integral_neg" -> "analysis", "lcm_eq_zero_iff" -> "algebra", "polynomial.separable_X" -> "algebra", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le'" -> "analysis", "zmod.inv_coe_unit" -> "data", "local_equiv.image_trans_source" -> "data", "has_fderiv_at.restrict_scalars" -> "analysis", "minimal_polynomial.aeval" -> "algebra", "perfect_closure.mk_add_mk" -> "algebra", "submonoid.monotone_map" -> "algebra", "commute.inv_inv_iff" -> "algebra", "tactic.abel.const_add_term" -> "tactic", "ordinal.lift_one" -> "set_theory", "times_cont_mdiff_within_at.comp'" -> "geometry", "nat.cast_pow" -> "algebra", "roption.get_or_else_some" -> "data", "is_R_or_C.im_to_complex" -> "data", "add_submonoid.localization_map.eq_iff_exists" -> "algebra", "qpf.is_lawful_functor" -> "data", "measure_theory.outer_measure.trim_eq_infi'" -> "analysis", "is_compact.tendsto_subseq" -> "topology", "option.none_bind'" -> "data", "rat.le_floor" -> "data", "additive.is_add_subgroup_iff" -> "algebra", "edist_le_tsum_of_edist_le_of_tendsto" -> "topology", "eq_of_forall_le_iff" -> "algebra", "eq_inv_of_mul_left_eq_one" -> "algebra", "nat_degree_scale_roots" -> "algebra", "category_theory.eq_to_hom_map" -> "category_theory", "push_neg.not_not_eq" -> "tactic", "function.update_comp_eq_of_not_mem_range" -> "data", "set.exists_of_ssubset" -> "data", "category_theory.iso.cancel_iso_hom_left" -> "category_theory", "int.sign_eq_one_of_pos" -> "init", "mem_nhds_within_Ioi_iff_exists_Ioo_subset" -> "topology", "nnreal.coe_le_coe" -> "data", "option.ne_none_iff_is_some" -> "data", "dim_pos" -> "algebra", "is_greatest.mono" -> "order", "is_basis.repr_eq_single" -> "algebra", "well_founded.well_founded_iff_has_min" -> "order", "continuous_linear_map.fderiv" -> "analysis", "finset.sum_eq_zero_iff_of_nonpos" -> "algebra", "array.ext" -> "init", "Sup_eq_supr" -> "order", "nat.div_lt_iff_lt_mul'" -> "data", "smooth_manifold_with_corners.compatible_of_mem_maximal_atlas" -> "geometry", "category_theory.limits.zero_of_from_zero" -> "category_theory", "isometric.coe_to_real_linear_equiv_of_map_zero" -> "analysis", "category_theory.limits.cocones.whiskering_equivalence_counit_iso" -> "category_theory", "array.write_eq_write'" -> "init", "is_coprime.prod_left_iff" -> "algebra", "enat.with_top_equiv_coe" -> "data", "pnat.xgcd_type.rq_eq" -> "data", "category_theory.preadditive.epi_iff_cancel_zero" -> "category_theory", "embedding.continuous_on_iff" -> "topology", "fin.val_one" -> "data", "filter.inf_ne_bot_iff_frequently_right" -> "order", "measurable_space.monotone_map" -> "analysis", "list.append_inj" -> "data", "list.nodupkeys.pairwise_ne" -> "data", "nat.mod_add_mod" -> "data", "linear_dependent_iff" -> "algebra", "submonoid.localization_map.map_mul_left" -> "algebra", "ulift.mul_down" -> "algebra", "finset.card_congr" -> "data", "list.unzip_revzip" -> "data", "zsqrtd.mul_pos" -> "data", "pow_boole" -> "algebra", "ennreal.inner_le_Lp_mul_Lq" -> "analysis", "measurable_fst" -> "analysis", "subring.multiset_prod_mem" -> "algebra", "multiset.powerset_len_zero_left" -> "data", "uniform_continuous_of_rat" -> "topology", "pgame.equiv_congr_right" -> "set_theory", "ite_eq_tt_distrib" -> "init", "int.sub_nat_self" -> "init", "measure_theory.measure.haar.prehaar_mono" -> "analysis", "mv_power_series.coeff_monomial" -> "algebra", "dfinsupp.prod_add_index" -> "data", "decidable.or_iff_not_and_not" -> "logic", "mvpfunctor.const.get_map" -> "data", "category_theory.Monad.Mon_to_Monad_obj" -> "category_theory", "convex_halfspace_re_le" -> "analysis", "measure_theory.l1.simple_func.to_simple_func_of_simple_func" -> "analysis", "equiv.arrow_congr_comp" -> "data", "list.length_scanl" -> "data", "add_submonoid.localization_map.lift_spec" -> "algebra", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_hom_assoc" -> "category_theory", "zmod.val_min_abs_def_pos" -> "data", "pgame.le_of_lt" -> "set_theory", "submonoid.comap_comap" -> "algebra", "abs_sub_abs_le_abs_sub" -> "algebra", "cardinal.mk_image_eq_of_inj_on" -> "set_theory", "strict_weak_order.not_lt_of_equiv'" -> "init", "fintype.card_eq_sum_ones" -> "data", "finset.sum_mul_sum" -> "algebra", "subgroup.mem_closure_singleton" -> "algebra", "seq1.bind_ret" -> "data", "primrec.option_map\:2081" -> "computability", "add_monoid_hom.iterate_map_zero" -> "algebra", "measure_theory.integral_indicator" -> "analysis", "measure_theory.l1.measurable" -> "analysis", "pow_le_max_of_min_le" -> "algebra", "free_comm_ring.exists_finite_support" -> "algebra", "opposite.equiv_to_opposite_symm_apply" -> "data", "finsupp.lmap_domain_comp" -> "algebra", "fin.val_zero" -> "init", "differentiable_on.ccos" -> "analysis", "linear_map.to_pmap_apply" -> "algebra", "localization_map.mk'_self" -> "algebra", "category_theory.nat_iso.trans_app" -> "category_theory", "polynomial.of_mem_support_derivative" -> "data", "principal_seg.cod_restrict_apply" -> "set_theory", "le_inv_of_neg" -> "algebra", "fin.last_val" -> "data", "measure_theory.measure.zero_le" -> "analysis", "category_theory.functor.const.obj_obj" -> "category_theory", "open_add_subgroup.ext" -> "topology", "add_monoid_hom.range_top_iff_surjective" -> "algebra", "sub_add_sub_cancel'" -> "algebra", "linear_map.add_apply" -> "algebra", "submodule.coe_eq_zero" -> "algebra", "real.image_Icc" -> "topology", "add_submonoid.mrange_inr" -> "algebra", "padic_norm_z.eq_of_norm_add_lt_left" -> "data", "two_dvd_bit0" -> "algebra", "adic_completion.eval_apply" -> "algebra", "complex.continuous_cos" -> "analysis", "multiset.coe_filter" -> "data", "nat.div_lt_iff_lt_mul" -> "init", "cast_eq" -> "init", "equiv.perm.card_support_swap_mul" -> "algebra", "continuous_multilinear_map.mk_pi_field_apply" -> "analysis", "con.refl" -> "algebra", "roption.coe_none" -> "data", "finset.filter_subset_filter" -> "data", "cardinal.ord_le" -> "set_theory", "list.lookmap_cons_none" -> "data", "fin.ext" -> "data", "set.surj_on_Union_Union" -> "data", "ordinal.le_add_sub" -> "set_theory", "topological_space.opens.map_comp_inv_app" -> "topology", "is_R_or_C.abs_sub_le" -> "data", "add_submonoid.mem_sup" -> "algebra", "finset.disjoint_iff_inter_eq_empty" -> "data", "coe_frobenius_equiv_symm" -> "algebra", "of_add_to_add" -> "algebra", "interval_integral.integral_has_strict_deriv_at_of_tendsto_ae_right" -> "analysis", "ennreal.some_eq_coe" -> "data", "unique_mdiff_on.unique_diff_on" -> "geometry", "set.preimage_mul_const_Ici" -> "data", "set.Ioi_inter_Ioi" -> "data", "fixed_points.minpoly.ne_one" -> "algebra", "category_theory.limits.binary_cofan.is_colimit.hom_ext" -> "category_theory", "ring_hom.coe_one" -> "algebra", "finsupp.lsingle_apply" -> "algebra", "ring_hom.range_top_of_surjective" -> "algebra", "and.congr_right_iff" -> "logic", "cardinal.ord_zero" -> "set_theory", "ordinal.ord_cof_eq" -> "set_theory", "eq_sub_iff_add_eq'" -> "algebra", "dioph.reindex_dioph_fn" -> "number_theory", "stream.const_eq" -> "data", "ordinal.div_add_mod" -> "set_theory", "set.coe_inclusion" -> "data", "right_ord_continuous.map_cInf" -> "order", "mem_nhds_within_Iic_iff_exists_Icc_subset" -> "topology", "ring.fractional_ideal.fractional_inf" -> "algebra", "unique_mdiff_on.smooth_bundle_preimage" -> "geometry", "dvd_lcm_right" -> "algebra", "inner_product_geometry.cos_angle_sub_add_angle_sub_rev_eq_neg_cos_angle" -> "geometry", "convex_hull_exists_dist_ge" -> "analysis", "list.prod_erase" -> "data", "matrix.special_linear_group.det_coe_matrix" -> "algebra", "set.finite.finite_subsets" -> "data", "zorn.chain.total" -> "order", "asymptotics.is_O_with_iff" -> "analysis", "continuous_multilinear_curry_fin0_symm_apply" -> "analysis", "measure_theory.measure.finite_at_filter.filter_sup" -> "analysis", "ordinal.sub_eq_of_add_eq" -> "set_theory", "Module.range_eq_top_of_epi" -> "algebra", "real.sin_square" -> "data", "category_theory.is_iso.hom_inv_id_assoc" -> "category_theory", "real.is_conjugate_exponent.nonneg" -> "data", "list.perm.kerase" -> "data", "submonoid.powers_subset" -> "algebra", "measurable_supr" -> "analysis", "measure_theory.l1.norm_eq_norm_to_fun" -> "analysis", "typevec.append_fun_inj" -> "data", "filter.frequently_true_iff_ne_bot" -> "order", "cardinal.lift_succ" -> "set_theory", "add_subgroup.gc_map_comap" -> "algebra", "category_theory.monoidal_category.left_assoc_tensor_map" -> "category_theory", "or_eq_of_eq_true_left" -> "init", "measure_theory.inner_content_exists_compact" -> "analysis", "int.add_assoc_aux2" -> "init", "upper_bounds_Iio" -> "order", "category_theory.functor.sum_obj_inl" -> "category_theory", "add_submonoid.multiples_eq_closure" -> "algebra", "ennreal.top_rpow_def" -> "analysis", "fin.le_last" -> "data", "add_con.induction_on\:2082" -> "algebra", "is_coprime.of_mul_add_right_left" -> "algebra", "set.prod_univ_range_eq" -> "data", "filter.rcomap'_sets" -> "order", "category_theory.limits.functor_category_limit_cone_\[Pi]_app_app" -> "category_theory", "alg_equiv.map_one" -> "algebra", "real.sin_arctan" -> "analysis", "equiv.add_left_symm" -> "data", "subalgebra.sum_mem" -> "algebra", "linear_map.coprod_inl_inr" -> "algebra", "ennreal.bot_eq_zero" -> "data", "list.forall\:2082_nil_right_iff" -> "data", "quotient_map.continuous" -> "topology", "nat.gcd_eq_right" -> "data", "set.countable_encodable" -> "data", "filter.tendsto_at_bot_of_monotone_of_filter" -> "order", "category_theory.limits.cone.functor_w" -> "category_theory", "neg_one_gsmul" -> "algebra", "compl_le_iff_compl_le" -> "order", "sum.naturality" -> "control", "set.sInter_image" -> "data", "cardinal.lt_lift_iff" -> "set_theory", "mfderiv_within_id" -> "geometry", "simple_graph.trace_adj_matrix" -> "combinatorics", "multiset.mem_sub_of_nodup" -> "data", "exists_unique.unique" -> "logic", "finset.sort_eq" -> "data", "multiset.card_antidiagonal" -> "data", "exists_nat_pow_near" -> "algebra", "int.eq_one_of_dvd_one" -> "data", "set.range_smul_range" -> "algebra", "multiset.bind_hcongr" -> "data", "polynomial.comp_eq_sum_left" -> "data", "list.map_eq_map" -> "data", "add_subgroup.sub_mem" -> "algebra", "gcd_dvd_gcd_mul_right" -> "algebra", "int.le_of_dvd" -> "data", "asymptotics.is_o_id_const" -> "analysis", "associates.prod_add" -> "algebra", "list.mem_iff_nth" -> "data", "pequiv.bot_trans" -> "data", "dim_span_le" -> "algebra", "finset.val_eq_zero" -> "data", "multiset.count_eq_zero_of_not_mem" -> "data", "weighted_vsub_mem_vector_span" -> "algebra", "mv_polynomial.rename_rename" -> "data", "Sup_inter_le" -> "order", "fderiv_sum" -> "analysis", "inner_product_space.of_core.inner_mul_inner_self_le" -> "analysis", "padic_norm.add_eq_max_of_ne" -> "data", "mv_polynomial.C_sub" -> "data", "subsingleton.set_cases" -> "data", "mul_min_of_nonneg" -> "algebra", "linear_map.range_smul" -> "algebra", "exists_ratio_deriv_eq_ratio_slope" -> "analysis", "coe_sort_ff" -> "init", "pos_num.cast_sub'" -> "data", "inv_add_inv" -> "algebra", "category_theory.category_of_elements.comp_val" -> "category_theory", "times_cont_mdiff.times_cont_mdiff_tangent_map" -> "geometry", "has_deriv_within_at.rpow_of_one_le" -> "analysis", "list.mem_lookup_kunion_middle" -> "data", "is_lub_univ" -> "order", "game.add_comm" -> "set_theory", "measure_theory.integrable_add" -> "analysis", "commute.gpow_left" -> "algebra", "nnreal.div_self_le" -> "data", "int.le_mul_of_div_le" -> "data", "dioph.abs_poly_dioph" -> "number_theory", "asymptotics.is_O_neg_left" -> "analysis", "inf_compl_eq_bot" -> "order", "ring.fractional_ideal.le_iff" -> "algebra", "linear_map.exists_right_inverse_of_surjective" -> "algebra", "complex.tendsto_inv" -> "topology", "roption.map_id'" -> "data", "ordinal.power_zero" -> "set_theory", "inf_le_inf" -> "order", "mv_polynomial.map_X" -> "data", "multiset.le_smul_erase_dup" -> "data", "list.to_finset_cons" -> "data", "add_monoid_hom.prod_unique" -> "algebra", "filter.eventually_eq_principal" -> "order", "ennreal.sub_lt_sub_self" -> "data", "deriv_sin" -> "analysis", "alg_hom.map_mul" -> "algebra", "submodule.span_zero" -> "algebra", "category_theory.under.post_obj" -> "category_theory", "category_theory.comonad.coalgebra.EilenbergMoore_to_category_struct_to_has_hom_hom" -> "category_theory", "zsqrtd.nonneg_mul" -> "data", "metric.emetric_ball_nnreal" -> "topology", "pnat.xgcd_type.reduce_b" -> "data", "imp_of_not_imp_not" -> "tactic", "measure_theory.l1.smul_to_fun" -> "analysis", "has_strict_deriv_at_id" -> "analysis", "filter.rcomap'_rcomap'" -> "order", "opposite.unop_eq_iff_eq_op" -> "data", "add_submonoid.coe_eq_coe" -> "algebra", "seq.of_stream_cons" -> "data", "turing.blank_rel.symm" -> "computability", "multiset.filter_map_cons_some" -> "data", "is_subgroup.mem_trivial" -> "algebra", "filter.eventually_true" -> "order", "polynomial.map_div" -> "data", "onote.NF.zero_of_zero" -> "set_theory", "differentiable_within_at_inter" -> "analysis", "turing.TM1to0.tr_supports" -> "computability", "differentiable_within_at.congr_mono" -> "analysis", "category_theory.limits.prod_comparison_inv_natural_assoc" -> "category_theory", "finset.sum_bij_ne_zero" -> "algebra", "nnreal.continuous_at_rpow" -> "analysis", "prod_X_sub_smul.smul" -> "algebra", "real.sqrt_eq_zero_of_nonpos" -> "data", "subgroup.mem_normalizer_iff" -> "algebra", "finset.map_to_finset" -> "data", "category_theory.limits.colimit.pre_map" -> "category_theory", "commute.cast_nat_mul_self" -> "algebra", "finsupp.support_add_eq" -> "data", "free_group.red.antisymm" -> "algebra", "asymptotics.is_O.smul_is_o" -> "analysis", "local_homeomorph.restr_open_to_local_equiv" -> "topology", "inv_lt" -> "algebra", "mvpfunctor.comp.get_map" -> "data", "mdifferentiable_within_at_univ" -> "geometry", "tendsto_order_unbounded" -> "topology", "composition.ones_embedding" -> "combinatorics", "subring.closure_eq" -> "algebra", "additive.is_add_subgroup" -> "algebra", "rel_iso.to_equiv_injective" -> "order", "add_units.neg_add_cancel_left" -> "algebra", "add_div'" -> "algebra", "list.nodupkeys_iff_pairwise" -> "data", "category_theory.over.id_left" -> "category_theory", "roption.to_of_option" -> "data", "list.sublist_suffix_of_union" -> "data", "multiset.mem_of_mem_erase" -> "data", "traversable.foldl.unop_of_free_monoid" -> "control", "eq_of_uniformity_inf_nhds" -> "topology", "measurable_space.induction_on_inter" -> "analysis", "fin.cast_succ_lt_last" -> "data", "equiv.Pi_congr_left'_symm_apply" -> "data", "monoid_hom.coe_of_mdense" -> "algebra", "linear_equiv.map_ne_zero_iff" -> "algebra", "exists_deriv_eq_slope" -> "analysis", "valuation.supp_quot_supp" -> "algebra", "ring_char.eq" -> "algebra", "inner_product_space.of_core.abs_inner_le_norm" -> "analysis", "exists_ratio_has_deriv_at_eq_ratio_slope" -> "analysis", "multilinear_map.add_apply" -> "algebra", "turing.TM1to0.tr_eval" -> "computability", "finset.piecewise_insert_of_ne" -> "data", "deriv_within_log'" -> "analysis", "with_bot.coe_zero" -> "algebra", "segment_symm" -> "analysis", "measure_theory.simple_func.integral_sub" -> "analysis", "continuous.tendsto" -> "topology", "nat.mul_div_le_mul_div_assoc" -> "data", "cau_seq.sub_apply" -> "data", "lipschitz_with.continuous" -> "topology", "exists_norm_eq_infi_of_complete_subspace" -> "analysis", "finsupp.support_subset_iff" -> "data", "ring_hom.map_prod" -> "algebra", "convex_on.convex_epigraph" -> "analysis", "subring.add_mem" -> "algebra", "inner_product_geometry.cos_angle_add_angle_sub_add_angle_sub_eq_neg_one" -> "geometry", "pos_num.cast_to_num" -> "data", "multiset.coe_subset" -> "data", "list.unzip_left" -> "data", "mem_left_add_coset" -> "algebra", "archimedean_iff_rat_le" -> "algebra", "vector_space.eval_ker" -> "algebra", "category_theory.under.w" -> "category_theory", "Gromov_Hausdorff.HD_below_aux1" -> "topology", "matrix.det_permute" -> "algebra", "ennreal.coe_inv_le" -> "data", "cardinal.mk_univ_real" -> "data", "ennreal.coe_tsum" -> "topology", "primrec.comp" -> "computability", "multiset.exists_cons_of_mem" -> "data", "is_open_Iio" -> "topology", "plift.up_down" -> "init", "category_theory.over.construct_products.cones_equiv_inverse_2" -> "category_theory", "nat.div_eq_self" -> "data", "padic.cast_eq_of_rat" -> "data", "interval_integral.deriv_within_integral_of_tendsto_ae_right" -> "analysis", "differentiable_on_pow" -> "analysis", "set.union_subset_iff" -> "data", "finset.prod_range_eq_prod_fin" -> "data", "onote.NF_below_zero" -> "set_theory", "complex.sub_re" -> "data", "mem_nhds_within_Ioi_iff_exists_Ioo_subset'" -> "topology", "continuous_linear_map.add_comp" -> "topology", "generalized_continued_fraction.zero_le_of_denom" -> "algebra", "semimodule.restrict_scalars_smul_def" -> "algebra", "nat.partrec.code.rec_computable" -> "computability", "nat.modeq.modeq_of_modeq_mul_left" -> "data", "simple_graph.transpose_adj_matrix" -> "combinatorics", "iterated_fderiv_succ_eq_comp_right" -> "analysis", "dim_le_of_submodule" -> "algebra", "div_le_div'" -> "algebra", "add_left_eq_self" -> "algebra", "polynomial.irreducible_of_eisenstein_criterion" -> "algebra", "list.ext_le" -> "data", "category_theory.limits.image.as_\[Iota]" -> "category_theory", "is_min_on_iff" -> "order", "measurable_id" -> "analysis", "inv_mul_cancel_left'" -> "algebra", "zero_eq_edist" -> "topology", "fin.of_nat_zero" -> "init", "summable_sum" -> "topology", "set.bInter_insert" -> "data", "div_zero" -> "algebra", "vadd_left_cancel_iff" -> "algebra", "convex_halfspace_lt" -> "analysis", "forall_imp" -> "logic", "asymptotics.is_o.of_const_mul_right" -> "analysis", "bilin_form.neg_apply" -> "algebra", "matrix.dot_product_empty" -> "data", "real.log_neg" -> "analysis", "pfunctor.approx.head_succ'" -> "data", "compl_inf_eq_bot" -> "order", "ring_hom.iterate_map_neg" -> "algebra", "dim_fun" -> "algebra", "free_abelian_group.add_bind" -> "algebra", "lt_mul_of_one_le_of_lt'" -> "algebra", "finset.prod_subtype_of_mem" -> "algebra", "category_theory.functor_to_types.hcomp" -> "category_theory", "list.cons_ne_self" -> "data", "submonoid.localization_map.map_mul_right" -> "algebra", "category_theory.limits.biproduct.hom_ext'" -> "category_theory", "category_theory.equivalence.functor_map_inj_iff" -> "category_theory", "is_local_min_on.comp_antimono" -> "topology", "filter.tendsto_finset_preimage_at_top_at_top" -> "order", "primrec.vector_of_fn'" -> "computability", "set.Ioo_subset_Ioo" -> "data", "polynomial.coeff_smul'" -> "algebra", "real.sinh_add" -> "data", "set.infinite_univ" -> "data", "category_theory.limits.prod.symmetry_assoc" -> "category_theory", "subgroup.forall" -> "algebra", "affine_subspace.not_le_iff_exists" -> "algebra", "nnreal.inv_zero" -> "data", "matrix.special_linear_group.to_lin_mul" -> "algebra", "fderiv_within_mul_const" -> "analysis", "computation.thinkN_mem" -> "data", "linear_equiv.map_smul" -> "algebra", "free_abelian_group.zero_seq" -> "algebra", "subgroup.is_open_of_open_subgroup" -> "topology", "continuous_multilinear_map.zero_apply" -> "topology", "zsqrtd.bit1_im" -> "data", "list.func.nil_sub" -> "data", "equiv.inv_def" -> "data", "multiset.mem_erase_dup" -> "data", "cardinal.power_le_power_right" -> "set_theory", "pgame.wf_subsequent" -> "set_theory", "norm_num.int_div" -> "tactic", "mul_lt_mul_of_neg_left" -> "algebra", "is_max_filter.min" -> "order", "nat.not_mem_of_lt_Inf" -> "order", "uniform_space.first_countable_topology" -> "topology", "cardinal.lift_le" -> "set_theory", "finset.coe_insert" -> "data", "antilipschitz_with.mul_le_edist" -> "topology", "ordinal.div_le" -> "set_theory", "ring_hom.functions_ext" -> "algebra", "galois_connection.monotone_intro" -> "order", "ordinal.le_log" -> "set_theory", "normed_field.punctured_nhds_ne_bot" -> "analysis", "algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply" -> "algebra", "ideal.unit_mul_mem_iff_mem" -> "algebra", "isometric.point_reflection_fixed_iff" -> "analysis", "semimodule.eq_zero_of_zero_eq_one" -> "algebra", "measure_theory.outer_measure.map_apply" -> "analysis", "decidable.eq_or_lt_of_le" -> "init", "category_theory.limits.bicone_\[Iota]_\[Pi]_self" -> "category_theory", "real.tendsto_exp_neg_at_top_nhds_0" -> "analysis", "mv_polynomial.coeff_sub" -> "data", "set.image2_union_right" -> "data", "list.mem_inits" -> "data", "has_fderiv_at.fderiv" -> "analysis", "neg_one_smul" -> "algebra", "generalized_continued_fraction.denom_eq_conts_b" -> "algebra", "category_theory.limits.binary_fan.\[Pi]_app_left" -> "category_theory", "sub_right_lt_of_lt_add" -> "algebra", "convex_cone.add_mem" -> "analysis", "filter.frequently.mono" -> "order", "linear_equiv.of_submodule_symm_apply" -> "algebra", "irrational.sub_rat" -> "data", "ring_equiv.symm_trans" -> "data", "multiset.le_ndinter" -> "data", "convex_std_simplex" -> "analysis", "is_closed.closure_eq" -> "topology", "category_theory.limits.prod.symmetry'_assoc" -> "category_theory", "bdd_above.inter_of_right" -> "order", "add_monoid_hom.eq_on_mclosure" -> "algebra", "filter.tendsto_Ixx_class_principal" -> "order", "int.eq_of_sub_eq_zero" -> "init", "encodable.decode_unit_zero" -> "data", "is_R_or_C.of_real_eq_zero" -> "data", "pgame.mk_add_move_right_inl" -> "set_theory", "nat.shiftl'_add" -> "init", "uniform_continuous_neg" -> "topology", "add_semiconj_by.add_left" -> "algebra", "submonoid.closure_eq_mrange" -> "algebra", "ulift.one_down" -> "algebra", "Module.ker_eq_bot_of_mono" -> "algebra", "filter.sup_sets_eq" -> "order", "ennreal.sub_le_sub_add_sub" -> "data", "category_theory.monoidal_category.left_unitor_product_aux_triangle" -> "category_theory", "ideal.eq_bot_of_prime" -> "algebra", "is_measurable.union" -> "analysis", "affine_subspace.mem_coe" -> "algebra", "alg_hom.comp_id" -> "algebra", "list.pairwise.imp" -> "data", "multiplicity.pow'" -> "algebra", "nat.partrec.code.curry_inj" -> "computability", "quotient_group.eq_class_eq_left_coset" -> "algebra", "isometric.coe_to_homeomorph" -> "topology", "tendsto_uniformly.comp" -> "topology", "pfun.preimage_subset_core" -> "data", "multiset.mem_powerset_aux" -> "data", "ennreal.tsum_geometric" -> "analysis", "complex.of_real_pow" -> "data", "real.cos_le_one" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence.functor_map_app_hom" -> "category_theory", "times_cont_mdiff.prod_map" -> "geometry", "is_group_hom.one_iff_ker_inv" -> "algebra", "nat.partrec.code.encode_lt_prec" -> "computability", "linear_equiv.of_submodules_symm_apply" -> "algebra", "finset.sum_mono_set" -> "algebra", "add_monoid_hom.eq_of_eq_on_dense" -> "algebra", "function.embedding.cod_restrict_apply" -> "logic", "add_sub_comm" -> "algebra", "submodule.one_mul" -> "algebra", "summable_of_norm_bounded_eventually" -> "analysis", "ordinal.unbounded_of_unbounded_Union" -> "set_theory", "linear_pmap.right_le_sup" -> "algebra", "lie_subalgebra.mem_coe" -> "algebra", "equiv.perm.cycle_of_pow_apply_self" -> "algebra", "coe_fn_coe_trans" -> "logic", "int.nat_abs_div" -> "data", "measure_theory.ae_eq_fun.one_def" -> "analysis", "finsupp.subtype_domain_finsupp_sum" -> "data", "nat.choose_eq_zero_of_lt" -> "data", "composition_as_set.to_composition_blocks" -> "combinatorics", "ne_bot_of_le_ne_bot" -> "order", "hyperreal.is_st_Sup" -> "data", "polynomial.leading_coeff_mul_X_pow" -> "data", "nsmul_one" -> "algebra", "times_cont_diff_within_at.mono" -> "analysis", "computation.not_terminates_empty" -> "data", "ultrafilter_is_closed_basic" -> "topology", "pi_Lp.lipschitz_with_equiv" -> "topology", "monoid.closure_subset" -> "algebra", "is_closed_induced_iff" -> "topology", "convex_halfspace_im_lge" -> "analysis", "zero_lt_one'" -> "algebra", "set.compl_univ" -> "data", "set.Iic_singleton_of_bot" -> "data", "filter.eventually_eq.trans_le" -> "order", "subsemiring.nsmul_mem" -> "algebra", "nat.le_rec_on_trans" -> "data", "omega.nat.univ_close_of_valid" -> "tactic", "real.sin_square_pi_over_two_pow" -> "analysis", "add_sub_add_left_eq_sub" -> "algebra", "continuous_Sup_rng" -> "topology", "affine.simplex.altitude_def" -> "geometry", "finset.mem_insert_self" -> "data", "subgroup.closure_eq" -> "algebra", "norm_num.subst_into_mul" -> "tactic", "one_half_pos" -> "algebra", "padic_norm_e.norm_int_le_one" -> "data", "char_matrix_apply_eq" -> "algebra", "auto.not_implies_eq" -> "tactic", "filter.is_countably_generated.subseq_tendsto" -> "order", "measurable_infi" -> "analysis", "filter.is_bounded_top" -> "order", "list.perm.union_right" -> "data", "set.inv_preimage" -> "algebra", "emetric.totally_bounded_iff'" -> "topology", "nnreal.lt_inv_iff_mul_lt" -> "data", "roption.pure_eq_some" -> "data", "le_of_tendsto_of_tendsto" -> "topology", "setoid.eq_of_mem_classes" -> "data", "has_strict_fderiv_at.mem_implicit_to_local_homeomorph_of_complemented_source" -> "analysis", "ordinal.zero_mul" -> "set_theory", "multiset.Ico.map_add" -> "data", "monotonicity.not" -> "meta", "nat.sub_lt_self" -> "data", "equiv.sum_prod_distrib_apply_right" -> "data", "ordinal.sub_self" -> "set_theory", "category_theory.nat_iso.cancel_nat_iso_inv_right_assoc" -> "category_theory", "enat.to_with_top_coe'" -> "data", "div_eq_zero_iff" -> "algebra", "nat.rfind_min'" -> "computability", "asymptotics.is_O_with_const_const" -> "analysis", "frobenius_pth_root" -> "algebra", "turing.to_partrec.code.ok.zero" -> "computability", "differentiable_at.deriv_within" -> "analysis", "set.Ioi_subset_Ioi_iff" -> "data", "ring_hom.coe_range" -> "algebra", "min_lt_min" -> "algebra", "category_theory.adjunction.hom_equiv_naturality_right_symm" -> "category_theory", "znum.cast_bitm1" -> "data", "dense_inducing.closure_image_nhds_of_nhds" -> "topology", "category_theory.limits.bicone.to_binary_bicone_inl" -> "category_theory", "asymptotics.is_O_with.prod_left_snd" -> "analysis", "composition_as_set.card_boundaries_pos" -> "combinatorics", "list.infix_of_mem_join" -> "data", "power_series.order_finite_of_coeff_ne_zero" -> "algebra", "sum.uniformity" -> "topology", "set.Icc_eq_empty_iff" -> "data", "locally_finite.realizer.to_locally_finite" -> "data", "inv_gold" -> "data", "asymptotics.is_o.is_O" -> "analysis", "polynomial.eval_neg" -> "data", "list.length_revzip" -> "data", "tsum_geometric_of_norm_lt_1" -> "analysis", "open_subgroup.coe_injective" -> "topology", "int.dist_cast_real" -> "topology", "is_R_or_C.norm_sq_one" -> "data", "cardinal.mul_eq_max" -> "set_theory", "ring_hom.map_nat_cast" -> "data", "sub_le_self_iff" -> "algebra", "filter.tendsto.eventually" -> "order", "neg_lie" -> "algebra", "ordinal.omin_le" -> "set_theory", "function.support_sup" -> "data", "list.lookup_kunion_right" -> "data", "is_compact.image_of_continuous_on" -> "topology", "antisymm" -> "init", "equiv.perm.exists_gpow_eq_of_is_cycle" -> "algebra", "opposite.op_unop" -> "data", "polynomial.div_by_monic_eq_div" -> "data", "ennreal.mul_le_mul_left" -> "data", "zmod.cast_val" -> "data", "measure_theory.measure.add_le_add" -> "analysis", "submodule.linear_eq_on" -> "algebra", "zorn.zorn_subset\:2080" -> "order", "nat.even_mul" -> "data", "is_R_or_C.abs_neg" -> "data", "not_of_iff_false" -> "init", "category_theory.limits.prod_map_map" -> "category_theory", "set.Icc_subset_Ioi_iff" -> "data", "category_theory.limits.colimit.cocone_\[Iota]" -> "category_theory", "num.cmp_swap" -> "data", "matrix.mul_adjugate" -> "algebra", "submonoid.localization_map.mul_equiv_of_localizations_left_inv_apply" -> "algebra", "set.inter_neg" -> "algebra", "filter.pmap_res" -> "order", "list.forall_mem_of_fn_iff" -> "data", "cSup_Iic" -> "order", "category_theory.monoidal.Mon_functor_category_equivalence.unit_iso_hom_app_hom_app" -> "category_theory", "mul_aut.one_apply" -> "data", "list.init_append_last'" -> "data", "category_theory.monoidal_category.right_unitor_product_aux_square" -> "category_theory", "monoid_hom.mrestrict_apply" -> "algebra", "filter.germ.const_le_iff" -> "order", "Ioi_mem_nhds" -> "topology", "equiv.swap_apply_self" -> "data", "finset.sorted_zero_eq_min'" -> "data", "gaussian_int.to_complex_sub" -> "data", "asymptotics.is_O.const_mul_right" -> "analysis", "category_theory.limits.prod_map_comp_id_assoc" -> "category_theory", "wseq.exists_dropn_of_mem" -> "data", "nat.prime.coprime_pow_of_not_dvd" -> "data", "set.Icc_subset_Ioo_iff" -> "data", "is_compl.inf_eq_bot" -> "order", "real.sin_two_pi" -> "analysis", "subtype.coind_injective" -> "data", "finsupp.smul_apply" -> "data", "category_theory.quotient.lift_map" -> "category_theory", "lt_imp_lt_of_le_imp_le" -> "algebra", "pi_eq_sum_univ" -> "algebra", "continuous_on.preimage_open_of_open" -> "topology", "int.sub_nat_nat_add_left" -> "init", "ordinal.is_normal.bsup" -> "set_theory", "set.bUnion_subset_bUnion_right" -> "data", "generalized_continued_fraction.le_of_succ_succ_nth_continuants_aux_b" -> "algebra", "groupoid_of_pregroupoid_le" -> "geometry", "affine_span_nonempty" -> "algebra", "category_theory.limits.cone_of_cocone_left_op_X" -> "category_theory", "prod.snd_mul" -> "algebra", "mul_comm_div'" -> "algebra", "bounded_lattice.ext" -> "order", "nonneg_of_mul_nonneg_left" -> "algebra", "typevec.id_eq_nil_fun" -> "data", "commute.neg_one_right" -> "algebra", "ordinal.one_CNF" -> "set_theory", "mul_div_cancel_of_imp'" -> "algebra", "asymptotics.is_O_with.weaken" -> "analysis", "seq.nil_append" -> "data", "filter.ptendsto_def" -> "order", "linear_equiv.conj_id" -> "algebra", "list.cons_subset_cons" -> "init", "padic_seq.norm_nonzero_of_not_equiv_zero" -> "data", "int.modeq.modeq_mul_left" -> "data", "is_min_on.localize" -> "topology", "option.get_of_mem" -> "data", "deriv_within_const" -> "analysis", "polynomial.splits_of_splits_of_dvd" -> "algebra", "continuous_linear_equiv.is_O_sub_rev" -> "analysis", "finmap.lookup_union_right" -> "data", "length_perms_of_list" -> "data", "filter.eventually.frequently" -> "order", "is_closed_map_mul_right" -> "topology", "category_theory.prod.snd_map" -> "category_theory", "le_of_span_le_span" -> "algebra", "list.mem_sublists_len_self" -> "data", "mvqpf.Wrepr_equiv" -> "data", "path.target" -> "topology", "add_submonoid.localization_map.lift_left_inverse" -> "algebra", "nat.prime_dvd_prime_iff_eq" -> "data", "complex.differentiable_at_sinh" -> "analysis", "times_cont_diff_on.fderiv_within" -> "analysis", "submodule.mem_supr_of_mem" -> "algebra", "real.cos_pi_div_four" -> "analysis", "quot.induction_on\:2083" -> "data", "setoid.symm'" -> "data", "perfect_closure.mk_zero" -> "algebra", "circle_deg1_lift.mul_apply" -> "dynamics", "finset.mem_map'" -> "data", "ennreal.bit1_eq_top_iff" -> "data", "polynomial.degree_nonneg_iff_ne_zero" -> "data", "complex.arg_eq_arg_neg_add_pi_of_im_nonneg_of_re_neg" -> "analysis", "fin.find_eq_none_iff" -> "data", "state_t.run_map" -> "init", "int.mul_lt_mul" -> "init", "pnat.mod_coe" -> "data", "category_theory.non_preadditive_abelian.image.fac" -> "category_theory", "dense" -> "order", "matrix.det_permutation" -> "algebra", "omega.coeffs.val_set" -> "tactic", "asymptotics.is_O_bot" -> "analysis", "onote.NF.below_of_lt" -> "set_theory", "category_theory.arrow.lift_mk'_left_assoc" -> "category_theory", "filter.realizer.top_F" -> "data", "category_theory.iso.symm_eq_iff" -> "category_theory", "div_div_eq_div_mul" -> "algebra", "continuous_linear_equiv.map_neg" -> "topology", "category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom_assoc" -> "category_theory", "continuous_linear_equiv.self_comp_symm'" -> "topology", "neg_mul_eq_neg_mul" -> "algebra", "finset.prod_preimage_of_bij" -> "data", "image_le_of_liminf_slope_right_le_deriv_boundary" -> "analysis", "le_of_neg_of_one_div_le_one_div" -> "algebra", "submonoid.coe_ssubset_coe" -> "algebra", "category_theory.limits.is_limit.of_nat_iso.cone_of_hom_fac" -> "category_theory", "complex.cos_conj" -> "data", "asymptotics.is_O_with.congr_const" -> "analysis", "le_add_of_nonneg_of_le" -> "algebra", "turing.partrec_to_TM2.unrev_ok" -> "computability", "embedding.closure_eq_preimage_closure_image" -> "topology", "quotient.ind\:2082" -> "init", "ennreal.top_sub_coe" -> "data", "add_submonoid.localization_map.map_mk'" -> "algebra", "set.mem_powerset" -> "data", "is_R_or_C.abs_conj" -> "data", "category_theory.adjunction.equiv_homset_right_of_nat_iso_symm_apply" -> "category_theory", "list.perm.filter_map" -> "data", "cardinal.card_ord" -> "set_theory", "list.func.get_map" -> "data", "pnat.gcd_comm" -> "data", "galois_connection.id" -> "order", "complex.cpow_neg" -> "analysis", "lie_algebra.orthogonal.JB_transform" -> "algebra", "eq_pos_center_mass_card_le_dim_succ_of_mem_convex_hull" -> "analysis", "infi_emptyset" -> "order", "complex.I_mul_I" -> "data", "measure_theory.is_left_invariant_conj" -> "analysis", "finset.coe_image_subset_range" -> "data", "multiset.disjoint.symm" -> "data", "quadratic_form.pos_def.add" -> "algebra", "tendsto_nhds_within_mono_right" -> "topology", "set.image2_singleton" -> "data", "is_null_measurable.Union_nat" -> "analysis", "int.mul_self_le_mul_self" -> "init", "submonoid.localization_map.map_eq" -> "algebra", "generalized_continued_fraction.pair.coe_to_generalized_continued_fraction_pair" -> "algebra", "Cauchy.mem_uniformity'" -> "topology", "linear_map.mem_ker" -> "algebra", "modeq_three_digits_sum" -> "data", "adic_completion.eval_comp_of" -> "algebra", "filter.ext_iff" -> "order", "euclidean_geometry.dist_square_eq_dist_square_add_dist_square_sub_two_mul_dist_mul_dist_mul_cos_angle" -> "geometry", "mv_polynomial.eval_unique" -> "data", "cardinal.mk_Ioo_real" -> "data", "int.coe_nat_dvd" -> "data", "norm_num.clear_denom_mul" -> "tactic", "ennreal.of_real_to_real_le" -> "data", "alist.perm_lookup" -> "data", "multiset.card_singleton" -> "data", "ideal.comap_mono" -> "algebra", "multiplicative.is_submonoid_iff" -> "algebra", "set.image_smul" -> "algebra", "finset.inf_eq_inter" -> "data", "linear_map.std_basis_same" -> "algebra", "finset.prod_pair" -> "algebra", "monotone.const_add" -> "algebra", "is_R_or_C.of_real_one" -> "data", "mv_power_series.coeff_C" -> "algebra", "filter.liminf_eq_supr_infi_of_nat" -> "order", "submonoid.mem_Sup_of_directed_on" -> "algebra", "num.cast_one" -> "data", "measure_theory.inner_content_pos" -> "analysis", "lt_of_le_of_ne" -> "init", "topological_space.opens.to_Top_map" -> "topology", "id_rel_sub_separation_relation" -> "topology", "continuous_within_at.continuous_at" -> "topology", "measure_theory.measure.haar.echaar_mono" -> "analysis", "rel_iso.symm_apply_rel" -> "order", "localization.mk_eq_monoid_of_mk'" -> "algebra", "norm_num.clear_denom_lt" -> "tactic", "multiset.map_filter_map" -> "data", "interval_integral.deriv_integral_right" -> "analysis", "bounded_continuous_function.arzela_ascoli\:2082" -> "topology", "midpoint_add_self" -> "algebra", "bdd_above.mono" -> "order", "filter.has_basis.to_has_basis" -> "order", "mdifferentiable_on.comp" -> "geometry", "differentiable_at_inverse" -> "analysis", "int.of_nat_add_neg_succ_of_nat_of_ge" -> "data", "subalgebra.map_le" -> "algebra", "finmap.mem_of_lookup_eq_some" -> "data", "filter.tendsto_iff_ptendsto_univ" -> "order", "add_subgroup.gmultiples_subset" -> "algebra", "fin_enum.nodup_to_list" -> "data", "subgroup.mem_infi" -> "algebra", "equiv.image_compl" -> "data", "geom_series_zero" -> "algebra", "quotient_map.id" -> "topology", "forall_const" -> "logic", "finset.mem_subtype" -> "data", "ideal.eq_top_of_is_unit_mem" -> "algebra", "multiset.bind_map_comm" -> "data", "inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul" -> "analysis", "convex.translate_preimage_right" -> "analysis", "reader_t.run_pure" -> "init", "multiset.Ico.not_mem_top" -> "data", "finset.bInter_inter" -> "data", "ordinal.add_is_limit" -> "set_theory", "polynomial.coeff_X_one" -> "data", "metric.bounded_empty" -> "topology", "unique_factorization_domain.exists_reduced_factors'" -> "algebra", "set.insert_diff_singleton" -> "data", "set.Icc_subset_Icc" -> "data", "Mod.comap_map_hom" -> "category_theory", "category_theory.limits.pullback_cone.mk_\[Pi]_app_right" -> "category_theory", "int.lt_succ" -> "init", "list.nil_diff" -> "data", "monoid_algebra.mul_apply_antidiagonal" -> "data", "option.get_mem" -> "data", "finset.sum_hom_rel" -> "algebra", "linear_equiv_matrix'_apply" -> "algebra", "tactic.ring.horner_atom" -> "tactic", "monotone.mem_lower_bounds_image" -> "order", "with_one.ne_one_iff_exists" -> "algebra", "finset.inf_eq_infi" -> "data", "filter.eventually_lt_of_lt_liminf" -> "order", "tendsto_at_top_mul_right" -> "analysis", "fp.float.zero.valid" -> "data", "smul_algebra_smul_comm" -> "algebra", "lt_of_add_lt_add_right" -> "algebra", "tendsto_locally_uniformly.tendsto_comp" -> "topology", "category_theory.prod.sectl_map" -> "category_theory", "algebra.tensor_product.mul_assoc'" -> "algebra", "summable.add_compl" -> "topology", "totally_bounded.image" -> "topology", "multilinear_map.zero_apply" -> "algebra", "gpow_one" -> "algebra", "option_t.run_map" -> "init", "ennreal.coe_indicator" -> "data", "pos_num.add_succ" -> "data", "ennreal.sum_lt_top" -> "data", "finsupp.mul_sum" -> "data", "loc_path_connected_of_is_open" -> "topology", "zorn.zorn_partial_order" -> "order", "add_semiconj_by.neg_right_iff" -> "algebra", "linear_map.ker_eq_top" -> "algebra", "pfunctor.M.ichildren_mk" -> "data", "finset.sum_Ico_eq_sub" -> "algebra", "measure_theory.outer_measure.is_caratheodory_compl" -> "analysis", "decidable.not_lt" -> "init", "is_scalar_tower.algebra_comap_eq" -> "algebra", "seq.zip_with_nth_some" -> "data", "eq_add_neg_of_add_eq" -> "algebra", "one_lt_mul'" -> "algebra", "generalized_continued_fraction.int_fract_pair.exists_succ_nth_stream_of_gcf_of_nth_eq_some" -> "algebra", "continuous_within_at.add" -> "topology", "multiset.exists_mem_of_rel_of_mem" -> "data", "measurable_space.map_comp" -> "analysis", "multiset.nodup_map_on" -> "data", "submodule.sup_smul" -> "algebra", "cauchy_seq_iff_tendsto" -> "topology", "mv_polynomial.total_degree_C" -> "data", "contracting_with.exists_fixed_point'" -> "topology", "is_add_unit_add_unit" -> "algebra", "filter.germ.lift_pred_coe" -> "order", "contracting_with.fixed_point_unique" -> "topology", "associates.factors_le" -> "algebra", "category_theory.monad.free_obj_a" -> "category_theory", "inv_gold_conj" -> "data", "cau_seq.add_apply" -> "data", "max_eq_neg_min_neg_neg" -> "algebra", "tsum_mul_left" -> "topology", "linear_map.inr_injective" -> "algebra", "category_theory.functor.const.map_app" -> "category_theory", "monotone.map_is_least" -> "order", "set.preimage_mul_const_Ico_of_neg" -> "data", "is_R_or_C.norm_sq_of_real" -> "data", "circle_deg1_lift.translation_number_eq_rat_iff" -> "dynamics", "submonoid.mem_bot" -> "algebra", "inv_lt_of_inv_lt" -> "algebra", "category_theory.limits.epi_of_epi_image" -> "category_theory", "filter.ptendsto_of_ptendsto'" -> "order", "eq_min" -> "init", "add_monoid_hom.snd_comp_prod" -> "algebra", "commute.self_cast_int_mul_cast_int_mul" -> "algebra", "le_inf" -> "order", "submonoid.map_sup" -> "algebra", "rel_iso.coe_fn_injective" -> "order", "le_cSup" -> "order", "nhds_eq_comap_uniformity_aux" -> "topology", "is_closed_le'" -> "topology", "valuation.is_equiv.symm" -> "algebra", "zmod.cast_self" -> "data", "refl_bilin_form.ortho_sym" -> "algebra", "divp_assoc" -> "algebra", "filter.lift'_le" -> "order", "list.length_map" -> "init", "set.Ioc_union_Ioc_symm" -> "data", "mv_polynomial.is_integral_domain_fintype" -> "algebra", "monoid_algebra.one_def" -> "data", "subgroup.top_prod_top" -> "algebra", "linear_independent.repr_ker" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_at_chart" -> "geometry", "rat.neg_def" -> "data", "and.imp_left" -> "logic", "deriv_within_sinh" -> "analysis", "function.semiconj.bij_on_range" -> "data", "measure_theory.simple_func.integral_congr" -> "analysis", "linear_equiv.coe_fn_to_continuous_linear_equiv_of_continuous" -> "analysis", "category_theory.comma.snd_obj" -> "category_theory", "category_theory.limits.biproduct.\[Iota]_\[Pi]" -> "category_theory", "nhds_eq_order" -> "topology", "has_deriv_within_at.cos" -> "analysis", "padic_int.coe_int_eq" -> "data", "linear_map.convex_hull_image" -> "analysis", "int.cast_lt" -> "data", "nat.div_def_aux" -> "init", "set.mem_def" -> "data", "finset.mem_powerset_self" -> "data", "mul_mem_non_zero_divisors" -> "algebra", "is_path_connected_iff_path_connected_space" -> "topology", "local_ring.nonunits_add" -> "algebra", "uniform_space.comap_comap" -> "topology", "filter.lift'_cong" -> "order", "measure_theory.simple_func.range_const" -> "analysis", "times_cont_mdiff_on.of_succ" -> "geometry", "set.add_subset_add" -> "algebra", "set.subset_image_union" -> "data", "zsqrtd.conj_re" -> "data", "deriv.lhopital_zero_at_bot" -> "analysis", "ereal.neg_eq_iff_neg_eq" -> "data", "to_bool_false_eq_ff" -> "init", "ordered_add_comm_group.le_of_add_le_add_left" -> "algebra", "matrix.mul_vec_neg" -> "data", "nat.coprime.pow_right" -> "data", "is_measurable_le" -> "analysis", "false_of_ne" -> "init", "norm_image_sub_le_of_norm_deriv_le_segment_01" -> "analysis", "finset.sum_dite_eq" -> "algebra", "hyperreal.is_st_inj_real" -> "data", "times_cont_diff_groupoid_le" -> "geometry", "nat.coprime_zero_left" -> "data", "is_compact.is_glb_Inf" -> "topology", "cardinal.succ_ne_zero" -> "set_theory", "imp_false" -> "logic", "num.cmp_to_nat" -> "data", "nat.pred_eq_succ_iff" -> "data", "omega.subst_correct" -> "tactic", "d_array.read_write" -> "init", "category_theory.limits.coprod_map_id_comp_assoc" -> "category_theory", "free_group.inv_bind" -> "algebra", "interior_mono" -> "topology", "generalized_continued_fraction.of_terminated_at_iff_int_fract_pair_seq1_terminated_at" -> "algebra", "measure_theory.ae_eq_fun.mk_eq_mk" -> "analysis", "subtype.symm" -> "data", "convex.sum_mem" -> "analysis", "finset.disjoint_filter" -> "data", "lie_algebra.orthogonal.so_indefinite_equiv_apply" -> "algebra", "category_theory.functor.map_iso_refl" -> "category_theory", "ordinal.mod_zero" -> "set_theory", "is_lub.supr_eq" -> "order", "ennreal.measurable_of_measurable_nnreal_nnreal" -> "analysis", "list.chain_cons" -> "data", "exists_has_deriv_within_at_eq_of_gt_of_lt" -> "analysis", "ring.fractional_ideal.fractional_sup" -> "algebra", "set.sUnion_eq_bUnion" -> "data", "nat.subtype.lt_succ_self" -> "data", "polynomial.degree_monomial_le" -> "data", "mjoin_pure" -> "control", "list.subperm_append_right" -> "data", "multiset.le_cons_erase" -> "data", "left_inverse_add_left_sub" -> "algebra", "homeomorph.compact_preimage" -> "topology", "deriv_within_add_const" -> "analysis", "norm_num.lt_one_bit1" -> "tactic", "bounded_continuous_function.dist_le_two_norm" -> "topology", "set.univ_pi_nonempty_iff" -> "data", "list.nodupkeys.eq_of_fst_eq" -> "data", "metric.bounded.finite_measure" -> "analysis", "metric.inf_dist_le_Hausdorff_dist_of_mem" -> "topology", "valuation.ne_zero_iff" -> "algebra", "list.nodup_product" -> "data", "finset.sup_mono_fun" -> "data", "finset.insert_inter_of_mem" -> "data", "padic.complete'" -> "data", "wseq.seq_destruct_cons" -> "data", "functor.comp.seq_assoc" -> "control", "free_add_monoid.map_comp" -> "algebra", "multiset.add_sub_of_le" -> "data", "linear_order.concave_on_of_lt" -> "analysis", "differentiable_at.prod" -> "analysis", "neg_injective" -> "algebra", "monoid_hom.fst_comp_inr" -> "algebra", "inner_product_geometry.angle_smul_right_of_neg" -> "geometry", "linear_independent.comp" -> "algebra", "pgame.numeric_one" -> "set_theory", "order_top.upper_bounds_univ" -> "order", "times_cont_mdiff_on.smooth_on" -> "geometry", "ennreal.le_tsum" -> "topology", "int.nat_abs_bit0_step" -> "init", "list.range'_subset_right" -> "data", "real.tan_pi_div_four" -> "analysis", "real.exp_zero" -> "data", "gpow_mul'" -> "algebra", "is_compact.exists_Sup_image_eq" -> "topology", "decidable.not_iff_not" -> "logic", "add_submonoid.localization_map.of_add_equiv_of_localizations_eq" -> "algebra", "add_submonoid.mem_Inf" -> "algebra", "list.drop_left'" -> "data", "set.left_mem_Ioc" -> "data", "list.drop_take_succ_join_eq_nth_le" -> "data", "matrix.reindex_apply" -> "algebra", "differentiable_within_at.sinh" -> "analysis", "category_theory.limits.biprod.desc_eq" -> "category_theory", "dim_sup_add_dim_inf_eq" -> "algebra", "is_closed_inter" -> "topology", "nat.one_shiftl" -> "init", "direct_sum.of_add" -> "algebra", "linear_map.infi_ker_proj_le_supr_range_std_basis" -> "algebra", "multiset.coe_ndunion" -> "data", "submodule.mul_le_mul" -> "algebra", "pnat.coprime.pow" -> "data", "set.subset_range_enumerate" -> "data", "primrec.dom_bool\:2082" -> "computability", "set.image_add_const_Ioc" -> "data", "equiv.perm.disjoint_prod_perm" -> "algebra", "continuous_on_open_of_generate_from" -> "topology", "finsupp.mem_support_single" -> "data", "continuous_on.inv" -> "topology", "padic_int.valuation_zero" -> "data", "matrix.to_blocks_from_blocks\:2082\:2081" -> "data", "le_inv_of_le_inv" -> "algebra", "polynomial.mem_degree_lt" -> "algebra", "function.iterate_one" -> "logic", "differentiable_at.restrict_scalars" -> "analysis", "list.reverse_perm" -> "data", "lt_trans" -> "init", "category_theory.iso.trans_inv" -> "category_theory", "list.mem_nil_iff" -> "init", "has_deriv_at_filter.tendsto_nhds" -> "analysis", "set.image_compl_eq" -> "data", "basic_smooth_bundle_core.base_set" -> "geometry", "finset.mem_map" -> "data", "ennreal.inv_pow" -> "data", "ring_hom.mem_ker" -> "algebra", "convex_on_of_deriv2_nonneg" -> "analysis", "pgame.right_moves_mk" -> "set_theory", "algebraic_geometry.structure_presheaf_in_CommRing_obj" -> "algebraic_geometry", "vector.tail_of_fn" -> "data", "ordinal.card_zero" -> "set_theory", "category_theory.sum_comp_inr" -> "category_theory", "equiv.swap_apply_left" -> "data", "summable.compl_add" -> "topology", "isometric.ext" -> "topology", "con.con_gen_le" -> "algebra", "finsupp.disjoint_iff" -> "data", "category_theory.functor.const.unop_functor_op_obj_map" -> "category_theory", "nat.prime.not_dvd_mul" -> "data", "linear_equiv.coe_to_add_equiv" -> "algebra", "is_compact.is_lub_Sup" -> "topology", "monoid.closure_mono" -> "algebra", "category_theory.nat_trans.comp_app" -> "category_theory", "polynomial.degree_erase_lt" -> "data", "filter.germ.map_coe" -> "order", "units.coe_mk" -> "algebra", "inner_self_nonneg" -> "analysis", "order_top.bdd_above" -> "order", "monoid_hom.gclosure_preimage_le" -> "algebra", "continuous_linear_equiv.equiv_of_inverse_apply" -> "topology", "int.two_dvd_ne_zero" -> "data", "I_extend_range" -> "topology", "analytic_at.continuous_at" -> "analysis", "dim_fun_eq_lift_mul" -> "algebra", "le_div_iff'" -> "algebra", "set.subsingleton.mono" -> "data", "turing.TM0.step_supports" -> "computability", "homeomorph.to_local_homeomorph_target" -> "topology", "topological_space.opens.comap_mono" -> "topology", "le_of_eq_or_lt" -> "init", "subsemiring.prod_mem" -> "algebra", "convex.affine_preimage" -> "analysis", "complex.abs_exp_of_real" -> "data", "fpow_strict_mono" -> "algebra", "add_equiv.map_eq_zero_iff" -> "data", "filter.tendsto_inf" -> "order", "generalized_continued_fraction.fib_le_of_continuants_aux_b" -> "algebra", "infi_le_infi" -> "order", "asymptotics.is_O_self_const_mul" -> "analysis", "linear_map.comap_map_eq_self" -> "algebra", "multiset.attach_ndinsert" -> "data", "cardinal.lt_omega_iff_fintype" -> "set_theory", "is_measurable_Ico" -> "analysis", "set.image_mul_right" -> "algebra", "category_theory.equivalence.refl_counit_iso" -> "category_theory", "list.last'_is_none" -> "data", "span_int_eq_add_group_closure" -> "algebra", "finset.insert_def" -> "data", "many_one_equiv_refl" -> "computability", "stream.nth_of_bisim" -> "data", "category_theory.abelian.pseudoelement.exact_of_pseudo_exact" -> "category_theory", "nat.bodd_mul" -> "init", "add_group.closure_eq_mclosure" -> "algebra", "affine.simplex.monge_point_eq_affine_combination_of_points_with_circumcenter" -> "geometry", "has_deriv_at.lhopital_zero_left_on_Ioo" -> "analysis", "set.mem_Ioo_or_eq_right_of_mem_Ioc" -> "data", "with_zero.lt_of_mul_lt_mul_left" -> "algebra", "subsemiring.closure_induction" -> "algebra", "add_monoid_algebra.mul_apply" -> "data", "nat.partrec.code.encode_lt_rfind'" -> "computability", "unique_diff_within_at.eq_deriv" -> "analysis", "finset.coe_bind" -> "data", "ordinal.nat_cast_lt" -> "set_theory", "set.Ico_diff_Iio" -> "data", "add_comm_group.direct_limit.induction_on" -> "algebra", "int.lt_irrefl" -> "init", "nnreal.of_real_coe" -> "data", "nat.primrec'.of_eq" -> "computability", "category_theory.equiv_relation" -> "category_theory", "cardinal.add_lt_omega_iff" -> "set_theory", "multiset.Ico.filter_le_of_le" -> "data", "mul_aut.conj_symm_apply" -> "data", "add_submonoid.localization_map.mk'_eq_iff_eq" -> "algebra", "divp_divp_eq_divp_mul" -> "algebra", "hyperreal.not_infinite_pos_of_infinite_neg" -> "data", "category_theory.pi.comap_obj" -> "category_theory", "not_iff" -> "logic", "filter.tendsto.eventually_interval_integrable" -> "analysis", "TopCommRing.coe_of" -> "topology", "polynomial.zero_div_by_monic" -> "data", "has_sum_fintype" -> "topology", "nat.div_eq_iff_eq_mul_right" -> "data", "metric.uniformity_basis_edist" -> "topology", "nat.mul_mod" -> "data", "semiquot.mem_bind" -> "data", "cau_seq.equiv_lim" -> "data", "seq1.map_join'" -> "data", "submodule.quotient.mk_eq_mk" -> "algebra", "is_add_subgroup.coe_neg" -> "algebra", "category_theory.limits.kernel_zero_iso_source_inv" -> "category_theory", "list.foldl_cons" -> "data", "unique_diff_on_univ" -> "analysis", "interval_integrable.neg" -> "analysis", "finset.induction_on" -> "data", "prod.map_fst" -> "data", "lower_bounds_empty" -> "order", "fin.cons_zero" -> "data", "list.perm.bind_right" -> "data", "nat.div_mul_cancel" -> "init", "has_strict_deriv_at.mul" -> "analysis", "alg_hom.comp_algebra_map" -> "algebra", "add_commute.add_left" -> "algebra", "norm_fst_le" -> "analysis", "category_theory.monoidal_category.unitors_equal.cells_4'" -> "category_theory", "category_theory.comonad.cofree_obj_a" -> "category_theory", "set.mul_mem_mul" -> "algebra", "nat.primrec'.tail" -> "computability", "irreducible_iff_of_associated" -> "algebra", "multiset.lift_beta" -> "data", "int.eq_one_of_mul_eq_one_right" -> "data", "subring.prod_mono" -> "algebra", "multiset.mem_ndinter" -> "data", "finset.centroid_def" -> "algebra", "polynomial.mod_by_monic_eq_mod" -> "data", "subgroup.coe_map" -> "algebra", "set.finite.bdd_above_bUnion" -> "data", "Sup_inf_Sup" -> "order", "monoid_hom.coe_mk'" -> "algebra", "polynomial.separable_map" -> "algebra", "add_pow_char_pow_of_commute" -> "algebra", "compl_singleton_mem_nhds" -> "topology", "one_lt_div_of_neg" -> "algebra", "category_theory.abelian.pseudoelement.zero_of_map_zero" -> "category_theory", "nat.le_add_of_sub_le_left" -> "data", "list.erase_dup_sublist" -> "data", "mv_power_series.map_comp" -> "algebra", "hyperreal.gt_of_neg_of_infinitesimal" -> "data", "enat.with_top_equiv_symm_zero" -> "data", "finsupp.support_zip_with" -> "data", "list.concat_eq_reverse_cons" -> "data", "trace_eq_neg_char_poly_coeff" -> "algebra", "ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot" -> "algebra", "measurable_space.ext" -> "analysis", "category_theory.limits.cokernel_iso_of_eq_trans" -> "category_theory", "with_top.mul_coe" -> "algebra", "multiset.nat.card_antidiagonal" -> "data", "finset.sum_union" -> "algebra", "le_nhds_iff_adhp_of_cauchy" -> "topology", "mv_polynomial.is_integral_domain_fin" -> "algebra", "measure_theory.outer_measure.is_caratheodory_iff_le'" -> "analysis", "has_deriv_within_at.smul_const" -> "analysis", "computation.lift_rel_think_left" -> "data", "list.insert_nth_comm" -> "data", "abs_nonneg" -> "algebra", "ring_hom.srestrict_apply" -> "algebra", "category_theory.limits.prod.associator_inv" -> "category_theory", "measure_theory.ae_add_measure_iff" -> "analysis", "nnreal.Lp_add_le" -> "analysis", "real.exp_add" -> "data", "state_t.run_get" -> "init", "equiv.smul_def" -> "data", "topological_space.compacts.bot_val" -> "topology", "continuous_linear_map.times_cont_diff" -> "analysis", "polynomial.nat_degree_to_subring" -> "algebra", "interval_integral.integral_has_strict_fderiv_at_of_tendsto_ae" -> "analysis", "multiset.filter_map_filter_map" -> "data", "has_fderiv_within_at_univ" -> "analysis", "dist_le_of_trajectories_ODE_of_mem_set" -> "analysis", "category_theory.monad.forget_creates_limits.\[Gamma]_app" -> "category_theory", "nat.pred_le_pred" -> "init", "ring.closure_mono" -> "algebra", "set.disjoint_disjointed'" -> "data", "set.image_eq_preimage_of_inverse" -> "data", "ring.fractional_ideal.is_principal_iff" -> "algebra", "tangent_bundle.times_cont_mdiff_within_at_proj" -> "geometry", "filter.eventually_le.trans" -> "order", "finset.inter_subset_inter" -> "data", "omega.mul_symdiv_eq" -> "tactic", "rat_inv_continuous_lemma" -> "data", "list.kerase_keys_subset" -> "data", "nat.zero_mod" -> "init", "function.surjective.forall\:2083" -> "logic", "padic.exi_rat_seq_conv_cauchy" -> "data", "category_theory.limits.prod.braiding_inv" -> "category_theory", "coe_sort_coe_trans" -> "logic", "fin.coe_fin_le" -> "data", "cardinal.aleph_idx.initial_seg_coe" -> "set_theory", "functor.comp.functor_comp_id" -> "control", "wseq.destruct_terminates_of_nth_terminates" -> "data", "set_has_maximal_iff_noetherian" -> "algebra", "lists'.mem_of_subset" -> "set_theory", "finset.prod_inter_mul_prod_diff" -> "algebra", "floor_sub_int" -> "algebra", "list.length_join" -> "data", "localization_map.exist_integer_multiples_of_finset" -> "algebra", "group.normal_closure_subset" -> "algebra", "dioph.inject_dummies" -> "number_theory", "nnreal.has_sum_geometric" -> "analysis", "finsupp.sum_map_range_index" -> "data", "with_top.mul_def" -> "algebra", "polynomial.degree_sum_le" -> "data", "ODE_solution_unique_of_mem_set" -> "analysis", "mv_polynomial.eval\:2082_comp_left" -> "data", "bounded_continuous_function.add_apply" -> "topology", "set.preimage_add_const_Ioo" -> "data", "set.diff_subset_diff" -> "data", "measure_theory.measure.haar.chaar_sup_eq" -> "analysis", "boole_mul" -> "algebra", "matrix.map_apply" -> "data", "filter.tendsto.basis_right" -> "order", "primrec\:2082.swap" -> "computability", "continuous_linear_equiv.skew_prod_symm_apply" -> "topology", "encodable.length_le_encode" -> "data", "category_theory.eq_to_iso.inv" -> "category_theory", "function.semiconj.comp_eq" -> "logic", "unique_mdiff_on.unique_diff_on_inter_preimage" -> "geometry", "order_dual.dual_lt" -> "order", "computable.option_bind" -> "computability", "complex.of_real_cosh" -> "data", "zmod.val_cast_nat" -> "data", "localization_map.coeff_integer_normalization_mem_support" -> "algebra", "submonoid.mem_nhds_one" -> "topology", "polynomial.div_X_add" -> "data", "finset.sup_le_iff" -> "data", "asymptotics.is_o.congr_right" -> "analysis", "rank_zero" -> "algebra", "measurable_nndist" -> "analysis", "tactic.ring_exp.pow_e_pf_exp" -> "tactic", "category_theory.eq_to_hom_refl" -> "category_theory", "multiset.nodup_product" -> "data", "nat.add_sub_add_right" -> "init", "vector.map_cons" -> "data", "omega.term.val_sub" -> "tactic", "rel_embedding.is_strict_total_order'" -> "order", "norm_num.bit0_succ" -> "tactic", "set.bij_on.to_local_equiv_target" -> "data", "one_lt_fpow" -> "algebra", "continuous_inclusion" -> "topology", "true_equivalence" -> "data", "formal_multilinear_series.le_comp_radius_of_summable" -> "analysis", "with_top.coe_le_coe" -> "order", "cardinal.two_le_iff'" -> "set_theory", "dfinsupp.single_zero" -> "data", "le_bsupr" -> "order", "deriv.neg'" -> "analysis", "differentiable_within_at.const_mul" -> "analysis", "list.mem_to_finset" -> "data", "measure_theory.measure_Union_le" -> "analysis", "cancel_factors.cancel_factors_lt" -> "tactic", "is_open_bInter" -> "topology", "filter.strict_mono_subseq_of_id_le" -> "order", "fin.coe_succ" -> "data", "set.mem_or_mem_of_mem_union" -> "data", "continuous_if" -> "topology", "polynomial.degree_le_mono" -> "algebra", "tensor_product.lift.tmul'" -> "algebra", "add_monoid_hom.fst_comp_inl" -> "algebra", "category_theory.eq_to_hom_app" -> "category_theory", "has_deriv_at.exp" -> "analysis", "affine_map.homothety_mul" -> "algebra", "lie_algebra.orthogonal.mem_so" -> "algebra", "encodable.skolem" -> "data", "closure_eq_cluster_pts" -> "topology", "affine_map.ext" -> "algebra", "tendsto_uniformly_on_univ" -> "topology", "asymptotics.is_O_with.symm" -> "analysis", "ideal.exists_maximal" -> "algebra", "mem_closure_of_is_glb" -> "topology", "list.last_congr" -> "data", "polynomial.coeff_sum" -> "data", "num.ppred_to_nat" -> "data", "subsemiring.mem_closure_iff" -> "algebra", "nat.mul_pos" -> "init", "continuous_multilinear_map.continuous_eval" -> "analysis", "decidable.not_iff_comm" -> "logic", "Ico_mem_nhds_within_Iio" -> "topology", "nndist_smul" -> "analysis", "add_submonoid.localization_map.map_units" -> "algebra", "measure_theory.integrable_on_union" -> "analysis", "add_group_with_zero_nhd.nhds_eq" -> "topology", "char.ne_of_vne" -> "init", "list.eq_of_sublist_of_length_eq" -> "data", "filter.sInter_comap_sets" -> "order", "ordinal.mul_is_limit_left" -> "set_theory", "real.arsinh_sinh" -> "analysis", "finset.prod_eq_zero_iff" -> "algebra", "monoid_hom.coe_mrange_restrict" -> "algebra", "category_theory.limits.bicone.to_cocone_\[Iota]_app" -> "category_theory", "matrix.cons_zero_zero" -> "data", "omega.coeffs.val_sub" -> "tactic", "polynomial.splits_prod" -> "algebra", "linear_map.prod_eq_sup_map" -> "algebra", "is_open_gt'" -> "topology", "filter.mem_infi_sets" -> "order", "pgame.add_comm_equiv" -> "set_theory", "stream.nth_zero_iterate" -> "data", "list.take_sum_join" -> "data", "le_supr_of_le" -> "order", "finset.filter_ne" -> "data", "galois_connection.u_unique" -> "order", "linear_map.coe_fn_congr" -> "algebra", "emetric.nhds_eq" -> "topology", "nat.decreasing_induction_self" -> "data", "real.sqrt_eq_iff_mul_self_eq" -> "data", "continuous_on.integrable_on_compact" -> "analysis", "set.inter_diff_assoc" -> "data", "sub_ne_zero" -> "algebra", "filter.ptendsto'_of_ptendsto" -> "order", "turing.blank_rel.trans" -> "computability", "encodable.decode2_inj" -> "data", "lt_add_of_nonneg_of_lt'" -> "algebra", "filter.binfi_sets_eq" -> "order", "add_comm" -> "algebra", "list.to_finset_surjective" -> "data", "fintype.sum_fiberwise" -> "data", "not_eq_of_eq_false" -> "init", "measure_theory.measure.restrict_apply_univ" -> "analysis", "vector_span_eq_span_vsub_set_right" -> "algebra", "complex.of_real_nat_cast" -> "data", "con.lift_unique" -> "algebra", "multiset.pi_cons" -> "data", "is_local_extr_const" -> "topology", "is_add_unit_iff_exists_neg" -> "algebra", "enat.coe_le_coe" -> "data", "polynomial.leading_coeff_X_add_C" -> "data", "Set.pair_mem_prod" -> "set_theory", "localization_map.ring_equiv_of_ring_equiv_mk'" -> "algebra", "totally_bounded_iff_subset" -> "topology", "cardinal.add_one_eq" -> "set_theory", "ordinal.omega_le" -> "set_theory", "derivation.commutator_coe_linear_map" -> "algebra", "antilipschitz_with.subtype_coe" -> "topology", "irrational.of_rat_add" -> "data", "nat.inv_pos_of_nat" -> "data", "list.nodup_insert" -> "data", "filter.map_at_top_finset_sum_le_of_sum_eq" -> "order", "closure_mono" -> "topology", "submonoid.mem_coe" -> "algebra", "multiset.disjoint_singleton" -> "data", "neg_of_neg_pos" -> "algebra", "list.forall_mem_union" -> "data", "submodule.quot_equiv_of_eq_bot_apply_mk" -> "algebra", "infi_real_pos_eq_infi_nnreal_pos" -> "topology", "int.mul_div_cancel_left" -> "data", "add_monoid_hom.mem_ker" -> "algebra", "div_lt_div" -> "algebra", "commute.cast_int_mul_cast_int_mul" -> "algebra", "convex.affinity" -> "analysis", "add_monoid_hom.coe_mrange" -> "algebra", "tactic.ring2.horner_expr.cseval_pow" -> "tactic", "mul_action.mem_fixed_points'" -> "algebra", "quotient_group.ker_lift_mk" -> "algebra", "choose_middle_le_pow" -> "data", "category_theory.limits.coequalizer.iso_target_of_self_inv" -> "category_theory", "cauchy_seq_bdd" -> "topology", "submodule.comap_fst" -> "algebra", "local_equiv.coe_mk" -> "data", "set.countable.image" -> "data", "uniform_continuous_nndist" -> "topology", "emetric.diam_subsingleton" -> "topology", "list.filter_map_some" -> "data", "add_monoid_algebra.one_def" -> "data", "norm_indicator_le_of_subset" -> "analysis", "ennreal.rpow_add" -> "analysis", "linear_independent_empty_type" -> "algebra", "summable.add" -> "topology", "multiplicity.pow_dvd_iff_le_multiplicity" -> "algebra", "set.Ico_diff_Ioo_same" -> "data", "set.Ioi_subset_Ici_iff" -> "data", "category_theory.limits.bicone.to_binary_bicone_fst" -> "category_theory", "localization.ring_equiv_of_quotient_mk" -> "algebra", "indicator_eventually_eq" -> "order", "num.to_znum_inj" -> "data", "set.add_union" -> "algebra", "complex.conj_bit0" -> "data", "complex.continuous_linear_map.im_apply" -> "analysis", "filter.map_id" -> "order", "continuous_at_const" -> "topology", "stream.append_stream_head_tail" -> "data", "nat.eq_one_of_dvd_one" -> "init", "scale_roots_eval\:2082_eq_zero" -> "algebra", "convex_on_dist" -> "analysis", "measure_theory.simple_func.coe_comp" -> "analysis", "inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two" -> "analysis", "pnat.xgcd_type.qp_eq" -> "data", "list.infix_refl" -> "data", "is_compl_top_bot" -> "order", "option.map_some" -> "data", "formal_multilinear_series.comp_partial_sum_target_tendsto_at_top" -> "analysis", "fin.coe_fin_lt" -> "data", "with_zero.mul_inv_rev" -> "algebra", "matrix.tail_zero" -> "data", "rat.mk_ne_zero_of_ne_zero" -> "data", "add_right_injective" -> "algebra", "multiset.map_const" -> "data", "set.subset_sUnion_of_subset" -> "data", "smooth.inv" -> "geometry", "set.Ioc_union_Ioc" -> "data", "category_theory.yoneda_evaluation_map_down" -> "category_theory", "nnreal.pow_eq_zero" -> "data", "subgroup.map_supr" -> "algebra", "iff.trans" -> "init", "monoid_hom.lift_of_surjective_comp_apply" -> "algebra", "fin.succ_rec_on_succ" -> "data", "ennreal.coe_rpow_of_nonneg" -> "analysis", "subring.coe_add" -> "algebra", "fintype.of_equiv_card" -> "data", "list.sublists_len_succ_cons" -> "data", "continuous_linear_equiv.ext\:2081" -> "topology", "isometric.add_right_apply" -> "topology", "add_submonoid.localization_map.add_equiv_of_localizations_left_neg" -> "algebra", "mul_div_assoc'" -> "algebra", "option.map_id'" -> "data", "omega.int.is_nnf_push_neg" -> "tactic", "lie_subalgebra.mem_coe'" -> "algebra", "nat.div_mod_unique" -> "data", "category_theory.coyoneda_obj_map" -> "category_theory", "le_antisymm" -> "init", "with_zero.mul_div_cancel" -> "algebra", "cardinal_mk_eq_cardinal_mk_field_pow_dim" -> "algebra", "filter.tendsto_at_bot_of_add_bdd_below_right'" -> "order", "mul_lt_mul_of_le_of_lt" -> "algebra", "finset.fold_op_rel_iff_and" -> "data", "set.Ico_subset_Iio_self" -> "data", "int.nonneg_of_pos" -> "init", "measure_theory.ae_eq_fun.ext" -> "analysis", "is_open_add_left" -> "topology", "category_theory.nat_trans.id_hcomp_app" -> "category_theory", "norm_num.nat_div" -> "tactic", "is_ring_hom.comp" -> "algebra", "submodule.map_mul" -> "algebra", "gold_add_gold_conj" -> "data", "ext_chart_at_continuous_at" -> "geometry", "list.chain_split" -> "data", "deriv_csinh" -> "analysis", "equiv.sigma_preimage_equiv_apply" -> "data", "associates.le_of_mul_le_mul_right" -> "algebra", "category_theory.functor.map_presheaf_obj_X" -> "algebraic_geometry", "geom_series_one" -> "algebra", "computable.vector_of_fn" -> "computability", "dist_pos" -> "topology", "monoid_hom.map_mrange" -> "algebra", "nat.primrec'.prim_iff\:2081" -> "computability", "mv_power_series.inv_of_unit_eq'" -> "algebra", "int.sign_neg_one" -> "init", "nat.bit1_le_bit0_iff" -> "data", "nat.modeq.modeq_add_cancel_left" -> "data", "set.Ico_union_Ici_eq_Ici" -> "data", "dioph.sub_dioph" -> "number_theory", "ring.fractional_ideal.span_singleton_mul_span_singleton" -> "algebra", "list.sorted_nil" -> "data", "times_cont_diff_on.prod_map" -> "analysis", "ordinal.lift_cof" -> "set_theory", "matrix.update_column_self" -> "data", "submodule.restrict_scalars_top" -> "algebra", "filter.eventually_map" -> "order", "mv_polynomial.monomial_mul" -> "data", "multiset.erase_dup_zero" -> "data", "nat.le_add_right" -> "init", "exists_nhds_quarter" -> "topology", "differentiable_within_at.const_smul" -> "analysis", "of_digits_zmodeq" -> "data", "subgroup.normal_closure_normal" -> "algebra", "has_fpower_series_on_ball.add" -> "analysis", "linear_map.deriv" -> "analysis", "polynomial.induction_on" -> "data", "ennreal.to_real_add_le" -> "data", "differentiable_on.cos" -> "analysis", "alist.lookup_to_alist" -> "data", "is_preconnected_Ioo" -> "topology", "asymptotics.is_o.congr_left" -> "analysis", "int.shiftl_coe_nat" -> "data", "local_equiv.prod_coe" -> "data", "interval_integrable.refl" -> "analysis", "category_theory.discrete.nat_iso_hom_app" -> "category_theory", "linear_map.equiv_prod_of_surjective_of_is_compl_apply" -> "algebra", "measurable.prod_mk" -> "analysis", "function.embedding.equiv_to_embedding_trans_symm_to_embedding" -> "logic", "fderiv_neg" -> "analysis", "nhds_inf" -> "topology", "inv_image.trans" -> "init", "measure_theory.simple_func.eapprox_comp" -> "analysis", "metric.bounded_iff_subset_ball" -> "topology", "filter.binfi_sup_right" -> "order", "ennreal.top_ne_one" -> "data", "rat.mk_pnat_num" -> "data", "filter.eventually_eq.div" -> "order", "CommGroup.coe_of" -> "algebra", "deriv_within_fpow" -> "analysis", "irrational.of_inv" -> "data", "with_one.lift_unique" -> "algebra", "complex.continuous_linear_map.im_norm" -> "analysis", "category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom" -> "category_theory", "lucas_lehmer.X.closed_form" -> "number_theory", "differentiable_within_at.cexp" -> "analysis", "polynomial.coeff_mul_degree_add_degree" -> "data", "complex.tanh_zero" -> "data", "inf_le_inf_right" -> "order", "continuous_multilinear_map.norm_map_cons_le" -> "analysis", "list.subset_append_right" -> "init", "submodule.smul_mem" -> "algebra", "formal_multilinear_series.comp_along_composition_norm" -> "analysis", "pgame.nim.sum_first_loses_iff_eq" -> "set_theory", "rat.mul_nonneg" -> "data", "one_sub_gold" -> "data", "mul_equiv.map_ne_one_iff" -> "data", "cauchy_seq_of_dist_le_of_summable" -> "topology", "zero_pow" -> "algebra", "finmap.mem_union" -> "data", "is_coprime.add_mul_right_right" -> "algebra", "finmap.insert_entries_of_neg" -> "data", "metric.compact_iff_seq_compact" -> "topology", "zorn.chain_chain_closure" -> "order", "mv_polynomial.mem_support_not_mem_vars_zero" -> "data", "semidirect_product.range_inl_eq_ker_right_hom" -> "algebra", "set.inter_Inter" -> "data", "is_local_min_on.congr" -> "topology", "real.sin_add" -> "data", "sub_lt_sub_left" -> "algebra", "complex.continuous_re" -> "topology", "set.image_one" -> "algebra", "lie_mem_left" -> "algebra", "nat.div_lt_self" -> "init", "int.bit0_pos" -> "init", "finsupp.total_single" -> "algebra", "rat.zero_mk_pnat" -> "data", "category_theory.Monad.Monad_Mon_equiv_unit_iso" -> "category_theory", "continuous_linear_equiv.units_equiv_aut_symm_apply" -> "topology", "times_cont_diff_within_at.prod_map'" -> "analysis", "measure_theory.integrable.add" -> "analysis", "linear_map.range_comp" -> "algebra", "tsum_nonneg" -> "topology", "category_theory.whiskering_left_obj_obj" -> "category_theory", "differentiable.snd" -> "analysis", "min_mul_of_nonneg" -> "algebra", "list.length_split_wrt_composition_aux" -> "combinatorics", "exists_unique.exists" -> "logic", "is_bounded_bilinear_map.has_strict_fderiv_at" -> "analysis", "decidable.or_iff_not_imp_left" -> "logic", "category_theory.limits.types.prod_map" -> "category_theory", "pnat.xgcd_type.flip_v" -> "data", "category_theory.cancel_mono" -> "category_theory", "add_equiv.to_add_monoid_hom_apply" -> "data", "set.nonempty_of_ssubset'" -> "data", "lists'.to_of_list" -> "set_theory", "lt_mul_of_one_lt_of_lt" -> "algebra", "nat.lcm_zero_left" -> "data", "normed_field.tendsto_inv" -> "analysis", "eq_neg_iff_add_eq_zero" -> "algebra", "differentiable_on_fst" -> "analysis", "complex.one_im" -> "data", "add_group_with_zero_nhd.neg_Z" -> "topology", "is_preconnected.Icc_subset" -> "topology", "convex.mem_Ioc" -> "analysis", "int.neg_succ_of_nat_eq'" -> "data", "padic_val_nat.mul" -> "data", "finset.prod_subtype" -> "data", "polynomial.separable_iff_derivative_ne_zero" -> "algebra", "stream.inits_core_eq" -> "data", "subsemiring.list_sum_mem" -> "algebra", "list.mem_traverse" -> "control", "real.cos_pos_of_neg_pi_div_two_lt_of_lt_pi_div_two" -> "analysis", "category_theory.iso.symm_self_conj" -> "category_theory", "list.zip_cons_cons" -> "data", "differentiable.exp" -> "analysis", "disjoint.sup_left" -> "order", "measure_theory.measure.haar.prehaar_mem_haar_product" -> "analysis", "mdifferentiable_on.mono" -> "geometry", "isometric.point_reflection_symm" -> "analysis", "filter.exists_ultrafilter_iff" -> "order", "add_subgroup.multiset_sum_mem" -> "algebra", "int.eq_coe_of_zero_le" -> "init", "int.even_pow" -> "data", "multiset.card_le_of_le" -> "data", "differentiable_at.sub" -> "analysis", "to_topological_space_mono" -> "topology", "ideal.map_eq_bot_iff_le_ker" -> "algebra", "disjoint_iff" -> "order", "is_coprime.map" -> "algebra", "category_theory.limits.colimit.\[Iota]_desc" -> "category_theory", "list.tendsto_cons'" -> "topology", "pgame.le_zero_iff_zero_le_neg" -> "set_theory", "metric.dist_le_diam_of_mem'" -> "topology", "category_theory.limits.cokernel_image_\[Iota]_hom" -> "category_theory", "prime_spectrum.basic_open_open" -> "algebraic_geometry", "succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul" -> "algebra", "min_choice" -> "algebra", "matrix.cramer_is_linear" -> "algebra", "computation.lift_rel.swap" -> "data", "is_R_or_C.nat_cast_im" -> "data", "mul_self_sub_mul_self_eq" -> "algebra", "localization_map.ext" -> "algebra", "norm_num.zero_adc" -> "tactic", "with_zero.zero_lt_coe" -> "algebra", "holor.cprank_max_add" -> "data", "category_theory.limits.biprod.lift_eq" -> "category_theory", "is_compact.uniform_continuous_on_of_continuous'" -> "topology", "category_theory.arrow.mk_hom" -> "category_theory", "list.nth_mem" -> "data", "powers.self_mem" -> "algebra", "mvqpf.cofix.mk_dest" -> "data", "times_cont_diff_within_at.neg" -> "analysis", "polynomial.coeff_X_pow_self" -> "data", "submonoid.comap_le_comap_iff_of_surjective" -> "algebra", "turing.reaches.to\:2080" -> "computability", "is_unit.mul_left_inj" -> "algebra", "inner_product_geometry.norm_add_square_eq_norm_square_add_norm_square_iff_angle_eq_pi_div_two" -> "geometry", "zero_lt_bit0" -> "algebra", "quot.factor_mk_eq" -> "data", "metric.uniform_continuous_iff" -> "topology", "category_theory.limits.limit.lift_\[Pi]" -> "category_theory", "cardinal.ord_nat" -> "set_theory", "mv_polynomial.is_homogeneous_C" -> "algebra", "norm_num.clear_denom_simple_div" -> "tactic", "continuous.comp" -> "topology", "fin.find_eq_some_iff" -> "data", "nat.bit0_ne_one" -> "init", "power_series.order_mul_ge" -> "algebra", "multiset.map_congr" -> "data", "turing.list_blank.cons_bind" -> "computability", "filter.pure_sets" -> "order", "surj_on_Icc_of_monotone_surjective" -> "data", "is_local_extr.deriv_eq_zero" -> "analysis", "has_deriv_at_filter_iff_tendsto" -> "analysis", "znum.zneg_bitm1" -> "data", "list.zip_append" -> "data", "filter.Liminf_bot" -> "order", "list.chain'_split" -> "data", "zmod.legendre_sym_eq_one_iff" -> "number_theory", "add_submonoid.gc_map_comap" -> "algebra", "right_ord_continuous.order_dual" -> "order", "wseq.lift_rel_map" -> "data", "nat.size_eq_zero" -> "data", "ring_hom.coe_of" -> "algebra", "set.diff_inter" -> "data", "zmod.le_div_two_iff_lt_neg" -> "data", "emetric.diam_mono" -> "topology", "has_strict_fderiv_at.add" -> "analysis", "mul_div_assoc" -> "algebra", "equiv.swap_core_self" -> "data", "ennreal.sum_lt_top_iff" -> "data", "metric.completion.coe_isometry" -> "topology", "setoid.comap_eq" -> "data", "mul_divp_cancel" -> "algebra", "category_theory.epi_iff_surjective" -> "category_theory", "measurable.nndist" -> "analysis", "has_ftaylor_series_up_to.has_fderiv_at" -> "analysis", "ordinal.add_le_add_left" -> "set_theory", "nat.bit0_ne_bit1" -> "init", "tsum_le_tsum_of_inj" -> "topology", "multiset.coe_sub" -> "data", "function.uncurry_def" -> "logic", "generalized_continued_fraction.int_fract_pair.seq1_fst_eq_of" -> "algebra", "category_theory.limits.binary_cofan.mk_\[Iota]_app_left" -> "category_theory", "computation.of_results_bind" -> "data", "sup_lt_iff" -> "order", "ne.intro" -> "init", "lagrange.eq_interpolate" -> "algebra", "bitraversable.tsnd_comp_tsnd" -> "control", "nat.Inf_eq_zero" -> "order", "measure_theory.simple_func.integral_add_measure" -> "analysis", "div_div_eq_mul_div" -> "algebra", "finset.prod_insert_of_eq_one_if_not_mem" -> "algebra", "int.neg_inj" -> "init", "rat.add_assoc" -> "data", "con.inf_def" -> "algebra", "ideal.mul_eq_inf_of_coprime" -> "algebra", "submodule.prod_coe" -> "algebra", "ring_hom.iterate_map_smul" -> "algebra", "free_group.inv_mk" -> "algebra", "mv_polynomial.eval\:2082_neg" -> "data", "equiv.coe_prod_congr" -> "data", "category_theory.Monad.of_to_mon_end_iso_inv_app_hom" -> "category_theory", "onote.eq_of_cmp_eq" -> "set_theory", "emetric.inf_edist_le_edist_of_mem" -> "topology", "differentiable_within_at.smul" -> "analysis", "equiv.perm.sign_bij_aux_surj" -> "algebra", "one_lt_bit1" -> "algebra", "div_eq_mul_inv" -> "algebra", "continuous_linear_map.coe_prod" -> "topology", "measure_theory.integrable_at_filter.filter_mono" -> "analysis", "poly.sumsq_nonneg" -> "number_theory", "nat.partrec'.part_iff\:2081" -> "computability", "derive_fintype.finset_above.mem_cons_of_mem" -> "tactic", "ideal.mem_jacobson_iff" -> "algebra", "linear_map.span_inl_union_inr" -> "algebra", "list.foldr_eq_of_comm'" -> "data", "min_assoc" -> "init", "measure_theory.ae_eq_refl" -> "analysis", "formal_multilinear_series.comp_assoc" -> "analysis", "Top.presheaf.pushforward.id_hom_app" -> "topology", "deriv_rpow_of_one_le" -> "analysis", "quadratic_eq_zero_iff_of_discrim_eq_zero" -> "algebra", "approximates_linear_on.inverse_approx_map_dist_self" -> "analysis", "closure_induced" -> "topology", "is_extr_on.localize" -> "topology", "linear_map.comp_eq_id_comm" -> "algebra", "cardinal.ord_le_type" -> "set_theory", "function.surjective.sigma_map" -> "data", "ordinal.card_typein" -> "set_theory", "antilipschitz_with.to_right_inv_on" -> "topology", "pgame.grundy_value_zero" -> "set_theory", "filter.comap_has_basis" -> "order", "list.concat_cons" -> "data", "imp_or_distrib" -> "logic", "ordinal.limit_rec_on_zero" -> "set_theory", "nat.lxor_zero" -> "data", "int.neg_neg_of_pos" -> "init", "measure_theory.outer_measure.coe_smul" -> "analysis", "multiset.le_add_right" -> "data", "filter.high_scores" -> "order", "turing.tape.map_mk\:2082" -> "computability", "set.prod_range_range_eq" -> "data", "uniformly_extend_spec" -> "topology", "continuous_linear_equiv.subsingleton_or_norm_symm_pos" -> "analysis", "set.inj_on.mono" -> "data", "cauchy_seq_of_le_geometric_two" -> "analysis", "int.lt_of_sub_one_le" -> "init", "dfinsupp.support_sum" -> "data", "pfunctor.M.corec_def" -> "data", "local_homeomorph.prod_trans" -> "topology", "filter.tendsto_at_bot_pure" -> "order", "fin.cast_succ_cast_lt" -> "data", "continuous_linear_map.norm_id_le" -> "analysis", "num.dvd_iff_mod_eq_zero" -> "data", "add_neg_le_iff_le_add" -> "algebra", "cardinal.nat_succ" -> "set_theory", "seq1.join_cons" -> "data", "equiv.perm.sign_aux_swap" -> "algebra", "complex.sin_of_real_im" -> "data", "computation.results_ret" -> "data", "category_theory.monoidal_category.left_unitor_nat_iso_hom_app" -> "category_theory", "category_theory.limits.colimit.\[Iota]_post" -> "category_theory", "with_top.one_ne_top" -> "algebra", "category_theory.limits.image_mono_iso_source_inv_\[Iota]" -> "category_theory", "pgame.nim.nim_def" -> "set_theory", "nat.partrec.code.const_inj" -> "computability", "coe_affine_span" -> "algebra", "continuous_linear_map.map_sub" -> "topology", "is_add_group_hom.neg_ker_zero" -> "algebra", "dioph.and_dioph" -> "number_theory", "is_totally_disconnected_empty" -> "topology", "set.countable_encodable'" -> "data", "stream.interleave_even_odd" -> "data", "ideal.mem_of_one_mem" -> "algebra", "filter.seq_mono" -> "order", "linear_map.inr_apply" -> "algebra", "geom_sum\:2082_mul_add" -> "algebra", "complex.norm_sq_eq_abs" -> "data", "real.sin_bound" -> "data", "category_theory.bifunctor.diagonal" -> "category_theory", "multilinear_map.uncurry_right_apply" -> "algebra", "ring_hom.eq_of_eq_on_set_dense" -> "algebra", "set.eq_on.inj_on_iff" -> "data", "monoid_algebra.lift_unique" -> "data", "nat.find_greatest_spec" -> "data", "finsupp.bot_eq_zero" -> "data", "differentiable_at.differentiable_within_at" -> "analysis", "units.to_Aut_hom" -> "category_theory", "list.zip_map_right" -> "data", "measure_theory.integral_non_integrable" -> "analysis", "complex.norm_sq_div" -> "data", "is_compact.inter_left" -> "topology", "finset.mem_image" -> "data", "multiset.filter_map_some" -> "data", "Top.presheaf_to_Type_obj" -> "topology", "ennreal.sub_infi" -> "data", "padic_val_rat.neg" -> "data", "polynomial.monic_X" -> "data", "add_commute.eq" -> "algebra", "submodule.fg_prod" -> "algebra", "is_preconnected.Iio_cSup_subset" -> "topology", "local_homeomorph.refl_target" -> "topology", "int.prime.dvd_mul" -> "algebra", "filter.eventually_le.is_local_max" -> "topology", "fintype.card_perm" -> "data", "add_subgroup.is_open_of_open_add_subgroup" -> "topology", "finsupp.order_iso_multiset_symm_apply" -> "data", "list.Ico.bag_inter_consecutive" -> "data", "mul_eq_mul_of_div_eq_div" -> "algebra", "quadratic_form.add_lin_mul_lin" -> "algebra", "has_deriv_at_filter.neg" -> "analysis", "category_theory.adjunction.monad_\[Mu]_app" -> "category_theory", "roption.mem_to_option" -> "data", "units.val_coe" -> "algebra", "norm_num.add_bit0_bit0" -> "tactic", "has_fderiv_within_at.comp_has_deriv_within_at" -> "analysis", "nat.dist_eq_sub_of_le" -> "data", "int_prod_range_nonneg" -> "analysis", "submodule.mk_eq_zero" -> "algebra", "ordinal.lift.principal_seg_top" -> "set_theory", "nat.sub_add_min_cancel" -> "init", "finsupp.range_total" -> "algebra", "measurable_of_continuous_on_compl_singleton" -> "analysis", "finset.erase_dup_eq_self" -> "data", "category_theory.functor.op_map" -> "category_theory", "list.suffix_or_suffix_of_suffix" -> "data", "category_theory.adjunction.left_triangle_components_assoc" -> "category_theory", "int.div2_val" -> "data", "encodable.decode_sum_val" -> "data", "matrix.mul_mul_left" -> "data", "polynomial.map_mod" -> "data", "cardinal.two_le_iff" -> "set_theory", "ennreal.sup_eq_max" -> "data", "monoid_hom.map_mul_inv" -> "algebra", "multiset.powerset_len_coe" -> "data", "multiset.card_powerset_len" -> "data", "mem_closure_iff_nhds_basis" -> "topology", "submonoid.coe_coe" -> "algebra", "finset.nat.antidiagonal_zero" -> "data", "free_comm_ring.is_supported_one" -> "algebra", "matrix.col_vec_mul" -> "data", "inv_one" -> "algebra", "asymptotics.is_O_const_const" -> "analysis", "int.sub_mod" -> "data", "Gromov_Hausdorff.to_GH_space_continuous" -> "topology", "measure_theory.simple_func.norm_integral_le_integral_norm" -> "analysis", "set.Icc_subset_Ici_iff" -> "data", "list.append_inj_right'" -> "data", "mul_left_iterate" -> "algebra", "finset.sdiff_eq_self" -> "data", "smul_lt_smul_of_pos" -> "algebra", "ennreal.to_real_le_of_le_of_real" -> "data", "mem_own_left_add_coset" -> "algebra", "metric.tendsto_uniformly_iff" -> "topology", "roption.get_eq_of_mem" -> "data", "continuous_linear_equiv.comp_fderiv_within" -> "analysis", "turing.TM2.stmts_trans" -> "computability", "list.perm_inv_core" -> "data", "roption.of_option_eq_get" -> "data", "measure_theory.outer_measure.of_function_le" -> "analysis", "closure_minimal" -> "topology", "nat.zero_ne_bit0" -> "init", "vector.to_list_mk" -> "data", "cardinal.mk_sum_compl" -> "set_theory", "linear_map.ker_id_sub_eq_of_proj" -> "algebra", "multilinear_map.map_smul_univ" -> "algebra", "one_lt_two" -> "algebra", "generalized_continued_fraction.of_correctness_of_nth_stream_eq_none" -> "algebra", "ring_hom.map_geom_series\:2082" -> "algebra", "linear_independent_subtype" -> "algebra", "CommRing.colimits.quot_zero" -> "algebra", "finset.insert_sdiff_of_mem" -> "data", "filter.frequently_Sup" -> "order", "submodule.span_image" -> "algebra", "zsqrtd.sq_le_mul" -> "data", "add_subgroup.coe_supr_of_directed" -> "algebra", "category_theory.limits.cokernel_cofork.condition_assoc" -> "category_theory", "units.inv_mul'" -> "algebra", "le_add_of_neg_add_le_right" -> "algebra", "filter.tendsto_at_top_mono'" -> "order", "qpf.comp_map" -> "data", "set.univ_add_univ" -> "algebra", "local_homeomorph.refl_local_equiv" -> "topology", "summable_of_norm_bounded" -> "analysis", "filter.eventually_eq.times_cont_mdiff_at_iff" -> "geometry", "finset.exists_ne_one_of_prod_ne_one" -> "algebra", "cardinal.lift_down" -> "set_theory", "fin.succ_above_above" -> "data", "has_fpower_series_on_ball.has_fpower_series_at" -> "analysis", "nnreal.div_add_div" -> "data", "cardinal.lift_lt_univ'" -> "set_theory", "is_R_or_C.of_real_fpow" -> "data", "finsupp.support_on_finset_subset" -> "data", "znum.cast_add" -> "data", "measure_theory.measure.haar_outer_measure_eq_infi" -> "analysis", "category_theory.limits.epi_of_target_iso_zero" -> "category_theory", "pythagorean_triple.is_classified_of_is_primitive_classified" -> "number_theory", "set.indicator_self_add_compl" -> "data", "mv_polynomial.sum_homogeneous_component" -> "algebra", "list.filter_cons_of_pos" -> "init", "nhds_contain_boxes_of_compact" -> "topology", "multiset.erase_lt" -> "data", "ordered_ring.mul_lt_mul_of_pos_right" -> "algebra", "multiset.countp_pos" -> "data", "quotient_add_group.coe_add" -> "algebra", "list.mem_diff_of_mem" -> "data", "zmod.cast_hom_apply" -> "data", "polynomial.to_subring_zero" -> "algebra", "is_path_connected.subset_path_component" -> "topology", "multiset.count_pos" -> "data", "turing.tr_reaches" -> "computability", "lt_mul_of_inv_mul_lt_left" -> "algebra", "finset.union_sdiff_self_eq_union" -> "data", "multiset.mem_singleton_self" -> "data", "cardinal.sup_le_sum" -> "set_theory", "add_monoid_hom.coprod_apply" -> "algebra", "finset.min'_lt_max'_of_card" -> "data", "set.image_surjective" -> "data", "int.modeq.trans" -> "data", "uniformity_comap" -> "topology", "frobenius_def" -> "algebra", "filter.at_top_finset_eq_infi" -> "order", "open_embedding_inr" -> "topology", "three_dvd_iff" -> "data", "normed_ring.inverse_one_sub_nth_order" -> "analysis", "ideal.comap_jacobson_of_surjective" -> "algebra", "sum.lex_inr_inl" -> "data", "mem_comp_comp" -> "topology", "add_submonoid.coe_bot" -> "algebra", "category_theory.constant_of_preserves_morphisms" -> "category_theory", "is_R_or_C.norm_sq_eq_def" -> "data", "ring.direct_limit.of_zero" -> "algebra", "asymptotics.is_o_iff" -> "analysis", "pgame.grundy_value_add" -> "set_theory", "uniformity_basis_edist_nnreal" -> "topology", "list.mem_singleton" -> "data", "category_theory.equivalence.cancel_unit_right" -> "category_theory", "has_deriv_within_at.congr_mono" -> "analysis", "pi_Lp.neg_apply" -> "topology", "smooth_pow" -> "geometry", "abs_abs" -> "algebra", "polynomial.eval\:2082_sub" -> "data", "complex.continuous_tan" -> "analysis", "contract_left_apply" -> "algebra", "set.compl_inv" -> "algebra", "filter.tendsto.prod_mk_nhds" -> "topology", "set.mem_sUnion_of_mem" -> "data", "real.continuous_mul" -> "topology", "filter.prod_comm" -> "order", "finsupp.sum_comm" -> "data", "set.countable_iff_exists_surjective" -> "data", "zmod.cast_sub" -> "data", "cfilter.mem_to_filter_sets" -> "data", "list.Ico.filter_le_of_le" -> "data", "min_max_distrib_left" -> "algebra", "Iio_mem_nhds" -> "topology", "nat.pow_dvd_pow" -> "data", "heq.subst" -> "init", "direct_sum.single_eq_lof" -> "algebra", "nat.bit_lt_bit0" -> "data", "alist.lookup_erase" -> "data", "submonoid.localization_map.mul_inv" -> "algebra", "times_cont_diff_on_iff_continuous_on_differentiable_on_deriv" -> "analysis", "hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg" -> "data", "stream.even_cons_cons" -> "data", "fintype.pi_finset_subset" -> "data", "continuous_on_extend_from" -> "topology", "filter.eventually_eq.mul" -> "order", "measure_theory.measure.haar.nonempty_Inter_cl_prehaar" -> "analysis", "has_strict_deriv_at.sum" -> "analysis", "measure_theory.simple_func.integrable_iff_fin_meas_supp" -> "analysis", "open_add_subgroup.mem_nhds_zero" -> "topology", "pairwise_disjoint_on_bool" -> "data", "times_cont_mdiff_on_snd" -> "geometry", "neg_add_lt_left_of_lt_add" -> "algebra", "multiset.bind_cons" -> "data", "units.mul_lift_right_inv" -> "algebra", "add_submonoid.coe_ssubset_coe" -> "algebra", "semiquot.get_mem" -> "data", "nat.even_zero" -> "data", "mul_action_hom.to_quotient_apply" -> "algebra", "nsmul_zero" -> "algebra", "d_array.ext'" -> "init", "decidable.not_imp" -> "logic", "list.join_eq_nil" -> "data", "category_theory.limits.prod.map_iso_inv" -> "category_theory", "list.func.get_add" -> "data", "nat.succ_injective" -> "data", "pmf.pure_bind" -> "analysis", "measure_theory.l1.simple_func.of_simple_func_sub" -> "analysis", "linarith.int.coe_nat_one_mul" -> "tactic", "cardinal.add_le_add" -> "set_theory", "category_theory.equivalence.cancel_counit_inv_right" -> "category_theory", "metric.inf_dist_nonneg" -> "topology", "tendsto_at_top_infi_nat" -> "topology", "filter.mem_at_top" -> "order", "tendsto_neg" -> "topology", "list.index_of_cons_self" -> "data", "continuous_on.continuous_within_at" -> "topology", "int.pred_nat_succ" -> "data", "complex.of_real_rat_cast" -> "data", "finset.mem_fin_range" -> "data", "fin.sum_univ_succ" -> "data", "one_div_nonpos" -> "algebra", "inner_add_right" -> "analysis", "multiset.coe_join" -> "data", "finset.choose_property" -> "data", "inf_comm" -> "order", "riesz_extension.step" -> "analysis", "omega.nat.preform.holds_constant" -> "tactic", "concave_on.smul" -> "analysis", "cau_seq.const_le" -> "data", "classical.exists_true_of_nonempty" -> "init", "associated.symm" -> "algebra", "list.sublists_aux\:2081_concat" -> "data", "list.index_of_argmax" -> "data", "finset.image_subset_iff" -> "data", "list.forall\:2082_length_eq" -> "data", "filter_basis.eq_infi_principal" -> "order", "subsemiring.mem_supr_of_directed" -> "algebra", "real.exp_lt_exp" -> "data", "computation.equiv_of_mem" -> "data", "local_equiv.prod_source" -> "data", "abs_le_of_le_of_neg_le" -> "algebra", "linear_map.prod_apply" -> "algebra", "continuous_linear_map.has_fderiv_at_filter" -> "analysis", "category_theory.curry_natural_left" -> "category_theory", "tendsto_swap_uniformity" -> "topology", "pell.xy_modeq_yn" -> "number_theory", "cluster_pt.of_le_nhds" -> "topology", "category_theory.limits.cokernel_not_mono_of_nonzero" -> "category_theory", "submodule.findim_quotient_add_findim" -> "algebra", "subsemiring.Inf_to_submonoid" -> "algebra", "int.of_nat_add" -> "init", "edist_triangle4" -> "topology", "zsqrtd.bit0_im" -> "data", "ctop.realizer.is_basis" -> "data", "is_G\[Delta]_Inter_of_open" -> "topology", "partrec.rfind_opt" -> "computability", "multilinear_map.map_sum_finset" -> "algebra", "set.mem_of_mem_inter_right" -> "data", "is_add_subgroup.of_add_neg" -> "algebra", "option.orelse_none'" -> "data", "cauchy_seq_tendsto_of_complete" -> "topology", "alg_hom.commutes" -> "algebra", "distrib_three_right" -> "algebra", "roption.eta" -> "data", "has_mfderiv_within_at.mono" -> "geometry", "tactic.ring_exp.prod_congr" -> "tactic", "mv_polynomial.eval\:2082_monomial" -> "data", "prime_spectrum.subset_vanishing_ideal_zero_locus" -> "algebraic_geometry", "div_le_div_right_of_neg" -> "algebra", "matrix.diagonal_apply_ne'" -> "data", "model_with_corners_self_coe" -> "geometry", "magma.free_semigroup.map_of" -> "algebra", "is_trichotomous.swap" -> "order", "nat.zero_shiftl" -> "init", "submodule.mem_bot" -> "algebra", "pSet.equiv.eq" -> "set_theory", "order_top.tendsto_at_top_nhds" -> "topology", "inv_le_of_inv_le" -> "algebra", "formal_multilinear_series.comp_along_composition_nnnorm" -> "analysis", "euclidean_geometry.orthogonal_projection_linear" -> "geometry", "discrete_valuation_ring.unit_mul_pow_congr_unit" -> "algebra", "sup_of_le_left" -> "order", "add_subgroup.bot_sum_bot" -> "algebra", "measure_theory.l1.of_fun_to_fun" -> "analysis", "fixed_points.minpoly.irreducible_aux" -> "algebra", "linear_map.subtype_comp_cod_restrict" -> "algebra", "cardinal.le_sup" -> "set_theory", "is_bounded_bilinear_map_smul" -> "analysis", "hyperreal.infinite_mul_of_not_infinitesimal_infinite" -> "data", "cardinal.mk_compl_eq_mk_compl_infinite" -> "set_theory", "irrational_neg_iff" -> "data", "set.finite.exists_finset" -> "data", "relation.refl_trans_gen.symmetric" -> "logic", "free_group.map.id" -> "algebra", "localization.mk_one_eq_of" -> "algebra", "is_compact.compl_mem_sets" -> "topology", "real.rpow_mul" -> "analysis", "continuous_linear_equiv.comp_times_cont_diff_within_at_iff" -> "analysis", "ring_equiv.injective" -> "data", "emetric.inf_edist_closure" -> "topology", "implies.trans" -> "init", "category_theory.limits.kernel_comp_is_iso_inv" -> "category_theory", "filter.is_cobounded_bot" -> "order", "submodule.smul_bot" -> "algebra", "function.is_fixed_pt.left_of_comp" -> "dynamics", "exists_elim_eq_left" -> "tactic", "add_subgroup.coe_mk" -> "algebra", "hyperreal.not_infinite_pos_add_infinite_neg" -> "data", "vector.remove_nth_insert_nth_ne" -> "data", "eq_add_of_sub_eq" -> "algebra", "measure_theory.integrable_on.left_of_union" -> "analysis", "measure_theory.l1.neg_part_to_fun_eq_min" -> "analysis", "lt_inv_of_lt_inv" -> "algebra", "pos_num.succ_to_nat" -> "data", "list.attach_map_val" -> "data", "list.pairwise_cons" -> "data", "turing.reaches\:2081_fwd" -> "computability", "pnat.dvd_lcm_left" -> "data", "is_submonoid.multiset_prod_mem" -> "algebra", "adjoin_root.aeval_eq" -> "algebra", "mv_polynomial.monomial_single_add" -> "data", "bit0_eq_two_mul" -> "algebra", "is_local_max.sub" -> "topology", "nat.is_coprime_iff_coprime" -> "algebra", "continuous_nnnorm" -> "analysis", "polynomial.degree_pow" -> "data", "div_neg_eq_neg_div" -> "algebra", "filter.has_countable_basis.is_countably_generated" -> "order", "minimal_polynomial.algebra_map'" -> "algebra", "filter.germ.coe_mul" -> "order", "set.range_quot_mk" -> "data", "category_theory.limits.types.pi_lift" -> "category_theory", "is_glb_of_is_glb_of_tendsto" -> "topology", "supr_of_empty'" -> "order", "polynomial.degree_restriction" -> "algebra", "finset.Ico.card" -> "data", "list.nil_lt_cons" -> "data", "mul_left_inv" -> "algebra", "multiset.countp_add" -> "data", "mem_nhds_sets_iff" -> "topology", "finite_cover_balls_of_compact" -> "topology", "topological_add_group_is_uniform" -> "topology", "units.coe_dvd" -> "algebra", "multiset.map_bind" -> "data", "add_submonoid.localization_map.epic_of_localization_map" -> "algebra", "min_self" -> "init", "add_equiv.symm_apply_apply" -> "data", "submonoid.closure_mono" -> "algebra", "multiset.Ico.add_consecutive" -> "data", "stream.map_eq_apply" -> "data", "tensor_product.induction_on" -> "algebra", "mv_power_series.coeff_X_pow" -> "algebra", "measure_theory.l1.simple_func.eq" -> "analysis", "ne.elim" -> "init", "mem_skew_adjoint_matrices_lie_subalgebra_unit_smul" -> "algebra", "list.erase_diff_erase_sublist_of_sublist" -> "data", "associates.factors_0" -> "algebra", "composition.size_up_to_zero" -> "combinatorics", "linear_recurrence.is_sol_iff_mem_sol_space" -> "algebra", "finset.affine_combination_apply" -> "algebra", "bool.of_nat_to_nat" -> "data", "pgame.domineering.card_of_mem_left" -> "set_theory", "list.length_sigma" -> "data", "set.infinite_univ_iff" -> "data", "perfect_closure.lift_on_mk" -> "algebra", "tendsto_nhds_of_cauchy_seq_of_subseq" -> "topology", "multiset.to_finset_eq" -> "data", "measure_theory.integrable.mono" -> "analysis", "hyperreal.infinite_mul_infinite" -> "data", "real.exists_floor" -> "data", "multiset.strong_induction_eq" -> "data", "div_left_inj'" -> "algebra", "is_max_on.inter" -> "order", "list.rel_sum" -> "data", "ordinal.lt_pred" -> "set_theory", "filter.germ.coe_one" -> "order", "iterated_fderiv_within_zero_fun" -> "analysis", "equiv.sum_prod_distrib_apply_left" -> "data", "measure_theory.simple_func.map_map" -> "analysis", "onote.oadd_lt_oadd_3" -> "set_theory", "rat.mk_nonneg" -> "data", "complex.has_deriv_at_cosh" -> "analysis", "primrec.list_tail" -> "computability", "ordinal.le_of_dvd" -> "set_theory", "filter.realizer.principal_\[Sigma]" -> "data", "rat.cast_div_of_ne_zero" -> "data", "times_cont_diff_within_at_local_invariant_prop_mono" -> "geometry", "primrec.nat_sqrt" -> "computability", "int.neg_add_le_right_of_le_add" -> "init", "add_submonoid.monotone_map" -> "algebra", "subring.pow_mem" -> "algebra", "monoid_hom.id_comp" -> "algebra", "set.preimage_Union" -> "data", "finset.mem_singleton_self" -> "data", "matrix.mul_mul_right" -> "data", "well_founded.fix_eq" -> "init", "int.zero_div" -> "data", "set.union_Union" -> "data", "mdifferentiable.mdifferentiable_on" -> "geometry", "list.perm.refl" -> "data", "summable.has_sum_iff" -> "topology", "times_cont_diff_within_at_local_invariant_prop_id" -> "geometry", "alg_hom.coe_add_monoid_hom_injective" -> "algebra", "euclidean_geometry.angle_eq_of_ne" -> "geometry", "countable_sInter_mem_sets" -> "order", "set.mem_interval_of_ge" -> "data", "nat.div2_two" -> "init", "tendsto_uniformly_on.mono" -> "topology", "multiset.filter_eq_self" -> "data", "real.totally_bounded_ball" -> "topology", "gcd_same" -> "algebra", "set.mem_smul" -> "algebra", "many_one_equiv.of_equiv" -> "computability", "dfinsupp.filter_apply_pos" -> "data", "matrix.mul_vec_cons" -> "data", "uniformity_has_basis_closure" -> "topology", "rat.div_lt_div_iff_mul_lt_mul" -> "data", "category_theory.under.map_obj_right" -> "category_theory", "matrix.diagonal_to_lin" -> "algebra", "nat.dvd_prime_pow" -> "data", "category_theory.arrow.mk_left" -> "category_theory", "turing.TM1.stmts\:2081_supports_stmt_mono" -> "computability", "continuous_linear_map.coe_id" -> "topology", "cau_seq.completion.mk_eq" -> "data", "norm_num.int_cast_bit1" -> "tactic", "set.piecewise_univ" -> "data", "is_scalar_tower.algebra_map_eq" -> "algebra", "with_top.coe_sup" -> "order", "exists_is_basis" -> "algebra", "dfinsupp.support_subset_iff" -> "data", "finset.prod_ite_eq'" -> "algebra", "onote.of_nat_one" -> "set_theory", "subring.coe_top" -> "algebra", "quotient_map_quot_mk" -> "topology", "fn_min_add_fn_max" -> "algebra", "semiquot.pure_inj" -> "data", "int.mul_comm" -> "init", "linear_map.pi_apply_eq_sum_univ" -> "algebra", "mat_poly_equiv_coeff_apply" -> "algebra", "category_theory.limits.parallel_pair_obj_one" -> "category_theory", "filter.unbounded_of_tendsto_at_bot'" -> "order", "set.mul_empty" -> "algebra", "ring_hom.srange_top_of_surjective" -> "algebra", "rel_iso.trans_apply" -> "order", "continuous_linear_map.fderiv_within" -> "analysis", "submodule.ker_inr" -> "algebra", "list.permutations_aux2_fst" -> "data", "list.diff_nil" -> "data", "matrix.to_blocks_from_blocks\:2082\:2082" -> "data", "list.pairwise_filter_of_pairwise" -> "data", "category_theory.limits.colimit.hom_iso_hom" -> "category_theory", "submodule.Inf_coe" -> "algebra", "ordinal.type_def" -> "set_theory", "list.nth_le_of_mem" -> "data", "nat.pow_two" -> "data", "bitvec.to_nat_of_nat" -> "data", "finset.disjoint_of_subset_right" -> "data", "finsupp.multiset_sum_sum" -> "data", "nat.add_lt_add_left" -> "init", "mul_self_gpow" -> "algebra", "approximates_linear_on.inverse_approx_map_dist_self_le" -> "analysis", "asymptotics.is_O_with.prod_left" -> "analysis", "option.map_none'" -> "data", "con.symm" -> "algebra", "onote.split_eq_scale_split'" -> "set_theory", "list.nodup_sublists" -> "data", "measure_theory.ae_eq_fun.add_to_germ" -> "analysis", "pell.xn_modeq_x2n_add_lem" -> "number_theory", "free_group.to_group.range_eq_closure" -> "algebra", "euclidean_domain.div_add_mod" -> "algebra", "affine_subspace.mem_direction_iff_eq_vsub" -> "algebra", "interior_frontier" -> "topology", "has_deriv_at_unique" -> "analysis", "measurable_space.dynkin_system.ext" -> "analysis", "num.of_znum'_to_nat" -> "data", "is_closed_closure" -> "topology", "padic_norm_e.norm_p" -> "data", "list.map_snd_zip" -> "data", "exists_linear_independent" -> "algebra", "affine_subspace.vadd_mem_iff_mem_direction" -> "algebra", "has_ftaylor_series_up_to_on_top_iff" -> "analysis", "mat_poly_equiv_smul_one" -> "algebra", "multiset.nodup_union" -> "data", "metric.second_countable_of_countable_discretization" -> "topology", "vector_span_singleton" -> "algebra", "pi_eq_generate_from" -> "topology", "computation.equiv.symm" -> "data", "filter.mem_inf_sets_of_right" -> "order", "nat.gcd_dvd_gcd_mul_right_right" -> "data", "nhds_within_subtype" -> "topology", "monotone.map_bdd_below" -> "order", "list.revzip_sublists'" -> "data", "submonoid.mem_supr_of_directed" -> "algebra", "finset.weighted_vsub_vadd_affine_combination" -> "algebra", "polynomial.exists_irreducible_of_nat_degree_pos" -> "algebra", "is_submonoid.list_prod_mem" -> "algebra", "fraction_map.injective" -> "algebra", "set.prod_univ" -> "data", "filter.prod_mem_prod" -> "order", "add_subgroup.list_sum_mem" -> "algebra", "category_theory.arrow.id_left" -> "category_theory", "char_p.cast_eq_zero" -> "algebra", "turing.tape.move_left_nth" -> "computability", "gold_ne_zero" -> "data", "vector3.append_left" -> "number_theory", "multiset.quot_mk_to_coe''" -> "data", "eq_zero_of_one_div_eq_zero" -> "algebra", "multiset.antidiagonal_coe'" -> "data", "hyperreal.abs_lt_real_iff_infinitesimal" -> "data", "add_monoid.coe_mul" -> "algebra", "ring_hom.map_dvd" -> "algebra", "category_theory.over.iso_mk_inv_left" -> "category_theory", "list.eq_repeat_of_mem" -> "data", "submodule.map_comap_le" -> "algebra", "mul_equiv.to_monoid_hom_apply" -> "data", "function.is_fixed_pt.map" -> "dynamics", "category_theory.is_iso.inv_inv" -> "category_theory", "right_ord_continuous.coe_to_order_embedding" -> "order", "has_strict_deriv_at.iterate" -> "analysis", "filter.generate_union" -> "order", "eq_max" -> "init", "quotient_dense_of_dense" -> "topology", "measure_theory.integrable_finset_sum" -> "analysis", "enat.dom_of_le_some" -> "data", "Mon_.hom.ext" -> "category_theory", "sup_le_sup_left" -> "order", "is_Hausdorff.infi_pow_smul" -> "algebra", "int.le_nat_abs" -> "init", "topological_space.opens.local_homeomorph_subtype_coe_coe" -> "topology", "measure_theory.integral_mul_left" -> "analysis", "is_bounded_linear_map.has_fderiv_at_filter" -> "analysis", "is_compact.exists_forall_le" -> "topology", "neg_nonneg_of_nonpos" -> "algebra", "has_strict_fderiv_at.map_implicit_function_eq" -> "analysis", "list.take_append_of_le_length" -> "data", "category_theory.preadditive.neg_comp_neg" -> "category_theory", "inner_neg_right" -> "analysis", "add_monoid_hom.ext_int" -> "data", "convex_hull_eq" -> "analysis", "sub_eq_iff_eq_add'" -> "algebra", "fintype.univ_unit" -> "data", "real.rpow_neg" -> "analysis", "equiv.perm.cycle_of_gpow_apply_self" -> "algebra", "classical.em" -> "init", "set.mem_diff_singleton" -> "data", "complex.re_le_abs" -> "data", "ordinal.type_out'" -> "set_theory", "multiset.filter_congr" -> "data", "left_coset_assoc" -> "algebra", "multiset.disjoint_ndinsert_left" -> "data", "div_mul_comm'" -> "algebra", "measure_theory.measure_eq_trim" -> "analysis", "nnreal.one_div" -> "data", "lie_smul" -> "algebra", "prime_multiset.prod_add" -> "data", "set.Ioc_disjoint_Ioc_same" -> "data", "algebra.restrict_scalars_equiv_symm_apply" -> "algebra", "polynomial.tendsto_infinity" -> "topology", "category_theory.nat_trans.unop_app" -> "category_theory", "multiset.powerset_aux'_cons" -> "data", "int.mul_nonpos_of_nonneg_of_nonpos" -> "init", "pequiv.single_apply" -> "data", "subgroup.closure_univ" -> "algebra", "gc_coinduced_induced" -> "topology", "rat.cast_fpow" -> "algebra", "category_theory.evaluation_obj_obj" -> "category_theory", "matrix.sum_cramer" -> "algebra", "mv_polynomial.vars_0" -> "data", "metric.complete_of_convergent_controlled_sequences" -> "topology", "and_false" -> "init", "convex.mem_Ico" -> "analysis", "subring.closure_sUnion" -> "algebra", "equiv.to_pequiv_symm" -> "data", "mem_self_adjoint_matrices_submodule" -> "algebra", "vsub_self" -> "algebra", "Gromov_Hausdorff.eq_to_GH_space_iff" -> "topology", "continuous_linear_map.coe_cod_restrict_apply" -> "topology", "tactic.ring_exp.sub_pf" -> "tactic", "finset.single_le_sum" -> "algebra", "wseq.to_list_of_list" -> "data", "submodule.span_eq" -> "algebra", "not_eq_of_eq_true" -> "init", "list.nodupkeys_join" -> "data", "one_one_reducible.mk" -> "computability", "multilinear_map.map_piecewise_add" -> "algebra", "filter.tendsto.Icc" -> "order", "multiset.coe_countp" -> "data", "inf_bot_eq" -> "order", "metric.uniform_embedding_iff'" -> "topology", "measure_theory.induced_outer_measure_eq_extend" -> "analysis", "abstract_completion.uniform_continuous_compare_equiv" -> "topology", "ideal.is_prime.mem_or_mem" -> "algebra", "filter.eventually_eq.fderiv_within_eq" -> "analysis", "polynomial.splits_prod_iff" -> "algebra", "has_deriv_at_id'" -> "analysis", "one_divp" -> "algebra", "abs_dist_sub_le_dist_add_add" -> "analysis", "set.Union_add_right_image" -> "algebra", "mv_polynomial.coeff_X_pow" -> "data", "is_coprime.mul_add_right_right_iff" -> "algebra", "fderiv_within_congr" -> "analysis", "tendsto_mul" -> "topology", "pos_num.lt_iff_cmp" -> "data", "times_cont_diff_within_at.congr" -> "analysis", "nat.partrec.code.eval_id" -> "computability", "set.eq_on_comm" -> "data", "pos_and_pos_or_neg_and_neg_of_mul_pos" -> "algebra", "sym2.rel.trans" -> "data", "uniform_space.completion.extension_comp_coe" -> "topology", "rat.add_le_add_left" -> "data", "subtype.range_coe" -> "data", "bool.bxor_bnot_left" -> "data", "equiv.perm.sign_aux3_symm_trans_trans" -> "algebra", "trichotomous" -> "init", "finset.prod_sum_elim" -> "algebra", "function.funext_iff" -> "logic", "commute.self_gpow" -> "algebra", "filter.mul_le_mul" -> "order", "model_with_corners.image" -> "geometry", "rat.mul_inv_cancel" -> "data", "is_open_map.comp" -> "topology", "turing.to_partrec.code.zero_eval" -> "computability", "range_half_space" -> "geometry", "emetric.Hausdorff_edist_le_of_mem_edist" -> "topology", "times_cont_diff_snd" -> "analysis", "le_zero_iff" -> "algebra", "mul_equiv.map_mul" -> "data", "padic_norm_e.eq_of_norm_add_lt_right" -> "data", "set.Union_eq_Union_finset" -> "data", "category_theory.Monad.comp_to_nat_trans" -> "category_theory", "finset.sum_range_succ" -> "algebra", "is_group_hom.inv_iff_ker'" -> "algebra", "category_theory.right_adjoint_preserves_mono" -> "category_theory", "int.lt_div_of_mul_lt" -> "data", "list.nodup_update_nth" -> "data", "ceil_nonneg" -> "algebra", "int.cast_of_nat" -> "data", "convex_closed_ball" -> "analysis", "is_closed_map_mul_left" -> "topology", "composition.size_up_to_strict_mono" -> "combinatorics", "list.length_eq_one" -> "data", "nat.even_pow" -> "data", "cardinal.aleph_le" -> "set_theory", "mvqpf.comp.get_mk" -> "data", "digits_ne_nil_iff_ne_zero" -> "data", "zmod.nat_abs_val_min_abs_le" -> "data", "category_theory.shift_zero_eq_zero" -> "category_theory", "int.nat_abs_abs" -> "data", "roption.induction_on" -> "data", "metric.cauchy_seq_iff" -> "topology", "mem_integral_closure_iff_mem_fg" -> "algebra", "measure_theory.integrable_on.mono_set" -> "analysis", "nat.div_div_eq_div_mul" -> "init", "real.tan_pos_of_pos_of_lt_pi_div_two" -> "analysis", "linarith.nat_eq_subst" -> "tactic", "has_fderiv_at.add_const" -> "analysis", "polynomial.eq_of_monic_of_associated" -> "data", "monoid_hom.fst_comp_prod" -> "algebra", "digits_one_succ" -> "data", "multiset.cons_inter_distrib" -> "data", "list.le_maximum_of_mem" -> "data", "exists_of_bex" -> "logic", "primrec.nat_bodd" -> "computability", "is_measurable_prod" -> "analysis", "pos_tangent_cone_at_mono" -> "analysis", "free_group.map_inv" -> "algebra", "multiset.union_le_union_left" -> "data", "semidirect_product.right_inr" -> "algebra", "has_fderiv_at.const_add" -> "analysis", "cardinal.mul_le_mul_left" -> "set_theory", "exists_sum_is_basis" -> "algebra", "nat.fact_one" -> "data", "category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv_assoc" -> "category_theory", "finset.card_singleton" -> "data", "finset.center_mass_smul" -> "analysis", "iterated_deriv_eq_equiv_comp" -> "analysis", "primrec.encode" -> "computability", "category_theory.limits.walking_pair.equiv_bool_symm_apply_tt" -> "category_theory", "category_theory.limits.biproduct.lift_eq" -> "category_theory", "one_one_equiv_refl" -> "computability", "list.unzip_eq_map" -> "data", "principal_ideal_ring.mem_submonoid_of_factors_subset_of_units_subset" -> "algebra", "is_max_filter.is_extr" -> "order", "generalized_continued_fraction.succ_nth_convergent'_eq_squash_gcf_nth_convergent'" -> "algebra", "mv_polynomial.homogeneous_component_apply" -> "algebra", "asymptotics.is_O_with.congr" -> "analysis", "Set.choice_mem_aux" -> "set_theory", "tsum_geometric_of_lt_1" -> "analysis", "complex.cosh_mul_I" -> "data", "equiv_iso_iso_hom" -> "category_theory", "int.pos_of_neg_neg" -> "init", "padic.of_rat_zero" -> "data", "lucas_lehmer.mersenne_coe_X" -> "number_theory", "set.union_inv" -> "algebra", "set.mk_preimage_prod_left_eq_empty" -> "data", "category_theory.limits.alternative_cone_X" -> "category_theory", "polynomial.is_root.def" -> "data", "computation.eq_of_bisim" -> "data", "valuation.map_add" -> "algebra", "wseq.flatten_ret" -> "data", "set.inj_on.image_bInter_eq" -> "data", "norm_num.le_one_bit1" -> "tactic", "finset.card_eq_succ" -> "data", "filter.has_basis.separation_rel" -> "topology", "mul_gpow_neg_one" -> "algebra", "tt_bxor" -> "init", "vsub_vadd" -> "algebra", "list.perm.kinsert" -> "data", "dense_bUnion_interior_of_closed" -> "topology", "Ring.coe_of" -> "algebra", "localization_map.lift_mk'" -> "algebra", "fin.eq_last_of_not_lt" -> "data", "finmap.union_cancel" -> "data", "subgroup.mem_prod" -> "algebra", "Module.monoidal_category.left_unitor_hom_apply" -> "algebra", "local_homeomorph.image_eq_target_inter_inv_preimage" -> "topology", "int.coe_zero_le" -> "init", "list.tail_nil" -> "data", "caratheodory.mem_convex_hull_erase" -> "analysis", "linear_map.map_coprod_prod" -> "algebra", "subalgebra.coe_nat_mem" -> "algebra", "metric.tendsto_nhds_within_nhds" -> "topology", "onote.cmp_compares" -> "set_theory", "I_extend_zero" -> "topology", "sub_abs_le_abs_sub" -> "algebra", "tensor_product.lift_aux_tmul" -> "algebra", "category_theory.comma.map_right_comp_hom_app_right" -> "category_theory", "continuous_linear_map.map_smul" -> "topology", "category_theory.whiskering_right_map_app_app" -> "category_theory", "neg_add_le_iff_le_add'" -> "algebra", "category_theory.limits.cocone_of_cone_left_op_\[Iota]_app" -> "category_theory", "monoid.coe_mul" -> "algebra", "poly.induction" -> "number_theory", "measure_theory.outer_measure.le_of_function" -> "analysis", "affine.simplex.centroid_eq_affine_combination_of_points_with_circumcenter" -> "geometry", "measure_theory.l1.simple_func.integrable" -> "analysis", "le_Inf" -> "order", "complex.exp_mul_I" -> "data", "category_theory.functor.map_conj" -> "category_theory", "finset.card_erase_lt_of_mem" -> "data", "generalized_continued_fraction.convergents_eq_convergents'" -> "algebra", "int.mul_sign" -> "data", "set.Ioc_subset_Icc_self" -> "data", "set.finite.exists_maximal_wrt" -> "data", "has_strict_fderiv_at.local_inverse_unique" -> "analysis", "exists_compact_subset" -> "topology", "tactic.group.gpow_trick_sub" -> "tactic", "measure_theory.measure.map_apply" -> "analysis", "filter.zero_add" -> "order", "punit.neg_eq" -> "algebra", "list.last'_append_cons" -> "data", "con.trans" -> "algebra", "lt_sub_left_of_add_lt" -> "algebra", "nat.primrec.pred" -> "computability", "monoid_algebra.mul_single_apply_aux" -> "data", "AddCommGroup.colimits.cocone_naturality" -> "algebra", "multiset.inf_le" -> "data", "has_deriv_within_at.cosh" -> "analysis", "has_ftaylor_series_up_to_on.eq_ftaylor_series_of_unique_diff_on" -> "analysis", "subgroup.top_prod" -> "algebra", "wseq.think_equiv" -> "data", "continuous_linear_map.lmul_left_apply" -> "analysis", "polynomial.div_by_monic_mul_pow_root_multiplicity_eq" -> "data", "equiv.perm.cycle_of_cycle" -> "algebra", "add_submonoid.map_comap_map" -> "algebra", "finset.prod_powerset_insert" -> "algebra", "function.right_inverse.comp_eq_id" -> "logic", "is_subgroup.gpow_mem" -> "algebra", "mem_comp_of_mem_ball" -> "topology", "equiv.set.sum_diff_subset_apply_inr" -> "data", "pgame.domineering.move_left_card" -> "set_theory", "function.injective.sigma_map" -> "data", "ennreal.continuous_on_to_nnreal" -> "topology", "one_div_le_of_neg" -> "algebra", "linear_map.trace_aux_eq'" -> "algebra", "multiset.sigma_singleton" -> "data", "finset.mem_range_iff_mem_finset_range_of_mod_eq" -> "algebra", "is_cau_series_of_abv_le_cau" -> "data", "char.val_of_nat_eq_of_is_valid" -> "init", "cardinal.countable_iff" -> "set_theory", "nat.add_mod_add_of_le_add_mod" -> "data", "set.image_congr" -> "data", "measure_theory.integrable_indicator_iff" -> "analysis", "padic_val_rat.inv" -> "data", "uniform_continuous.prod_mk" -> "topology", "topological_space.opens.Sup_s" -> "topology", "cau_seq.one_apply" -> "data", "ideal.mul_sup" -> "algebra", "irrational.of_sub_rat" -> "data", "category_theory.limits.pushout_cocone.mk_\[Iota]_app_left" -> "category_theory", "polynomial.dvd_iff_is_root" -> "data", "subgroup.inv_mem" -> "algebra", "set.subset_univ" -> "data", "polynomial.separable_or" -> "algebra", "dfinsupp.zero_apply" -> "data", "set.nonempty_diff" -> "data", "fract_eq_iff" -> "algebra", "hyperreal.omega_ne_zero" -> "data", "set.image_preimage_eq_inter_range" -> "data", "unique_diff_on_convex" -> "analysis", "computation.tail_empty" -> "data", "option.is_none_some" -> "data", "ennreal.sub_infty" -> "data", "real.cos_arccos" -> "analysis", "roption.bind_some_right" -> "data", "has_strict_fderiv_at.add_const" -> "analysis", "list.foldr_permutations_aux2" -> "data", "real.pi_le_four" -> "analysis", "ennreal.lt_top_of_mul_lt_top_left" -> "data", "equiv.perm.apply_eq_self_iff_of_same_cycle" -> "algebra", "norm_bound" -> "analysis", "vector.to_list_cons" -> "data", "list.perm.prod_eq" -> "data", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_obj_mul_app" -> "category_theory", "int.mod_add_cancel_left" -> "data", "int.lt_to_nat" -> "data", "padic_int.norm_sub_mod_part_aux" -> "data", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae" -> "analysis", "add_submonoid.localization_map.map_map" -> "algebra", "continuous_multilinear_curry_left_equiv_apply" -> "analysis", "fin.exists_fin_succ" -> "data", "polynomial.degree_X_pow_le" -> "data", "list.not_exists_mem_nil" -> "data", "seq1.ret_bind" -> "data", "int.lt_of_sub_pos" -> "init", "structure_groupoid.local_invariant_prop.lift_prop_at_of_lift_prop_within_at" -> "geometry", "subtype.ext" -> "data", "filter.supr_principal" -> "order", "measure_theory.integral_mul_right" -> "analysis", "has_strict_fderiv_at.snd" -> "analysis", "tendsto_of_le_liminf_of_limsup_le" -> "topology", "quotient_group.ker_lift_mk'" -> "algebra", "continuous_add_right" -> "topology", "affine_map.affine_apply_line_map" -> "algebra", "times_cont_diff_within_at_top" -> "analysis", "fin.lt_succ" -> "data", "filter.tendsto.add_add" -> "order", "card_nth_roots_subgroup_units" -> "algebra", "Set.mem_funs" -> "set_theory", "ordered_comm_group.mul_lt_mul_left'" -> "algebra", "galois_insertion.l_inf_u" -> "order", "matrix.det_update_column_smul" -> "algebra", "dfinsupp.zip_with_apply" -> "data", "set.inclusion_inclusion" -> "data", "is_absolute_value.abv_one'" -> "data", "with_bot.sup_eq_max" -> "order", "multiplicity.multiplicity_self" -> "algebra", "equiv.perm.sign_aux_one" -> "algebra", "simple_graph.ne_of_adj" -> "combinatorics", "local_homeomorph.prod_to_local_equiv" -> "topology", "pythagorean_triple.is_primitive_classified_of_coprime_of_pos" -> "number_theory", "times_cont_mdiff_on.mono" -> "geometry", "is_bounded_bilinear_map.fderiv_within" -> "analysis", "finmap.insert_to_finmap" -> "data", "generalized_continued_fraction.le_of_succ_nth_denom" -> "algebra", "finset.centroid_weights_eq_const" -> "algebra", "category_theory.op_op_equivalence_counit_iso" -> "category_theory", "measure_theory.l1.norm_Integral_le_one" -> "analysis", "cau_seq.lim_lt" -> "data", "ennreal.tendsto_mul" -> "topology", "list.take_left" -> "data", "Kuratowski_embedding.exists_isometric_embedding" -> "topology", "measure_theory.integral_sub" -> "analysis", "proof_irrel_heq" -> "logic", "monoid_algebra.single_eq_algebra_map_mul_of" -> "data", "int.neg_add_lt_right_of_lt_add" -> "init", "decidable_eq_inl_refl" -> "init", "ennreal.rpow_zero" -> "analysis", "bifunctor.snd_comp_snd" -> "control", "nat.cast_lt" -> "data", "polynomial.separable_X_add_C" -> "algebra", "continuous_le_rng" -> "topology", "set.image_univ_of_surjective" -> "data", "finset.attach_empty" -> "data", "add_monoid.subset_closure" -> "algebra", "nnreal.le_coe_of_real" -> "data", "uniform_space.completion.dense_embedding_coe" -> "topology", "set.image_injective" -> "data", "turing.TM1.stmts\:2081_trans" -> "computability", "padic_int.coe_coe_int" -> "data", "coinduced_le_iff_le_induced" -> "topology", "composition.embedding_comp_inv" -> "combinatorics", "add_subgroup.coe_add" -> "algebra", "nonempty_sum" -> "logic", "set.Ico_self" -> "data", "ideal.comap_infi" -> "algebra", "finsupp_tensor_finsupp_symm_single" -> "algebra", "filter.eventually_iff_exists_mem" -> "order", "ideal.is_primary_of_is_maximal_radical" -> "algebra", "relation.refl_trans_gen.cases_head" -> "logic", "real.sin_inj_of_le_of_le_pi_div_two" -> "analysis", "tsum_zero" -> "topology", "mul_action.smul_mem_orbit_smul" -> "algebra", "category_theory.limits.wide_pullback_shape.hom_id" -> "category_theory", "category_theory.whisker_right_comp" -> "category_theory", "list.Ico.map_add" -> "data", "mem_pos_tangent_cone_at_of_segment_subset" -> "analysis", "relation.refl_trans_gen_iff_eq_or_trans_gen" -> "logic", "set.disjointed_of_mono" -> "data", "is_local_min_on.inf" -> "topology", "list.filter_filter_map" -> "data", "category_theory.limits.limit.w" -> "category_theory", "measure_theory.lebesgue_outer_Ico" -> "analysis", "list.prod_repeat" -> "algebra", "list.pairwise_reverse" -> "data", "polynomial.monomial_add" -> "data", "ennreal.mul_rpow_of_nonneg" -> "analysis", "cau_seq.le_lim" -> "data", "filter.tendsto_at_top_pure" -> "order", "typevec.const_nil" -> "data", "pequiv.le_def" -> "data", "algebra.tensor_product.congr_apply" -> "algebra", "num.add_to_znum" -> "data", "ordinal.mod_self" -> "set_theory", "relator.rel_exists_of_total" -> "logic", "pell.y_mul_dvd" -> "number_theory", "pfunctor.approx.agree_trival" -> "data", "is_group_hom.injective_iff" -> "algebra", "linear_pmap.domain_mono" -> "algebra", "exists_ge_of_linear" -> "algebra", "set.mem_insert_of_mem" -> "data", "hyperreal.is_st_iff_abs_sub_lt_delta" -> "data", "ordinal.pred_succ" -> "set_theory", "set.Ico_def" -> "data", "linear_map.to_span_singleton_one" -> "algebra", "submonoid.closure_induction" -> "algebra", "mdifferentiable_within_at_inter" -> "geometry", "is_R_or_C.inv_def" -> "data", "set.nonempty.of_image" -> "data", "category_theory.limits.span_left" -> "category_theory", "le_add_left" -> "algebra", "has_strict_fderiv_at.eq_implicit_function_of_complemented" -> "analysis", "not_exists_of_forall_not" -> "logic", "exists_vector_succ" -> "number_theory", "measure_theory.l1.norm_integral_le" -> "analysis", "category_theory.concrete_category.epi_of_surjective" -> "category_theory", "eq_ff_eq_not_eq_tt" -> "init", "le_of_not_ge" -> "init", "bex.elim" -> "logic", "set.enumerate_eq_none_of_sel" -> "data", "char.of_nat_eq_of_not_is_valid" -> "init", "inf_apply" -> "order", "is_local_extr.comp_mono" -> "topology", "array.to_list_reverse" -> "data", "add_commute.neg_neg" -> "algebra", "padic_norm.eq_fpow_of_nonzero" -> "data", "monoid_hom.iterate_map_one" -> "algebra", "bdd_above_singleton" -> "order", "inner_neg_neg" -> "analysis", "complex.neg_re" -> "data", "mul_semiring_action_hom.map_sub" -> "algebra", "differentiable.ccos" -> "analysis", "ctop.realizer.ext'" -> "data", "continuous_within_at.congr_mono" -> "topology", "has_fderiv_at.iterate" -> "analysis", "fin.snoc_last" -> "data", "ring_hom.prod_map_def" -> "algebra", "dense_sUnion_interior_of_closed" -> "topology", "semiconj_by.mul_right" -> "algebra", "sesq_form.smul_left" -> "algebra", "submodule.dim_sup_add_dim_inf_eq" -> "algebra", "rel.preimage_union" -> "data", "linear_equiv.trans_symm" -> "algebra", "is_scalar_tower.of_algebra_map_eq" -> "algebra", "primrec.succ" -> "computability", "measure_theory.simple_func.piecewise_empty" -> "analysis", "pgame.turn_bound_ne_zero_of_right_move" -> "set_theory", "list.nth_update_nth_eq" -> "data", "category_theory.functor.left_op_map" -> "category_theory", "set.eq_of_Ico_disjoint" -> "data", "polynomial.monic_map" -> "data", "add_one_gsmul" -> "algebra", "traversable.pure_transformation_apply" -> "control", "set.subset_bInter" -> "data", "list.sum_singleton" -> "data", "sequentially_complete.le_nhds_of_seq_tendsto_nhds" -> "topology", "matrix.sum_mul" -> "data", "is_lub.union" -> "order", "complex.continuous_linear_map.of_real_coe" -> "analysis", "succ_ne_self" -> "algebra", "ordinal.add_le_add_iff_left" -> "set_theory", "multiset.sum_map_mul_right" -> "data", "mv_polynomial.sum_mv_polynomial_eq_zero" -> "algebra", "isometric.add_left_to_equiv" -> "topology", "dist_le_range_sum_of_dist_le" -> "topology", "list.forall_mem_of_forall_mem_union_left" -> "data", "polynomial.degree_le_zero_iff" -> "data", "emetric.tendsto_at_top" -> "topology", "complex.cosh_conj" -> "data", "power_series.coeff_zero_eq_constant_coeff" -> "algebra", "fintype.univ_empty" -> "data", "Module.monoidal_category.associator_hom_apply" -> "algebra", "bilin_form.comp_injective" -> "algebra", "filter.rcomap_rcomap" -> "order", "measurable_space.generate_from_le_generate_from" -> "analysis", "submodule.mem_left_iff_eq_zero_of_disjoint" -> "algebra", "set.inter_subset_left" -> "data", "filter.tendsto_at_top_finset_of_monotone" -> "order", "dim_add_le_dim_add_dim" -> "algebra", "function.is_periodic_pt.minimal_period_le" -> "dynamics", "complex.zero_cpow" -> "analysis", "mul_self_div_self" -> "algebra", "set.Iic_union_Ici" -> "data", "computable.unpair" -> "computability", "measure_theory.is_lebesgue_measurable_Iio" -> "analysis", "with_top.sup_eq_max" -> "order", "function.right_inverse.surjective" -> "init", "list.sublists_len_succ_nil" -> "data", "local_homeomorph.to_open_embedding" -> "topology", "open_subgroup.is_closed" -> "topology", "eq_zero_of_mul_eq_self_right" -> "algebra", "list.rotate'_cons_succ" -> "data", "mul_right_iterate" -> "algebra", "category_theory.whisker_right_left" -> "category_theory", "nat.test_bit_bitwise" -> "init", "is_R_or_C.abs_sub" -> "data", "set.exists_mem_of_nonempty" -> "data", "has_deriv_at_fpow" -> "analysis", "list.nth_map" -> "data", "filter.union_mem_sup" -> "order", "hyperreal.infinite_pos_add_infinite_pos" -> "data", "set.image2_image_left" -> "data", "tensor_product.tmul_zero" -> "algebra", "free_add_semigroup.lift_add" -> "algebra", "is_local_max_on_const" -> "topology", "category_theory.limits.cocone.whisker_\[Iota]" -> "category_theory", "closed_embedding.comp" -> "topology", "measure_theory.outer_measure.trim_zero" -> "analysis", "ring_hom.map_sub" -> "algebra", "nat.min_fac_one" -> "data", "convex_on.comp_affine_map" -> "analysis", "mul_semiring_action_hom.map_one" -> "algebra", "ennreal.inv_eq_top" -> "data", "multiset.self_mem_range_succ" -> "data", "cardinal.lift_umax" -> "set_theory", "finset.fold_min_lt" -> "data", "has_fderiv_within_at_iff_tendsto" -> "analysis", "linear_pmap.domain_mk_span_singleton" -> "algebra", "free_semigroup.lift_mul" -> "algebra", "int.cast_eq_zero" -> "data", "filter.eventually_eq.mfderiv_eq" -> "geometry", "induced_order_topology'" -> "topology", "summable_of_summable_norm" -> "analysis", "monoid_hom.map_pow" -> "algebra", "continuous_linear_map.zero_apply" -> "topology", "category_theory.functor.as_equivalence_functor" -> "category_theory", "set.Ioo_eq_empty_iff" -> "data", "ideal.mem_Inf" -> "algebra", "times_cont_diff_within_at.congr_of_eventually_eq'" -> "analysis", "list.le_minimum_of_mem'" -> "data", "is_null_measurable_measure_eq" -> "analysis", "bilin_form.is_adjoint_pair_iff_comp_left_eq_comp_right" -> "algebra", "composition.length_sigma_composition_aux" -> "analysis", "Module.monoidal_category.right_unitor_naturality" -> "algebra", "generalized_continued_fraction.zeroth_convergent_eq_h" -> "algebra", "subgroup.coe_infi" -> "algebra", "set.abs_sub_le_of_subinterval" -> "data", "uniform_continuous_dist" -> "topology", "add_aut.coe_mul" -> "data", "int.sub_self" -> "init", "local_homeomorph.restr_source'" -> "topology", "mfderiv_within_univ" -> "geometry", "lie_gsmul" -> "algebra", "submodule.exists_of_lt" -> "algebra", "omega.int.val_canonize" -> "tactic", "polynomial.nat_degree_X_le" -> "data", "dense_range.induction_on\:2082" -> "topology", "filter.frequently.mem_of_closed" -> "topology", "nat.gcd_zero_left" -> "init", "wseq.map_nil" -> "data", "list.drop_append" -> "data", "nnreal.has_sum_iff_tendsto_nat" -> "topology", "mul_equiv.trans_apply" -> "data", "free_group.red.step.append_left" -> "algebra", "forall_lt_iff_le" -> "algebra", "multiset.zero_product" -> "data", "zsqrtd.bit0_re" -> "data", "push_neg.not_le_eq" -> "tactic", "stream.map_iterate" -> "data", "is_bounded_bilinear_map.fderiv" -> "analysis", "lipschitz_with.restrict" -> "topology", "finite_field.sum_pow_lt_card_sub_one" -> "algebra", "polynomial.sum_over_range'" -> "data", "disjoint_self" -> "order", "isometric.coe_vadd_const_symm" -> "analysis", "nnreal.div_le_iff" -> "data", "is_group_hom.map_inv" -> "algebra", "linear_equiv.arrow_congr_comp" -> "algebra", "enat.le_of_lt_add_one" -> "data", "local_equiv.trans_source" -> "data", "fin.sum_pow_mul_eq_add_pow" -> "data", "prod.forall" -> "data", "convex.interior" -> "analysis", "monotone.map_max" -> "algebra", "mem_closure_iff_ultrafilter" -> "topology", "submodule.closed_of_finite_dimensional" -> "analysis", "semiconj_by.neg_right_iff" -> "algebra", "is_closed_map.id" -> "topology", "finset.max'_mem" -> "data", "sup_of_le_right" -> "order", "norm_sub_le" -> "analysis", "filter.has_basis.map" -> "order", "submodule.span_prod_le" -> "algebra", "measure_theory.ae_restrict_eq_bot" -> "analysis", "int.neg_succ_mul_coe_nat" -> "data", "multiset.le_union_right" -> "data", "array.write_to_list" -> "data", "submonoid.comap_infi_map_of_injective" -> "algebra", "set.monotone_union" -> "data", "alist.mem_lookup_union_middle" -> "data", "measure_theory.measure_eq_inter_diff" -> "analysis", "local_homeomorph.eq_on_source.symm'" -> "topology", "rat.mul_num_denom" -> "data", "category_theory.limits.binary_fan.mk_\[Pi]_app_right" -> "category_theory", "local_equiv.refl_restr_source" -> "data", "real.sin_arcsin" -> "analysis", "finset.centroid_singleton" -> "algebra", "cardinal.bit1_lt_bit1" -> "set_theory", "Mon_.hom.ext_iff" -> "category_theory", "and_iff_left" -> "init", "normed_ring.inverse_add_norm_diff_first_order" -> "analysis", "ne_true_of_not" -> "init", "linear_equiv.coe_of_top_symm_apply" -> "algebra", "comp_rel_mono" -> "topology", "prime_multiset.prod_of_pnat_multiset" -> "data", "continuous_linear_map.smul_right_comp" -> "topology", "opposite.unop_inj_iff" -> "data", "list.mem_pmap" -> "data", "is_compact.uniform_continuous_on_of_continuous" -> "topology", "relator.rel_forall_of_total" -> "logic", "measure_theory.lintegral_nnnorm_neg" -> "analysis", "measurable.mul" -> "analysis", "iterated_deriv_within_univ" -> "analysis", "typevec.drop_fun_append_fun" -> "data", "category_theory.cancel_mono_id" -> "category_theory", "nat.add_right_comm" -> "init", "affine_map.zero_linear" -> "algebra", "mdifferentiable_const" -> "geometry", "category_theory.sum.inverse_associator_map_inl" -> "category_theory", "Module.Mon_Module_equivalence_Algebra.algebra_map" -> "category_theory", "algebraic_geometry.LocallyRingedSpace.hom_ext" -> "algebraic_geometry", "ennreal.top_rpow_of_neg" -> "analysis", "uniform_space.completion.extension_coe" -> "topology", "is_R_or_C.re_to_complex" -> "data", "ordinal.dvd_add_iff" -> "set_theory", "local_homeomorph.prod_coe" -> "topology", "zmod.mul_inv_of_unit" -> "data", "submonoid.mem_sup_right" -> "algebra", "is_preconnected_iff_ord_connected" -> "topology", "rat.num_one" -> "data", "pSet.mem.mk" -> "set_theory", "submonoid.comap_supr_map_of_injective" -> "algebra", "char_matrix_apply_nat_degree" -> "algebra", "mdifferentiable_on.continuous_on" -> "geometry", "relation.comp_eq" -> "logic", "filter.countable_binfi_eq_infi_seq" -> "order", "deriv_mul" -> "analysis", "lie_algebra.equiv.of_eq_apply" -> "algebra", "tendsto_diag_uniformity" -> "topology", "int.add_lt_add_right" -> "init", "measure_theory.ae_eq_fun.integrable.sub" -> "analysis", "interval_integral.integral_add_adjacent_intervals_cancel" -> "analysis", "dvd_choose_of_middling_prime" -> "number_theory", "right_ord_continuous.id" -> "order", "alist.union_erase" -> "data", "polynomial.degree_map_le" -> "data", "finset.val_inj" -> "data", "set.mem_range_indicator" -> "data", "submonoid.pow_mem" -> "algebra", "cardinal.mk_nat" -> "set_theory", "totally_bounded_subset" -> "topology", "polynomial.eval_C" -> "data", "open_embedding_id" -> "topology", "congr_arg_heq" -> "logic", "ge_trans" -> "init", "set.sum.elim_range" -> "data", "le_of_neg_le_neg" -> "algebra", "nat.shiftr_eq_div_pow" -> "init", "num.cast_to_int" -> "data", "is_local_max.comp_continuous" -> "topology", "nnreal.two_inv_lt_one" -> "data", "set.Ioi_subset_Ioo_union_Ici" -> "data", "measure_theory.integrable_on.mono_measure" -> "analysis", "measure_theory.simple_func.add_eq_map\:2082" -> "analysis", "topological_space.opens.coe_mk" -> "topology", "topological_space.opens.map_iso_hom_app" -> "topology", "char.val_of_nat_eq_of_not_is_valid" -> "init", "cau_seq.const_mul" -> "data", "real.cosh_sub" -> "data", "filter.map_comap_of_surjective'" -> "order", "affine_independent_set_iff_linear_independent_vsub" -> "algebra", "times_cont_diff_on_of_differentiable_on" -> "analysis", "nat.dist_mul_left" -> "data", "max_assoc" -> "init", "lagrange.eval_basis" -> "algebra", "int.bodd_sub_nat_nat" -> "data", "measure_theory.ae_restrict_eq" -> "analysis", "category_theory.limits.id_zero" -> "category_theory", "category_theory.over.map_obj_left" -> "category_theory", "continuous_within_at.inv" -> "topology", "measure_theory.measure.restrict_smul" -> "analysis", "is_bounded_linear_map.has_fderiv_within_at" -> "analysis", "equiv.perm.sign_swap'" -> "algebra", "equiv.surjective" -> "data", "ordinal.nat_cast_mod" -> "set_theory", "partrec.to\:2082" -> "computability", "seq.join_cons" -> "data", "asymptotics.is_o.mono" -> "analysis", "polynomial.aeval_X" -> "data", "stream.eta" -> "data", "measure_theory.simple_func.coe_injective" -> "analysis", "complex.mul_re" -> "data", "linear_equiv.coe_coe" -> "algebra", "submodule.map_comp" -> "algebra", "list.right_unique_forall\:2082" -> "data", "is_R_or_C.re_add_im" -> "data", "is_compl.compl_eq" -> "order", "id.bind_eq" -> "init", "principal_seg.init" -> "set_theory", "is_closed_std_simplex" -> "analysis", "category_theory.monoidal_category.right_assoc_tensor_map" -> "category_theory", "ext_chart_continuous_at_symm" -> "geometry", "quotient_add_group.ker_lift_mk" -> "algebra", "not_and'" -> "logic", "list.perm.inter_left" -> "data", "convex_on_of_deriv_mono" -> "analysis", "has_sum_ite_eq" -> "topology", "fin.cons_self_tail" -> "data", "measure_theory.simple_func.map_preimage_singleton" -> "analysis", "int.bitwise_xor" -> "data", "list.take_prefix" -> "data", "polynomial.mul_comp" -> "data", "div_two_sub_self" -> "algebra", "subtype.preirreducible_space" -> "topology", "set.bUnion_subset_Union" -> "data", "dlist.of_list_to_list" -> "data", "string.lt_iff_to_list_lt" -> "data", "irrational.of_pow" -> "data", "finset.subset.antisymm" -> "data", "int.lcm_zero_left" -> "algebra", "ring_hom.comp_id" -> "algebra", "homological_complex.kernel_map_id" -> "algebra", "differentiable_const" -> "analysis", "ennreal.tsum_comm" -> "topology", "submodule.infi_coe" -> "algebra", "differentiable_within_at.prod" -> "analysis", "multiset.disjoint_cons_left" -> "data", "pnat.eq_one_of_lt_two" -> "data", "algebra.tensor_product.rid_tmul" -> "algebra", "nnreal.rpow_nat_inv_pow_nat" -> "analysis", "filter.is_basis.mem_filter_iff" -> "order", "real.continuous_cos" -> "analysis", "lucas_lehmer.X.left_distrib" -> "number_theory", "set.bdd_below_bdd_above_iff_subset_interval" -> "data", "category_theory.differential_object.hom.ext_iff" -> "category_theory", "not_and_self_iff" -> "logic", "multiset.revzip_powerset_aux'" -> "data", "add_monoid_hom.map_multiset_sum" -> "data", "apply_dite" -> "logic", "roption.map_some" -> "data", "turing.reaches\:2080.refl" -> "computability", "has_sum_nat_add_iff'" -> "topology", "add_monoid_hom.map_rat_cast_smul" -> "algebra", "is_glb_cInf" -> "order", "real.tan_neg_of_neg_of_pi_div_two_lt" -> "analysis", "mvpfunctor.W_ind" -> "data", "nat.modeq.modeq_zero_iff" -> "data", "real.rpow_le_rpow_iff" -> "analysis", "array.mem.def" -> "data", "category_theory.limits.is_limit.of_nat_iso.cone_of_hom_of_cone" -> "category_theory", "ideal.map_jacobson_of_surjective" -> "algebra", "submodule.comap_le_comap_smul" -> "algebra", "set.Union_image_right" -> "data", "measurable_find_greatest" -> "analysis", "is_least_singleton" -> "order", "lagrange.basis_empty" -> "algebra", "multiset.sup_mono" -> "data", "semidirect_product.inl_aut_inv" -> "algebra", "filter.is_countably_generated.has_countable_basis" -> "order", "order.cofinal.le_above" -> "order", "is_bounded_linear_map.differentiable_on" -> "analysis", "list.split_cons_of_eq" -> "data", "set.mem_image_of_injective" -> "data", "filter.eventually_eq.fun_comp" -> "order", "continuous_within_at_inter'" -> "topology", "measure_theory.ae_eq_fun.comp\:2082_to_germ" -> "analysis", "category_theory.adjunction.unit_naturality_assoc" -> "category_theory", "filter.eventually_and" -> "order", "linear_map.coe_inj" -> "algebra", "field.to_is_field" -> "algebra", "add_subgroup.closure_Union" -> "algebra", "monotonicity.pi" -> "meta", "int.neg_succ" -> "data", "list.perm.product_right" -> "data", "mul_action_hom.id_comp" -> "algebra", "or_iff_right_of_imp" -> "init", "add_submonoid.mem_nhds_zero" -> "topology", "int.nat_abs_add_nonneg" -> "init", "times_cont_diff_on_of_locally_times_cont_diff_on" -> "analysis", "fderiv_within_subset" -> "analysis", "localization_map.map_comp" -> "algebra", "is_group_hom.mk'" -> "algebra", "fderiv_within.comp_deriv_within" -> "analysis", "game.zero_add" -> "set_theory", "pell.is_pell_one" -> "number_theory", "AddCommMon.coe_of" -> "algebra", "padic_int.unit_coeff_coe" -> "data", "add_semiconj_by.conj_mk" -> "algebra", "matrix.to_linear_equiv_symm_apply" -> "algebra", "Gromov_Hausdorff.candidates_b_dist_mem_candidates_b" -> "topology", "measure_theory.to_outer_measure_eq_induced_outer_measure" -> "analysis", "fintype.univ_pempty" -> "data", "is_basis_singleton_one" -> "algebra", "finset.filter_empty" -> "data", "is_closed_compl_iff" -> "topology", "function.curry_uncurry" -> "init", "contracting_with.fixed_point_lipschitz_in_map" -> "topology", "supr_union" -> "order", "set.sup_eq_union" -> "data", "is_unit.lift_right_inv_mul" -> "algebra", "ideal.map_sup_comap_of_surjective" -> "algebra", "push_neg.not_lt_eq" -> "tactic", "is_glb_Ioc" -> "order", "real.arctan_lt_pi_div_two" -> "analysis", "complex.has_deriv_at_exp" -> "analysis", "category_theory.monoidal_category.unitors_equal.cells_1_7" -> "category_theory", "encodable.encode_inl" -> "data", "omega.forall_mem_repeat_zero_eq_zero" -> "tactic", "measure_theory.ae_eq_fun.mk_coe_fn" -> "analysis", "galois_insertion.l_supr_of_ul_eq_self" -> "order", "tendsto_locally_uniformly_on.tendsto_comp" -> "topology", "localization_map.mul_mk'_eq_mk'_of_mul" -> "algebra", "tsum_neg" -> "topology", "with_bot.some_le_some" -> "order", "filter.ultrafilter_of_spec" -> "order", "list.monotone_sum_take" -> "data", "nat.sub_induction" -> "init", "zero_dvd_iff" -> "algebra", "inv_injective'" -> "algebra", "lim_norm" -> "analysis", "add_sub_cancel'_right" -> "algebra", "summable.sigma" -> "topology", "nat.partrec'.idv" -> "computability", "continuous.comp_continuous_on" -> "topology", "associates.irreducible_mk_iff" -> "algebra", "matrix.cramer_apply" -> "algebra", "typevec.append_prod_append_fun" -> "data", "matrix.row_mul_col_apply" -> "data", "subgroup.normal_comap" -> "algebra", "norm_num.nat_cast_bit0" -> "tactic", "finset.sigma_preimage_mk" -> "data", "ennreal.bot_lt_iff_ne_bot" -> "data", "iterated_deriv_within_zero" -> "analysis", "measure_theory.measure.join_dirac" -> "analysis", "finset.coe_erase" -> "data", "commute.inv_inv'" -> "algebra", "nhds_nhds_eq_uniformity_uniformity_prod" -> "topology", "category_theory.is_equivalence.inv_fun_id_inv_comp" -> "category_theory", "lie_subalgebra.ext_iff" -> "algebra", "polynomial.as_sum" -> "data", "submodule.map_inr" -> "algebra", "norm_num.int_cast_neg" -> "tactic", "continuous_on.comp" -> "topology", "inner_product_geometry.cos_angle_mul_norm_mul_norm" -> "geometry", "nat.cast_commute" -> "data", "cauchy_seq_finset_iff_vanishing" -> "topology", "ennreal.zero_rpow_of_pos" -> "analysis", "has_strict_deriv_at.add" -> "analysis", "matrix.diagonal_transpose" -> "data", "contracting_with.edist_le_of_fixed_point" -> "topology", "continuous_at.neg" -> "topology", "set.bij_on.to_local_equiv_to_fun" -> "data", "list.tfae.out" -> "data", "isometric.point_reflection_to_equiv" -> "analysis", "multiset.to_finsupp_apply" -> "data", "fin.heq_fun_iff" -> "data", "quotient.map'_mk'" -> "data", "polynomial.next_coeff_X_sub_C" -> "data", "nat.dist_eq_intro" -> "data", "compare_reals.compare_uc" -> "topology", "false_iff" -> "init", "circle_deg1_lift.translation_number_mono" -> "dynamics", "list.sigma_cons" -> "data", "units.coe_hom_apply" -> "algebra", "option.map_some'" -> "data", "mul_le_mul_of_mul_div_le" -> "algebra", "power_series.coeff_mk" -> "algebra", "list.argmax_eq_none" -> "data", "algebra.tensor_product.alg_equiv_of_linear_equiv_tensor_product_apply" -> "algebra", "matrix.cons_dot_product" -> "data", "or_self_left" -> "logic", "real.log_inv" -> "analysis", "pi_Lp.antilipschitz_with_equiv" -> "topology", "int.dvd_nat_abs_of_of_nat_dvd" -> "data", "measure_theory.outer_measure.trim_congr" -> "analysis", "fintype.card_finset" -> "data", "rel.comp_assoc" -> "data", "linear_action_zero" -> "algebra", "category_theory.monoidal_category.triangle_assoc_comp_left_inv" -> "category_theory", "set.subset_insert" -> "data", "set.subsingleton.eq_empty_or_singleton" -> "data", "nat.not_prime_one" -> "data", "times_cont_diff_on.neg" -> "analysis", "vector.tail_cons" -> "data", "continuous_on.mono" -> "topology", "finset.card_union_eq" -> "data", "one_lt_inv" -> "algebra", "is_max_on.bicomp_mono" -> "order", "is_open_iff_generate_intervals" -> "topology", "complex.two_cosh" -> "data", "ulift.up_down" -> "init", "disjoint.mono_right" -> "order", "vector.to_list_of_fn" -> "data", "tactic.ring.unfold_sub" -> "tactic", "filter.eventually.exists_forall_of_at_bot" -> "order", "polynomial.mod_by_monic_zero" -> "data", "set.mem_singleton_of_eq" -> "data", "omega.unsat_of_unsat_lin_comb" -> "tactic", "div_helper" -> "algebra", "linear_equiv.of_top_symm_apply" -> "algebra", "list.perm_append_right_iff" -> "data", "tendsto_inv_at_top_zero'" -> "analysis", "commute.mul_left" -> "algebra", "filter.join_principal_eq_Sup" -> "order", "mvqpf.const.get_mk" -> "data", "set.Ici_subset_Icc_union_Ioi" -> "data", "free_group.map.unique" -> "algebra", "set_coe.exists" -> "data", "mul_lt_mul'''" -> "algebra", "min_lt_iff" -> "algebra", "multiset.ndunion_le" -> "data", "real.sinh_strict_mono" -> "analysis", "multiset.fold_cons'_right" -> "data", "category_theory.monoidal_of_has_finite_coproducts.left_unitor_hom" -> "category_theory", "list.not_mem_of_nodup_cons" -> "data", "function.commute.iterate_eq_of_map_eq" -> "logic", "preserves_products_iso_hom_\[Pi]" -> "category_theory", "has_deriv_at.lhopital_zero_at_top" -> "analysis", "polynomial.nonzero.of_polynomial_ne" -> "data", "padic_norm_e.add_eq_max_of_ne'" -> "data", "add_subgroup.mem_Sup_of_directed_on" -> "algebra", "matrix.smul_mat_empty" -> "data", "list.rel_bind" -> "data", "equiv.self_comp_symm" -> "data", "category_theory.currying_counit_iso_hom_app_app" -> "category_theory", "nnreal.young_inequality" -> "analysis", "prod_primes_dvd" -> "number_theory", "norm_lt_of_mem_ball" -> "analysis", "hyperreal.infinite_pos_iff_infinitesimal_inv_pos" -> "data", "nat.units_eq_one" -> "data", "metric.exists_ball_subset_ball" -> "topology", "vector.nodup_iff_nth_inj" -> "data", "push_neg.not_and_eq" -> "tactic", "category_theory.limits.wide_pushout_shape.hom_id" -> "category_theory", "computable.list_concat" -> "computability", "encodable.supr_decode2" -> "data", "to_mul_add" -> "algebra", "set.Icc_diff_Ioc_same" -> "data", "rat.cast_id" -> "data", "prime_spectrum.union_zero_locus" -> "algebraic_geometry", "matrix.sum_cramer_apply" -> "algebra", "num.cast_to_znum" -> "data", "finset.Ico.mem" -> "data", "pequiv.injective_of_forall_ne_is_some" -> "data", "matrix.neg_cons" -> "data", "filter.has_basis.sInter_sets" -> "order", "map_nhds_subtype_coe_eq" -> "topology", "padic_int.mod_part_nonneg" -> "data", "matrix.special_linear_group.to_GL_one" -> "algebra", "real.sqrt_zero" -> "data", "nat.rfind_min" -> "computability", "asymptotics.is_O_with.sub" -> "analysis", "submodule.mem_top" -> "algebra", "set.finite.mem_to_finset" -> "data", "cardinal.mk_subset_ge_of_subset_image" -> "set_theory", "subgroup.normal.comap" -> "algebra", "set.preimage_const_mul_Ioc_of_neg" -> "data", "list.range_succ_eq_map" -> "data", "finset.prod_comp" -> "algebra", "submodule.prod_inf_prod" -> "algebra", "nat.mul_zero" -> "init", "add_submonoid.mem_map" -> "algebra", "sigma.ext" -> "data", "finset.coe_empty" -> "data", "alg_hom.ext" -> "algebra", "ennreal.mul_le_iff_le_inv" -> "data", "category_theory.limits.biprod.map_snd" -> "category_theory", "polynomial.is_splitting_field.finite_dimensional" -> "algebra", "ring_hom.map_one_ne_zero" -> "algebra", "filter.eventually_eq.fderiv_eq" -> "analysis", "fintype.card_subtype_le" -> "data", "computation.eq_thinkN" -> "data", "polynomial.map_monic_eq_zero_iff" -> "data", "additive.is_add_group_hom" -> "algebra", "of_irreducible_mul" -> "algebra", "is_basis.total_repr" -> "algebra", "erased.out_inj" -> "data", "mem_nhds_iff_exists_Ioo_subset" -> "topology", "submodule.is_principal.eq_bot_iff_generator_eq_zero" -> "algebra", "exists_nhds_split" -> "topology", "alg_hom.id_apply" -> "algebra", "continuous_on.congr" -> "topology", "ordinal.zero_lt_one" -> "set_theory", "mul_inv_of_self" -> "algebra", "nat.bodd_div2_eq" -> "data", "filter.ne_bot.comap_of_range_mem" -> "order", "multiset.mem_to_finset" -> "data", "matrix.update_row_self" -> "data", "ennreal.has_sum_coe" -> "topology", "finsupp.single_apply" -> "data", "add_submonoid.closure_Union" -> "algebra", "finset.sum_boole" -> "algebra", "category_theory.currying_functor_obj_obj" -> "category_theory", "differentiable_on.const_mul" -> "analysis", "set.preimage_mul_const_Iic" -> "data", "set.Union_subset_iff" -> "data", "filter.ne_bot_of_le" -> "order", "matrix.mul_adjugate_apply" -> "algebra", "mul_self_le_mul_self_iff" -> "algebra", "complex.differentiable_at_cos" -> "analysis", "left_coset_right_coset" -> "algebra", "filter.has_basis.prod_self" -> "order", "set.fst_image_prod_subset" -> "data", "affine.simplex.sum_points_with_circumcenter" -> "geometry", "structure_groupoid.trans" -> "geometry", "char_p.exists_unique" -> "algebra", "set.mem_mul" -> "algebra", "W.depth_pos" -> "data", "dvd.elim" -> "algebra", "polynomial.leading_coeff_prod" -> "algebra", "indicator_union_eventually_eq" -> "order", "polynomial.leading_coeff_of_injective" -> "data", "finsupp.total_apply" -> "algebra", "list.sublists_aux_cons_eq_sublists_aux\:2081" -> "data", "array.read_write" -> "init", "semidirect_product.map_right" -> "algebra", "category_theory.limits.biprod.inr_snd" -> "category_theory", "Mod.comap_obj_act" -> "category_theory", "set.image_subset_image_iff" -> "data", "unique_mdiff_on_iff_unique_diff_on" -> "geometry", "measure_theory.ae_eq_fun.mk_to_germ" -> "analysis", "free_semigroup.traverse_eq" -> "algebra", "list.erasep_of_forall_not" -> "data", "pequiv.symm_bot" -> "data", "bool.coe_sort_ff" -> "data", "formal_multilinear_series.partial_sum_continuous" -> "analysis", "units.mk_semiconj_by" -> "algebra", "has_fderiv_at_snd" -> "analysis", "finset.insert_subset" -> "data", "padic_int.norm_int_lt_one_iff_dvd" -> "data", "closure_inter_subset_inter_closure" -> "topology", "list.dvd_sum" -> "data", "list.update_nth_eq_nil" -> "data", "rat.le_antisymm" -> "data", "tendsto_neg_nhds_within_Iio_neg" -> "topology", "multiset.coe_eq_zero" -> "data", "hyperreal.not_infinitesimal_of_infinite" -> "data", "computable.fst" -> "computability", "real.is_conjugate_exponent.ne_zero" -> "data", "topological_space.opens.gc" -> "topology", "filter.principal_empty" -> "order", "num.cast_pos" -> "data", "list.rotate_length_mul" -> "data", "ennreal.mul_rpow_of_ne_zero" -> "analysis", "finite_dimensional.exists_is_basis_finset" -> "algebra", "nat.sqrt_aux_1" -> "data", "max_mul_mul_le_max_mul_max" -> "algebra", "equiv.sum_congr_symm" -> "data", "differentiable_within_at_id" -> "analysis", "ideal.sup_mul" -> "algebra", "finsupp.comap_smul_apply" -> "data", "deriv_within_subset" -> "analysis", "computable_pred.computable_of_one_one_reducible" -> "computability", "category_theory.prod.inverse_associator_map" -> "category_theory", "set.Ioc_subset_Ioc_union_Ioc" -> "data", "interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left" -> "analysis", "finset.sum_nsmul" -> "algebra", "complex.continuous_inv" -> "topology", "nnreal.inv_pos" -> "data", "int.lt_neg_of_lt_neg" -> "init", "filter.has_basis.mem_of_mem" -> "order", "max_zero_sub_eq_self" -> "algebra", "multiset.disjoint_add_right" -> "data", "list.rel_of_chain_cons" -> "data", "times_cont_diff_on_congr" -> "analysis", "filter.has_basis_infi_principal" -> "order", "euclidean_geometry.reflection_symm" -> "geometry", "is_compact.exists_is_least" -> "topology", "finsupp.map_range_finset_sum" -> "data", "times_cont_mdiff_on.prod_mk" -> "geometry", "zmod.pow_card_sub_one_eq_one" -> "algebra", "multiset.sections_add" -> "data", "set.ord_connected_iff" -> "data", "subsemiring.mem_Inf" -> "algebra", "computation.bind_ret" -> "data", "metric.completion.mem_uniformity_dist" -> "topology", "fpow_mul'" -> "algebra", "ideal.comap_map_comap" -> "algebra", "metric.uniform_embedding_iff" -> "topology", "ennreal.lt_add_right" -> "data", "AddCommGroup.colimits.quot_add" -> "algebra", "list.foldl_map'" -> "data", "multilinear_map.map_zero" -> "algebra", "rel_iso.map_rel_iff" -> "order", "measure_theory.measure_congr" -> "analysis", "list.mem_permutations" -> "data", "primrec\:2082.curry" -> "computability", "int.mul_le_mul_of_nonpos_right" -> "init", "equiv.empty_sum_apply_inr" -> "data", "continuous_within_at_snd" -> "topology", "associates.normalize_out" -> "algebra", "wseq.map_join" -> "data", "linarith.eq_of_not_lt_of_not_gt" -> "tactic", "prime_multiset.prod_of_prime" -> "data", "filter.realizer.of_equiv_F" -> "data", "is_bounded_linear_map_prod_multilinear" -> "analysis", "supr_singleton" -> "order", "set.indicator_finset_bUnion" -> "data", "one_add_gsmul" -> "algebra", "finset.sum_empty" -> "algebra", "set.image_inter" -> "data", "lucas_lehmer.order_ineq" -> "number_theory", "ideal.le_radical" -> "algebra", "complex.rat_cast_re" -> "data", "cauchy_seq.mem_entourage" -> "topology", "category_theory.monoidal_category.unitors_equal.cells_10_13" -> "category_theory", "add_commute.units_neg_left" -> "algebra", "function.surjective.comp" -> "init", "and_comm" -> "init", "order.cofinal.above_mem" -> "order", "nnreal.lt_sub_iff_add_lt" -> "data", "add_aut.inv_def" -> "data", "is_local_min_on.fderiv_within_nonneg" -> "analysis", "mvpfunctor.Wp_ind" -> "data", "measure_theory.measure.measurable_coe" -> "analysis", "left_inverse_neg" -> "algebra", "bifunctor.fst_snd" -> "control", "distrib_mul_action_hom.ext" -> "algebra", "polynomial.multiplicity_finite_of_degree_pos_of_monic" -> "data", "measure_theory.measure.haar.is_left_invariant_chaar" -> "analysis", "int.zero_lt_one" -> "init", "int.sub_le_sub_right" -> "init", "decidable.and_iff_not_or_not" -> "logic", "list.mem_iff_nth_le" -> "data", "filter.tendsto.div" -> "analysis", "polynomial.root_X_sub_C" -> "data", "commute.refl" -> "algebra", "dfinsupp.single_apply" -> "data", "affine.triangle.orthocenter_mem_altitude" -> "geometry", "computation.bind_congr" -> "data", "polynomial.degree_pos_induction_on" -> "data", "exists_gpow_eq_one" -> "algebra", "mul_inv_eq_iff_eq_mul" -> "algebra", "dual_pair.coeffs_apply" -> "algebra", "category_theory.abelian.pseudoelement.zero_morphism_ext'" -> "category_theory", "preimage_equivalence" -> "order", "open_add_subgroup.mem_coe_opens" -> "topology", "le_nhds_of_cauchy_adhp_aux" -> "topology", "real.rpow_one" -> "analysis", "is_local_max.neg" -> "topology", "differentiable_at.smul" -> "analysis", "multiset.sum_map_add" -> "data", "imp_congr" -> "init", "multiset.mem_ndinsert" -> "data", "inner_sum" -> "analysis", "subgroup.subset_normal_closure" -> "algebra", "has_mfderiv_within_at.union" -> "geometry", "finset.not_mem_erase" -> "data", "finsupp.unique_single" -> "data", "list.ilast'_mem" -> "data", "normal_separation" -> "topology", "ideal.le_comap_sup" -> "algebra", "free_abelian_group.neg_bind" -> "algebra", "continuous_multilinear_map.map_smul" -> "topology", "dfinsupp.sum_map_range_index" -> "data", "finset.range_eq_Ico" -> "data", "Gromov_Hausdorff.totally_bounded" -> "topology", "matrix.mul_val_succ" -> "data", "ennreal.one_rpow" -> "analysis", "is_unit_of_add_is_unit_right" -> "algebra", "submonoid.coe_comap" -> "algebra", "concave_on_iff_convex_hypograph" -> "analysis", "finset.sum_attach" -> "algebra", "irrational.of_fpow" -> "data", "nnreal.div_one" -> "data", "prod.fst_surjective" -> "data", "list.not_eq_key" -> "data", "subring.forall" -> "algebra", "encodable.decode_option_zero" -> "data", "trichotomous_of" -> "init", "function.support_min" -> "data", "primrec\:2082.nat_iff'" -> "computability", "vector.naturality" -> "data", "metric.bounded_iff_mem_bounded" -> "topology", "subgroup.normal_in_normalizer" -> "algebra", "typevec.append_fun_comp_split_fun" -> "data", "ordinal.lt_mul_div_add" -> "set_theory", "cSup_union" -> "order", "ennreal.nhds_of_ne_top" -> "topology", "multiset.filter_map_map" -> "data", "open_subgroup.ext" -> "topology", "isometry.isometric_on_range_apply" -> "topology", "mvpfunctor.M.bisim'" -> "data", "add_monoid_hom.map_real_smul" -> "topology", "category_theory.limits.parallel_pair_obj_zero" -> "category_theory", "complete_space_coe_iff_is_complete" -> "topology", "irreducible.separable" -> "algebra", "list.func.map_add_map" -> "data", "matrix.cons_nonzero_iff" -> "data", "is_bounded_le_nhds" -> "topology", "category_theory.limits.coprod_map_map" -> "category_theory", "list.eq_nil_of_prefix_nil" -> "data", "finsupp.inf_apply" -> "data", "monotone.add_strict_mono" -> "algebra", "list.find_mem" -> "data", "continuous_snd" -> "topology", "is_integral_of_noetherian" -> "algebra", "list.inter_subset_right" -> "data", "encodable.sorted_univ_nodup" -> "data", "nat.shiftr_add" -> "init", "list.map_nil" -> "data", "order.cofinal_meets_ideal_of_cofinals" -> "order", "adjoin_root.eval\:2082_root" -> "algebra", "linear_map.std_basis_eq_single" -> "algebra", "prod.smul_snd" -> "algebra", "add_subgroup.normal_comap" -> "algebra", "equiv.forall_congr" -> "data", "tendsto_inv_zero_at_top" -> "analysis", "sub_one_lt_floor" -> "algebra", "structure_groupoid.local_invariant_prop.lift_prop_within_at_inter" -> "geometry", "pos_num.add_to_nat" -> "data", "pequiv.inj" -> "data", "has_deriv_within_at.union" -> "analysis", "induced_mono" -> "topology", "finset.card_pos" -> "data", "convex_interval" -> "analysis", "is_preconnected.union" -> "topology", "finsupp.filter_zero" -> "data", "set.inter_eq_self_of_subset_left" -> "data", "complex.differentiable_at_sin" -> "analysis", "tendsto_at_top_supr" -> "topology", "set.ne_empty_iff_nonempty" -> "data", "bilin_form.sub_left" -> "algebra", "finmap.keys_ext" -> "data", "pgame.nim.exists_move_left_eq" -> "set_theory", "tendsto_const_uniformity" -> "topology", "set.subset_inter_iff" -> "data", "matrix.one_mul" -> "data", "real.of_rat_lt" -> "data", "nnreal.rpow_sub'" -> "analysis", "mul_neg_of_neg_of_pos" -> "algebra", "smul_lie" -> "algebra", "has_sum_mul_left_iff" -> "topology", "le_sub_left_of_add_le" -> "algebra", "bdd_above_iff_subset_Iic" -> "order", "one_div_neg" -> "algebra", "set.Union_union" -> "data", "nat.partrec.code.of_nat_code_eq" -> "computability", "int.gcd_dvd_gcd_of_dvd_right" -> "algebra", "list.bind_eq_bind" -> "data", "lie_algebra.equiv.symm_symm" -> "algebra", "gaussian_int.to_complex_zero" -> "data", "ring_hom.map_iterate_pth_root" -> "algebra", "matrix.transpose_map" -> "data", "category_theory.limits.biprod.symmetry_assoc" -> "category_theory", "finset.card_eq_zero" -> "data", "add_neg" -> "algebra", "card_vector" -> "data", "mem_left_add_coset_left_add_coset" -> "algebra", "category_theory.Monad.of_Mon_func" -> "category_theory", "category_theory.limits.equalizer.fork_\[Iota]" -> "category_theory", "pnat.xgcd_type.flip_w" -> "data", "mul_right_inj'" -> "algebra", "is_topological_fiber_bundle_snd" -> "topology", "real.cos_pi" -> "analysis", "norm_sum_le_of_le" -> "analysis", "two_ne_zero'" -> "algebra", "real.Lp_add_le_of_nonneg" -> "analysis", "ennreal.rpow_nat_cast" -> "analysis", "times_cont_diff_within_at.comp" -> "analysis", "set.piecewise_empty" -> "data", "filter.tendsto_Ixx_class_of_subset" -> "order", "bounded_continuous_function.equicontinuous_of_continuity_modulus" -> "topology", "free_group.map.of" -> "algebra", "linear_action_act_add" -> "algebra", "mul_pow" -> "algebra", "submodule.range_mkq" -> "algebra", "multiset.sum_cons" -> "data", "filter.germ.const_lt" -> "order", "ordinal.lift_type_fin" -> "set_theory", "norm_sub_le_of_le" -> "analysis", "not_prime_zero" -> "algebra", "nhds_top_order" -> "topology", "real.is_conjugate_exponent.sub_one_ne_zero" -> "data", "deriv_within_congr" -> "analysis", "affine.simplex.eq_circumradius_of_dist_eq" -> "geometry", "ordinal.le_sup" -> "set_theory", "pgame.add_lt_add_right" -> "set_theory", "cardinal.sum_lt_prod" -> "set_theory", "list.product_cons" -> "data", "finsupp.supported_empty" -> "algebra", "multiset.le_inter_iff" -> "data", "list.lt_eq_not_ge" -> "init", "finsupp.single_injective" -> "data", "uniform_continuous_of_const" -> "topology", "real.one_lt_rpow" -> "analysis", "is_max_on.sup" -> "order", "polynomial.nat_degree_nat_cast" -> "data", "commute.mul_gpow" -> "algebra", "Gromov_Hausdorff.HD_candidates_b_dist_le" -> "topology", "linear_map.map_comap_eq_self" -> "algebra", "set.compl_bInter" -> "data", "sub_sub_sub_cancel_left" -> "algebra", "not.imp_symm" -> "logic", "polynomial.map_add" -> "data", "subspace.closed_complemented_of_quotient_finite_dimensional" -> "analysis", "set.image_const_sub_Ioc" -> "data", "fintype.well_founded_of_trans_of_irrefl" -> "data", "generalized_continued_fraction.of_one_le_nth_part_denom" -> "algebra", "is_R_or_C.of_real_sub" -> "data", "filter.principal_le_lift'" -> "order", "list.filter_map_cons" -> "data", "is_local_min.bicomp_mono" -> "topology", "infi_univ" -> "order", "continuous_linear_map.proj_ker_of_right_inverse_comp_inv" -> "topology", "nat.case_strong_induction_on" -> "init", "equiv.coe_add_left" -> "data", "equiv.subsingleton" -> "data", "set.ord_connected.inter" -> "data", "derivation.map_neg" -> "algebra", "complex.bit0_re" -> "data", "function.support_comp_subset" -> "data", "direct_sum.of_smul" -> "algebra", "add_con.to_add_submonoid_inj" -> "algebra", "bool.to_bool_and" -> "data", "rel.preimage_id" -> "data", "neg_dvd_of_dvd" -> "algebra", "principal_seg.top_eq" -> "set_theory", "is_extr_filter_const" -> "order", "multiset.Ico.filter_le_of_top_le" -> "data", "subgroup.is_open_mono" -> "topology", "fintype.prod_fiberwise" -> "data", "intermediate_value_Icc'" -> "topology", "local_homeomorph.ext" -> "topology", "pSet.mem.congr_left" -> "set_theory", "alist.perm_erase" -> "data", "set.nonempty_def" -> "data", "local_homeomorph.eq_on_source.symm_eq_on_target" -> "topology", "ordinal.not_succ_of_is_limit" -> "set_theory", "int.mul_div_cancel_of_mod_eq_zero" -> "data", "equiv.perm.eq_swap_of_is_cycle_of_apply_apply_eq_self" -> "algebra", "traversable.fold_map_map" -> "control", "equiv.sum_comm_symm" -> "data", "fpow_add_one" -> "algebra", "sub_le_sub_right" -> "algebra", "convex_on.comp_linear_map" -> "analysis", "nat.bit_lt_bit" -> "data", "int.bodd_add" -> "data", "submodule.range_fst" -> "algebra", "Top.continuous_prelocal_pred" -> "topology", "add_units.add_neg" -> "algebra", "traversable.foldl.of_free_monoid_comp_free_mk" -> "control", "gold_pos" -> "data", "complex.cpow_neg_one" -> "analysis", "minimal_polynomial.degree_le_of_ne_zero" -> "algebra", "equiv.perm.is_conj_swap" -> "algebra", "has_deriv_at_interval_left_endpoint_of_tendsto_deriv" -> "analysis", "turing.TM1to1.step_aux_move" -> "computability", "associates.mul_mono" -> "algebra", "complex.ext_iff" -> "data", "category_theory.iso.self_symm_conj" -> "category_theory", "findim_top" -> "algebra", "inv_mul_cancel_left" -> "algebra", "nat.not_two_dvd_bit1" -> "data", "finsupp.zip_with_apply" -> "data", "semiquot.eq_mk_of_mem" -> "data", "int.lt_mul_of_div_lt" -> "data", "nat.sub_one_sub_lt" -> "init", "category_theory.limits.biprod.inl_map" -> "category_theory", "real.differentiable_sin" -> "analysis", "add_monoid_hom.mrange_eq_map" -> "algebra", "sup_left_comm" -> "order", "mv_power_series.coeff_index_single_self_X" -> "algebra", "tangent_cone_mono" -> "analysis", "polynomial.nat_degree_prod_le" -> "algebra", "int.neg_pos_of_neg" -> "init", "filter.mem_principal_sets" -> "order", "measure_theory.simple_func.pair_preimage" -> "analysis", "tactic.ring_exp.base_to_exp_pf" -> "tactic", "add_monoid_hom.neg_apply" -> "algebra", "formal_multilinear_series.comp_partial_sum_target_subset_image_comp_partial_sum_source" -> "analysis", "int.add_mul_div_left" -> "data", "is_R_or_C.I_mul_I_of_nonzero" -> "data", "finset.max_eq_sup_with_bot" -> "data", "matrix.cons_val_fin_one" -> "data", "measure_theory.simple_func.fin_meas_supp.map" -> "analysis", "measure_theory.l1.simple_func.of_simple_func_to_simple_func" -> "analysis", "div_pow" -> "algebra", "submodule.span_span" -> "algebra", "set.ord_connected_Iic" -> "data", "Mod.regular_act" -> "category_theory", "pos_num.to_nat_to_int" -> "data", "subalgebra.res_inj" -> "algebra", "submonoid.localization_map.mul_equiv_of_mul_equiv_eq_map" -> "algebra", "mv_polynomial.rename_eq" -> "data", "rel_embedding.cod_restrict_apply" -> "order", "category_theory.limits.coprod.symmetry'" -> "category_theory", "algebraic_geometry.PresheafedSpace.id_base" -> "algebraic_geometry", "list.chain'.rel_head" -> "data", "padic_norm_e.is_norm" -> "data", "circle_deg1_lift.commute_nat_add" -> "dynamics", "primrec.nat_mod" -> "computability", "ordinal.lt_succ_self" -> "set_theory", "le_infi_iff" -> "order", "rel.core_univ" -> "data", "filter.comap_map" -> "order", "dist_add_add_le" -> "analysis", "polynomial.exists_root_of_degree_eq_one" -> "data", "int.dvd_lcm_right" -> "algebra", "mul_dvd_mul_iff_right" -> "algebra", "not_or" -> "init", "left_ord_continuous.iterate" -> "order", "category_theory.limits.cocone_of_cone_left_op_X" -> "category_theory", "continuous_linear_map.map_add" -> "topology", "written_in_ext_chart_model_space" -> "geometry", "computable\:2082.comp" -> "computability", "reader_t.goto_mk_label" -> "control", "times_cont_diff_within_at.of_le" -> "analysis", "algebraic_geometry.PresheafedSpace.as_coe" -> "algebraic_geometry", "norm_num.sle_one_bit1" -> "tactic", "measurable_iff_le_map" -> "analysis", "inner_div_norm_mul_norm_eq_one_iff" -> "analysis", "finset.center_mass_mem_convex_hull" -> "analysis", "filter.germ.const_min" -> "order", "list.func.equiv_refl" -> "data", "measure_theory.measure.restrict_sum" -> "analysis", "real.cosh_neg" -> "data", "polynomial.irreducible_of_irreducible_map" -> "data", "mvfunctor.liftp_def" -> "control", "sub_floor_div_mul_nonneg" -> "algebra", "category_theory.monoidal.Mon_functor_category_equivalence.functor_obj_obj_X" -> "category_theory", "deriv_within_pow" -> "analysis", "set.preimage_mul_const_Ioo_of_neg" -> "data", "lie_algebra.special_linear.E_apply_one" -> "algebra", "bounded_continuous_function.norm_def" -> "topology", "list.rotate'_rotate'" -> "data", "bernoulli_zero" -> "number_theory", "to_bool_iff" -> "init", "module.direct_limit.lift_of" -> "algebra", "deriv_const'" -> "analysis", "emetric.diam_le_of_forall_edist_le" -> "topology", "bit0_le_bit0" -> "algebra", "pgame.numeric_add" -> "set_theory", "Sup_eq_bot" -> "order", "multilinear_map.curry_uncurry_right" -> "algebra", "isometric.trans_apply" -> "topology", "real.iter_deriv_exp" -> "analysis", "zero_pow_eq_zero" -> "algebra", "smooth.add" -> "geometry", "complex.linear_map.coe_im" -> "data", "nhds_within_univ" -> "topology", "linear_map.coprod_inr" -> "algebra", "free_group.to_group.mul" -> "algebra", "inv_pow" -> "algebra", "measure_theory.ae_eq_fun.edist_eq_coe" -> "analysis", "vector.continuous_remove_nth" -> "topology", "nat.cast_add_one_pos" -> "data", "category_theory.under.mk_hom" -> "category_theory", "multiset.mem_antidiagonal" -> "data", "list.continuous_insert_nth" -> "topology", "computable_pred.not" -> "computability", "continuous_linear_map.smul_right_one_one" -> "topology", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge'" -> "analysis", "group.gpowers_eq_closure" -> "algebra", "submonoid.localization_map.eq'" -> "algebra", "cardinal.le_sum" -> "set_theory", "category_theory.equivalence.fun_inv_id_assoc_inv_app" -> "category_theory", "deriv_within.neg" -> "analysis", "nat.zero_eq_mul" -> "data", "typevec.append1_drop_last" -> "data", "multiplicity.not_finite_iff_forall" -> "algebra", "measure_theory.simple_func.lintegral_eq_of_measure_preimage" -> "analysis", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_hom" -> "category_theory", "add_submonoid.zero_mem" -> "algebra", "matrix.diagonal_apply_eq" -> "data", "multiset.nodup_cons_of_nodup" -> "data", "seq.destruct_eq_cons" -> "data", "cau_seq.add_pos" -> "data", "left_eq_inf" -> "order", "zmod.exists_pow_two_eq_neg_one_iff_mod_four_ne_three" -> "number_theory", "multiset.disjoint_of_subset_left" -> "data", "multiset.mem_coe" -> "data", "measure_theory.ae_eq_fun.pair_mk_mk" -> "analysis", "mul_le_one'" -> "algebra", "lucas_lehmer.X.neg_snd" -> "number_theory", "has_fpower_series_at.sub" -> "analysis", "category_theory.monoidal_functor.id_to_lax_monoidal_functor_to_functor" -> "category_theory", "filter.eventually_eq.eq_of_nhds_within" -> "topology", "function.semiconj\:2082.eq" -> "logic", "finsupp.comap_smul_single" -> "data", "function.surjective.image_surjective" -> "data", "function.semiconj.iterate_left" -> "logic", "sup_inf_right" -> "order", "associates.dvd_eq_le" -> "algebra", "sup_apply" -> "order", "real.mk_eq_mk" -> "data", "asymptotics.is_O.trans_le" -> "analysis", "filter.tendsto_neg_at_bot_at_top" -> "order", "affine_subspace.vadd_mem_of_mem_direction" -> "algebra", "rat.cast_add_of_ne_zero" -> "data", "filter.mem_traverse_sets_iff" -> "order", "dioph.of_no_dummies" -> "number_theory", "tactic.interval_cases.mem_set_elems" -> "tactic", "nhds_bind_nhds_within" -> "topology", "list.func.sub_nil" -> "data", "is_compl.symm" -> "order", "with_zero.ne_zero_iff_exists" -> "algebra", "finset.range_zero" -> "data", "edist_le_of_edist_le_geometric_two_of_tendsto\:2080" -> "analysis", "euclidean_geometry.orthogonal_projection_fn_mem_orthogonal" -> "geometry", "measure_theory.inner_content_comap" -> "analysis", "category_theory.limits.cones.forget_map" -> "category_theory", "order.le_cof" -> "set_theory", "cardinal.mk_Ioi_real" -> "data", "category_theory.pi.comp_apply" -> "category_theory", "finset.sum_eq_zero_iff_of_nonneg" -> "algebra", "min_mul_max" -> "algebra", "scale_roots_aeval_eq_zero_of_aeval_mk'_eq_zero" -> "algebra", "int.mul_lt_of_lt_div" -> "data", "cardinal.ord_is_limit" -> "set_theory", "category_theory.over.construct_products.cones_equiv_functor_obj_X" -> "category_theory", "filter.tendsto_at_top_add_right_of_le'" -> "order", "affine.simplex.circumcenter_mem_affine_span" -> "geometry", "equiv.sigma_preimage_equiv_symm_apply_snd_fst" -> "data", "category_theory.limits.cokernel.\[Pi]_desc_assoc" -> "category_theory", "disjoint.sup_right" -> "order", "int.mod_eq_zero_of_dvd" -> "data", "cancel_factors.sub_subst" -> "tactic", "div_le_div_of_le" -> "algebra", "list.pairwise_singleton" -> "data", "eq_of_fin_equiv" -> "algebra", "localization_map.lift_left_inverse" -> "algebra", "comp_le_uniformity3" -> "topology", "filter.bot_prod" -> "order", "polynomial.lcoeff_apply" -> "data", "con.induction_on" -> "algebra", "finite_dimensional.findim_pos" -> "algebra", "finset.min_singleton" -> "data", "tsum_mul_right" -> "topology", "composition_as_set.boundary_zero" -> "combinatorics", "continuous.continuous_within_at" -> "topology", "mvqpf.id_map" -> "data", "abs_div" -> "algebra", "subsemiring.Inf_to_add_submonoid" -> "algebra", "convex.mem_to_cone'" -> "analysis", "list.prod_ne_zero" -> "data", "category_theory.preadditive.epi_of_cokernel_zero" -> "category_theory", "cardinal.is_inaccessible.mk" -> "set_theory", "lt_add_of_neg_add_lt_right" -> "algebra", "pfunctor.M.bisim'" -> "data", "cardinal.le_iff_exists_add" -> "set_theory", "linarith.int.coe_nat_mul_bit1" -> "tactic", "multiset.map_single_le_powerset" -> "data", "alg_hom.comp_assoc" -> "algebra", "add_equiv.to_fun_apply" -> "data", "partrec.cond" -> "computability", "equiv.perm.sign_bij" -> "algebra", "add_comm_group.direct_limit.directed_system" -> "algebra", "int.le_add_of_neg_le_sub_left" -> "init", "measure_theory.measure_lt_top" -> "analysis", "real.angle.coe_sub" -> "analysis", "category_theory.limits.pullback_cone.mk_X" -> "category_theory", "nat.cast_dvd" -> "data", "is_cau_geo_series_const" -> "data", "finset.erase_insert_subset" -> "data", "finset.prod_hom" -> "algebra", "norm_num.sle_bit1_bit0" -> "tactic", "nat.div_dvd_of_dvd" -> "data", "lebesgue_number_lemma_sUnion" -> "topology", "set.piecewise_insert_self" -> "data", "nat.sub_cancel" -> "data", "strict_mono.comp" -> "order", "measure_theory.ae_eq_fun.coe_fn_edist" -> "analysis", "mvqpf.cofix.ext_mk" -> "data", "finset.filter_val" -> "data", "filter.eventually_lift'_powerset'" -> "order", "cardinal.cantor" -> "set_theory", "linear_independent_iff_not_smul_mem_span" -> "algebra", "linear_map_algebra_module.smul_apply" -> "algebra", "int.modeq.modeq_neg" -> "data", "finsupp.of_multiset_strict_mono" -> "data", "category_theory.limits.prod.lift_fst" -> "category_theory", "filter.map_comap_le" -> "order", "set.insert_diff_self_of_not_mem" -> "data", "add_submonoid.mem_sup_right" -> "algebra", "set.maps_to_bUnion" -> "data", "list.sublists_aux\:2081_eq_sublists_aux" -> "data", "fderiv_within_id'" -> "analysis", "inv.is_group_hom" -> "algebra", "list.length_range'" -> "data", "category_theory.limits.kernel_fork.condition_assoc" -> "category_theory", "topological_space.opens.is_basis_iff_cover" -> "topology", "ennreal.mul_ne_top" -> "data", "continuous_linear_map.norm_id" -> "analysis", "neg_pos_of_neg" -> "algebra", "add_monoid_hom.coprod_inl_inr" -> "algebra", "measure_theory.measure.zero_to_outer_measure" -> "analysis", "nat.succ_sub" -> "init", "units.eq_iff" -> "algebra", "pgame.relabel_move_left" -> "set_theory", "category_theory.limits.cocones.equivalence_of_reindexing_functor_obj" -> "category_theory", "real.cos_inj_of_nonneg_of_le_pi" -> "analysis", "category_theory.uncurry_curry" -> "category_theory", "real.deriv_exp" -> "analysis", "measure_theory.measure.le_iff" -> "analysis", "has_deriv_at.sum" -> "analysis", "algebraic_closure.adjoin_monic.is_integral" -> "algebra", "is_add_group_hom.map_zero" -> "algebra", "finset.subset_insert_iff" -> "data", "bool.bxor_bnot_bnot" -> "data", "has_ftaylor_series_up_to_on.differentiable_on" -> "analysis", "algebra.is_algebraic_of_finite" -> "algebra", "category_theory.bifunctor.map_id" -> "category_theory", "set.bij_on_Inter_of_directed" -> "data", "seq1.bind_assoc" -> "data", "commute.inv_right" -> "algebra", "matrix.empty_mul_empty" -> "data", "list.inter_cons_of_not_mem" -> "data", "ennreal.to_real_of_real'" -> "data", "omega.nat.neg_free_neg_elim_core" -> "tactic", "lt_inv" -> "algebra", "isometry.vadd_vsub" -> "analysis", "is_integral_of_mem_closure" -> "algebra", "finset.Ico.filter_lt" -> "data", "set.empty_prod" -> "data", "differentiable_within_at.mul" -> "analysis", "multiset.nodup_map" -> "data", "nat.pow_dvd_pow_iff" -> "data", "affine_subspace.mk'_eq" -> "algebra", "monoid_hom.iterate_map_inv" -> "algebra", "int.add_lt_add_of_le_of_lt" -> "init", "inv_div" -> "algebra", "category_theory.limits.walking_pair.swap_apply_left" -> "category_theory", "finset.sum_map" -> "algebra", "category_theory.functor.hom_obj" -> "category_theory", "category_theory.sum.inverse_associator_obj_inr_inl" -> "category_theory", "image_range_order_of" -> "algebra", "nat.sub.right_comm" -> "init", "category_theory.nat_iso.app_inv" -> "category_theory", "set.Iio_subset_Iic_iff" -> "data", "measure_theory.measure.haar.chaar_mem_haar_product" -> "analysis", "mul_inv_lt_of_lt_mul'" -> "algebra", "list.countp_append" -> "data", "not_and_of_not_or_not" -> "logic", "many_one_equiv.trans" -> "computability", "category_theory.monad.forget_creates_colimits.cocone_point_A" -> "category_theory", "nat.one_lt_iff_ne_zero_and_ne_one" -> "data", "neq_of_not_iff" -> "init", "subset_interior_iff_nhds" -> "topology", "filter.lift'_principal" -> "order", "ideal.integral_closure.eq_bot_of_comap_eq_bot" -> "algebra", "finsupp.coe_leval'" -> "data", "finset.sort_sorted" -> "data", "pnat.gcd_one" -> "data", "equiv.refl_apply" -> "data", "fin.one_lt_succ_succ" -> "data", "monotone.mem_upper_bounds_image" -> "order", "list.unzip_zip" -> "data", "dist_le_tsum_of_dist_le_of_tendsto\:2080" -> "topology", "matrix.cons_val_succ" -> "data", "sym2.elems_iff_eq" -> "data", "is_preconnected.mem_intervals" -> "topology", "list.enum_from_map_fst" -> "data", "pi.one_comp" -> "algebra", "norm_num.lt_bit0_bit0" -> "tactic", "wseq.lift_rel_append" -> "data", "submodule.smul_le" -> "algebra", "findim_span_le_card" -> "algebra", "bilin_form.comp_apply" -> "algebra", "gsmul_eq_mul" -> "algebra", "monotone.mul_const'" -> "algebra", "subgroup.prod_mono_right" -> "algebra", "bilin_form.is_adjoint_pair.eq" -> "algebra", "nat.modeq.coprime_of_mul_modeq_one" -> "data", "function.has_right_inverse.surjective" -> "init", "filter.lift_assoc" -> "order", "sub_lt_sub_iff_left" -> "algebra", "pequiv.mem_single" -> "data", "uniform_space.completion.uniform_inducing_coe" -> "topology", "continuous_linear_map.sum_apply" -> "topology", "rank_comp_le2" -> "algebra", "uniform_space.completion.uniform_embedding_coe" -> "topology", "has_deriv_within_at.has_fderiv_within_at" -> "analysis", "gcd_dvd_gcd_mul_left_right" -> "algebra", "ite_mul" -> "algebra", "list.foldr_hom" -> "data", "nat.coprime.coprime_mul_left_right" -> "data", "fin.coe_coe_of_lt" -> "data", "algebra.is_algebraic_iff" -> "algebra", "le_iff_eq_or_lt" -> "algebra", "mul_le_of_le_one_right" -> "algebra", "list.take_left'" -> "data", "subsemiring.map_supr" -> "algebra", "fin.tail_update_succ" -> "data", "finset.min_of_mem" -> "data", "nat.rfind_opt_mono" -> "computability", "ordinal.enum_typein" -> "set_theory", "cardinal.mk_compl_finset_of_omega_le" -> "set_theory", "algebra.tensor_product.ext" -> "algebra", "cinfi_le" -> "order", "continuous_infi_dom" -> "topology", "list.take_append" -> "data", "category_theory.monoidal_category.left_unitor_tensor_inv" -> "category_theory", "polynomial.eval_nat_cast" -> "data", "union_upper_bounds_subset_upper_bounds_inter" -> "order", "composition.ones_length" -> "combinatorics", "complex.uniform_continuous_inv" -> "topology", "ideal.span_singleton_mul_left_unit" -> "algebra", "interval_integral.norm_integral_le_abs_integral_norm" -> "analysis", "relation.trans_gen.head'" -> "logic", "asymptotics.is_O_with_neg_left" -> "analysis", "linear_independent_bUnion_of_directed" -> "algebra", "option.mem_to_list" -> "data", "le_mul_iff_one_le_left" -> "algebra", "with_top.coe_eq_one" -> "algebra", "hyperreal.ne_zero_of_infinite" -> "data", "differentiable_at.has_fderiv_at" -> "analysis", "nat.primrec'.unpair\:2081" -> "computability", "set.compl_set_of" -> "data", "submonoid.mem_supr_of_mem" -> "algebra", "continuous.prod_map" -> "topology", "topological_space.opens.union_eq" -> "topology", "filter.frequently_imp_distrib_right" -> "order", "multiset.cons_union_distrib" -> "data", "option.lift_or_get_none_left" -> "data", "mul_lt_mul_right_of_neg" -> "algebra", "alist.lookup_insert_ne" -> "data", "finsupp.single_finset_sum" -> "data", "set.Ioi_subset_Ioi" -> "data", "nat.add_lt_of_lt_sub_right" -> "data", "add_monoid_hom.ext_iff" -> "algebra", "times_cont_diff_within_at_snd" -> "analysis", "primrec.list_foldr" -> "computability", "neg_lt_of_neg_lt" -> "algebra", "add_submonoid.localization_map.of_add_equiv_of_dom_id" -> "algebra", "times_cont_mdiff_on.comp" -> "geometry", "function.comp_const" -> "logic", "category_theory.limits.cokernel_is_iso_comp_hom" -> "category_theory", "map_nhds_induced_eq" -> "topology", "inner_zero_left" -> "analysis", "nat.mul_sub_right_distrib" -> "init", "free_add_semigroup.lift_of_add" -> "algebra", "semiconj_by.units_inv_symm_left_iff" -> "algebra", "one_le_fpow_of_nonneg" -> "algebra", "finset.sort_to_finset" -> "data", "has_fpower_series_at.analytic_at" -> "analysis", "polynomial.monic.leading_coeff" -> "data", "unique_factorization_domain.no_factors_of_no_prime_factors" -> "algebra", "local_homeomorph.symm_image_inter_target_eq" -> "topology", "add_add_neg_cancel'_right" -> "algebra", "ordinal.typein_injective" -> "set_theory", "vsub_set_subset_vector_span" -> "algebra", "filter.germ.lt_def" -> "order", "nat.le_of_sub_eq_zero" -> "init", "set.mem_union_left" -> "data", "filter.mem_top_sets_iff_forall" -> "order", "bot_eq_top_of_dim_eq_zero" -> "algebra", "monoid_hom.eq_of_eq_on_mtop" -> "algebra", "compl_Inf" -> "order", "subtype.forall'" -> "data", "is_R_or_C.abs_to_real" -> "data", "padic_seq.stationary_point_spec" -> "data", "multiset.Ico.filter_lt_of_top_le" -> "data", "is_R_or_C.is_cau_seq_im" -> "data", "has_deriv_within_at.has_deriv_at" -> "analysis", "nhds_subtype" -> "topology", "pnat.mk_bit0" -> "data", "trans_rel_left" -> "init", "is_closed_separation_rel" -> "topology", "is_monoid_hom.comp" -> "algebra", "int.neg_succ_lt_zero" -> "init", "dvd_iff_dvd_digits_sum" -> "data", "continuous_at.prod_map'" -> "topology", "list.maximum_mem" -> "data", "list.nth_update_nth_of_lt" -> "data", "one_le_inv'" -> "algebra", "primrec.list_join" -> "computability", "nat.gcd_dvd_gcd_mul_right" -> "data", "ordinal.pos_iff_ne_zero" -> "set_theory", "mem_comp_rel" -> "topology", "filter.germ.map_const" -> "order", "has_deriv_within_at_pow" -> "analysis", "measurable_iff_comap_le" -> "analysis", "finset.max_singleton" -> "data", "multiset.count_eq_zero" -> "data", "has_le.le.le_or_lt" -> "algebra", "multiset.bind_congr" -> "data", "seq.append_assoc" -> "data", "deriv_within_cos" -> "analysis", "computation.tail_ret" -> "data", "denumerable.raise'_chain" -> "data", "list.pairwise.iff" -> "data", "finset.mem_of_mem_inter_right" -> "data", "differentiable_within_at.div_const" -> "analysis", "computable_pred.computable_iff_re_compl_re" -> "computability", "primrec.vector_head" -> "computability", "submonoid.localization_map.mk'_eq_of_eq" -> "algebra", "ulift.sub_down" -> "algebra", "tensor_product.mk_compr\:2082_inj" -> "algebra", "filter.push_pull'" -> "order", "nhds_within_prod_eq" -> "topology", "bifunctor.comp_snd" -> "control", "filter.is_cobounded_ge_of_top" -> "order", "option.mem_unique" -> "data", "monoid_hom.coprod_inl_inr" -> "algebra", "multilinear_map.curry_left_apply" -> "algebra", "free_group.reduce.cons" -> "algebra", "nat.div_eq_sub_div" -> "init", "induced_iff_nhds_eq" -> "topology", "complex.continuous_abs" -> "topology", "nat.eq_mul_of_div_eq_right" -> "data", "category_theory.evaluation_uncurried_obj" -> "category_theory", "differentiable_at.fderiv_within" -> "analysis", "finset.sum_inter_add_sum_diff" -> "algebra", "has_deriv_at_filter.const_sub" -> "analysis", "has_fpower_series_on_ball.continuous_on" -> "analysis", "continuous_linear_map.deriv" -> "analysis", "pgame.first_wins_of_equiv" -> "set_theory", "function.embedding.ext" -> "logic", "dvd_refl" -> "algebra", "list.func.length_pointwise" -> "data", "mvqpf.cofix.bisim_rel" -> "data", "subgroup.mem_Inf" -> "algebra", "nat.zero_div" -> "init", "set.finite.convex_hull_eq" -> "analysis", "gsmul_coe_nat" -> "algebra", "equiv.sum_compl_apply_inr" -> "data", "int.sub_nat_nat_sub" -> "init", "set.pair_eq_singleton" -> "data", "zero_linear_action" -> "algebra", "ennreal.rpow_neg_one" -> "analysis", "inv_mul_le_right_of_le_mul" -> "algebra", "fintype.card_eq_one_iff" -> "data", "is_add_group_hom.neg_iff_ker'" -> "algebra", "is_compact.inter" -> "topology", "ideal.leading_coeff_nth_mono" -> "algebra", "ennreal.has_sum" -> "topology", "multiset.count_union" -> "data", "polynomial.derivative_monomial" -> "data", "list.func.forall_val_of_forall_mem" -> "data", "filter.tendsto.integral_sub_linear_is_o_ae" -> "analysis", "continuous_within_at.union" -> "topology", "finmap.mem_keys" -> "data", "isometric.coe_to_real_linear_equiv_of_map_zero_symm" -> "analysis", "ring.fractional_ideal.right_inverse_eq" -> "algebra", "set.mem_Ici_Ioi_of_subset_of_subset" -> "data", "int.le_add_of_sub_right_le" -> "init", "filter.ultrafilter_map" -> "order", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_is_iso_comp_hom" -> "category_theory", "tactic.ring_exp.add_overlap_pf_zero" -> "tactic", "list.revzip_map_fst" -> "data", "finmap.mem_singleton" -> "data", "nat.size_bit" -> "data", "measurable_of_measurable_on_compl_singleton" -> "analysis", "norm_indicator_le_norm_self" -> "analysis", "ennreal.exists_nat_mul_gt" -> "data", "ring_hom.coe_snd" -> "algebra", "finset.inter_singleton_of_mem" -> "data", "differentiable.sqrt" -> "analysis", "submonoid.coe_mul" -> "algebra", "cardinal.cantor_function_aux_nonneg" -> "data", "hash_map.valid.idx_enum" -> "data", "category_theory.monoidal_category.right_unitor_nat_iso_hom_app" -> "category_theory", "category_theory.over.construct_products.cones_equiv_functor_obj_\[Pi]_app" -> "category_theory", "real.sqrt_two_add_series_lt_two" -> "analysis", "multilinear_map.map_sub" -> "algebra", "function.right_inverse.comp" -> "logic", "ordinal.cof_sup_le" -> "set_theory", "prod.snd_vadd" -> "algebra", "category_theory.currying_inverse_obj_obj_map" -> "category_theory", "set.image_subset" -> "data", "pgame.turn_bound_ne_zero_of_left_move" -> "set_theory", "set.preimage_const_add_Iic" -> "data", "and_self" -> "init", "additive.simple_add_group_iff" -> "algebra", "galois_insertion.l_sup_u" -> "order", "primrec\:2082.nat_iff" -> "computability", "multiset.ndinter_subset_right" -> "data", "category_theory.abelian.coimages.coimage.fac" -> "category_theory", "linear_pmap.map_zero" -> "algebra", "punit_eq_punit" -> "init", "is_open_Ioi" -> "topology", "nat.primrec'.pred" -> "computability", "set.Ioc_union_Ioc_union_Ioc_cycle" -> "data", "is_local_min_on.max" -> "topology", "seq.map_id" -> "data", "uniformity_lift_le_comp" -> "topology", "approximates_linear_on.inverse_approx_map_fixed_iff" -> "analysis", "cauchy.mono'" -> "topology", "ring_hom.ext" -> "algebra", "finset.prod_eq_single" -> "algebra", "interval_integral.deriv_integral_left" -> "analysis", "list.perm.cons_inv" -> "data", "eventually_countable_forall" -> "order", "add_subgroup.prod_mono" -> "algebra", "tactic.ring_exp.pow_p_pf_cons" -> "tactic", "linear_equiv.conj_trans" -> "algebra", "submodule.map_comap_subtype" -> "algebra", "category_theory.functor.const.op_obj_op_inv_app" -> "category_theory", "real.is_conjugate_exponent.mul_eq_add" -> "data", "ennreal.tendsto_at_top" -> "topology", "submonoid.localization_map.epic_of_localization_map" -> "algebra", "list.eq_repeat" -> "data", "category_theory.functor.map_cocone_\[Iota]" -> "category_theory", "ordinal.lt_limit" -> "set_theory", "continuous_left_of_strict_mono_surjective" -> "topology", "zmod.cast_zero" -> "data", "nat.coprime.coprime_mul_right_right" -> "data", "isometric.point_reflection_midpoint_left" -> "analysis", "onote.scale_power_aux" -> "set_theory", "pequiv.single_trans_of_mem" -> "data", "roption.mem_assert" -> "data", "submodule.fg_iff_finite_dimensional" -> "algebra", "category_theory.limits.cones.postcompose_equivalence_counit_iso" -> "category_theory", "set.inter_inv" -> "algebra", "is_compact.prod" -> "topology", "filter.map_infi_eq" -> "order", "set.bij_on.surj_on" -> "data", "category_theory.adjunction.functoriality_counit'_app_hom" -> "category_theory", "nnreal.pow_ne_zero" -> "data", "valuation.map_add_supp" -> "algebra", "norm_num.add_pos_neg_pos" -> "tactic", "is_local_max.fderiv_eq_zero" -> "analysis", "submodule.sup_eq_range" -> "algebra", "one_div_le_one_div_of_le" -> "algebra", "measure_theory.monotone_lintegral" -> "analysis", "set.exists_range_iff'" -> "data", "continuous_add_left" -> "topology", "iterated_deriv_within_eq_iterate" -> "analysis", "list.sorted_merge_sort" -> "data", "set.union_prod" -> "data", "power_series.order_one" -> "algebra", "polynomial.separable.of_pow" -> "algebra", "rel_iso.map_top" -> "order", "infi_subtype''" -> "order", "int.of_nat_one" -> "init", "linear_map.fun_left_comp" -> "algebra", "finsupp.multiset_map_sum" -> "data", "category_theory.comma.fst_obj" -> "category_theory", "cSup_le" -> "order", "nat.min_zero" -> "init", "pgame.add_zero_equiv" -> "set_theory", "set.indicator_le_self" -> "data", "finsupp.erase_single" -> "data", "multiset.nodup_filter_map" -> "data", "times_cont_mdiff_at_const" -> "geometry", "commute.symm" -> "algebra", "rel_iso.refl_apply" -> "order", "open_add_subgroup.neg_mem" -> "topology", "multiset.rel_add_left" -> "data", "turing.reaches\:2080.single" -> "computability", "subring.range_snd" -> "algebra", "list.eq_iff_join_eq" -> "data", "complex.tan_arg" -> "analysis", "nat.prime_iff_prime_int" -> "algebra", "filter.is_bounded_ge_of_bot" -> "order", "fderiv_mul_const" -> "analysis", "function.iterate_mul" -> "logic", "submonoid.bot_prod_bot" -> "algebra", "set.diagonal_eq_range" -> "data", "open_embedding.continuous_inv_fun" -> "topology", "num.to_nat_to_int" -> "data", "le_sub_iff_add_le" -> "algebra", "partrec.option_some_iff" -> "computability", "nonempty_plift" -> "logic", "equiv.perm.is_cycle_swap_mul_aux\:2082" -> "algebra", "list.mmap_with_index_aux_spec_cons" -> "data", "multiplicity_eq_zero_of_coprime" -> "algebra", "continuous_multilinear_map.curry0_uncurry0" -> "analysis", "matrix_equiv_tensor_apply_std_basis" -> "algebra", "ennreal.div_lt_top" -> "data", "rel.mem_preimage" -> "data", "multilinear_map.cons_smul" -> "algebra", "list.traverse_cons" -> "control", "gfp_induct" -> "order", "add_group_with_zero_nhd.nhds_zero_eq_Z" -> "topology", "limit_zero_of_norm_tendsto_zero" -> "data", "is_bounded_linear_map.add" -> "analysis", "measure_theory.measure.haar.prehaar_sup_eq" -> "analysis", "mem_nhds_within_Ioi_iff_exists_Ioc_subset" -> "topology", "nat.eq_zero_of_gcd_eq_zero_left" -> "data", "finset.prod_congr" -> "algebra", "smooth_within_at.prod_map" -> "geometry", "cardinal.bit0_le_bit1" -> "set_theory", "is_absolute_value.abv_div" -> "data", "prime_spectrum.mem_zero_locus" -> "algebraic_geometry", "multiset.powerset_aux_perm" -> "data", "interval_integral.integral_has_fderiv_within_at_of_tendsto_ae" -> "analysis", "left_ord_continuous.lt_iff" -> "order", "has_strict_fderiv_at.const_smul" -> "analysis", "polynomial.coeff_to_subring'" -> "algebra", "real.differentiable_exp" -> "analysis", "multiset.prod_map_mul" -> "data", "submodule.comap_liftq" -> "algebra", "filter.Liminf_eq_supr_Inf" -> "order", "multiset.not_mem_zero" -> "data", "category_theory.limits.pushout_cocone.of_cocone_X" -> "category_theory", "id.pure_eq" -> "init", "rel_embedding.is_well_order" -> "order", "list.length_eq_zero" -> "data", "quotient.induction_on\:2082" -> "init", "nat.div_mul_le_self" -> "init", "set.surj_on_iff_surjective" -> "data", "multiset.count_erase_of_ne" -> "data", "cardinal.mk_subtype_le_of_subset" -> "set_theory", "metric.completion.dist_triangle" -> "topology", "ordinal.lt_bsup" -> "set_theory", "continuous_iff_continuous_on_univ" -> "topology", "zsqrtd.nonneg_add_lem" -> "data", "add_monoid_hom.single_apply" -> "algebra", "list.mem_keys_kerase_of_ne" -> "data", "multiset.abs_sum_le_sum_abs" -> "data", "subsingleton_iff" -> "logic", "mul_inv_le_iff_le_mul'" -> "algebra", "set.union_subset" -> "data", "interval_integral.integral_has_strict_fderiv_at" -> "analysis", "int.modeq.modeq_add_cancel_right" -> "data", "dense_inducing_pure" -> "topology", "set.inter_comm" -> "data", "int.le.intro_sub" -> "init", "real.cos_add_two_pi" -> "analysis", "finset.inter_left_comm" -> "data", "subtype.preimage_coe_nonempty" -> "data", "finite_dimensional.exists_nontrivial_relation_sum_zero_of_dim_succ_lt_card" -> "algebra", "filter.eventually_le_congr" -> "order", "list.sublist_of_cons_sublist_cons" -> "data", "rel_iso.apply_inv_self" -> "order", "heq_iff_eq" -> "logic", "category_theory.initial_mono" -> "category_theory", "continuous_linear_map.proj_apply" -> "topology", "set.interval_of_le" -> "data", "turing.partrec_to_TM2.split_at_pred_ff" -> "computability", "finsupp.sum_mul" -> "data", "measure_theory.simple_func.pair_preimage_singleton" -> "analysis", "category_theory.limits.limit.hom_ext" -> "category_theory", "set.nonempty_inter_iff_exists_right" -> "data", "list.erasep_sublist" -> "data", "mv_polynomial.eval_monomial" -> "data", "nat.mul_right_eq_self_iff" -> "data", "multiset.smul_prod" -> "algebra", "is_basis.mk_range_eq_dim" -> "algebra", "finset.insert_singleton_self_eq" -> "data", "units.coe_le_coe" -> "algebra", "polynomial.expand_C" -> "algebra", "category_theory.left_adjoint_preserves_epi" -> "category_theory", "ennreal.mul_div_cancel'" -> "data", "multiplicity.finite_iff_dom" -> "algebra", "multiset.sort_eq" -> "data", "tensor_algebra.lift_comp_\[Iota]" -> "algebra", "add_equiv.to_equiv_symm" -> "data", "subgroup.closure_mono" -> "algebra", "finmap.induction_on\:2082" -> "data", "list.perm_comp_perm" -> "data", "topological_space.opens.map_id_hom_app" -> "topology", "normed_space.double_dual_bound" -> "analysis", "typevec.eq_nil_fun" -> "data", "pell.yn_one" -> "number_theory", "mv_power_series.coeff_zero_mul_X" -> "algebra", "smul_sub" -> "algebra", "generalized_continued_fraction.continuants_aux_recurrence" -> "algebra", "list.take'_eq_take" -> "data", "dim_range_of_surjective" -> "algebra", "times_cont_diff_on_iff_ftaylor_series" -> "analysis", "inner_product_geometry.cos_angle" -> "geometry", "has_fderiv_at.const_smul_algebra" -> "analysis", "list.pairwise.chain'" -> "data", "int.eq_zero_of_sign_eq_zero" -> "init", "ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem" -> "algebra", "mul_sub_left_distrib" -> "algebra", "ideal.comap_ne_top" -> "algebra", "mem_nhds_uniformity_iff_left" -> "topology", "char_poly_monic" -> "algebra", "lt_mul_of_one_lt_left'" -> "algebra", "matrix.adjugate_zero" -> "algebra", "complex.is_cau_exp" -> "data", "int.neg_of_nat_of_succ" -> "init", "filter.tendsto_def" -> "order", "category_theory.whisker_left_comp" -> "category_theory", "wseq.nth_add" -> "data", "bool.bxor_bnot_right" -> "data", "bool.band_elim_right" -> "data", "finset.convex_hull_eq" -> "analysis", "option.eq_none_iff_forall_not_mem" -> "data", "is_unit.mk0" -> "algebra", "continuous_within_at.mono" -> "topology", "set.preimage_mul_const_Iio" -> "data", "lt_mul_of_le_of_one_lt" -> "algebra", "list.disjoint_of_disjoint_append_left_right" -> "data", "localization_map.to_map_injective" -> "algebra", "num.cast_sub'" -> "data", "turing.partrec_to_TM2.copy_ok" -> "computability", "alt_bilin_form.self_eq_zero" -> "algebra", "multiset.bind_def" -> "data", "differentiable_on.continuous_on" -> "analysis", "ordinal.power_ne_zero" -> "set_theory", "classical.epsilon_singleton" -> "init", "quadratic_form.map_add_self" -> "algebra", "asymptotics.is_O.smul" -> "analysis", "turing.tr_eval'" -> "computability", "continuous_multilinear_map.op_norm_nonneg" -> "analysis", "category_theory.induced_functor_map" -> "category_theory", "continuous_linear_map.proj_ker_of_right_inverse_apply_idem" -> "topology", "linear_pmap.sup_h_of_disjoint" -> "algebra", "category_theory.single_obj.to_End_def" -> "category_theory", "uniform_space.completion.uniform_continuous_coe" -> "topology", "complex.cosh_sq_sub_sinh_sq" -> "data", "sum.inr_ne_inl" -> "data", "real.tan_zero" -> "data", "cardinal.mk_preimage_of_injective" -> "set_theory", "finset_is_basis_of_linear_independent_of_card_eq_findim" -> "algebra", "primrec\:2082.encode_iff" -> "computability", "nat.le_three_of_sqrt_eq_one" -> "data", "deriv_within_sum" -> "analysis", "nat.primrec.cases1" -> "computability", "eq_or_lt_of_le" -> "algebra", "alg_hom.map_neg" -> "algebra", "summable_of_absolute_convergence_real" -> "analysis", "metric.continuous_on_iff" -> "topology", "submodule.restrict_scalars'_injective" -> "algebra", "padic_seq.not_lim_zero_const_of_nonzero" -> "data", "ideal.is_prime.mem_of_pow_mem" -> "algebra", "valuation.map_sub_le_max" -> "algebra", "geom_series_mul_neg" -> "analysis", "deriv_within_rpow_of_one_le" -> "analysis", "inf_le_left" -> "order", "finset.card_def" -> "data", "category_theory.limits.pullback_cone.condition_assoc" -> "category_theory", "circle_deg1_lift.translation_number_conj_eq'" -> "dynamics", "list.chain_iff_nth_le" -> "data", "alist.ext_iff" -> "data", "matrix.diag_transpose" -> "algebra", "not_or_distrib" -> "logic", "finset.sum_lt_sum" -> "algebra", "list.lookup_all_length_le_one" -> "data", "list.maximum_eq_coe_iff" -> "data", "equiv.perm.mem_iff_of_subtype_apply_mem" -> "algebra", "list.sublist_append_right" -> "data", "deriv_within_sqrt" -> "analysis", "set.union_eq_compl_compl_inter_compl" -> "data", "subsingleton_or_nontrivial" -> "logic", "bilin_form.mul_to_matrix" -> "algebra", "linear_equiv.coe_fn_to_continuous_linear_equiv_of_continuous_symm" -> "analysis", "convex_cone.comap_id" -> "analysis", "matrix.cons_vec_mul_vec" -> "data", "mul_right_injective" -> "algebra", "zmod.val_add" -> "data", "divp_inv" -> "algebra", "finset.bind_val" -> "data", "stream.length_take" -> "data", "tendsto_inverse_at_top_nhds_0_nat" -> "analysis", "composition_as_set_card" -> "combinatorics", "list.rel_perm" -> "data", "ordinal.infinite_pigeonhole" -> "set_theory", "set.indicator_rel_indicator" -> "data", "measure_theory.integrable.smul_measure" -> "analysis", "perfect_closure.zero_def" -> "algebra", "is_add_unit_of_add_is_add_unit_left" -> "algebra", "cau_seq.const_pos" -> "data", "localization.mul_equiv_of_quotient_monoid_of" -> "algebra", "Class.mem_hom_left" -> "set_theory", "list.perm_ext" -> "data", "complex.mul_im" -> "data", "has_deriv_at_filter.mono" -> "analysis", "submonoid.mem_comap" -> "algebra", "option.some_ne_none" -> "data", "set.mem_Icc" -> "data", "tensor_product.congr_tmul" -> "algebra", "alg_equiv.surjective" -> "algebra", "zmod.val_min_abs_eq_zero" -> "data", "free_add_semigroup.map_of" -> "algebra", "metric.totally_bounded_of_finite_discretization" -> "topology", "differentiable_within_at.comp" -> "analysis", "complex.log_neg_I" -> "analysis", "left_ne_zero_of_mul_eq_one" -> "algebra", "real.is_conjugate_exponent.symm" -> "data", "measure_theory.measure.chaar_le_haar_outer_measure" -> "analysis", "subring.coe_coe" -> "algebra", "semiconj_by.units_gpow_right" -> "algebra", "has_sum_sum_of_ne_finset_zero" -> "topology", "cardinal.sum_lt_of_is_regular" -> "set_theory", "quotient_add_group.coe_neg" -> "algebra", "fderiv_within_zero_of_not_differentiable_within_at" -> "analysis", "is_unit.mul_left_eq_zero" -> "algebra", "many_one_degree.le_add_right'" -> "computability", "set.empty_card" -> "data", "function.partial_inv_of_injective" -> "logic", "polynomial.roots_C" -> "data", "multiset.cons_le_cons" -> "data", "list.minimum_nil" -> "data", "measure_theory.integral_neg" -> "analysis", "metric.tendsto_locally_uniformly_on_iff" -> "topology", "convex_halfspace_le" -> "analysis", "ideal.map_bot" -> "algebra", "multiset.cons_sigma" -> "data", "setoid.eqv_gen_eq" -> "data", "multiset.coe_foldr_swap" -> "data", "lt_of_lt_of_le" -> "init", "set.compl_Iio" -> "data", "nhds_left'_sup_nhds_right" -> "topology", "generalized_continued_fraction.part_num_none_iff_s_none" -> "algebra", "nat.bit0_le_bit1_iff" -> "data", "list.length_permutations_aux" -> "data", "list.ne_nil_of_length_pos" -> "data", "semiconj_by.cast_int_mul_right" -> "algebra", "list.countp_pos" -> "data", "nat.le_div_iff_mul_le" -> "init", "category_theory.op_id_unop" -> "category_theory", "finsupp.single_eq_of_ne" -> "data", "is_local_max_on.has_fderiv_within_at_nonpos" -> "analysis", "linear_map.map_cod_restrict" -> "algebra", "mul_left_inj" -> "algebra", "is_local_min_on.fderiv_within_eq_zero" -> "analysis", "matrix.det_smul" -> "algebra", "ring_hom.injective" -> "algebra", "category_theory.iso.conj_apply" -> "category_theory", "iff.elim" -> "init", "list.bi_unique_forall\:2082" -> "data", "fderiv_mul" -> "analysis", "well_founded.min_mem" -> "order", "tensor_product.smul_add" -> "algebra", "ring_equiv.apply_symm_apply" -> "data", "int.eq_mul_of_div_eq_left" -> "data", "pgame.first_loses_is_zero" -> "set_theory", "asymptotics.is_o.def" -> "analysis", "map_smul_eq_smul_map" -> "algebra", "asymptotics.is_O_with_prod_left" -> "analysis", "function.embedding.set_value_eq" -> "logic", "hash_map.find_aux_iff" -> "data", "ordinal.bsup_id" -> "set_theory", "differentiable_within_at.sin" -> "analysis", "infi_le_binfi" -> "order", "is_noetherian_submodule" -> "algebra", "filter.germ.const_div" -> "order", "AddCommGroup.image.fac" -> "algebra", "category_theory.op_op_equivalence_unit_iso" -> "category_theory", "divp_one" -> "algebra", "finset.sum_induction" -> "algebra", "real.zero_rpow" -> "analysis", "one_one_equiv.le_congr_right" -> "computability", "multiset.choose_property" -> "data", "alg_hom.map_zero" -> "algebra", "submonoid.localization_map.map_id" -> "algebra", "structure_groupoid.symm" -> "geometry", "ring.fractional_ideal.fractional_map" -> "algebra", "ring_equiv.map_ne_zero_iff" -> "data", "tactic.ring.pow_add_rev" -> "tactic", "ordinal.lift_id" -> "set_theory", "nat_ceil_add_nat" -> "algebra", "has_deriv_at.sub_const" -> "analysis", "multiset.mem_map_of_injective" -> "data", "le_iff_le_iff_lt_iff_lt" -> "algebra", "prime_spectrum.vanishing_ideal_union" -> "algebraic_geometry", "associates.coe_unit_eq_one" -> "algebra", "multilinear_map.mk_pi_ring_apply_one_eq_self" -> "algebra", "dense_inducing.continuous_at_extend" -> "topology", "category_theory.limits.prod_left_unitor_hom_naturality" -> "category_theory", "submodule.mul_le" -> "algebra", "monoid_hom.map_prod" -> "algebra", "fintype.sum_eq_zero" -> "data", "commute.pow_pow_self" -> "algebra", "real.continuous_rpow_of_ne_zero" -> "analysis", "list.subset_cons_diff" -> "data", "category_theory.limits.has_limit.iso_of_equivalence_\[Pi]" -> "category_theory", "multiset.le_iff_exists_add" -> "data", "real.sqrt_one_add_sinh_sq" -> "analysis", "filter.Limsup_le_of_le" -> "order", "norm_num.adc_zero" -> "tactic", "int.to_nat_one" -> "data", "category_theory.iso.to_alg_equiv_to_fun" -> "algebra", "measure_theory.integrable_on_finite_union" -> "analysis", "semiquot.is_pure_univ" -> "data", "direct_sum.ext" -> "algebra", "irreducible.ne_zero" -> "algebra", "add_monoid_hom.map_list_sum" -> "data", "deriv.scomp" -> "analysis", "continuous_linear_equiv.coe_comp_coe_symm" -> "topology", "alist.lookup_erase_ne" -> "data", "euclidean_domain.mod_eq_sub_mul_div" -> "algebra", "pnat.dvd_one_iff" -> "data", "convex_cone.map_id" -> "analysis", "set.inter_union_distrib_right" -> "data", "metric.ball_eq_ball" -> "topology", "filter.tendsto_at_top_add_const_left" -> "order", "complex.abs_one" -> "data", "complete_space_of_is_complete_univ" -> "topology", "int.modeq.modeq_iff_dvd" -> "data", "cardinal.lt_ord_succ_card" -> "set_theory", "list.mem_iota" -> "data", "filter.tendsto_sup" -> "order", "subgroup.ext'_iff" -> "algebra", "free_group.map.id'" -> "algebra", "set.mem_diagonal" -> "data", "matrix.dot_product_smul" -> "data", "local_homeomorph.preimage_open_of_open" -> "topology", "category_theory.whisker_right_id'" -> "category_theory", "cardinal.one_le_one" -> "set_theory", "multiset.le_add_left" -> "data", "abstract_completion.map_id" -> "topology", "ennreal.one_lt_top" -> "data", "mv_power_series.coeff_map" -> "algebra", "measure_theory.measure.finite_at_principal" -> "analysis", "filter.exists_sets_subset_iff" -> "order", "ordinal.mul_omega_power_power" -> "set_theory", "subtype.val_eq_coe" -> "data", "complex.neg_pi_lt_arg" -> "analysis", "set.exists_max_image" -> "data", "real.sin_nonneg_of_nonneg_of_le_pi" -> "analysis", "finmap.keys_erase_to_finset" -> "data", "multiset.erase_comm" -> "data", "sum.map_comp_map" -> "data", "measurable.prod" -> "analysis", "ordinal.type_eq" -> "set_theory", "list.foldr_nil" -> "data", "heq_of_heq_of_eq" -> "init", "set.indicator_le_indicator_of_subset" -> "data", "category_theory.equivalence.unit_inverse_comp" -> "category_theory", "turing.reaches\:2080.tail'" -> "computability", "list.chain.iff" -> "data", "category_theory.Monad.Monad_to_Mon_obj" -> "category_theory", "le_sup_left'" -> "order", "uniformity_dist_of_mem_uniformity" -> "topology", "measurable_inl" -> "analysis", "Class.iota_val" -> "set_theory", "div_two_lt_of_pos" -> "algebra", "vadd_left_injective" -> "algebra", "complex.abs_cos_add_sin_mul_I" -> "data", "continuous.borel_measurable" -> "analysis", "polynomial.nat_degree_div_by_monic" -> "data", "ite_add_zero" -> "algebra", "set.sUnion_inter_sUnion" -> "data", "complex.cos_add_sin_mul_I_pow" -> "data", "commute.map" -> "algebra", "add_semiconj_by.units_coe_iff" -> "algebra", "category_theory.limits.is_colimit.of_nat_iso.cocone_of_hom_fac" -> "category_theory", "tsum_add_tsum_compl" -> "topology", "int.zero_ne_one" -> "init", "tactic.ring.subst_into_pow" -> "tactic", "num.add_succ" -> "data", "set.piecewise_preimage" -> "data", "set.indicator_smul" -> "data", "linear_equiv_matrix_range" -> "algebra", "list.kerase_sublist" -> "data", "int.neg_add_le_left_of_le_add" -> "init", "category_theory.limits.coprod_map_map_assoc" -> "category_theory", "is_closed_map_add_left" -> "topology", "add_subgroup.mem_sup_left" -> "algebra", "ideal.mul_right_self_sup" -> "algebra", "category_theory.abelian.pseudo_equal_trans" -> "category_theory", "nat.not_prime_zero" -> "data", "wseq.equiv.trans" -> "data", "galois_connection.l_u_l_eq_l" -> "order", "contract_right_apply" -> "algebra", "con.con_gen_mono" -> "algebra", "finset.range_add_one'" -> "data", "pequiv.mem_of_set_iff" -> "data", "has_deriv_within_at_iff_has_fderiv_within_at" -> "analysis", "category_theory.equivalence.inverse_as_equivalence" -> "category_theory", "cardinal.sum_const" -> "set_theory", "is_invariant_subring.coe_subtype_hom'" -> "algebra", "nat.psub_eq_sub" -> "data", "polynomial.degree_eq_one_of_irreducible_of_splits" -> "algebra", "is_open_map_iff_nhds_le" -> "topology", "measure_theory.measure.measurable_bind'" -> "analysis", "stream.identity" -> "data", "category_theory.equivalence.trans_unit_iso" -> "category_theory", "list.filter_map_eq_map" -> "data", "add_nsmul" -> "algebra", "ring.direct_limit.of_pow" -> "algebra", "fixed_points.next_le" -> "order", "add_monoid_hom.mem_range" -> "algebra", "is_measurable_prod_of_nonempty" -> "analysis", "znum.zneg_succ" -> "data", "is_compact.Sup_mem" -> "topology", "open_embedding_sigma_mk" -> "topology", "set.prod_subset_preimage_fst" -> "data", "Class.sep_hom" -> "set_theory", "category_theory.functor.const_comp_inv_app" -> "category_theory", "euclidean_domain.lcm_dvd" -> "algebra", "finset.sum_ite_eq" -> "algebra", "abstract_completion.extend_coe" -> "topology", "list.subperm.perm_of_length_le" -> "data", "continuous_map.coe_inj" -> "topology", "set.eq_on.maps_to_iff" -> "data", "free_add_magma.lift_add" -> "algebra", "closure_empty_iff" -> "topology", "real.of_rat_eq_cast" -> "data", "finsupp.map_domain_congr" -> "data", "linear_map.flip_apply" -> "algebra", "continuous_multilinear_map.ext" -> "topology", "measure_theory.measure.lintegral_bind" -> "analysis", "filter.eventually_le_at_bot" -> "order", "nat.coprime.coprime_dvd_right" -> "data", "subsemiring.mem_prod" -> "algebra", "is_max_on_dual_iff" -> "order", "set.finite.bUnion" -> "data", "category_theory.faithful.of_comp" -> "category_theory", "eq_of_forall_edist_le" -> "topology", "complex.cos_arg" -> "analysis", "category_theory.over.iterated_slice_forward_map" -> "category_theory", "with_top.coe_zero" -> "algebra", "int.lcm_def" -> "algebra", "rel_embedding.le_map_sup" -> "order", "nhds_within_Ioi_self_ne_bot'" -> "topology", "zmod.neg_one_ne_one" -> "data", "is_clopen_empty" -> "topology", "continuous_linear_map.map_zero" -> "topology", "set.preimage_const_add_Icc" -> "data", "int.add_neg_of_neg_of_nonpos" -> "init", "matrix.mul_to_lin" -> "algebra", "measurable.ennreal_add" -> "analysis", "complex.continuous_linear_map.of_real_apply" -> "analysis", "category_theory.equivalence.functor_unit_comp" -> "category_theory", "mem_own_right_add_coset" -> "algebra", "filter.map_zero" -> "order", "floor_ring_unique" -> "algebra", "uniform_space.ring_sep_rel" -> "topology", "con.con_gen_idem" -> "algebra", "filter.eventually_eq.inv" -> "order", "filter.is_cobounded_principal" -> "order", "is_coprime.symm" -> "algebra", "typevec.to_subtype_of_subtype_assoc" -> "data", "has_mfderiv_at.mfderiv" -> "geometry", "finset.ne_of_mem_erase" -> "data", "neg_add_lt_iff_lt_add" -> "algebra", "mfderiv_comp" -> "geometry", "linear_map.mem_range" -> "algebra", "list.Ico.nodup" -> "data", "exists_of_linear_independent_of_finite_span" -> "algebra", "semiquot.blur_eq_blur'" -> "data", "multiplicity.zero" -> "algebra", "polynomial.dvd_term_of_dvd_eval_of_dvd_terms" -> "data", "auto.by_contradiction_trick" -> "tactic", "mv_polynomial.degrees_C" -> "data", "pfun.core_eq" -> "data", "nat.xgcd_val" -> "data", "dioph.dioph_comp" -> "number_theory", "nat.coprime.gcd_both" -> "data", "submonoid.localization_map.of_mul_equiv_of_localizations_eq" -> "algebra", "algebra.adjoin_union_coe_submodule" -> "algebra", "linear_equiv.comp_coe" -> "algebra", "cardinal.power_self_eq" -> "set_theory", "midpoint_add_add" -> "algebra", "measure_theory.ae_restrict_ne_bot" -> "analysis", "filter.has_basis.inf" -> "order", "is_coprime.mul_left_iff" -> "algebra", "decidable.forall_or_distrib_right" -> "logic", "inv_mul_cancel_right" -> "algebra", "linear_map.comp_assoc" -> "algebra", "list.last_append" -> "data", "transitive_one_one_reducible" -> "computability", "fin.ext_iff" -> "data", "omega.int.implies_neg_elim" -> "tactic", "real.exists_cos_eq_zero" -> "analysis", "subalgebra.smul_mem" -> "algebra", "isometric.self_comp_symm" -> "topology", "option.cons_head_tail" -> "number_theory", "pgame.not_first_loses_of_first_wins" -> "set_theory", "linear_equiv.map_eq_comap" -> "algebra", "is_max_filter.comp_mono" -> "order", "multiset.sum_map_sum_map" -> "data", "has_fderiv_at.prod" -> "analysis", "set.image_mul" -> "algebra", "induced_top" -> "topology", "list.chain'_iff_nth_le" -> "data", "metric.mk_uniformity_basis" -> "topology", "many_one_degree.le_comap_right" -> "computability", "convex_halfspace_im_le" -> "analysis", "convex_Icc" -> "analysis", "category_theory.non_preadditive_abelian.mono_of_cancel_zero" -> "category_theory", "set.comp_eq_of_eq_on_range" -> "data", "units.is_unit_mul_units" -> "algebra"|>