(* ::Package:: *)

Graph[{"group.exists_list_of_mem_closure", "lt_add_one", "differentiable_at.smul_const", "tangent_bundle_proj_open", "tactic.ring_exp.mul_pp_pf_overlap", "eq_ff_of_not_eq_tt", "equiv.of_injective_apply", "times_cont_diff.differentiable", "nat.elim_zero", "simple_graph.adj_iff_exists_edge", "int.lt_of_le_sub_one", "multiset.card_eq_zero", "filter.eventually_bot", "pow_eq_zero", "valuation.self_le_supp_comap", "map_cluster_pt_iff", "hyperreal.is_st_st'", "list.append_inj'", "set.mem_diff_of_mem", "matrix.dot_product_assoc", "is_scalar_tower.algebra.ext", "int.neg_le_sub_left_of_le_add", "finset.filter_inter", "list.lookup_all_cons_eq", "linear_equiv.of_injective_apply", "continuous_linear_map.extend_zero", "norm_sub_square_eq_norm_square_add_norm_square_iff_inner_eq_zero", "turing.partrec_to_TM2.tr_pos_num_nat_end", "algebra.adjoin_singleton_eq_range", "primrec.nat_elim\:2081", "function.sometimes_spec", "mem_image_univ_iff_mem_range", "inf_eq_min", "category_theory.comonad.coalgebra.hom.comp_f", "list.not_mem_of_count_eq_zero", "list.chain'.cons", "pnat.xgcd_type.reduce_reduced'", "tensor_product.tmul_sum", "polynomial.monic.next_coeff_mul", "algebra.tensor_product.comm_tmul", "zmod.exists_pow_two_eq_two_iff", "free_add_semigroup.add_bind", "list.nil_bag_inter", "has_fderiv_within_at.union", "computation.get_think", "category_theory.limits.limit.pre_pre", "finset.sum_range_eq_sum_fin", "set.union_inter_cancel_right", "turing.tape.move_right_mk'", "polynomial.mul_div_by_monic_eq_iff_is_root", "category_theory.limits.biproduct.total", "lie_algebra.equiv.coe_to_linear_equiv", "heq_of_eq_rec_left", "int.sub_lt_sub_of_lt_of_le", "ideal.comap_bot_le_of_injective", "sesq_form.zero_right", "filter.singleton_mem_pure_sets", "is_glb.cInf_eq", "multiplicity.multiplicity_lt_iff_neg_dvd", "category_theory.over.over_morphism.ext", "real.sqrt_div", "polynomial.coe_C", "computation.eq_empty_of_not_terminates", "bnot_eq_true_eq_eq_ff", "subsemiring.coe_nat_mem", "bilin_form.mem_skew_adjoint_submodule", "inner_sub_sub_self", "monoid_hom.mclosure_preimage_le", "with_zero.div_coe", "category_theory.coyoneda_obj_obj", "structure_groupoid.local_invariant_prop.lift_prop_on_congr", "euclidean_geometry.angle_comm", "list.pairwise_of_forall", "formal_multilinear_series.change_origin_eval", "filter.frequently_at_bot'", "continuous_multiset_prod", "is_integral_zero", "norm_num.inv_one_div", "set.sep_univ", "monoid_hom.eq_on_mclosure", "times_cont_diff_at.times_cont_diff_within_at", "ne_of_mem_of_not_mem", "erased.out_proof", "set.compl_compl", "polynomial.coeff_single", "measure_theory.lintegral_indicator", "int.mod_two_eq_zero_or_one", "vector.to_list_nil", "nat.partrec.code.curry_prim", "is_invariant_subring.coe_subtype_hom", "category_theory.graded_object.comap_eq_symm", "nat.odd_of_mod_four_eq_three", "discrete_valuation_ring.associated_pow_irreducible", "measure_theory.measure.haar_outer_measure_self_pos", "category_theory.limits.kernel_not_epi_of_nonzero", "add_submonoid.sup_eq_range", "is_local_max.add", "bounded_continuous_function.const_apply", "bitvec.to_fin_val", "min_add_max", "edist_lt_top", "eq_or_eq_neg_of_pow_two_eq_pow_two", "is_lub.Sup_eq", "onote.repr_scale", "mem_nhds_within_Iic_iff_exists_mem_Ico_Ioc_subset", "local_homeomorph.eq_of_local_equiv_eq", "rel.image_comp", "list.range_eq_range'", "linear_map.map_injective", "of_set_mem_times_cont_diff_groupoid", "set.mem_add", "convex_cone.mem_inf", "nat.add_right_cancel", "quadratic_form.polar_add_right", "turing.TM1.step_supports", "unique_diff_within_at.mono_nhds", "equiv.perm.same_cycle.trans", "equiv.to_fun_as_coe", "bilin_form.ortho_zero", "nat.one_le_two_pow", "emetric.diam_pair", "polynomial.splits_mul", "with_bot.coe_bit0", "nat.shiftl_eq_mul_pow", "pfun.core_inter", "local_homeomorph.mdifferentiable.range_mfderiv_eq_univ", "set.maps_to_Union_Union", "norm_num.nat_succ_eq", "pgame.zero_left_moves", "computation.eq_thinkN'", "filter.map_at_top_finset_prod_le_of_prod_eq", "lcm_dvd_lcm_mul_left", "local_homeomorph.mk_coe_symm", "nnreal.rpow_lt_rpow_of_exponent_gt", "is_R_or_C.sub_conj", "composition.length_gather", "eqv_gen.is_equivalence", "filter.has_basis.cauchy_seq_iff'", "cau_seq.equiv_def\:2083", "measure_theory.l1.of_fun_add", "set.eq_empty_iff_forall_not_mem", "encodable.mem_sorted_univ", "set.interval_subset_interval_iff_mem", "comp_rel_assoc", "computation.results.length", "quotient_ring.quotient_map_coe_coe", "cardinal.pos_iff_ne_zero", "is_noetherian_ring.exists_factors", "list.perm.foldl_eq'", "is_bounded_bilinear_map.continuous", "computable.vector_tail", "right_eq_sup", "Top.sheaf_condition.fork_\[Iota]", "model_with_corners.mk_coe", "measurable_space.comap_id", "set.preimage_mul_const_Ioi_of_neg", "is_connected.Ioo_cInf_cSup_subset", "complex.exp_zero", "or_and_distrib_left", "finset.card_lt_card", "primrec.nat_min", "free_monoid.closure_range_of", "local_homeomorph.subtype_restr_def", "option.ext", "finsupp.zero_not_mem_frange", "padic_seq.norm_eq_of_add_equiv_zero", "mul_le_mul_left", "real.sin_sub_pi_div_two", "is_group_hom.mem_ker", "ordinal.nfp_eq_self", "category_theory.abelian.pseudoelement.zero_apply", "wseq.join_ret", "con.coe_one", "differentiable.differentiable_on", "decidable.iff_iff_not_or_and_or_not", "add_monoid_hom.iterate_map_add", "nnreal.div_pos", "continuous_right_of_strict_mono_surjective", "metric.bounded_closed_ball", "list.count_nil", "filter.tendsto_at_top_of_add_bdd_above_right'", "cauchy_seq_finset_iff_vanishing_norm", "computation.has_map_eq_map", "complex.sin_add_two_pi", "set.diff_diff", "matrix.vec_mul_vec_mul", "is_basis.to_dual_swap_eq_to_dual", "turing.list_blank.cons_mk", "asymptotics.is_O.exists_pos", "nat.succ_sub_sub_succ", "Inf_insert", "sym2.mk_has_mem_right", "filter.of_sets_filter_eq_generate", "alg_equiv.symm_symm", "equiv.subset_image", "set.diff_eq_self", "list.chain'_reverse", "local_equiv.trans_refl", "wseq.dropn_congr", "equiv.perm.sign_aux3_mul_and_swap", "quotient.hrec_on\:2082'_mk'", "equiv.set.of_eq_apply", "isometric.to_homeomorph_to_equiv", "rel.image_union", "Module.monoidal_category.right_unitor_hom_apply", "measure_theory.ae_eq_fun.neg_to_germ", "closure_inter_open", "polynomial.splitting_field.adjoin_roots", "equiv_of_is_basis_trans_symm", "nat.shiftl'_tt_ne_zero", "equiv.coe_vadd_const", "function.embedding.injective", "is_local_max.has_deriv_at_eq_zero", "local_homeomorph.prod_target", "is_local_min.add", "submodule.restrict_scalars'_inj", "has_fderiv_at_filter.mono", "submodule.mul_sup", "computable.encode", "quadratic_form.associated_lin_mul_lin", "category_theory.monoidal_category.associator_nat_iso_inv_app", "category_theory.limits.cone.category_to_category_struct_comp_hom", "nat.mul_div_assoc", "cau_seq.const_sub", "set.nonempty_Icc", "finite_dimensional.finite_dimensional_iff_dim_lt_omega", "is_noetherian_ring_of_fg", "many_one_degree.add_le", "add_submonoid.localization_map.mk'_self'", "function.has_left_inverse.injective", "int.cast_sub_nat_nat", "list.length_take_le", "normalize_idem", "le_inv_mul_of_mul_le", "add_gsmul", "multiset.ext'", "norm_num.sub_pos", "circle_deg1_lift.monotone", "free_abelian_group.sub_seq", "set.mem_sInter", "finset.union_idempotent", "list.exists_or_eq_self_of_erasep", "vector.continuous_insert_nth", "pSet.subset.congr_right", "filter.germ.coe_comp_tendsto'", "sub_le_sub_iff_right", "strict_mono.iterate", "matrix.findim_matrix", "asymptotics.is_O.join", "tensor_product.mk_apply", "nat.decreasing_induction_succ'", "mdifferentiable_within_at.mfderiv_within_congr_mono", "category_theory.limits.biprod.braid_natural_assoc", "multiset.sup_erase_dup", "multiset.sort_sorted", "open_embedding.to_local_homeomorph_coe", "vector.continuous_insert_nth'", "pmf.bind.summable", "ordinal.add_omega", "differentiable.sub", "set.Union_lt_succ", "lt_add_of_le_of_pos", "denumerable.raise'_sorted", "filter.eventually_eq_set", "nat.sub_eq_zero_of_le", "ordinal.sup_lt", "isometric.point_reflection_midpoint_right", "alg_equiv.symm_apply_apply", "differentiable_at.const_mul", "embedding_open", "lucas_lehmer.X.one_fst", "continuous_Inf_dom", "list.sum_hom", "convex_on_id", "category_theory.abelian.pseudoelement.comp_comp", "set.eq_univ_of_univ_subset", "category_theory.functor.left_unitor_inv_app", "typevec.comp_assoc", "int.lt_add_of_neg_add_lt", "nat.choose_symm_add", "fin.tail_update_zero", "set.maps_to_Inter", "finset.prod_Ico_reflect", "filter.tendsto_neg_at_top_at_bot", "cardinal.mk_image_le", "submodule.quotient.eq", "associates.sup_mul_inf", "initial_seg.eq_or_principal", "nat.primrec.add", "turing.TM2to1.step_run", "convex_on.exists_ge_of_mem_convex_hull", "ennreal.Icc_mem_nhds", "continuous_multilinear_map.map_sum_finset", "pfun.image_def", "pgame.not_first_wins_of_first_loses", "list.sublist.erasep", "filter.eventually_eq.times_cont_diff_within_at_iff", "polynomial.coeff_X", "wseq.eq_or_mem_iff_mem", "measurable_bsupr", "nhds_induced", "stream.tails_eq_iterate", "all_mem_nhds_filter", "add_equiv.map_zero", "typevec.last_fun_prod", "is_add_group_hom.map_neg", "upper_bounds_mono_mem", "complex.has_deriv_at_cos", "list.erase_dup_cons_of_not_mem'", "mv_polynomial.total_degree_X", "floor_add_fract", "mvpfunctor.W_path_dest_left_W_path_cases_on", "list.perm.sizeof_eq_sizeof", "nodup_perms_of_list", "has_deriv_at.cosh", "is_preirreducible_empty", "equiv.conj_symm", "add_monoid_hom.to_range_ker", "linear_map.ker_smul", "unique_factorization_domain.exists_reduced_factors", "emetric.Hausdorff_edist_closure\:2081", "set.singleton_inter_eq_empty", "computation.exists_results_of_mem", "finset.sum_mul_boole", "hyperreal.st_of_is_st", "set.Icc_union_Ici_eq_Ici", "mul_smul", "complex.im_le_abs", "filter.lift'_ne_bot_iff", "turing.to_partrec.code_is_ok", "nat.add_le_add_iff_le_right", "cardinal.mul_lt_omega_iff", "geom_series\:2082_one", "finsupp.is_basis_single", "cardinal.one_le_iff_ne_zero", "nat.prime.irrational_sqrt", "ideal.mem_pi", "has_sum.neg", "commutative_ring_iff_abelian_lie_ring", "real.exp_nat_mul", "set.Ioi_inter_Iio", "set.Ici_subset_Ioi", "finset.insert_eq", "is_basis.comp", "euclidean_domain.gcd_eq_zero_iff", "rel.core_inter", "infi_congr_Prop", "stream.composition", "list.foldr_eta", "primrec.of_equiv_iff", "canonically_ordered_semiring.mul_le_mul_right'", "computation.mem_unique", "computation.results.val_unique", "add_subgroup.coe_map", "filter.comap_mono", "polynomial.card_roots_sub_C'", "hyperreal.epsilon_pos", "finmap.to_finmap_cons", "vector.head'_to_list", "nat.zero_le", "hyperreal.not_infinite_real", "multiplicity.pow", "set.subset_insert_diff_singleton", "polynomial.differentiable", "computation.parallel_empty", "finset.disjoint_sdiff", "seq.head_nil", "erased.bind_def", "measure_theory.simple_func.pos_part_sub_neg_part", "pgame.equiv_congr_left", "list.perm.rec_heq", "with_zero.one_div", "padic_val_nat_primes", "topological_fiber_bundle_core.local_triv_fst", "ring_hom.coe_pow", "semidirect_product.right_hom_inr", "irrational_sub_rat_iff", "mul_right_inj", "list.cons_inj", "vector.nth_eq_nth_le", "roption.get_or_else_none", "char_p.int_cast_eq_zero_iff", "list.sum_nil", "ne_top_of_le_ne_top", "setoid.eqv_class_mem", "le_of_forall_lt'", "category_theory.is_iso.inv_id", "gcd_dvd_gcd_mul_right_right", "norm_zero", "function.injective.map_at_top_finset_sum_eq", "times_cont_mdiff_on_const", "of_digits_one", "bounded_continuous_function.dist_le_two_norm'", "filter.prod_at_top_at_top_eq", "int.add_zero", "deriv_const", "polynomial.derivative_expand", "polynomial.splits_X_sub_C", "set.Ioi_union_left", "direct_sum.to_module.unique", "differentiable_within_at.ccosh", "filter.tendsto.uniformity_trans", "nat.exists_infinite_primes", "units.coe_mk_of_mul_eq_one", "filter.infi_ne_bot_of_directed", "category_theory.non_preadditive_abelian.neg_sub", "measure_theory.ae_eq_fun.edist_smul", "local_equiv.symm_maps_to", "exists_between_of_forall_le", "real.cos_pi_div_two_sub", "char_dvd_card_solutions", "zsqrtd.coe_int_re", "is_max_filter.add", "compact_space.tendsto_subseq", "circle_deg1_lift.translate_gpow", "set.countable.union", "ring.direct_limit.of.zero_exact_aux2", "fpow_ne_zero_of_ne_zero", "uniform_space.has_basis_symmetric", "is_R_or_C.bit1_re", "continuous_linear_map.coe_add'", "sup_right_idem", "finset.union_subset", "power_series.coeff_trunc", "uniform_space.has_basis_nhds", "equiv.symm_symm", "finsupp.to_multiset_to_finsupp", "filter.eventually_eq.has_deriv_at_filter_iff", "continuous_at_of_locally_lipschitz", "category_theory.monoidal_of_has_finite_products.tensor_hom", "finsupp.filter_pos_add_filter_neg", "is_absolute_value.abv_sub_le", "prime_spectrum.ext", "nat.sub_add_min", "tsum_sub", "has_mfderiv_within_at.continuous_within_at", "is_compact.is_seq_compact", "ideal.maximal_of_no_maximal", "monotonicity.false", "category_theory.nat_iso.op_inv", "sub_pow_char_of_commute", "mv_polynomial.rename_monomial", "equiv.coe_subtype_equiv_codomain", "matrix.dot_product_zero'", "category_theory.split_epi.id", "int.neg_add_neg", "smodeq.smul", "pnat.coprime.factor_eq_gcd_right", "with_one.one_ne_coe", "has_deriv_within_at_inv", "wseq.append_assoc", "filter.lift_mono", "tendsto_extend_from", "linear_map.to_continuous_linear_map\:2081_apply", "is_R_or_C.div_I", "primrec.encdec", "finset.union_inter_cancel_left", "subsemiring.mem_bot", "finset.prod_erase", "ennreal.continuous_inv", "ne_top_of_lt", "nnreal.div_rpow", "mv_polynomial.aeval_X", "char_p.false_of_nonzero_of_char_one", "has_fderiv_at_filter.is_O_sub_rev", "quotient_add_group.lift_mk", "fin.coe_val_eq_self", "quadratic_form.equivalent.symm", "alg_equiv.to_lie_equiv_apply", "supr_le_supr", "semiquot.eq_pure", "computable.option_some_iff", "bounded_continuous_function.coe_smul", "set.insert_comm", "affine_map.const_linear", "basic_smooth_bundle_core.smooth_within_at_proj", "submodule.restrict_scalars'_top", "map_cinfi_of_continuous_at_of_monotone", "submodule.span_insert_eq_span", "is_integral_one", "category_theory.limits.is_limit.unique_up_to_iso_hom", "classical.cases_true_false", "linear_map.exists_left_inverse_of_injective", "matrix.transpose_empty_cols", "has_sum_subtype_support", "finset.mul_sum", "category_theory.functor.sum_obj_inr", "set.interval_of_ge", "uniform_space.eq_of_separated_of_uniform_continuous", "finset.bUnion_singleton", "rel_iso.coe_fn_to_equiv", "local_homeomorph.coe_coe_symm", "linear_map.inj_of_disjoint_ker", "ordinal.mul_omega_dvd", "nat.eq_zero_of_le_div", "ring_hom.eq_int_cast", "pnat.coe_bit0", "rel_embedding.trans_apply", "nat.one_add_le_iff", "tendsto_norm_at_top_at_top", "Kuratowski_embedding.embedding_of_subset_dist_le", "mv_polynomial.pderivative_monomial_single", "filter.sequence_mono", "add_submonoid.coe_top", "finset.subset_empty", "nat.gcd_eq_right_iff_dvd", "matrix.row_cons", "set.bUnion_image", "has_sum_zero", "commute.units_coe_iff", "category_theory.limits.coprod.inl_map_assoc", "add_submonoid.mem_Sup_of_directed_on", "zmod.ring_hom_surjective", "with_top.zero_eq_coe", "finset.inter_univ", "not_and_self", "ball.imp_right", "finite_dimensional.findim_pos_iff", "vector_span_def", "continuous_on_iff'", "ball_congr", "vsub_mem_vector_span_of_mem_span_points_of_mem_span_points", "formal_multilinear_series.comp_change_of_variables_length", "turing.TM1to1.supports_stmt_move", "polynomial.exists_root_of_splits", "nat.eq_of_dvd_of_div_eq_one", "continuous_map.image_coev", "set.compl_comp_compl", "sylow.mem_vectors_prod_eq_one_iff", "function.embedding.total", "is_glb_pair", "ctop.of_equiv_val", "measure_theory.meas_ge_le_lintegral_div", "category_theory.limits.colimit.is_colimit_desc", "function.surjective.preimage_subset_preimage_iff", "pow_ite", "real.arcsin_eq_zero_iff", "is_R_or_C.abs_mul", "linear_map.fun_left_apply", "structure_groupoid.local_invariant_prop.lift_prop_at_congr_of_eventually_eq", "inv_mul_eq_one", "free_comm_ring.lift_of", "supr_sup_eq", "pgame.impartial.good_right_move_iff_first_wins", "subalgebra.nsmul_mem", "state_t.run_monad_map", "rat.cast_pow", "tactic.ring2.horner_expr.cseval_add_const", "list.nth_le_of_eq", "iff_false_intro", "multiset.pi.cons_ne", "nnreal.inv_le", "group.mem_conjugates_self", "Kuratowski_embedding.embedding_of_subset_coe", "hyperreal.exists_st_of_not_infinite", "irrational_inv_iff", "unit_associated_one", "localization_map.mem_map_to_map_iff", "list.sublists_reverse", "bifunctor.snd_id", "submodule.quotient.quot_mk_eq_mk", "int.coe_nat_ne_zero_iff_pos", "is_compact.is_measurable", "nat.le_trans", "is_local_max.deriv_eq_zero", "sup_ind", "nat.mod_mul_right_mod", "bundle_trivialization.coe_mk", "mul_action.bijective", "is_add_subgroup.gsmul_coe", "int.lt_add_of_pos_left", "approximates_linear_on.to_local_homeomorph_source", "semiconj_by.inv_symm_left_iff'", "associates.forall_associated", "category_theory.over.post_map_right", "eq_or_lt_of_not_lt", "nat.prime.coprime_iff_not_dvd", "multiset.map_singleton", "gcd_eq_left_iff", "matrix.mul_empty", "contracting_with.aposteriori_dist_iterate_fixed_point_le", "continuous_linear_equiv.is_O_comp_rev", "nat.land_zero", "quotient_add_group.ker_mk", "subtype.coe_image_subset", "category_theory.limits.kernel.condition_assoc", "pell.eq_of_xn_modeq_lem2", "polynomial.eisenstein_criterion_aux.le_nat_degree_of_map_eq_mul_X_pow", "linear_independent.restrict_of_comp_subtype", "commute.one_left", "initial_seg.antisymm_to_fun", "bitvec.of_fin_val", "uniform_extend_subtype", "list_all.imp", "bounded_continuous_function.ext_iff", "with_top.coe_eq_zero", "finset.center_mass_ite_eq", "neg_sub_neg", "polynomial.expand_eq_zero", "is_greatest_Iic", "filter.mem_lift", "int.exists_sum_two_squares_add_one_eq_k", "primrec.list_nth\:2081", "measure_theory.measure.restrict_apply", "typevec.append_fun_aux", "finsupp.is_basis.tensor_product", "is_add_subgroup.of_sub", "nhds_discrete", "equiv.add_def", "measure_theory.mul_meas_ge_le_lintegral", "enorm.coe_fn_injective", "preimage_neg", "conj_injective", "emetric.complete_of_convergent_controlled_sequences", "polynomial.eval\:2082_smul", "lie_algebra.equiv.coe_to_lie_equiv", "complex.sin_of_real_re", "eckmann_hilton.group.is_unital", "formal_multilinear_series.change_origin_has_sum", "continuous_linear_equiv.coe_refl'", "smooth_within_at_snd", "ring_hom.iterate_map_pow", "int.sub_nat_nat_add_neg_succ_of_nat", "primrec\:2082.pair", "nnreal.of_real_eq_zero", "set.image_eq_Union", "sum_geometric_two_le", "submodule.bot_ne_top", "alist.mem_lookup_union", "category_theory.iso.conj_Aut_pow", "zmod.neg_eq_self_mod_two", "omega.nat.valid_of_unsat_not", "encodable.decode2_is_partial_inv", "differentiable_within_at.differentiable_at", "state_t.run_adapt", "ff_eq_tt_eq_false", "filter.tendsto_at_top_add_nonneg_right'", "add_con.lift_range", "ideal.span_zero", "bool.bxor_iff_ne", "sdiff_eq", "is_closed.mem_of_nhds_within_ne_bot", "set.Union_eq_comp_Inter_comp", "ordinal.lift_univ", "dense_range.induction_on", "model_with_corners.right_inv", "polynomial.coeff_mul_X_zero", "if_ctx_congr", "is_measurable_eq", "continuous_map.ext", "filter.eventually_or_distrib_right", "lipschitz_with.mul_edist_le", "add_submonoid.localization_map.neg_inj", "add_submonoid.bot_sum_bot", "holor.slice_zero", "extend_from_eq", "euclidean_geometry.orthogonal_projection_vsub_mem_direction_orthogonal", "nat.Inf_mem", "cardinal.mk_empty", "uniform_space.completion.map\:2082_coe_coe", "algebra.tensor_product.assoc_aux_2", "dfinsupp.sum_zero", "bitvec.to_nat_lt", "matrix.ker_diagonal_to_lin", "perfect_closure.eq_pth_root", "list.mem_sublists_len", "bilin_form.is_adjoint_pair.add", "set.sUnion_eq_Union", "category_theory.non_preadditive_abelian.\[CapitalDelta]_map", "has_deriv_at.inv", "dist_comm", "filter.ne_bot.comap_of_surj", "equiv.coe_neg", "add_monoid_hom.injective_iff", "add_submonoid.map_id", "topological_space.opens.map_obj", "int.mul_one", "list.singleton_disjoint", "prod.mk_vadd_mk", "add_submonoid.add_mem", "ring_hom.prod_comp_prod_map", "nhds_contain_boxes.symm", "cardinal.lift_mk", "pos_num.cast_pos", "add_monoid_hom.eq_of_eq_on_top", "tactic.ring2.horner_expr.cseval_mul", "padic_int.mk_coe", "fin.succ_above_ne", "dvd_gcd_iff", "vector_span_image_eq_span_vsub_set_right_ne", "set.compl_subset_iff_union", "ite_add", "continuous_multilinear_map.curry_left_norm", "add_submonoid.top_prod_top", "multiset.disjoint_union_left", "category_theory.yoneda_pairing_map", "circle_deg1_lift.translation_number_le_ceil_sub", "multiset.eq_of_le_of_card_le", "sum_add_tsum_nat_add", "alist.union_comm_of_disjoint", "partrec.merge'", "set.prod_eq_seq", "is_refl.swap", "is_R_or_C.mul_re", "set.image_neg_Ico", "turing.reaches_total", "finset.choose_mem", "category_theory.preadditive.mono_of_cancel_zero", "nhds_within_eq_of_open", "category_theory.mono_comp", "inducing_id", "int.div_of_neg_of_pos", "nnreal.of_real_lt_of_real_iff", "homological_complex.graded_homology_obj", "filter.germ.const_sup", "topological_space.compacts.map_val", "traversable.traverse_map'", "has_fderiv_at_inverse", "mv_polynomial.eval\:2082_mul", "tangent_map_within_eq_tangent_map", "interval_integral.integral_has_deriv_within_at_right", "function.commute.iterate_right", "finmap.mem_replace", "set.Ici_diff_left", "set.eq_on_refl", "algebraic_geometry.structure_sheaf_stalk_to_fiber_injective", "category_theory.over.iterated_slice_equiv_inverse", "measure_theory.measure_union", "directed.le_sequence", "category_theory.Monad.of_Mon_str_\[Mu]", "cardinal.one_le_iff_pos", "subring.mul_mem", "matrix.vec_mul_neg", "norm_prod_le_iff", "generalized_continued_fraction.int_fract_pair.stream_eq_none_of_fr_eq_zero", "local_homeomorph.eventually_right_inverse", "nat.dvd_lcm_right", "hyperreal.infinite_pos_mul_of_infinite_neg_not_infinitesimal_neg", "pgame.nim.nim_wf_lemma", "continuous_on_iff_continuous_restrict", "if_simp_congr_prop", "wseq.flatten_equiv", "option_t.run_monad_map", "linear_map.mul_eq_one_of_mul_eq_one", "formal_multilinear_series.id_comp", "mv_polynomial.eval\:2082_sub", "measure_theory.lintegral_add_measure", "measurable_space.dynkin_system.generate_le", "dioph.mod_dioph", "list.nodup_append", "asymptotics.is_O_with.join'", "polynomial.eval_prod", "list.nth_le_take'", "lt_of_mul_lt_mul_right", "nnreal.mul_ne_zero'", "equiv.point_reflection_midpoint_right", "function.embedding.trans_apply", "free_abelian_group.lift.map_hom", "measure_theory.simple_func.fin_meas_supp.of_map", "of_digits_one_cons", "set.diff_subset", "nnreal.inv_eq_zero", "category_theory.monoidal_category.unitors_equal.cells_9_13", "category_theory.hom_of_element_eq_iff", "continuous_at_snd", "pnat.add_sub_of_lt", "compact_iff_finite_subfamily_closed", "nat.primrec.sub", "measure_theory.integrable.mono_measure", "category_theory.limits.image_mono_iso_source_inv_\[Iota]_assoc", "canonically_ordered_semiring.one_le_pow_of_one_le", "summable_of_nonneg_of_le", "finset.mono_of_fin_bij_on", "submonoid.localization_map.mul_equiv_of_localizations_left_inv", "convex_halfspace_re_gt", "nat.partrec.prec'", "is_bounded_bilinear_map.differentiable_at", "affine_subspace.direction_of_nonempty_eq_direction", "polynomial.map_monomial", "list.subperm_cons_erase", "category_theory.pi.sum_map_app", "ordinal.typein_surj", "ennreal.inv_eq_inv", "list.perm_split", "quadratic_ne_zero_of_discrim_ne_square", "algebraic_closure.exists_root", "left_add_coset_mem_left_add_coset", "int.coe_nat_div", "dfinsupp.mk_injective", "local_equiv.of_set_source", "category_theory.currying_unit_iso_hom_app_app_app", "has_fpower_series_on_ball.change_origin", "emetric.inf_edist_image", "int.mul_sub", "cardinal.cantor_function_succ", "deriv_within_fderiv_within", "filter.ultrafilter_bind", "category_theory.abelian.pseudoelement.epi_of_pseudo_surjective", "filter.tendsto.Ico", "uniq_inv_of_is_field", "closed_nhds_basis", "add_monoid_hom.id_comp", "continuous_map.continuous_induced", "is_path_connected.preimage_coe", "list.length_enum_from", "add_self_iff_eq_zero", "floor_le", "ideal.mul_mem_mul_rev", "category_theory.limits.image.iso_strong_epi_mono_hom_comp_\[Iota]", "nat.totient_zero", "category_theory.coe_comp", "bounded_continuous_function.norm_const_eq", "stream.nil_append_stream", "finset.bUnion_insert_update", "is_R_or_C.rat_cast_re", "deriv_within_const_add", "primrec.subtype_val", "affine_map.id_comp", "iterated_deriv_within_succ'", "lucas_lehmer.X.\[Omega]b_mul_\[Omega]", "add_submonoid.localization_map.comp_eq_of_eq", "category_theory.limits.equalizer.iso_source_of_self_hom", "polynomial.coeff_mul_monomial", "mem_nhds_within_Ici_iff_exists_mem_Ioc_Ico_subset", "polynomial.degree_derivative_le", "alg_equiv.to_linear_equiv_apply", "add_submonoid.comap_comap", "norm_add_le_of_le", "list.eq_or_mem_of_mem_insert", "lucas_lehmer.X.one_snd", "mv_polynomial.eval_eq'", "int.mod_mul_left_mod", "ennreal.top_mem_upper_bounds", "set.diff_self", "zmod.cast_mod_int", "bounded_continuous_function.norm_smul_le", "multiset.countp_filter", "congr_arg", "joined.symm", "measure_theory.simple_func.lintegral_smul", "list.prod_range_succ", "set.image_neg_Ioi", "and_iff_right_iff_imp", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_comp_is_iso_inv", "pfunctor.M.iselect_nil", "set.Icc_self", "set.maps_to'", "set.Union_of_singleton", "onote.zero_lt_one", "set.Ici_subset_Ico_union_Ici", "category_theory.limits.limit_uncurry_iso_limit_comp_lim_inv_\[Pi]", "ring_hom.restrict_apply", "list.range_subset", "quotient.induction_on\:2082'", "list.nil_product", "asymptotics.is_O.trans_tendsto_nhds", "divp_eq_div", "topological_fiber_bundle_core.continuous_proj", "nat.min_fac_pos", "list.alternating_sum_cons_cons'", "metric.closed_ball_zero", "alist.lookup_union_left", "category_theory.abelian.images.image.fac_assoc", "is_open_map_add_right", "list.argmax_concat", "nat.mul_div_cancel'", "nat.sqrt_aux_0", "nhds_one_symm", "is_preconnected.Ioi_cInf_subset", "mem_right_coset_right_coset", "of_mul_injective", "iterated_fderiv_one_apply", "vector.insert_nth_comm", "set.Ioc_subset_Ioc_right", "category_theory.limits.biproduct.inl_map", "computable_pred.computable_of_many_one_reducible", "normalize_zero", "ennreal.inv_lt_one", "hyperreal.infinite_pos_iff_infinite_of_nonneg", "summable.prod_factor", "polynomial.eval_monomial", "mul_right_comm", "multiset.map_hcongr", "submodule.prod_equiv_of_is_compl_symm_apply_left", "left_ne_zero_of_mul", "apply_ite", "metric.compact_space_iff_seq_compact_space", "fintype.prod_extend_by_one", "enat.coe_lt_coe", "ennreal.continuous_at_mul_const", "normed_field.norm_mul", "algebra.algebra_map_eq_smul_one", "add_commute.symm", "category_theory.iso.trans_symm", "measure_theory.outer_measure.le_smul_caratheodory", "nat.prime.dvd_iff_not_coprime", "rat.lt_def", "is_preconnected_Ico", "set.union_empty_iff", "con.comp_mk'_apply", "turing.list_blank.map_modify_nth", "list.perm_option_to_list", "intermediate_value_univ", "mul_aut.coe_mul", "monoid_hom.map_exists_right_inv", "turing.blank_rel.refl", "alg_equiv.comp_symm", "ideal.mem_span_pair", "omega.sat_eq_elim", "is_add_group_hom.comp", "measure_theory.lintegral_finset_sum", "is_totally_separated_singleton", "computation.destruct_eq_think", "lower_bounds_le_upper_bounds", "infi_lt_iff", "complex.arg_real_mul", "asymptotics.is_o.trans", "list.countp_eq_length_filter", "finset.mem_sort", "submodule.smul_mem_span_smul'", "frontier_closed_ball'", "list.map_filter_map", "set.preimage_const_sub_Ici", "uniform_space.ball_mem_nhds", "list.merge_sort_eq_self", "set.preimage_mono", "continuous_linear_equiv.surjective", "int.mul_div_assoc", "list.nodup_pmap", "matrix.matrix_eq_sum_std_basis", "ennreal.bit1_eq_one_iff", "power_series.nat_le_order", "measure_theory.measure.dirac_apply_of_mem", "pgame.le_of_relabelling", "finset.mem_preimage", "is_preirreducible_iff_closed_union_closed", "rtendsto'_nhds", "norm_num.pow_bit0", "open_embedding.is_open_map", "unique_diff_within_at_univ", "category_theory.monoidal_of_has_finite_coproducts.left_unitor_inv", "pell.xn_zero", "localization_map.mk'_mem_iff", "set.Ioc_subset_Ioc_union_Icc", "equiv.conj_trans", "pgame.not_le", "tactic.ring.pow_add_rev_right", "mv_polynomial.is_basis_monomials", "cardinal.lt_univ'", "filter.eventually_imp_distrib_left", "is_clopen_union", "multiset.to_finset_cons", "nat.sub_lt_of_pos_le", "real.cos_two_mul", "finsupp.filter_single_of_neg", "convex.convex_hull_eq", "add_le_of_le_sub_right", "filter.frequently.forall_exists_of_at_top", "submodule.map_mkq_eq_top", "filter.has_basis_generate", "with_top.is_lub_Sup'", "filter.join_mono", "tendsto_sub_comap_self", "submodule.is_open_mono", "zmod.nat_abs_val_min_abs_neg", "set.neg_neg", "set.Ioi_inter_Iic", "roption.mem_bind_iff", "ff_bor", "bdd_below.inter_of_left", "poly.sumsq_eq_zero", "is_bounded_bilinear_map_deriv_coe", "real.arctan_zero", "is_R_or_C.abs_im_le_abs", "filter.ext", "irrational_nrt_of_notint_nrt", "category_theory.symmetric_of_has_finite_coproducts_to_braided_category_braiding", "add_units.add_lift_right_neg", "turing.partrec_to_TM2.tr_nat_zero", "conjugate_i", "linear_map.lipschitz_of_bound", "list.count_tail", "mul_eq_one_iff_eq_one_of_one_le", "is_compact.integrable_on_of_nhds_within", "int.test_bit_ldiff", "cardinal.out_embedding", "composition.card_boundaries_eq_succ_length", "smodeq.def", "set.eq_on.eventually_eq", "multiset.inf_erase_dup", "category_theory.monoidal_category.left_unitor_product_aux_perimeter", "int.le_sub_one_of_lt", "finset.piecewise_insert_self", "nat_ceil_le", "list.length_insert_of_not_mem", "Inf_lt_iff", "tactic.abel.const_add_termg", "set.image_eq_empty", "category_theory.limits.types.sigma_map", "is_extr_filter.comp_tendsto", "measure_theory.simple_func.add_lintegral", "mul_lt_of_lt_one_of_lt", "inv_sub_inv", "tactic.ring_exp.add_pf_sum_gt", "continuous_multiset_sum", "enorm.coe_max", "finset.affine_combination_linear", "measure_theory.simple_func.integral_eq_lintegral'", "category_theory.graded_object.shift_functor_map_apply", "euclidean_geometry.angle_add_angle_add_angle_eq_pi", "list.cons_subset_of_subset_of_mem", "roption.coe_some", "subalgebra.mul_mem", "vector.tendsto_insert_nth", "lipschitz_with.dist_left", "commute.cast_nat_mul_left", "primrec.dom_denumerable", "turing.reaches\:2080.tail", "bitraversable.tsnd_eq_snd_id'", "measure_theory.ae_eq_fun.lintegral_mono", "hash_map.mem_insert", "category_theory.functor.to_cocone_\[Iota]_app", "le_not_le_of_lt", "valuation.is_equiv_of_map_strict_mono", "category_theory.image_to_kernel_map_epi_of_epi_of_zero", "exists_pair_ne", "is_add_submonoid.smul_mem", "uniform_space.compact_iff_seq_compact", "num.bit0_of_bit0", "complex.abs_of_nat", "prod.swap_swap_eq", "complex.add_re", "ordinal.CNF_sorted", "polynomial.nat_degree_comp_le", "category_theory.uncurry.map_app", "measure_theory.ae_eq_fun.measurable", "computation.lift_rel_map", "set.nonempty.mul", "polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero", "computable.nat_strong_rec", "lipschitz_with.of_edist_le", "real.sin_pos_of_pos_of_le_one", "generalized_continued_fraction.exists_int_eq_of_part_denom", "primrec.option_map", "min_add_add_left", "tactic.ring_exp.pow_p_pf_singleton", "pnat.exists_prime_and_dvd", "set.compl_Union", "monoid_algebra.lift_single", "nat.succ_div_of_dvd", "measure_theory.measure.finite_at_filter.inf_of_right", "multiset.rel_map", "classical.cases_on", "affine_map.comp_assoc", "category_theory.sum.associator_map_inl_inr", "category_theory.limits.prod_functor_map_app", "ideal.mem_quotient_iff_mem", "coe_subset_nonunits", "deriv_within_cexp", "vector.remove_nth_insert_nth", "finset.map_refl", "zmod.neg_val'", "category_theory.abelian.pseudoelement.sub_of_eq_image", "pnat.bit1_le_bit1", "set.piecewise_insert", "matrix.transpose_row", "list.nil_sigma", "set.mem_to_finset", "is_greatest_union_iff", "set.indicator_self_add_compl_apply", "nat.sub_lt_sub_left_iff", "affine_subspace.span_Union", "measurable.neg", "circle_deg1_lift.floor_map_map_zero_le", "pnat.gcd_rel_right", "finsupp.ker_lsingle", "differentiable_on.const_smul", "mvqpf.cofix.dest_mk", "norm_eq_zero", "list.sum_join", "filter.comap_comap", "multiset.nodup_ext", "ite_mul_one", "exists_open_with_compact_closure", "lie_group_core.to_lie_group", "ordinal.power_le_power_iff_right", "is_open_empty", "power_series.inv_mul", "finset.sum_piecewise", "subsemiring.closure_eq", "lower_bounds_Ico", "nat.pow_right_strict_mono", "ennreal.mul_max", "set.preimage_add_right_zero", "pow_eq_zero'", "list.append_eq_nil", "local_homeomorph.of_set_source", "finset.prod_product'", "has_deriv_at.div", "differentiable_within_at.sum", "localization_map.map_map", "onote.repr_power", "quotient.lift_beta", "tsum_nonpos", "list.nodupkeys_cons", "prod.fst_swap", "set.image_swap_eq_preimage_swap", "zmod.cast_int_cast", "subalgebra.list_sum_mem", "mv_polynomial.eval_rename_prodmk", "opposite.unop_inv", "submonoid.le_comap_of_map_le", "filter.add_assoc", "matrix.is_unit_nonsing_inv_det", "fin.sum_univ_cast_succ", "cardinal.omega_le_aleph'", "ideal.quotient.maximal_of_is_field", "category_theory.functor.equiv_functor_map", "is_R_or_C.abs_cast_nat", "polynomial.induction_on'", "polynomial.leading_coeff_comp", "bilin_form.zero_right", "multilinear_map.continuous_of_bound", "prime_spectrum.zero_locus_empty_iff_eq_top", "category_theory.limits.prod.associator_hom", "units.coe_gpow", "inv_lt_inv'", "mem_segment_translate", "cardinal.mk_bounded_subset_le", "punit.inv_eq", "norm_num.le_neg_pos", "stream.unfolds_head_eq", "finmap.keys_val", "seq.of_list_append", "filter.Liminf_le_Liminf_of_le", "omega.symmod_add_one_self", "nat.to_add_pow", "list.sublists'_reverse", "iterated_deriv_succ'", "submodule.neg_mem_iff", "right_ord_continuous.comp", "filter.eventually.prod_mk_nhds", "abelianization.lift.of", "multiset.eq_repeat'", "set.Ioc_inter_Ioc", "polynomial.div_by_monic_one", "set.preimage_bInter", "equiv.coe_mul_right", "pnat.one_coprime", "algebraic_geometry.PresheafedSpace.id_c_app", "category_theory.limits.cocones.whiskering_equivalence_functor", "submodule.lt_iff_le_and_exists", "matrix.to_lin_one", "is_irreducible.nonempty", "pgame.domineering.move_left_smaller", "pnat.one_gcd", "add_subgroup.mem_inf", "set.mk_preimage_prod_left_eq_if", "Ioo_mem_nhds_within_Ici", "category_theory.preadditive.comp_neg", "measure_theory.tendsto_measure_Union", "pgame.left_response_spec", "times_cont_diff_at.neg", "differentiable.cos", "Module.monoidal_category.pentagon", "category_theory.equivalence.equivalence_mk'_unit_inv", "matrix.range_diagonal", "presented_group.to_group.unique", "add_semiconj_by.zero_left", "cardinal.lift_mk_eq", "continuous_linear_equiv.coe_fn_of_bijective", "le_add_of_sub_right_le", "self_div_two_le_harmonic_two_pow", "fixed_points.next_eq", "le_of_mul_le_mul_left", "tendsto_locally_uniformly_on_univ", "has_fderiv_within_at_id", "continuous_linear_equiv.comp_times_cont_diff_on_iff", "list.perm.product_left", "measure_theory.simple_func.const_mul_eq_map", "list.mem_permutations_aux2'", "nat.succ_add", "not_exists_not", "pos_num.divmod_to_nat", "padic_norm_e.nonarchimedean'", "fact.bit1.pos", "measure_theory.ae_eq_fun.lintegral_zero", "list.eq_nil_of_suffix_nil", "is_R_or_C.of_real_bit1", "set.inj_on.right_inv_on_of_left_inv_on", "multiset.union_le", "add_units.min_coe", "set.preimage_mul_const_Icc_of_neg", "metric.dist_le_diam_of_mem", "measure_theory.lintegral_congr", "cardinal.mk_range_eq_lift", "not_surjective_fintype_infinite", "measurable_to_encodable", "or_iff_not_and_not", "lagrange.eq_zero_of_eval_eq_zero", "set.image_mul_right'", "quadratic_form.map_zero", "nat.elim_succ", "typevec.typevec_cases_nil\:2082_append_fun", "fintype.prod_eq_one", "category_theory.op_equiv_symm_apply", "has_fderiv_within_at.sub_const", "is_irreducible.image", "primrec_pred.comp", "typevec.drop_fun_id", "is_greatest_pair", "cardinal.pow_le", "zsqrtd.sqrtd_im", "prod.lt_def", "polynomial.coeff_sub", "local_equiv.prod_trans", "nonempty_quotient_iff", "is_basis.total_comp_repr", "function.is_periodic_pt.apply", "supr_range", "list.length_concat", "asymptotics.is_O_snd_prod'", "concave_on.convex_hypograph", "vector.to_list_map", "filter.eventually_of_mem", "rat.mul_self_num", "mul_mul_inv_of_self_cancel", "ideal.quotient_inf_to_pi_quotient_bijective", "inducing_is_closed", "znum.zneg_pred", "filter.eventually_eq.is_min_filter_iff", "add_one_pow_unbounded_of_pos", "filter.has_basis.lift", "set.eq_preimage_subtype_val_iff", "nat.le_rec_on_succ'", "equiv.coe_plift", "measure_theory.lintegral_supr_directed", "filter.preimage_mem_comap", "fixed_points.is_integral", "emetric.nonempty_compacts.to_closeds.uniform_embedding", "normed_group.tendsto_nhds_zero", "iterated_fderiv_zero_apply", "znum.cast_bit0", "mvqpf.cofix.dest_corec\:2081", "is_add_submonoid.smul_coe", "measure_theory.induced_outer_measure_eq_infi", "category_theory.nat_trans.exchange", "compact_iff_compact_univ", "convex.norm_image_sub_le_of_norm_deriv_within_le", "digits_of_digits", "padic_int.norm_lt_one_mul", "multiset.nodup_range", "multiset.to_finset_nsmul", "filter.eventually_eq.add", "turing.tr_eval_dom", "array.to_list_length", "bilin_form.neg_right", "uniformity_prod", "omega.nat.exists_clause_holds_core", "finset.sum_ite_eq'", "seq1.map_id", "measure_theory.simple_func.coe_mul", "list.cons_injective", "pnat.xgcd_type.is_special_iff", "image_le_of_deriv_right_lt_deriv_boundary'", "is_preconnected_iff_preconnected_space", "affine_subspace.mk'_nonempty", "add_submonoid.localization_map.add_equiv_of_add_equiv_mk'", "finset.fold_singleton", "affine_subspace.coe_direction_eq_vsub_set", "times_cont_diff.times_cont_diff_fderiv_apply", "continuous_on_id", "char_zero_of_inj_zero", "filter.infi_sets_eq", "local_equiv.refl_target", "finset.nonempty_encodable", "digits_eq_nil_iff_eq_zero", "deriv_within_inv", "t2_separation", "neg_le_sub_right_of_le_add", "list.kerase_nil", "cardinal.lift_nat_cast", "int.coe_nat_le", "turing.list_blank.induction_on", "continuous_linear_map.is_complete_ker", "num.shiftl_to_nat", "real.sin_pi_over_two_pow_succ", "list.perm.kreplace", "finset.mem_of_min", "nat.lt_iff_le_not_le", "num.gcd_to_nat_aux", "times_cont_mdiff_within_at_inter", "category_theory.discrete.equivalence_unit_iso", "quotient_group.coe_pow", "mv_polynomial.eval\:2082_eq_eval_map", "omega.int.push_neg_equiv", "pgame.lt_iff_le_not_le", "function.surjective.exists", "list.disjoint_append_left", "prime_multiset.prod_dvd_iff'", "equiv.arrow_congr'_symm", "category_theory.monoidal.tensor_obj_map", "znum.cast_lt", "quotient_add_group.eq_class_eq_left_coset", "filter.tendsto_at_top_add_const_right", "tendsto_neg_nhds_within_Ioi", "add_subgroup.coe_top", "mem_uniformity_is_closed", "finset.mem_powerset", "multiset.sub_cons", "functor.comp.seq_pure", "seq.head_dropn", "finite_dimensional.findim_eq_dim", "list.last_mem", "times_cont_diff_within_at_inter", "category_theory.limits.biprod.hom_ext'", "tactic.ring_exp.simple_pf_exp_one", "nnreal.div_eq_div_iff", "multiset.mem_join", "polynomial.monic.nat_degree_mul", "category_theory.functor.cocones_obj", "dense_sInter_of_open", "function.injective.map_at_top_finset_prod_eq", "multiset.nat.nodup_antidiagonal", "uniform_space.separation_prod", "nat.sub_mono_left_strict", "set.Ici_top", "linear_equiv.symm_apply_eq", "is_coprime.dvd_of_dvd_mul_left", "set.union_subset_union_left", "tsum_eq_single", "finset.prod_dvd_of_coprime", "le_neg_add_iff_add_le", "left_ord_continuous.mono", "ordinal.deriv_limit", "subsemiring.add_mem", "cSup_inter_le", "ring.fractional_ideal.mem_zero_iff", "add_monoid.closure_singleton", "measure_theory.measure.restrict_zero", "computation.lift_rel_return_left", "multiset.subset.trans", "nat.prime.multiplicity_self", "znum.lt_to_int", "mem_closure_iff_nhds_within_ne_bot", "set.diff_subset_iff", "gaussian_int.norm_le_norm_mul_left", "mem_lower_bounds", "prod.ext", "measure_theory.measure.dirac_bind", "int.of_nat_eq_coe", "lucas_lehmer.s_zmod_eq_s", "measure_theory.outer_measure.trim_trim", "exp_neg_inv_glue.f_aux_deriv", "list.tail_sum", "ennreal.sub_eq_zero_of_le", "category_theory.faithful.of_comp_iso", "times_cont_mdiff_on_of_locally_times_cont_mdiff_on", "ring_hom.codomain_trivial_iff_range_trivial", "category_theory.limits.cones.forget_obj", "mul_le_of_le_inv_mul", "finset.sum_update_of_mem", "measure_theory.measure_bUnion", "submodule.prod_equiv_of_is_compl_symm_apply_fst_eq_zero", "function.injective.comp_inj_on", "is_lub_pair", "vector.nth_update_nth_of_ne", "subsemiring.srange_subtype", "opposite.unop_op", "category_theory.nat_iso.op_hom", "is_local_max_on.is_local_max", "pfun.core_res", "monoid_algebra.lift_unique'", "set.Union_add_left_image", "pequiv.symm_single", "ordinal.one_lt_omega", "lie_subalgebra.ext", "rel_iso.symm_apply_apply", "complex.lim_eq_lim_im_add_lim_re", "one_div_mul_sub_mul_one_div_eq_one_div_add_one_div", "is_R_or_C.inv_zero", "submodule.quot_equiv_of_eq_bot_symm_apply", "rat.coe_int_inj", "norm_num.dvd_eq_nat", "list.mfoldr_cons", "list.cons_sublist_cons_iff", "Sup_Prop_eq", "mv_polynomial.C_inj", "neg_le", "differentiable_within_at.comp'", "list.forall\:2082_zip", "submodule.range_of_le", "is_least.union", "nat.fact_dvd_fact", "real.sqrt_mul_self", "topological_fiber_bundle_core.local_triv_trans", "list.traverse_append", "int.mul_lt_mul_of_neg_left", "right_ord_continuous.iterate", "nat.choose_succ_self_right", "pmf.coe_le_one", "ideal.map_comap_le", "set.add_singleton", "category_theory.action_category.hom_as_subtype", "approximates_linear_on.mono_num", "is_extr_on.on_preimage", "monoid_hom.to_fun_eq_coe", "lcm_eq_one_iff", "list.ext", "ring_hom.map_eq_zero", "le_cinfi", "linear_map.neg_apply", "real.sin_pi_div_two", "list.nodup_diff", "pequiv.equiv_to_pequiv_to_matrix", "is_greatest.unique", "is_basis_empty_bot", "list.chain'.append_overlap", "stream.drop_drop", "is_local_min.sup", "is_linear_map.mk'_apply", "norm_num.le_bit1_bit1", "seq.tail_nil", "uniform.continuous_on_iff'_right", "lipschitz_with.diam_image_le", "times_cont_diff_at_top", "turing.eval_maximal\:2081", "tensor_algebra.\[Iota]_comp_lift", "int.neg_succ_of_nat_eq", "matrix.comp_to_matrix_mul", "filter.lift_le", "hyperreal.gt_of_tendsto_zero_of_neg", "computable.id", "is_irreducible_iff_sUnion_closed", "measure_theory.l1.simple_func.uniform_embedding", "localization.ring_equiv_of_quotient_apply", "nat.dvd_fact", "is_coprime.of_prod_right", "equiv.perm.sign_swap", "polynomial.coeff_monomial_mul", "finset.image_inter", "real.exp_monotone", "finset.le_inf_iff", "list.perm.filter", "ennreal.tendsto_of_real", "set.indicator_mul", "ne_zero_of_lt", "filter.mem_binfi", "metric.Hausdorff_dist_comm", "is_min_on.max", "add_monoid_hom.map_add_neg", "add_submonoid.le_comap_of_map_le", "succ_nsmul'", "filter.tendsto_at_bot_of_add_bdd_below_left'", "norm_num.pow_bit1", "lt_mem_nhds", "equiv.symm_trans", "filter.Inter_mem_sets", "category_theory.op_op_equivalence_inverse", "pmf.bind_comm", "measure_theory.outer_measure.is_caratheodory_compl_iff", "inner_product_geometry.angle_neg_neg", "invariant_basis_number_field", "function.embedding.coe_image", "cardinal.power_mul", "add_monoid_algebra.mul_def", "pequiv.trans_bot", "affine.simplex.monge_plane_comm", "pow_pos", "fixed_points.minpoly.minimal_polynomial", "algebraic_geometry.PresheafedSpace.mk_coe", "list.foldl_assoc", "multiset.mem_product", "deriv.lhopital_zero_nhds", "ideal.quotient.maximal_ideal_iff_is_field_quotient", "mul_gpow", "filter.tendsto_at_bot_embedding", "localization.induction_on", "complex.tan_conj", "is_R_or_C.bit0_im", "supr_apply", "nat.zero_lt_bit1", "computation.lift_rel_bind", "ordinal.power_right_inj", "frontier_Ioo", "category_theory.limits.pushout_cocone.mk_\[Iota]_app_right", "znum.zneg_pos", "localization_map.algebra_map_eq", "ring.fractional_ideal.zero_le", "lt_neg_of_lt_neg", "times_cont_mdiff_at.prod_mk", "category_theory.limits.kernel_is_iso_comp_inv_comp_kernel_\[Iota]", "convex.combo_affine_apply", "list.eq_of_sublist_of_length_le", "padic.of_rat_eq", "linarith.le_of_le_of_eq", "nat.prime.dvd_choose_self", "cardinal.mk_quotient_le", "refl_mem_uniformity", "multiset.sections_zero", "fib_is_sol_fib_rec", "let_eq", "set.preimage_add_const_Iic", "submodule.nonzero_mem_of_bot_lt", "smooth_within_at_const", "add_magma.free_add_semigroup.of_add_assoc", "valuation.coe_coe", "gaussian_int.to_real_im", "padic_norm_z.padic_norm_e_of_padic_int", "Algebra.of_self_iso_inv", "category_theory.monad.algebra.hom.comp_f", "filter.germ.coe_eq", "sup_eq_right", "many_one_degree.le_refl", "set.image_neg_Ici", "continuous_multilinear_map.norm_image_sub_le_of_bound", "real.sqrt_inj", "set.Ico_subset_Icc_union_Ioo", "ennreal.div_zero_iff", "nnreal.continuous.sub", "real.tan_nonneg_of_nonneg_of_le_pi_div_two", "finset.card_attach_fin", "gpow_mul_comm", "ennreal.tendsto.mul", "monoid_hom.comap_ker", "multiplicity.finite_int_iff_nat_abs_finite", "add_subgroup.closure_union", "inf_Sup_eq", "strict_weak_order.erefl", "mem_nhds_left", "category_theory.equivalence.symm_inverse", "or_eq_of_eq", "category_theory.limits.pushout_cocone.mk_\[Iota]_app_zero", "set.Ico_subset_Ico_left", "continuous_linear_map.op_norm_neg", "set.prod_image_seq_comm", "real.cau_seq_converges", "mat_poly_equiv_symm_apply_coeff", "pnat.mul_div_exact", "if_eq_of_eq_false", "list.sum_smul", "pnat.ne_zero", "real.one_le_exp", "measure_theory.measure.mem_cofinite", "submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul", "pgame.equiv_refl", "is_bounded_bilinear_map.is_bounded_linear_map_deriv", "subtype.connected_space", "ideal.is_jacobson_iff_Inf_maximal", "pgame.mk_add_move_left_inl", "subring.ext'", "add_submonoid.localization_map.lift_comp", "turing.reaches\:2081_eq", "polynomial.aeval_alg_hom_apply", "dense_embedding.inj_iff", "filter.tendsto_at_bot_at_bot_iff_of_monotone", "nhds_of_nhds_within_of_nhds", "neg_lt_zero", "subgroup.coe_supr_of_directed", "uniform_continuous_fst", "submodule.quotient.nontrivial_of_lt_top", "dvd_sub", "ordinal.CNF_ne_zero", "euclidean_domain.mul_right_not_lt", "measure_theory.integral_smul_measure", "ordinal.power_one", "category_theory.category_of_elements.to_comma_map", "nat.mul_self_lt_mul_self", "complex.sum_div_fact_le", "set.countable.mono", "is_basis.to_dual_range", "category_theory.limits.colimit.pre_post", "is_R_or_C.two_ne_zero", "filter.map_mono", "list.exists_chain_of_relation_refl_trans_gen", "fract_eq_fract", "formal_multilinear_series.change_origin_summable_aux3", "continuous_linear_map.smul_right_one_pow", "real.sin_pi_sub", "ideal.radical_eq_jacobson", "associates.mk_eq_zero", "real.sqrt_mul_self_eq_abs", "add_monoid_hom.map_indicator", "submonoid.closure_Union", "nonneg_add_comm_group.zero_lt_iff_nonneg_nonneg", "uniform_space.completion.induction_on\:2082", "topological_group.t1_space", "function.cantor_surjective", "prod.snd_inv", "lie_algebra.orthogonal.indefinite_diagonal_assoc", "ring.direct_limit.of_injective", "gcd_eq_normalize", "measure_theory.simple_func.piecewise_univ", "semidirect_product.lift_inr", "multiplicity.one_left", "category_theory.iso.comp_inv_eq", "le_is_glb_iff", "sum.swap_swap", "subalgebra.neg_mem", "exp_neg_inv_glue.nonneg", "real.volume_Ioc", "multiset.fold_hom", "free_magma.map_of", "list.nth_le_reverse_aux1", "lie_algebra.special_linear.sl_non_abelian", "pnat.pos", "subring.prod_mono_left", "cauchy_seq_tendsto_of_is_complete", "euclidean_domain.gcd_self", "nnreal.sub_sub_cancel_of_le", "pnat.not_prime_one", "submodule.smul_sup", "filter.mem_infi_finite", "is_max_on_const", "nnreal.inv_one", "finset.mem_erase_of_ne_of_mem", "partrec.map_encode_iff", "ennreal.pow_ne_top", "pnat.Ico.mem", "convex.image_sub_lt_mul_sub_of_deriv_lt", "function.commute.iterate_pos_le_iff_map_le", "nat.one_div_le_one_div", "coe_nnnorm", "set.image_sub_const_Ioc", "has_strict_fderiv_at.is_O_sub_rev", "mul_left_continuous", "topological_space.open_nhds.map_id_obj", "measure_theory.measure.measure_univ_eq_zero", "mul_semiring_action_hom.id_comp", "real.sin_eq_zero_iff_of_lt_of_lt", "relator.rel_exists_of_left_total", "injective_of_increasing", "bitvec.to_nat_append", "add_con.to_setoid_inj", "uniform_continuous_iff_eventually", "galois_connection.dfun", "real.uniform_continuous_inv", "category_theory.equivalence.cancel_unit_right_assoc'", "findim_vector_span_of_affine_independent", "list.sublist_of_infix", "mul_self_add_mul_self_eq_zero", "multiplicity.eq_top_iff", "multiset.disjoint_comm", "equiv.set.sum_compl_apply_inr", "subgroup.inv_mem_iff", "finset.prod_attach_univ", "prod.ext_iff", "is_max_on.localize", "polynomial.restriction_one", "filter.tendsto_at_bot_add", "list.nil_bind", "category_theory.limits.prod_left_unitor_inv_naturality", "measure_theory.simple_func.map_apply", "ennreal.max_eq_zero_iff", "subset_span_points", "polynomial.dvd_term_of_is_root_of_dvd_terms", "is_min_on.is_extr", "matrix.rank_diagonal", "set.interval_of_lt", "finset.disjoint_union_right", "rat.cast_mul", "zsqrtd.norm_one", "coe_homeomorph_of_strict_mono_continuous", "finset.prod_equiv", "not_nonempty_fintype", "open_subgroup.one_mem", "vsub_left_cancel", "d_array.of_beq_eq_tt", "roption.get_some", "Module.monoidal_category.tensor_id", "asymptotics.is_o_one_iff", "linear_map.trace_aux_range", "stream.homomorphism", "submodule.colon_mono", "real.pi_gt_sqrt_two_add_series", "add_con.ext'", "finset.sum_eq_zero_iff", "finset.set_of_mem", "fin.coe_cast", "band_coe_iff", "set.finite.convex_hull_eq_image", "subring.coe_int_mem", "Top.presheaf.pushforward.comp_inv_app", "ennreal.inv_ne_zero", "bxor_ff", "padic_int.exists_mem_range", "asymptotics.is_o_iff_tendsto", "two_pos", "differentiable_at_snd", "stream.tail_even", "set.finite_bind", "padic_norm_e.image", "pequiv.single_subsingleton_eq_refl", "con.coe_mul", "finset.prod_add", "dfinsupp.mk_sub", "list.length_bind", "rel.inv_inv", "iterated_fderiv_within_inter_open", "free_add_magma.traverse_add'", "polynomial.splits_mul_iff", "semiconj_by.neg_right", "exists_is_basis_fintype", "int.to_nat_sub", "num.cast_inj", "list.last_concat", "tsum_of_norm_bounded", "map_nhds_within", "category_theory.limits.types.colimit_equiv_quot_symm_apply", "category_theory.limits.fork.app_zero_right", "hyperreal.coe_mul", "list.last'_is_some", "category_theory.monoidal_functor.map_tensor", "algebra.adjoin_algebra_map", "polynomial.aeval_C", "measure_theory.restrict_mono_ae", "metric.exists_dist_lt_of_Hausdorff_dist_lt'", "measurable_snd", "add_con.le_def", "int.modeq.modeq_of_modeq_mul_left", "algebraic_closure.coe_to_step_of_le", "submodule.prod_top", "multiset.map_eq_zero", "list.erase_dup_cons_of_not_mem", "sym2.from_rel_irreflexive", "commute.inv_left", "finsupp.mem_support_finset_sum", "iterated_deriv_eq_iterated_fderiv", "to_bool_congr", "algebra.smul_def", "finsupp.ext_iff", "tendsto_at_top_add_tendsto_right", "local_homeomorph.restr_univ", "dim_quotient_le", "nat.pred_eq_sub_one", "dioph.dvd_dioph", "monoid_algebra.of_apply", "list.map_singleton", "pgame.first_loses_of_equiv_iff", "galois_connection.lower_bounds_u_image_subset", "padic_int.mod_part_lt_p", "list.infix_iff_prefix_suffix", "eq_div_iff", "add_commute.add_right", "le_of_mul_le_mul_right'", "nat.lt_pow_self", "local_homeomorph.to_homeomorph_symm_coe", "one_le_padic_val_nat_of_dvd", "iterated_fderiv_apply_eq_iterated_deriv_mul_prod", "polynomial.eval\:2082_X_pow", "times_cont_diff_within_at_inter'", "add_comm_group.direct_limit.of_f", "filter.inter_mem_sets", "subgroup.comap_inf", "measure_theory.measure.count_apply_eq_top", "stream.map_id", "quotient_group_saturate", "nat.subtype.of_nat_surjective", "nat.min_fac_aux_has_prop", "pell.is_pell_nat", "set_coe_cast", "times_cont_mdiff_within_at.times_cont_mdiff_at", "category_theory.limits.image_mono_iso_source_hom_self_assoc", "list.head_le_sum", "category_theory.tensoring_right_monoidal_\[CurlyEpsilon]_is_iso", "category_theory.sum.associator_obj_inl_inl", "ring_hom.one_def", "asymptotics.is_O_with_of_le'", "int.sub_nat_nat_of_lt", "pell.yn_succ_succ", "pfunctor.M.agree_iff_agree'", "nat.bit_le_bit1", "int.normalize_of_nonneg", "power_series.eq_zero_or_eq_zero_of_mul_eq_zero", "circle_deg1_lift.semiconj_by_iff_semiconj", "nnreal.ne_iff", "continuous_multilinear_map.norm_map_snoc_le", "ennreal.tsum_sigma'", "set.surjective_onto_image", "measure_theory.simple_func.piecewise_apply", "complex.of_real_tanh_of_real_re", "sub_le_self", "Sup_pair", "vector.head_cons", "measure_theory.ae_eq_fun.mk_le_mk", "pnat.dvd_iff", "int.eq_one_of_mul_eq_self_right", "has_strict_fderiv_at.const_sub", "category_theory.abelian.image_\[Iota]_eq_image_\[Iota]", "polynomial.separable_def'", "continuous_linear_map.coe_id'", "eq_add_of_sub_eq'", "measure_theory.lintegral_zero", "multiset.product_singleton", "with_zero.coe_inv", "coe_of_digits", "bex.intro", "asymptotics.is_o.join", "filter.realizer.mem_sets", "padic_norm_e.eq_rat_norm", "euclidean_geometry.angle_eq_zero_of_angle_eq_pi_right", "relator.left_unique_flip", "semidirect_product.inl_aut", "list.kinsert_def", "one_lt_div", "Ioc_mem_nhds_within_Ioi", "semiconj_by.sub_left", "smodeq.refl", "eq_of_eqv_lt", "filter.is_bounded.is_cobounded_flip", "cardinal.add_lt_omega", "subring.closure_le", "set.eq_on.bij_on_iff", "open_subgroup.coe_subgroup_le", "one_left_coset", "localization.mk_one_eq_monoid_of_mk", "cardinal.mul_lt_omega_iff_of_ne_zero", "submodule.mk_quotient_equiv_of_is_compl_apply", "real.cos_arctan", "finset.min'_le", "nat.size_zero", "con.ext_iff", "finset.cons_eq_insert", "list.prod_nil", "nnreal.of_real_mono", "card_pow_eq_one_eq_order_of_aux", "nat.fib_zero", "list.length_pos_of_mem", "has_deriv_within_at.mul", "tactic.abel.term_atomg", "continuous_linear_equiv.symm_comp_self'", "vsub_mem_vector_span", "euclidean_geometry.orthogonal_projection_mem", "nonpos_of_mul_nonpos_right", "function.injective.nonempty_apply_iff", "pell.eq_pell_lem", "category_theory.functor.unop_obj", "euclidean_domain.mul_div_assoc", "complex.cosh_neg", "polynomial.splitting_field_aux.splits", "ennreal.continuous_const_mul", "metric.mem_closure_range_iff", "has_fderiv_at_filter.const_smul_algebra", "submodule.coe_zero", "add_pos_of_pos_of_nonneg", "finset.sum_lt_sum_of_nonempty", "int.bit0_nonneg", "zero_le_mul_right", "polynomial.not_irreducible_C", "matrix.to_blocks_from_blocks\:2081\:2082", "set.range_sigma_mk", "dist_vadd_cancel_right", "ideal.radical_eq_Inf", "card_perms_of_finset", "list.sum_range_succ", "set.mem_of_mem_diff", "continuous_on_const", "fin.succ_above_pos", "filter.germ.comp_tendsto'_coe", "continuous_linear_map.has_deriv_at", "complex.lim_im", "multiset.antidiagonal_map_snd", "isometric.point_reflection_dist_fixed", "or_congr", "submonoid.localization_map.mk'_sec", "computation.destruct_ret", "tendsto_pure_nhds", "ideal.radical_mul", "set.Iio_union_right", "poly.isp", "category_theory.monad.forget_creates_colimits.cocone_point_a", "submodule.span_empty", "measure_theory.measure.compl_mem_cofinite", "rank_le_domain", "norm_num.mul_pos_neg", "set.subset_bUnion_of_mem", "dfinsupp.sum_add_index", "category_theory.monoidal_category.unitors_equal", "if_eq_of_eq", "num.lxor_to_nat", "subsemiring.list_prod_mem", "ring.direct_limit.of_add", "filter.has_basis.forall_nonempty_iff_ne_bot", "model_with_corners_prod_coe", "formal_multilinear_series.comp_change_of_variables_blocks_fun", "functor.comp.id_map", "differentiable_at.csin", "nat.lt_sub_left_of_add_lt", "convex.is_linear_preimage", "mv_polynomial.ext_iff", "filter.has_basis.mem_of_superset", "set.one_mem_one", "add_units.max_coe", "category_theory.equivalence.fun_inv_map", "free_abelian_group.lift.add'", "gcd_monoid.irreducible_iff_prime", "prod_mk_sum", "nat.succ_le_of_lt", "linear_map.ker_pi", "polynomial.card_nth_roots", "unique.ext_iff", "measurable_space.map_id", "mul_inv_of_mul_self_cancel", "finset.erase_empty", "equiv.perm.cycle_of_one", "list.revzip_swap", "measure_theory.l1.eq", "opposite.unop_mul", "is_coprime_zero_right", "computation.get_equiv", "qpf.mem_supp", "category_theory.monoidal_functor.map_right_unitor", "cardinal.power_lt_omega", "has_deriv_at.pow", "category_theory.monoidal_category.left_unitor_conjugation", "abs_sub_le_iff", "Ico_map_val_min_abs_nat_abs_eq_Ico_map_id", "submodule.comap_comp", "commute.gpow_self", "subring.closure_union", "add_monoid_hom.range_eq_map", "contracting_with.efixed_point_eq_of_edist_lt_top", "rel_embedding.map_rel_iff", "vector.nth_tail", "onote.oadd_mul", "with_top.coe_le_iff", "computation.mem_bind", "is_measurable_interval", "equiv.to_embedding_coe_fn", "nnreal.rpow_le_one_of_one_le_of_nonpos", "ring_equiv.image_eq_preimage", "vsub_right_cancel_iff", "zero_lt_one", "set.empty_diff", "quotient_map.of_quotient_map_compose", "real.le_sqrt_of_sqr_le", "setoid.eq_eqv_class_of_mem", "mul_div_right_comm", "function.semiconj.maps_to_fixed_pts", "continuous_linear_equiv.coord_self", "real.inner_le_Lp_mul_Lq_of_nonneg", "padic_norm_e.add", "fin.mk_one", "measure_theory.l1.simple_func.of_simple_func_smul", "measure_theory.dirac_ae_eq", "has_fderiv_at_filter.prod", "category_theory.coe_id", "injective_of_affine_independent", "iff.elim_right", "set.Inter_eq_Inter_finset'", "measure_theory.measure.haar.prehaar_sup_le", "list.map_subset", "mv_power_series.coeff_inv", "times_cont_diff_of_differentiable_iterated_deriv", "measure_theory.ae_eq_fun.lift_rel_iff_coe_fn", "free_group.red.not_step_singleton", "int.neg_succ_of_nat_lt_zero", "traversable.fold_map_hom", "dist_le_tsum_dist_of_tendsto\:2080", "vector3.cons_fs", "submonoid.localization_map.mul_equiv_of_mul_equiv_eq_map_apply", "category_theory.limits.im_obj", "int.neg_nonpos_of_nonneg", "mem_interior_iff_mem_nhds", "nat.lt_of_lt_of_le", "set.eq_empty_of_subset_empty", "set.preimage_neg_Ioc", "sub_lt_sub", "multiset.card_cons", "category_theory.comma.map_left_comp_inv_app_left", "zsqrtd.zero_re", "zsqrtd.sq_le_add", "polynomial.nat_degree_mul'", "affine_map.to_fun_eq_coe", "multiset.coe_card", "polynomial.frange_of_subring", "ennreal.top_div", "continuous_on_Icc_extend_from_Ioo", "ideal.eq_jacobson_iff_Inf_maximal'", "Group.coe_of", "filter_basis.mem_filter_iff", "asymptotics.is_o_norm_right", "category_theory.limits.map_pair_iso_inv", "affine.triangle.orthocenter_mem_affine_span", "list.find_eq_none", "monoid_hom.prod_map_def", "cau_seq.not_lim_zero_of_pos", "finset.infi_finset_image", "tsum_subtype", "Algebra.coe_comp", "ideal.one_eq_top", "gaussian_int.nat_abs_norm_mod_lt", "primrec.option_is_some", "list.map_take", "infi_split", "mul_lt_mul_right", "min_le_right_of_le", "set.interval_self", "category_theory.pi.sum_obj_obj", "real.cos_ne_zero_iff", "equiv.trans_assoc", "is_closed_map.comp", "omega.nat.preterm.val_add", "list.nodup_map", "measure_theory.norm_set_integral_le_of_norm_le_const_ae'", "nat.coprime.mul_right", "affine_subspace.span_union", "differentiable_on.fst", "metric.completion.uniform_continuous_dist", "set.le_eq_subset", "zero_eq_nndist", "mul_lt_iff_lt_one_left", "metric.frontier_ball_subset_sphere", "nat.sub_le_left_iff_le_add", "finset.mem_inter", "list.map_congr", "list.length_remove_nth", "nat.find_le", "continuous_multilinear_map.map_zero", "magma.free_semigroup.lift_unique", "function.commute.right_bij_on_fixed_pts_comp", "dvd_of_associated", "localization_map.of_id", "times_cont_diff.continuous_fderiv", "alg_equiv.to_fun_apply", "Module.Mon_Module_equivalence_Algebra.ring_add", "min_le_left", "mem_ball_comp", "complex.zero_re", "submonoid.mem_closure_singleton_self", "submonoid.mem_Sup_of_mem", "abs_inner_div_norm_mul_norm_eq_one_of_ne_zero_of_ne_zero_mul", "cardinal.sum_le_sup", "metric.Hausdorff_dist_empty'", "I_symm_one", "category_theory.limits.cocones.whiskering_obj", "cardinal.power_ne_zero", "measure_theory.outer_measure.exists_is_measurable_superset_of_trim_eq_zero", "category_theory.limits.limit.lift_\[Pi]_assoc", "fin.cons_snoc_eq_snoc_cons", "category_theory.arrow.w_assoc", "perfect_closure.quot_mk_eq_mk", "seq.exists_of_mem_map", "ring_hom.comp_apply", "edist_le_range_sum_of_edist_le", "list.all_cons", "simple_graph.adj_matrix_mul_vec_const_apply", "pequiv.coe_mk_apply", "list.count_cons_of_ne", "associates.prod_eq_zero_iff", "measurable_space.comap_comp", "filter.le_iff_forall_inf_principal_compl", "congr", "nnreal.summable_coe", "std_simplex_eq_inter", "filter.is_lawful_monad", "mv_power_series.trunc_C", "category_theory.currying_functor_obj_map", "tactic.ring.horner_add_horner_gt", "nat.mul_mod_mul_right", "list.length_iota", "category_theory.limits.coequalizer.cofork_\[Iota]_app_one", "local_equiv.inv_image_trans_target", "is_least.is_glb", "finset.subset.refl", "measure_theory.simple_func.restrict_preimage", "set.inv_on.symm", "nat.with_bot.lt_zero_iff", "monoid_hom.prod_comp_prod_map", "finset.insert_val", "topological_space.open_nhds.map_id_obj_unop", "of_endo_map_action", "strict_mono_of_monotone_of_injective", "onote.NF.of_dvd_omega_power", "interior_Ioi", "cluster_pt.ne_bot", "to_matrix_to_bilin_form", "finset.sum_attach_univ", "padic_val_rat.padic_val_rat_self", "finset.bind_subset_bind_of_subset_left", "opposite.op_eq_iff_eq_unop", "ideal.is_jacobson_iff_Inf_maximal'", "finset.Ico.succ_top", "polynomial.map_zero", "list.perm.union_left", "num.cast_to_nat", "list.length_foldr_permutations_aux2", "min_le_left_of_le", "mvpfunctor.map_obj_append1", "forall_true_iff'", "measure_theory.l1.simple_func.eq_iff", "equiv.image_eq_preimage", "set.range_inl_union_range_inr", "ball.imp_left", "equiv.is_lawful_functor", "real.sin_two_mul", "padic_int.valuation_nonneg", "is_cyclic_of_card_pow_eq_one_le", "nat.gcd_def", "set.Inter_eq_comp_Union_comp", "real.pow_arith_mean_le_arith_mean_pow", "int.sub_lt_sub", "one_one_reducible.to_many_one", "filter.tendsto_at_top_add_left_of_le'", "Liminf_nhds", "nsmul_nonneg", "Cauchy.Cauchy_eq", "local_homeomorph.eq_on_source_iff", "uniform_continuous.dist", "approximates_linear_on.antilipschitz", "zsqrtd.coe_int_im", "polynomial.eval_sum", "polynomial.monic.ne_zero_of_zero_ne_one", "is_lub.of_subset_of_superset", "set.finite.induction_on", "ring.fractional_ideal.div_nonzero", "category_theory.uncurry_natural_left_assoc", "state_t.run_pure", "commute.symm_iff", "linear_map.comp_zero", "add_eq_of_eq_sub", "associates.quot_mk_eq_mk", "set.surj_on.inter_inter", "list.reverse_core_eq", "measure_theory.l1.norm_of_fun_eq_lintegral_norm", "nat.zero_lt_bit0", "eq_neg_of_eq_neg", "is_bounded_linear_map.smul", "closure_Ioo", "onote.NF.of_dvd_omega", "bilin_form.comp_left_comp_right", "set.Iic_diff_Iio_same", "set.Ioo_subset_Ico_self", "nat.add_mod_eq_add_mod_right", "Lim_nhds_within", "fintype.card_congr", "power_series.coeff_X_pow_self", "category_theory.full_subcategory_inclusion.obj", "list.append_right_cancel", "finsupp.lmap_domain_supported", "edist_ne_top_of_mem_ball", "cardinal.mk_Prop", "wseq.join_cons", "ulift.smul_down'", "submodule.is_principal.generator_mem", "nat.div2_one", "real.arccos_eq_pi_div_two_sub_arcsin", "rel_iso.coe_fn_symm_mk", "hyperreal.infinite_iff_infinitesimal_inv", "dfinsupp.sum_single", "enat.add_right_cancel_iff", "is_bounded_linear_map.differentiable", "char_poly_map_eval_self", "category_theory.limits.pullback_cone.is_limit.hom_ext", "order_topology.t2_space", "hyperreal.infinite_pos_abs_iff_infinite_abs", "filter.rmap_rmap", "list.length_pos_of_sum_pos", "list.nodup_cons_of_nodup", "deriv_within_ccosh", "unique_mdiff_within_at.mono", "list.perm_comm", "free_add_monoid.lift_apply", "nhds_within_Ioi_ne_bot'", "turing.tape.map_move", "matrix.trace_one", "finite_dimensional.trans", "list.length_range", "nat.eq_mul_of_div_eq_left", "multiset.ndinter_cons_of_not_mem", "ring.fractional_ideal.span_singleton_zero", "sub_lt_iff_lt_add'", "submonoid.localization_map.to_map_injective", "filter.tendsto_Ixx_class_inf", "int.of_nat_dvd_of_dvd_nat_abs", "padic_int.mem_nonunits", "asymptotics.is_O.of_bound", "list.suffix_iff_eq_drop", "list.take_repeat", "int.sub_eq_add_neg", "category_theory.monoidal_category.triangle_assoc_comp_left", "metric.nonempty_ball", "nat.succ_pred_eq_of_pos", "nat.le_of_lt", "or_of_or_of_imp_left", "nat.mod_eq_zero_of_dvd", "complex.cos_pi_sub", "list.chain'.iff_mem", "filter.mp_sets", "list.unzip_zip_right", "cau_seq.eq_lim_of_const_equiv", "directed.mono", "exists_imp_exists", "category_theory.prod_comp_snd", "set.maps_to_sUnion", "category_theory.monoidal.Mon_functor_category_equivalence_functor", "is_extr_on_const", "is_group_hom.injective_of_trivial_ker", "topological_space.is_open_sUnion_countable", "cauchy_seq_finset_of_geometric_bound", "list.permutations_aux2_append", "semidirect_product.lift_comp_inr", "nat.Inf_le", "set.union_add", "adjoin_root.mk_self", "nat.gcd_dvd_gcd_of_dvd_left", "interval_integral.norm_integral_le_of_norm_le_const_ae", "zmod.eq_iff_modeq_nat", "monoid_hom.map_is_conj", "int.ldiff_bit", "bool.bxor_assoc", "normalize_one", "gaussian_int.nat_cast_complex_norm", "list.perm.kunion_right", "equiv.perm.disjoint_prod_right", "differentiable_at.iterate", "computation.ret_bind", "composition_as_set.to_composition_boundaries", "category_theory.discrete.equivalence_counit_iso", "add_subgroup.closure_le", "pfunctor.M.head_mk", "ordinal.lt_lift_iff", "is_local_min.on", "norm_num.clear_denom_add", "is_compact.nonempty_Inter_of_directed_nonempty_compact_closed", "continuous_pow", "mul_equiv.apply_symm_apply", "nat.bit_lt_bit_iff", "neg_mul_eq_neg_mul_symm", "is_open_union", "tactic.abel.term_neg", "subset_interior_iff_subset_of_open", "real.pi_lt_3141593", "nnreal.exists_le_has_sum_of_le", "mem_nhds_within_of_mem_nhds", "cau_seq.sub_lim_zero", "is_glb_Ioo", "localization_map.map_left_cancel", "cardinal.power_def", "affine.triangle.orthocenter_eq_smul_vsub_vadd_circumcenter", "local_equiv.map_source", "ctop.realizer.is_closed_iff", "circle_deg1_lift.map_sub_nat", "set.Iic_diff_right", "cardinal_le_dim_of_linear_independent'", "ennreal.tendsto.const_div", "encodable.encode_ff", "complex.differentiable_at_cosh", "ennreal.coe_sub", "complex.one_re", "category_theory.limits.pushout_cocone.mk_\[Iota]_app", "list.not_mem_nil", "prime_spectrum.le_vanishing_ideal_zero_locus", "add_subgroup.comap_inf", "fintype.pi_finset_univ", "induced_id", "localization.ring_equiv_of_quotient_symm_mk", "list.sorted_cons", "localization_map.lin_coe_apply", "list.ball_nil", "local_homeomorph.is_O_congr", "finsupp.sum_subtype_domain_index", "omega.coeffs.val_between_map_mul", "nnreal.of_real_lt_iff_lt_coe", "ring.fractional_ideal.coe_ne_bot_iff_nonzero", "function.injective.exists_ne", "ordinal.le_bsup", "le_iff_lt_or_eq", "one_half_lt_one", "multiset.map_subset_map", "nat.gcd_one_right", "multiset.filter_zero", "nat.succ_pos'", "add_submonoid.localization_map.add_equiv_of_localizations_symm_apply", "deriv_within_neg", "is_R_or_C.zero_re", "quotient_group.range_ker_lift_injective", "finsupp.antidiagonal_zero", "set.image_eta", "op_geom_series", "module.direct_limit.lift_unique", "set.bij_on_Inter", "list.bind_ret_eq_map", "centroid_mem_affine_span_of_nonempty", "int.neg_nat_succ", "set.interval_subset_interval_right", "category_theory.limits.is_limit.uniq_cone_morphism", "is_valid_char_range_1", "set.preimage_mul_const_Ioo", "wseq.head_some_of_head_tail_some", "nnreal.of_real_lt_of_real_iff'", "rat.uniform_continuous_add", "stream.unfolds_eq", "norm_num.int_mod_neg", "traversable.to_list_eq_self", "le_of_nhds_le_nhds", "padic_val_rat.padic_val_rat_of_int", "one_div", "category_theory.limits.limit.is_limit_lift", "filter.rtendsto_iff_le_comap", "category_theory.limits.prod.lift_comp_comp", "filter.lift_principal", "complex.I_ne_zero", "summable.mul_right", "padic_seq.norm_const", "list.unzip_nil", "rel_iso.map_rel_iff''", "mul_lt_one", "subtype.restrict_def", "with_one.coe_mul", "filter.tendsto_at_bot_of_add_const_right", "subring.map_bot", "measurable.nnreal_coe", "set.nonempty.snd", "set.image_const_sub_Iio", "polynomial.is_unit_map", "tensor_algebra.lift_unique", "add_group.gmultiples_eq_closure", "category_theory.monoidal.Mon_functor_category_equivalence_counit_iso", "differentiable.div_const", "tendsto_uniformly.tendsto_comp", "omega.nat.preterm.val_const", "cauchy_seq_iff_le_tendsto_0", "nat.sub_le_sub_left_iff", "max_min_distrib_right", "is_absolute_value.abv_pos", "mul_self_sub_one_eq", "quadratic_form.pos_def.smul", "monoid_hom.coe_fst", "dist_le_range_sum_dist", "mv_power_series.X_pow_eq", "lipschitz_with.weaken", "finset.prod_sdiff", "alg_hom.map_smul", "supr_eq_dif", "turing.TM1.stmts_supports_stmt", "finset.bUnion_coe", "onote.power_def", "filter.is_countably_generated_at_top", "int.coe_nat_add_out", "measurable_space.is_measurable_supr", "card_units_lt", "list.mem_of_mem_inter_right", "filter.tendsto.add", "dense_embedding_pure", "is_closed_property", "alt_bilin_form.neg", "continuous_ulift_up", "free_group.mul_mk", "game.add_le_add_left", "measurable_pi_lambda", "dioph.inject_dummies_lem", "category_theory.comonad.forget_map", "tactic.ring_exp.simple_pf_var_one", "int.nat_abs_bit1_nonneg_step", "localization_map.to_map_eq_zero_iff", "order_iso.to_galois_connection", "tactic.ring.horner_add_horner_lt", "inv_lt_of_neg", "zsqrtd.coe_int_sub", "submodule.coe_set_eq", "measure_theory.simple_func.lintegral_zero", "polynomial.derivative_sum", "list.mem_append_eq", "is_alg_closed.degree_eq_one_of_irreducible", "typevec.to_subtype_of_subtype", "set.preimage_sub_const_Ioo", "finset.filter_inter_filter_neg_eq", "differentiable_on.sinh", "sup_comm", "nat.test_bit_ldiff", "zmod.card_units", "list.range'_eq_map_range", "polynomial.exists_irreducible_of_degree_pos", "finset.bUnion_preimage_singleton", "linear_map.linear_proj_of_is_compl_of_proj", "finsupp.supported_Inter", "is_bounded_linear_map.fst", "zmod.trace_pow_card", "mv_power_series.coeff_zero_C", "metric.nhds_basis_ball_inv_nat_pos", "function.surjective.surj_on", "ennreal.rpow_eq_zero_iff", "bit0_zero", "ordinal.add_sub_add_cancel", "ring_hom.map_iterate_frobenius", "complex.abs_of_real", "matrix.empty_add_empty", "complex.conj_inj", "submodule.mem_sup_right", "mul_le_mul_three", "filter.univ_mem_sets", "inv_lt_one'", "submonoid.comap_infi", "matrix.proj_diagonal", "fin.eq_iff_veq", "submonoid.localization_map.sec_spec", "continuous.measurable2", "continuous_linear_equiv.has_strict_fderiv_at", "category_theory.over.colimit_\[Iota]_app", "differentiable_at.cexp", "option_t.run_pure", "measure_theory.simple_func.lintegral_restrict", "is_compact.inter_Inter_nonempty", "is_open_map_smul_of_ne_zero", "complex.exp_nat_mul", "emetric.ball_subset_closed_ball", "quadratic_form.lin_mul_lin_comp", "multiset.card_zero", "ennreal.of_real_le_iff_le_to_real", "continuous_linear_map.is_bounded_linear_map_comp_right", "with_zero.mul_right_inv", "continuous_linear_map.ext_iff", "deriv.lhopital_zero_at_top", "localization_map.integer_normalization_spec", "padic_norm_e.add_eq_max_of_ne", "mv_polynomial.C_0", "abs_pos_of_ne_zero", "lt_of_not_ge'", "monoid_algebra.mul_apply", "mul_le_iff_le_one_left", "Algebra.of_self_iso_hom", "mul_aut.inv_apply_self", "Mod.comp_hom'", "inner_product_geometry.angle_smul_right_of_pos", "with_top.add_top", "int.div_eq_of_eq_mul_right", "mv_polynomial.sum_to_iter_C", "list.kerase_append_right", "set.not_nonempty_iff_eq_empty", "monoid_algebra.mul_zero", "turing.eval_maximal", "equiv.coe_of_bijective", "fraction_map.num_mul_denom_eq_num_iff_eq'", "pgame.left_wins_of_equiv", "fin.vne_of_ne", "has_mfderiv_within_at_const", "lebesgue_number_lemma_of_metric_sUnion", "real.log_abs", "hyperreal.not_infinitesimal_of_infinite_neg", "is_max_on.is_local_max", "is_R_or_C.I_to_complex", "midpoint_self", "finset.choose_spec", "is_seq_closed_iff_is_closed", "is_R_or_C.of_real_alg", "set.mem_empty_eq", "category_theory.limits.pushout.hom_ext", "decidable_linear_ordered_add_comm_group.tendsto_nhds", "times_cont_diff.comp_continuous_linear_map", "linear_equiv.lie_conj_symm", "category_theory.Monad.to_of_mon_end_iso_inv_app_to_nat_trans_app", "nat.Inf_def", "measure_theory.ae_eq_fun.coe_fn_smul", "filter.is_countably_generated.exists_antimono_seq", "category_theory.adjunction.right_triangle_components", "continuous_at.continuous_within_at", "list.func.eq_of_equiv", "subsemiring.coe_map", "mul_ne_zero_iff", "free_ring.coe_mul", "qpf.fix.rec_eq", "category_theory.comma.map_left_obj_right", "continuous_sup_rng_right", "neg_add_eq_sub", "int.nat_abs_mul_self", "open_add_subgroup.mem_coe_add_subgroup", "nat.primes.coe_pnat_nat", "wseq.length_eq_map", "stream.approx_zero", "hash_map.valid.idx_enum_1", "eq_false_intro", "valuation.unit_map_eq", "min_eq_left_of_lt", "setoid.is_partition.pairwise_disjoint", "finset.subset_iff", "lower_bounds_mono", "measure_theory.outer_measure.Union", "lagrange.eval_interpolate", "quotient.rep_spec", "nat.size_one", "open_embedding_of_embedding_open", "submonoid.localization_map.mk'_self'", "set.mem_compl", "list.perm.eq_nil", "approximates_linear_on.to_local_homeomorph_coe", "filter.mem_bot_sets", "submodule.top_coe", "linear_map.image_convex_hull", "category_theory.abelian.pseudoelement.comp_apply", "fin.lt_iff_coe_lt_coe", "differentiable_within_at.smul_algebra", "with_top.add_one_le_of_lt", "roption.of_to_option", "principal_ideal_ring.irreducible_iff_prime", "separation_rel_comap", "list.sigma_nil", "subring.mem_Inf", "linear_equiv.map_zero", "filter.eventually_lift'_iff", "finset.mono_of_fin_eq_mono_of_fin_iff", "int.dvd_antisymm", "list.nil_subset", "nat.primrec'.prec'", "pgame.nim.non_zero_first_wins", "category_theory.limits.fork.app_zero_left", "multiset.card_smul", "bool.band_comm", "not_lt_of_gt", "equiv.sum_assoc_apply_in1", "finset.Ico.inter_consecutive", "padic_int.valuation_p_pow_mul", "set.mem_image_elim_on", "is_min_on_const", "sequentially_complete.seq_mem", "continuous_linear_map.comp_add", "hyperreal.coe_lt_coe", "has_strict_fderiv_at.continuous_at", "add_submonoid.mem_supr_of_directed", "free_group.reduce.rev", "ring_equiv.map_sub", "rel_iso.injective", "finset.range_subset", "seq.nth_tail", "nat.succ_div_of_not_dvd", "circle_deg1_lift.translate_iterate", "metric.completion.dist_self", "ennreal.of_real_add", "units.conj_pow", "pequiv.trans_eq_some", "fpow_injective", "measure_theory.integral_finset_sum", "category_theory.limits.biprod.braiding'_inv", "fderiv_sub", "tendsto_subseq_of_bounded", "multiset.mem_inter", "category_theory.limits.image.eq_fac", "has_fderiv_at.continuous_at", "lie_neg", "ceil_le", "category_theory.non_preadditive_abelian.\[Sigma]_comp", "fin.is_lt", "set.image_const_add_Ioo", "measure_theory.measure.haar.prehaar_empty", "finmap.erase_to_finmap", "filter.mem_supr_sets", "directed_on.mono", "Cauchy.separated_pure_cauchy_injective", "ideal.le_jacobson", "list.lookup_ext", "alg_hom.ext_iff", "finset.union_eq_empty_iff", "measurable_equiv.trans_to_equiv", "has_ftaylor_series_up_to.has_ftaylor_series_up_to_on", "uniform_embedding.dense_embedding", "finmap.induction_on", "measurable.is_lub", "measure_theory.measure.haar_outer_measure_pos_of_is_open", "structure_groupoid.local_invariant_prop.lift_prop_within_at_mono", "deriv_within_sin", "ne_false_of_self", "semiquot.mem_pure", "monoid_hom.coe_mrange", "ideal.span_singleton_lt_span_singleton", "category_theory.is_equivalence.inv_fun_map", "nsmul_add", "gaussian_int.nat_abs_norm_eq", "real.sin_square_pi_over_two_pow_succ", "galois_coinsertion.u_sup_l", "left_eq_sup", "list.forall_mem_of_forall_mem_cons", "has_strict_fderiv_at.eventually_right_inverse", "supr_prod", "int.lxor_bit", "list.sublists_nil", "real.sqrt_mul'", "measure_theory.l1.simple_func.coe_smul", "bitvec.of_nat_succ", "differentiable_at_fpow", "set.bUnion_eq_Union", "Cauchy.mem_uniformity", "equiv.perm.same_cycle_apply", "normed_ring.inverse_one_sub", "mv_polynomial.monomial_add_single", "mul_gpow_self", "polynomial.splits_of_degree_eq_one", "category_theory.limits.prod.map_iso_hom", "bitraversable.comp_tsnd", "subsemiring.coe_mul", "cau_seq.lt_of_lt_of_eq", "nndist_comm", "category_theory.limits.is_limit.unique_up_to_iso_inv", "polynomial.commute_X", "polynomial.mod_by_monic_eq_self_iff", "equiv.perm.eq_sign_of_surjective_hom", "lie_algebra.special_linear.Eb_val", "measure_theory.measure.is_left_invariant_haar_measure", "ring_hom.map_closure", "inducing.tendsto_nhds_iff", "differentiable_on.neg", "set.right_mem_Iic", "continuous_linear_equiv.comp_continuous_iff", "add_units.eq_add_neg_iff_add_eq", "inv_mul_lt_right_of_lt_mul", "pequiv.mem_trans", "category_theory.limits.coprod.inl_map", "measurable_const", "div_le_one", "mvpfunctor.map_eq", "hyperreal.coe_eq_one", "ennreal.inv_two_add_inv_two", "mv_polynomial.map_C", "polynomial.monic_of_injective", "bounded_continuous_function.norm_coe_le_norm", "is_min_on_dual_iff", "dim_bot", "power_series.coeff_monomial", "filter.map_infi_le", "is_noetherian_of_submodule_of_noetherian", "category_theory.functor.map_presheaf_obj_presheaf", "category_theory.non_preadditive_abelian.add_assoc", "list.insert_pos", "complex.uniform_continuous_add", "is_connected_iff_sUnion_disjoint_open", "finset.Ico.val", "category_theory.limits.image.pre_comp_comp", "formal_multilinear_series.continuous_on", "deriv.lhopital_zero_at_bot_on_Iio", "continuous_iff_is_closed", "nat.monotone_fact", "add_monoid_hom.iterate_map_gsmul", "has_le.le.lt_or_le", "algebraic_geometry.PresheafedSpace.comp_c_app", "le_mul_of_one_le_of_le", "nat.unpair_le_right", "pow_left_inj", "sub_le_iff_le_add'", "is_R_or_C.of_real_int_cast", "cardinal.mk_Union_le_sum_mk", "inv_of_one", "has_fderiv_at_filter.iterate", "pos_num.cmp_eq", "continuous.sub", "is_glb_Ico", "continuous_linear_map.mem_range", "computable.eqv", "affine_map.ext_iff", "complex.exp_eq_one_iff", "local_homeomorph.preimage_open_of_open_symm", "set.bInter_singleton", "sub_gsmul", "le_sub_iff_add_le'", "findim_span_eq_card", "category_theory.arrow.mk_right", "and_congr", "has_ftaylor_series_up_to_on_zero_iff", "finset.erase_subset", "lie_add_group_core.to_topological_add_group", "nat.strong_induction_on", "int.div_zero", "ordinal.sup_ord", "linarith.nat_le_subst", "onote.repr_power_aux\:2082", "category_theory.limits.cocones.whiskering_equivalence_inverse", "ordinal.type_def'", "tensor_product.zero_tmul", "distrib_mul_action_hom.map_zero", "list.lookup_kinsert", "ennreal.add_lt_add_iff_left", "category_theory.discrete.equivalence_functor", "measurable_space.comap_le_iff_le_map", "function.commute.iterate_le_of_map_le", "seq.map_tail", "eq_of_le_of_forall_ge_of_dense", "category_theory.limits.types.coprod_map", "card_subgroup_dvd_card", "union_mem_uniformity_sum", "cau_seq.tendsto_limit", "function.commute.comp_iterate", "set.mk_preimage_prod_right_eq_empty", "linear_map.continuous_of_bound", "ordinal.typein_inj", "local_equiv.trans_symm_self", "function.semiconj.symm_adjoint", "quotient.induction_on\:2083", "set.Iic_union_Ioo_eq_Iio", "add_lt_iff_neg_left", "set.inter_subset_inter_left", "semiconj_by.eq", "set.preimage_id", "uniform_embedding_comap", "ennreal.add_supr", "nndist_dist", "filter.eventually_eq.is_local_extr_iff", "exists_unique_of_exists_of_unique", "summable_mul_right_iff", "units.coe_inv", "padic.rat_dense", "list.minimum_singleton", "fraction_map.to_map_eq_zero_iff", "multiplicity.pow_multiplicity_dvd", "nat.lor_bit", "equiv.perm.is_cycle_inv", "add_neg_eq_iff_eq_add", "pi_generate_from_eq_fintype", "submodule.mem_coe", "submonoid.localization_map.eq_iff_eq", "mem_nhds_within_Iio_iff_exists_Ico_subset", "closure_diff", "polynomial.nat_degree_prod_of_monic", "int.bodd_coe", "filter.tendsto_iff_ultrafilter", "add_subgroup.map_map", "set.mem_pi", "function.inv_fun_eq_of_injective_of_right_inverse", "borel_eq_generate_from_of_subbasis", "ideal.is_fg_degree_le", "semiquot.ext_s", "roption.map_map", "is_lub_lt_iff", "filter.monotone_lift", "filter.mem_seq_sets_iff", "is_measurable.prod", "int.sub_nat_nat_elim", "set.embedding_of_subset_apply_mk", "multiset.fmap_def", "continuous_within_at.comp", "set.seq_eq_set_seq", "multiset.sum_hom", "primrec.nat_cases\:2081", "int.mul_self_lt_mul_self", "prime_multiset.add_sub_of_le", "monoid_hom.map_gpow", "add_monoid_hom.mem_mrange", "smooth_add", "magma.free_semigroup.of_mul_assoc_left", "times_cont_mdiff_within_at_fst", "set.disjoint.union_right", "pell.x_pos", "continuous_within_at_inter", "set.image_congr'", "rel_embedding.acc", "sylow.mk_vector_prod_eq_one_injective", "submodule.span_smul_span", "nnreal.coe_multiset_prod", "nat.mod_mod", "int.nat_abs_pow", "set.set_of_false", "refl_sesq_form.ortho_sym", "pnat.mk_one", "int.div_eq_iff_eq_mul_left", "topological_space.sUnion_basis_of_is_open", "infi_sum", "list.index_of_cons", "submodule.quotient.mk_smul", "sub_eq_iff_eq_add", "inf_eq_right", "Module.mono_of_ker_eq_bot", "structure_groupoid.local_invariant_prop.lift_prop_on_symm_of_mem_maximal_atlas", "convex_cone.convex", "category_theory.limits.types.limit_equiv_sections_apply", "free_group.quot_lift_on_mk", "filter.eventually.prod_inl", "nnreal.mul_finset_sup", "ennreal.of_real_pos", "tactic.abel.term_add_termg", "polynomial.map_div_by_monic", "ennreal.le_sub_add_self", "int.lt_add_succ", "set.mem_inv", "holor.cprank_upper_bound", "multiset.erase_add_left_neg", "filter.germ.lift_pred_const", "function.is_periodic_pt.iterate", "cardinal.lift_mul", "times_cont_diff.continuous", "equiv.perm.swap_mul_self_mul", "submonoid.list_prod_mem", "poly.subst_eval", "differentiable.ccosh", "free_monoid.one_def", "differentiable_within_at_fpow", "set.ord_connected_Inter", "equiv.option_equiv_sum_punit_some", "category_theory.op_op_equivalence_functor", "submodule.findim_le", "times_cont_mdiff_const", "mul_lt_mul_iff_right", "category_theory.limits.biprod.inr_fst_assoc", "real.angle.angle_eq_iff_two_pi_dvd_sub", "smooth_at_const", "asymptotics.is_o.sub", "pell.yn_zero", "set.Union_range_eq_Union", "fintype.card_of_finset'", "discrete_valuation_ring.iff_pid_with_one_nonzero_prime", "set.nonempty_Ioi", "nat.partrec'.of_eq", "iff_iff_eq", "pnat.coe_eq_one_iff", "real.totally_bounded_Icc", "free_magma.traverse_eq", "asymptotics.is_O_with_self_const_mul'", "is_R_or_C.conj_involutive", "metric.tendsto_uniformly_on_iff", "add_monoid_algebra.prod_single", "turing.tape.move_right_n_head", "hyperreal.coe_eq_zero", "is_open_singleton_true", "complex.of_real_ne_zero", "add_commute.units_coe", "enat.with_top_equiv_top", "set.range_eq_empty", "pgame.move_right_right_moves_neg_symm", "matrix.special_linear_group.inv_val", "nhds_contain_boxes_of_singleton", "measure_theory.measure.map_comap_subtype_coe", "add_monoid.coe_one", "monoid_hom.ext_int", "opt_param_eq", "finset.prod_apply_dite", "int.mod_two_ne_one", "inv_lt_inv_iff", "neg_one_mul", "le_mul_of_one_le_right", "set.nonempty_inter_iff_exists_left", "gt_of_gt_of_ge", "lt_add_of_neg_add_lt_left", "is_R_or_C.ext_iff", "pnat.coprime.gcd_mul_left_cancel_right", "units.smul_eq_zero", "pnat.eq", "list.append_ne_nil_of_ne_nil_right", "localization_map.mk'_eq_mul_mk'_one", "finset.min_le_of_mem", "set.finite.subset", "hyperreal.infinite_neg_iff_infinite_of_neg", "norm_norm'", "ennreal.of_real_lt_iff_lt_to_real", "setoid.exists_of_mem_partition", "seq1.map_join", "has_deriv_within_at.limsup_slope_le'", "sequentially_complete.set_seq_mem", "category_theory.nat_iso.unop_hom", "norm_num.adc_bit1_one", "polynomial.monic.as_sum", "measurable.ennreal_sub", "hyperreal.is_st_st", "is_local_max.comp_antimono", "differentiable.smul", "exists_mem_inter_of_exists_mem_inter_affine_span_of_affine_independent", "div_self", "continuous_on.prod_map", "not_and_not_right", "pgame.le_trans_aux", "euclidean_domain.gcd_val", "infi_eq_of_tendsto", "ring_hom.coe_mk", "category_theory.limits.types.lift_\[Pi]_apply'", "local_homeomorph.restr_source_inter", "magma.free_semigroup.lift_of", "option.seq_some", "polynomial.eisenstein_criterion_aux.eval_zero_mem_ideal_of_eq_mul_X_pow", "finset.sum_bij", "affine_subspace.inf_coe", "set.image2_smul", "sub_lt_iff_lt_add", "category_theory.limits.inv_prod_comparison_map_snd_assoc", "smooth_manifold_with_corners.chart_mem_maximal_atlas", "pell.xn_succ", "category_theory.uncurry_natural_right_assoc", "primrec\:2082.to_comp", "nnreal.half_lt_self", "nat.subtype.le_succ_of_forall_lt_le", "bitraversable.id_tsnd", "nsmul_eq_mul'", "list.sorted_insertion_sort", "nat.le_add_one_iff", "sub_div", "multiset.union_le_union_right", "filter.comap_const_of_mem", "category_theory.abelian.pseudoelement.pseudo_zero_aux", "list.subset_append_of_subset_left", "affine.triangle.eq_orthocenter_of_forall_mem_altitude", "structure_groupoid.local_invariant_prop.lift_prop_within_at_congr_iff", "bool.to_bool_false", "nonempty_of_exists", "one_one_equiv.to_many_one", "multiset.powerset_coe", "set.union_eq_Union", "multiset.filter_add", "list.prod_take_mul_prod_drop", "units.inv_mul_cancel_left", "distrib_mul_action_hom.map_smul", "lt_inv_mul_iff_mul_lt", "linear_map.finsupp_sum", "times_cont_mdiff_at_fst", "category_theory.equiv_of_fully_faithful_symm_apply", "list.last_eq_nth_le", "power_series.inv_eq_inv_aux", "eq_zero_iff_of_associated", "eq.substr", "category_theory.equivalence.equivalence_mk'_counit_inv", "asymptotics.is_o_pow_id", "ultrafilter_comap_pure_nhds", "list.disjoint_cons_right", "closure_Iio", "image_norm_le_of_norm_deriv_right_le_deriv_boundary", "asymptotics.is_O_with.join", "set.preimage_const_mul_Iio_of_neg", "Inf_union", "coe_monoid_hom", "multiset.sub_add_cancel", "list.count_filter", "ring.direct_limit.of_f", "set.inclusion_injective", "multiset.cons_erase", "has_fderiv_at_iff_is_o_nhds_zero", "eq_one_of_left_cancel_mul_self", "infi_eq_top", "sup_le", "onote.zero_def", "has_fderiv_at.smul_algebra", "submodule.ker_liftq", "tendsto_indicator_bUnion_finset", "int.cast_injective", "mv_power_series.X_inj", "summable.comp_injective", "gold_irrational", "measure_theory.measure.haar.prehaar_pos", "fraction_map.is_integer_of_is_unit_denom", "asymptotics.is_O.congr", "is_unit_one", "measure_theory.simple_func.const_zero", "local_equiv.eq_on_source.symm'", "hyperreal.infinitesimal_iff_infinite_inv", "padic_int.ideal_eq_span_pow_p", "quotient.sound'", "category_theory.limits.coprod_map_id_id", "complex.arg_neg_one", "inv_le_one_of_one_le", "local_homeomorph.of_set_symm", "nat.mul_le_mul_left", "Top.presheaf.stalk_pushforward.comp", "ideal.mem_supr_of_mem", "real.quotient_mk_eq_mk", "ennreal.lt_iff_exists_add_pos_lt", "int.le_div_iff_mul_le", "dvd_normalize_iff", "wseq.destruct_congr_iff", "punit.Sup_eq", "real.one_lt_rpow_of_pos_of_lt_one_of_neg", "ennreal.to_nnreal_eq_zero_iff", "multiset.Ico.eq_cons", "degree_scale_roots", "list.zip_map'", "add_semiconj_by.units_coe", "with_one.cases_on", "unique_mdiff_on.unique_mdiff_on_preimage", "has_fderiv_at.lim_real", "category_theory.limits.pushout_cocone.mk_inr", "segment_eq_image'", "CommRing.colimits.cocone_naturality_components", "filter.tendsto_pure_left", "hyperreal.not_infinite_neg_add_infinite_pos", "not_mem_affine_span_diff_of_affine_independent", "inv_image.irreflexive", "uniform.continuous_at_iff'_left", "add_commute.all", "option.some_orelse", "tsum_sigma", "list.is_infix.trans", "complex.has_deriv_at_sinh", "differentiable_on.smul", "measure_theory.l1.simple_func.norm_Integral_le_one", "set.image_compl_preimage", "emetric.Hausdorff_edist_comm", "pfun.core_def", "int.cast_inj", "fin.coe_mul", "set.bInter_union", "list.nil_subperm", "lt_asymm", "real.continuous_tan", "topological_fiber_bundle_core.mem_triv_change_source", "int.of_nat_sub", "category_theory.under.limit_X", "bool.bnot_band", "abstract_completion.continuous_extend", "subalgebra.coe_int_mem", "category_theory.limits.is_image.self_lift", "pythagorean_triple.mul_iff", "is_noetherian_iff_well_founded", "has_deriv_within_at.cexp", "fin.coe_val_of_lt", "int.mul_le_mul_of_nonneg_left", "wseq.join_think", "composition.ext_iff", "polynomial.degree_mod_by_monic_lt", "real.cos_one_pos", "list.perm.map", "list.nodup_reverse", "pi_Lp.smul_apply", "uniform.continuous_at_iff'_right", "continuous_linear_map.op_norm_extend_le", "fin.eq_of_veq", "palindrome.reverse_eq", "mvpfunctor.M.dest'_eq_dest'", "list.pairwise.imp_mem", "polynomial.coeff_restriction'", "set.disjoint_union_left", "int.to_nat_eq_max", "category_theory.adjunction.core_hom_equiv.hom_equiv_naturality_right_symm", "ring_equiv.to_ring_hom_refl", "filter.monotone_principal", "mul_nonneg_iff_right_nonneg_of_pos", "category_theory.faithful.div_faithful", "category_theory.limits.diagram_of_cones.mk_of_has_limits_obj", "category_theory.iso.refl_inv", "Top.presheaf.pushforward.id_hom_app'", "has_fderiv_within_at_snd", "ideal.mem_leading_coeff", "traversable.naturality'", "list.bind_map", "int.distrib_left", 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"category_theory.limits.cone.extend_\[Pi]", "is_R_or_C.bit1_im", "category_theory.monoidal.Mon_functor_category_equivalence.unit_iso_inv_app_hom_app", "linear_equiv_iso_Module_iso_inv", "nat.le_rec_on_succ_left", "many_one_equiv.le_congr_left", "measure_theory.outer_measure.le_trim", "measure_theory.l1.coe_pos_part", "list.find_cons_of_pos", "normal_of_eq_add_cosets", "category_theory.limits.prod.left_unitor_hom", "convex_hull_eq_union_convex_hull_finite_subsets", "int.bodd_add_div2", "uniform_space.completion.map_unique", "binfi_inf", "finset.gsmul_sum", "asymptotics.is_o_iff_forall_is_O_with", "complex.uniform_continuous_mul_const", "category_theory.preadditive.mono_of_kernel_zero", "qpf.liftp_iff_of_is_uniform", "matrix.subsingleton_of_empty_left", "nnreal.continuous_coe", "linear_map.antilipschitz_of_bound", "add_semiconj_by.neg_symm_left", "nonempty_preirreducible_inter", "power_series.constant_coeff_inv_of_unit", "subalgebra.to_submodule_injective", 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"category_theory.monoidal_of_has_finite_coproducts.tensor_hom", "exists_has_deriv_at_eq_zero", "smooth_snd", "mv_polynomial.coeff_sum", "function.support_inv", "not_lt_of_lt", "filter.germ.map\:2082_coe", "filter.basis_sets", "gcd_mul_lcm", "finset.mem_disj_union", "category_theory.abelian.full_image_factorisation", "Mon_.assoc_flip", "nat.not_prime_mul", "bit0_gsmul", "list.modify_nth_tail_id", "unique_factorization_domain.integer_of_integral", "category_theory.limits.span_map_snd", "nat.decreasing_induction_succ_left", "finsupp.single_multiset_sum", "measure_theory.simple_func.integral_smul", "pequiv.trans_symm_eq_iff_forall_is_some", "measure_theory.l1.simple_func.uniform_continuous", "and_iff_not_or_not", "multiset.mem_sections", "finset.Ico.filter_lt_of_ge", "inv_of_eq_right_inv", "list.cons_eq_append_iff", "measure_theory.simple_func.integral_add", "add_submonoid.prod_bot_sup_bot_prod", "ideal.jacobson_eq_self_of_is_maximal", "free_group.to_group.of", "finset.prod_apply", "nnreal.div_lt_iff", "has_fderiv_within_at.snd", "subalgebra.fg_bot", "set.piecewise_same", "group.closure_eq_mclosure", "one_sub_gold_conj", "add_con.ker_lift_mk", "continuous_linear_map.uncurry_left_apply", "concave_on_const", "real.deriv_sinh", "ideal.zero_mem", "ring_hom.eq_rat_cast", "uniform_space.core_eq", "norm_image_sub_le_of_norm_deriv_le_segment_01'", "set.dual_Icc", "multiset.card_erase_of_mem", "cardinal.zero_lt_one", "unique_diff_on_Iic", "has_sum_geometric_two'", "qpf.Wequiv.symm", "local_equiv.coe_trans", "Liminf_eq_of_le_nhds", "with_one.lift_one", "finmap.insert_insert_of_ne", "measure_theory.integral_eq", "le_of_forall_le'", "initial_seg.coe_coe_fn", "multiset.subset_ndunion_left", "pnat.xgcd_type.flip_b", "is_local_max_on.comp_mono", "inner_product_geometry.norm_add_square_eq_norm_square_add_norm_square'", "local_homeomorph.continuous_on_symm", "subring.mem_prod", "finset.prod_Ico_eq_mul_inv", "subring.sum_mem", "matrix.diagonal_mul_diagonal'", "is_measurable_eball", "prod.snd_swap", "ring.fractional_ideal.coe_ideal_span_singleton", "list.filter_map_filter", "lebesgue_number_lemma", "concave_on_id", "gsmul_eq_smul", "submonoid.coe_supr_of_directed", "finset.infi_insert", "bool.tt_eq_to_bool_iff", "rat.uniform_continuous_abs", "filter.seq_eq_filter_seq", "emetric.inf_edist_zero_of_mem", "with_zero.cases_on", "ring.fractional_ideal.coe_zero", "pnat.coprime.mul_right", "gpow_sub", "map_ext_congr", "derivation.ext", "complex.conj_bit1", "unique_diff_within_at.prod", "cardinal.lift_mk_fin", "zmod.exists_pow_two_eq_prime_iff_of_mod_four_eq_three", "primrec.of_equiv_symm_iff", "submodule.mul_comm", "mul_lt_of_lt_of_le_one'", "onote.repr_mul", "mul_sub_right_distrib", "filter.comap_ne_bot", "measure_theory.measure.le_restrict_apply", "composition_as_set.boundaries_nonempty", "differentiable_within_at.const_add", "measure_theory.sum_measure_preimage_singleton", "complex.sin_int_mul_pi", "finsupp.sum_comap_domain", "homeomorph.to_local_homeomorph_source", "continuous_linear_map.op_norm_le_bound", "ennreal.top_ne_nat", "pi.multiset_prod_apply", "measure_theory.simple_func.restrict_apply", "ring_hom.apply_apply", "is_bounded_linear_map.fderiv_within", "multiset.singleton_add", "continuous_linear_equiv.is_O_sub", "relation.refl_gen.to_refl_trans_gen", "polynomial.leading_coeff_monomial", "measure_theory.l1.integral_eq", "local_equiv.image_inter_source_eq'", "subsemiring.one_mem", "polynomial.monic_mul_leading_coeff_inv", "is_cau_of_decreasing_bounded", "int.mod_lt_of_pos", "cauchy_seq_of_edist_le_of_summable", "ordinal.le_nfp_self", "measure_theory.ae_eq_fun.to_germ_injective", "list.any_of_mem", "iff_def", "measure_theory.simple_func.fin_meas_supp_iff_support", "minimal_polynomial.irreducible", "list.enum_from_nth", "int.modeq.modeq_of_modeq_mul_right", "equiv.perm.inv_eq_iff_eq", "matrix.mul_apply", "nat.totient_le", "nat.psub_add", "add_magma.free_add_semigroup.lift_unique", "nat.lxor_eq_zero", "bilin_form.lin_mul_lin_comp_left", "localization_map.is_integer_add", "pos_num.cast_one'", "le_inv_mul_iff_mul_le", "nat.one_le_pow'", "category_theory.limits.braid_natural_assoc", "complex.log_neg_one", "field.direct_limit.inv_mul_cancel", "set.smul_set_empty", "polynomial.mod_def", "add_submonoid.localization_map.mk'_add_cancel_right", "semiconj_by.cast_nat_mul_left", "complex.of_real_mul", "fin.succ_lt_succ_iff", "ring_hom.coe_prod_map", "multiset.coe_prod", "is_unit_iff_of_associated", "differentiable.sum", "cardinal.mul_eq_self", "functor.comp.run_map", "pfun.dom_of_mem_fix", "lipschitz_with.sub", "polynomial.smul_eval", "polynomial.nat_degree_remove_factor'", "local_equiv.eq_on_source.source_eq", "matrix.det_adjugate_eq_one", "lipschitz_with.neg", "add_neg_cancel_left", "written_in_ext_chart_comp", "local_homeomorph.symm_symm", "computation.results_think_iff", "turing.partrec_to_TM2.move\:2082_ok", "mvfunctor.liftr_last_rel_iff", "complex.cos_two_mul'", "fderiv_within_fst", "complex.exp_add_mul_I", "filter.realizer.top_\[Sigma]", "set.powerset_empty", "associates.irreducible_iff_prime_iff", "add_le_add_iff_right", "continuous_sup_dom", "submodule.of_le_apply", "dfinsupp.map_range_single", "list.erase_dup_idempotent", "pequiv.symm_trans_rev", "midpoint_comm", "encodable.encode_tt", "submonoid.localization_map.mk'_spec", "finsupp.mem_antidiagonal_support", "alist.keys_nodup", "mul_lt_mul_iff_left", "num.cast_to_znum_neg", "rat.one_mul", "computable.nat_cases", "strict_antimono_of_deriv_neg", "emetric.inf_edist_le_inf_edist_add_Hausdorff_edist", "generalized_continued_fraction.int_fract_pair.nth_stream_fr_nonneg", "div_lt_div'", "norm_sub_norm_le", "emetric.is_closed_subsets_of_is_closed", "pnat.xgcd_type.finish_is_special", "multiplicity.finite_mul_aux", "add_subgroup.range_gmultiples_hom", "mem_maximal_atlas_iff", "local_equiv.trans_refl_restr", "function.support_inf", "semiconj_by.inv_inv_symm", "local_homeomorph.continuous_within_at_iff_continuous_within_at_comp_left", "left_ord_continuous.map_Sup", "measure_theory.outer_measure.coe_add", "category_theory.monoidal_category.tensor_left_tensor_inv_app", "equiv.coe_trans", "eq_bot_of_singletons_open", "ennreal.Inf_add", "bitvec.of_fin_to_fin", "finsupp.single_eq_single_iff", "category_theory.functor.map_cone_X", "homological_complex.image_map_\[Iota]", "cau_seq.lim_add", "uniform_space.completion.is_add_group_hom_map", "associates.le_mul_right", "power_series.inv_eq_zero", "category_theory.functor.unop_map", "semiquot.exists_mem", "to_bilin_form_to_matrix", "composition.size_up_to_succ'", "fin.mem_find_of_unique", "real.tan_surjective", "monoid_hom.prod_unique", "set.maps_to_range", "nat.prime_three", "nat.zero_max", "dvd.elim_left", "left_dvd_or_dvd_right_of_dvd_prime_mul", "nat.lt_of_le_of_lt", "nat.sub_le_iff", "metric.nonempty_compacts.dist_eq", "local_homeomorph.mdifferentiable.mdifferentiable_at", "inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two", "localization.monoid_of_eq_of", "prime_spectrum.punit", "linear_order.convex_on_of_lt", "measure_theory.measure.add_le_add_left", "bool_eq_false", "uniform_space.completion.dense", "generalized_continued_fraction.convergents'_stable_of_terminated", "hyperreal.infinite_neg_iff_infinite_and_neg", "ring.fractional_ideal.span_singleton_one", "ring_char.spec", "rat_add_continuous_lemma", "CommRing.colimits.cocone_naturality", "induced_generate_from_eq", "nat.dist.def", "pfun.as_subtype_eq_of_mem", "finset.eq_univ_iff_forall", "complex.cos_add_two_pi", "list.map_eq_nil", "array.read_eq_read'", "add_subgroup.mem_supr_of_mem", "tactic.ring_exp.atom_to_sum_pf", "category_theory.curry.map_app_app", "int.sub_one_le_of_lt", "multiset.add_cons", "list.sublists_len_aux_append", "le_antisymm_iff", "tendsto_uniformly_on.tendsto_locally_uniformly_on", "smul_eq_mul", "set.image2_union_left", "list.perm.length_eq", "list.maximum_singleton", "subring.coe_bot", "category_theory.limits.image.fac_lift", "is_R_or_C.re_le_abs", "add_submonoid.localization_map.mk'_add", "complex.log_exp", "cardinal.mk_preimage_of_injective_of_subset_range", "mv_polynomial.pderivative_monomial", "subtype.map_injective", "int.add_mod_self_left", "category_theory.adjunction.core_hom_equiv.hom_equiv_naturality_left", "measure_theory.l1.continuous_pos_part", "open_add_subgroup.ext_iff", "add_con.Inf_to_setoid", "num.mod_to_nat", "emetric.tendsto_locally_uniformly_on_iff", "list.filter_eq_self", "mul_action.mem_orbit_smul", "interior_closed_ball", "is_clopen_compl_iff", "num_dvd_of_is_root", "coinduced_sup", "category_theory.iso.to_equiv_id", "stream.mem_of_nth_eq", "real.rpow_pos_of_pos", "category_theory.limits.pullback.lift_fst_assoc", "mv_polynomial.total_degree_sub", "turing.list_blank.cons_head_tail", "tactic.group.gpow_trick_one", "polynomial.degree_div_le", "ennreal.div_pos_iff", "continuous_linear_map.ratio_le_op_norm", "alg_equiv.to_Algebra_iso_inv", "con.lift_on_beta", "pnat.gcd_rel_left'", "measure_theory.integrable.norm", "list.mem_keys_of_mem", "nat.two_step_induction", "nat.mod_mul_right_div_self", "complex.cpow_add", "composition.blocks_pos'", "set.Ioc_self", "nnreal.rpow_le_one", "finset.mul_card_le", "polynomial.factor_dvd_of_not_is_unit", "equiv_of_dim_eq_lift_dim", "subsemiring.closure_Union", "subring.zero_mem", "fraction_map.to_map_ne_zero_of_mem_non_zero_divisors", "complex.norm_sq_of_real", "nat.coprime_of_dvd", "dense_of_subset_dense", "perfect_closure.int_cast", "emetric.diam_union'", "computation.lift_rel.trans", "tsum_Union_decode2", "algebraic_geometry.PresheafedSpace.id_c", "hyperreal.epsilon_lt_pos", "bool.bor_inr", "primrec.nat_elim'", "topological_space.opens.map_id_obj'", "formal_multilinear_series.comp_id", "differentiable_on.rpow_of_one_le", "set.eq_on.eventually_eq_nhds_within", "pSet.equiv.refl", "set.singleton_mul", "initial_seg.antisymm_symm", "list.subset_def", "int.even_mul", "list.forall\:2082_eq_eq_eq", "irrational.mul_rat", "add_submonoid.map_supr", "free_comm_ring.induction_on", "archimedean_iff_nat_lt", "lebesgue_number_lemma_seq", "one_le_inv_of_le_one", "rel_iso.coe_mul", "uniform_space.to_core_to_topological_space", "polynomial.pow_comp", "filter.infi_eq_generate", "category_theory.eq_to_hom_trans_assoc", "nat.div2_succ", "vector_space.erange_coe", "onote.repr_sub", "finset.coe_univ", "submodule.le_comap_map", "equiv.perm.is_swap_of_subtype", "category_theory.prod.swap_map", "typevec.drop_append1'", "category_theory.limits.limit.pre_post", "Top.stalk_to_fiber_injective", "is_bounded_linear_map.zero", "traversable.foldl_map", "bex_of_exists", "category_theory.limits.diagram_of_cones.mk_of_has_limits_map_hom", "polynomial.is_unit_of_self_mul_dvd_separable", "homological_complex.homology_map_2", "tangent_cone_inter_nhds", "free_comm_ring.is_supported_sub", "cau_seq.mul_not_equiv_zero", "tsum_eq_tsum_of_has_sum_iff_has_sum", "continuous_quot_lift", "free_abelian_group.hom_equiv_apply", "filter.tendsto.uniformity_symm", "trunc.out_eq", "equiv.perm.gpow_apply_eq_of_apply_apply_eq_self", "category_theory.limits.bicone.to_binary_bicone_inr", "linear_equiv.injective", "continuous_linear_equiv.of_bijective_symm_apply_apply", "set.eq_on_of_left_inv_on_of_right_inv_on", "int.lcm_self", "uniform_space.completion.nonempty_completion_iff", "CommRing.colimits.quot_one", "category_theory.limits.cofork.left_app_one", "dfinsupp.subtype_domain_zero", "category_theory.equivalence.inv_fun_id_assoc_hom_app", "list.func.add_nil", "seq.mem_append_left", "pSet.equiv.symm", "finset.prod_dite_eq'", "set.preimage_empty", "ordinal.log_not_one_lt", "category_theory.limits.pullback.condition_assoc", "lt_neg_add_iff_add_lt", "mem_of_is_lub_of_is_closed", "abs_two", "neg_div_neg_eq", "trunc.ind", "multiset.revzip_powerset_aux_perm_aux'", "add_aut.mul_apply", "simple_graph.adj_matrix_vec_mul_apply", "function.bijective_id", "le_nhds_iff", "uniform_continuous_comap", "category_theory.limits.is_colimit.hom_ext", "int.of_nat_add_neg_succ_of_nat", "set.surj_on_empty", "exists_has_deriv_at_eq_zero'", "nat.partrec.code.comp_prim", "times_cont_mdiff_within_at_inter'", "free_semigroup.pure_seq", "finset.weighted_vsub_of_point_insert", "nhds_within_Ico_eq_nhds_within_Iio", "real.tendsto_inv", "category_theory.limits.is_image.fac_lift", "filter.germ.const_bot", "zero_lie", "prime.ne_one", "open_embedding.target", "set.Iic_disjoint_Ioc", "measure_theory.outer_measure.map_id", "nat.coprime_one_left", "sub_one_lt", "finset.has_sum_compl_iff", "left_ord_continuous.map_sup", "game.le_refl", "ring_equiv.to_ring_hom_apply_symm_to_ring_hom_apply", "with_top.sum_lt_top", "measure_theory.simple_func.is_measurable_preimage", "finset.sum_eq_sum_Ico_succ_bot", "num.test_bit_to_nat", "hyperreal.not_infinite_neg", "mv_power_series.inv_mul", "finset.prod_range_div", "set.preimage_sub_const_Ici", "polynomial.nat_degree_mul_le", "zmod.val_one", "localization_map.mk'_self'", "int.mul_neg_of_pos_of_neg", "infi_singleton", "complex.log_of_real_re", "category_theory.pi.eval_map", "matrix.is_adjoint_pair_equiv", "commute.zero_left", "list.forall\:2082_take", "Module.coe_comp", "equiv.naturality", "ring.fractional_ideal.mem_one_iff", "mul_le_mul'", "nat.cast_le", "submodule.annihilator_supr", "ideal.span_singleton_le_span_singleton", "ordinal.lift_lift", "turing.TM2to1.tr_respects_aux", "eq_of_one_div_eq_one_div", "has_deriv_within_at_id", "nat.primrec.prec1", "mem_pregroupoid_of_eq_on_source", "equiv.mul_equiv_symm_apply", "list.nth_le_map_rev", "summable.neg", "continuous_on_if'", "group.subset_closure", "composition_as_set.blocks_partial_sum", "generalized_continued_fraction.int_fract_pair.succ_nth_stream_eq_some_iff", "int.add_sub_cancel", "finset.mem_def", "units.coe_lift_right", "real.cos_lt_cos_of_nonneg_of_le_pi", "asymptotics.is_o.triangle", "one_one_reducible.trans", "finset.mono_of_fin_unique'", "and.assoc", "power_series.coeff_of_lt_order", "is_ring_hom.map_neg", "multiset.erase_dup_ext", "add_con.ker_apply_eq_preimage", "not_irreducible_zero", "galois_connection.dual", "real.le_mk_of_forall_le", "algebra.tensor_product.mul_assoc", "category_theory.over.over_right", "pgame.neg_def", "submonoid.localization_map.map_spec", "fraction_map.is_unit_denom_of_num_eq_zero", "encodable.decode_nat", "add_aut.apply_inv_self", "monoid_hom.coe_mk", "set.image_smul_prod", "string.le_iff_to_list_le", "mem_nonunits_iff", "local_homeomorph.trans_target", "nat.div_eq_of_eq_mul_left", "has_fderiv_at.mul_const", "continuous_linear_map.ker_cod_restrict", "pi.smul_apply", "finset.image_val", "power_series.coeff_X", "d_array.of_beq_eq_ff", "nhds_within_Ioo_eq_nhds_within_Iio", "is_open_map.is_open_range", "nat.div_lt_of_lt_mul", "ideal.comap_injective_of_surjective", "lower_bounds_Icc", "pos_num.cast_lt", "cardinal.mul_lt_of_lt", "summable.summable_compl_iff", "ordinal.omega_ne_zero", "convex.neg_preimage", "int.ne_neg_of_pos", "one_div_lt_one_div", "continuous_linear_equiv.homothety_inverse", "filter.eventually_eq.is_local_min_iff", "set.preimage_mul_right_one", "int.modeq.modeq_add_cancel_left", "filter.tendsto_at_top_at_top_iff_of_monotone", "ideal.mem_leading_coeff_nth", "add_submonoid.mem_prod", "measure_theory.simple_func.mul_eq_map\:2082", "int.mod_abs", "or.elim", "metric.nhds_basis_ball", "list.mem_union_left", "ordinal.zero_mod", "filter.one_mul", "list.insert_neg", "measure_theory.ae_eq_fun.coe_fn_mk", "nnreal.coe_rpow", "pequiv.mem_single_iff", "mv_polynomial.coe_zero", "set.nonempty_Ioo", "int.cast_lt_zero", "metric.ball_subset", "turing.TM1to1.tr_tape'_move_right", "affine_subspace.mem_direction_iff_eq_vsub_right", "list.eq_of_sorted_of_perm", "set.image_bInter_subset", "category_theory.monoidal.left_unitor_hom_app", "category_theory.comma.map_right_obj_left", "nat.mul_comm", "dfinsupp.prod_sum_index", "exists_subset_affine_independent_affine_span_eq_top", "finset.prod_Ico_add", "measure_theory.ae_eq_bot", "deriv_forall_lt_or_forall_gt_of_forall_ne", "metric.uniformity_basis_dist", "set.Iio_subset_Iic_union_Ioo", "rel_embedding.collapse_apply", "pell.xz_sub", "set.nonempty_Iic", "cancel_factors.div_subst", "polynomial.X_pow_mul_assoc", "list.nat.length_antidiagonal", "subalgebra.ext", "multiset.nodup_singleton", "finset.subtype_map", "local_equiv.coe_symm_mk", "multiset.repeat_zero", "zmodeq_of_digits_digits", "hyperreal.coe_max", "padic_norm_z.add_eq_max_of_ne", "mv_polynomial.eval_eq", "nat.lt_of_test_bit", "submonoid.map_sup_comap_of_surjective", "submodule.fg_sup", "iterated_fderiv_within_univ", "matrix.from_blocks_apply\:2082\:2081", "plift.down_up", "real.sin_zero", "units.mul_right_inj", "finset.sum_pow_mul_eq_add_pow", "ideal.span_mul_span", "mul_nonneg", "is_closed_map.of_inverse", "exists_floor", "commute.cast_int_mul_right", "ennreal.mul_eq_mul_right", "guard_false", "nat.sub_add_eq_max", "pell.dz_val", "category_theory.over.mk_left", "is_open_Inter_prop", "deriv_within_mul_const", "norm_num.int_cast_zero", "times_cont_mdiff_within_at_snd", "category_theory.monoidal_category.pentagon_inv", "cardinal.sup_le_sup", "list.mem_zip", "category_theory.quotient.induction", "inner_product_geometry.angle_zero_left", "with_top.top_ne_nat", "category_theory.limits.span_right", "int.gcd_pos_of_non_zero_right", "finsupp.lsubtype_domain_apply", "erased.bind_eq_out", "mul_mul_div", "mdifferentiable_within_at.mono", "mul_le_one", "closure_lt_subset_le", "convex.antimono_of_deriv_nonpos", "matrix.zero_apply", "add_commute.units_neg_right_iff", "measure_theory.ae_mono", "list.nth_le_join", "int.neg_mul_neg", "set.ord_connected_singleton", "trunc.exists_rep", "measurable_equiv.measurable_coe_iff", "affine_subspace.direction_sup", "category_theory.limits.is_limit.of_nat_iso.cone_fac", "function.surjective.exists\:2083", "nhds_add", "list.nodup_sublists_len", "padic_int.ker_to_zmod_pow", "isometric.to_real_linear_equiv_apply", "holor.cprank_max_1", "set.abs_sub_right_of_mem_interval", "padic_norm_z.padic_val_of_cong_pow_p", "monoid_algebra.mul_single_one_apply", "measure_theory.measure.map_mul_left_eq_self", "is_measurable.is_null_measurable", "pow_succ", "finset.sum_involution", "real.cos_square", "add_submonoid.mem_supr_of_mem", "set.disjoint.preimage", "psigma.ext_iff", "smooth_fst", "nat.two_not_dvd_two_mul_sub_one", "continuous_multilinear_map.has_sum_eval", "d_array.read_write_of_ne", "tendsto_multiset_prod", "list.tail_cons", "abs_abs_sub_abs_le_abs_sub", "function.bij_on_fixed_pts_comp", "cardinal.lift_zero", "is_R_or_C.of_real_add", "measurable_neg", "partrec\:2082.unpaired", "metric.Hausdorff_dist_zero_iff_closure_eq_closure", "convex_on.subset", "real.continuous_rpow_of_pos", "set.Union_diff", "normed_ring.summable_geometric_of_norm_lt_1", "finsupp.sum_single_index", "set.ord_connected_Ici", "embedding.tendsto_nhds_iff", "linear_map.map_smul", "mv_polynomial.iter_to_sum_X", "asymptotics.is_o.prod_left_snd", "polynomial.separable.map", "finset.infi_union", "is_measurable.compl", "ff_band", "lipschitz_with.dist", "category_theory.id_nonzero", "real.uniform_continuous_mul_const", "int.eq_one_of_mul_eq_one_left", "continuous_linear_map.coe_subtype_val", "num.cast_zero'", "ordinal.lt_omega", "int.add_lt_of_lt_sub_right", "power_series.mul_inv", "list.last_repeat_succ", "category_theory.prod.sectl_obj", "subsemiring.prod_mono_right", "list.nodup_inter_of_nodup", "filter.realizer.map_\[Sigma]", "continuous.lim_eq", "nat.bit_le", "int.modeq.symm", "has_mfderiv_within_at_inter'", "finset.max_insert", "has_ftaylor_series_up_to_on_succ_iff_right", "is_preconnected_interval", "submodule.zero_eq_bot", "filter.germ.mk'_eq_coe", "is_extr_on.comp_antimono", "ideal.radical_le_jacobson", "tendsto_coe_int_real_at_top_iff", "set.disjoint_iff_inter_eq_empty", "add_left_comm", "inner_product_geometry.angle_eq_pi_iff", "subsemiring.mem_closure_iff_exists_list", "metric.tendsto_nhds_nhds", "adjoin_root.mk_C", "filter.comap_top", "not_nonempty_pempty", "turing.blank_extends.below_of_le", "fderiv.snd", "add_con.mk'_surjective", "omega.update_eq", "filter.seq_pure", "rat.commute_cast", "set.preimage_diff", "pos_tangent_cone_at_univ", "finmap.mem_iff", "dist_le_of_le_geometric_of_tendsto\:2080", "ordinal.log_zero", "rat.zero_mk_nat", "uniform_space_eq", "ideal.comap_lt_comap_of_integral_mem_sdiff", "bounded_continuous_function.dist_coe_le_dist", "generalized_continued_fraction.convergent_eq_num_div_denom", "continuous_on_if", "ordinal.power_lt_power_iff_right", "has_deriv_at.rpow", "times_cont_diff_at.sum", "pgame.subsequent.left_move", "continuous_multilinear_curry_fin1_symm_apply", "measure_theory.measure.haar.index_empty", "nnreal.coe_bit0", "fintype.eq_of_subsingleton_of_sum_eq", "matrix.bit0_apply", "pgame.move_left_mk", "real.le_sqrt", "scale_roots_eval\:2082_eq_zero_of_eval\:2082_div_eq_zero", "ordinal.is_limit.pos", "affine_span_eq_top_of_affine_independent_of_card_eq_findim_add_one", "exists_eq'", "associates.factors_mul", "is_min_filter.add", "complex.conj_involutive", "hyperreal.coe_eq_coe", "filter.prod_map_at_bot_eq", "ordinal.cof_sup_le_lift", "nnreal.one_le_rpow_of_pos_of_le_one_of_nonpos", "restrict_scalars_ker", "list.argmax_mem", "set.univ_eq_true_false", "ennreal.half_pos", "padic_int.pow_p_dvd_int_iff", "dioph.pell_dioph", "two_smul", "finset.mem_cons", "pos_num.bit1_of_bit1", "add_magma.free_add_semigroup.of_add", "is_R_or_C.mul_self_abs", "computation.orelse_ret", "emetric.Hausdorff_edist_def", "bool.bor_comm", "hyperreal.coe_min", "finset.prod_filter_ne_one", "algebra.tensor_product.one_def", "list.sizeof_lt_sizeof_of_mem", "ennreal.to_real_of_real_mul", "pell.yn_modeq_a_sub_one", "has_fderiv_at_filter.is_O_sub", "cardinal.nat_eq_lift_eq_iff", "algebraic_closure.of_step_succ", "filter.eventually_le.congr", "affine.simplex.monge_point_vsub_face_centroid_weights_with_circumcenter_eq_sub", "category_theory.limits.diagram_of_cones.mk_of_has_limits_cone_points", "set.Icc_subset_Ioc_iff", "measure_theory.simple_func.fin_meas_supp.mul", "well_founded_submodule_gt", "filter.tendsto_prod_self_iff", "continuous_linear_map.has_sum", "local_equiv.symm_image_inter_target_eq'", "measure_theory.lebesgue_length_eq_infi_Ioo", "dvd_of_dvd_neg", "nat.modeq.modeq_iff_dvd'", "alg_hom.id_comp", "lt_mul_of_one_lt_of_le", "stream.corec'_eq", "div_neg_of_neg_of_pos", "measure_theory.integrable_congr", "zsqrtd.of_int_im", "int.even_add", "category_theory.prod.sectr_obj", "Limsup_nhds", "stream.map_append_stream", "is_open_add_right", "equiv_iso_iso_inv", "int.add_neg_cancel_right", "is_bounded_linear_map_continuous_multilinear_map_comp_linear", "matrix.vec_mul_one", "filter.mem_traverse_sets", "add_commute.zero_left", "matrix.adjugate_def", "add_right_cancel_iff", "category_theory.limits.has_colimit.iso_of_nat_iso_\[Iota]_hom", "with_top.none_eq_top", "ideal.is_prime_radical", "turing.list_blank.head_cons", "totally_bounded_empty", "irrational_sqrt_rat_iff", "free_group.red.step.to_red", "convex.norm_image_sub_le_of_norm_has_fderiv_within_le'", "mul_inv_cancel_left'", "list.sublists_eq_sublists'", "is_basis.ext", "is_G\[Delta]_sInter", "stream.inits_tail", "is_open_supr_iff", "ideal.map_surjective_of_surjective", "fin.coe_of_nat_eq_mod'", "prod_X_sub_smul.monic", "is_closed_empty", "euclidean_geometry.angle_nonneg", "filter.countable_binfi_eq_infi_seq'", "lists'.mem_equiv_left", "is_closed.closure_subset", "ordinal.lift_down", "map_supr_of_continuous_at_of_monotone", "trans_of", "dist_self", "is_basis.mk_eq_dim'", "ennreal.coe_lt_coe", "filter.lift'_lift_assoc", "order_top.ext", "asymptotics.is_o.smul", "refl_of", "zero_pow'", "metric.inf_dist_empty", "subsemiring.closure_univ", "category_theory.limits.braid_natural", "ideal.exists_le_maximal", "list.any_iff_exists", "continuous_const", "complex.cos_int_mul_two_pi", "category_theory.limits.cofork.condition", "ennreal.inv_eq_zero", "local_equiv.eq_on_source.trans'", "linear_map.coe_restrict_scalars_eq_coe", "measure_theory.integral_eq_zero_of_ae", "ring_equiv.coe_ring_hom", "is_R_or_C.abs_ne_zero", "nonempty_of_not_bdd_above", "cau_seq.inv_aux", "metric.mem_closure_iff", "measurable.sub", "set.diff_union_self", "continuous_linear_equiv.fst_equiv_of_right_inverse", "category_theory.limits.limit.post_\[Pi]", "smooth.comp_smooth_on", "polynomial.irreducible_of_monic", "stream.cycle_eq", "is_algebraic_iff_is_integral", "nonempty.forall", "add_comm_group.is_Z_bilin.zero_left", "finset.min_eq_inf_with_top", "list.partition_eq_filter_filter", "surj_on_Ioc_of_monotone_surjective", "category_theory.comma.map_right_map_right", "add_group.subset_closure", "metric.lipschitz_inf_dist", "submodule.mkq_map_self", "circle_equiv_apply", "filter.eventually_comap", "deriv_within_pow'", "category_theory.is_iso.inv_comp", "submodule.ker_inl", "setoid.refl", "set.piecewise_eq_on_compl", "differentiable_on_fpow", "continuous_within_at.preimage_mem_nhds_within", "stream.nth_succ_iterate", "nat.le_of_mul_le_mul_left", "computation.has_bind_eq_bind", "nat.size_bit1", "convex_on_iff_convex_epigraph", "relator.rel_eq", "finsupp.map_domain_support", "is_totally_disconnected_singleton", "exists_nat_one_div_lt", "set.surj_on.maps_to_inv_fun_on", "set.Inter_eq_Inter_finset", "padic_val_rat.padic_val_rat_le_padic_val_rat_iff", "filter.eventually_inf_principal", "fin.cast_succ_inj", "list.map_length_split_wrt_composition", "measure_theory.simple_func.smul_apply", "omega.rhs_correct", "list.tendsto_nhds", "add_units.add_right_symm", "is_coprime.add_mul_right_left", "category_theory.evaluation_obj_map", "pfun.preimage_eq", "submodule.span_Union", "list.sorted_of_sorted_cons", "nat.div_one", "polynomial.not_monic_zero", "real.neg_one_le_cos", "fintype.card_of_subsingleton", 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"pfun.image_union", "int.nonneg_or_nonneg_neg", "matrix.row_vec_mul", "zero_gsmul", "refl", "ordinal.lift_is_succ", "list.nodup_sublists'", "fin.succ_rec_on_zero", "mul_lt_one'", "with_top.sum_lt_top_iff", "primrec.option_guard", "generalized_continued_fraction.of_part_num_eq_one", "polynomial.splits_of_splits_mul", "path_connected_space_iff_connected_space", "metric.diam_le_of_forall_dist_le", "padic_seq.norm_equiv", "isometry.continuous", "filter.has_basis.eq_binfi", "fin.zero_le", "metric.Hausdorff_dist_self_zero", "circle_deg1_lift.transnum_aux_seq_def", "euclidean_geometry.reflection_apply", "associates.out_mul", "units.mk0_inj", "subsemiring.exists", "nat.dist_add_add_left", "computable.list_nth", "list.mem_rotate", "nat.partrec.code.const_prim", "pell.eq_pell", "has_fderiv_within_at_iff_has_deriv_within_at", "measure_theory.lintegral_eq_zero_iff", "ennreal.coe_le_coe", "finset.union_eq_right_iff_subset", "nnreal.sub_eq_zero", "and.imp", 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"image_norm_le_of_liminf_right_slope_norm_lt_deriv_boundary", "normalize_lcm", "ring_hom.ext_zmod", "tactic.ring_exp.add_pf_sum_overlap", "zmod.cast_unit_of_coprime", "lfp_eq", "set.sUnion_mono", "roption.eq_some_iff", "exists_Ioc_subset_of_mem_nhds'", "linear_map.map_neg\:2082", "polynomial.coeff_restriction", "multiset.antidiagonal_cons", "set.preimage_mul_const_Ioc", "smodeq.add", "algebraic_geometry.SheafedSpace.mk_coe", "free_comm_ring.is_supported_of", "char_p.char_ne_zero_of_fintype", "last_digit_ne_zero", "dense_inter_of_G\[Delta]", "if_ctx_congr_prop", "multiset.prod_cons", "nhds_within_inter", "measurable.of_neg", "tensor_product.lift.tmul", "of_heq_true", "deriv_within_inter", "int.le_add_of_neg_add_le", "has_mfderiv_within_at.mdifferentiable_within_at", "setoid.ker_lift_injective", "padic.rat_dense'", "list.nat.nodup_antidiagonal", "topological_space.opens.map_comp_hom_app", "submodule.is_principal.span_singleton_generator", "semiquot.mem_pure'", 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"ideal.mul_le_left", "int.sub_one_lt_iff", "int.add_pos", "add_submonoid.localization_map.of_add_equiv_of_add_equiv_apply", "nat.gcd_mul_lcm", "add_submonoid.closure_mono", "nat.add_div_eq_of_le_mod_add_mod", "list.exists_of_mem_keys", "abs_le_max_abs_abs", "complex.uniform_continuous_im", "ordinal.lt_sup", "is_R_or_C.norm_sq_to_real", "category_theory.limits.cones.whiskering_map_hom", "set.empty_subset", "continuous_equiv_fun_basis", "submonoid.localization_map.lift_injective_iff", "pnat.lcm_coe", "set.inter_left_comm", "set.disjoint_image_image", "cau_seq.completion.of_rat_sub", "finset.card_eq_sum_card_image", "category_theory.limits.prod.lift_snd", "wseq.destruct_flatten", "onote.scale_eq_mul", "pell.yz_succ", "nat.mul_eq_zero", "stream.bisim_simple", "list.forall\:2082_refl", "finset.sum_equiv", "category_theory.limits.biproduct.hom_ext", "polynomial.degree_lt_wf", "cardinal.add_one_of_omega_le", "matrix_equiv_tensor.inv_fun_add", "Mon.colimits.quot_mul", 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"gt.lt", "symmetrize_mono", "add_lt_of_neg_of_lt", "measure_theory.ae_eq_fun.integrable.neg", "irreducible.is_unit_or_is_unit", "option.iget_of_mem", "has_fderiv_within_at.neg", "with_top.sum_eq_top_iff", "continuous_sup_rng_left", "category_theory.limits.is_limit.hom_lift", "of_add_nsmul", "ordinal.is_normal.limit_lt", "multiset.le_union_left", "eq.subset", "list.rel_map", "hyperreal.st_le_of_le", "finset.prod_nonneg_of_card_nonpos_even", "add_con.symm", "finset.ext", "omega.nat.exists_clause_holds", "partrec.bind", "dim_range_add_dim_ker", "ordering.compares.eq_lt", "mem_closure_of_tendsto", "wseq.to_seq_of_seq", "finset.prod_product", "submonoid.dense_induction", "omega.nat.neg_free_neg_elim", "linear_map.id_apply", "category_theory.limits.is_limit.cone_points_iso_of_equivalence_hom", "polynomial.degree_eq_zero_of_is_unit", "finset.disjoint_empty_right", "set.smul_set_mono", "measure_theory.measure.coe_add", "nnreal.inv_le_of_le_mul", "complex.differentiable_sinh", 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"mdifferentiable_within_at.mdifferentiable_at", "alg_equiv.injective", "hyperreal.infinite_neg_mul_of_not_infinitesimal_neg_infinite_pos", "local_homeomorph.trans_target''", "right_ord_continuous.map_Inf'", "units.mul_right_dvd", "category_theory.limits.kernel_zero_iso_source_hom", "ctop.realizer.nhds_\[Sigma]", "polynomial.C_sub", "dist_le_zero", "mv_polynomial.homogeneous_component_zero", "zmod.gauss_lemma", "set.mem_image", "finset.fold_congr", "zmod.val_mul", "mvpfunctor.W_rec_eq", "vector_allp_iff_forall", "is_coprime.add_mul_right_right_iff", "is_local_extr.has_deriv_at_eq_zero", "list.pw_filter_cons_of_neg", "int.coe_nat_pos", "continuous_within_at_Ioc_iff_Ioi", "filter.le_map_comap_of_surjective", "continuous_multilinear_map.cons_add", "category_theory.limits.has_zero_object.from_zero_ext", "has_fderiv_at_filter.comp", "pgame.le_of_le_of_equiv", "hash_map.not_contains_empty", "nat.sum_totient", "polynomial.mod_by_monic_eq_of_not_monic", "set.finite.is_measurable", "complex.norm_sq_add", "submodule.comap_subtype_self", "multiples.zero_mem", "finset.exists_min_image", "is_coprime.prod_right_iff", "category_theory.equivalence.functor_unit", "nat.zero_shiftr", "list.nodup_union", "bitraversable.tfst_comp_tfst", "Exists.fst", "sum.map_id_id", "pgame.numeric.le_move_right", "affine.simplex.sum_point_weights_with_circumcenter", "fderiv.comp", "dim_pos_iff_exists_ne_zero", "cau_seq.completion.of_rat_zero", "matrix.bit1_apply_ne", "uniform_embedding_subtype_coe", "finset.coe_mul", "category_theory.equivalence.inverse_inv", "many_one_degree.le_add_right", "ordinal.lt_cof_type", "filter.tendsto_at_top_add_nonneg_left", "finsupp.order_iso_multiset_apply", "traversable.mfoldl.of_free_monoid_comp_free_mk", "omega.clause.holds_append", "associates.mk_dvd_mk", "set.monotone_powerset", "measure_theory.lebesgue_length_empty", "turing.TM0.machine.map_step", "real.log_neg_iff", "formal_multilinear_series.comp_coeff_zero", "has_ftaylor_series_up_to.continuous", 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"matrix.reindex_alg_equiv_symm_apply", "complex.exp_ne_zero", "contracting_with.dist_le_mul", "principal_seg.trans_top", "int.gcd_one_left", "is_local_max_on.neg", "semidirect_product.right_hom_comp_inl", "matrix.smul_std_basis_matrix", "left_ord_continuous.le_iff", "list.sublists_append", "set.preimage_subset_iff", "localization_map.integer_normalization_map_to_map", "circle_deg1_lift.commute_add_nat", "mv_polynomial.indicator_mem_restrict_degree", "ring.fractional_ideal.div_one", "category_theory.limits.binary_fan.mk_\[Pi]_app_left", "free_group.prod.inv", "category_theory.nat_trans.vcomp_app'", "approximates_linear_on.continuous", "subring.closure_mono", "list.suffix_refl", "ennreal.tendsto_nhds_top", "nat.mod_mul_left_div_self", "finset.sum_dite", "cardinal.mk_real", "real.rpow_arith_mean_le_arith_mean_rpow", "continuous_linear_equiv.uniform_embedding", "measure_theory.lebesgue_outer_le_length", "eq_neg_iff_eq_neg", "category_theory.id_of_comp_right_id", "add_add_add_comm", "summable_geometric_of_norm_lt_1", "linear_map.ext", "dlist.to_list_append", "if_true", "equiv.perm.sign_subtype_perm", "set.image2_swap", "primrec.nat_bit", "subring.mk'_to_add_subgroup", "Top.presheaf_to_Types_obj", "galois_connection.u_inf", "semiconj_by.units_inv_right", "algebraic_geometry.SheafedSpace.id_base", "Gromov_Hausdorff.candidates_b_of_candidates_mem", "uniform_space.completion.map_coe", "fin.find_spec", "pnat.gcd_props", "set.ord_connected_univ", "uniform_space.completion.continuous_map\:2082", "multiset.le_cons_of_not_mem", "add_group.closure_subset", "pnat.xgcd_type.finish_v", "set.eq_on.symm", "int.coe_nat_mul_out", "finsupp.mem_support_on_finset", "mvfunctor.map_map", "list.foldl_with_index_aux_spec_cons", "refl_sesq_form.eq_zero", "int.sub_nat_nat_eq_coe", "set.maps_to.union_union", "mul_pos", "skew_adjoint_lie_subalgebra_equiv_apply", "le_mul_of_one_le_left'", "encodable.encode_inr", "matrix.det_diagonal", "has_deriv_within_at.rpow", "add_submonoid.localization_map.eq", "mnat_monoid_hom_ext", "category_theory.limits.image.lift_fac_assoc", "filter.germ.const_inf", "int.add_mod_eq_add_mod_right", "finset.sup_eq_union", "set.piecewise_eq_on", "category_theory.limits.parallel_pair_map_left", "set.Icc_diff_right", "typevec.split_drop_fun_last_fun", "filter.has_basis.ge_iff", "dfinsupp.support_single_ne_zero", "cau_seq.lt_lim", "smul_smul", "set.Icc_subset_interval", "linear_pmap.le_Sup", "plift.ext", "mem_nhds_within_Ici_iff_exists_Icc_subset'", "monoid_algebra.exists_left_inverse_of_injective", "category_theory.limits.coequalizer.cofork_\[Pi]", "submodule.span_le", "gpow_neg", "rel_embedding.coe_fn_inj", "filter.eventually_const", "option.is_none_iff_eq_none", "quadratic_form.lin_mul_lin_add", "is_min_on.inter", "free_group.red.enum.complete", "norm_unit_one", "polynomial.eval_mul_X_sub_C", "lt_of_incomp_of_lt", "set.nonempty_Ico", "alg_equiv.map_neg", "is_R_or_C.norm_sq_div", "pgame.impartial.not_first_wins", 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"add_comm_group.is_Z_bilin.sub_left", "affine_subspace.top_coe", "list.rel_filter_map", "int.bodd_neg", "euclidean_geometry.inter_eq_singleton_orthogonal_projection_fn", "set.mem_image_eq", "quot.exists_rep", "category_theory.curry_natural_left_assoc", "list.length_le_of_infix", "circle_deg1_lift.continuous_pow", "asymptotics.is_O_with_zero_right_iff", "le_add_of_neg_le_sub_left", "tactic.ring_exp.mul_coeff_pf_one_mul", "emetric.mem_closed_ball_self", "hash_map.find_erase_eq", "filter.le_comap_map", "inner_product_geometry.angle_self_neg_of_nonzero", "hash_map.valid.modify", "primrec.vector_length", "finite_dimensional.not_linear_independent_of_infinite", "category_theory.limits.prod.pentagon_assoc", "alg_equiv.map_mul", "set.Ioi_subset_Ici_self", "category_theory.iso.conj_Aut_hom", "list.length_of_fn", "polynomial.degree_lt_mono", "list.join_append", "free_group.reduce.idem", "classical.not_ball", "is_cobounded_ge_nhds", "bot_apply", "polynomial.monic_X_pow_sub", "inv_gpow", "fintype.injective_iff_surjective", "ordinal.power_omega", "category_theory.iso_whisker_right_hom", "units.op_pow", "submonoid.closure_union", "times_cont_diff_within_at.congr_of_eventually_eq", "mul_bit1", "alg_hom.map_pow", "prime_multiset.to_of_nat_multiset", "add_subgroup.mem_supr_of_directed", "alt_sesq_form.neg", "ennreal.tsum_le_tsum", "rat.cast_lt_zero", "fin.coe_cast_lt", "rat.le_total", "Sup_empty", "complex.sinh_sub", "measure_theory.inner_content_le", "left_mem_segment", "finset.prod_fin_eq_prod_range", "turing.tape.move_right_left", "ext_chart_continuous_at_symm'", "complex.continuous_linear_map.re_norm", "subspace.coe_prod_equiv_of_closed_compl_symm", "cardinal.power_nat_le", "nontrivial_of_invariant_basis_number", "set.mem_image2_eq", "smooth.mul", "holor.zero_mul", "nat.mul_le_mul", "set.subset_union_left", "list.nth_le_split_wrt_composition_aux", "filter.at_top_basis", "lt_base_pow_length_digits'", "ordinal.limit_rec_on_succ", "multiset.disjoint_map_map", "set.Iio_subset_Iio_union_Ico", "has_deriv_within_at.const_add", "bounded_continuous_function.coe_zero", "midpoint_eq_iff", "ordinal.omega_pos", "zero_div", "Class.diff_hom", "finset.fold_op_distrib", "filter.eventually_top", "nat.lt_add_of_zero_lt_left", "omega.coeffs.val_eq_of_le", "asymm_of", "submodule.fg_of_fg_map_of_fg_inf_ker", "polynomial.degree_mul_leading_coeff_inv", "enat.coe_add", "prime_spectrum.coe_vanishing_ideal", "filter.prod_lift'_lift'", "finsupp.unique_single_eq_iff", "differentiable.pow", "analytic_at.comp", "num.bit1_of_bit1", "list.not_mem_range_self", "le_non_zero_divisors_of_domain", "monoid.closure_singleton", "structure_groupoid.local_invariant_prop.lift_prop_on_indep_chart", "digits_zero_of_eq_zero", "localization_map.eq_zero_of_fst_eq_zero", "abstract_completion.uniform_continuous_compare", "measurable.ennreal_induction", "set_is_basis_of_linear_independent_of_card_eq_findim", "ordinal.lift_zero", "set.Iio_union_Ici", "abstract_completion.uniform_continuous_map\:2082", "ennreal.to_real_max", "ideal.is_jacobson_iff_prime_eq", "submonoid.localization_map.mul_equiv_of_localizations_right_inv_apply", "measure_theory.measure.haar.chaar_mem_cl_prehaar", "filter.lift_lift'_same_eq_lift'", "nat.primrec.const", "inducing.comp", "inner_product_space.of_core.inner_smul_left", "continuous_within_at.closure_le", "list.subperm.subset", "category_theory.over.comp_left", "continuous_linear_map.comp_id", "multiset.mem_erase_of_ne", "has_strict_fderiv_at.smul_algebra_const", "real.two_le_pi", "localization.mul_equiv_of_quotient_symm_mk'", "filter.mem_at_bot_sets", "lt_min_iff", "lower_bounds_Ici", "differentiable_at_fst", "local_homeomorph.restr_eq_of_source_subset", "add_con.lift_unique", "category_theory.adjunction.counit_naturality", "finset.inter_sdiff", "supr_split_single", "embedding.compact_iff_compact_image", "set.ord_connected_Icc", "ideal.comap_inf", "set.inter_self", "add_le_of_le_sub_left", "norm_num.is_prime_helper", "mul_action.inv_smul_smul", "ordinal.lift_add", "add_subgroup.exists", "choose_le_middle", "submodule.sum_mem", "formal_multilinear_series.has_fpower_series_on_ball", "list.prod_append", "circle_deg1_lift.le_iterate_pos_iff", "emetric.ball_disjoint", "measurable.infi_Prop", "add_submonoid.map_inr", "interior_interior", "not_lt", "continuous.dist", "inner_product_geometry.norm_sub_square_eq_norm_square_add_norm_square_iff_angle_eq_pi_div_two", "vector.cons_head", "polynomial.nat_degree_int_cast", "abs_of_neg", "polynomial.nat_degree_X_pow_sub_C", "semidirect_product.lift_unique", "pequiv.to_matrix_swap", "differentiable.fst", "is_max_on_univ_iff", "fintype.pi_finset_disjoint_of_disjoint", "set.singleton_nonempty", "subsemiring.mem_to_add_submonoid", "real.le_rpow_add", "option.map_injective", "enorm.top_map", "continuous_linear_equiv.comp_differentiable_on_iff", "eq_div_of_mul_eq", "sub_eq_zero", "multiset.map_id'", "continuous_within_at.comp'", "polynomial.map_multiset_prod", "mul_inv_cancel_left", "category_theory.monoidal_of_has_finite_products.right_unitor_hom", "polynomial.degree_le_iff_coeff_zero", "category_theory.limits.coprod.map_iso_hom", "measure_theory.measure.restrict_le_self", "set.Ioc_union_Ioo_eq_Ioo", "quotient.fin_choice_aux_eq", "continuous_on_empty", "multiset.prod_map_add", "mdifferentiable_on_univ", "model_prod_range_prod_id", "nat.coprime_or_dvd_of_prime", "measure_theory.lintegral_Union", "category_theory.limits.cocones.precompose_map_hom", "is_measurable.of_compl", "list.subset_append_left", "tendsto_uniformly_on.tendsto_comp", "nat.ppred_eq_none", "is_greatest.is_greatest_iff_eq", "ideal.quotient.eq", "asymptotics.is_o.trans_is_O", "finset.prod_filter", "summable.sigma_factor", "associates.mk_one", "pnat.coprime.factor_eq_gcd_left", "le_mul_of_inv_mul_le", "nhds_within_Ioi_self_ne_bot", "affine_subspace.direction_eq_top_iff_of_nonempty", "con.lift_comp_mk'", "mv_polynomial.degrees_X", "composition.single_blocks", "list.choose_property", "asymptotics.is_O_of_le'", "uniform_embedding.comp", "matrix.diagonal_apply_ne", "submodule.map_subtype_le", "ext_chart_preimage_mem_nhds_within'", "complex.conj_re", "is_open_sigma_iff", "gcd_dvd_gcd_mul_left", "list.prod_rotate_eq_one_of_prod_eq_one", "eq_iff_eq_cancel_left", "mul_sub_le_image_sub_of_le_deriv", "multiset.cons_swap", "ennreal.infi_add", "fintype.right_inverse_bij_inv", "category_theory.limits.parallel_pair_functor_obj", "dvd_and_not_dvd_iff", "category_theory.limits.limit.cone_\[Pi]", "list.mem_map_of_injective", "forall_2_true_iff", "filter.Limsup_le_Limsup", "basic_smooth_bundle_core.mem_atlas_iff", "real.is_conjugate_exponent.sub_one_pos", "list.lookup_kerase", "turing.TM0.map_init", "category_theory.category_of_elements.comma_equivalence_functor", "function.mem_periodic_pts", "mv_power_series.constant_coeff_inv", "semiconj_by.inv_right_iff", "category_theory.abelian.mono_of_epi_of_mono_of_mono", "le_inf_sup", "localization.mul_equiv_of_quotient_symm_mk", "frobenius_add", "metric.inf_dist_le_inf_dist_add_Hausdorff_dist", "set.mem_of_mem_inter_left", "polynomial.monic.def", "bitvec.add_lsb_div_two", "free_add_magma.pure_bind", "measure_theory.outer_measure.is_caratheodory_Union_lt", "relation.comp_iff", "polynomial.integral_normalization_coeff_ne_nat_degree", "is_add_group_hom.neg_ker_zero'", "int.sub_nat_nat_of_ge", "free_add_magma.add_map_seq", "continuous_linear_map.apply_ker", "convex.translate_preimage_left", "multiset.forall_mem_map_iff", "list.kinsert_nodupkeys", "summable_geometric_two", "composition.one_le_blocks'", "list.sorted_ordered_insert", "enat.to_with_top_lt", "submodule.coe_quot_equiv_of_eq_bot_symm", "normalize_associated", "enat.get_coe", "inner_add_left", "order.sequence_of_cofinals.encode_mem", "has_deriv_at.lhopital_zero_nhds_left", "relation.refl_trans_gen_of_transitive_reflexive", "set.mem_sUnion", "list.pairwise_of_sublist", "polynomial.splits_one", "commute.fpow_right", "add_equiv.map_sum", "mul_lt_one_of_lt_one_of_le_one", "div_le_div_left", "sum.traverse_eq_map_id", "nhds_mul", "primrec.nat_cases", "nnreal.rpow_lt_rpow_of_exponent_lt", "has_fderiv_within_at_inv", "add_monoid_hom.prod_map_def", "array.to_array_to_list", "measure_theory.norm_integral_le_of_norm_le", "uniform_continuous.add", "bilin_form.coe_fn_to_linear_map", "computable.to\:2082", "filter.has_basis.tendsto_Ixx_class", "uniform_space.completion.map_comp", "gfp_gfp", "cau_seq.mul_lim_zero_left", "differentiable_on.mul", "complex.exp_add", "multiset.filter_le_filter", "list.mem_erase_of_ne", "int.coe_nat_mod", "interval_integrable.trans", "subring.neg_mem", "computation.lift_rel_def", "exists_Ioo_extr_on_Icc", "eckmann_hilton.mul_comm", "exists_preirreducible", "nat.le_sub_right_iff_add_le", "is_local_max.bicomp_mono", "is_R_or_C.conj_bit0", "is_basis.range", "associates.map_subtype_coe_factors'", "hash_map.valid.insert", "function.is_periodic_pt.eq_of_apply_eq", "bdd_above_Ioc", "multiset.prod_map_prod_map", "order_embedding.map_le_iff", "category_theory.Monad.assoc_func_app", "category_theory.whisker_right_id", "list.index_of_nth_le", "is_basis.le_span", "ideal.eq_jacobson_iff_Inf_maximal", "is_open_const", "finset.sum_nonpos", "rat.lift_binop_eq", "is_closed.is_closed_le", "localization_map.mk'_self''", "finset.piecewise_coe", "int.bit1_val", "category_theory.prod.swap_obj", "category_theory.limits.types.limit_ext", "linear_map.comp_cod_restrict", "complex.mk_eq_add_mul_I", "localization.r_eq_r'", "add_equiv.to_AddCommMon_iso_hom", "continuous_of_le_add_edist", "vadd_eq_add", "monotone.le_is_glb_image", "mvqpf.mem_supp", "mv_polynomial.eval\:2082_prod", "complex.lim_abs", "nat.lxor_assoc", "pequiv.symm_injective", "matrix.empty_mul_vec", "units.coe_neg_one", "alist.empty_union", "seq.destruct_eq_nil", "sup_le_sup_right", "set.ord_connected_Ioi", "convex_on.map_sum_le", "linear_map.range_eq_top", "tensor_product.lift_mk", "vector3.append_add", "bilin_form.map_sum_left", "category_theory.functor.congr_obj", "matrix.update_row_ne", "composition.lt_size_up_to_index_succ", "category_theory.limits.prod_right_unitor_inv_naturality", "and_congr_right", "finset.le_sup", "times_cont_mdiff.continuous", "neg_of_mul_neg_right", "set.ord_connected_Iio", "map_seq", "set.card_image_of_inj_on", "int.gcd_one_right", "is_open_analytic_at", "is_preconnected_Icc", "mem_powers_iff_mem_gpowers", "category_theory.End.mul_def", "equiv.perm.apply_inv_self", "set.range_unique", "strict_mono.bot_preimage_bot'", "finset.summable", "list.foldl_with_index_aux_eq_foldl_with_index_aux_spec", "circle_deg1_lift.exists_eq_add_translation_number", "ex_of_psig", "imp.swap", "topological_fiber_bundle_core.local_triv'_fst", "localization_map.map_right_cancel", "mv_polynomial.C_mul'", "not_true", "is_clopen_iff", "dioph.dioph_pfun_comp1", "ideal.quotient.mk_eq_mk", "localization_map.mk'_mul", "not_false", "subtype.mk_eq_mk", "symmetrize_rel_subset_self", "nat.partrec'.rfind_opt", "padic.norm_eq_pow_val", "rel.mem_image", "submodule.le_def", "equiv.set_value_eq", "to_add_one", "set.neg_subset_neg", "monoid_algebra.mul_apply_right", "nonneg_add_comm_group.not_zero_pos", "algebra.tensor_product.mul_apply", "is_open_map_snd", "add_con.add_con_gen_idem", "turing.list_blank.nth_modify_nth", "times_cont_diff.add", "is_R_or_C.abs_nonneg", "category_theory.functor.left_op_obj", "has_fderiv_within_at.unique_diff_within_at_of_continuous_linear_equiv", "nat.sub_lt_iff", "tactic.ring_exp.simple_pf_prod_one", "enat.with_top_equiv_symm_lt", "has_mfderiv_within_at_univ", "nat.primrec'.prim_iff", "function.iterate_zero_apply", "asymptotics.is_o.prod_rightl", "int.add_neg_cancel_left", "int.lcm_assoc", "set.one_subset", "nat.cofinite_eq_at_top", "complex.norm_sq_I", "differentiable_at.mul", "emetric.mem_ball'", "dim_map_le", "con.sup_eq_con_gen", "pnat.dvd_lcm_right", "asymptotics.is_O.of_const_mul_right", "add_con.induction_on", "multiset.map_union", "submonoid.mul_mem", "linear_independent_Union_finite", "open_subgroup.mul_mem", "measure_theory.l1.simple_func.of_simple_func_neg", "relator.rel_imp", "matrix.mul_apply'", "pfun.core_restrict", "finset.filter_ne'", "has_fderiv_at.lim", "add_monoid_hom.coe_of_mdense", "vsub_right_cancel", "set.Union_eq_range_sigma", "mul_sub_lt_image_sub_of_lt_deriv", "pi.const_zero", "real.sin_pos_of_pos_of_le_two", "wseq.lift_rel.refl", "add_submonoid.coe_subtype", "nat.prime.mul_eq_prime_pow_two_iff", "exp_neg_inv_glue.f_aux_iterated_deriv", "set.sUnion_subset_iff", "interior_Ioo", "multiset.eq_zero_of_forall_not_mem", "tensor_product.sum_tmul", "onote.NF.snd'", "ennreal.tendsto_to_nnreal", "image_le_of_deriv_right_le_deriv_boundary", "set.mem_prod_eq", "prod.mk_eq_zero", "uniform_space.mem_nhds_iff", "deriv_within_zero_of_not_differentiable_within_at", "frontier_lt_subset_eq", "add_self_div_two", "pnat.coprime.gcd_mul_left_cancel", "pythagorean_triple.normalize", "euclidean_domain.mul_div_cancel_left", "measurable_binfi", "submodule.coe_sort_coe", "hyperreal.not_infinite_zero", "has_ftaylor_series_up_to_on.has_strict_fderiv_at", "succ_nsmul", "set.smul_set_union", "dense_range.comp", "nat.bit0_lt", "nat.mul_div_left", "prod.fst_zero", "multiset.sum_smul", "dense_range_iff_closure_range", "is_measurable.Union_Prop", "mv_power_series.monomial_mul_monomial", "W.depth_lt_depth_mk", "add_le_add_left", "complex.sinh_of_real_im", "monoid_algebra.mul_single_apply", "nat.gcd_pos_of_pos_left", "linear_map.range_id", "set.compl_eq_univ_diff", "list.rotate_cons_succ", "AddCommGroup.kernel_iso_ker_over_inv_left_to_fun_val", "iff.to_eq", "matrix.nonsing_inv_apply", "gcd_is_unit_iff", "circle_deg1_lift.translation_number_eq_of_dist_bounded", "asymptotics.is_O_iff_is_O_with", "filter.nonempty_of_mem_sets", "turing.proj_map_nth", "filter.mem_principal_self", "discrete_valuation_ring.irreducible_iff_uniformizer", "znum.cast_to_int", "smodeq.bot", "submodule.eq_top_of_disjoint", "generalized_continued_fraction.int_fract_pair.one_le_succ_nth_stream_b", "polynomial.smul_eval_smul", "set.prod_subset_preimage_snd", "free_add_semigroup.lift_unique", "finmap.mem_def", "pos_of_mul_pos_left", "is_group_hom.trivial_ker_iff_eq_one", "times_cont_diff_at.comp", "list.pmap_eq_map", "filter.realizer.bot_F", "simple_graph.adj_matrix_apply", "set.Iic_disjoint_Ioi", "continuous_multilinear_map.bounds_bdd_below", "hyperreal.not_real_of_infinitesimal_ne_zero", "measure_theory.measure.measurable_dirac", "finite_field.pow_card_sub_one_eq_one", "list.not_mem_cons_of_ne_of_not_mem", "add_con.coe_zero", "continuous_subtype_coe", "cau_seq.lt_of_eq_of_lt", "multiset.count_erase_self", "euclidean_geometry.orthogonal_projection_vsub_mem_direction", "equiv.perm.one_lt_nonfixed_point_card_of_ne_one", "pgame.right_wins_of_equiv_iff", "free_comm_ring.is_supported_zero", "finset.card_erase_le", "list.remove_nth_eq_nth_tail", "Class.mem_univ", "enat.top_eq_none", "real.sqrt_aux_nonneg", "AddCommGroup.has_limit.lift_apply", "has_deriv_at.congr_of_eventually_eq", "is_unit.map", "le_add_iff_nonneg_right", "list.perm.prod_eq'", "category_theory.limits.cofork.right_app_one", "lipschitz_with.list_prod", "inf_le_left'", "encodable.encode_injective", "lt_sub_iff_add_lt", "pmf.bind_apply", "list.eq_of_mem_singleton", "category_theory.limits.colimit.pre_map'", "affine_subspace.direction_inf_of_mem", "set.indicator_nonpos'", "is_scalar_tower.algebra_map_smul", "cast_proof_irrel", "finsupp.coe_lsum", "equiv_equiv_iso_inv", "category_theory.limits.biprod.braiding'_eq_braiding", "has_deriv_within_at.sub", "equiv.symm_to_local_equiv", "real.mk_le_of_forall_le", "set.disjoint_left", "exists_and_distrib_left", "category_theory.monoidal.Mon_functor_category_equivalence.functor_obj_map_hom", "not_irreducible_one", "monic_scale_roots_iff", "opposite.op_inj_iff", "mul_semiring_action_hom.map_neg", "set.set_of_app_iff", "padic_norm.neg", "set.bInter_mono", "category_theory.cancel_epi", "measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto_ae", "cardinal.summable_cantor_function", "add_monoid_hom.coe_prod_map", "finset.union_empty", "two_dvd_bit1", "complex.log_zero", "set.inter_subset_inter", "is_basis.equiv_fun_apply", "zsqrtd.add_le_add_left", "pell.asq_pos", "stream.cons_nth_inits_core", "quotient_group.ker_lift_injective", "polynomial.add_comp", "submonoid.localization_map.lift_id", "set.Ioc_eq_empty", "mem_affine_span_iff_eq_affine_combination", "of_digits_neg_one", "list.count_pos", "affine_map.vsub_apply", "circle_deg1_lift.translation_number_eq_of_semiconj_by", "linear_recurrence.sol_eq_of_eq_init", "pnat.factor_multiset_lcm", "normed_algebra.zero_ne_one", "submonoid.coe_bot", "list.inter_eq_nil_iff_disjoint", "card_quotient_dvd_card", "pullback_nonzero", "countable_Inter_mem_sets", "fpow_neg", "AddCommGroup.image_map", "mul_action.orbit_eq_iff", "list.revzip_sublists", "lt_iff_lt_of_le_iff_le", "padic_seq.eq_zero_iff_equiv_zero", "multiset.le_inter", "mul_fpow", "finset.card_disjoint_union", "compact_of_finite_subfamily_closed", "min_le_iff", "linear_equiv.continuous_symm", "zsqrtd.norm_zero", "filter.map_map", "turing.reaches\:2080_eq", "ennreal.top_mul", "category_theory.limits.biprod.inl_snd_assoc", "zmod.val_cast_of_lt", "rel.image_inter", "linear_map.ker_zero", "linear_independent_of_zero_eq_one", "free_add_semigroup.lift_of", "measure_theory.l1.simple_func.dist_to_simple_func", "nat.le_succ_of_le", "measure_theory.ae_eq_fun.integrable.smul", "category_theory.limits.cones.postcompose_map_hom", "hyperreal.is_st_le_of_le", "continuous_at.add", "vadd_vsub_assoc", "function.surjective.prod_map", "cardinal.lt_cof_power", "is_R_or_C.conj_re", "polynomial.map_neg", "multiplicity.dvd_of_multiplicity_pos", "tendsto_locally_uniformly_on.comp", "measure_theory.simple_func_sequence_tendsto", "typevec.repeat_eq_iff_eq", "wseq.head_of_seq", "mul_action.mem_fixed_by", "nat.not_even_bit1", "measure_theory.measure.eq_zero_of_not_nonempty", "multiset.erase_add_right_neg", "category_theory.limits.cocones.forget_obj", "list.perm.eq_singleton", "eq_iff_iff", "hyperreal.infinite_pos_mul_infinite_neg", "has_fpower_series_at.radius_pos", "hyperreal.not_real_of_infinite", "category_theory.unop_id", "function.involutive.right_inverse", "pgame.add_move_right_inl", "bounded_continuous_function.forall_coe_zero_iff_zero", "measure_theory.l1.simple_func.coe_sub", "lt_of_neg_of_one_div_lt_one_div", "real.log_exp", "cau_seq.const_lt", "set.indicator_empty", "pfun.pure_defined", "has_fderiv_at.differentiable_at", "mul_lt_one_of_nonneg_of_lt_one_right", "mul_semiring_action_hom.map_smul", "lt_add_of_lt_of_nonneg'", "equiv.perm.is_cycle_swap_mul_aux\:2081", "set.image_sub_const_Iic", "mem_nhds_sets", "pnat.mk_lt_mk", "hyperreal.epsilon_mul_omega", "nhds_prod_eq", "category_theory.under.post_map_left", "ext_chart_at_to_inv", "category_theory.uncurry.obj_obj", "hyperreal.infinitesimal_neg", "polynomial.leading_coeff_X", "lcm_dvd_lcm", "mv_polynomial.total_degree_multiset_prod", "multiset.mem_pmap", "separated_equiv", "model_with_corners.left_inv'", "filter.frequently_principal", "pfun.mem_dom", "pequiv.matrix_mul_apply", "asymptotics.is_O_fst_prod", "add_left_neg", "linear_map.comap_injective", "int.succ_pred", "fin.find_min", "filter.eventually_eq.deriv_eq", "linear_order.ext", "computation.results_of_terminates", "mul_inv_le_of_le_mul", "multiplicative.is_subgroup", "list.mfoldl_nil", "finset.map_filter", "interval_integral.deriv_within_integral_of_tendsto_ae_left", "list.filter_congr", "interval_integral.integral_has_deriv_within_at_of_tendsto_ae_left", "submodule.subtype_comp_of_le", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_map_hom_app", "free_comm_ring.is_supported_upwards", "exists_compact_superset", "add_commute.neg_left_iff", "category_theory.non_preadditive_abelian.coimage.fac", "equiv.refl_symm", "list.func.equiv_of_eq", "filter.mem_infi_finite'", "is_subgroup.mul_mem_cancel_right", "category_theory.comonad.cofree_obj_A", "linear_map.map_sub", "filter.comap_inf", "filter.mem_rcomap'", "midpoint_sub_left", "cmp_swap", "localization_map.ext_iff", "circle_deg1_lift.coe_mk", "multiset.le_ndinsert_self", "differentiable_on.div_const", "lipschitz_with_iff_dist_le_mul", "setoid.symm", "set.mem_bUnion", "cardinal.ord_le_ord", "quotient.lift_on_beta\:2082", "finset.inter_self", "real.is_conjugate_exponent.conj_eq", "prime_spectrum.zero_locus_inf", "int.div_mul_cancel_of_mod_eq_zero", "compl_sup", "bounded_continuous_function.coe_const", "list.nil_eq_append_iff", "differentiable.csin", "nat.lt_of_succ_lt", "array.rev_list_foldr_aux", "is_R_or_C.ext", "rat.zero_iff_num_zero", "matrix.map_zero", "dist_le_of_trajectories_ODE", "finset.weighted_vsub_of_point_indicator_subset", "int.neg_succ_of_nat_of_nat", "nat.not_succ_lt_self", "int.neg_le_of_neg_le", "function.semiconj.maps_to_range", "ordinal.CNF_fst_le", "list.enum_from_map_snd", "finsupp.map_domain_single", "is_integral_iff_is_integral_closure_finite", "list.func.pointwise_nil", "lipschitz_with.edist_le_mul", "rat.num_div_eq_of_coprime", "polynomial.eval\:2082_eq_eval_map", "circle_deg1_lift.translation_number_le_of_le_add", "int.sub_lt_of_sub_lt", "list.nth_of_mem", "int.zero_shiftr", "list.drop_append_of_le_length", "free_group.red.nil_iff", "exists_pos_add_of_lt", "submodule.ext", "submodule.prod_mono", "has_strict_fderiv_at.prod", "category_theory.limits.coprod.inr_desc", "pure_id_seq", "computation.mem_of_get_eq", "with_bot.coe_le_coe", "lagrange.interpolate_add", "not_not_of_not_imp", "category_theory.monad.forget_creates_colimits.lifted_cocone_is_colimit_desc_f", "is_coprime.add_mul_right_left_iff", "category_theory.op_op_obj", "vector.eq", "mv_power_series.coeff_one", "category_theory.limits.coequalizer.\[Pi]_desc_assoc", 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"semiquot.bind_def", "submonoid.closure_empty", "polynomial.mul_X_pow_eq_zero", "list.foldr_map'", "inf_le_left_of_le", "pell.xy_modeq_of_modeq", "hash_map.find_insert", "linear_map.mul_eq_one_comm", "max_add_add_right", "formal_multilinear_series.change_origin_radius", "is_local_min_on_const", "filter.ne_bot.mono", "ennreal.tsum_eq_top_of_eq_top", "mem_nhds_unbounded", "finset.sep_def", "nat.fact_mul_fact_dvd_fact", "real.mk_near_of_forall_near", "finset.union_assoc", "nnreal.mul_sup", "mv_power_series.is_unit_constant_coeff", "free_magma.map_mul'", "exists_unique.intro2", "lie_subalgebra.mem_map_submodule", "vector.head_of_fn", "set.Icc_subset_Icc_right", "set.image_swap_prod", "finset.card_le_mul_card_image", "div_add_div_same", "add_con.inf_iff_and", "Gromov_Hausdorff.GH_dist_eq_Hausdorff_dist", "mv_polynomial.rename_eval\:2082", "metric.is_open_iff", "add_localization.induction_on", "nhds_within_Ioc_eq_nhds_within_Ioi", "is_max_on.min", "abelianization.lift.unique", 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"reader_t.run_monad_map", "sub_pos_of_lt", "filter.germ.const_abs", "lt_one_add", "tactic.abel.term_add_constg", "inv_eq_of_mul_eq_one", "dist_le_norm_add_norm", "hash_map.contains_iff", "category_theory.limits.im_map", "matrix.diagonal_map", "irreducible.not_unit", "polynomial.derivative_zero", "linear_equiv.map_sub", "lie_algebra.map_lie", "matrix.smul_eq_diagonal_mul", "local_homeomorph.continuous_on", "mv_polynomial.total_degree_one", "homeomorph.homeomorph_mk_coe_symm", "multiset.nodup_pi", "is_lub.upper_bounds_eq", "semidirect_product.inv_right", "list.subset_of_cons_subset", "polynomial.splits_of_is_unit", "multiset.nodup_zero", "set.ord_connected_of_Ioo", "convex_cone.ext'_iff", "valuation.is_equiv.trans", "category_theory.iso.conj_comp", "lists.is_list_to_list", "list.kunion_nil", "units.mul_inv_of_eq", "complex.I_re", "computation.get_eq_of_mem", "topological_space.first_countable_topology.tendsto_subseq", "set.subset_of_mem_powerset", 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"add_submonoid.localization_map.mk'_surjective", "set.preimage_mul_const_Iic_of_neg", "cardinal.mk_subset_ge_of_subset_image_lift", "set.Ici_inter_Iic", "units.coe_one", "category_theory.biprod.unipotent_lower_hom", "dfinsupp.filter_pos_add_filter_neg", "set.image_neg_Iio", "int.neg_eq_of_add_eq_zero", "complex.exp_conj", "monotone.mul_strict_mono", "ereal.coe_real_inj'", "complex.int_cast_re", "filter.frequently_imp_distrib_left", "padic_norm.nonneg", "measure_theory.l1.of_fun_zero", "int.neg_add_cancel_left", "multiset.coe_nodupkeys", "vector.of_fn_nth", "pi.mul_apply", "set.surj_on.comp", "is_measurable.Inter_Prop", "category_theory.monad.forget_creates_colimits.new_cocone_X", "continuous_linear_equiv.times_cont_diff_on_comp_iff", "is_bounded_linear_map.is_O_comp", "nat.find_greatest_zero", "is_open_map_sigma_mk", "linear_independent_span", "polynomial.degree_one_le", "function.comp_app", "add_submonoid.localization_map.mk'_add_cancel_left", "Ioo_mem_nhds_within_Iio", "local_homeomorph.restr_coe", "equiv.forall\:2082_congr'", "subring.top_prod_top", "category_theory.iso.hom_inv_id_app_assoc", "add_subgroup.le_normalizer", "int.neg_mul_eq_mul_neg", "fixed_points.coe_algebra_map", "set.finite_subset_Union", "mv_polynomial.is_homogeneous.inj_right", "fderiv_within.snd", "int.modeq.exists_unique_equiv", "emetric.mem_closed_ball", "category_theory.limits.cocones.precompose_equivalence_unit_iso", "fin.succ_above_descend", "uniform_embedding_subtype_emb", "category_theory.limits.types.filtered_colimit.r_eq", "filter.tendsto_at_top_of_add_const_right", "opposite.coe_unop_add_hom", "canonically_ordered_semiring.zero_lt_one", "mdifferentiable_within_at_inter'", "multiset.mem_ndunion", "set.eq_or_mem_of_mem_insert", "polynomial.root_mul_left_of_is_root", "free_group.induction_on", "ordinal.le_zero", "polynomial.card_roots_sub_C", "metric.to_glue_r_isometry", "qpf.recF_eq", "filter.pure_le_iff", "le_of_lt", "functor.map_id", "filter.eventually.filter_mono", "cardinal.card_typein_lt", "ideal.comap_is_maximal_of_surjective", "local_homeomorph.restr_to_local_equiv'", "eq_false_of_not_eq_true", "measure_theory.measure.bind_bind", "is_closed_prod", "dist_le_Ico_sum_dist", "ceil_sub_int", "padic_norm.of_int", "differentiable_snd", "is_ring_hom.of_semiring", "con.to_submonoid_inj", "mul_action.inv_smul_eq_iff", "norm_add_le", "fderiv_within_sub_const", "vsub_set_empty", "set.neg_preimage", "one_lt_inv_of_inv", "category_theory.comma.comp_left", "pow_mul", "pos_num.size_eq_nat_size", "category_theory.over.hom_mk_right", "polynomial.degree_add_le", "bool.cond_to_bool", "category_theory.limits.coprod.associator_hom", "has_fpower_series_at.continuous_at", "decidable.le_or_lt", "vadd_left_cancel", "monotone.le_map_Sup", "complex.is_cau_seq_abs", "quadratic_form.to_matrix_comp", "strict_fderiv_of_cont_diff", "list.lookup_all_sublist", "primrec.option_iget", "padic_int.coe_mul", "hash_map.find_empty", "is_R_or_C.abs_div", "nhds_is_mul_hom", "category_theory.limits.prod_functor_obj_map", "prod.swap_left_inverse", "int.shiftl_add", "filter.has_basis.has_basis_self_subset", "stream.corec_id_f_eq_iterate", "array.read_foreach", "pell.eq_pow_of_pell", "deriv_within_csin", "prod.snd_injective", "one_lt_gold", "bilin_form.comp_left_apply", "add_con.map_apply", "list.last_eq_of_concat_eq", "has_deriv_at.lhopital_zero_right_on_Ioo", "measure_theory.l1.simple_func.integral_congr", "list.perm.diff", "set.powerset_inter", "int.ne_of_nat_abs_ne_nat_abs_of_nonneg", "wseq.nth_terminates_le", "inv_le_one'", "add_units.coe_le_coe", "convex.mem_to_cone", "composition.blocks_fun_congr", "rat.of_int_eq_mk", "filter.germ.map\:2082_const", "list.perm_cons", "subtype.map_id", "function.support_sum", "generate_from_mono", "finset.eq_of_card_le_one_of_prod_eq", "list.subset_erase_dup", "has_mfderiv_within_at.nhds_within", "submonoid.comap_surjective_of_injective", "linear_map.surjective_of_injective", "list.mem_permutations_aux_of_perm", "cardinal.mk_preimage_of_injective_lift", "set.image_add_const_Ioi", "additive.normal_add_subgroup_iff", "category_theory.iso.symm_hom", "ring_hom.iterate_map_gsmul", "list.exists_erase_eq", "power_series.coeff_zero_mul_X", "nat.odd_mul_odd_div_two", "multiset.powerset_aux_perm_powerset_aux'", "is_local_min.congr", "submonoid.comap_inf_map_of_injective", "finmap.erase_erase", "times_cont_diff_on.continuous_on_fderiv_within", "function.is_fixed_pt.is_periodic_pt", "set.inv_subset", "pgame.mk_lt_mk", "pfun.image_mono", "gt_of_mul_lt_mul_neg_left", "nat.prime_def_lt", "relation.trans_gen.to_refl", "nat.dvd_mul_right", "continuous_linear_map.smul_right_apply", "continuous_multilinear_curry_left_equiv_symm_apply", "power_series.constant_coeff_zero", "nat.div_eq_of_lt_le", "nat.even_bit0", "fin.coe_injective", "mv_polynomial.eval\:2082_eq'", "is_local_max.min", "mem_nhds_right", "ordinal.lift.principal_seg_coe", "normed_ring.inverse_continuous_at", "list.length_map_accumr", "multiset.range_zero", "nnreal.coe_eq", "equiv.perm.disjoint_one_left", "hash_map.keys_empty", "subtype.exists_set_subtype", "topological_fiber_bundle_core.open_source'", "cluster_pt_principal_iff_frequently", "add_con.mem_coe", "set.image_const_sub_Ico", "submonoid.mem_sup_left", "div_div_div_cancel_right", "zsqrtd.zero_im", "finsupp.prod_ite_eq'", "dfinsupp.sum_sub_index", "div_mul_eq_div_mul_one_div", "category_theory.End.one_def", "segment_eq_image", "ennreal.infi_sum", "filter.tendsto_at_bot_add_nonpos_right", "pell.eq_of_xn_modeq_lem1", "pgame.le_of_restricted", "mem_left_coset_left_coset", "cardinal.eq_one_iff_subsingleton_and_nonempty", "finset.powerset_empty", "measure_theory.ae_eq_fun.edist_zero_eq_coe", "mul_action_hom.comp_apply", "measure_theory.l1.of_fun_eq_mk", "model_with_corners.continuous", "quadratic_form.polar_comm", "mvfunctor.of_mem_supp", "finset.sum_range_sub'", "cancel_factors.add_subst", "and_or_distrib_right", "set.image_const_add_Ioc", "filter.prod_ne_bot", "sum_hom_units_eq_zero", "compact_covered_by_mul_left_translates", "complete_univ", "inner_product_geometry.angle_comm", "polynomial.derivative_X", "free_add_monoid.add_def", "multiset.card_erase_le", "finsupp.filter_single_of_pos", "measure_theory.ae_eq_fun.coe_fn_neg", "list.insert_nil", "cauchy_seq_finset_of_norm_bounded", "nat.lxor_self", "set.image2_inter_subset_left", "nat.mod_two_ne_zero", "category_theory.iso.cancel_iso_hom_right", "rel_embedding.is_preorder", "mul_equiv.to_Mon_iso_inv", "list.sublists_aux\:2081_bind", "min_right_comm", "local_equiv.ext", "setoid.ext'", "uniform_inducing.uniform_continuous_iff", "finmap.insert_insert", "filter.tendsto_principal", "zmod.val_eq_zero", "is_prime.to_maximal_ideal", "nat.le_of_le_of_sub_le_sub_right", "ring_hom.ker_eq_bot_iff_eq_zero", "ideal.integral_closure.is_maximal_of_is_maximal_comap", "ideal.is_primary.to_is_prime", "irrational.neg", "list.perm.append", "semiconj_by.gpow_right", "list.prod_take_of_fn", "nat.cast_bit1", "fin.init_snoc", "metric.ball_zero", "holor.mul_scalar_mul", "ennreal.coe_le_iff", "presented_group.to_group.inv", "measure_theory.integrable_at_filter.inf_of_left", "tsum_supr_decode2", "ordinal.le_min", "zmod.coe_val_min_abs", "is_R_or_C.abs_to_complex", "category_theory.limits.fork.equalizer_ext", "set.Ioi_subset_Ioc_union_Ioi", "continuous_linear_map.coe_add", "ring_hom.iterate_map_frobenius", "function.iterate_zero", "add_ite", "add_submonoid.ext'_iff", "nat.add_mod_add_ite", "add_submonoid.mem_bot", "submodule.lt_of_le_of_findim_lt_findim", "pi.comp_one", "inv_inj", "linear_independent.to_subtype_range", "polynomial.map_mod_div_by_monic", "Cauchy.nonempty_Cauchy_iff", "mem_uniformity_of_uniform_continuous_invariant", "add_submonoid.localization_map.exists_of_sec_mk'", "primrec.decode2", "pnat.mod_add_div", "category_theory.monad.algebra.EilenbergMoore_to_category_struct_comp", "is_asymm.swap", "real.of_near", "polynomial.degree_eq_nat_degree", "dioph.dioph_fn_comp1", "real.continuous_log", "category_theory.is_equivalence.functor_unit_comp", "of_to_bool_true", "cardinal.ord.order_embedding_coe", "filter.mem_of_finite_sUnion_ultrafilter", "is_local_min_on.neg", "div_lt_div_right", "finset.Ico_\:2124.card", "Set.mem_union", "finmap.empty_union", "compl_injective", "function.injective.comp", "subring.gc_map_comap", "submodule.comap_snd", "submodule.ker_mkq", "sigma.exists", "bilin_form.smul_right", "ennreal.coe_of_nnreal_hom", "rat.sub_def", "prime_spectrum.zero_locus_sup", "category_theory.limits.is_colimit.unique_up_to_iso_inv", "stream.exists_of_mem_map", "continuous_linear_map.coe_apply'", "rat.cast_min", "gaussian_int.to_complex_def", "isometric.vadd_const_to_equiv", "mv_polynomial.degrees_sub", "nhds_eq_nhds_emetric_ball", "matrix.zero_empty", "denumerable.prod_of_nat_val", "set.ord_connected.interval_subset", "multiset.prod_zero", "free_monoid.hom_eq", "stream.nth_tails", "function.support_subset_iff'", "relation.refl_trans_gen_idem", "set.preimage_const_mul_Icc_of_neg", "finset.exists_ne_zero_of_sum_ne_zero", "has_fderiv_at.const_sub", "quotient_group.lift_mk'", "mv_polynomial.monomial_eq", "is_basis.to_dual_inj", "nat.right_distrib", "asymptotics.is_O.const_mul_left", "filter.eq_Inf_of_mem_sets_iff_exists_mem", "has_deriv_at_filter_const", "category_theory.yoneda.obj_map_id", "mv_power_series.coeff_zero_eq_constant_coeff_apply", "list.filter_filter", "nat.exists_eq_add_of_lt", "add_eq_zero_iff_eq_zero_of_nonneg", "int.add_neg", "contracting_with.dist_fixed_point_fixed_point_of_dist_le'", "nat.test_bit_succ", "asymptotics.is_O_norm_right", "pgame.lt_irrefl", "multiset.pairwise_of_nodup", "category_theory.differential_object.hom.id_f", "cardinal.wf", "continuous_at.preimage_mem_nhds", "nat.one_lt_pow", "measurable_add", "gsmul_int_one", "list.nth_le_split_wrt_composition", "partrec.merge", "ordinal.card_eq_zero", "polynomial.map_list_prod", "metric.mem_iff_inf_dist_zero_of_closed", "pairwise_disjoint_fiber", "alist.union_empty", "prod.fst_add", "linear_map.range_eq_of_proj", "submodule.comap_coe", "mat_poly_equiv_eval", "has_fderiv_within_at.smul_algebra", "metric.ball_subset_closed_ball", "nat.zero_ne_one", "relation.refl_trans_gen.total_of_right_unique", "mv_polynomial.hom_C", "set.image_union", "is_group_hom.one_ker_inv", "computation.mem_parallel", "array.push_back_rev_list", "mv_polynomial.total_degree_list_prod", "uniform_space.compact_space_iff_seq_compact_space", "finsupp.filter_curry", "list.index_of_eq_length", "ennreal.coe_two", "metric.uniform_continuous_inf_dist_Hausdorff_dist", "Set.pair_inj", "nat.bit0_lt_bit1", "ennreal.sum_le_tsum", "dvd_add", "module.algebra_map_End_apply", "category_theory.pre_id", "incomp_trans_of", "ring_hom.ext_iff", "measure_theory.lintegral_edist_lt_top", "polynomial.roots_prod_X_sub_C", "list.perm.kunion_left", "is_preconnected.intermediate_value\:2082", "cau_seq.const_lim_zero", "subsemiring.mem_closure", "category_theory.over.iso_mk_hom_left", "complex.cos_sub_sin_I", "lipschitz_with.iterate", "is_unit_iff_ne_zero", "category_theory.monoidal_category.unitors_equal.cells_3_4", "has_deriv_within_at.limsup_norm_slope_le", "real.pi_div_two_pos", "tendsto_inv_at_top_zero", "set.bUnion_subset", "pgame.not_lt", "multiset.join_add", "measurable_space.is_measurable_infi", "prod.mk_eq_one", "submodule.comap_smul'", "is_bounded_bilinear_map.is_O'", "closed_ball_Icc", "left_ord_continuous.map_Sup'", "has_deriv_within_at.sinh", "supr_bool_eq", "has_deriv_within_at_inter", "nat.cast_add_one_ne_zero", "cInf_upper_bounds_eq_cSup", "int.cast_le", "mul_div_mul_left", "tendsto_of_tendsto_of_tendsto_of_le_of_le'", "turing.TM2to1.add_bottom_map", "linear_equiv_iso_Module_iso_hom", "turing.frespects_eq", "image.is_submonoid", "vector3.append_cons", "option.lift_or_get_some_some", "pythagorean_triple.coprime_classification", "affine_map.decomp", "convex.norm_image_sub_le_of_norm_has_deriv_within_le", "hyperreal.infinite_pos_mul_of_not_infinitesimal_neg_infinite_neg", "linear_map.to_add_monoid_hom_coe", "affine_subspace.direction_mk'", "is_subgroup.inv_mem_iff", "nat.even.add", "category_theory.adjunction.cocones_iso_component_inv_app", "category_theory.functor.to_cone_X", "sup_eq_max", "has_sum.summable", "pgame.le_refl", "free_abelian_group.lift.ext", "category_theory.limits.prod.left_unitor_inv", "ordinal.lift_card", "encodable.decode_option_succ", "finset.image_const", "ordinal.lift_down'", "local_equiv.prod_coe_symm", "list.exists_of_mem_join", "int.sub_nat_nat_of_sub_eq_zero", "submonoid.localization_map.of_mul_equiv_of_localizations_eq_iff_eq", "polynomial.ring_hom_eval\:2082_algebra_map_int", "fin.succ_last", "category_theory.functor.map_hom_inv", "localization_map.mk'_surjective", "free_add_semigroup.traverse_eq", "set.indicator_preimage_of_not_mem", "category_theory.arrow.lift_mk'_left", "finset.mem_union", "complex.of_real_smul", "measure_theory.outer_measure.trim_le_trim", "lucas_lehmer.mersenne_int_ne_zero", "power_series.is_unit_constant_coeff", "generalized_continued_fraction.second_continuant_aux_eq", "measure_theory.integral_eq_lintegral_of_nonneg_ae", "alg_hom.injective_cod_restrict", "real.Ioo_eq_ball", "zsqrtd.add_im", "is_add_group_hom.injective_of_trivial_ker", "category_theory.under.under_left", "ideal.sup_mul_right_self", "decidable_linear_ordered_add_comm_group.eq_of_abs_sub_nonpos", "div_mul_cancel_of_invertible", "category_theory.nat_trans.congr_app", "list.mem_of_mem_erase", "turing.TM2to1.tr_eval_dom", "group.closure_subset", "quadratic_form.discr_smul", "real.pi_gt_three", "fin.val_mul", "encodable.decode_of_equiv", "nat.coprime_primes", "category_theory.limits.coprod_map_comp_id", "list.sublists'_singleton", "list.filter_of_map", "nat.mod_add_div", "set.union_left_comm", "continuous.neg", "ring.fractional_ideal.map_comp", "ennreal.lt_iff_exists_coe", "polynomial.eval\:2082_monomial", "prime_spectrum.is_open_iff", "inner_div_norm_mul_norm_eq_neg_one_iff", "computation.parallel_congr_left", "linear_map.ker_prod", "ring_hom.mem_srange", "finsupp.sum_ite_eq", "is_add_group_hom.add", "tendsto_nhds_unique'", "strict_mono.add_monotone", "finset.fold_max_lt", "is_absolute_value.abs_abv_sub_le_abv_sub", "add_con.add", "filter.tendsto.inv", "zmod.cast_one'", "le_max_iff", "set.bUnion_preimage_singleton", "list.chain'.rel_head'", "circle_deg1_lift.iterate_pos_lt_iff", "list.lookmap_of_forall_not", "category_theory.monad.forget_creates_colimits.new_cocone_\[Iota]", "has_fderiv_at_filter_real_equiv", "fintype.subtype_card", "nhds_within_Ico_eq_nhds_within_Ici", "linear_independent.total_repr", "linear_map.trace_aux_eq", "deriv_add", "ennreal.inv_one", "finset.mem_insert", "uniform_space.of_core_eq_to_core", "nat.mod_eq_sub_mod", "add_left_iterate", "filter.tendsto_at_bot'", "inv_inv", "decidable.le_iff_le_iff_lt_iff_lt", "affine.simplex.inner_monge_point_vsub_face_centroid_vsub", "nat.lt_add_one_iff", "is_unit_pow", "circle_deg1_lift.commute_add_int", "ordered_ring.mul_le_mul_of_nonneg_left", "finsupp.sum_zero_index", "multiset.nodup_inter_left", "with_top.nat_ne_top", "filter.tendsto_infi", "is_G\[Delta]_Inter", "nnreal.tendsto_coe", "measure_theory.integrable.sub", "power_series.X_dvd_iff", "nhds_translation", "filter.exists_lt_of_tendsto_at_bot", "filter.frequently_or_distrib_right", "pell.yn_modeq_two", "category_theory.limits.biprod.braiding_hom", "set.range_nonempty", "lt_mul_of_inv_mul_lt_right", "generalized_continued_fraction.terminated_at_iff_s_none", "filter.comap_supr", "nat.le_rec_on_succ", "ordinal.mul_add", "dfinsupp.prod_subtype_domain_index", "tensor_product.ext", "asymptotics.is_o_refl_left", "cardinal.cof_is_regular", "omega.nat.nnf_equiv", "finsupp.sigma_sum", "measurable_equiv.symm_to_equiv", "infi_eq_if", "nat.partrec.code.eval_eq_rfind_opt", "exists_deriv_eq_zero'", "ennreal.supr_add_supr_of_monotone", "set.dual_Ici", "set.sInter_union", "algebra.tensor_product.include_left_apply", "mdifferentiable_on_iff_differentiable_on", "nat.lt_one_add_iff", "pfunctor.M.bisim_equiv", "polynomial.coeff_expand_mul'", "multiset.le_erase_dup", "finset.sum_filter", "has_fderiv_at.has_fderiv_at_filter", "wseq.lift_rel_o.imp", "cardinal.omega_ne_zero", "category_theory.limits.biprod.lift_desc_assoc", "ordinal.is_normal.nfp_fp", "finsupp.lsingle_range_le_ker_lapply", "free_add_magma.traverse_pure", "continuous_induced_dom", "differentiable_on.prod", "surj_on_Iic_of_monotone_surjective", "multiset.eq_union_left", "linear_map.mk_continuous_apply", "add_subgroup.top_prod_top", "zmod.prime_ne_zero", "padic_val_rat_def", "order_iso.map_bot", "zero_eq_mul_self", "mvqpf.comp.get_map", "filter.at_bot_countable_basis", "subsemiring.closure_eq_of_le", "lie_algebra.equiv.apply_symm_apply", "UniformSpace.coe_comp", "add_halves", "convex.is_path_connected", "list.sum_append", "enat.with_top_equiv_symm_coe", "cauchy_map_iff", "mv_polynomial.is_homogeneous_zero", "circle_deg1_lift.translation_number_of_eq_add_int", "complex.of_real_eq_coe", "pequiv.trans_single_of_mem", "linear_equiv.coe_of_eq_apply", "free_magma.pure_bind", "smooth_manifold_with_corners.compatible", "model_with_corners_prod_to_local_equiv", "monotone.mul", "int.neg_succ_of_nat_mul_neg_of_nat", "con.Sup_def", "measure_theory.induced_outer_measure_exists_set", "nat.sub_le", "set.to_finset_inj", "norm_num.add_pos_neg_neg", "uniformity_subtype", "list.perm.nil_eq", "submodule.inf_orthogonal", "set.mem_seq_iff", "decidable.le_of_not_lt", "linear_pmap.sup_le", "eq_inv_mul_of_mul_eq", "category_theory.iso.symm_symm_eq", "finset.sum_singleton", "multiset.Ico.map_sub", "has_fderiv_at.const_mul", "filter.is_basis.mem_filter_basis_iff", "lt_neg", "measurable.max", "set.finite.compact_convex_hull", "metric.second_countable_of_almost_dense_set", "category_theory.fork_\[Iota]_comp_cofork_\[Pi]_assoc", "monoid_hom.eq_on_closure", "set.eq_empty_of_not_nonempty", "filter.mem_hyperfilter_of_finite_compl", "list.reverse_reverse", "lt_of_mul_lt_mul_left'", "is_irreducible.is_preirreducible", "list.chain_of_chain_cons", "finset.inter_distrib_right", "closed_embedding_sigma_mk", "ring.fractional_ideal.exists_eq_span_singleton_mul", "vector_span_eq_top_of_affine_independent_of_card_eq_findim_add_one", "pgame.lt_of_lt_of_le", "complex.sin_two_pi", "nat.modeq.modeq_mul_left'", "fin.eta", "local_equiv.restr_univ", "set.finite.dependent_image", "finsupp_tensor_finsupp_single", "multilinear_map.smul_apply", "neg_div", "filter.le_lift", "lie_algebra.orthogonal.JD_transform", "local_equiv.coe_trans_symm", "local_homeomorph.continuous_at", "div_div_div_div_eq", "category_theory.limits.has_image_map.factor_map", "set.image_const_add_Ici", "measure_theory.outer_measure.union_null", "mul_semiring_action_hom.id_apply", "int.coe_nat_abs", "category_theory.monoidal_of_has_finite_products.right_unitor_inv", "nat.le_sub_add", "deriv.lhopital_zero_left_on_Ioo", "multiset.to_finsupp_to_multiset", "int.add_pos_of_nonneg_of_pos", "approximates_linear_on.injective", "category_theory.non_preadditive_abelian.add_comp", "set.union_mul", "int.lt_add_one_of_le", "continuous_linear_map.norm_def", "norm_sub_mul_self", "no_top_order.upper_bounds_univ", "nhds_eq_comap_uniformity", "ordinal.type_lt", "multiset.range_succ", "subtype.ne_of_val_ne", "category_theory.differential_object.hom.ext", "tsum_prod", "list.length_pos_of_mem_split_wrt_composition", "mul_lt_of_le_one_of_lt'", "principal_seg.trans_apply", "category_theory.limits.biprod.braiding_inv", "implicit_function_data.prod_map_implicit_function", "support_scale_roots_eq", "filter.eventually_eq.neg", "complex.tanh_neg", "sum.comp_traverse", "ereal.coe_real_lt", "filter.tendsto_at_top_of_monotone_of_subseq", "is_bounded_bilinear_map_smul_algebra", "is_R_or_C.norm_sq_pos", "generalized_continued_fraction.first_continuant_aux_eq_h_one", "has_deriv_at.has_deriv_at_filter", "algebra.left_comm", "le_nhds_of_cauchy_adhp", "category_theory.dite_comp", "pgame.numeric_rec", "equiv.set.apply_range_symm", "generalized_continued_fraction.first_denominator_eq", "free_abelian_group.map_neg", "real.angle.coe_two_pi", "with_zero.coe_inj", "uniform_continuous_sub", "locally_finite_of_finite", "list.nodup_of_nodup_append_left", "eq_one_div_of_mul_eq_one_left", "polynomial.le_nat_degree_of_ne_zero", "free_group.to_group.one", "complex.norm_sq_eq_zero", "add_subgroup.zero_mem", "bounded_continuous_function.continuous_comp", "comp_symm_mem_uniformity_sets", "measure_theory.lintegral_const", "harmonic_tendsto_at_top", "matrix.mul_nonsing_inv", "padic_norm.one", "category_theory.limits.biprod.inl_fst", "mvqpf.cofix.dest_corec'", "set.right_mem_Icc", "smul_ite", "differentiable_within_at.csin", "cardinal.eq_of_add_eq_of_omega_le", "set.empty_add", "nat.find_greatest_le", "complex.eq_conj_iff_real", "traversable.traverse_map", "convex.affine_image", "num.of_nat_to_znum", "iff_congr", "tendsto_of_uniform_continuous_subtype", "category_theory.epi_comp", "polynomial.coe_mul", "pgame.star_first_wins", "multiset.zero_ndunion", "ennreal.zero_div", "neg_pow", "measure_theory.measure.haar.chaar_self", "nat.lt_of_succ_le", "nat.succ_pnat_coe", "list.nil_union", "matrix.diagonal_comp_std_basis", "simple_graph.card_neighbor_set_eq_degree", "mul_lt_mul_of_lt_of_le", "finset.sum_bij'", "set.mem_compl_eq", "polynomial.C_pow", "is_compl_compl", "ordinal.succ_le", "free_group.to_group.inv", "category_theory.functor.map_conj_Aut", "int.neg_zero", "uniform_continuous_on_iff_restrict", "Module.Mon_Module_equivalence_Algebra.inverse_obj_2", "polynomial.mod_by_monic_one", "equiv.swap_core_comm", "add_lt_of_lt_of_nonpos'", "multiset.card_pos_iff_exists_mem", "normed_ring.inverse_add_norm_diff_second_order", "le_Sup", "linear_map.pi_apply", "open_embedding.prod", "list.sublists_perm_sublists'", "continuous_linear_equiv.ext", "category_theory.curry.obj_obj_obj", "list.nodupkeys_singleton", "multiset.countp_le_of_le", "asymptotics.is_O_with.prod_rightl", "Set.choice_is_func", "metric.exists_dist_lt_of_Hausdorff_dist_lt", "local_homeomorph.preimage_interior", "convex_on_univ_of_deriv_mono", "nnreal.coe_one", "list.pmap_congr", "category_theory.limits.colimit.\[Iota]_pre_assoc", "category_theory.equivalence.equivalence_mk'_counit", "add_con.ker_rel", "filter.lift_lift_same_le_lift", "con.Inf_to_setoid", "has_fpower_series_on_ball.mono", "filter.mem_infi_iff", "multiset.inf_eq_inter", "real.pi_pos", "list.tendsto_remove_nth", "linear_map.snd_eq_coprod", "sub_eq_zero_iff_eq", "mvqpf.recF_eq", "function.is_periodic_pt.mul_const", "category_theory.over.iterated_slice_equiv_counit_iso", "polynomial.monic_pow", "list.infix_of_suffix", "continuous_linear_map.has_fderiv_at", "range_quadrant", "dense_sInter_of_G\[Delta]", "category_theory.limits.image.ext", "sigma.eq", "pequiv.of_set_univ", "rat.cast_eq_zero", "iterated_fderiv_within_inter", "continuous_supr_rng", "set.bij_on.union", "nat.coprime.coprime_div_left", "local_homeomorph.eventually_left_inverse'", "hyperreal.coe_pos", "real.sqrt_two_add_series_step_up", "convex_Ico", "category_theory.monoidal.left_unitor_inv_app", "equiv.ext", "nat.mod_pow_succ", "monotone.infi_comp_eq", "dfinsupp.filter_apply_neg", "int.dvd_of_mul_dvd_mul_left", "le_bot_iff", "asymptotics.is_O_const_of_tendsto", "measure_theory.tendsto_integral_of_l1", "set.image_add_const_Iio", "finset.has_sum_iff_compl", "times_cont_mdiff_at_top", "complex.norm_eq_abs", "filter.germ.const_inj", "add_equiv.to_AddMon_iso_inv", "pgame.equiv_nim_iff_grundy_value_eq", "continuous.mul", "nat.partrec'.vec.prim", "computation.results.terminates", "sum_add_tsum_compl", "category_theory.adjunction.monad_\[Eta]_app", "cau_seq.le_total", "measure_theory.measure.haar.chaar_nonneg", "inner_self_eq_norm_square", "roption.bind_some_eq_map", "uniformity_has_basis_closed", "set.singleton_pi", "closure_Icc", "interval_integral.norm_integral_le_integral_norm_Ioc", "is_open_iff_ball_subset", "AddCommGroup.lift_\[Pi]_apply", "category_theory.over.iterated_slice_forward_forget", "equiv.subtype_preimage_symm_apply_coe_pos", "order_embedding.is_well_order", "real.Inf_lt", "linear_equiv.of_top_apply", "with_top.coe_add", "is_unit_iff_dvd_one", "stream.map_tail", "bilin_form.add_left", "is_open_map_sum", "Top.presheaf_to_Types_map", "with_top.well_founded_lt", "category_theory.monoidal_of_has_finite_products.left_unitor_inv", "metric.Hausdorff_dist_image", "onote.split_dvd", "iterated_fderiv_succ_apply_right", "tensor_product.ite_tmul", "nat.size_pow", "category_theory.comma.map_right_comp_inv_app_right", "computation.destruct_think", "nat.one_lt_bit1", "set.image_add", "matrix.trace_mul_comm", "lt_neg_add_of_add_lt", "finset.sum_range_add_sum_Ico", "rel.image_subset", "onote.repr_inj", "int.neg_le_neg", "free_add_semigroup.map_add", "fderiv_within_snd", "category_theory.equivalence.refl_functor", "nat.le_sub_right_of_add_le", "ennreal.coe_zero", "measure_theory.ae_eq_fun.lintegral_mk", "equiv.perm.sign_mul", "finset.sigma_image_fst_preimage_mk", "continuous.integrable_on_compact", "finset.inter_insert_of_mem", "category_theory.limits.cones.whiskering_obj", "set.preimage_subset_preimage_iff", "category_theory.monad.algebra.hom.id_f", "rat.coe_int_num_of_denom_eq_one", "units.neg_inv", "eq_of_le_of_forall_le_of_dense", "is_R_or_C.conj_eq_zero", "num.of_to_nat", "set.nonempty.some_mem", "set.preimage_eq", "asymptotics.is_o_const_mul_right_iff'", "filter.principal_ne_bot_iff", "filter.eventually_prod_iff", "ring_hom.is_unit_map", "multiset.revzip_powerset_aux", "smooth_at.prod_mk", "roption.map_none", "wseq.equiv.ext", "submodule.comap_mkq_embedding_eq", "finset.map_subset_iff_subset_preimage", "sym_sesq_form.sym", "lcm_comm", "filter.map_bot", "cardinal.mk_compl_of_omega_le", "times_cont_mdiff_on_iff_times_cont_diff_on", "gcd_mul_right", "approximates_linear_on.to_local_homeomorph_target", "pnat.xgcd_type.flip_is_reduced", "int.le_of_lt", "lt_sub_iff_add_lt'", "pfunctor.M.mk_inj", "complex.of_real_exp", "directed_on_iff_directed", "is_measurable_range_inr", "continuous_linear_map.ker_coe", "category_theory.split_mono.id_assoc", "fintype.prod_apply", "rel_iso.of_surjective_coe", "ennreal.max_zero_left", "category_theory.monoidal_category.tensor_left_iff", "option.map_eq_some'", "set.image2_empty_left", "localization.induction_on\:2083", "multiset.foldl_add", "monoid_algebra.alg_hom_ext", "ordered_ring.mul_lt_mul_of_pos_left", "finset.pi_val", "list.prod_reverse", "local_homeomorph.of_set_univ_eq_refl", "continuous_multilinear_map.op_norm_add_le", "decidable.not_exists_not", "has_lt.lt.false", "nat.primrec'.nil", "mul_mul_mul_comm", "unit_of_invertible_inv", "category_theory.limits.prod_right_unitor_hom_naturality_assoc", "nat.choose_mul_fact_mul_fact", "set.Iio_subset_Iic_self", "list.rel_sections", "bifunctor.fst_id", "monoid_hom.comp_coprod", "ordinal.add_absorp_iff", "category_theory.biprod.of_components_eq", "int.lcm_comm", "is_measurable.Union", "differentiable_within_at.const_smul_algebra", "local_ring.le_maximal_ideal", "nat.dvd_add_iff_left", "convex_on.smul", "ideal.subset_span", "group.subset_conjugates_of_set", "multiset.card_range", "one_nsmul", "finset.affine_combination_of_eq_one_of_eq_zero", "homeomorph.refl_to_local_homeomorph", "div_mul_cancel_of_imp", "int.le_neg_add_of_add_le", "finset.union_val", "nat.pred_succ", "neg_lt_sub_right_of_lt_add", "category_theory.monoidal.Mon_functor_category_equivalence_unit_iso", "set_is_basis_of_span_eq_top_of_card_eq_findim", "add_con.coe_add", "nat.bit1_lt_bit0", "finsupp.induction", "ring_hom.map_mul", "fin.coe_sub_nat", "add_subgroup.mem_closure", "mul_self_eq_one_iff", "has_mfderiv_within_at.congr_of_eventually_eq", "set.image_comp", "prod.fst_inv", "one_div_lt_of_neg", "subgroup.coe_mk", "filter.tendsto_at_bot_add_right_of_ge", "ring_hom.prod_apply", "add_localization.add_equiv_of_quotient_apply", "continuous_multilinear_map.map_add_univ", "map_nhds", "category_theory.functor.image_preimage", "localization_map.is_unit_comp", "nat.modeq.modeq_add", "function.left_id", "mdifferentiable.continuous", "real.sqrt_sqr_eq_abs", "subgroup.prod_mono", "list.filter_false", "preimage_interior_subset_interior_preimage", "generalized_continued_fraction.succ_nth_fib_le_of_nth_denom", "category_theory.limits.eq_zero_of_image_eq_zero", "interior_empty", "ennreal.zero_ne_top", "polynomial.degree_eq_iff_nat_degree_eq", "pnat.gcd_eq_left", "ideal.radical_top", "bounded_continuous_function.arzela_ascoli\:2081", "quotient_add_group.range_ker_lift_surjective", "is_measurable.congr", "complex.exists_forall_abs_polynomial_eval_le", "add_eq_of_eq_neg_add", "measure_theory.hahn_decomposition", "submodule.quotient.mk_zero", "is_R_or_C.of_real_im", "array.mem_to_list_enum", "add_submonoid.mrange_inl_sup_mrange_inr", "filter.limsup_const", "is_local_min_on.bicomp_mono", "category_theory.preadditive.neg_comp_neg_assoc", "int.div_eq_of_eq_mul_left", "category_theory.op_equiv_apply", "polynomial.is_root_of_eval\:2082_map_eq_zero", "cSup_singleton", "interval_integral.integral_symm", "continuous_apply", "game.add_left_neg", "finset.coe_filter", "cardinal.lift_mk_le", "category_theory.is_iso.iso.inv_hom", "polynomial.eval\:2082_restriction", "computation.equiv_ret_of_mem", "commute.inv_left'", "polynomial.nat_degree_prod", "not_of_not_imp", "function.right_inverse.injective", "submodule.lt_top_of_findim_lt_findim", "free_abelian_group.map_pure", "inv_lt_inv''", "category_theory.functor.map_hom_congr", "filter.tendsto_fst", "hyperreal.lt_of_is_st_lt", "finset.coe_image", "ennreal.le_of_real_iff_to_real_le", "neg_add_eq_of_eq_add", "typevec.last_fun_subtype_val", "list.last'_append_of_ne_nil", "ennreal.supr_sub", "padic.const_equiv", "uniform_space.completion.uniform_continuous_completion_separation_quotient_equiv", "le_mul_iff_one_le_right'", "denumerable.of_nat_encode", "finsupp.mem_span_iff_total", "category_theory.preadditive.neg_comp", "equiv.conj_comp", "nsmul_le_nsmul", "le_neg_add_of_add_le", "is_open_iff_mem_nhds", "mul_lt_one_of_lt_one_of_le_one'", "set.preimage_const_mul_Ico_of_neg", "Module.Mon_Module_equivalence_Algebra.inverse_obj_one", "fixed_points.of_eval\:2082", "is_R_or_C.conj_conj", "filter.tendsto_at_bot_principal", "dfinsupp.zip_with_def", "set.sInter_eq_Inter", "function.semiconj.comp_right", "pnat.xgcd_type.step_wf", "category_theory.op_op_map", "function.semiconj.iterate_right", "list.count_bag_inter", "pow_bit1", "finsupp.frange_single", "category_theory.limits.biprod.symmetry", "pell.pell_zd_succ_succ", "additive.normal_add_subgroup", "subring.top_prod", "filter.map_pure", "computation.length_ret", "nat.lt_trans", "continuous_on_iff", "polynomial.ne_zero_of_monic_of_zero_ne_one", "nat.add_one_le_iff", "set.sUnion_eq_univ_iff", "nat.Sup_def", "measure_theory.measure_Union_null", "list.minimum_eq_none", "antilipschitz_with.mul_le_dist", "free_abelian_group.map_zero", "nat.fact_zero", "add_monoid.exists_list_of_mem_closure", "cau_seq.lim_eq_of_equiv_const", "option.bind_comm", "multiset.nodup_erase_eq_filter", "padic.cast_eq_of_rat_of_nat", "filter.mem_add", "linear_independent_iff_not_mem_span", "multiset.inf_singleton", "list.mem_join", "lie_skew", "submodule.ker_of_le", "add_submonoid.mem_comap", "emetric.Hausdorff_edist_le_of_inf_edist", "cardinal.is_strong_limit.is_limit", "has_fderiv_within_at.add", "vadd_mem_span_points_of_mem_span_points_of_mem_vector_span", "differentiable_within_at.inv", "category_theory.limits.pullback.lift_snd_assoc", "ordinal.typein_le_typein", "ennreal.coe_nat_mono", "typevec.split_fun_inj", "rat.denom_dvd", "emetric.is_open_iff", "prod.edist_eq", "band_eq_false_eq_eq_ff_or_eq_ff", "filter.comap_ne_bot_iff", "multiset.ndinsert_le", "category_theory.monoidal.right_unitor_hom_app", "nat.eq_zero_of_add_eq_zero_right", "inv_mul_mul_self", "metric.inf_dist_le_inf_dist_of_subset", "exist_quadratic_eq_zero", "lt_inv_of_neg", "add_commute.right_comm", "filter.tendsto_at_top_add_nonneg_left'", "mv_polynomial.eval\:2082_comp_right", "list.prefix_concat", "matrix.empty_vec_mul", "matrix.dot_product_cons", "category_theory.limits.types.initial", "setoid.eq_iff_rel_eq", "strict_mono_mul_left_of_pos", "is_local_max.comp_mono", "cau_seq.not_lim_zero_of_not_congr_zero", "measure_theory.outer_measure.of_function_eq", "nat.partrec'.of_part", "convex_sInter", "primrec.dom_bool", "asymptotics.is_O_with_norm_left", "add_commute.zero_right", "list.filter_map_eq_filter", "times_cont_diff_of_differentiable_iterated_fderiv", "int.sub_left_lt_of_lt_add", "nndist_triangle", "omega.int.preform.sat_or", "circle_deg1_lift.lt_map_of_int_lt_translation_number", "sequentially_complete.set_seq_mono", "prod.fst_prod", "nnnorm_zero", "hyperreal.infinite_neg_mul_of_infinite_neg_not_infinitesimal_pos", "denumerable.list_of_nat_zero", "neg_lt_sub_iff_lt_add", "polynomial.nat_degree_eq_of_degree_eq", "nat.eq_zero_of_add_eq_zero", "vector.mk_to_list", "filter.supr_sets_eq", "finsupp.sum_sum_index", "measure_theory.l1.of_fun_sub", "polynomial.ne_zero_of_monic", "ring_equiv.bijective", "measure_theory.simple_func.is_measurable_fiber", "list.sublist_cons_of_sublist", "Class.to_Set_of_Set", "filter.germ.max_def", "add_localization.mk_zero_eq_add_monoid_of_mk", "polynomial.separable.inj_of_prod_X_sub_C", "iterated_fderiv_within_inter'", "fderiv_within_add", "list.map_id'", "nat.lt_add_left", "lt_base_pow_length_digits", "set.maps_to.mono", "filter.is_ultrafilter.unique", "linear_map.map_zero", "mv_polynomial.eval\:2082_mul_monomial", "cau_seq.completion.inv_mk", "function.commute.self_iterate", "measure_theory.outer_measure.measure_of_eq_coe", "measure_theory.simple_func.pair_apply", "primorial_le_4_pow", "differentiable.iterate", "ennreal.continuous_mul_const", "frontier_Ici", "int.units_inv_eq_self", "joined.mem_path_component", "dense_range.nhds_within_ne_bot", "prime_multiset.coe_pnat_injective", "has_deriv_at.const_add", "multiset.to_finset_union", "has_deriv_at.iterate", "add_submonoid.localization_map.add_equiv_of_add_equiv_eq_map", "is_coprime.mul_add_left_left", "neg_add_self", "turing.mem_eval", "traversable.id_sequence", "ordinal.type_le'", "cardinal.extend_function_of_lt", "filter.sup_join", "category_theory.limits.types.image_map", "continuous_id'", "uniform_embedding.prod", "nat.div_eq_of_lt", "list.singleton_sublist", "asymptotics.is_O_with_zero", "add_comm_group.direct_limit.lift_sub", "complex.add_im", "submodule.span_mono", "finsupp.mem_support_multiset_sum", "list.ne_of_not_mem_cons", "multiset.add_comm", "is_linear_map.with_bound", "linear_equiv.refl_apply", "znum.bit0_of_bit0", "ordinal.mul_le_mul", "hyperreal.infinitesimal_sub_is_st", "prime_multiset.prod_dvd_iff", "setoid.ext_iff", "category_theory.biprod.inr_of_components", "int.nat_abs_of_nat", "circle_deg1_lift.map_map_zero_le", "measure_theory.outer_measure.restrict_apply", "list.append_ne_nil_of_ne_nil_left", "stream.head_zip", "simple_graph.mem_neighbor_set", "add_subgroup.coe_gsmul", "submonoid.map_injective_of_injective", "associates.prod_le_prod_iff_le", "zmod.mul_inv_eq_gcd", "bool.to_bool_not", "pfun.mem_restrict", "category_theory.functor.map_presheaf_map_f", "set.finite.image", "set.image_singleton", "ennreal.coe_eq_one", "category_theory.limits.cokernel.\[Pi]_desc", "continuous_linear_equiv.has_fderiv_at", "localization_map.injective", "is_measurable_ball", "quadratic_form.associated_comp", "cmp_using_eq_gt", "mv_polynomial.is_id", "nat.partrec.code.prec_prim", "category_theory.functor.id_map", "finset.mem_attach", "nat.add_mul_mod_self_right", "asymptotics.is_o.trans_tendsto", "finset.sum_centroid_weights_eq_one_of_cast_card_ne_zero", "add_localization.add_equiv_of_quotient_mk", "computable.sum_inr", "primrec.nat_bodd_div2", "asymptotics.is_O_with_fst_prod", "linear_equiv.of_linear_symm_apply", "exists_nhds_half_neg", "filter.tendsto_finset_image_at_top_at_top", "matrix.neg_vec_mul", "ordinal.bsup_le", "setoid.ext", "filter.eventually_eq.sub", "set.subsingleton.image", "has_deriv_at_filter.sub_const", "measurable_inv", "power_series.order_eq_nat", "add_nonpos", "circle_deg1_lift.translation_number_eq_int_iff", "exists_prop", "subring.mk'_to_submonoid", "iterated_fderiv_within_one_apply", "is_R_or_C.inv_im", "submonoid.localization_map.mk'_mul", "znum.of_int_cast", "list.length_cons", "tactic.ring_exp.mul_pf_zero", "subalgebra.range_subset", "exists_int_pow_near", "finset.sum_le_sum_of_subset_of_nonneg", "fn_min_mul_fn_max", "real.sin_add_two_pi", "not_bdd_above_iff", "add_subgroup.mem_closure_singleton", "category_theory.limits.cocone.of_cofork_\[Iota]", "add_submonoid.coe_injective", "add_units.coe_add_right", "norm_num.rat_cast_neg", "pgame.lt_def", "bnot_eq_ff_eq_eq_tt", "measurable.add", "finite_dimensional.exists_is_basis_finite", "continuous_linear_map.coe_inj", "filter.is_compl_principal", "ordinal.power_dvd_power", "filter.eventually.mono", "submodule.mem_orthogonal'", "hyperreal.st_add", "iterated_fderiv_zero_eq_comp", "list.insert_of_mem", "is_local_max_on.inf", "category_theory.functor.id_obj", "category_theory.limits.zero_of_comp_mono", "filter.prod_same_eq", "hash_map.mk_valid", "prime_multiset.coe_prod", "linear_map.range_cod_restrict", "ordinal.enum_le_enum", "is_lub_of_is_glb_of_tendsto", "linear_map.prod_map_apply", "set.preimage_const_add_Ioi", "joined_in_iff_joined", "set.preimage_const_sub_Ioo", "le_add_of_neg_le_sub_right", "equiv.perm.disjoint_mul_left", "set.union_diff_cancel", "local_homeomorph.image_open_of_open", "nat.sqrt_le_sqrt", "complex.bit1_im", "mdifferentiable_within_at.congr_mono", "finset.map_val", "of_digits_mod", "category_theory.functor_to_types.inv_hom_id_app_apply", "is_bounded_bilinear_map_apply", "AddCommGroup.coe_of", "list.ne_and_not_mem_of_not_mem_cons", "measure_theory.extend_eq", "emetric.uniform_continuous_iff", "nat.sub_sub_sub_cancel_right", "metric.continuous_at_iff'", "nat.lcm_one_right", "metric.ball_mem_nhds", "continuous_linear_equiv.coe_refl", "function.inv_fun_on_eq", "not_imp_eq_of_eq_false_right", "eq_irreducible_component", "real.tan_nonpos_of_nonpos_of_neg_pi_div_two_le", "measure_theory.simple_func.const_mul_lintegral", "rat.mk_pnat_eq", "is_closed_Iic", "commute.fpow_fpow_self", "ring_hom.closure_preimage_le", "interval_integral.integral_interval_sub_left", "filter.map_def", "differentiable_on.restrict_scalars", "pgame.impartial.first_wins_symm'", "free_group.red.step.length", "commute.zero_right", "int.neg_lt_sub_left_of_lt_add", "mvqpf.supp_map", "subsemiring.ext'_iff", "eq_top_mono", "traversable.pure_traverse", "real.continuous_rpow_aux2", "has_fderiv_at_filter.fst", "zmod.val_injective", "multiset.Ico.succ_singleton", "multiset.coe_erase_dup", "model_with_corners.to_local_equiv_coe_symm", "is_basis.mem_span", "zero_le_one", "add_localization.r_iff_exists", "traversable.mfoldl.unop_of_free_monoid", "hyperreal.neg_of_infinite_neg", "is_measurable_range_inl", "is_preconnected.eq_univ_of_unbounded", "metric.lipschitz_inf_dist_pt", "mul_aut.apply_inv_self", "measure_theory.l1.simple_func.eq'", "add_le_iff_nonpos_right", "finsupp.subtype_domain_zero", "real.sqrt_two_add_series_one", "list.nodup_filter", "nat.div_def", "bounded_continuous_function.dist_eq", "finset.prod_apply_ite", "list.eq_or_ne_mem_of_mem", "list.tail_suffix", "monoid_hom.eq_lift_of_surjective", "set.diff_Union", "except_t.run_pure", "measure_theory.measure.regular.conj", "irrefl_of", "dfinsupp.lmk_apply", "pos_num.cmp_to_nat_lemma", "add_lt_of_neg_of_lt'", "metric.bounded_iff_ediam_ne_top", "set.Ioo_subset_Ioo_iff", "exists_nhds_half", "mem_ball_symmetry", "turing.TM2to1.add_bottom_modify_nth", "set.Union_empty", "ring.fractional_ideal.fractional_mul", "polynomial.eval\:2082_hom", "filter.tendsto_at_top_add", "linear_map.le_ker_iff_map", "euclidean_domain.mod_self", "mvpfunctor.M.dest_corec", "onote.add_NF_below", "nat.partrec.of_eq_tot", "lists.lt_sizeof_cons'", "equiv.set.sum_compl_apply_inl", "quot.lift\:2082_mk", "zmod.exists_pow_two_eq_prime_iff_of_mod_four_eq_one", "is_connected.closure", "euclidean_domain.gcd.induction", "padic_int.sub_zmod_repr_mem", "ordinal.log_le_self", "mvpfunctor.M.dest_map", "le_add_of_le_of_nonneg", "add_submonoid.localization_map.mk'_sec", "holor_index.drop_drop", "is_closed_discrete", "turing.blank_extends.refl", "pSet.resp.euc", "add_magma.free_add_semigroup.of_add_assoc_left", "module.card_fintype", "upper_bounds_mono", "matrix.ring_hom.map_det", "set.right_inv_on.congr_left", "Inf_image", "multilinear_map.cons_add", "dvd_antisymm_of_normalize_eq", "iterated_fderiv_within_eq_equiv_comp", "bind_pure", "dfinsupp.prod_finset_sum_index", "set.mem_compl_image", "nat.shiftl_sub", "finset.bInter_finset_image", "category_theory.limits.image.fac", "onote.oadd_lt_oadd_2", "finset.sup_union", "tt_eq_ff_eq_false", "ordinal.is_normal.fp_iff_deriv", "closed_under_restriction'", "set.snd_image_prod", "nat.coprime.mul_dvd_of_dvd_of_dvd", "nhds_within_ne_bot_of_mem", "differentiable_at.sum", "nnreal.sub_zero", "bilin_form.to_matrix_smul", "pnat.xgcd_type.finish_is_reduced", "initial_seg.refl_apply", "category_theory.limits.cocones.whiskering_map_hom", "metric.mem_ball", "dense_embedding.prod", "ennreal.to_real_sum", "set.preimage_const_sub_Ioc", "pgame.zero_first_loses", "set.ext", "category_theory.functor.cocones_map_app", "monoid_hom.lift_of_surjective_comp", "finset.prod_singleton", "frontier_Iic", "mul_right_cancel", "fpow_sub_one", "pow_mul'", "function.minimal_period_pos_of_mem_periodic_pts", "add_commute.neg_left", "list.rotate_eq_take_append_drop", "multiset.sub_le_sub_left", "int.lcm_one_left", "set.sInter_singleton", "computation.empty_promises", "int.norm_cast_rat", "is_least.bdd_below", "finset.map_empty", "is_compact.finite_measure_of_nhds_within", "set.compl_Iic", "list.singleton_perm_singleton", "category_theory.limits.mono_of_is_limit_parallel_pair", "pgame.lt_iff_neg_gt", "classical.epsilon_spec", "option.to_finset_none", "equiv.set.range_apply", "int.of_nat_mul_neg_succ_of_nat", "exists_deriv_eq_zero", "nhds_le_uniformity", "Mod.hom.ext_iff", "polynomial.zero_mod_by_monic", "monoid_hom.iterate_map_frobenius", "has_ftaylor_series_up_to_on_succ_iff_left", "set.insert_diff_of_not_mem", "mem_smul_set_iff_inv_smul_mem", "quotient_add_group.induction_on'", "tactic.ring_exp.pow_p_pf_zero", "pgame.add_le_add_right", "is_local_extr_on.comp_continuous_on", "rat.cast_coe_nat", "list.continuous_at_length", "top_sup_eq", "of_digits_lt_base_pow_length", "generalized_continued_fraction.squash_gcf_eq_self_of_terminated", "mv_polynomial.is_homogeneous_one", "is_closed_univ", "div_le_div_iff", "finsupp.to_multiset_zero", "mv_polynomial.map_range_eq_map", "bxor_self", "ideal.jacobson_eq_bot", "is_glb.unique", "subalgebra.fg_def", "finset.le_max_of_mem", "times_cont_mdiff_within_at.of_succ", "nsmul_add_comm", "pgame.lt_asymm", "compact_univ_pi", "tactic.abel.unfold_sub", "monotone.map_Inf_le", "multiset.mem_to_list", "le_or_lt", "fderiv.comp_deriv", "subset_Icc_cInf_cSup", "nat.ldiff_bit", "is_local_min_on.sub", "int.even_bit0", "is_submonoid.coe_one", "real.exp_le_exp", "dfinsupp.sum_neg", "asymptotics.is_o_const_iff", "category_theory.Comonad.comp_to_nat_trans", "multiset.countp_pos_of_mem", "free_ring.coe_surjective", "nontrivial_of_ne", "to_add_injective", "int.cast_id", "ordinal.le_cof_type", "valuation.is_equiv.of_eq", "times_cont_diff_within_at.sub", "interval_integral.integral_const", "real.pi_gt_3141592", "eq_one_of_pow_eq_one", "abstract_completion.extend_comp_coe", "set.bij_on.to_local_equiv_source", "set.update_preimage_univ_pi", "real.rpow_le_rpow_of_exponent_le", "embedding.comp", "encodable.decode_sigma_val", "fin.succ_pred", "max_le_iff", "local_homeomorph.restr_source", "ennreal.sub_eq_zero_iff_le", "category_theory.monad.forget_creates_limits.new_cone_\[Pi]", "multiset.foldr_cons", "partrec.map", "associates.mul_eq_one_iff", "list.count_concat", "times_cont_mdiff_on_chart", "encodable.Union_decode2_cases", "filter.tendsto_at_top_mono", "le_neg_of_le_neg", "list.subset_inter", "int.lt_add_of_neg_add_lt_left", "closure_Ici", "polynomial.expand_one", "continuous_linear_map.isometry_iff_norm_image_eq_norm", "sub_le_of_abs_sub_le_left", "mv_polynomial.C_mul_monomial", "wseq.lift_rel_join", "asymptotics.is_o_const_smul_left_iff", "cauchy.comap'", "int.dist_cast_rat", "measure_theory.integrable_on_const", "con.mem_coe", "hyperreal.infinitesimal_neg_iff", "filter.tendsto_at_top_of_add_bdd_above_left'", "list.kerase_of_not_mem_keys", "filter.is_cobounded_top", "pequiv.of_set_eq_some_iff", "list.reverse_eq_nil", "ennreal.rpow_neg", "finset.insert_inter_of_not_mem", "real.is_conjugate_exponent.one_div_ne_zero", "monoid.image_closure", "nat.binary_rec_eq", "function.equiv.refl", "equiv.subtype_equiv_codomain_symm_apply_eq", "matrix.cramer_column_self", "finset.sdiff_inter_self_left", "set.subset_compl_iff_disjoint", "filter.generate_Union", "coe_ff", "list.eq_repeat'", "category_theory.limits.cones.postcompose_equivalence_unit_iso", "associates.prod_mk", "category_theory.limits.biprod.braid_natural", "ordinal.is_normal.le_nfp", "nat.nat_zero_eq_zero", "ordinal.is_normal.sup", "list.nodup_concat", "num.of_nat_to_znum_neg", "mv_polynomial.eval\:2082_hom_X", "ordinal.lift_type_eq", "zmod.val_coe_unit_coprime", "set.finite_Union", "units.norm_pos", "is_preconnected_Iic", "mul_le_mul_iff_right", "list.keys_nil", "le_mul_of_inv_mul_le_right", "set.Union_disjointed_of_mono", "is_open_compl_iff", "asymptotics.is_o_norm_left", "nnreal.rpow_le_rpow", "category_theory.limits.kernel_fork.\[Iota]_of_\[Iota]", "measure_theory.lintegral_eq_supr_eapprox_lintegral", "metric.to_inductive_limit_isometry", "set.indicator_univ", "local_homeomorph.to_homeomorph_coe", "real.sqrt_le", "max_eq_right", "category_theory.Monad.Monad_Mon_equiv_counit_iso", "joined_in.mem", "fin.coe_eq_cast_succ", "real.sqrt_two_add_series_nonneg", "turing.tape.map_write", "fintype.card_bool", "with_bot.coe_lt_coe", "list.mem_foldr_permutations_aux2", "metric.inf_dist_le_dist_of_mem", "pfunctor.M.default_consistent", "rel.codom_inv", "has_fderiv_within_at.has_deriv_within_at", "euclidean_domain.mul_div_cancel", "quadratic_form.equivalent.trans", "lists'.mem_of_subset'", "nat.primrec'.of_prim", "fin.comp_snoc", "cau_seq.completion.of_rat_neg", "ordinal.zero_power", "list.drop_one", "topological_space.open_nhds.inclusion_map_iso_inv", "mem_nhds_within_Iio_iff_exists_Ioo_subset", "measure_theory.simple_func.zero_lintegral", "free_group.map.inv", "multiset.Ico.pred_singleton", "quotient_prod_linear_equiv", "int.cast_bit0", "many_one_degree.le_trans", "list.erase_cons_head", "ordinal.mul_is_limit", "has_deriv_within_at.inv", "circle_deg1_lift.map_lt_of_translation_number_lt_nat", "list.perm.count_eq", "convex_Iic", "computation.bind_ret'", "sesq_form.neg_left", "is_local_max_on.min", "linear_pmap.eq_of_le_of_domain_eq", "norm_num.ne_zero_of_pos", "range_proj_I", "measure_theory.measure.haar.le_index_mul", "category_theory.pi.id_apply", "filter.sup_principal", "polynomial.degree_pow'", "bilin_form.add_right", "filter.tendsto_of_not_nonempty", "lt_add_iff_pos_left", "category_theory.over.w", "affine.simplex.mk_of_point_points", "ordinal.cof_eq_zero", "set.union_diff_cancel_right", "ordinal.add_le_of_limit", "polynomial.separable.of_dvd", "set.subset_subset_Union", "nat.find_min", "is_null_measurable_of_complete", "mdifferentiable_on_const", "list.product_nil", "multiplicative.is_mul_hom", "fintype.card_empty", "functor.comp.run_pure", "submodule.is_compl_orthogonal_of_is_complete", "set.univ_eq_empty_iff", "mv_power_series.zero_mul", "filter.exists_le_of_tendsto_at_top", "real.pow_nat_rpow_nat_inv", "mul_gsmul_left", "set.maps_to.inter", "Cauchy.dense_embedding_pure_cauchy", "nat.add_lt_add", "continuous.inv", "primrec.fin_curry\:2081", "padic_int.coe_add", "filter.filter_eq_iff", "real.abs_rpow_le_abs_rpow", "real.tanh_neg", "set.eval_image_univ_pi", "tendsto_iff_of_dist", "alist.extract_eq_lookup_erase", "polynomial.aeval_def", "fin.cast_succ_zero", "lt_is_lub_iff", "prime_spectrum.subset_zero_locus_vanishing_ideal", "filter.rtendsto_def", "times_cont_mdiff.of_le", "metric.diam_subsingleton", "measure_theory.lintegral_infi_ae", "ring.direct_limit.lift_pow", "order_of_eq_one_iff", "multiset.attach_zero", "wseq.mem_rec_on", "one_open_separated_mul", "filter.infi_ne_bot_iff_of_directed'", "filter.lift_lift'_same_le_lift'", "is_open_set_pi", "complex.of_real_cos_of_real_re", "measure_theory.simple_func.mem_restrict_range", "matrix.tail_cons", "add_submonoid.localization_map.lift_unique", "traversable.traverse_comp", "multiset.powerset_len_coe'", "mul_aut.inv_def", "category_theory.equivalence.trans_functor", "linear_map.id_comp", "ordinal.add_is_normal", "continuous_at_iff_continuous_left_right", "linear_map.map_le_range", "continuous_linear_equiv.self_comp_symm", "set.card_insert", "tangent_bundle.smooth_within_at_proj", "nat.succ_add_eq_succ_add", "topological_fiber_bundle_core.mem_local_triv_at_source", "unique.eq_default", "commute.gpow_right", "matrix.reindex_symm_apply", "mdifferentiable_at_atlas", "topological_space.opens.ext_iff", "set.left_mem_Icc", "measure_theory.extend_Union_le_tsum_nat", "is_preconnected_of_forall", "affine.simplex.monge_point_mem_monge_plane", "finset.lt_inf_iff", "hyperreal.infinitesimal_sub_st", "cau_seq.add_lim_zero", "mul_lt_of_lt_one_of_le", "unit.ext", "roption.eq_none_iff'", "pfunctor.M.iselect_cons", "norm_num.sle_bit1_bit1", "alg_equiv.map_add", "category_theory.limits.functor_category_limit_cone_X", "generalized_continued_fraction.of_h_eq_int_fract_pair_seq1_fst_b", "linear_map.inl_injective", "Gromov_Hausdorff.to_GH_space_lipschitz", "list.empty_eq", "set.image_add_const_Ici", "free_ring.map_of", "polynomial.monic.ne_zero", "category_theory.abelian.exact_iff", "turing.partrec_to_TM2.tr_respects", "complex.abs_exp_sub_one_le", "continuous_of_uniform_approx_of_continuous", "has_strict_deriv_at.smul", "zsqrtd.smuld_val", "principal_seg.cod_restrict_top", "local_homeomorph.trans_assoc", "setoid.le_def", "polynomial.eval\:2082_neg", "ordering.compares.eq_gt", "algebra.lmul_right_apply", "finsupp.total_map_domain", "joined_in.of_line", "category_theory.whisker_right_app", "category_theory.abelian.pseudoelement.pseudo_exact_of_exact", "simple_graph.mem_edge_finset", "list.chain_succ_range'", "int.mod_eq_of_lt", "int.neg_of_neg_pos", "category_theory.limits.cofork.of_\[Pi]_app_one", "add_left_injective", "rat.dist_eq", "semidirect_product.right_inl", "eq.congr", "mul_self_iff_eq_one", "geom_sum\:2082_mul_comm", "real.continuous_rpow", "qpf.liftr_iff", "ordinal.add_le_add_iff_right", "filter.map_eq_comap_of_inverse", "mat_poly_equiv_char_matrix", "vector3.cons_fz", "function.iterate_succ'", "pos_num.cast_inj", "gronwall_bound_\[CurlyEpsilon]0", "closure_le_eq", "nat.partrec.rfind'", "bdd_above_Iic", "convex_hull_diam", "subalgebra.multiset_sum_mem", "add_submonoid.coe_map", "real.fpow_arith_mean_le_arith_mean_fpow", "circle_deg1_lift.iterate_le_of_map_le_add_int", "filter.mem_iff_inf_principal_compl", "primrec.list_index_of\:2081", "finset.inter_right_comm", "linarith.int.coe_nat_bit0_mul", "tensor_product.lift_compr\:2082", "measure_theory.all_ae_tendsto_of_real_norm", "set.union_self", "linear_equiv.coord_self", "generalized_continued_fraction.part_num_eq_s_a", "uniformity_edist", "sum.elim_inl", "quadratic_form.map_sub", "computable.vector_nth", "cardinal.mk_ord_out", "bitraversable.tsnd_id", "list.eq_cons_of_length_one", "summable_geometric_of_abs_lt_1", "semidirect_product.one_right", "asymptotics.is_o_const_mul_right_iff", "multiset.rel_join", "with_top.lattice_eq_DLO", "bex_or_distrib", "int.coe_nat_lt_coe_nat_iff", "polynomial.next_coeff_C_eq_zero", "padic_int.zero_ne_one", "ordinal.card_omega", "times_cont_mdiff_at.prod_map", "sub_floor_div_mul_lt", "ring_hom.map_add", "polynomial.has_fderiv_at", "exists_of_exists_unique", "eq_of_heq", "has_fderiv_within_at.congr_mono", "category_theory.limits.limit.cone_point_unique_up_to_iso_hom_comp_assoc", "is_glb.insert", "tangent_bundle.times_cont_mdiff_on_proj", "convex.combo_to_vadd", "submodule.map_bot", "encodable.encode_of_equiv", "matrix.head_transpose", "nnreal.coe_multiset_sum", "ordinal.lt_div", "mul_self_mul_inv", "set.image2_add", "is_open_lt", "one_lt_pow", "local_homeomorph.eq_on_source.restr", "ordinal.cof_type", "int.of_nat_nonneg", "is_open_inter", "asymptotics.is_O_with.exists_nonneg", "ordinal.cof_type_le", "category_theory.iso.cancel_iso_inv_left", "prime_spectrum.zero_locus_span", "ordinal.nat_lt_omega", "turing.list_blank.nth_map", "ideal.mem_of_polynomial", "set.surj_on.inv_on_inv_fun_on", "set.preimage_const_mul_Iic", "ring.direct_limit.lift_of", "nat.prime_def_le_sqrt", "dim_prod", "one_le_mul", "polynomial.coeff_X_pow", "rat.add_def", "euclidean_geometry.vsub_orthogonal_projection_mem_direction_orthogonal", "category_theory.category_of_elements.ext", "filter.comap_lift_eq", "zero_sub", "local_homeomorph.of_set_trans'", "add_semiconj_by.eq", "principal_seg.equiv_lt_top", "znum.cast_zero", "ideal.mul_top", "turing.tape.move_right_nth", "list.rotate'_zero", "category_theory.limits.cocone.category_to_category_struct_id_hom", "list.sublist.exists_perm_append", "pSet.definable.eq", "turing.tape.map_fst", "has_fpower_series_on_ball.tendsto_locally_uniformly_on'", "submodule.comap_id", "submodule.mul_le_mul_right", "borel_eq_generate_Ioi", "polynomial.coeff_add", "measurable_space.comap_map_le", "multiset.rel_cons_right", "rat.cast_of_int", "category_theory.under.forget_map", "midpoint_sub_sub", "list.kerase_append_left", "symm_of_uniformity", "matrix.from_blocks_apply\:2082\:2082", "filter.mem_top_sets", "funext", "mv_polynomial.sum_monomial", "free_monoid.lift_eval_of", "category_theory.category_of_elements.id_val", "many_one_equiv.le_congr_right", "strict_mono.div_const", "set.bij_on.image_eq", "measure_theory.l1.coe_sub", "mem_left_coset", "with_top.some_eq_coe", "list.zip_swap", "finset.image_val_of_inj_on", "cSup_le_iff", "tangent_map_comp_at", "function.uncurry_bicompr", "multiset.inf_ndinsert", "real.cos_pi_div_sixteen", "multiset.union_add_inter", "smooth_on.neg", "finset.Ico.filter_le_of_le", "finset.prod_univ_pi", "measure_theory.integral_add", "set.preimage_const_sub_Icc", "int.add_lt_add_left", "onote.oadd_add", "semidirect_product.lift_comp_inl", "with_zero.div_zero", "add_neg'", "neg_add_eq_iff_eq_add", "cardinal.omega_le", "filter.mem_infi", "finset.insert_idem", "mem_normalizer_fintype", "tendsto_list_prod", "localization.mul_equiv_of_quotient_apply", "top_apply", "category_theory.connected_zigzag", "char_poly_nat_degree_eq_dim", "eventually_nhds_within_nhds_within", "pgame.lt_def_le", "set.piecewise_insert_of_ne", "units.exists_iff_ne_zero", "measure_theory.sum_measure_le_measure_univ", "ordinal.sup_lt_ord", "typevec.fst_prod_mk", "real.log_le_log", "is_linear_map.map_sub", "is_max_filter.max", "list.nodup_of_nodup_cons", "metric.completion.dist_eq", "linarith.zero_mul_eq", "typevec.last_fun_comp", "tactic.group.gpow_trick_one'", "seq_compact_space.tendsto_subseq", "submonoid.localization_map.mul_equiv_of_mul_equiv_eq", "lim_norm_zero'", "digits_add", "array.pop_back_idx", "nat.prime.pos", "ordinal.nat_cast_inj", "int.sub_nat_nat_add_right", "cInf_singleton", "convex_halfspace_ge", "tactic.ring_exp.mul_pf_sum", "finset.prod_const", "nnreal.inv_rpow", "filter.inf_map_at_top_ne_bot_iff", "riesz_lemma", "subsemiring.comap_comap", "cardinal.power_add", "metric.diam_empty", "affine_subspace.ext", "polynomial.nodup_of_separable_prod", "tsum_eq_tsum_of_ne_zero_bij", "add_le_of_nonpos_of_le'", "padic_norm.padic_norm_p", "nat.subtype.exists_succ", "primrec.nat_elim", "measurable_space.dynkin_system.has_union", "enat.to_with_top_coe", "tactic.abel.subst_into_smul", "filter.frequently_or_distrib_left", "function.surjective.preimage_injective", "rat.cast_add", "finsupp.sum_single", "real.continuous_cosh", "is_basis.repr_total", "functor.comp.functor_id_comp", "finset.prod_update_of_mem", "measurable.sum_rec", "continuous_linear_map.is_closed_ker", "dim_le_of_injective", "list.foldr_cons", "computable.list_cons", "category_theory.preadditive.comp_sum_assoc", "category_theory.limits.types.sigma_\[Iota]", "eq_cosets_of_normal", "mnat_monoid_hom_eq", "quadratic_eq_zero_iff", "cardinal.lift_lt_univ", "continuous_Inf_rng", "polynomial.separable_def", "nat.cast_bit0", "metric.sum.one_dist_le'", "geom_sum_Ico_mul", "category_theory.nat_trans.right_op_app", "add_submonoid.mem_coe", "vadd_right_cancel_iff", "generalized_continued_fraction.continuants_recurrence", "real.arccos_cos", "multiset.cons_bind", "measure_theory.simple_func.monotone_approx", "polynomial.mod_by_monic_X_sub_C_eq_C_eval", "ordinal.nat_cast_le", "image_le_of_liminf_slope_right_lt_deriv_boundary'", "dioph.ex1_dioph", "concave_on.concave_le", "nat.add_def", "bounded_continuous_function.coe_neg", "joined_in.trans", "ring.direct_limit.induction_on", "mem_closure_of_continuous", "add_semiconj_by.units_of_coe", "eventually_countable_ball", "list.append_inj_left'", "subgroup.normal_of_comm", "algebraic_geometry.SheafedSpace.id_c_app", "is_local_min_const", "add_submonoid.localization_map.lift_mk'_spec", "measure_theory.simple_func_sequence_tendsto'", "category_theory.non_preadditive_abelian.sub_comp", "char.veq_of_eq", "is_max_on.on_preimage", "applicative_transformation.preserves_seq", "finsupp.sum_map_domain_index", "one_one_equiv.trans", "false_of_true_eq_false", "homeomorph.induced_eq", "submodule.smul_assoc", "add_neg_of_neg_of_nonpos", "num.cast_of_znum", "dfinsupp.map_range_def", "pos_num.min_fac_to_nat", "hyperreal.not_infinite_add", "lt_mul_of_lt_of_one_lt'", "mul_inv_le_iff_le_mul", "linear_map.comp_id", "matrix.to_lin_of_equiv", "set.image_mul_left", "hyperreal.coe_inv", "list.nodup_enum_map_fst", "deriv_id''", "lucas_lehmer.X.add_fst", "equiv.perm.sign_bij_aux_inj", "finmap.mem_list_to_finmap", "list.chain.imp", "gcd_comm", "continuous_linear_equiv.snd_equiv_of_right_inverse", "subtype.range_val", "list.pairwise_map_of_pairwise", "measure_theory.measure.haar.index_defined", "computable.part", "complex.of_real_re", "cardinal.aleph'_aleph_idx", "Set.image.mk", "inner_product_geometry.sin_angle_mul_norm_mul_norm", "add_le_iff_nonpos_left", "nhds_mono", "add_monoid_hom.comap_ker", "multiset.quot_mk_to_coe", "set.Ico_union_Icc_eq_Icc", "set.mem_image2_of_mem", "implicit_function_data.right_map_implicit_function", "add_group.mem_closure_union_iff", "ring.direct_limit.of_mul", "subgroup.mem_bot", "uniformity_sum_of_open_aux", "polynomial.leading_coeff_zero", "finite_dimensional_direction_affine_span_of_finite", "ennreal.top_add", "finset.sdiff_inter_self_right", "omega.int.neg_free_neg_elim", "pfun.preimage_mono", "add_right_cancel", "cardinal.aleph'_omega", "not_bdd_below_iff", "smooth_on_univ", "ideal.mul_mem_mul", "computation.parallel_congr_lem", "filter.has_basis_binfi_principal'", "is_closed_union", "continuous_linear_equiv.bijective", "monoid_hom.eq_on_inv", "list.perm.erasep", "category_theory.full_subcategory_inclusion.map", "array.mem_rev_list", "nat.mul_left_inj", "times_cont_diff_on.continuous_on_fderiv_within_apply", "Module.Mon_Module_equivalence_Algebra.functor_obj", "free_group.red.trans", "set.Ici_diff_Ioi_same", "polynomial.eval\:2082_algebra_map_int_X", "set.compl_sUnion", "local_equiv.restr_coe", "gold_sub_gold_conj", "cardinal.lift_one", "set.image_preimage_eq_of_subset", "fin.coe_cast_succ", "ring.fractional_ideal.map_equiv_refl", "interval_integrable.sub", "times_cont_mdiff_on_chart_symm", "additive.is_add_monoid_hom", "filter.has_basis.restrict_subset", "nat.pow_succ", "int.le_trans", "free_ring.coe_zero", "list.length_take", "enat.with_top_equiv_le", "finset.singleton_subset_iff", "primrec.dom_fintype", "lcm_mul_left", "canonically_ordered_semiring.mul_pos", "zsqrtd.nonneg_iff_zero_le", "equiv.arrow_congr'_apply", "Module.monoidal_category.tensor_comp", "neg_convex_on_iff", "prod.snd_prod", "asymptotics.is_o.trans_is_O_with", "complex.abs_mul", "finset.min_eq_none", "finsupp.map_range_zero", "list.eq_of_infix_of_length_eq", "equiv.to_local_equiv_source", "measure_theory.outer_measure.sum_apply", "nat.cast_max", "is_measurable_Iic", "ennreal.sub_add_self_eq_max", "discrete_valuation_ring.has_unit_mul_pow_irreducible_factorization.unique_irreducible", "set.Iio_union_Ico_eq_Iio", "filter.lift_mono'", "nnreal.coe_tsum", "strict_mono.const_mul", "int.add_right_neg", "is_open.is_connected_iff_is_path_connected", "mul_eq_zero_of_left", "strict_mono.top_preimage_top'", "infi_top", "filter.ultrafilter_ultrafilter_of", "finset.filter_true_of_mem", "punit.bot_eq", "map_infi_of_continuous_at_of_monotone", "ne_zero_of_one_div_ne_zero", "tangent_map_tangent_bundle_proj", "finset.card_le_card_of_inj_on", "category_theory.functor.empty_ext'", "power_series.coeff_one_X", "polynomial.leading_coeff_C", "list.cons_bag_inter_of_pos", "emetric.closed_ball_subset_closed_ball", "function.embedding.to_fun_eq_coe", "set.maps_to_bInter", "equiv.set.univ_symm_apply", "finset.Ico.to_finset", "has_deriv_at.scomp", "concave_on.add", "is_integral_of_noetherian'", "list.rotate'_mod", "associates.rel_associated_iff_map_eq_map", "ereal.neg_neg", "turing.tape.mk'_nth_nat", "map_infi_of_continuous_at_of_monotone'", "set.finite.seq", "list.concat_nil", "hyperreal.is_st_sub", "int.pred_neg_pred", "alist.erase_erase", "free_group.red.step.cons_bnot_rev", "linear_map.inl_apply", "add_submonoid.localization_map.map_spec", "lt_abs", "hyperreal.epsilon_ne_zero", "mdifferentiable_on_id", "with_one.coe_inj", "times_cont_mdiff_on_of_mem_maximal_atlas", "abstract_completion.induction_on", "nat.bit_tt", "set.Ico_eq_empty", "measure_theory.lintegral_eq_nnreal", "linear_independent_of_span_eq_top_of_card_eq_findim", "category_theory.limits.binary_bicone.to_cocone_X", "cardinal.mk_compl_eq_mk_compl_finite_same", "category_theory.functor.flip_map_app", "local_homeomorph.eq_on_source.source_eq", "Mon.colimits.quot_one", "subset_connected_component", "category_theory.graded_object.comap_eq_trans", "Top.sheaf_condition.fork_\[Pi]_app_walking_parallel_pair_zero", "add_monoid_hom.map_neg", "subgroup.bot_prod_bot", "int.default_eq_zero", "filter.frequently.forall_exists_of_at_bot", "add_submonoid.localization_map.lift_add_left", "is_open_bUnion", "finset.sum_preimage'", "bitraversable.tfst_eq_fst_id'", "gsmul_lie", "int.nat_abs_bit0", "generalized_continued_fraction.first_continuant_eq", "list_all_congr", "pgame.impartial.first_loses_symm", "filter.pure_bind", "uniform_space.mem_nhds_iff_symm", "list.disjoint_of_disjoint_append_right_left", "interior_maximal", "ennreal.not_mem_Ioo_self_sub", "roption.mem_of_option", "nat.partrec'.cons", "set.inter_eq_compl_compl_union_compl", "category_theory.limits.cones.functoriality_obj_X", "set.right_inv_on.surj_on", "fin.succ_succ_ne_one", "set.ord_connected_iff_interval_subset", "tactic.ring.horner_add_const", "open_subgroup.is_open", "int.units_nat_abs", "ordinal.enum_type", "monoid_hom.eq_of_eq_on_top", "monoid_hom.map_iterate_pth_root", "finsupp.prod_map_range_index", "is_preconnected_Ici", "finset.inter_val_nd", "turing.reaches\:2080.trans", "list.exists_mem_of_length_pos", "is_bounded_bilinear_map.times_cont_diff", "is_measurable.Inter", "commute.cast_nat_mul_cast_nat_mul", "set.preimage_neg_Iic", "refl_bilin_form.eq_zero", "finite_field.prod_univ_units_id_eq_neg_one", "sym_sesq_form.is_refl", "filter.inter_mem_inf_sets", "category_theory.functor.to_cocone_X", "lt_floor_add_one", "category_theory.sum.associator_obj_inr", "interval_integral.deriv_within_integral_right", "le_add_of_neg_add_le", "map_csupr_of_continuous_at_of_monotone", "cInf_insert", "function.injective.has_sum_iff", "linear_map.map_le_map_iff", "eq_self_iff_true", "finsupp.prod_finset_sum_index", "Inf_empty", "vector3.insert_fz", "bdd_below.inter_of_right", "finsupp.supported_union", "supr_pos", "category_theory.limits.equalizer.condition_assoc", "nat.primrec.swap'", "measurable.ennreal_coe", "vadd_vsub", "ordinal.nat_lt_limit", "filter.nmem_hyperfilter_of_finite", "equiv.summable_iff", "decidable.le_imp_le_iff_lt_imp_lt", "has_deriv_within_at.limsup_slope_le", "add_subgroup.closure_eq_of_le", "tendsto_const_nhds_within", "nat.mul_le_mul_right", "add_neg_cancel_right", "polynomial.eval\:2082_mul", "pi_generate_from_eq", "has_deriv_at_iff_tendsto_slope", "le_of_forall_lt", "buffer.ext", "polynomial.is_splitting_field.splits_iff", "linear_pmap.le_of_eq_locus_ge", "zsqrtd.sq_le_of_le", "function.inv_fun_on_mem", "list.eq_nil_of_sublist_nil", "num.zero_add", "finsupp.sum_apply", "list.nodup_append_comm", "int.sub_add_cancel", "cardinal.one_lt_omega", "free_group.red.step.append_left_iff", "multiset.Ico.filter_lt_of_le_bot", "floor_mono", "order_of_dvd_of_pow_eq_one", "free_abelian_group.seq_add", "list.init_append_last", "asymptotics.is_O_with.sum", "padic_int.norm_lt_one_iff_dvd", "field.closure_subset", "vsub_add_vsub_cancel", "polynomial.comp_X", "subgroup.map_sup", "convex_on_pow_of_even", "submodule.smul_mono_left", "dfinsupp.erase_same", "hyperreal.infinite_iff_infinite_pos_abs", "filter.tendsto.inf", "finset.insert_val_of_not_mem", "set.Iio_union_Icc_eq_Iic", "ordinal.div_mul_cancel", "finset.sum_eq_single", "set.image_subset_preimage_of_inverse", "lt_mul_iff_one_lt_right'", "ideal.quotient.mk_surjective", "filter.le_comap_top", "add_subgroup.coe_coe", "padic_val_nat_def", "complex.norm_sq_inv", "list.doubleton_eq", "set.insert_union", "real.neg_one_le_sin", "cau_seq.trichotomy", "imp_eq_of_eq_true_left", "bot_eq_zero", "primrec.subtype_mk", "submonoid.localization_map.map_comp_map", "Class.empty_hom", "subsemiring.mem_mk'", "ring_equiv.to_fun_eq_coe_fun", "unique_diff_on.unique_diff_within_at", "filter.image_mem_sets", "cardinal.one_lt_bit0", "tactic.abel.zero_term", "continuous_linear_equiv.is_O_comp", "list.pairwise.and", "list.nth_rotate", "linarith.mul_neg", "mul_mono_nonneg", "is_R_or_C.nat_cast_re", "derivation.smul_apply", "add_monoid_hom.coprod_comp_inl", "finite_dimensional.lt_omega_of_linear_independent", "list.is_suffix.trans", "equiv.trans_to_local_equiv", "polynomial.map_expand", "is_coprime_comm", "set.Union_image_preimage_sigma_mk_eq_self", "affine.simplex.monge_point_vsub_face_centroid_eq_weighted_vsub_of_points_with_circumcenter", "real.tan_neg", "derivation.to_fun_eq_coe", "mv_polynomial.eval\:2082_hom_congr", "function.partial_inv_left", "measure_theory.ae_eq_fun.edist_self", "neg_lt", "AddCommGroup.injective_of_mono", "eq_zero_of_abs_eq_zero", "finset.bInter_singleton", "inv_inj'", "equiv.perm.card_support_swap", "submodule.gc_map_comap", "set.Icc_subset_Iio_iff", "exists_eq_right", "nnreal.coe_add", "finset.sum_boole_mul", "Icc_mem_nhds_within_Ici", "not_is_unit_zero", "category_theory.arrow.id_right", "is_greatest.nonempty", "category_theory.limits.is_limit.hom_ext", "znum.add_one", "has_fderiv_at_filter_const", "cluster_pt.mono", "is_glb_Inf", "turing.partrec_to_TM2.K'.elim_update_stack", "multiset.filter_inter", "le_compl_of_le_compl", "ideal.radical_eq_top", "nnreal.summable_geometric", "measure_theory.restrict_congr", "max_sub_min_eq_abs", "set.range_restrict", "pow_inv_comm", "finset.piecewise_eq_of_mem", "submodule.quotient.mk_surjective", "cardinal.lt_succ", "local_homeomorph.trans_symm_eq_symm_trans_symm", "equiv.perm.sign_of_subtype", "Set.choice_mem", "set.finite_range_find_greatest", "set.Iic_subset_Iic", "pequiv.single_trans_of_eq_none", "category_theory.limits.coprod.map_desc_assoc", "associates.factors'_cong", "submonoid.localization_map.mul_equiv_of_localizations_apply", "linear_map.pi_comp", "set.sInter_eq_comp_sUnion_compl", "pequiv.single_trans_single_of_ne", "circle_deg1_lift.map_int_of_map_zero", "category_theory.symmetric_of_has_finite_products_to_braided_category_braiding", "filter.prod_principal_principal", "inducing.map_nhds_eq", "alist.insert_insert_of_ne", "fderiv_add_const", "measure_theory.outer_measure.map_map", "semiconj_by.units_of_coe", "multiset.mem_ndinsert_self", "has_strict_fderiv_at.smul", "submonoid.mem_carrier", "add_con.Sup_eq_add_con_gen", "set.union_nonempty", "embedding.continuous_iff", "fderiv.comp_fderiv_within", "continuous_linear_map.coe_prod_map'", "measure_theory.measure_bUnion_finset", "finset.has_sum", "tangent_map_within_univ", "preserves_limits_iso_hom_\[Pi]", "associates.eq_of_prod_eq_prod", "padic_norm.nonzero", "list.init_eq_of_concat_eq", "ne_zero_of_abs_ne_zero", "int.even_iff", "dfinsupp.eq_mk_support", "int.add_le_add_left", "computation.get_ret", "list.foldl_nil", "finset.prod_extend_by_one", "function.semiconj.inj_on_image", "multiset.sub_add'", "seq.nats_nth", "is_unit_iff_exists_inv'", "continuous_linear_equiv.comp_has_fderiv_at_iff", "affine_map.homothety_one", "tactic.ring_exp.simple_pf_sum_zero", "compl_le_compl", "rat.add_mul", "has_deriv_at.lhopital_zero_left_on_Ioc", "ordinal.type_mul", "filter.tendsto.smul", "equiv.to_local_equiv_target", "complex.sinh_add_cosh", "free_group.red.step.sublist", "measure_theory.l1.simple_func.coe_add", "complex.norm_sq_pos", "fderiv_within_smul", "list.rotate_nil", "norm_sub_rev", "filter.tendsto_add_at_top_nat", "mvqpf.fix.rec_unique", "ideal.mem_infi", "real.cosh_sq_sub_sinh_sq", "AddCommGroup.image.lift_fac", 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"set.indicator_preimage", "deriv_csin", "bool.exists_bool", "free_monoid.map_comp", "matrix.adjugate_eq_one_of_card_eq_one", "list.sorted_singleton", "norm_num.subst_into_add", "filter.Liminf_le_Limsup", "ennreal.inv_ne_top", "set.sInter_bUnion", "group.mem_closure_union_iff", "add_monoid_algebra.single_mul_single", "Set.mem_pair_sep", "interior_eq_iff_open", "tactic.ring_exp.pow_pf_zero", "turing.to_partrec.code.id_eval", "function.comp_iterate_pred_of_pos", "padic_norm_e.eq_padic_norm'", "nat.bodd_bit0", "function.iterate_id", "local_equiv.trans_source'", "pequiv.to_matrix_bot", "complex.abs_pos", "multiset.prod_eq_zero", "has_deriv_at.ccos", "computation.lift_rel_aux.swap", "continuous_linear_map.to_span_singleton_norm", "continuous_on.comp_continuous", "nat.coe_cast_ring_hom", "pnat.lt_add_one_iff", "is_bounded_bilinear_map_comp_multilinear", "category_theory.limits.cocones.functoriality_obj_\[Iota]_app", "compl_unique", "finset.prod_bij", "pos_num.sub'_one", 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"derive_fintype.finset_above.mem_union_left", "int.sub_eq_zero_of_eq", "category_theory.limits.limit.post_post", "Module.epi_of_range_eq_top", "finmap.not_mem_empty", "list.perm.singleton_eq", "abstract_completion.dense_inducing", "ext_chart_preimage_mem_nhds", "matrix_equiv_tensor.inv_fun_algebra_map", "initial_seg.coe_fn_to_rel_embedding", "group.image_closure", "isometry_subtype_coe", "submonoid.localization_map.lift_comp", "list.mmap_with_index_aux_eq_mmap_with_index_aux_spec", "option.bind_eq_some'", "set.preimage_mul_const_Ioi", "turing.blank_rel.equivalence", "category_theory.monoidal_functor.comp_\[Mu]_is_iso", "is_open_Inter", "list.exists_of_kerase", "real.sin_neg", "galois_connection.u_top", "ring_hom.lift_of_surjective_comp", "compact_of_finite_subcover", "ext_chart_at_continuous_on", "min_eq_right_of_lt", "list.pairwise_of_pairwise_map", "real.cos_pi_over_two_pow", "category_theory.Monad.Monad_Mon_equiv_inverse", "filter.germ.lift_rel_coe", "list.suffix_append", "has_deriv_within_at.nhds_within", "Top.subpresheaf_to_Types_obj", "filter.tendsto_at_top_at_top", "topological_space.opens.supr_def", "times_cont_diff_on_snd", "primrec.to\:2082", "set.right_mem_interval", "category_theory.limits.coprod.inr_map", "euclidean_domain.lcm_eq_zero_iff", "matrix.mul_vec_zero", "add_monoid.image_closure", "semiconj_by.pow_right", "tangent_map_id", "equivalence_of_one_one_equiv", "dvd_iff_dvd_of_digits", "times_cont_diff.sub", "cInf_union", "finset.subset_union_right", "is_coprime.of_add_mul_right_right", "primrec\:2082.of_nat_iff", "forall_eq'", "nat.ppred_eq_pred", "inv_le_inv_of_le", "set.Ioc_union_Ioc_eq_Ioc", "equiv.perm.sign_symm_trans_trans", "cardinal.succ_is_regular", "algebraic_closure.adjoin_monic.exists_root", "list.lookup_nil", "nhds_order_unbounded", "algebra.coe_top", "set.diff_Inter", "asymptotics.is_O.congr_left", "inv_le_of_neg", "fin.ne_iff_vne", "normed_field.nnnorm_inv", "is_compact.image", "add_submonoid.localization_map.symm_comp_of_add_equiv_of_localizations_apply", "eq_neg_add_iff_add_eq", "or_comm", "gc_nhds", "bdd_below_bdd_above_iff_subset_Icc", "smooth_on_id", "list.pairwise_filter_map", "polynomial.leading_coeff_one", "composition.boundary_last", "complex.conj_conj", "tactic.abel.zero_smulg", "lt_of_mul_lt_mul_neg_right", "category_theory.Monad.of_to_mon_end_iso_hom_app_hom", "int.add_left_comm", "set.sigma_to_Union_bijective", "has_strict_fderiv_at.to_local_left_inverse", "open_of_uniformity_sum_aux", "category_theory.equivalence.trans_inverse", "list.nodup_erase_eq_filter", "nhds_le_nhds_iff", "add_submonoid.localization_map.lift_spec_add", "continuous_linear_map.is_O_comp", "bifunctor.map_equiv_apply", "sigma.ext_iff", "set.preimage_mul_right_one'", "gsmul_of_nat", "function.bijective.iterate", "set.preimage_set_of_eq", "div_lt_one_of_neg", "linear_equiv.symm_trans_apply", "segment_same", "ennreal.sub_le_iff_le_add", "norm_num.int_div_neg", "complex.sin_square", "category_theory.equivalence.pow_zero", "free_abelian_group.seq_zero", "equiv.swap_apply_def", "category_theory.iso.trans_mk", "finset.sum_lt_sum_of_subset", "rat.mk_eq_div", "differentiable.sub_const", "quotient_group.induction_on", "monoid_hom.snd_comp_prod", "many_one_degree.of_le_of'", "mvqpf.Wequiv.symm", "is_compact.is_least_Inf", "Gromov_Hausdorff.isometry_optimal_GH_injl", "has_fderiv_at.add", "category_theory.limits.kernel.lift_zero", "nnnorm_neg", "category_theory.limits.is_colimit.cocone_points_iso_of_equivalence_inv", "relation.trans_gen.trans_left", "pnat.xgcd_type.is_reduced_iff", "add_localization.mk_eq_add_monoid_of_mk'_apply", "list.exists_cons_of_ne_nil", "set.preimage_add_left_zero", "subring.mem_top", "uniform_continuous_id", "finset.affine_combination_vsub", "is_noetherian_ring.irreducible_induction_on", "unique.ext", "category_theory.under.iso_mk_inv_right", "continuous_linear_equiv.subsingleton_or_nnnorm_symm_pos", "nat.abs_cast", "fin.coe_cast_add", "nhds_within_le_comap", "list.tail_eq_of_cons_eq", "int.sub_le_self", "closed_embedding.closed_iff_image_closed", "turing.tape.move_left_mk'", "function.support_neg", "is_R_or_C.is_cau_seq_abs", "with_top.add_lt_top", "matrix.dot_product_comm", "group.normal_closure_subset_iff", "summable_mul_left_iff", "relation.symmetric_join", "category_theory.unop_comp", "roption.get_eq_iff_eq_some", "category_theory.limits.cospan_map_id", "category_theory.non_preadditive_abelian.\[CapitalDelta]_\[Sigma]", "real.has_deriv_at_exp", "stream.append_append_stream", "zsqrtd.coe_nat_im", "nat.cast_min", "differentiable_within_at.cos", "filter.mem_one", "list.chain'_of_chain'_map", "rat_mul_continuous_lemma", "category_theory.monoidal_category.tensor_right_map", "convex_singleton", "continuous_at.tendsto", "enat.to_with_top_zero'", "turing.TM0.machine.map_respects", "finsupp.to_multiset_add", "real.rpow_lt_rpow_of_exponent_gt", "nat.partrec'.comp\:2081", "has_fderiv_at_id", "is_alg_closed.of_exists_root", "has_fderiv_at_unique", "nat.lt_of_succ_lt_succ", "list.perm.inter", "list.diff_cons", "int.coe_gcd", "ring_hom.domain_nontrivial", "multiset.disjoint_to_finset", "polynomial.nat_degree_le_of_degree_le", "measure_theory.l1.simple_func.edist_eq", "int.dvd_iff_mod_eq_zero", "neg_div'", "finset.sdiff_eq_self_iff_disjoint", "equiv.id_map", "list.lookup_all_eq_nil", "cardinal.prod_const", "multiset.mem_of_le", "function.injective.no_zero_divisors", "mul_lt_mul'", "nat.min_fac_eq_two_iff", "equiv.perm.support_swap", "padic_int.mul_inv", "category_theory.limits.cone.of_pullback_cone_\[Pi]", "is_basis.dual_basis_is_basis", "differentiable_on.sub", "nat.bit0_ne", "set.piecewise_eq_of_not_mem", "mdifferentiable_within_at_const", "measure_theory.outer_measure.dirac_apply", "pequiv.to_matrix_refl", "linear_map.smul_comp", "pgame.lt_of_lt_of_equiv", "polynomial.irreducible_X", "ennreal.finset_sum_supr_nat", "dense_bInter_of_G\[Delta]", "finset.erase_val", "finset.attach_map_val", "mdifferentiable_within_at_id", "hyperreal.infinite_mul_of_infinite_not_infinitesimal", "finite_field.exists_root_sum_quadratic", "le_or_gt", "nat.add_div_le_add_div", "filter.seq_mem_seq_sets", "ring_hom.injective_iff", "mem_right_add_coset_right_add_coset", "sup_left_idem", "has_deriv_at.const_smul", "Top.presheaf.germ_res", "polynomial.nat_degree_expand", "complex.of_real_int_cast", "wseq.exists_of_mem_map", "ideal.map_le_of_le_comap", "subgroup.coe_to_submonoid", "direct_sum.induction_on", "unique_mdiff_within_at_iff_unique_diff_within_at", "closure_compl", "eq_mpr_heq", "group.subset_normal_closure", "Module.id_apply", "matrix.lie_conj_symm_apply", "convex_cone.smul_mem_iff", "turing.reaches\:2080.head", "monoid_hom.mul_apply", "function.injective2.right", "category_theory.limits.coequalizer.hom_ext", "finsupp.count_to_multiset", "set.preimage_singleton_nonempty", "tendsto_nhds_unique", "functor.ext", "int.neg_of_nat_add", "frobenius_neg", "nnreal.half_pos", "tangent_bundle_model_space_chart_at", "finset.prod_add_prod_eq", "set.Ioo_subset_Ioc_union_Ioo", "finset.union_subset_union", "inv_mul_eq_iff_eq_mul", "edist_le_tsum_of_edist_le_of_tendsto\:2080", "wseq.map_ret", "metric.isometry_on_inr", "finset.range_image_pred_top_sub", "is_absolute_value.abv_pow", "free_add_magma.pure_seq", "measure_theory.norm_set_integral_le_of_norm_le_const_ae''", "finset.mono_of_fin_last", "lift_nhds_left", "list.mfoldr_eq_foldr", "nnreal.continuous_of_real", "real.add_one_le_exp_of_nonneg", "measurable.ennnorm", "is_coprime.dvd_of_dvd_mul_right", "topological_space.opens.supr_mk", "submodule.map_zero", "multiset.card_powerset", "category_theory.limits.coprod_map_comp_id_assoc", "int.neg_add_le_of_le_add", "omega.lin_comb_holds", "function.commute.symm", "tensor_product.ext_fourfold", "units.mul_inv_cancel_right", "real.norm_eq_abs", "filter.is_countably_generated.tendsto_of_seq_tendsto", "free_group.quot_mk_eq_mk", "with_bot.add_bot", "strict_mono.lt_iff_lt", "nat.lt_pred_iff", "frobenius_inj", "gt_trans", "times_cont_diff.sum", "ordinal.power_mul", "metric.inf_dist_singleton", "category_theory.comp_dite", "sub_add_eq_sub_sub_swap", "traversable.mfoldr_map", "ordering.compares_iff_of_compares_impl", "units.coe_mul", "normal.splits", "is_coprime.mul_add_right_right", "computation.orelse_empty", "ideal.integral_closure.comap_lt_comap", "localization_map.map_id", "compact_singleton", "coord_norm'", "one_div_le_one_div_of_neg", "set.preimage_union", "add_comm_group.direct_limit.lift_zero", "bit0_lt_bit0", "module.End.exists_eigenvalue", "polynomial.ext", "bor_eq_true_eq_eq_tt_or_eq_tt", "differentiable_at.congr_of_eventually_eq", "is_subgroup.trivial_eq_closure", "complex.differentiable_exp", "finset.update_eq_piecewise", "nat.pow_succ_log_gt_self", "nnreal.sub_def", "category_theory.monoidal.left_unitor_hom_apply", "nnreal.coe_mul", "filter.eventually_le.is_local_max_on", "category_theory.limits.coprod.symmetry", "submodule.mul_le_mul_left", "wseq.dropn_tail", "rat.num_zero", "fintype.univ_of_subsingleton", "multiset.Ico.filter_lt_of_ge", "fintype.card_coe", "int.lt_add_of_neg_add_lt_right", "pnat.factor_multiset_of_prime", "set.subset_Inter", "alg_equiv_iso_Algebra_iso_inv", "pSet.mem_Union", "Mon_.id_hom'", "category_theory.limits.colimit.hom_ext", "power_series.X_pow_eq", "euclidean_geometry.exists_unique_dist_eq_of_affine_independent", "well_founded.lt_sup", "function.is_periodic_pt.trans_dvd", "euclidean_domain.gcd_dvd_right", "relation.comp_assoc", "summable_geometric_two'", "nat.mod_mul_left_mod", "measure_theory.mem_ae_map_iff", "has_fderiv_within_at.smul_algebra_const", "polynomial.is_local_ring_hom_expand", "tfae_mem_nhds_within_Ioi", "stone_cech_extend_extends", "modeq_eleven_digits_sum", "ideal.coe_closure", "opposite.op_inv", "localization.ind", "CommMon.coe_of", "mul_sub_mul_div_mul_neg_iff", "set.subset_image_diff", "matrix.cons_add", "multiset.coe_count", "has_deriv_at.has_fderiv_at_equiv", "topological_space.opens.subset_coe", "to_uniform_space_eq", "polynomial.algebra_map_apply", "list.pw_filter_idempotent", "zmod.expand_card", "category_theory.equivalence.symm_counit_iso", "sequentially_complete.seq_is_cauchy_seq", "ring.fractional_ideal.mul_left_mono", "filter.extraction_of_frequently_at_top", "findim_span_set_eq_card", "differentiable_at.mul_const", "con.lift_apply_mk'", "approximates_linear_on.mono_set", "filter.has_basis.eq_generate", "of_add_gsmul", "set.preimage_eq_preimage", "mul_le_iff_le_one_left'", "coe_add_monoid_hom", "enat.add_eq_top_iff", "affine.simplex.direction_monge_plane", "filter.tendsto_id", "real.Inf_def", "findim_euclidean_space", "open_embedding.to_local_equiv_source", "mv_power_series.X_pow_dvd_iff", "multilinear_map.sum_apply", "list.sublist.diff_right", "smul_add", "lift_of_splits", "filter.frequently_high_scores", "local_equiv.refl_trans", "int.add_one_le_of_lt", "int.lt_neg_add_of_add_lt", "pnat.mk_coe", "alg_hom.coe_to_monoid_hom", "norm_num.le_one_bit0", "fixed_points.prev_eq", "set.indicator_le'", "submonoid.map_supr_comap_of_surjective", "if_ctx_simp_congr_prop", "ennreal.inv_le_iff_le_mul", "ennreal.coe_finset_sum", "list.map\:2082_nil", "nat.primrec'.comp\:2081", "category_theory.over.colimit_X", "category_theory.Monad.of_Mon_str_\[Eta]", "roption.bind_some", "euclidean_domain.gcd_zero_right", "sub_eq_sub_iff_sub_eq_sub", "real.Sup_of_not_bdd_above", "category_theory.nat_trans.sum_app_inr", "span_lt_of_subset_of_card_lt_findim", "gaussian_int.to_complex_mul", "filter.map_add_at_top_eq_nat", "ennreal.tsum_add", "ideal.map_pi", "int.neg_div_of_dvd", "cSup_intro", "mul_self_pos", "ext_chart_at_open_source", "nat.pred_sub", "times_cont_diff_at.prod_map", "functor.map_comp_map", "algebra.of_id_apply", "mfderiv_within_const", "linarith.nat_lt_subst", "submonoid.ext'", "abs_sub_lt_iff", "list.foldl1_eq_foldr1", "int.add_comm", "localization.ring_equiv_of_quotient_of", "category_theory.comma.map_right_id_inv_app_right", "one_lt_mul_of_lt_of_le", "add_pow_char", "padic_int.pmul_comm", "measure_theory.integrable.add_measure", "neg_add_le_of_le_add", "exists_pow_eq_one", "pequiv.ext", "category_theory.monoidal_functor.comp_to_lax_monoidal_functor", "has_sum.add", "nat.div_eq_iff_eq_mul_left", "measure_theory.ae_eq_fun.coe_fn_mul", "pgame.equiv_zero_iff_grundy_value", "cardinal.mk_le_mk_of_subset", "cau_seq.lim_eq_lim_of_equiv", "function.embedding.ext_iff", "cardinal.cantor_function_aux_tt", "has_fderiv_at_filter_fst", "nonempty_of_not_bdd_below", "omega.nat.unsat_of_unsat_dnf", "is_strict_weak_order_of_is_total_preorder", "fintype.linear_order.is_well_order", "list.filter_eq_foldr", "add_submonoid.coe_coe", "not_unbounded_iff", "list.sublist_append_left", "continuous_linear_map.is_O_sub", "polynomial.degree_monomial", "pnat.gcd_dvd_right", "submonoid.localization_map.mk'_spec'", "ennreal.add_lt_add_iff_right", "asymptotics.is_O_with_bot", "int.of_nat_mul_of_nat", "measure_theory.simple_func.seq_apply", "set.preimage_subset_image_of_inverse", "is_R_or_C.zero_im", "derivation.map_algebra_map", "category_theory.limits.binary_fan.\[Pi]_app_right", "div_lt_iff_of_neg", "category_theory.monad.forget_creates_colimits.lifted_cocone_X", "Set.induction_on", "is_basis.to_dual_apply", "polynomial.leading_coeff_add_of_degree_lt", "multiset.disjoint_right", "int.mod_add_div_aux", "set.not_mem_empty", "uniform_space.ring_sep_quot", "bounded_continuous_function.coe_add", "nnreal.bdd_above_coe", "complex.has_deriv_at_sin", "nat.pow_le_pow_of_le_left", "emetric.cauchy_iff", "set.seq_of_forall_finite_exists", "dist_triangle_right", "cardinal.aleph_succ", "category_theory.comma.nat_trans_app", "char_poly_sub_diagonal_degree_lt", "category_theory.iso_whisker_right_inv", "and_not_self_iff", "nnreal.div_div_eq_div_mul", "category_theory.abelian.pseudoelement.eq_zero_iff", "normal_subgroup_of_comm_group", "filter.prod_lift_lift", "category_theory.monoidal.functor_category.tensor_obj_obj", "add_submonoid.localization_map.neg_unique", "supr_empty", "ennreal.nhds_coe_coe", "disjoint_bot_right", "measure_theory.simple_func.map_const", "ideal.jacobson_eq_iff_jacobson_quotient_eq_bot", "pnat.sub_coe", "pi_norm_le_iff", "times_cont_diff_at.differentiable", "matrix.special_linear_group.one_apply", "is_coprime.mul_add_right_left", "qpf.fix.ind_aux", "nat.one_le_pow", "mono_of_deriv_nonneg", "nnreal.nndist_eq", "int.mod_neg", "measure_theory.measure_union_null", "closure_Ico", "submonoid.copy_eq", "pgame.move_right_left_moves_neg", "to_topological_space_top", "ring_hom.coe_inj", "monoid_hom.coprod_unique", "pell.xn_add", "fin.mk_zero", "open_add_subgroup.coe_injective", "ordinal.lt_succ", "category_theory.pi.comap_comp_hom_app", "set.ssubset_iff_of_subset", "vector.comp_traverse", "minimal_polynomial.coeff_zero_eq_zero", "add_submonoid.localization_map.mk'_add_eq_mk'_of_add", "hyperreal.infinite_pos_iff_infinite_and_pos", "category_theory.comma.map_left_id_inv_app_left", "mul_mem_nonunits_left", "add_comm_group.is_Z_bilin.zero", "ennreal.rpow_lt_one", "primrec.list_find_index\:2081", "nnreal.mul_rpow", "complex.cos_sub_pi_div_two", "uniform_continuous.prod_mk_left", "mv_polynomial.rename_injective", "mdifferentiable_within_at.continuous_within_at", "set.eq_univ_iff_forall", "category_theory.monad.forget_obj", "bundle_trivialization.coe_coe", "mul_nsmul_assoc", "matrix.trace_transpose_mul", "poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_2", "ring_equiv.map_one", "asymptotics.is_O.add", "ring.fractional_ideal.map_equiv_apply", "convex_on.translate_left", "filter.eventually_eq.refl", "znum.of_int'_eq", "stream.coinduction", "filter.has_basis.tendsto_iff", "linarith.mul_nonpos", "set.image2_image2_left", "filter.germ.induction_on\:2083", "open_subgroup.coe_subset", "inf_le_right_of_le", "cardinal.one_lt_iff_nontrivial", "nat.one_lt_two_pow'", "submonoid.localization_map.is_unit_comp", "is_scalar_tower.aeval_apply", "fintype.sum_sum_type", "preserves_limits_iso_hom_\[Pi]_assoc", "pgame.nim.grundy_value", "times_cont_diff.times_cont_diff_at", "lcm_dvd", "quotient_group.coe_mul", "surjective_of_continuous'", "nat.one_pow", "Class.Union_hom", "option.guard_eq_some'", "pell.xn_modeq_x2n_sub", "real.cos_pi_div_eight", "inner_div_norm_mul_norm_eq_neg_one_of_ne_zero_of_neg_mul", "padic_seq.lift_index_right", "imp_intro", "sub_right_comm", "category_theory.functor.left_unitor_hom_app", "padic.coe_neg", "filter.germ.map_id", "has_deriv_within_at.comp", "function.left_inverse.injective", "ennreal.mul_inv_cancel", "ordinal.omega_is_limit", "compact_covered_by_add_left_translates", "nat.prime.multiplicity_choose", "set.indicator_neg", "concave_on.translate_right", "asymptotics.is_O.congr'", "int.sub_left_le_of_le_add", "is_max_on.is_extr", "finset.inter_assoc", "except_t.ext", "list.eq_or_mem_of_mem_cons", "mem_subalgebra_of_subring", "int.neg_mul_eq_neg_mul_symm", "matrix.dot_product_neg", "list.sum_map_mul_left", "finset.ext_iff", "computation.exists_of_mem_map", "finset.empty_subset", "nat.le_of_succ_le_succ", "array.read_mem", "multiset.disjoint_union_right", "subgroup.range_gpowers_hom", "emetric.is_open_ball", "polynomial.fderiv", "int.normalize_of_neg", "znum.mod_to_int", "iterated_fderiv_within_zero_eq_comp", "finset.coe_union", "deriv_exp", "mul_lt_one_of_le_one_of_lt_one'", "multiset.card_lt_of_lt", "int.modeq.exists_unique_equiv_nat", "lipschitz_with.of_le_add", "sub_le_sub_iff_left", "add_subgroup.top_prod", "nat.coprime_div_gcd_div_gcd", "set.inter_bUnion", "category_theory.limits.cone.naturality_concrete", "ordinal.lift_pred", "polynomial.of_irreducible_expand", "finset.union_eq_left_iff_subset", "ctop.to_topsp_is_topological_basis", "mdifferentiable_at_iff_differentiable_at", "complex.uniform_continuous_re", "functor.map_equiv_refl", "has_strict_fderiv_at_iff_has_strict_deriv_at", "multiset.naturality", "ring_hom.iterate_map_add", "pfun.mem_image", "subtype.image_preimage_coe", "filter.tendsto.eventually_interval_integrable_ae", "filter.tendsto.limsup_eq", "category_theory.limits.coprod.left_unitor_hom", "subtype.val_prop", "list.erase_cons", "inner_product_geometry.angle_le_pi", "category_theory.non_preadditive_abelian.sub_self", "mem_left_coset_iff", "encodable.choose_spec", "submodule.fg_def", "finset.union_sdiff_symm", "nat.succ_mul_succ_eq", "mv_power_series.mul_add", "quotient_add_group.eq", "set.subset_diff", "set.countable.exists_surjective", "free_comm_ring.is_supported_neg", "has_strict_deriv_at_inv", "zmod.cast_pow'", "nat.eq_zero_of_zero_dvd", "principal_ideal_ring.associates_irreducible_iff_prime", "ordered_add_comm_group.add_lt_add_left", "filter.eventually_bind", "hyperreal.infinite_pos_omega", "submonoid.localization_map.of_mul_equiv_of_dom_eq", "times_cont_mdiff_at.mdifferentiable_at", "abs_sub_square", "int.zero_mul", "finset.image_mono", "sub_le_sub_left", "nnreal.of_real_le_of_real_iff", "linear_independent_unique", "linear_equiv.trans_apply", "ring_hom.map_div", "equiv.refl_to_embedding", "computation.get_bind", "gfp_eq", "polynomial.subsingleton_of_monic_zero", "has_strict_deriv_at_fpow", "ordinal.div_lt", "homological_complex.image_to_kernel_map_comp_kernel_map_assoc", "is_max_filter.sub", "hyperreal.not_infinite_neg_of_infinite_pos", "derivation.map_smul", "relation.join_of_equivalence", "sdiff_le_sdiff", "list.chain'.imp_head", "embedding_id", "monoid_hom.map_multiset_prod", "tendsto_coe_nat_real_at_top_at_top", "semiconj_by.cast_int_mul_left", "bilin_form.is_skew_adjoint_bracket", "module.algebra_map_End_eq_smul_id", "is_irreducible.closure", "zorn.succ_spec", "ideal.zero_eq_bot", "monoid_hom.injective_iff", "is_clopen_inter", "metric.bounded_bUnion", "filter.has_basis.eq_infi", "bilin_form.lin_mul_lin_comp", "has_deriv_within_at.congr_of_eventually_eq", "supr_insert", "list.perm_middle", "minimal_polynomial.not_is_unit", "filter.eventually_eq_inf_principal_iff", "right_ord_continuous.le_iff", "linear_independent_sUnion_of_directed", "asymptotics.is_O_const_mul_left_iff", "filter.mem_at_top_sets", "set.prod_eq", "euclidean_domain.mod_zero", "times_cont_mdiff_within_at_congr", "fin.add_one_pos", "ideal.mem_sup_right", "bor_ff", "subtype.trans", "euclidean_geometry.orthogonal_projection_vadd_smul_vsub_orthogonal_projection", "pnat.bot_eq_zero", "filter.le_of_map_le_map_inj_iff", "quotient_group.open_coe", "inv_neg", "equiv.coe_const_vadd", "measure_theory.lintegral_sum_measure", "measure_theory.ae_eq_fun.zero_def", "complex.cos_two_mul", "galois_insertion.l_u_eq", "is_integral_of_subring", "free_group.to_group_eq_prod_map", "is_open_map.functor_obj_val", "dim_span", "quadratic_form.coe_fn_neg", "category_theory.iso.hom_inv_id_app", "ring_hom.ext_nat", "Class.fval_ex", "times_cont_diff_on_of_differentiable_on_deriv", "complex.exp_bound", "div_mul_eq_mul_div", "is_bounded_bilinear_map.has_fderiv_at", "add_submonoid.localization_map.map_add_left", "finsupp.emb_domain_eq_map_domain", "ordinal.sub_sub", "sigma_mk_injective", "zero_lt_iff_ne_zero", "int.eq_zero_of_dvd_of_nonneg_of_lt", "sym2.congr_right", "add_units.coe_lt_coe", "function.support_prod_mk", "is_asymm.is_antisymm", "measure_theory.l1.sub_to_fun", "measure_theory.l1.mk_to_fun", "polynomial.coeff_eq_zero_of_degree_lt", "submodule.smul_mem_smul", "inv_ne_zero", "continuous_multilinear_map.smul_apply", "real.log_nonpos", "derivation.Rsmul_apply", "polynomial.nat_degree_X", "localization_map.surj", "measure_theory.mem_dirac_ae_iff", "subgroup.is_open_of_mem_nhds", "set.pairwise_on.mono'", "filter.eventually.self_of_nhds", "convex_Ioc", "lipschitz_with.le_add_mul", "dense_inducing.continuous_extend_of_cauchy", "is_coprime_one_left", "finset.insert_eq_of_mem", "function.left_inverse_inv_fun", "submodule.mem_Sup_of_mem", "continuous_linear_equiv.comp_has_fderiv_at_iff'", "times_cont_diff_neg", "list.le_maximum_of_mem'", "continuous_inf_dom_right", "ordinal.card_add", "poly.sub_eval", "multiset.erase_add_right_pos", "pgame.grundy_value_nim_add_nim", "fin.pred_mk_succ", "iterated_deriv_within_succ", "measure_theory.norm_integral_le_integral_norm", "equiv.left_inverse_symm", "finset.prod_pow_eq_pow_sum", "continuous_linear_map.smul_apply", "option.some_inj", "mul_assoc", "normed_ring.inverse_one_sub_norm", "alist.keys_replace", "category_theory.limits.cone_of_split_mono_\[Pi]_app_zero", "mul_lt_one_of_le_one_of_lt_one", "is_R_or_C.char_zero_R_or_C", "finset.card_eq_of_bijective", "real.sin_add_pi", "times_cont_mdiff_fst", "finset.max_empty", "hyperreal.coe_zero", "div_mul_div_cancel", "nat.primrec'.sqrt", "sub_le", "category_theory.nat_trans.app_naturality", "infi_le_infi2", "set.Inter_inter", "ordinal.mod_eq_of_lt", "Class.union_hom", "frontier_Icc", "set.Iio_subset_Iic", "unique_diff_within_at_inter'", "list.foldl_eq_of_comm_of_assoc", "ennreal.nat_ne_top", "matrix.rank_vec_mul_vec", "int.coe_nat_dvd_right", "zsqrtd.coe_int_inj", "contracting_with.dist_inequality", "with_zero.div_eq_div", "finset.infi_insert_update", "zsqrtd.ext", "continuous_on_congr", "measure_theory.lintegral_supr_ae", "partrec.rfind", "linear_map.ext\:2082", "polynomial.expand_contract", "and_self_right", "set.union_subset_union_right", "measure_theory.ae_eq_fun.quot_mk_eq_mk", "measure_theory.measure.le_add_left", "polynomial.roots_prod", "tangent_bundle.times_cont_mdiff_proj", "add_localization.add_equiv_of_quotient_symm_mk'", "pnat.gcd_coe", "free_magma.mul_eq", "omega.unsat_lin_comb_of", "equiv.set.image_symm_preimage", "num.nat_size_to_nat", "filter.eq_of_map_eq_map_inj'", "times_cont_diff.of_le", "AddCommGroup.kernel_iso_ker_inv_comp_\[Iota]", "set.nonempty.of_diff", "category_theory.limits.cocone.whisker_X", "mul_action.fixed_eq_Inter_fixed_by", "sub_pow_char_pow_of_commute", "int.of_nat_zero", "vector3.rec_on_nil", "is_max_on.on_subset", "tactic.ring2.horner_expr.cseval_add", "inducing_open", "category_theory.limits.pushout.condition_assoc", "metric.sum.dist_eq", "open_add_subgroup.mem_coe", "closed_embedding_id", "lt_of_not_ge", "mul_action_hom.ext", "complex.cos_of_real_re", "mem_nhds_within_subtype", "ring_hom.ext_rat", "add_monoid_hom.coe_range", "turing.list_blank.bind_mk", "monotone_or", "set.compl_inter_self", "polynomial.C_comp", "onote.NF.snd", "open_subgroup.mem_nhds_one", "semiquot.nonempty", "add_con.lift_funext", "category_theory.limits.has_equalizers_of_pullbacks_and_binary_products.pullback_fst_eq_pullback_snd", "wseq.map_append", "zsqrtd.nonnegg_cases_left", "zero_lt_mul_right", "ptendsto'_nhds", "submodule.map_liftq", "list.of_fn_eq_pmap", "set.set_of_set", "list.length_pos_of_sum_ne_zero", "true_iff", "continuous_at.div", "subring.comap_comap", "multiset.singleton_le", "filter.mem_sets_of_superset", "mul_le_mul_iff_left", "filter.eventually.prod_mk", "is_glb_Ioi", "one_mul", "category_theory.equivalence.counit_inv_functor_comp", "open_embedding.open_iff_preimage_open", "psigma.mk.inj_iff", "measure_theory.measure.measurable_lintegral", "measure_theory.simple_func.pos_part_map_norm", "set.bInter_subset_of_mem", "Sup_inf_eq", "set.maps_to_sInter", "ideal.mul_mem_left", "ideal.is_primary_inf", "has_deriv_at.lhopital_zero_at_top_on_Ioi", "is_unit.mul_lift_right_inv", "measure_theory.measure.restrict_Union_le", "polynomial.nat_degree_le_of_dvd", "lagrange.interpolate_empty", "category_theory.limits.limit.map_\[Pi]", "norm_num.sle_one_bit0", "group.conjugates_subset", "pequiv.symm_trans", "lt_mul_iff_one_lt_left", "cardinal.power_one", "ordinal.mul_le_of_limit", "cardinal.lt_univ", "ordinal.is_normal.is_limit", "convex.sub", "norm_num.sub_neg", "option.eq_some_iff_get_eq", "continuous_linear_map.unit_le_op_norm", "matrix.cramer_map_is_linear", "iff_iff_not_or_and_or_not", "uniform_continuous_const", "metric.bounded_singleton", "set.subset_union_right", "encodable.decode_ge_two", "matrix.col_add", "list.mem_range'", "add_monoid_algebra.mul_single_apply_aux", "category_theory.ulift_functor_map", "semidirect_product.inr_inj", "finsupp.map_domain_notin_range", "list.filter_append", "exp_neg_inv_glue.zero_of_nonpos", "normed_space.inclusion_in_double_dual_isometry", "is_R_or_C.smul_re", "polynomial.C_add", "group.mem_conjugates_of_set_iff", "set.Ici_diff_Ici", "measure_theory.outer_measure.trim_smul", "adjoin_root.mk_X", "measure_theory.induced_outer_measure_eq'", "power_series.inv_of_unit_eq", "list.reverse_repeat", "real.rpow_def", "wseq.head_terminates_of_mem", "cardinal.mk_image_eq", "subgroup.coe_comap", "exists_unique.intro", "enat.coe_lt_top", "tactic.ring_exp.mul_pf_c_prod", "left_ord_continuous.map_is_greatest", "subgroup.mem_closure", "measure_theory.l1.continuous_neg_part", "int.sign_eq_neg_one_iff_neg", "enat.add_lt_add_iff_right", "to_matrix_to_lin", "mv_polynomial.eval\:2082_rename", "times_cont_diff_within_at_nat", "relation.trans_gen.tail'", "floor_fract", "subtype.prop", "ring_hom.coe_fst", "nat.prime.eq_two_or_odd", "finset.ne_empty_of_mem", "isometric.coe_vadd_const", "finset.prod_union", "category_theory.nat_trans.unop_id", "commute.cast_int_mul_left", "mul_action.mem_orbit_iff", "power_series.coeff_zero_C", "gt_iff_lt", "composition_as_set.card_boundaries_eq_succ_length", "finsupp.single_add", "ordinal.mul_lt_of_lt_div", "sum.map_inl", "primrec.nat_iff", "abstract_completion.uniform_continuous_extension\:2082", "Inf_le_Inf", "is_subgroup.eq_trivial_iff", "is_max_filter.filter_inf", "filter.germ.induction_on\:2082", "polynomial.derivative_pow", "enat.get_add", "mul_aut.mul_def", "filter.tendsto.ne_bot", "mv_polynomial.total_degree_eq", "rat.cast_inv", "matrix.smul_apply", "set.enumerate_eq_none", "free_group.map.mul", "has_strict_fderiv_at_fst", "galois_connection.l_unique", "pfunctor.M.approx.P_mk", "differentiable_within_at.fderiv_within_congr_mono", "has_deriv_at.const_sub", "tendsto_left_nhds_uniformity", "scale_roots_ne_zero", "qpf.supp_eq", "lie_submodule.quotient.mk_bracket", "affine_subspace.coe_direction_eq_vsub_set_right", "set.Ico_eq_empty_iff", "decidable.peirce", "fin.univ_cast_succ", "primrec\:2082.comp\:2082", "ordinal.univ_id", "filter.map_mul", "vector.cons_val", "ideal.quotient.zero_eq_one_iff", "pell.xn_ge_a_pow", "is_R_or_C.norm_sq_neg", "equiv.prod_punit_apply", "local_ring.maximal_ideal_unique", "submonoid.multiset_prod_mem", "cancel_factors.neg_subst", "is_order_right_adjoint_cSup", "commute.all", "eckmann_hilton.mul_assoc", "sub_eq_sub_iff_add_eq_add", "ennreal.mul_le_mul", "linear_map.proj_comp_std_basis", "measure_theory.lintegral_Union_le", "filter.tendsto_at_bot_add_left_of_ge", "continuous_multilinear_map.norm_def", "ordinal.nat_cast_eq_zero", "unique_diff_on.prod", "pfunctor.M.head'_eq_head", "set.Iio_inter_Iio", "list.mem_lookup_iff", "multiset.Ico.filter_le_of_le_bot", "list.pairwise.and_mem", "cauchy_seq_of_edist_le_of_tsum_ne_top", "ordinal.mod_one", "con.mk'_surjective", "order_embedding.lt_embedding_apply", "list.head_eq_head'", "galois_connection.is_lub_u", "wseq.destruct_cons", "continuous_of_strict_mono_surjective", "localization_map.lift_unique", "vector.insert_nth_val", "module_equiv_finsupp_apply_basis", "multiset.count_cons_self", "nat.add_sub_cancel'", "real.angle.coe_zero", "mv_polynomial.range_eval\:1d62", "tendsto_nhds_within_of_tendsto_nhds_of_eventually_within", "pgame.add_lt_add_left", "matrix_equiv_tensor_apply_symm", "monoid_hom.map_mul", "iff_eq_true_of_eq", "dfinsupp.filter_def", "abstract_completion.map\:2082_coe_coe", "category_theory.whisker_left_app", "measure_theory.measure_eq_extend", "galois_insertion.strict_mono_u", "filter.ultrafilter_iff_compl_mem_iff_not_mem", "nat.sub_lt_sub_right_iff", "turing.TM1to0.tr_respects", "linear_equiv.conj_apply", "pnat.xgcd_type.flip_is_special", "linear_map.supr_range_std_basis", "category_theory.groupoid.is_isomorphic_iff_nonempty_hom", "filter.comap_principal", "asymptotics.is_O_with.exists_pos", "pell.xn_modeq_x4n_add", "pmf.map_comp", "primrec.cond", "bitvec.of_nat_to_nat", "polynomial.coeff_C_mul_X", "add_submonoid.mem_multiples", "gsmul_neg_succ_of_nat", "is_R_or_C.conj_inj", "riesz_extension.exists_top", "category_theory.limits.cocone.category_to_category_struct_to_has_hom_hom", "submodule.map_id", "set.Union_disjointed", "imp_eq_true_of_eq", "formal_multilinear_series.apply_composition_update", "is_closed_irreducible_component", "basic_smooth_bundle_core.coe_chart_at_fst", "pgame.add_left_neg_equiv", "Mod.hom.ext", "bifunctor.map_equiv_refl_refl", "differentiable.mul_const", "multiset.countp_sub", "monoid_algebra.submodule.exists_is_compl", "continuous_multilinear_map.coe_coe", "setoid.ker_mk_eq", "equiv.to_iso_hom", "int.add_le_add", "is_clopen_univ", "to_topological_space_infi", "nat.add_sub_assoc", "dual_pair.decomposition", "list.forall\:2082_map_right_iff", "alg_equiv.coe_refl", "dim_le_of_surjective", "submonoid.coe_subset_coe", "ordinal.deriv_succ", "not_of_eq_false", "real.exists_sup", "nnreal.bot_eq_zero", "mvpfunctor.supp_eq", "list.eq_of_suffix_of_length_eq", "ring_equiv.coe_mul_equiv", "nnreal.one_lt_rpow", "pnat.xgcd_type.v_eq_succ_vp", "geom_sum\:2082_mul", "measure_theory.measure.haar.index_union_le", "has_sum_single", "power_series.coeff_zero_eq_constant_coeff_apply", "algebra.mem_bot", "circle_deg1_lift.iterate_pos_le_iff", "metric.uniformity_edist", "ftaylor_series_within_univ", "nhds_within_Iio_ne_bot", "function.embedding.coe_sum_map", "category_theory.limits.coequalizer.condition", "filter.empty_in_sets_eq_bot", "quotient.out_eq'", "zmod.char_poly_pow_card", "measure_theory.inner_content_Union_nat", "cau_seq.completion.mk_mul", "is_path_connected.union", "category_theory.limits.cokernel.\[Pi]_of_epi", "enat.lt_add_one", "measure_theory.outer_measure.is_caratheodory_iff", "submonoid.localization_map.of_mul_equiv_of_localizations_comp", "complex.smul_im", "smooth_on.prod_mk", "continuous_linear_map.coe_proj_ker_of_right_inverse_apply", "opposite.unop_one", "contracting_with.exists_fixed_point", "lie_subalgebra.coe_bracket", "has_deriv_at.cexp", "power_series.order_eq_top", "padic_norm_e.nonarchimedean", "list.nodupkeys_of_sublist", "padic_norm_e.norm_p_lt_one", "ordinal.add_le_add_right", "inv_le_one", "add_units.neg_add", "char_p.neg_one_ne_one", "inner_product_space.of_core.inner_add_left", "is_add_unit_iff_exists_neg'", "nat.mul_mod_mul_left", "measure_theory.lintegral_const_mul'", "id_comp_rel", "option.to_finset_some", "supr_supr_eq_right", "num.succ'_to_nat", "nat.of_add_mul", "free_group.to_word.inj", "real.sin_int_mul_pi", "algebra.tensor_product.map_tmul", "one_lt_mul_of_le_of_lt", "add_submonoid.closure_singleton_eq", "multiset.filter_sub", "ideal.mem_inf", "multiset.le_iff_subset", "add_units.map_id", "ennreal.coe_ne_top", "interval_integral.integral_has_deriv_at_right", "bilin_form.mul_to_matrix_mul", "sym_bilin_form.sym", "list.enum_nth", "pgame.le_congr", "category_theory.abelian.coimages.coimage_strong_epi_mono_factorisation_to_mono_factorisation_m", "topological_space.opens.local_homeomorph_subtype_coe_target", "adjoin_root.lift_mk", "bilin_form.is_adjoint_pair.sub", "bor_self", "has_fderiv_at_filter_iff_has_deriv_at_filter", "category_theory.limits.prod_right_unitor_inv_naturality_assoc", "times_cont_diff_on_of_continuous_on_differentiable_on", "nat.mul_self_lt_mul_self_iff", "subtype.ext_iff", "multiset.le_sum_of_subadditive", "norm_num.int_sub_hack", "mem_path_component_of_mem", "submodule.mem_supr", "add_units.add_left_inj", "add_submonoid.localization_map.lift_add_right", "exists_subset_is_basis", "Sup_singleton", "multiset.inf_ndunion", "interval_integral.integral_of_ge", "measure_theory.l1.simple_func.norm_of_simple_func", "is_least.insert", "bundle_trivialization.continuous_at_proj", "nat.gcd.induction", "list.map_reverse_core", "measure_theory.integrable_const", "continuous_linear_equiv.lipschitz", "int.of_nat_mul", "has_ftaylor_series_up_to.differentiable", "category_theory.comma.map_left_obj_left", "encodable.encode_list_cons", "nat.smul_def", "zmod.ne_neg_self", "cardinal.min_le", "rat.le_def'", "basic_smooth_bundle_core.smooth_at_proj", "category_theory.limits.is_colimit.uniq_cocone_morphism", "category_theory.limits.cone_of_split_mono_\[Pi]_app_one", "ideal.exists_coeff_ne_zero_mem_comap_of_root_mem", "subring.mem_Sup_of_directed_on", "multiset.le_filter", "rat.totally_bounded_Icc", "pfunctor.approx.agree_children", "padic_norm_z", "asymptotics.is_o.trans_le", "measure_theory.integrable_iff_of_real", "category_theory.limits.types.jointly_surjective'", "power_series.coeff_map", "polynomial.eval\:2082_comp", "closure_ball", "approximates_linear_on.inverse_continuous_on", "finite_dimensional.fintype_card_le_findim_of_linear_independent", "submonoid.exists", "set.sUnion_image", "differentiable_at.comp_differentiable_within_at", "category_theory.limits.colimit.\[Iota]_post_assoc", "inv_ne_one", "category_theory.induced_functor_obj", "add_submonoid.localization_map.of_add_equiv_of_dom_comp", "mul_lt_mul''", "imp_congr_eq", "ring_hom.map_inv", "category_theory.monoidal.tensor_unit_map", "measure_theory.simple_func.integrable_pair", "ordered_comm_group.le_of_mul_le_mul_left", "int.commute_cast", "list.disjoint_left", "not_lt_of_ge", "con.sup_def", "add_submonoid.localization_map.surj", "is_compact.exists_is_glb", "sesq_form.ortho_smul_right", "multiset.lt_cons_self", "pi.vadd_apply", "nat.le_sub_left_of_add_le", "cardinal.ord_card_le", "category_theory.limits.image_\[Iota]_comp_eq_zero", "option.bind_some", "category_theory.monoidal_functor.id_to_lax_monoidal_functor_\[Mu]", "measurable_mul_left", "int.dvd_of_mul_dvd_mul_right", "has_fderiv_at.comp_has_deriv_at", "encodable.encode_none", "free_abelian_group.seq_neg", "padic_int.prime_p", "is_closed_diagonal", "filter.at_bot_basis", "int.add_lt_of_lt_neg_add", "deriv_pow''", "galois_connection.l_bot", "lucas_lehmer.order_\[Omega]", "ennreal.inv_involutive", "ring_hom.ker_is_prime", "nat.triangle_succ", "polynomial.degree_pos_of_eval\:2082_root", "complex.abs_sub_le", "metric.exists_dist_lt_of_inf_dist_lt", "commute.inv_inv", "list.nodup_of_nodup_map", "set.union_right_comm", "abs_mul", "multiset.filter_subset", "set.preimage_mul_const_Ioc_of_neg", "contracting_with.efixed_point_eq_of_edist_lt_top'", "commute.inv_right_iff", "measure_theory.integral_nonpos_of_nonpos_ae", "cont_t.run_cont_t_map_cont_t", "list.length_split_wrt_composition", "has_mfderiv_at_const", "add_submonoid.prod_mono", "set.inter_Union", "circle_deg1_lift.map_add_one", "real.has_sum_pow_div_log_of_abs_lt_1", "list.append_nil", "ideal.comap_lt_comap_of_root_mem_sdiff", "to_add_inv", "category_theory.limits.has_zero_morphisms.ext", "add_submonoid.localization_map.map_id", "nat.cast_zero", "has_deriv_at.csin", "real.zero_rpow_nonneg", "finset.Ico.diff_right", "submonoid.mrange_fst", "category_theory.limits.cokernel_not_iso_of_nonzero", "real.cos_lt_cos_of_nonneg_of_le_pi_div_two", "dfinsupp.support_single_subset", "category_theory.monoidal_category.triangle_assoc_comp_right", "equiv.coe_ulift", "isometric.continuous", "localization_map.epic_of_localization_map", "finset.sum_Ico_consecutive", "fract_add", "multiplicity.one_right", "seq.terminated_stable", "set.sInter_Union", "true_implies_iff", "pi.zero_apply", "submonoid.localization_map.map_left_cancel", "lie_submodule.quotient.is_quotient_mk", "nnreal.sub_le_self", "real.sqrt_nonneg", "denumerable.raise_lower'", "linear_equiv.dim_eq_lift", "multiset.nodup_iff_le", "int.lt_add_of_neg_lt_sub_left", "is_cyclic_of_order_of_eq_card", "composition_as_set.blocks_fun_pos", "localization_map.integer_normalization_eval\:2082_eq_zero", "finite_dimensional.findim_pos_iff_exists_ne_zero", "filter.eventually_sup", "bifunctor.fst_comp_snd", "alg_hom.to_linear_map_inj", "analytic_at.add", "list.repeat_sublist_repeat", "partrec.none", "filter.generate_univ", "category_theory.limits.limit_uncurry_iso_limit_comp_lim_hom_\[Pi]_\[Pi]", "complex.of_real_log", "list.alternating_sum_eq_finset_sum", "polynomial.coeff_X_zero", "prime.dvd_of_dvd_pow", "ennreal.coe_range_mem_nhds", "dfinsupp.add_apply", "valuation.zero_iff", "dvd.intro_left", "category_theory.limits.cofork.left_app_one_assoc", "exists_ratio_deriv_eq_ratio_slope'", "prime_spectrum.preimage_comap_zero_locus", "is_basis.dual_dim_eq", "cauchy_seq_of_le_tendsto_0", "uniform_space.completion.coe_neg", "submonoid.mrange_inl_sup_mrange_inr", "multiset.ndinter_le_left", "prod.mk.inj_iff", "measure_theory.measure.lift_linear_apply", "deriv_within_smul_const", "submodule.smul_mem_iff'", "category_theory.monoidal.Mon_functor_category_equivalence.functor_obj_obj_one", "nat.mul_self_inj", "eq_iff_modeq_int", "deriv_within_rpow", "measure_theory.measure.restrict_mono", "local_homeomorph.coe_trans_symm", "local_homeomorph.mk_coe", "commute.add_left", "list.sum_const_nat", "eq_false_of_or_eq_false_right", "semiquot.ext", "add_subgroup.mem_bot", "measure_theory.simple_func.smul_eq_map", "punit.add_eq", "wseq.mem_congr", "submonoid.localization_map.of_mul_equiv_of_dom_comp", "alist.keys_empty", "tendsto_locally_uniformly.comp", "with_zero.zero_div", "supr_le_supr_of_subset", "category_theory.limits.cofork.\[Pi]_of_\[Pi]", "category_theory.functor.map_cocone_X", "contracting_with.edist_efixed_point_lt_top'", "measure_theory.le_to_measure_apply", "tactic.ring.horner_pow", "is_R_or_C.im_sq_le_norm_sq", "nat.pow_dvd_pow_iff_pow_le_pow", "finset.mem_mul", "nat.xgcd_zero_left", "implicit_function_data.map_pt_mem_to_local_homeomorph_target", "omega.coeffs.val_between_eq_zero", "topological_add_group.ext", "continuous_sigma_map", "free_comm_ring.lift_comp_of", "fin.add_def", "nat.mul_pred_left", "free_semigroup.map_pure", "ne_bot_of_gt", "mv_polynomial.is_homogeneous.sum", "multiset.count_repeat", "forall_comm", "add_group.closure_add_subgroup", "set.prod_image_image_eq", "string.empty_ne_str", "mvqpf.comp_map", "one_lt_mul_of_lt_of_le'", "category_theory.over.iterated_slice_forward_obj", "finset.eq_of_veq", "has_deriv_within_at.sub_const", "primrec.option_some", "deriv_within_ccos", "subring.prod_top", "set.indicator_add_eq_right", "list.length_pos_iff_exists_mem", "polynomial.mul_coeff_zero", "differentiable_on.mono", "relator.rel_not", "cauchy_seq.is_cau_seq", "ideal.comap_top", "emetric.diam_triple", "emetric.edist_le_diam_of_mem", "filter.tendsto.Ioc", "function.commute.iterate_self", "Exists.snd", "linear_equiv.coe_uncurry_symm", "infi_bool_eq", "category_theory.category_of_elements.comma_equivalence_inverse", "group.closure_subgroup", "int.eq_neg_succ_of_lt_zero", "set.surj_on.union_union", "matrix.lie_transpose", "ennreal.mul_div_assoc", "padic.of_rat_neg", "multiset.sum_hom_rel", "CommSemiRing.coe_of", "polynomial.eval_one", "not_le", "free_group.one_eq_mk", "one_one_reducible.disjoin_left", "ennreal.Sup_add", "exists_rat_lt", "geom_series\:2082_with_one", "ideal.sub_mem", "order_of_eq_card_of_forall_mem_gpowers", "quotient_group.induction_on'", "localization.one_rel", "pow_length_le_mul_of_digits", "has_fderiv_at_filter.sub_const", "Sup_mem_closure", "filter.mem_pmap", "measure_theory.ae_eq_fun.edist_comm", "submodule.findim_mono", "category_theory.monoidal_of_has_finite_coproducts.associator_hom", "mv_polynomial.total_degree_pow", "wseq.mem_of_mem_tail", "nnreal.coe_list_prod", "continuous_on.neg", "finset.not_mem_map_subtype_of_not_property", "linear_map.pi_eq_zero", "set.inter_empty_of_inter_sUnion_empty", "CommRing.colimits.quot_add", "eq_zero_of_neg_eq", "list.prefix_or_prefix_of_prefix", "int.bit_val", "function.surjective_iff_has_right_inverse", "measure_theory.measure.measurable_join", "complex.abs_add", "le_of_one_div_le_one_div", "localization.ring_equiv_of_quotient_symm_of", "div_eq_filter_card", "list.lex.append_left", "eq_inv_of_mul_right_eq_one", "finmap.lookup_is_some", "int.coe_nat_bit0", "gold_conj_ne_zero", "int.sub_nonpos_of_le", "set.nonempty.left", "filter.germ.map'_coe", "num.le_to_nat", "compact_std_simplex", "real.rpow_lt_rpow", "ennreal.to_real_nonneg", "hyperreal.is_st_mul", "smooth_id", "set.singleton_add_singleton", "fderiv_within_const_sub", "partrec.some", "le_cInf_iff", "or_eq_of_eq_true_right", "supr_emptyset", "add_con.coe_eq", "is_closed.Inf_mem", "mv_polynomial.C_pow", "convex.smul", "int.coe_nat_one", "is_open.interior_eq", "is_group_hom.one_iff_ker_inv'", "function.commute.comp_left", "multiset.coe_inter", "differentiable_within_at.rpow", "onote.NF_below_iff_top_below", "nsmul_eq_mul", "ordinal.card_nat", "mul_dvd_mul_iff_left", "list.mem_keys", "differentiable_at.fderiv_within_prod", "norm_num.add_neg_pos_pos", "uniform_space.completion.continuous_mul", "category_theory.functor.ext", "subtype.coe_preimage_self", "semiconj_by.units_inv_right_iff", "generalized_continued_fraction.int_fract_pair.succ_nth_stream_b_le_nth_stream_fr_inv", "list.sum_take_succ", "eq_orthogonal_projection_of_mem_of_inner_eq_zero", "ennreal.tsum_mul_left", "num.of_nat_cast", "is_local_extr.has_fderiv_at_eq_zero", "category_theory.over.construct_products.cones_equiv_unit_iso_2", "mv_polynomial.eval\:2082_eq", "category_theory.limits.binary_cofan.\[Iota]_app_right", "discrete_valuation_ring.of_has_unit_mul_pow_irreducible_factorization", "int.mod_mul_right_mod", "polynomial.C_0", "ring_hom.map_multiset_sum", "interval_integral.integral_has_strict_deriv_at_of_tendsto_ae_left", "nnreal.tendsto_pow_at_top_nhds_0_of_lt_1", "pnat.coprime.gcd_mul", "int.mod_mod_of_dvd", "list.perm.insert", "measure_theory.simple_func.restrict_const_lintegral", "padic_int.norm_units", "category_theory.limits.walking_pair.swap_symm_apply_tt", "list.alternating_prod_cons_cons", "subring.coe_supr_of_directed", "fin.comp_cons", "equiv.sigma_congr_right_symm_apply", "filter.congr_sets", "dioph.proj_dioph_of_nat", "set.infinite.to_subtype", "cau_seq.lim_neg", "finset.map_subset_map", "structure_groupoid.id_mem", "multiset.map_eq_map", "multiset.erase_dup_add", "prime_spectrum.zero_locus_union", "turing.pointed_map.mk_val", "category_theory.limits.cokernel_cofork.\[Pi]_of_\[Pi]", "array.ext'", "mv_polynomial.degrees_mul", "submodule.mem_colon'", "linear_map.disjoint_std_basis_std_basis", "set.image_image2", "mv_power_series.coeff_mul", "set.surj_on.congr", "computation.lift_rel_aux.ret_left", "le_of_lt_or_eq", "finset.subset_product", "continuous_add", "analytic_at.neg", "continuous_bot", "relation.church_rosser", "has_sum.tsum_eq", "is_open.unique_diff_within_at", "finsupp.eq_zero_of_zero_eq_one", "category_theory.limits.epi_of_is_colimit_parallel_pair", "filter.mul_one", "structure_groupoid.compatible_of_mem_maximal_atlas", "order_iso.right_ord_continuous", "normed_space.dual_def", "inv_le", "perfect_closure.nat_cast_eq_iff", "option.is_none_none", "nat.dvd_of_mul_dvd_mul_right", "padic_val_nat_zero", "isometric.point_reflection_self", "dvd_iff_dvd_of_rel_right", "buffer.lt_aux_3", "linear_map.prod_eq_inf_comap", "category_theory.iso.to_alg_equiv_inv_fun", "has_fderiv_at.congr_of_eventually_eq", "tsum_geometric_two", "subgroup.ext'", "le_div_iff", "int.mul_pos", "category_theory.limits.has_image_map.factor_map_assoc", "int.eq_succ_of_zero_lt", "finset.supr_finset_image", "set.image2_singleton_left", "multiset.powerset_len_zero_right", "Module.exact_iff", "opposite.op_injective", "fpow_of_nat", "multiset.singleton_ne_zero", "category_theory.limits.pushout_cocone.condition_assoc", "matrix.dot_product_diagonal", "free_add_magma.map_pure", "sum.lex_acc_inl", "submonoid.range_subtype", "mul_nsmul", "set.Ioc_disjoint_Ioc", "multiset.sup_le", "list.mem_cons_eq", "asymptotics.is_O_with.const_smul_left", "computation.ret_orelse", "ennreal.coe_min", "multiset.erase_dup_subset'", "function.is_periodic_pt_iff_minimal_period_dvd", "add_units.add_neg_cancel_right", "ideal.is_jacobson_iso", "continuous_multilinear_map.curry_uncurry_right", "associates.factor_set.coe_add", "is_lub_Iic", "ring_hom.prod_unique", "bool.cond_tt", "supr_and'", "gcd_eq_zero_iff", "with_top.top_add", "category_theory.adjunction.left_triangle_components", "inv_of_mul_self", "fin.succ.inj", "polynomial.degree_C_le", "zero_le", "seq.map_nil", "measure_theory.lintegral_const_mul_le", "rel_embedding.collapse_F.not_lt", "int.neg_neg", "padic_norm_e.one'", "list.length_of_fn_aux", "generalized_continued_fraction.terminated_at_iff_s_terminated_at", "rat.mk_nat_eq", "matrix.linear_equiv_matrix_mul", "asymptotics.is_o.add_add", "polynomial.differentiable_within_at", "set.diff_compl", "set.bij_on.congr", "category_theory.quotient.functor_map", "isometry.lipschitz", "nat.coprime_one_right_iff", "seq.le_stable", "polynomial.nat_degree_map", "cardinal.bit0_ne_zero", "category_theory.nat_iso.cancel_nat_iso_inv_left", "measure_theory.simple_func.restrict_of_not_measurable", "equiv.set.sum_diff_subset_apply_inl", "summable_of_nnnorm_bounded", "nnreal.mul_le_iff_le_inv", "ennreal.infi_add_infi", "topological_space.opens.inclusion_to_fun", "nat.prod_factors", "multilinear_map.map_add", "finsupp.single_zero", "list.Ico.zero_bot", "add_group.closure_mono", "num.size_eq_nat_size", "set.nonempty_image_iff", "filter.tendsto_prod_iff", "nat.min_fac_zero", "interval_integral.integral_has_strict_deriv_at_left", "ennreal.nhds_zero", "filter.mem_bind_sets'", "monoid_hom.eq_of_eq_on_dense", "filter.tendsto.Ioo", "homeomorph.symm_comp_self", "dim_eq_of_surjective", "cluster_pt.of_inf_right", "compact_space_uniformity", "ring_hom.cancel_right", "measure_theory.outer_measure.Union_null", "monoid_algebra.group_smul.linear_map_apply", "mul_lt_iff_lt_one_right", "ennreal.to_real_eq_zero_iff", "nat.bit1_val", "add_units.coe_map", "mv_power_series.coeff_inv_aux", "nat.choose_pos", "inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four", "is_R_or_C.conj_neg_I", "category_theory.limits.fork.\[Iota]_of_\[Iota]", "filter.le_def", "finsupp.lsum_apply", "real.uniform_continuous_mul", "rank_add_le", "composition_as_set.blocks_length", "measure_theory.integral_add_measure", "ennreal.coe_bit0", "decidable.lt_trichotomy", "Set.mem_singleton", "filter.is_countably_generated.countable_generating_set", "polynomial.not_unit_X_sub_C", "set.finite.mul", "measure_theory.integrable_iff_norm", "list.tfae_nil", "int.gcd_dvd_gcd_of_dvd_left", "nat.coprime.eq_one_of_dvd", "computable.list_append", "multiset.erase_zero", "con.ext'", "int.gcd_dvd_gcd_mul_left_right", "category_theory.limits.kernel.condition", "onote.repr_of_nat", "category_theory.iso.comp_hom_eq_id", "asymptotics.is_O.symm", "is_closed_infi_iff", "category_theory.adjunction.equiv_homset_left_of_nat_iso_apply", "function.commute.iterate_pos_lt_iff_map_lt", "measure_theory.outer_measure.Union_eq_of_caratheodory", "ctop.realizer.is_open_iff", "cardinal.one_lt_bit1", "cardinal.powerlt_aux", "prime_iff_of_associated", "interval_integral.integral_sub", "infi_infi_eq_right", "ordinal.power_log_le", "polynomial.pairwise_coprime_X_sub", "cardinal.mk_quot_le", "multiset.disjoint_add_left", "is_compact.inter_right", "nat.lcm_one_left", "filter.eventually_lt_of_limsup_lt", "filter.countable_binfi_principal_eq_seq_infi", "fin.succ_zero_eq_one", "filter.tendsto_comap_iff", "category_theory.under.forget_obj", "Mon_.comp_hom'", "mfderiv_within_zero_of_not_mdifferentiable_within_at", "multiset.not_mem_of_nodup_cons", "uniform_space.comap_quotient_le_uniformity", "metric.mem_closed_ball", "sum.inl_ne_inr", "norm_num.le_bit0_bit1", "topological_space.opens.comap_id", "ordinal.omega_le_cof", "prod_X_sub_smul.coeff", "finsupp.subtype_domain_apply", "finset.union_left_comm", "set.infinite.exists_subset_card_eq", "list.chain'.append", "set.sInter_subset_sInter", "list.exists_of_length_succ", "dense_inducing.nhds_within_ne_bot", "equiv.perm.sign_aux_inv", "ideal.gc_map_comap", "polynomial.monomial_zero_left", "relation.trans_gen.head'_iff", "list.disjoint_of_nodup_append", "is_glb.of_subset_of_superset", "Inf_le", "sub_lt_self_iff", "ordinal.mk_initial_seg", "euclidean_geometry.dist_reflection", "is_R_or_C.div_im", "list.repeat_add", "norm_num.bit0_mul", "int.div_eq_div_of_mul_eq_mul", "deriv_pow'", "set.eq_finite_Union_of_finite_subset_Union", "affine.simplex.sum_circumcenter_weights_with_circumcenter", "category_theory.monoidal_category.inv_tensor", "bit1_zero", "affine_independent_set_of_affine_independent", "free_group.sum_mk", "is_open_mul_left", "equivalence_of_many_one_equiv", "applicative.pure_seq_eq_map'", "ordinal.succ_eq_add_one", "asymptotics.is_o.is_O_with", "padic.valuation_one", "seq_compact.lebesgue_number_lemma_of_metric", "times_cont_mdiff_within_at.of_le", "valuation.is_equiv.val_eq", "mul_le_of_le_one_left", "le_imp_le_iff_lt_imp_lt", "multiset.to_finsupp_zero", "dense_range.induction_on\:2083", "submonoid.localization_map.lift_mk'_spec", "div_div_cancel'", "finsupp.support_neg", "set.union_assoc", "mv_polynomial.monomial_add", "exists_dual_vector", "multiset.coe_keys", "list.subperm.erase", "cardinal.sum_mk", "ordinal.nat_cast_mul", "finset.Ico.eq_empty_iff", "add_monoid_hom.add_apply", "subgroup.mem_sup_left", "isometric.edist_eq", "fraction_map.integer_normalization_eq_zero_iff", "ring_hom.map_neg", "is_unit.mem_submonoid_iff", "add_comm_group.is_Z_bilin.zero_right", "le_nat_ceil", "frontier_inter_subset", "multiset.pi_cons_injective", "emetric.is_closed_ball_top", "subsemiring.range_fst", "inv_lt_one", "nat.find_greatest_spec_and_le", "mul_dvd_mul_left", "pgame.numeric.move_left_lt", "times_cont_diff_within_at.comp_continuous_linear_map", "ordinal.type_fin", "option.not_is_some_iff_eq_none", "list.lookmap_some", "gaussian_int.to_complex_one", "ordinal.typein_top", "is_lub_Sup", "units.mul_inv_cancel_left", "category_theory.Kleisli.comp_def", "linear_map.range_coprod", "list.argmax_nil", "padic_norm_e.mul'", "zsqrtd.mul_im", "max_min_distrib_left", "euclidean_geometry.inter_eq_singleton_orthogonal_projection", "list.forall_mem_map_iff", "ennreal.add_sub_cancel_of_le", "category_theory.iso.ext", "complex.conj_bijective", "finsupp.sum_add", "euclidean_domain.div_self", "measure_theory.l1.neg_part_to_fun_eq_max", "free_add_monoid.hom_eq", "filter.is_bounded_sup", "category_theory.functor.flip_obj_obj", "pi.linear_independent_std_basis", "roption.not_mem_none", "add_sub", "iterated_fderiv_within_succ_apply_left", "measure_theory.all_ae_of_real_F_le_bound", "det_eq_sign_char_poly_coeff", "prime_spectrum.comap_id", "multiplicative.simple_group_iff", "con.map_apply", "free_comm_ring.exists_finset_support", "measure_theory.measure.coe_smul", "submonoid.mrange_inr'", "set.mk_preimage_prod_left", "polynomial.map_injective", "is_compl.inf_sup", "hyperreal.infinite_iff_abs_lt_abs", "category_theory.exists_zigzag'", "nat.succ_mul_choose_eq", "relation.refl_trans_gen_lift'", "affine_map.line_map_apply_zero", "dist_eq_zero", "nat.eq_or_lt_of_not_lt", "fixed_points.smul_polynomial", "subring.coe_prod", "tactic.ring.add_neg_eq_sub", "formal_multilinear_series.mem_comp_partial_sum_source_iff", "set.left_mem_Ico", "alg_equiv.bijective", "fin.mk_eq_subtype_mk", "is_add_group_hom.zero_ker_neg", "monoid.exists_list_of_mem_closure", "subset_tangent_cone_prod_left", "nat.coprime_self", "continuous_multilinear_map.mk_pi_ring_apply_one_eq_self", "subsingleton_or_exists_ne", "filter.has_basis.ext", "differentiable_within_at.csinh", "measure_theory.simple_func.finset_sup_apply", "finset.lt_fold_max", "continuous_linear_map.pi_comp", "bool.default_bool", "set.indicator_sub", "real.sin_add_pi_div_two", "continuous_multilinear_map.bound", "finset.sum_subtype_eq_sum_filter", "ennreal.rpow_lt_rpow", "ordinal.zero_eq_type_empty", "linear_map.ker_smul'", "lists.sizeof_pos", "nat.lt_of_add_lt_add_left", "filter.sup_of_ultrafilters", "irrational.of_neg", "polynomial.has_deriv_within_at", "real.continuous_inv", "distrib_mul_action_hom.ext_iff", "multilinear_map.norm_image_sub_le_of_bound'", "nat.primrec.pow", "nnreal.eq_iff", "dioph.vec_ex1_dioph", "is_add_monoid_hom.of_add", "measure_theory.lebesgue_outer_trim", "fderiv_const_add", "list.append_left_cancel", "category_theory.bifunctor.map_id_comp", "complex.cosh_of_real_im", "convex.norm_image_sub_le_of_norm_fderiv_le'", "list.nth_modify_nth", "iterated_fderiv_within_succ_apply_right", "and_eq_of_eq", "set.image_prod", "convex_cone.mem_Inf", "has_sum.has_sum_of_sum_eq", "pnat.factor_multiset_pow", "pSet.equiv.euc", "gpow_bit0", "list.prefix_iff_eq_append", "set.inter_distrib_right", "submodule.map_inf_eq_map_inf_comap", "adic_completion.coe_eval", "topological_space.compacts.sup_val", "emetric.inf_edist_union", "wseq.join_map_ret", "equiv.prod_sum_distrib_apply_right", "has_fpower_series_on_ball.analytic_at_of_mem", "ulower.up_eq_up", "dense_embedding.subtype", "complete_space_congr", "polynomial.map_sum", "finsupp.mem_to_multiset", "right_add_coset_mem_right_add_coset", "measurable_space.dynkin_system.of_measurable_space_to_measurable_space", "is_mul_hom.comp", "multiset.sup_ndinsert", "nat.lt_succ_of_le", "stream.corec_def", "complex.tanh_of_real_im", "metric.complete_of_cauchy_seq_tendsto", "nat.mul_self_sub_mul_self_eq", "zero_add", "con.inf_iff_and", "function.semiconj\:2082.comp", "subring.mem_closure_iff", "times_cont_diff_on.continuous_on", "is_coprime_zero_left", "category_theory.iso.conj_Aut_mul", "ite_smul", "finset.sum_mul", "model_with_corners.target", "free_add_monoid.of_def", "measure_theory.integral_zero_measure", "norm_num.mul_bit0'", "neg_dvd", "bitraversable.tfst_comp_tsnd", "metric.is_closed_ball", "padic_norm_e.sub_rev", "int.lcm_dvd", "topological_space.opens.map_iso_inv_app", "mv_polynomial.coeff_X", "list.perm.bag_inter_right", "bit0_eq_zero", "category_theory.limits.walking_pair.swap_apply_right", "measure_theory.lintegral_norm_eq_lintegral_edist", "exists_prop_of_false", "iff_eq_of_eq_true_left", "lt_mul_of_lt_of_one_lt", "add_localization.induction_on\:2083", "pnat.dvd_prime", "isometric.isometry", "category_theory.quotient.comp_right", "finsupp.map_range_add", "cau_seq.lim_le", "num.lor_to_nat", "function.comp_const_right", "of_mul_inv", "category_theory.kernel_comp_cokernel_assoc", "filter.mem_inf_sets_of_left", "nat.sub_le_right_of_le_add", "denumerable.of_nat_of_decode", "int.le_add_one", "linear_equiv.of_injective_endo_right_inv", "mul_two", "filter.is_countably_generated.exists_seq", "is_max_on.neg", "span_lt_top_of_card_lt_findim", "category_theory.limits.is_limit.of_nat_iso.hom_of_cone_of_hom", "traversable.naturality_pf", "polynomial.degree_X_pow_sub_C", "set.Iic_union_Ioi", "lebesgue_number_lemma_of_metric", "measure_theory.simple_func.fin_meas_supp.map_iff", "num.land_to_nat", "int.mod_add_div", "countable_bInter_mem_sets", "set.bij_on.subset_range", "primrec.list_of_fn", "category_theory.over.construct_products.cones_equiv_functor_2", "category_theory.monoidal_category.right_unitor_conjugation", "nat.succ_le_succ", "complex.deriv_sin", "add_units.map_comp", "rel_iso.surjective", "nat.test_bit_zero", "smul_inv_smul'", "bool.ff_ne_tt", "filter.eventually_eq.symm", "filter.lift_comm", "zorn.chain_closure_succ_fixpoint_iff", "free_magma.traverse_mul'", "mul_equiv.ext", "turing.to_partrec.code.exists_code", "cancel_factors.mul_subst", "is_add_unit_of_add_eq_zero", "category_theory.monoidal_category.associator_nat_iso_hom_app", "num.bit_to_nat", "filter.rcomap_sets", "nonempty_unique_or_exists_ne", "set.neg_subset", "has_fpower_series_at.neg", "add_submonoid.localization_map.map_right_cancel", "continuous_supr_dom", "tendsto_locally_uniformly.continuous", "string.to_list_inj", "finset.max'_le", "ring_equiv.to_opposite_apply", "polynomial.differentiable_on", "vector.cons_head_tail", "mv_polynomial.eval_indicator_apply_eq_zero", "set.preimage_add_preimage_subset", "cardinal.mk_rat", "nat.fact_lt", "continuous_linear_map.coe_snd'", "subring.prod_mono_right", "int.bitwise_bit", "inf_eq_top_iff", "is_integral_of_mem_of_fg", "category_theory.graded_object.zero_apply", "one_le_pow_of_one_le'", "computation.lift_rel_of_mem", "add_submonoid.localization_map.lift_eq", "list.tfae_of_cycle", "real.deriv_cos'", "filter.tendsto.basis_left", "nnreal.rpow_one", "local_equiv.refl_source", "computation.results.len_unique", "nat.div_div_self", "set.mem_union", "multiplicity.multiplicity_pow_self", "filter.prod_mono", "measure_theory.outer_measure.le_inter_add_diff", "pell.yn_succ", "multiset.singleton_coe", "add_submonoid.mrange_snd", "Top.prelocal_predicate.sheafify_of", "subsemiring.mem_inf", "list.rel_mem", "real.exp_strict_mono", "quadratic_form.to_fun_eq_apply", "interval_integral.FTC_filter.finite_at_inner", "exp_neg_inv_glue.f_aux_has_deriv_at", "fintype.sum_congr", "norm_num.mul_neg_neg", "mem_skew_adjoint_matrices_submodule", "is_integral_tower_bot_of_is_integral", "Cauchy.extend_pure_cauchy", "of_digits_digits", "ordinal.mul_is_normal", "galois_coinsertion.u_supr_of_lu_eq_self", "set.maps_to.congr", "cardinal.aleph'_is_normal", "Set.eval_mk", "add_submonoid.subset_closure", "deriv_div", "finmap.union_to_finmap", "linear_map.fun_congr_left_apply", "differentiable_on.add_const", "inner_smul_left", "submodule.map_coe", "self_mem_nhds_within", "set.preimage_injective", "mul_action.orbit_equiv_quotient_stabilizer_symm_apply", "div_one", "cardinal_lt_omega_of_dim_lt_omega", "category_theory.pi.sum_obj_map", "surreal.add_assoc", "iff_eq_of_eq_true_right", "int.shiftl_neg_succ", "upper_bounds_Icc", "continuous_multilinear_map.fin0_apply_norm", "int.nat_abs_one", "mvqpf.supp_eq_of_is_uniform", "finset.subset.trans", "filter.has_basis.restrict", "circle_deg1_lift.iterate_eq_of_map_eq_add_int", "with_top.coe_lt_coe", "list.prod_cons", "polynomial.hom_eval\:2082", "ennreal.coe_mem_upper_bounds", "asymptotics.is_o_congr", "multiset.powerset_len_cons", "mv_polynomial.is_noetherian_ring_fin", "mem_ext_chart_source", "compact_iff_compact_in_subtype", "measurable.of_inv", "dist_le_of_le_geometric_two_of_tendsto\:2080", "set.inv_subset_inv", "le_mem_nhds", "znum.cast_one", "submodule.coe_supr_of_directed", "topological_space.open_nhds.inclusion_obj", "padic_norm.padic_norm_p_of_prime", "eq_vadd_iff_vsub_eq", "differentiable_at.const_smul_algebra", "sup_top_eq", "multiset.pure_def", "nat.choose_symm", "array.to_list_nth_le", "strict_mono_mul_right_of_pos", "continuous_multilinear_map.curry0_norm", "category_theory.monoidal_category.unitors_equal.cells_15", "category_theory.limits.fork.app_zero_right_assoc", "finset.le_fold_max", "holor.mul_assoc", "multiset.Ico.inter_consecutive", "qpf.cofix.bisim'", "matrix.mul_smul", "is_lub_Ioc", "affine_subspace.affine_span_eq_Inf", "left_inverse_inv", "multiset.sup_singleton", "is_open_map_smul_of_unit", "complex.deriv_cos", "ideal.map_supr_comap_of_surjective", "heq_self_iff_true", "set.Ico_pnat_card", "set.inj_on_preimage", "associates.mk_pow", "tendsto_of_liminf_eq_limsup", "times_cont_mdiff_within_at_id", "sub_le_sub", "normalize_eq_one", "hash_map.find_insert_ne", "differentiable_fst", "list.perm.countp_eq", "pnat.dvd_iff'", "has_mfderiv_within_at.comp", "subring.prod_bot_sup_bot_prod", "hyperreal.infinite_neg_mul_infinite_neg", "relation.transitive_refl_trans_gen", "has_deriv_at_filter.add_const", "has_deriv_within_at.liminf_right_slope_norm_le", "exists_lt_of_cInf_lt", "continuous_linear_map.fst_prod_snd", "num.add_one", "vsub_sub_vsub_cancel_left", "enat.coe_ne_top", "finsupp.coe_leval", "stream.tail_inits", "is_measurable.nhds_within_is_measurably_generated", "UniformSpace.hom_ext", "cInf_le_cSup", "category_theory.braided_functor.id_to_monoidal_functor", "category_theory.preadditive.sub_comp", "power_series.map_comp", "fraction_map.num_denom_reduced", "is_R_or_C.conj_im", "mv_polynomial.C_1", "set.image_factorization_eq", "prod.lex_def", "list.injective_foldl_comp", "subgroup.exists", "onote.le_def", "category_theory.limits.kernel.lift_\[Iota]", "asymptotics.is_O_comm", "nat.bit_ne_zero", "zsqrtd.nonneg_muld", "asymptotics.is_O_with.trans", "set.sigma_to_Union_injective", "submonoid.localization_map.map_comp", "linear_equiv.symm_symm", "char_p.char_p_to_char_zero", "generalized_continued_fraction.of_part_num_eq_one_and_exists_int_part_denom_eq", "alist.mem_erase", "lattice.ext", "padic_int.appr_lt", "mvpfunctor.comp_map", "gronwall_bound_continuous_\[CurlyEpsilon]", "set.inter_eq_self_of_subset_right", "filter.is_ultrafilter.em", "cau_seq.const_equiv", "tendsto_pow_at_top_nhds_0_of_norm_lt_1", "associated_mul_mul", "list.head_eq_of_cons_eq", "algebraic_geometry.PresheafedSpace.comp_base", "semiconj_by.neg_left_iff", "finset.affine_combination_eq_weighted_vsub_of_point_vadd_of_sum_eq_one", "dvd_dvd_iff_associated", "submodule.mem_div_iff_smul_subset", "add_subgroup.prod_mono_right", "generalized_continued_fraction.terminated_stable", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_comp_is_iso_hom", "open_embedding.source", "deriv_smul", "continuous_top", "submonoid.localization_map.mk'_mul_cancel_left", "category_theory.limits.pushout.inr_desc", "rat.cast_inj", "turing.to_partrec.cont_eval_fix", "div_sub_div_same", "deriv_within_div", "znum.zneg_neg", "smodeq.mono", "pi.list_prod_apply", "set.mem_inter_iff", "con.lift_surjective_of_surjective", "typevec.drop_fun_diag", "monoid_hom.map_mclosure", "continuous_edist", "int.add_lt_of_lt_sub_left", "cardinal.mul_power", "polynomial.map_id", "set.empty_inter", "topological_space.opens.is_basis_iff_nbhd", "zsqrtd.nonneg_total", "measure_theory.le_extend", "category_theory.comma.map_right_obj_right", "free_group.red.step.cons_cons_iff", "ring_hom.eq_nat_cast", "constr_neg", "add_aut.coe_one", "contracting_with.edist_efixed_point_le", "measurable_inv'", "nat.rfind_opt_dom", "category_theory.action_category.stabilizer_iso_End_symm_apply", "differentiable_on.inv", "ennreal.inv_bijective", "equiv.coe_plift_symm", "asymptotics.is_o.mul_is_O", "finset.image_subset_iff_subset_preimage", "ring_hom.id_comp", "div_le_div_iff'", "add_submonoid.map_sup", "embedding.mk'", "set.disjoint_singleton_left", "omega.coeffs.val_except_eq_val_except", "local_homeomorph.trans_target'", "ordinal.unbounded_of_unbounded_sUnion", "padic_val_rat.div", "or.right_comm", "multiset.coe_to_list", "add_submonoid.mem_sup_left", "category_theory.image_to_kernel_map_zero_left", "open_dom_of_pcontinuous", "is_closed_map_add_right", "category_theory.iso.to_equiv_fun", "add_con.lift_surjective_of_surjective", "units.inv_eq_of_mul_eq_one", "ite_eq_ff_distrib", "set.image_mul_left_Icc'", "equiv.inv_symm", "set.finite.countable", "rat.dist_cast", "continuous_linear_equiv.units_equiv_aut_apply_symm", "lipschitz_with.dist_right", "times_cont_diff_within_at_succ_iff_has_fderiv_within_at", "add_subgroup.comap_top", "equiv_functor.map_equiv_symm_apply", "dist_norm_norm_le", "complex.div_im", "hyperreal.infinitesimal_inv_of_infinite", "affine_subspace.mem_affine_span_singleton", "multiset.add_union_distrib", "set.surj_on_bUnion", "complex.eq_conj_iff_re", "le_imp_le_of_lt_imp_lt", "is_R_or_C.of_real_neg", "pnat.factor_multiset_mul", "asymptotics.is_O_const_smul_left_iff", "neg_add'", "filter.tendsto_sub_at_top_nat", "monoid_hom.mrange_top_iff_surjective", "order_of_pos", "measure_theory.le_infi2_lintegral", "set.preimage_add_const_Iio", "ennreal.zero_to_real", "function.update_comp_eq_of_injective", "homological_complex.kernel_map_condition", "times_cont_diff_within_at.times_cont_diff_at", "filter.ultrafilter_of_le", "many_one_reducible_refl", "set.preimage_singleton_eq_empty", "continuous_Prop", "norm_add_pow_two", "multiset.filter_cons_of_neg", "continuous_linear_equiv.trans_to_linear_equiv", "category_theory.limits.has_image.uniq", "uniform_space.completion.continuous.mul", "hyperreal.not_infinitesimal_of_infinite_pos", "is_max_filter.neg", "cardinal.mk_subtype_of_equiv", "holor_index.take_take", "asymptotics.is_O_with.congr_right", "category_theory.functor.const.op_obj_op_hom_app", "unique_factorization_domain.dvd_of_dvd_mul_right_of_no_prime_factors", "list.mem_of_mem_last'", "category_theory.pre_map", "roption.bind_assoc", "filter.eventually.exists_measurable_mem", "function.injective_id", "finset.card_union_le", "real.sin_pi_div_eight", "finset.disjoint_val", "structure_groupoid.local_invariant_prop.lift_prop_on_of_locally_lift_prop_on", "category_theory.limits.limit.lift_post", "equiv.perm.one_def", "quadratic_form.equivalent.refl", "composition.size_up_to_of_length_le", "classical.dec", "list.nodup_sigma", "ordinal.add_sub_cancel_of_le", "measure_theory.l1.integral_zero", "submodule.restrict_scalars_mem", "pnat.coe_bit1", "setoid.ker_eq_lift_of_injective", "ideal.span_singleton_eq_bot", "power_series.monomial_zero_eq_C_apply", "wseq.bind_assoc", "wseq.lift_rel.swap", "finset.mul_def", "model_with_corners_self_coe_symm", "linear_independent_iff_total_on", "category_theory.adjunction.right_triangle_components_assoc", "mv_polynomial.total_degree_neg", "list.lookup_all_nodup", "prod_subset_compl_diagonal_iff_disjoint", "list.not_mem_append", "category_theory.limits.prod_left_unitor_hom_naturality_assoc", "linear_map.range_le_ker_iff", "directed.sequence_mono_nat", "set.Iio_subset_Iic_union_Ico", "add_submonoid.localization_map.add_equiv_of_localizations_apply", "enat.pos_iff_one_le", "continuous_id", "list.update_nth_eq_modify_nth", "one_lt_of_inv_inv", "linear_equiv.to_Module_iso_inv", "ideal.is_maximal_of_is_maximal_disjoint", "nat.succ_sub_one", "norm_num.inv_one", "pi_Lp.norm_eq", "discrete_valuation_ring.of_ufd_of_unique_irreducible", "not_ball_of_bex_not", "tactic.ring_exp.pow_pp_pf_one", "stream.nth_odd", "category_theory.limits.cokernel_cofork.condition", "is_min_on.add", "subgroup.mem_inf", "filter.tendsto_at_bot_add_right_of_ge'", "generalized_continued_fraction.convergent_eq_conts_a_div_conts_b", "affine_subspace.direction_affine_span_insert", "bifunctor.snd_fst", "euclidean_domain.mod_lt", "pgame.left_wins_of_equiv_iff", "uniform_space_comap_id", "nonneg_of_neg_nonpos", "continuous_multilinear_map.sum_apply", "linarith.int.coe_nat_bit1_mul", "measure_theory.measure.add_le_add_right", "prod.snd_sum", "function.semiconj.maps_to_image", "mdifferentiable.comp", "int.nat_abs_neg_of_nat", "submonoid.localization_map.of_mul_equiv_of_localizations_apply", "canonically_ordered_semiring.mul_le_mul_left'", "nnreal.bdd_below_coe", "times_cont_mdiff_on.continuous_on_tangent_map_within", "rat.mk_pnat_denom", "approximates_linear_on.lipschitz_sub", "differentiable_within_at.congr_of_eventually_eq", "nhds_Inf", "is_add_subgroup.mem_norm_comm", "add_submonoid.localization_map.eq_iff_eq", "polynomial.coeff_mk", "mv_polynomial.eval\:2082_sum", "mv_polynomial.is_homogeneous.add", "stream.nth_nats", "linear_map.map_add", "is_add_submonoid.coe_zero", "set.empty_pi", "finset.fold_hom", "stream.head_map", "category_theory.prod.associator_obj", "real.sin_lt", "int.to_nat_le_to_nat", "list.length_repeat", "subsemiring.coe_Sup_of_directed_on", "antilipschitz_with.cod_restrict", "composition_as_set.to_composition_length", "nat.lt_succ_self", "filter.eventually_Sup", "mv_polynomial.vars_C", "open_subgroup.mem_coe_opens", "has_deriv_at_neg", "int.neg_of_nat_eq_sub_nat_nat_zero", "set.range_factorization_eq", "metric.Hausdorff_dist_triangle'", "con.ker_apply_eq_preimage", "filter.tendsto_map'_iff", "category_theory.limits.biprod.symmetry'", "cardinal.nat_cast_le", "turing.tape.map_mk\:2081", "add_units.ext", "pi.is_basis_fun\:2080", "nnreal.coe_of_real", "list.alternating_sum_cons_cons", "eq_of_inf_eq_sup_eq", "encodable.decode_list_succ", "add_submonoid.localization_map.sec_spec", "surjective_proj_I", "traversable.map_traverse'", "nat.gcd_mul_left", "finset.max'_singleton", "imp_and_distrib", "algebraic_geometry.PresheafedSpace.restrict_carrier", "equiv.swap_comm", "quadratic_form.zero_apply", "list.forall_of_pairwise", "mul_self_sub_mul_self", "linear_map.inr_eq_prod", "inv_pos", "is_R_or_C.abs_of_nonneg", "submodule.map_smul''", "finset.disjoint_singleton", "fintype.card_sum", "ordinal.mod_lt", "cardinal.extend_function_finite", "finset.sum_congr", "neg_eq_of_add_eq_zero", "quotient_add_group.induction_on", "finset.card_univ_diff", "local_homeomorph.trans_symm_self", "asymptotics.is_O_with.prod_rightr", "submonoid.mrange_inl'", "eq.to_iff", "vector3.rec_on_cons", "ring_hom.eq_on_set_closure", "lucas_lehmer.int.coe_nat_two_pow_pred", "add_monoid_hom.iterate_map_smul", "stream.nats_eq", "emetric.ball_mem_nhds", "quotient.eq", "real.arcsin_pos", "equiv.coe_units_equiv_ne_zero", "is_closed_sigma_mk", "metric.Hausdorff_dist_le_diam", "add_submonoid.comap_inf", "real.is_conjugate_exponent.one_div_pos", "unique_mdiff_within_at_univ", "finset.sum_hom", "prod.swap_right_inverse", "subalgebra.sub_mem", "mvfunctor.liftp_last_pred_iff", "times_cont_mdiff_on_top", "int.of_nat_add_of_nat", "multiset.count_ne_zero", "list.mem_of_fn", "map_Inf_of_continuous_at_of_monotone", "set.interval_of_gt", "has_deriv_within_at_iff_tendsto", "mfderiv_within_congr", "measure_theory.measure_eq_induced_outer_measure", "local_equiv.trans_symm_eq_symm_trans_symm", "perfect_closure.of_apply", "contracting_with.one_sub_K_pos", "hyperreal.pos_of_infinite_pos", "turing.partrec_to_TM2.tr_num_nat_end", "nat.gcd_self", "complex.abs_re_le_abs", "smooth_within_at_iff", "pmf.bind_bind", "mem_nhds_subtype", "category_theory.zero_mul_hom", "algebra.smul_mul_assoc", "filter.lift'_id", "pgame.le_iff_sub_nonneg", "is_closed_imp", "list.to_finset_eq", "compact_Icc", "function.right_inverse_inv_fun", "int.of_nat_mul_neg_of_nat", "measure_theory.simple_func.measurable", "fpow_le_of_le", "set.inter_preimage_subset", "ordinal.succ_lt_of_not_succ", "has_strict_fderiv_at.has_strict_deriv_at", "free_semigroup.map_mul", "list.rotate_zero", "is_coprime.pow_left", "cardinal.sum_le_sum", "ideal.quotient_map_C_eq_zero", "has_deriv_at_id", "ordering.compares.eq_eq", "Meas.coe_of", "uniform_embedding_def", "filter.germ.coe_coe_mul_hom", "is_coprime.add_mul_left_left", "measure_theory.l1.dist_eq", "filter.eventually_false_iff_eq_bot", "filter.prod_pure_pure", "is_bounded_linear_map.fderiv", "structure_groupoid.local_invariant_prop.lift_prop_at_congr_iff_of_eventually_eq", "measure_theory.measure.dirac_apply'", "measure_theory.measure.map_id", "rel.core_comp", "function.directed_pts_of_period_pnat", "continuous_linear_equiv.map_eq_zero_iff", "matrix.det_update_row_add", "turing.TM1to1.supports_stmt_read", "multiset.mem_bind", "multiplicity.finite_of_finite_mul_left", "category_theory.monoidal_category.unitors_equal.cells_1_4", "add_monoid_algebra.support_mul", "nat.min_fac_dvd", "uniform_space.completion.extension_map", "fin.univ_succ", "circle_deg1_lift.ceil_map_map_zero_le", "is_add_submonoid.multiset_sum_mem", "free_add_semigroup.map_pure", "free_group.red.cons_cons", "mul_self_le_mul_self", "equiv.swap_swap", "real.pi_gt_314", "supr_univ", "circle_deg1_lift.map_one_add", "measure_theory.measure_mono", "is_local_min.deriv_eq_zero", "mt", "wseq.destruct_append", "times_cont_diff_on.comp_continuous_linear_map", "pnat.dvd_antisymm", "int.to_nat_add", "submonoid.localization_map.mul_inv_left", "set.mem_of_mem_of_subset", "filter.tendsto_pure", "real.is_conjugate_exponent.sub_one_mul_conj", "polynomial.expand_eq_sum", "affine.simplex.points_with_circumcenter_point", "continuous_at_id", "forall_or_distrib_left", "finsupp.on_finset_sum", "set.subsingleton_singleton", "algebra.tensor_product.lid_tmul", "finset.image_image", "zsqrtd.d_pos", "has_fderiv_within_at.maps_to_tangent_cone", "category_theory.nat_trans.vcomp_app", "category_theory.limits.kernel_condition_apply", "padic_val_rat.mul", "mdifferentiable_at.mfderiv", "finset.bInter_insert", "prod.fst_eq_iff", "eq_div_iff_mul_eq", "typevec.append1_cases_append1", "pnat.gcd_eq_left_iff_dvd", "finmap.lookup_singleton_eq", "inf_ind", "mul_eq_zero", "equiv.perm.same_cycle_inv_apply", "false_of_true_iff_false", "filter.mem_inf_sets", "has_ftaylor_series_up_to_on_univ_iff", "measure_theory.simple_func.ennreal_rat_embed_encode", "compact_of_is_closed_subset", "monoid_hom.map_one", "continuous_linear_equiv.symm_to_linear_equiv", "associates.prod_eq_one_iff", "asymptotics.is_o.prod_rightr", "bilin_form.map_sum_right", "set.image_neg", "nat.tendsto_pow_at_top_at_top_of_one_lt", "algebra.bijective_algbera_map_iff", "local_homeomorph.continuous_at_iff_continuous_at_comp_left", "polynomial.degree_eq_iff_nat_degree_eq_of_pos", "not_and_of_not_right", "prime_of_associated", "pythagorean_triple.is_primitive_classified_of_coprime", "num.size_to_nat", "units.coe_neg", "dfinsupp.sum_single_index", "hyperreal.infinite_neg_def", "normal_iff_eq_cosets", "linear_map.ker_eq_bot_of_injective", "palindrome.iff_reverse_eq", "set.Ioc_union_Ioi_eq_Ioi", "tactic.abel.unfold_smulg", "nat.primrec'.unpair\:2082", "differentiable_at.exp", "smooth_within_at_id", "times_cont_diff_within_at.prod", "equiv.perm.mul_apply", "category_theory.currying_counit_iso_inv_app_app", "filter.tendsto_at_bot_at_bot", "filter.Limsup_top", "associates.prime_mk", "cardinal.mk_singleton", "multiset.rel_zero_right", "add_submonoid.coe_add", "int.nat_abs_zero", "ennreal.add_top", "generalized_continued_fraction.numerators_recurrence", "fact.succ.pos", "Inf_apply", "polynomial.eq_C_of_nat_degree_le_zero", "pgame.star_lt_zero", "category_theory.limits.is_colimit.hom_desc", "function.injective.preimage_surjective", "is_min_filter.neg", "circle_deg1_lift.translation_number_le_of_le_add_int", "nat.prime.multiplicity_choose_aux", "char_dvd_card_solutions_family", "commute.mul_pow", "measure_theory.le_to_outer_measure_caratheodory", "is_cyclic.card_pow_eq_one_le", "commute.div_right", "perfect_closure.eq_iff'", "measure_theory.induced_outer_measure_caratheodory", "set.preimage_sub_const_Icc", "differentiable_within_at.sub", "times_cont_diff.times_cont_diff_on", "exists_congr", "filter.Inter_mem_sets_of_fintype", "set.union_diff_cancel'", "computable\:2082.comp\:2082", "uniform.tendsto_nhds_right", "measure_theory.ae_eq_fun.lintegral_add", "primrec.band", "list.mem_append", "primrec.vector_of_fn", "neg_of_mul_pos_right", "base_pow_length_digits_le'", "decidable.lt_or_gt_of_ne", "list.foldl_join", "add_magma.free_add_semigroup.map_of", "vector.nth_update_nth_eq_if", "function.right_id", "multiset.ext", "continuous_linear_map.op_norm_le_of_lipschitz", "array.to_list_to_array", "finset.card_compl", "finset.insert_subset_insert", "with_top.some_lt_some", "has_groupoid_of_le", "list.modify_nth_eq_take_cons_drop", "list.of_mem_lookup", "mul_le_mul_right", "primrec.list_range", "category_theory.abelian.pseudoelement.zero_eq_zero'", "add_submonoid.localization_map.symm_comp_of_add_equiv_of_localizations_apply'", "measure_theory.integrable.right_of_add_measure", "primrec.subtype_val_iff", "set.pi_nonempty_iff", "multiset.nodup_filter", "is_coprime.of_mul_right_left", "real.angle.sin_eq_iff_eq_or_add_eq_pi", "semiconj_by.cast_nat_mul_cast_nat_mul", "direct_sum.to_group_add", "set.bij_on.mk", "normal.is_integral", "real.arcsin_le_pi_div_two", "nonote.repr_add", "finsupp.erase_add", "filter.prod_at_bot_at_bot_eq", "local_homeomorph.trans_source''", "add_submonoid.map_le_iff_le_comap", "is_local_max.sup", "pos_num.divmod_to_nat_aux", "with_top.inf_eq_min", "complex.sin_sub_pi_div_two", "free_add_monoid.map_of", "norm_num.rat_cast_bit1", "submonoid.localization_map.eq_of_eq", 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"category_theory.limits.cone.whisker_X", "Gromov_Hausdorff.GH_dist_le_nonempty_compacts_dist", "list.erasep_map", "times_cont_mdiff_within_at.prod_mk", "nat.add_one_ne_zero", "valuation.ext_iff", "filter.is_countably_generated.tendsto_iff_seq_tendsto", "monoid_algebra.prod_single", "set.preimage_neg_Ici", "filter.infi_sup_left", "dfinsupp.mem_support_iff", "eq_inv_iff_mul_eq_one", "set.eval_image_pi", "rat.add_left_neg", "list.pairwise_middle", "function.semiconj.id_right", "is_closed.frontier_eq", "measure_theory.exists_nonempty_inter_of_measure_univ_lt_tsum_measure", "is_unit.map'", "measure_theory.measure.sum_apply", "nat.pred_le_iff", "filter.map_neg", "multiset.powerset_len_le_powerset", "nat.mul_div_mul", "relation.trans_gen.trans", "ordinal.succ_lt_succ", "mv_power_series.coeff_index_single_X", "real.zero_rpow_le_one", "is_compact.binary_compact_cover", "option.mem_to_finset", "principal_seg.lt_le_apply", "ennreal.sub_self", "multiset.bind_zero", "typevec.drop_fun_to_subtype", "category_theory.monoidal_category.tensor_right_tensor_hom_app", "nat.eq_zero_of_add_eq_zero_left", "localization.mul_equiv_of_quotient_symm_monoid_of", "nnreal.sub_lt_self", "nat.sqrt_eq", "continuous_proj_I", "submonoid.sup_eq_range", "nat.coprime.mul", "has_fderiv_within_at.mul_const", "order_bot.ext", "category_theory.over.iterated_slice_backward_map", "is_R_or_C.norm_sq_conj", "emetric.inf_edist_singleton", "list.chain.imp'", "wseq.to_list_cons", "alist.perm_insert", "cardinal.not_countable_real", "subalgebra.one_mem", "differentiable_at_pow", "nat.prime.two_le", "pfunctor.liftr_iff", "measure_theory.measure.le_add_right", "category_theory.limits.types.filtered_colimit.colimit_eq_iff", "list.sum_cons", "nnreal.coe_indicator", "alg_hom.comp_to_linear_map", "submodule.sub_mem", "int.gcd_assoc", "norm_num.int_cast_one", "multiset.insert_eq_cons", "dvd_pow", "function.is_periodic_pt.apply_iterate", "polynomial.map_C", "nat.div_mod_eq_mod_mul_div", "int.le_of_coe_nat_le_coe_nat", 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"set.range_ite_subset'", "power_series.coeff_inv_of_unit", "add_comm_group.direct_limit.of.zero_exact", "mv_polynomial.degrees_indicator", "int.cast_pow", "set.Inter_subset", "norm_image_sub_le_of_norm_deriv_le_segment", "list.lookup_all_cons_ne", "is_null_measurable.compl", "multiset.coe_pmap", "tendsto_nhds_within_of_tendsto_nhds", "equiv.perm.sign_one", "ideal.span_le", "ennreal.zero_lt_coe_iff", "local_equiv.of_set_symm", "add_subgroup.closure_eq", "gcd_zero_right", "pequiv.of_set_eq_refl", "infi_true", "nat.odd_of_mod_four_eq_one", "list.sublist.subperm", "tactic.ring.zero_horner", "typevec.split_fun_comp", "category_theory.limits.cone_left_op_of_cocone_X", "set.preimage_sub_const_Ioi", "structure_groupoid.locality", "znum.neg_of_int", "multiset.sizeof_lt_sizeof_of_mem", "continuous_multilinear_map.bounds_nonempty", "deriv_neg'", "vector.to_list_append", "padic.of_rat_mul", "isometry.injective", "ctop.realizer.mem_nhds", "continuous_linear_map.coe_neg", "real.sinh_bijective", "nat.partrec.some", "set.bij_on_empty", "submonoid.gc_map_comap", "onote.omega_le_oadd", "is_coprime.of_add_mul_left_right", "function.minimal_period_pos_iff_mem_periodic_pts", "onote.lt_def", "euclidean_geometry.orthogonal_projection_mem_orthogonal", "local_homeomorph.is_O_with_congr", "finset.card_insert_le", "polynomial.coeff_zero_eq_aeval_zero", "list.suffix_iff_eq_append", "nhds_within_restrict'", "multiset.not_mem_range_self", "multiset.comp_traverse", "polynomial.X_sub_C_ne_zero", "is_coprime.mul_left", "setoid.ker_iff_mem_preimage", "rat.num_pos_iff_pos", "mv_power_series.mul_one", "polynomial.coeff_C_zero", "monotone.le_map_sup", "continuous_on_iff_is_closed", "ideal.add_mem_iff_left", "linear_map.infi_ker_proj", "metric.diam_nonneg", "quotient.map_mk", "rel_embedding.is_trans", "finset.singleton_bind", "half_sub", "list.rel_of_pairwise_cons", "measure_theory.simple_func.lintegral_congr", "int.gcd_mul_right", "turing.TM2.stmts_supports_stmt", "filter.mem_sup_sets", "add_subgroup.mem_sup_right", "finset.sum_sdiff", "norm_pos_iff", "ext_chart_preimage_inter_eq", "norm_num.nat_cast_bit1", "fin.le_def", "emetric.mem_nhds_iff", "nat.lt_trichotomy", "set.empty_ne_univ", "with_zero.mul_zero", "minimal_polynomial.one", "multiset.cons_coe", "ordinal.limit_rec_on_limit", "ordinal.card_le_nat", "filter.is_countably_generated_of_seq", "affine_subspace.vsub_mem_direction", "enat.to_with_top_top", "list.Ico.filter_le_of_top_le", "pgame.first_loses_of_equiv", "padic_norm_e.triangle_ineq", "category_theory.limits.types.coprod_inr", "fintype.prod_congr", "power_series.coeff_inv", "one_one_reducible_refl", "set.image2_mul", "measure_theory.measure_sUnion", "measure_theory.ae_eq_fun.edist_mk_mk", "computation.empty_orelse", "supr_congr_Prop", "finset.card_mk", "category_theory.nat_iso.app_hom", "measure_theory.simple_func.range_map", "traversable.mfoldr_to_list", "nat.le_succ", "onote.NF.fst", "seq.map_nth", "gpow_eq_mod_order_of", "primrec.and", "is_add_subgroup_Union_of_directed", "pell.eq_of_xn_modeq'", "complex.tan_of_real_re", "category_theory.limits.colimit.pre_pre", "set.mem_Ioo_or_eq_endpoints_of_mem_Icc", "is_local_min.comp_mono", "computation.thinkN_equiv", "seq.ext", "is_coprime.of_add_mul_left_left", "ideal.jacobson_mono", "times_cont_diff_at.of_le", "computation.results_bind", "padic_int.valuation_one", "multiset.Ico.mem", "left_ord_continuous.coe_to_order_embedding", "polynomial.zero_comp", "circle_deg1_lift.dist_pow_map_zero_mul_translation_number_le", "linear_independent.union", "set.mem_range", "direct_sum.apply_eq_component", "is_min_filter_dual_iff", "topological_fiber_bundle_core.is_open_map_proj", "Gromov_Hausdorff.Hausdorff_dist_optimal", "sum_range_diag_flip", "free_group.red.enum.sound", "ring_hom.eq_of_eq_on_stop", "measure_theory.extend_Union_nat", "computation.parallel_congr_right", "category_theory.preadditive.comp_neg_assoc", "gsmul_sub", "polynomial.coe_zero", "category_theory.limits.cone.category_to_category_struct_to_has_hom_hom", "finset.map_eq_empty", "power_series.trunc_zero", "polynomial.C_inj", "filter.antimono_seq_of_seq", "measurable.inv", "add_monoid_hom.map_add_eq_zero", "subalgebra.is_algebraic_iff", "ideal.ne_top_iff_one", "measure_theory.is_left_invariant_conj'", "interval_integral.integral_has_deriv_within_at_left", "alg_equiv.to_lie_equiv_symm_apply", "multiplicity.int.coe_nat_multiplicity", "circle_deg1_lift.map_map_zero_lt", "matrix.reindex_linear_equiv_apply", "list.append_sublist_append_left", "is_R_or_C.mul_conj", "frobenius_zero", "metric.Hausdorff_dist_self_closure", "matrix.induction_on'", "mvqpf.cofix.bisim\:2082", "pnat.dvd_gcd", "list.pairwise_gt_iota", "rel.inv_id", "multilinear_map.mk_pi_ring_apply", "multiset.card_map", "many_one_reducible.trans", "subsemiring.coe_to_submonoid", "pfunctor.M.ext_aux", "alg_hom.map_sum", "tsum_geometric_of_abs_lt_1", "computation.length_think", "multiset.nodup_iff_count_le_one", "list.erase_dup_cons_of_mem'", "continuous_within_at.preimage_mem_nhds_within'", "wseq.mem_cons_iff", "polynomial.map_X", "rel.preimage_def", "real.exp_lt_one_iff", "is_unit_of_invertible", "mul_equiv.to_CommMon_iso_inv", "local_homeomorph.prod_coe_symm", "complex.cpow_one", "rel.core_preimage_gc", "char_p.cast_eq_mod", "tendsto_at_top_csupr", "set.bex_image_iff", "cardinal.lift_add", "real.continuous_exp", "polynomial.roots_X_sub_C", "function.iterate_succ_apply'", "structure_groupoid.local_invariant_prop.lift_prop_on_chart", "is_separated_def'", "antilipschitz_with.to_right_inverse", "is_cyclic.image_range_card", "has_fderiv_at_filter.has_deriv_at_filter", "continuous_linear_map.coe_comp'", "local_homeomorph.subtype_restr_source", "onote.NF_repr_split'", "interval_integral.integral_has_strict_deriv_at_right", "computable.bind_decode_iff", "category_theory.limits.is_colimit.cocone_points_iso_of_equivalence_hom", "one_dvd", "list.pairwise_append", "tactic.abel.term_atom", "polynomial.expand_mul", "edist_eq_zero", "set.union_inter_cancel_left", "finset.disjoint_iff_ne", "category_theory.prod_comp", "isometric.symm_apply_eq", "composition.ones_blocks_fun", "nat.pow_le_iff_le_left", "relation.refl_trans_gen_eq_self", "nat.pow_lt_iff_lt_right", "differentiable.comp", "caratheodory.shrink", "multiset.pi_zero", "is_glb_Ici", "differentiable_on.const_add", "char_p.ring_char_ne_one", "option.map_eq_some", "add_monoid.closure_subset", "finsupp.single_of_emb_domain_single", "finmap.mem_lookup_union_middle", "category_theory.limits.is_colimit.hom_iso_hom", "measure_theory.simple_func.fin_meas_supp.map\:2082", "real.angle.cos_eq_iff_eq_or_eq_neg", "commute.neg_right_iff", "finsupp.sum_fintype", "finset.sum_filter_of_ne", "filter.eventually.prod_inl_nhds", "polynomial.expand_monomial", "complex.of_real_cos", "not_forall_not", "function.surjective.forall\:2082", "matrix.row_smul", "of_mul_to_mul", "list.modify_nth_tail_length", "char_poly_coeff_eq_prod_coeff_of_le", "filter.is_countably_generated.comap", "topological_space.seq_tendsto_iff", "is_min_filter.filter_mono", "list.subset.trans", "roption.get_mem", "measure_theory.simple_func.map_lintegral", "category_theory.limits.pullback_cone.equalizer_ext", "path_component.nonempty", "div_mul_cancel", "multiset.prod_map_sum", "norm_num.min_fac_helper_0", "add_monoid_hom.coe_mrange_restrict", "list.pw_filter_map", "continuous_linear_map.mem_ker", "real.arcsin_eq_pi_div_two_sub_arccos", "nat.partrec.code.evaln_prim", "list.ordered_insert_length", "mul_ne_zero", "equiv.swap_mul_self", "continuous_coinduced_rng", "add_subgroup.coe_neg", "nat.fpow_ne_zero_of_pos", "continuous_multilinear_map.map_coord_zero", "nat.mul_assoc", "continuous_on.preimage_interior_subset_interior_preimage", "mv_polynomial.coeff_eq_zero_of_total_degree_lt", "is_R_or_C.abs_im_div_abs_le_one", "finset.sup_subset", "category_theory.limits.prod.pentagon", "pnat.mul_coe", "category_theory.limits.coprod.right_unitor_hom", "nnreal.mul_eq_mul_left", "multiset.rel_eq", "finsupp.map_domain_comp", "add_group.mclosure_neg_subset", "list.subperm.antisymm", "primrec.nat_sub", "localization_map.mk'_mul_mk'_eq_one", "lie_algebra.special_linear.sl_bracket", "submonoid.localization_map.of_mul_equiv_of_localizations_id", "category_theory.functor.as_equivalence_inverse", "generalized_continued_fraction.denominators_recurrence", "mv_polynomial.rename_X", "cau_seq.lt_trans", "submodule.mapq_mkq", "free_group.of.inj", "subsemiring.mem_coe", "tendsto_of_monotone", "holor.mul_left_distrib", "quotient_group.lift_mk", "category_theory.limits.cocones.precompose_obj_\[Iota]", "gaussian_int.prime_of_nat_prime_of_mod_four_eq_three", "continuous_multilinear_map.le_op_norm", "monotone.supr_comp_eq", "bdd_above_Ioo", "generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some_aux_comp", "set.subset_compl_comm", "category_theory.iso.refl_symm", "rat.num_dvd", "has_mfderiv_at.has_mfderiv_within_at", "category_theory.prod_id_fst", "dioph.ext", "nat.min_fac_le", "hyperreal.st_id_real", "set.preimage_add_left_zero'", "norm_tsum_le_tsum_norm", "is_unit_iff_exists_inv", "function.inv_on_fixed_pts_comp", "submodule.span_singleton_eq_bot", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp_assoc", "category_theory.non_preadditive_abelian.epi_of_zero_cancel", "summable_nat_add_iff", "opposite.unop_eq_one_iff", "matrix.transpose_neg", "group.conjugates_of_set_subset'", "inner_product_geometry.inner_eq_zero_iff_angle_eq_pi_div_two", "Exists.imp", "has_deriv_at_filter.prod", "eq_inv_iff_eq_inv", "list.smul_sum", "continuous_multilinear_map.map_piecewise_add", "continuous_mul", "set.bUnion_inter", "eleven_dvd_iff", "ordinal.CNF_pairwise_aux", "local_equiv.bij_on_source", "semiconj_by.inv_right", "convex.prod", "subgroup.normal.mem_comm_iff", "monotone.mul_strict_mono'", "mul_action.injective_of_quotient_stabilizer", "pgame.lt_iff_sub_pos", "local_equiv.restr_trans", "with_top.zero_ne_top", "set.compl_neg", "multiset.le_sup", "is_least.lower_bounds_eq", "ring_hom.iterate_map_mul", "has_mfderiv_at.comp", "affine_map.continuous_iff", "measure_theory.measure_mono_null", "complex.arg_one", "real.rpow_nat_cast", "set.indicator_of_mem", "polynomial.continuous_eval", "category_theory.monoidal_category.unitors_equal.cells_4", "submonoid.map_comap_map", "commute.self_fpow", "denom_dvd_of_is_root", "ne_iff_lt_or_gt", "function.is_periodic_pt.mod", "nat.coprime.dvd_of_dvd_mul_right", "ordinal.add_mul_limit", "nat.coprime.coprime_dvd_left", "submodule.subtype_apply", "nat.gcd_assoc", "fin.coe_add", "equiv.forall\:2083_congr'", "primrec.of_equiv_symm", "sum.inl.inj_iff", "list.Ico.filter_le", "totally_bounded_of_forall_symm", "mem_nhds_induced", "matrix.reindex_transpose", "set.Iio_diff_Iic", "distrib_mul_action_hom.id_apply", "measurable_equiv.coe_eq", "emetric.Hausdorff_edist_closure", "matrix.update_column_apply", "nhds_eq_uniformity_prod", "list.take_length", "auto.not_exists_eq", "list.merge_sort_cons_cons", "nat.partrec.code.encode_lt_pair", "nat.prime.dvd_mul", "list.mem_cons_iff", "set.insert_subset_insert", "linarith.mul_eq", "set.left_inv_on.surj_on", "enat.get_one", "finmap.lookup_union_left", "linear_map.compr\:2082_apply", "equiv.mul_right_symm", "list.Ico.eq_empty_iff", "tactic.ring.horner_add_horner_eq", "continuous_within_at_Icc_iff_Ici", "list.argmax_cons", "neg_lt_sub_iff_lt_add'", "circle_deg1_lift.map_int_add", "tactic.ring.const_add_horner", "category_theory.limits.colimit.post_post", "computation.promises_congr", "polynomial.irreducible_X_sub_C", "caratheodory.shrink'", "tactic.interactive.generalize_a_aux", "add_monoid_hom.map_add", "zmod.int_cast_surjective", "real.has_deriv_at_rpow_zero_of_one_le", "polynomial.coeff_monomial_zero_mul", "equiv.sigma_congr_left_apply", "measurable_inr", "right_ord_continuous.mono", "list.forall_mem_nil", "nat.pow_add", "lie_algebra.of_associative_algebra_hom_id", "fin.init_update_last", "subgroup.ext", "multilinear_map.uncurry_curry_left", "finset.prod_eq_fold", "is_closed_bUnion", "add_semiconj_by.units_neg_symm_left", "forall_prop_of_false", "ennreal.none_eq_top", "nat.with_bot.coe_nonneg", "add_monoid_hom.eq_of_eq_on_mdense", "string.iterator.next_to_string_mk_iterator", "mul_right_surjective", "AddCommGroup.zero_apply", "irrational.of_one_div", "emetric.inf_edist_le_Hausdorff_edist_of_mem", "nat.prime.pred_pos", "alist.lookup_is_some", "int.sqrt_eq", "list.mmap_with_index'_aux_eq_mmap_with_index_aux", "category_theory.monoidal_functor.id_to_lax_monoidal_functor_\[CurlyEpsilon]", "deriv.lhopital_zero_right_on_Ico", "submodule.mem_map_equiv", "function.commute.iterate_pos_lt_of_map_lt'", "continuous_linear_map.homothety_norm", "ennreal.embedding_coe", "eventually_eventually_le_nhds", "multiset.sigma_add", "is_submonoid.coe_pow", "measure_theory.outer_measure.measure_inter_union", "continuous_within_at.congr_of_eventually_eq", "category_theory.limits.map_pair_left", "traversable.to_list_spec", "list.nth_modify_nth_ne", "filter.is_ultrafilter.eventually_not", "finsupp.map_domain_apply", "pell.is_pell_norm", "multiset.cons_ne_zero", "dfinsupp.sum_sum_index", "neg_le_self", "hyperreal.is_st_of_tendsto", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge", "computation.results_of_terminates'", "power_series.constant_coeff_comp_C", "cau_seq.lt_total", "metric.emetric_ball", "fish_pipe", "polynomial.coe_expand", "finset.filter_eq'", "filter.ne_bot.prod", "measure_theory.measure.finite_at_filter.filter_mono_ae", "measure_theory.ae_eq_fun.comp_eq_mk", "lie_algebra.orthogonal.S_as_blocks", "ideal.add_mem", "int.mul_mod_left", "convex_on_rpow", "nat.bitwise_comm", "mem_nhds_within_Iio_iff_exists_Ioo_subset'", "finset.image_union", "cardinal.sup_eq_zero", "commute.gpow_gpow", "tendsto_of_tendsto_of_tendsto_of_le_of_le", "lt_mul_iff_one_lt_left'", "continuous_multilinear_map.norm_restr", "category_theory.adjunction.hom_equiv_apply_eq", "category_theory.limits.kernel_not_iso_of_nonzero", "not_tendsto_at_top_of_tendsto_nhds", "nat.primrec'.comp'", "measure_theory.l1.simple_func.of_simple_func_eq_of_fun", "alg_hom.map_nat_cast", "wseq.append_nil", "category_theory.limits.limit.map_pre'", "finset.card_le_of_inj_on", "computation.head_ret", "ideal.is_jacobson_of_surjective", "enat.coe_get", "complex.exp_eq_exp_iff_exp_sub_eq_one", "exists_comm", "asymptotics.is_o_prod_left", "mvqpf.cofix.abs_repr", "is_seq_closed_of_is_closed", "module.direct_limit.to_module_totalize_of_le", "set.exists_min_image", "has_fderiv_within_at.fderiv_within", "real.young_inequality", "dioph.pow_dioph", "mul_equiv.map_eq_one_iff", "multiset.rel_flip_eq", "subgroup.normal_closure_eq_infi", "has_strict_fderiv_at.congr_of_eventually_eq", "cInf_le_of_le", "ideal.is_maximal.eq_of_le", "Gromov_Hausdorff.GH_dist_le_of_approx_subsets", "opposite.unop_neg", "nat.div_eq_of_eq_mul_right", "charted_space_self_atlas", "ordinal.one_eq_lift_type_unit", "circle_deg1_lift.dist_map_zero_translation_number_le", "int.le_antisymm", "set.union_diff_self", "ennreal.inv_le_inv", "category_theory.limits.wide_pushout_shape.wide_span_map", "set.subset_eq_empty", "function.surjective.supr_comp", "pos_num.nat_size_to_nat", "Ioc_mem_nhds_within_Ici", "measure_theory.simple_func.support_eq", "equiv.point_reflection_fixed_iff_of_bit0_injective", "bilin_form.to_matrix_comp_right", "has_sum.map", "fderiv_within_mul", "turing.TM1.stmts_trans", "int.eq_one_of_mul_eq_self_left", "mv_power_series.constant_coeff_inv_of_unit", "int.sign_eq_one_iff_pos", "hash_map.append_of_modify", "derivation.map_one_eq_zero", "supr_congr", "prod.fst_vsub", "linear_map.trace_mul_comm", "add_units.coe_lift_right", "Class.iota_ex", "finsupp.single_eq_same", "list.kextract_eq_lookup_kerase", "nat.prime.sum_two_squares", "int.gcd_zero_right", "primrec.option_some_iff", "nat.min_fac_eq", "iff_self", "rec_heq_of_heq", "real.continuous_rpow_aux3", "list.rel_nodup", "cau_seq.le_antisymm", "mv_polynomial.coeff_zero_X", "polynomial.map_comp", "category_theory.preimage_comp", "category_theory.whiskering_left_obj_map", "is_null_measurable.diff_null", "category_theory.eq_to_iso_map", "ulower.up_down", "has_fderiv_at_filter.add_const", "algebra.tensor_product.mul_aux_apply", "measure_theory.lintegral_edist_triangle", "primrec.list_find_index", "zmod.cast_mul", "filter.subtype_coe_map_comap", "nnreal.rpow_lt_one_of_one_lt_of_neg", "qpf.Wequiv.refl", "gsmul_zero", "ideal.bot_is_maximal", "eq_add_of_add_neg_eq", "subsemiring.coe_supr_of_directed", "norm_num.mul_bit1_bit1", "ring_hom.map_list_sum", "times_cont_diff_at.continuous_at", "int.div_le_self", "classical.dec_pred", "is_local_max_on.sub", "findim_bot", "fderiv_snd", "category_theory.limits.binary_bicone.to_cone_\[Pi]_app_left", "cardinal.bit0_lt_bit1", "filter.principal_mono", "measure_theory.l1.coe_zero", "pfunctor.M.ext'", "fderiv_within_deriv_within", "primrec.nat_le", "asymptotics.is_O_with.const_mul_right'", "nat.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul", "real.sinh_injective", "div_lt_iff", "add_smul", "pmf.pure_apply", "circle_deg1_lift.translate_apply", "interval_integral.integral_Iic_sub_Iic", "set.monotone_preimage", "pgame.neg_congr", "fintype.prod_bool", "list.chain'_pair", "filter.germ.coe_smul'", "padic_norm_e.norm_int_lt_pow_iff_dvd", "pnat.pow_coe", "mv_polynomial.coe_eval\:2082_hom", "equiv.perm.is_cycle_swap", "zero_mul", "nnreal.tendsto_const_div_at_top_nhds_0_nat", "times_cont_mdiff_at.of_le", "continuous_linear_map.extend_unique", "continuous_iff_coinduced_le", "heq_of_eq_of_heq", "has_deriv_within_at.liminf_right_norm_slope_le", "circle_deg1_lift.translation_number_lt_of_forall_lt_add", "set.union_compl_self", "times_cont_mdiff_on_univ", "list.sublists'_cons", "frontier_compl", "le_min_iff", "multiset.card_sub", "free_abelian_group.zero_bind", "lt_div_iff_of_neg", "midpoint_add_right", "has_fderiv_within_at.lim", "set.Ico_union_Ico_eq_Ico", "bilin_form.comp_right_apply", "is_measurable_Icc", "omega.int.is_nnf_nnf", "free_semigroup.pure_bind", "add_eq_zero_iff_eq_neg", "category_theory.limits.colimit.cocone_morphism_hom", "nat.bit_decomp", "iff_subst", "is_add_group_hom.trivial_ker_of_injective", "nat.add_sub_cancel_left", "category_theory.sum.swap_map_inl", "equiv.perm.sign_prod_list_swap", "vsub_set_mono", "interval_integral.integral_same", "isometric.neg_to_equiv", "set.subset_union_of_subset_left", "add_monoid_hom.map_mrange", "lfp_induct", "cardinal.lift_omega", "category_theory.congr_app", "dist_sub_right", "ordinal.power_succ", "not_and_distrib", "iterated_deriv_one", "qpf.cofix.bisim_rel", "continuous_swap", "open_mapping", "add_subgroup.mem_infi", "finset.tsum_subtype", "Module.Mon_Module_equivalence_Algebra.ring_mul", "category_theory.over.iterated_slice_equiv_unit_iso", "bilin_form.to_quadratic_form_apply", "metric.bounded_of_compact_space", "pfun.coe_val", "set.preimage_sub_const_Iio", "set.ord_connected_dual", "set.not_mem_of_mem_diff", "polynomial.sum_C_index", "real.cosh_pos", "filter.nonempty_of_ne_bot", "bool.eq_tt_of_ne_ff", "Module.coe_of", "finset.sdiff_self", "measurable_neg_iff", "padic_int.is_unit_iff", "zero_lt_two", "polynomial.leading_coeff_eq_zero", "lt_of_sub_pos", "set.Union_range_eq_sUnion", "category_theory.equivalence.trans_counit_iso", "filter.mem_lift_sets", "submodule.exists_finset_of_mem_supr", "ordinal.nat_le_card", "category_theory.limits.binary_cofan.is_colimit.desc'_val", "not_ball", "affine.triangle.orthocenter_eq_monge_point", "metric.closed_ball_subset_closed_ball", "wseq.destruct_map", "tactic.abel.unfold_gsmul", "category_theory.iso.conj_id", "rel_iso.ext", "finsupp.erase_add_single", "is_basis.equiv_fun_self", "continuous_linear_map.sub_apply", "pos_num.cast_bit0", "nat.partrec'.to_part", "category_theory.comma.map_left_map_left", "polynomial.coeff_one", "norm_unit_mul_norm_unit", "or.left_comm", "set.prod_subset_iff", "is_glb_of_mem_nhds", "add_magma.free_add_semigroup.of_add_assoc_right", "differentiable_on_const", "homological_complex.homology_map_condition", "embedding_inr", "category_theory.currying_inverse_obj_obj_obj", "int.modeq.coe_nat_modeq_iff", "algebraic_geometry.structure_sheaf_stalk_to_fiber_surjective", "linear_map.smul_apply", "set.card_lt_card", "category_theory.nat_trans.sum_app_inl", "is_closed.Sup_mem", "list.id_traverse", "add_le_of_nonpos_of_le", "nat.zero_ne_bit1", "pell.xn_modeq_x2n_sub_lem", "real.arith_mean_le_rpow_mean", "multiset.cons_ndunion", "mvqpf.supp_preservation_iff_uniform", "Gromov_Hausdorff.isometry_optimal_GH_injr", "cau_seq.completion.zero_ne_one", "linear_independent_empty", "multiset.coe_product", "list.sorted.tail", "std_simplex_subset_closed_ball", "asymptotics.is_O_with.right_le_sub_of_lt_1", "mem_nhds_uniformity_iff_right", "finset.map_embedding_apply", "set.countable_Union", "ideal.span_eq_bot", "filter.is_basis.has_basis", "coinduced_compose", "is_lub_bsupr", "subtype.ext_iff_val", "padic.valuation_p", "submodule.linear_proj_of_is_compl_apply_right", "has_deriv_at.sub", "finset.bUnion_insert", "add_subgroup.neg_mem_iff", "finmap.mem_lookup_union", "stream.mem_const", "denumerable.decode_is_some", "category_theory.arrow.lift_mk'_right", "set.comp_indicator", "ne.irrefl", "smooth.times_cont_mdiff", "power_series.order_add_of_order_eq", "real.dist_0_eq_abs", "int.nat_abs_ne_zero_of_ne_zero", "computation.of_think_mem", "has_fderiv_within_at.congr_of_eventually_eq", "is_noetherian_ring_of_surjective", "sesq_form.zero_left", "is_lub_supr", "nnreal.rpow_lt_one", "tensor_product.uncurry_apply", "category_theory.op_comp", "affine_subspace.coe_direction_eq_vsub_set_left", "is_connected.nonempty", "add_commute.units_neg_left_iff", "mv_polynomial.coe_X", "squeeze_zero_norm'", "asymptotics.is_o_neg_right", "inv_of_mul", "free_magma.map_pure", "classical.strong_indefinite_description", "filter.lift'_lift'_assoc", "nat.bit_le_bit_iff", "linear_equiv.bijective", "nat.lt_succ_of_lt", "deriv_within_exp", "category_theory.biprod.unipotent_upper_hom", "lipschitz_with.pow", "roption.mem_unique", "add_equiv.trans_apply", "category_theory.iso_whisker_left_hom", "nat.even_sub", "int.add_assoc_aux1", "times_cont_mdiff_at_iff_times_cont_mdiff_on_nhds", "set.eq_of_mem_singleton", "is_closed.is_measurable", "differentiable.const_sub", "cardinal.eq", "linear_map.fun_congr_left_symm", "nnreal.one_lt_rpow_of_pos_of_lt_one_of_neg", "finset.image_singleton", "ennreal.bit1_inj", "summable_iff_vanishing_norm", "interval_integral.deriv_integral_of_tendsto_ae_left", "list.rotate_eq_self_iff_eq_repeat", "multiplicative.normal_subgroup", "polynomial.smul_X", "is_open_map_mul_left", "ring_equiv.to_ring_hom_trans", "mfderiv_within_comp", "polynomial.roots_one", "category_theory.equiv_of_fully_faithful_apply", "category_theory.under.hom_mk_right", "int.lt_of_sub_neg", "ite_eq_iff", "cardinal.prod_eq_zero", "abstract_completion.continuous_map", "equiv.summable_iff_of_has_sum_iff", "image_norm_le_of_norm_deriv_right_le_deriv_boundary'", "floor_zero", "filter.map_lift_eq", "nat.xgcd_aux_P", "set.preimage_add_const_Icc", "real.arcsin_neg", "measure_theory.measure.finite_at_filter.integrable_at_filter", "category_theory.limits.cone.of_pullback_cone_X", "pgame.impartial.no_good_left_moves_iff_first_loses", "submodule.map_le_iff_le_comap", "int.nat_abs_eq_zero", "finset.range_coe", "set.add_mem_add", "euclidean_domain.gcd_mul_lcm", "onote.NF_below.snd", "finsupp.filter_smul", "euclidean_domain.dvd_lcm_left", "subrel.rel_embedding_apply", "filter.germ.coe_tendsto", "traversable.free.map_eq_map", "nnreal.coe_nat_cast", "abs_neg", "category_theory.monoidal_category.right_unitor_product_aux_triangle", "tsum_sum", "multiset.prod_eq_foldr", "equiv.swap_apply_of_ne_of_ne", "subsemiring.pow_mem", "gcd_eq_right_iff", "int.sign_mul_abs", "algebra.fg_trans", "list.mem_of_mem_erasep", "filter.Liminf_top", "nat.mul_lt_mul_of_pos_left", "enat.add_top", "measurable_space.dynkin_system.has_Union", "emetric.nonempty_of_Hausdorff_edist_ne_top", "category_theory.prod.inverse_associator_obj", "ennreal.tendsto_pow_at_top_nhds_0_of_lt_1", "add_le_add_three", "cardinal.lt_omega_iff_finite", "set.set_of_eq_eq_singleton", "convex_hull_basis_eq_std_simplex", "one_one_equiv.symm", "segment_translate_image", "real.cos_zero", "has_ftaylor_series_up_to.of_le", "omega.nat.is_nnf_push_neg", "finsupp.is_basis_single_one", "nat.primrec'.const", "multiset.mem_powerset", "dfinsupp.lsingle_apply", "digits_lt_base", "category_theory.equivalence.inv_fun_id_assoc_inv_app", "coe_homeomorph_of_strict_mono_surjective", "min_le_right", "pi_Lp.dist", "continuous_mul_right", "formal_multilinear_series.geometric_bound_of_lt_radius", "multiset.Ico.eq_zero_of_le", "int.mem_to_nat'", "has_fderiv_at.const_smul", "multiset.prod_smul", "is_bounded_bilinear_map.is_bounded_linear_map_left", "antilipschitz_with_iff_le_mul_dist", "localization_map.eq_of_eq", "fderiv.fst", "differentiable.differentiable_at", "finsupp.prod_add_index", "filter.tendsto_iff_rtendsto", "metric.mem_ball_self", "category_theory.yoneda_obj_obj", "ideal.comap_Inf'", "onote.repr_power_aux\:2081", "measure_theory.lebesgue_outer_Ioo", "wseq.map_id", "filter.prod_map_at_top_eq", "real.continuous_sqrt", "measure_theory.norm_set_integral_le_of_norm_le_const_ae", "ennreal.coe_eq_coe", "nat.land_bit", "list.sum_eq_foldr", "ennreal.rpow_le_rpow_of_exponent_le", "div_lt_div_right_of_neg", "padic_norm_e.mul", "function.hfunext", "rat.inv_def'", "mul_eq_of_eq_mul_inv", "has_fpower_series_at.comp", "set.nonempty.image", "finite_dimensional.iff_fg", "algebra.tensor_product.mul_one", "punit.not_lt", "mul_right_cancel_iff", "ennreal.top_to_nnreal", "linear_map.coe_fn_sum", "with_top.top_mul_top", "finset.center_mass_segment'", "subring.coe_to_add_subgroup", "symm_of", "category_theory.nat_iso.naturality_1", "primrec.option_cases", "state_t.ext", "differentiable_at.csinh", "omega.int.exists_clause_holds", "measure_theory.l1.simple_func.norm_integral_le_norm", "zsqrtd.neg_im", "filter.germ.map_map", "topological_fiber_bundle_core.local_triv_at_fst", "primrec\:2082.mkpair", "is_max_on.comp_antimono", "measure_theory.simple_func.lintegral_eq_of_subset", "complex.exp_of_real_im", "nat.pow_log_le_self", "int.mul_le_mul", "list.nth_le_reverse_aux2", "dense_inducing.extend_eq_of_tendsto", "subgroup.closure_union", "associated_one_of_associated_mul_one", "tt_bor", "equiv.perm.ext", "measure_theory.simple_func.fin_meas_supp.meas_preimage_singleton_ne_zero", "ordinal.succ_lt_of_is_limit", "inv_mul_le_iff_le_mul", "composition.length_pos_of_pos", "category_theory.functor.cones_obj", "tactic.ring_exp.pow_pp_pf_c", "polynomial.degree_X_le", "padic_int.maximal_ideal_eq_span_p", "pell.eq_pow_of_pell_lem", "matrix.one_apply_ne'", "homological_complex.homology_map_condition_assoc", "inf_le_inf_left", "ennreal.measurable_of_measurable_nnreal", "list.zip_map_left", "is_add_hom.comp", "filter.germ.coe_inv", "finset.sum_mono_set_of_nonneg", "fintype.exists_equiv_fin", "normed_field.exists_norm_lt_one", "encodable.encode_nat", "complex.add_conj", "is_min_on_univ_iff", "nat.pow_le_iff_le_log", "finset.card_ne_zero_of_mem", "nat.mod_zero", "nat.one_add", "filter.tendsto.mono_left", "many_one_degree.le_add_left'", "times_cont_diff_within_at_fst", "dvd_mul_of_dvd_left", "homeomorph.is_open_map", "multiset.filter_le", "is_antisymm.swap", "multiset.zero_inter", "equiv.perm.fixed_point_card_lt_of_ne_one", "category_theory.limits.limit.map_pre", "function.embedding.coe_fn_mk", "omega.nat.sat_sub_elim", "ennreal.div_top", "contracting_with.efixed_point_is_fixed_pt'", "primrec\:2082.unpaired'", "submodule.fg_pow", "closure_prod_eq", "pow_one", "disjoint_bot_left", "sum.map_map", "lucas_lehmer.X.neg_fst", "set.image2_inter_subset_right", "set.Iic_subset_Iic_union_Ioc", "subalgebra.gsmul_mem", "sub_add_sub_cancel", "is_coprime.of_mul_add_left_right", "category_theory.limits.biprod.map_eq", "multiset.nodup_add", "measure_theory.measure.bind_dirac", "filter.tendsto_map'", "continuous_linear_map.zero_comp", "tactic.ring.horner_def'", "nat.exists_coprime", "add_monoid_algebra.mul_zero", "interval_integral.integral_interval_sub_interval_comm'", "category_theory.equivalence.refl_unit_iso", "coe_fn_coe_base", "filter.tendsto.is_cobounded_under_le", "is_closed.mem_of_ge_of_forall_exists_gt", "mv_polynomial.map_restrict_dom_eval\:2097", "add_submonoid.localization_map.lift_surjective_iff", "category_theory.limits.prod.lift_map_assoc", "ennreal.one_le_rpow", "category_theory.limits.cones.functoriality_obj_\[Pi]_app", "adic_completion.ext", "affine.simplex.sum_monge_point_vsub_face_centroid_weights_with_circumcenter", "prime_multiset.card_of_prime", "algebra.tensor_product.include_right_apply", "localization_map.exists_integer_multiple'", "ordinal.mul_le_mul_right", "finite_field.card_units", "omega.coeffs.val_between_eq_val_between", "is_bounded_bilinear_map.has_fderiv_within_at", "polynomial.eisenstein_criterion_aux.map_eq_C_mul_X_pow_of_forall_coeff_mem", "equiv.perm.same_cycle_cycle", "closure_eq_uniformity", "mem_nhds_within_Iic_iff_exists_Ioc_subset'", "iter_deriv_pow'", "nat.dvd_iff_mod_eq_zero", "free_add_magma.add_eq", "cardinal.add_eq_right", "measure_theory.measure.haar.chaar_empty", "isometric.neg_symm", "isometric.coe_add_left", "submonoid.comap_top", "ne_of_lt", "add_submonoid.mem_Sup_of_mem", "differentiable.continuous", "int.le_add_of_neg_add_le_left", "decidable.not_and_distrib'", "exists_exists_eq_and", "list.forall\:2082_iff_zip", "pnat.coprime.factor_eq_gcd_left_right", "measure_theory.integral_undef", "measurable_mul_right", "power_series.coeff_mul", "subgroup.mem_supr_of_mem", "supr_and", "ordinal.cof_ord_le", "linear_map.update_apply", "algebra.map_bot", "hyperreal.infinite_neg_add_infinite_neg", "set.preimage_eq_preimage'", "int.test_bit_bitwise", "nat.div_le_self", "is_local_max.has_fderiv_at_eq_zero", "measure_theory.simple_func.approx_apply", "function.mk_mem_periodic_pts", "ordinal.rel_iso_enum", "integral_closure.is_integral", "finset.sum_sigma", "pnat.mod_div_aux_spec", "subsemiring.mk'_to_add_submonoid", "nat.pos_pow_of_pos", "finset.disjoint_self_iff_empty", "fin.prod_univ_eq_prod_range", "mul_equiv.map_one", "finset.inter_empty", "submonoid.localization_map.mk'_one", "mv_polynomial.coeff_C", "real.div_rpow", "fderiv_within_const_smul", "continuous_linear_map.restrict_scalars_coe_eq_coe'", "subsemiring.coe_inf", "set.finite.insert", "measure_theory.outer_measure.le_of_content_compacts", "to_bool_ff_iff", "ennreal.of_real_mul", "monoid_hom.inl_apply", "nat.exists_eq_succ_of_ne_zero", "right_coset_mem_right_coset", "list.nodup_of_nodup_append_right", "convex_hull_to_cone_eq_Inf", "dvd_of_neg_dvd", "local_equiv.map_target", "caratheodory.step", "char.of_nat_ne_of_ne", "int.lt_iff_le_not_le", "submodule.one_eq_span", "galois_coinsertion.u_infi_of_lu_eq_self", "lcm_dvd_lcm_mul_right", "set.range_iff_surjective", "int.neg_succ_of_nat_coe", "add_submonoid.prod_top", "sigma.forall", "multiset.coe_ndinter", "category_theory.non_preadditive_abelian.add_zero", "roption.map_eq_map", "list.exists_mem_cons_of", "nnreal.rpow_nat_cast", "padic_int.to_zmod_spec", "linear_independent_iff''", "rat.cast_nonneg", "asymptotics.is_O.prod_rightl", "local_equiv.trans_target", "Module.of_self_iso_inv", "norm_num.not_prime_helper", "strict_mono.const_mul'", "semidirect_product.map_comp_inl", "real.log_nonneg", "lt_mul_of_lt_of_one_le", "matrix.det_mul_aux", "category_theory.eq_of_inv_eq_inv", "ordinal.zero_le", "continuous_inl", "category_theory.abelian.kernel_cokernel_eq_image_\[Iota]", "multiset.card_eq_card_of_rel", "nat.min_fac_prime", "submodule.coe_mem", "polynomial.degree_pos_of_ne_zero_of_nonunit", "multiset.pi.cons_swap", "multiset.cons_ndinter_of_mem", "finset.coe_nonempty", "set.insert_prod", "equiv.conj_refl", "linear_map.quotient_inf_equiv_sup_quotient_symm_apply_right", "int.modeq.modeq_of_dvd_of_modeq", "int.not_even_iff", "with_top.unop_sum", "function.semiconj_of_is_lub", "lt_add_of_neg_lt_sub_right", "linear_map.mem_range_self", "free_semigroup_free_magma_mul", "polynomial.coeff_derivative", "differentiable_at.sin", "list.reverse_injective", "ennreal.sub_mul", "affine_span_singleton_union_vadd_eq_top_of_span_eq_top", "padic_int.zmod_congr_of_sub_mem_span_aux", "equiv.tsum_eq", "fderiv_within_smul_const", "polynomial.deriv", "padic_norm_e.eq_of_norm_add_lt_left", "list.take'_left'", "has_ftaylor_series_up_to_on.continuous_linear_map_comp", "denumerable.list_of_nat_succ", "complex.cosh_add", "nnreal.sub_pos", "category_theory.non_preadditive_abelian.epi_of_zero_cokernel", "list.concat_ne_nil", "mv_polynomial.eval\:2082_eta", "nat.partrec'.part_iff", "continuous_on.prod", "state_t.run_put", "set.preimage_univ", "int.pos_of_sign_eq_one", "nat.le_of_lt_succ", "joined_in.some_path_mem", "mul_action_hom.map_smul", "add_lt_iff_neg_right", "pure_le_nhds", "subring.exists_list_of_mem_closure", "nat.sub_le_right_iff_le_add", "measure_theory.simple_func.coe_range", "subspace.coe_continuous_linear_proj_of_closed_compl'", "zmod.val_eq_ite_val_min_abs", "equiv.perm.same_cycle.refl", "list.tail_repeat", "or_iff_not_imp_right", "set.indicator_nonneg'", "ideal.mul_le", "is_glb_Icc", "minimal_polynomial.prime", "ennreal.coe_nat_le_coe_nat", "category_theory.arrow.hom_mk'_left", "omega.int.nnf_equiv", "free_group.prod.one", "set.Ioi_def", "eq_true", "associates.one_or_eq_of_le_of_prime", "fin.coe_nat_eq_last", "euclidean_domain.gcd_dvd", "measure_theory.l1.coe_neg", "supr_supr_eq_left", "computation.corec_eq", "bool.of_nat_le_of_nat", "finset.sum_le_sum_of_ne_zero", "set.surj_on.right_inv_on_inv_fun_on", "category_theory.limits.span_zero", "has_mfderiv_within_at.has_mfderiv_at", "interval_integral.measure_integral_sub_integral_sub_linear_is_o_of_tendsto_ae", "ennreal.sub_le_self", "category_theory.equivalence.symm_functor", "set_coe.forall", "lie_equiv_matrix'_apply", "cau_seq.mul_equiv_zero", "model_with_corners.left_inv", "pgame.omega_left_wins", "fg_adjoin_singleton_of_integral", "is_local_max_const", "pnat.coe_to_pnat'", "function.surjective_id", "mul_le_mul_right_of_neg", "subsemiring.prod_mono_left", "units.dvd_mul_right", "list.prefix_append", "zmod.int_coe_eq_int_coe_iff", "is_totally_disconnected_of_is_totally_separated", "ennreal.to_real_top_mul", "mul_neg_of_pos_of_neg", "unique_mdiff_on.tangent_bundle_proj_preimage", "classical.eq_false_or_eq_true", "pSet.mk_type_func", "computable.vector_head", "computation.terminates_def", "commute.self_cast_nat_mul_cast_nat_mul", "pequiv.mul_matrix_apply", "array.push_back_to_list", "nnreal.mul_div_assoc'", "hyperreal.st_infinite", "mul_equiv.to_Mon_iso_hom", "open_embedding_of_continuous_injective_open", "commute.units_inv_right", "category_theory.limits.kernel_comp_is_iso_hom", "real.tan_arctan", "alg_equiv.coe_ring_equiv_injective", "ideal.add_eq_sup", "add_monoid_hom.map_matrix_apply", "set.prod_sub_preimage_iff", "submodule.quotient.mk_neg", "category_theory.under.iso_mk_hom_right", "set.finite.is_closed_convex_hull", "cardinal.le_zero", "iff_true_left", "filter.map_lift'_eq", "linear_map.mul_app", "pnat.div_coe", "valuation.map_sub_swap", "irreducible_iff_nat_prime", "abstract_completion.map_coe", "has_strict_fderiv_at.fst", "filter.strict_mono_tendsto_at_top", "polynomial.C_mul", "ennreal.nhds_coe", "pgame.le_trans", "finset.sum_neg_distrib", "mv_polynomial.degrees_zero", "ordinal.type_subrel_lt", "is_open_iff_forall_mem_open", "primrec.eq", "real.sin_sq_le_one", "polynomial.coeff_mul_X", "add_left_surjective", "category_theory.functor.equiv_counit_iso", "filter.tendsto_at_bot_mono", "tensor_product.tmul_ite", "is_greatest.is_lub", "units.nhds", "category_theory.non_preadditive_abelian.add_def", "Top.presheaf.pushforward.comp_hom_app", "fract_mul_nat", "finset.union_right_comm", "lt_sub_right_of_add_lt", "euclidean_geometry.dist_square_smul_orthogonal_vadd_smul_orthogonal_vadd", "has_deriv_at_neg'", "fderiv_within_add_const", "pequiv.single_trans_single", "category_theory.iso.to_linear_equiv_inv_fun", "int.dvd_lcm_left", "nat.modeq.modeq_iff_dvd", "int.neg_pred", "map_cSup_of_continuous_at_of_monotone", "category_theory.pre_post_comm", "complex.abs_le_abs_re_add_abs_im", "asymptotics.is_O.triangle", "dist_pi_le_iff", "category_theory.limits.image.\[Iota]_zero", "equiv.perm.same_cycle_of_is_cycle", "rel.preimage_mono", "inner_smul_self_right", "differentiable_at.const_add", "finsupp.support_emb_domain", "polynomial.nat_degree_coe_units", "deriv_mul_const", "has_deriv_at_const", "euclidean_domain.gcd_dvd_left", "is_R_or_C.smul_im'", "finsupp.add_eq_zero_iff", "cardinal.zero_powerlt", "nhds_within_union", "set.bInter_subset_bInter_right", "vadd_right_cancel", "category_theory.monoidal_category.unitors_equal.cells_9", "submonoid.coe_top", "fpow_coe_nat", "add_submonoid.sum_mem", "euclidean_geometry.reflection_eq_iff_orthogonal_projection_eq", "continuous_at.mul", "cau_seq.cauchy\:2083", "polynomial.nat_degree_map'", "list.diff_subset", "multiset.foldl_swap", "has_deriv_at.lhopital_zero_nhds_right", "measure_theory.outer_measure.of_content_exists_open", "real.rpow_zero", "metric.diam_mono", "free_abelian_group.lift.neg", "subring.ext", "is_lub_Ico", "edist_dist", "model_with_corners.unique_diff_at_image", "category_theory.graded_object.comap_equiv_inverse", "set.subset.refl", "add_subgroup.le_def", "nat.pow_pos", "finmap.keys_empty", "category_theory.limits.prod_functor_obj_obj", "continuous_linear_map.restrict_scalars_coe_eq_coe", "direct_sum.of_injective", "category_theory.abelian.pseudo_equal_symm", "category_theory.limits.limit_iso_limit_curry_comp_lim_inv_\[Pi]", "list.append_sublist_append_right", "bounded_continuous_function.lipschitz_comp", "category_theory.limits.biproduct.lift_desc_assoc", "cauchy.le_nhds_Lim", "valuation.map_mul", "list.perm.eqv", "ordinal.lift_type_lt", "filter.eventually_iff", "is_scalar_tower.range_under_adjoin", "linear_recurrence.eq_mk_of_is_sol_of_eq_init'", "le_inv'", "padic_int.eq_zero_or_eq_zero_of_mul_eq_zero", "multiset.foldl_zero", "nat.primrec'.vec_iff", "set.to_finset_insert", "heq_of_eq_rec_right", "hyperreal.coe_abs", "norm_num.adc_bit0_bit1", "ring_hom.map_units_inv", "opposite.op_one", "complex.two_sinh", "set.image_const_sub_Ioi", "rel_sup_add", "interval_integral.deriv_within_integral_left", "nat.cast_pos", "measure_theory.induced_outer_measure_preimage", "one_one_reducible.of_equiv_symm", "pfun.mem_res", "sequentially_complete.seq_pair_mem", "iterated_fderiv_succ_eq_comp_left", "Sup_le_iff", "eq_zero_of_mul_eq_self_left", "abstract_completion.extend_map", "hyperreal.infinite_pos_add_not_infinite", "finset.forall_mem_insert", "free_group.to_word.mk", "continuous_coinduced_dom", "submonoid.map_inf_comap_of_surjective", "compl_supr", "topological_space.opens.map_id_obj_unop", "Set.mem_pair", "erased.join_eq_out", "free_add_monoid.lift_comp_of", "eq_sub_of_add_eq'", "nat.sqrt_lt", "multilinear_map.uncurry_curry_right", "interior_Iic", "continuous_linear_map.coe_zero", "galois_coinsertion.u_infi_l", "nat.rfind_dom", "omega.pred_mono_2'", "computation.of_results_think", "generalized_continued_fraction.zero_le_of_continuants_aux_b", "is_open_map.image_mem_nhds", "multiset.choose_mem", "category_theory.functor.map_arrow_map_left", "int.gcd_dvd_gcd_mul_right", "finset.eq_singleton_iff_unique_mem", "primrec_rel.of_eq", "list.map_sub_range'", "ennreal.div_self", "is_linear_map.convex_hull_image", "nat.bit1_ne_zero", "lt_cSup_of_lt", "gaussian_int.to_real_re", "traversable.foldl_to_list", "functor.of_mem_supp", "set.diff_subset_diff_right", "filter.eventually_eq.has_fderiv_at_filter_iff", "fin.val_add", "enat.to_with_top_top'", "add_aut.inv_apply_self", "zsqrtd.mul_nonneg", "list.chain'_nil", "prod.swap_prod_mk", "equiv.pempty_sum_apply_inr", "rat.abs_def", "measure_theory.integral_smul", "surj_on_Ico_of_monotone_surjective", "finsupp.prod_pow", "set.Ico_subset_Icc_union_Ico", "compl_inj_iff", "list.Ico.mem", "deriv_within_add", "set.mem_image_of_mem", "continuous_linear_equiv.prod_apply", "finset.sum_eq_zero", "filter.map_lift'_eq2", "normed_field.exists_norm_lt", "primrec.nat_add", "continuous_linear_equiv.map_zero", "list.nodup_of_sublist", "lipschitz_with.to_right_inverse", "times_cont_diff_on_top", "finset.sum_update_of_not_mem", "gcd_monoid.prime_of_irreducible", "pos_num.pred'_to_nat", "multiset.mem_map", "normalize_apply", "int.modeq.modeq_mul_right'", "mvfunctor.id_map", "finset.pi_disjoint_of_disjoint", "lt_add_of_pos_right", "nat.gcd_dvd_gcd_mul_left_right", "list.infix_append'", "turing.tape.write_self", "lucas_lehmer.s_mod_succ", "wseq.head_terminates_of_head_tail_terminates", "pure_id'_seq", "multiset.eq_zero_of_subset_zero", "filter.is_countably_generated_at_bot", "locally_finite_subset", "continuous_linear_map.add_apply", "ennreal.one_sub_inv_two", "wseq.seq_destruct_nil", "frontier_Ioc", "lt_of_nat_ceil_lt", "deriv_neg''", "category_theory.monoidal_functor.id_\[CurlyEpsilon]_is_iso", "or_assoc", "matrix.cons_val_one", "add_comm_group.direct_limit.of_zero", "partrec\:2082.comp\:2082", "inv_le'", "measure_theory.supr_lintegral_le", "finset.card_powerset_len", "polynomial.coeff_contract", "wseq.think_append", "convex_Ioi", "list.sublist_of_prefix", "linear_equiv.to_fun_apply", "ennreal.mul_pos", "algebraic_closure.le_max_ideal", "list.drop_length", "finset.sdiff_union_self_eq_union", "submodule.mul_mem_mul_rev", "has_le.le.trans_eq", "bool.band_assoc", "euclidean_geometry.dist_square_eq_dist_orthogonal_projection_square_add_dist_orthogonal_projection_square", "monoid_algebra.lift_of", "metric.dist_mem_uniformity", "set.bij_on.comp", "ennreal.not_lt_top", "linear_equiv.of_injective_endo_left_inv", "finset.inter_subset_left", "finset.measurable_prod", "list.func.get_set", "equiv.to_pequiv_refl", "nat.pow_le_iff_le_right", "tendsto_at_top_supr_nat", "finsupp.infi_ker_lapply_le_bot", "category_theory.prod.symmetry_inv_app", "set.add_comm", "fin.succ_injective", "has_sum_of_bounded_monoid_hom_of_has_sum", "submodule.supr_eq_span", "is_group_hom.inv_ker_one", "local_homeomorph.eventually_left_inverse", "filter.unbounded_of_tendsto_at_top'", "trunc.eq", "finset.le_iff_subset", "list.append_inj_left", "direct_sum.to_group_sub", "structure_groupoid.local_invariant_prop.lift_prop_within_at_inter'", "nhds_within_restrict''", "list.length_init", "finset.prod_inv_distrib", "polynomial.derivative_neg", "deriv_fpow", "nonneg_add_comm_group.nonneg_def", "commute.units_of_coe", "nat.add_mod_mod", "deriv_sum", "le_Inf_inter", "forall_ge_le_of_forall_le_succ", "num.cast_mul", "galois_connection.monotone_l", "times_cont_diff_top_iff_fderiv", "list.foldr_with_index_aux_spec_cons", "Vieta_formula_quadratic", "measure_theory.l1.coe_add", "finset.prod_subtype_map_embedding", "times_cont_diff_within_at.continuous_linear_map_comp", "differentiable_on.congr_mono", "finset.filter_congr_decidable", "is_local_max_on.inter", "commute.add_pow", "rat.zero_of_num_zero", "category_theory.iso.conj_Aut_apply", "uliftable.down_up", "submonoid.localization_map.lift_spec", "list.perm.append_left", "set.image_seq", "multilinear_map.map_smul", "equiv.perm.pow_apply_eq_of_apply_apply_eq_self", "vector.mem_iff_nth", "mul_inv_cancel_right'", "ring_equiv.surjective", "finsupp.lcongr_single", "category_theory.non_preadditive_abelian.sub_sub_sub", "monoid_hom.apply_apply", "uniform_space.completion.dense\:2083", "ennreal.inv_le_iff_inv_le", "affine_map.comp_apply", "concave_on.comp_linear_map", "fraction_ring.mk_eq_div", "multiplicity.mul'", "associates.dvd_out_iff", "int.le_div_of_mul_le", "nat.eq_prime_pow_of_dvd_least_prime_pow", "is_conj_one_left", "cauchy_iff_exists_le_nhds", "mvqpf.Wequiv.abs'", "category_theory.discrete.nat_trans_app", "asymptotics.is_O_congr", "add_commute.neg_right_iff", "minimal_polynomial.ne_zero", "mvqpf.corec_roll", "nat.eq_of_mul_eq_mul_left", "turing.TM1to1.exists_enc_dec", "nnreal.le_of_real_iff_coe_le", "multiset.erase_of_not_mem", "padic_norm_e.norm_p_pow", "embedding_of_rat", "finset.card_insert_of_not_mem", "subtype.ext_val", "lie_equiv_matrix'_symm_apply", "measure_theory.simple_func.eq_zero_of_mem_range_zero", "polynomial.is_splitting_field.mul", "int.sub_le_sub_left", "padic_norm.zero", "add_localization.ind", "filter.is_cobounded_le_of_bot", "lcm_eq_right_iff", "filter.mk_of_closure_sets", "real.is_topological_basis_Ioo_rat", "int.exists_least_of_bdd", "complex.exists_root", "wseq.join_nil", "nnreal.coe_lt_coe", "gronwall_bound_of_K_ne_0", "subalgebra.range_le", "indicator_norm_le_norm_self", "is_R_or_C.of_real_mul", "relator.rel_and", "finite_dimensional.dim_eq_card_basis", "inf_idem", "smooth_at_id", "metric.bounded_range_iff", "category_theory.nat_trans_from_connected", "omega.int.le_and_le_iff_eq", "multilinear_map.neg_apply", "multiset.exists_multiset_eq_map_quot_mk", "has_strict_fderiv_at.mem_implicit_to_local_homeomorph_of_complemented_target", "set.surj_on_bUnion_bUnion", "dim_eq_of_injective", "subsemiring.ext", "set.compl_inter", "neg_mul_neg", "closure_subset_iff_is_closed", "commute.neg_left_iff", "roption.mem_assert_iff", "punit.top_eq", "unique_factorization_domain.dvd_of_dvd_mul_left_of_no_prime_factors", "tendsto_neg_nhds_within_Iio", "finset.prod_pow_boole", "num.zneg_to_znum", "set.empty_card'", "gfp_comp", "sup_sdiff_same", "category_theory.bifunctor.diagonal'", "ennreal.mul_top", "subtype.coe_injective", "int.gcd_mul_lcm", "norm_num.clear_denom_simple_nat", "set.indicator_indicator", "real.range_cos", "set.surj_on.union", "function.support_prod", "submodule.zero_mem", "nat.zero_pow", "finsupp.total_range", "seq1.join_nil", "cardinal.ord_aleph_is_limit", "valuation.map_inv", "real.sqrt_two_add_series_monotone_left", "alist.lookup_empty", "multiset.erase_le", "category_theory.faithful.div_comp", "mv_polynomial.is_homogeneous.prod", "mv_polynomial.coe_C", "int.coe_nat_mul_neg_succ", "sub_eq_sub_add_sub", "pgame.zero_lt", "formal_multilinear_series.id_apply_one'", "adic_completion.eval_of", "finset.Ico.filter_lt_of_le_bot", "monotonicity.and", "multiset.mem_singleton", "list.Ico.filter_le_of_bot", "has_mfderiv_at_unique", "ceil_mono", "sub_right_inj", "nonempty_pprod", "filter.germ.const_comp_tendsto'", "znum.abs_to_znum", "max_left_comm", "iterated_deriv_succ", "mvqpf.recF_eq_of_Wequiv", "power_series.order_X", "fin.succ_ne_zero", "option.iget_some", "filter.eventually_eq.eventually_eq_nhds", "relation.equivalence_join", "ordinal.mod_def", "polynomial.monic_mul", "quot.out_eq", "typevec.prod_id", "is_unit.dvd", "filter.eventually_le.is_max_filter", "filter.map_le_iff_le_comap", "lipschitz_with.mul", "I_extend_one", "finset.card_bind", "lower_bounds_Ioi", "rat.norm_cast_real", "is_coprime.mul_add_left_right", "functor.map_map", "stream.nth_map", "category_theory.action_as_functor_map", "add_con.comap_eq", "sub_add", "is_irreducible_irreducible_component", "opposite.coe_op_add_hom", "has_deriv_at.lhopital_zero_at_bot", "stream.zip_inits_tails", "filter.germ.coe_lt", "minimal_polynomial.coeff_zero_ne_zero", "lists'.subset_nil", "add_semiconj_by.neg_neg_symm_iff", "ordinal.iterate_le_nfp", "cinfi_le_cinfi", "ideal.map_comap_map", "cau_seq.mul_pos", "le_of_not_le", "zmod.cast_add", "pequiv.to_matrix_symm", "category_theory.limits.kernel_is_iso_comp_hom_comp_kernel_\[Iota]", "filter.infi_sets_eq_finite", "iterated_fderiv_within_succ_eq_comp_right", "list.find_cons_of_neg", "local_equiv.prod_target", "list.of_mem_filter", "filter.is_bounded_under_inf", "deriv_within_const_sub", "finset.coe_ssubset", "finset.sigma_preimage_mk_of_subset", "matrix.adjugate_transpose", "measurable.fst", "continuous_sigma_mk", "one_div_lt_one_div_of_neg", "finmap.not_mem_erase_self", "add_neg_le_iff_le_add'", "finset.forall_mem_empty_iff", "differentiable_within_at.div", "finmap.ext_lookup", "add_equiv.coe_mk", "open_add_subgroup.zero_mem", "lagrange.interpolate_smul", "int.modeq.modeq_sub", "nat.gcd_mul_dvd_mul_gcd", "mv_polynomial.degrees_add", "linear_equiv.skew_prod_symm_apply", "polynomial.separable.mul", "pgame.nim.equiv_iff_eq", "submonoid.comap_map_comap", "equiv_of_is_basis_refl", "is_R_or_C.norm_sq_sub", "is_local_min_on.on_subset", "localization_map.mk'_eq_iff_mk'_eq", "cau_seq.lim_eq_zero_iff", "submonoid.coe_injective", "eq.trans", "finsupp.sum_ite_eq'", "qpf.recF_eq'", "continuous_linear_map.le_op_norm", "has_deriv_at_filter.sum", "circle_deg1_lift.commute_iff_commute", "ordinal.CNF_pairwise", "emetric.mem_closure_iff", "with_top.top_ne_zero", "zmod.cast_self'", "function.right_inverse_of_injective_of_left_inverse", "rat.coe_int_eq_of_int", "generalized_continued_fraction.int_fract_pair.nth_stream_fr_nonneg_lt_one", "metric.isometry_on_inl", "matrix_equiv_tensor_apply", "is_R_or_C.abs_re_le_abs", "finsupp.supported_Union", "reflexive_many_one_reducible", "category_theory.functor.sum_map_inl", "pell.eq_pell_zd", "finsupp.map_domain_add", "inf_nhds_at_top", "erased.map_def", "implicit_function_data.pt_mem_to_local_homeomorph_source", "not_forall", "nat.zero_lor", "ennreal.coe_bit1", "le_of_max_le_right", "initial_seg.init_iff", "is_open_map.continuous_on_range_of_left_inverse", "list.append_eq_append_iff", "int.le_add_of_nonneg_left", "list.foldl_op_eq_op_foldr_assoc", "matrix.bit1_apply_eq", "embedding_sigma_map", "mv_polynomial.eval\:2082_zero", "map_nhds_induced_of_surjective", "list.nodup_append_of_nodup", "padic.padic_norm_e_lim_le", "le_of_forall_le_of_dense", "convex.image_sub_le_mul_sub_of_deriv_le", "traversable.fold_mfoldl_cons", "category_theory.prod.fst_obj", "polynomial.monic.next_coeff_prod", "dvd_lcm_left", "set.subset.antisymm_iff", "list.sublist.map", "lower_bound_Ioc", "list.to_finset_card_of_nodup", "category_theory.equivalence.functor_as_equivalence", "norm_num.nat_cast_zero", "list.concat_perm", "is_least_Ici", "inv_eq_one_div", "computation.lift_rel_return_right", "pfunctor.approx.P_corec", "measure_theory.l1.simple_func.of_simple_func_eq_mk", "filter.tendsto_congr", "neg_zero", "times_cont_mdiff_at.smooth_at", "submodule.span_singleton_le_iff_mem", "mvqpf.liftr_map_last'", "nat.min_succ_succ", "int.modeq.modeq_mul_right", "nat.coprime_pow_primes", "polynomial.deriv_within", "distrib_mul_action_hom.coe_fn_coe", "le_of_add_le_add_right", "functor.comp.run_seq", "times_cont_mdiff_on_fst", "local_equiv.right_inv_on", "nat.partrec.code.smn", "zmod.quadratic_reciprocity", "set.Union_inter", "differentiable.add_const", "pnat.xgcd_type.flip_x", "polynomial.integral_normalization_aeval_eq_zero", "nat.unpair_mkpair", "finset.sum_filter_ne_zero", "option.not_mem_none", "real.rpow_nat_inv_pow_nat", "add_semiconj_by.neg_symm_left_iff", "measurable_space.is_measurable_Sup", "Sup_eq_supr'", "times_cont_diff_succ_iff_fderiv", "filter.has_basis.Limsup_eq_infi_Sup", "linear_map.sub_apply", "cau_seq.completion.inv_zero", "polynomial.degree_le_nat_degree", "one_lt_one_div", "list.singleton_eq", "nat.of_le_succ", "mul_gsmul_assoc", "omega.fun_mono_2", "symmetrize_mem_uniformity", "set.sInter_subset_of_mem", "category_theory.prod_preserves_connected_limits.\[Gamma]\:2081_app", "algebraic_closure.is_algebraic", "add_subgroup.coe_prod", "set.bUnion_pair", "finset.insert_erase_subset", "quadratic_form.coe_fn_smul", "mul_div_cancel_left_of_imp", "le_max_right", "measure_theory.l1.simple_func.uniform_inducing", "with_top.coe_Inf", "bitraversable.tfst_id", "Set.mem_sep", "isometry_id", "list.zip_unzip", "real.has_deriv_at_rpow_of_one_le", "finsupp.mul_apply", "finset.center_mass_eq_of_sum_1", "additive.is_add_submonoid_iff", "category_theory.limits.types.pi", "cardinal.powerlt_max", "cardinal.power_zero", "bsupr_le", "finsupp.eq_zero_of_comap_domain_eq_zero", "real.sqrt_prop", "metric.lipschitz_inf_dist_set", "sum.map_traverse", "ennreal.le_coe_iff", "matrix.minor_empty", "dfinsupp.single_smul", "setoid.trans'", "function.left_inverse.id", "equiv.conj_apply", "set.countable_singleton", "real.is_conjugate_exponent.conjugate_eq", "real.sqrt_two_add_series_zero", "is_glb_infi", "add_le_of_le_of_nonpos", "prime_multiset.prod_sup", "is_R_or_C.eq_conj_iff_real", "polynomial.degree_eq_one_of_irreducible_of_root", "cardinal.lift_id", "pgame.zero_right_moves", "multiset.cons_inter_of_neg", "typevec.drop_fun_split_fun", "rat.add_num_denom", "int.mul_lt_mul_of_pos_left", "distrib_mul_action_hom.map_neg", "irreducible_of_prime", "list.countp_nil", "finite_field.cast_card_eq_zero", "uniform_continuous.prod_mk_right", "submodule.mul_induction_on", "is_group_hom.inv_iff_ker", "ideal.is_local.le_jacobson", "monoid_hom.iterate_map_gpow", "seq1.join_join", "continuous_linear_equiv.differentiable_at", "filter.principal_eq_bot_iff", "finsupp.single_sub", "to_topological_space_inf", "complex.of_real_sinh_of_real_re", "list.length_rotate'", "smooth.smooth_on", "submonoid.mem_Inf", "ordinal.pred_le_self", "category_theory.limits.coprod.left_unitor_inv", "mul_mem_nonunits_right", "is_add_hom.neg", "wseq.destruct_think", "normed_ring.inverse_add_norm_diff_nth_order", "gold_conj_neg", "ennreal.sub_le_sub", "one_add_mul_le_pow'", "real.pi_div_two_le_two", "composition.blocks_fun_sigma_composition_aux", "computation.exists_of_mem_bind", "nnreal.add_div'", "set.mem_of_mem_insert_of_ne", "bool_of_nat_mem_Icc_of_mem_Icc_to_nat", "multiset.mem_of_mem_filter", "exists_unique_congr", "nat.bodd_two", "is_integral_domain.polynomial", "multiset.cons_le_cons_iff", "measure_theory.simple_func.integral_eq_lintegral", "mv_polynomial.eval_indicator_apply_eq_one", "asymptotics.is_o_bot", "topological_space.opens.val_eq_coe", "set.inj_on_empty", "polynomial.coeff_C", "category_theory.limits.cospan_left", "mvpfunctor.W_path_dest_right_W_path_cases_on", "stream.corec_id_id_eq_const", "continuous_iff_le_induced", "nat.modeq.modeq_of_dvd", "pi_Lp.edist", "category_theory.limits.colimit.w", "nat.succ_le_succ_iff", "set.eq_of_subset_of_subset", "is_add_subgroup.mem_add_center", "mvpfunctor.M.bisim", "initial_seg.le_add_apply", "category_theory.limits.prod.lift_comp_comp_assoc", "int.neg_succ_of_nat_coe'", "real.pi_lower_bound_start", "finsupp.lapply_apply", "fintype.card_unit", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp", "cardinal.lift_min", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le", "presented_group.to_group.mul", "contracting_with.fixed_point_is_fixed_pt", "ennreal.top_mul_top", "real.borel_eq_generate_from_Iio_rat", "closure_eq_self_union_frontier", "int.dvd_of_mod_eq_zero", "monotone.map_inf", "cardinal.mul_eq_right", "relation.trans_gen.trans_right", "int.of_nat_ge_zero", "nat.one_lt_two_pow", "initial_seg.lt_or_eq_apply_right", "equiv.symm_apply_eq", "finset.card_fin", "filter.inf_principal_ne_bot_iff", "is_add_subgroup.neg_mem_iff", "sym2.mk_has_mem", "path_component_congr", "exists_nat_gt", "function.iterate_succ_apply", "function.injective2.left", "set.diff_singleton_subset_iff", "convex_halfspace_im_gt", "list.map_diff", "omega.coeffs.dvd_val", "continuous_linear_map.smul_algebra_right_apply", "mdifferentiable.mfderiv_within", "finset.subset_univ", "monoid_hom.mem_ker", "dlist.to_list_empty", "quadratic_form.polar_add_left", "le_add_of_nonneg_right", "list.foldr_ext", "add_monoid_hom.functions_ext", "Algebra.id_apply", "pfunctor.M.isubtree_cons", "differentiable_at.has_deriv_at", "filter.tendsto_bot", "set.union_diff_cancel_left", "finsupp.emb_domain_inj", "submodule.map_smul", "list.mem_argmax_iff", "continuous_linear_map.lmul_left_right_norm_le", "is_closed.is_complete", "list.count_le_count_cons", "complex.re_eq_add_conj", "con.rel_eq_coe", "cardinal.ord_lt_ord", "mv_polynomial.map_injective", "submodule.not_le_iff_exists", "int.add_div_of_dvd", "has_fderiv_at_fst", "injective_of_surjective", "continuous.measurable", "nat.one_ne_zero", "category_theory.limits.inv_prod_comparison_map_fst_assoc", "category_theory.limits.prod_map_map_assoc", "subset_convex_hull", "differentiable.const_mul", "nat.bit_zero", "UniformSpace.completion_hom_val", "ring.fractional_ideal.coe_coe_ideal", "polynomial.eq_one_of_is_unit_of_monic", "semiconj_by.mul_left", "coe_sort_coe_base", "int.div_eq_zero_of_lt_abs", "list.func.get_map'", "sub_pow_char", "ring.closure_subset_iff", "finset.not_mem_empty", "nat.two_not_dvd_two_mul_add_one", "nat.fib_one", "ordinal.infinite_pigeonhole_card", "multiset.rel_add_right", "quadratic_form.comp_apply", "add_submonoid.localization_map.mk'_eq_iff_eq_add", "vector3.append_insert", "add_submonoid.coe_inf", "and_or_distrib_left", "nat.cast_with_bot", "mvpfunctor.comp.mk_get", "approximates_linear_on.inverse_approx_map_sub", "times_cont_diff.continuous_fderiv_apply", "diagonal_eq_range_diagonal_map", "norm_num.inv_neg", "infi_of_empty", "continuous_linear_map.has_fderiv_within_at", "submonoid.localization_map.mk'_surjective", "option.ne_none_iff_exists", "finset.left_eq_union_iff_subset", "mem_perms_of_list_of_mem", "category_theory.limits.has_zero_object.to_zero_ext", "ennreal.half_lt_self", "model_with_corners.unique_diff_preimage", "iff.symm", "hyperreal.coe_neg", "times_cont_diff_on.times_cont_diff_within_at", "submodule.mem_comap", "is_seq_compact.totally_bounded", "archimedean_iff_rat_lt", "distrib_mul_action_hom.id_comp", "multiset.ndinter_eq_zero_iff_disjoint", "lcm_same", "measure_theory.l1.integral_eq_norm_pos_part_sub", "category_theory.biprod.column_nonzero_of_iso", "list.head_lookup_all", "ennreal.one_eq_coe", "is_measurable_Ioi", "nat.mul_def", "times_cont_diff_within_at_local_invariant_prop", "primrec\:2082.comp", "lists'.cons_subset", "measure_theory.lebesgue_length_Ico", "supr_subtype'", "real.differentiable_at_cos", "iterated_deriv_zero", "circle_deg1_lift.tendsto_translation_number'", "filter.unbounded_of_tendsto_at_top", "int.shiftr_neg_succ", "equiv.point_reflection_involutive", "tensor_product.rid_tmul", "category_theory.yoneda.naturality", "category_theory.iso.eq_inv_comp", "metric.mem_of_closed'", "finmap.to_finmap_nil", "list.eq_of_prefix_of_length_eq", "metric.inf_dist_le_inf_dist_add_dist", "finset.prod_fiberwise", "mul_ne_zero_comm", "category_theory.limits.biprod.inr_map", "submodule.complete_of_finite_dimensional", "Module.monoidal_category.associator_naturality", "computation.destruct_eq_ret", "computation.rel_of_lift_rel", "vsub_eq_sub", "finset.prod_filter_of_ne", "list.argmax_two_self", "finset.prod_flip", "pgame.equiv_of_relabelling", "lt_or_gt_of_ne", "I_extend_extends", "ordinal.power_limit", "category_theory.limits.prod.right_unitor_inv", "edist_le_Ico_sum_of_edist_le", "irrational.of_mul_self", "linear_equiv.coe_prod", "category_theory.monoidal_category.right_unitor_product_aux_perimeter", "polynomial.continuous_within_at", "category_theory.nat_trans.op_app", "prod.one_eq_mk", "multiset.add_le_add_left", "differentiable_within_at_snd", "fintype.card_fin", "measurable.norm", "filter.eq_infi_of_mem_sets_iff_exists_mem", "vector.remove_nth_val", "finset.product_val", "measure_theory.limsup_lintegral_le", "set.Inter_set_of", "galois_insertion.u_injective", "function.uncurry_curry", "add_subgroup.mem_prod", "nhds_le_of_le", "UniformSpace.coe_mk", "vector.tendsto_cons", "units.conj_pow'", "function.comp.assoc", "category_theory.monoidal_category.id_tensor_comp_tensor_id", "localization_map.mk'_one", "bernoulli_def'", "list.length_pos_of_prod_ne_one", "filter.is_bounded_under.mono", "category_theory.abelian.pseudo_equal_refl", "mul_dvd_mul", "polynomial.has_deriv_at", "pfun.bind_defined", "category_theory.adjunction.hom_equiv_naturality_right", "or_self_right", "dfinsupp.subtype_domain_finsupp_sum", "finset.sum_Ico_reflect", "padic_norm.sub", "submonoid.localization_map.map_units", "ring_equiv.to_CommRing_iso_hom", "list.union_sublist_append", "map_Sup_of_continuous_at_of_monotone'", "sup_eq_left", "right_distrib", "nnreal.div_eq_mul_one_div", "finset.finite_to_set_to_finset", "nat.sub_add_eq_add_sub", "has_deriv_at.prod", "enat.top_add", "polynomial.splits_map_iff", "frontier_ball", "local_homeomorph.symm_source", "times_cont_diff_on.continuous_linear_map_comp", "rat.not_irrational", "list.repeat_perm", "power_series.span_X_is_prime", "inner_comm", "int.gcd_div", "num.mul_to_nat", "is_absolute_value.abv_neg", "preorder_hom.id_comp", "nat.le_add_left", "has_deriv_within_at_iff_tendsto_slope'", "bilin_form.zero_left", "submodule.mem_span", "Top.mono_iff_injective", "continuous_list_prod", "monoid_hom.comp_id", "minimal_polynomial.unique'", "bex_def", "set.eq_on_indicator", "onote.oadd_pos", "real.geom_mean_le_arith_mean_weighted", "continuous_neg", "has_deriv_within_at_neg", "localization_map.exists_integer_multiple", "mv_polynomial.rename_prodmk_eval\:2082", "category_theory.under.map_map_right", "filter.prod_infi_right", "real.lt_Sup", "polynomial.div_by_monic_eq_zero_iff", "finsupp.map_domain_smul", "complex.of_real_bit1", "is_max_filter_dual_iff", "add_submonoid.ext", "is_max_on.of_is_local_max_of_convex_univ", "category_theory.functor.hext", "matrix.mul_diagonal", "computable_pred.rice", "category_theory.preadditive.sum_comp", "list.lookmap_congr", "ordinal.min_le", "multiset.fold_eq_foldl", "infi_of_empty'", "multiset.filter_map_filter", "omega.term.val_add", "surjective_of_continuous", "decidable.or_iff_not_imp_right", "category_theory.coyoneda.naturality", "int.nat_abs_eq", "is_seq_closed_of_def", "measure_theory.measure.count_apply", "mv_power_series.constant_coeff_map", "nnreal.coe_list_sum", "smooth_on.prod_map", "set.subset_diff_union", "nat.sub_le_sub_left", "lt_is_glb_iff", "filter.comap_id", "list.length_le_of_sublist", "measure_theory.to_outer_measure_to_measure", "hyperreal.is_st_unique", "continuous_multilinear_map.uncurry0_norm", "equiv.arrow_congr_apply", "add_aut.one_def", "bounded_convex_hull", "polynomial.card_roots'", "sesq_form.ortho_smul_left", "pos_num.one_le_cast", "uniform_continuous\:2082.bicompl", "open_add_subgroup.is_closed", "stream.tail_interleave", "list.Ico.pairwise_lt", "complex.continuous_linear_map.im_coe", "finset.supr_insert", "complex.log_one", "add_monoid_hom.map_rat_module_smul", "finset.sdiff_union_inter", "affine_map.id_apply", "mvqpf.cofix.bisim", "smodeq.trans", "metric.bounded_of_compact", "continuous_linear_equiv.coord_norm", "polynomial.not_is_unit_X_sub_C", "affine_map.line_map_zero", "wseq.map_congr", "right_ne_zero_of_mul", "euclidean_domain.mod_one", "list.erase_dup_cons_of_mem", "measure_theory.ae_eq_fun.mk_mul_mk", "filter.tendsto.frequently", "tensor_product.direct_sum_lof_tmul_lof", "cardinal.mk_Icc_real", "le_sup_right_of_le", "lie_ring.of_associative_ring_bracket", "wseq.destruct_dropn", "real.cos_pos_of_le_one", "pSet.mem_powerset", "nat.zero_lt_one", "Top.comp_app", "int.neg_of_nat_zero", "num.div_to_nat", "int.zero_nonneg", "submodule.smul_mem_span_smul", "set.range_const", "ennreal.one_le_coe_iff", "commute.inv_right_iff'", "add_sub_sub_cancel", "measurable_space.map_mono", "category_theory.monad_hom.ext", "or.assoc", "is_cyclic_of_subgroup_integral_domain", "complex.im_sq_le_norm_sq", "congr_fun", "pell.dvd_of_ysq_dvd", "finsupp.restrict_dom_apply", "uniform_continuous.neg", "fintype.card_pi_finset", "set.Ioc_diff_Ioo_same", 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"nat.partrec.code.fixed_point", "rat.cast_mk", "has_deriv_within_at.scomp", "qpf.supp_preservation_iff_liftp_preservation", "prod_generate_from_generate_from_eq", "pequiv.to_pequiv_mul_matrix", "bifunctor.map_equiv_symm_apply", "pi.is_basis_std_basis", "rel_embedding.refl_apply", "convex.to_cone_eq_Inf", "Module.Mon_Module_equivalence_Algebra.ring_one", "turing.tape.exists_mk'", "set.mem_sep_eq", "nat.two_mul_ne_two_mul_add_one", "polynomial.degree_sub_le", "category_theory.limits.coprod_map_id_comp", "emetric.cauchy_seq_iff_le_tendsto_0", "principal_seg.top_lt_top", "multiset.mem_erase_iff_of_nodup", "nat.lt_add_of_pos_left", "continuous_linear_equiv.fderiv_within", "localization.mk_eq_monoid_of_mk'_apply", "add_monoid_hom.continuous_of_bound", "cardinal.add_one_le_succ", "list.filter_sublist_filter", "set.Union_mul_left_image", "set.empty_mul", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_fst", "uniform_embedding.embedding", "filter.is_countably_generated.eq_generate", "convex_cone.pointed_iff_not_blunt", "decidable.imp_or_distrib'", "set.mem_singleton", "filter.tendsto_at_bot_mono'", "real.coe_fib_eq", "category_theory.abelian.pseudoelement.apply_eq_zero_of_comp_eq_zero", "is_closed.mem_of_tendsto", "uniform_space.completion.uniform_continuous_extension", "computation.lift_rel_return", "continuous_quotient_lift", "vector.nth_update_nth_same", "findim_eq_zero", "asymptotics.is_O.prod_rightr", "continuous_multilinear_map.map_smul_univ", "add_units.add_left_symm", "free_comm_ring.restriction_of", "set.nonempty.prod", "submodule.quotient_equiv_of_is_compl_symm_apply", "and.comm", "equiv.point_reflection_midpoint_left", "category_theory.equivalence.inverse_map_inj_iff", "measure_theory.ae_eq_fun.coe_fn_comp", "rank_le_range", "eq_of_nndist_eq_zero", "turing.TM1to1.step_aux_write", "ring.fractional_ideal.eq_span_singleton_of_principal", "rat.cast_abs", "polynomial.prime_of_degree_eq_one_of_monic", "is_subgroup.of_div", "list.sublist.subset", "category_theory.monoidal_category.left_unitor_tensor", "filter.eventually_eq_bind", "is_compact.bdd_below", "partrec\:2082.unpaired'", "ennreal.top_pow", "set.compl_union", "local_homeomorph.eq_on_source.eq_on", "multiplicity.multiplicity_pow_self_of_prime", "ennreal.tsum_eq_supr_sum'", "vector.to_list_length", "dense_embedding_of_rat", "finset.sum_insert_of_eq_zero_if_not_mem", "set.eq_or_ssubset_of_subset", "semilattice_sup.ext", "computable.list_length", "is_bounded_bilinear_map.map_sub_left", "sup_assoc", "indicator_ae_eq_restrict_compl", "hyperreal.omega_pos", "ordinal.cof_eq_one_iff_is_succ", "lt_add_of_pos_of_le", "is_compl.right_unique", "rel.inv_comp", "subgroup.closure_induction", "multiset.subset.refl", "composition.mem_range_embedding", "filter.eventually_lift'_powerset", "real.sqrt_exists", "not_or_of_imp", "ennreal.lt_top_iff_ne_top", "equiv_functor.map_equiv_apply", "measure_theory.integrable.min_zero", "finset.mem_insert_of_mem", "contracting_with.efixed_point_is_fixed_pt", "finset.right_eq_union_iff_subset", "zsqrtd.coe_int_val", "free_magma.traverse_pure'", "cInf_intro", "uniform_continuous.prod_map", "minimal_polynomial.monic", "padic_norm_z.mul", "submonoid.map_le_iff_le_comap", "continuous_linear_equiv.continuous_within_at", "is_lub.bdd_above", "polynomial.eval\:2082_bit0", "set.Ioc_union_Ici_eq_Ioi", "cardinal.mk_le_of_injective", "nat.modeq.refl", "nnreal.tendsto_of_real", "ideal.top_pow", "iff_true_right", "category_theory.limits.equalizer.hom_ext", "nnreal.rpow_arith_mean_le_arith_mean_rpow", "category_theory.monoidal_category.left_unitor_nat_iso_inv_app", "tendsto_finset_sum", "list.prefix_append_right_inj", "dfinsupp.support_neg", "submonoid.localization_map.comp_eq_of_eq", "mem_of_is_closed_sequential", "list.mmap_with_index'_eq_mmap_with_index", "normed_field.nhds_within_is_unit_ne_bot", "typevec.snd_diag", "finset.image_preimage_of_bij", "bounded_continuous_function.coe_sub", "differentiable.smul_algebra", "quotient_map.comp", "nnreal.of_real_lt_of_real_iff_of_nonneg", "is_unit_unit", "multiset.map_traverse", "complex.two_cos", "category_theory.non_preadditive_abelian.lift_\[Sigma]", "set.eq_on.mono", "with_top.is_glb_Inf", "nat.choose_symm_of_eq_add", "pos_num.bit_to_nat", "lie_algebra.special_linear.E_apply_zero", "ordinal.typein_lt_type", "Gromov_Hausdorff.dist_GH_dist", "set.compl_image", "cardinal.omega_le_aleph", "subring.map_le_iff_le_comap", "neg_pos", "units.eq_inv_mul_iff_mul_eq", "filter.Iio_mem_at_bot", "mem_subalgebra_of_subsemiring", "string.str_ne_empty", "set.preimage_congr", "list.drop_drop", "list.length_drop", "measure_theory.measure.restrict_univ", "submodule.coe_prod_equiv_of_is_compl'", "finset.is_measurable", "polynomial.separable_prod", "multiset.length_ndinsert_of_mem", "pnat.coprime.coprime_dvd_left", "add_comm_group.direct_limit.of_add", "linear_equiv.eq_symm_apply", "equiv.traverse_eq_map_id", "tensor_product.smul.aux_of", "filter.is_bounded.mono", "cardinal.bit1_lt_bit0", "rat.cast_div", "list.cons_subperm_of_mem", "filter.map_one", "supr_image", "subring.map_map", "eq_true_of_and_eq_true_right", "isometry.comp", "commute.self_pow", "zmod.val_min_abs_def_zero", "category_theory.exp_comparison_natural_left", "gsmul_add_comm", "constr_sub", "category_theory.abelian.images.image_strong_epi_mono_factorisation_e_strong_epi", "AddCommGroup.ext", "smooth_on_iff", "model_with_corners.mk_coe_symm", "lists.equiv_atom", "int.neg_lt_of_neg_lt", "filter.has_basis.prod", "topological_space.opens.mem_supr", "multiset.countp_zero", "filter.lift'_infi", "nat.sub_eq_sub_min", "sub_sub_cancel", "ultrafilter_basis_is_basis", "list.func.length_neg", "sym2.rel.is_equivalence", "map_cluster_pt_of_comp", "list.minimum_le_of_mem", "localization_map.map_comap", "set.Union_pos", "dvd_iff_dvd_of_rel_left", "local_equiv.source_subset_preimage_target", "ennreal.max_zero_right", "add_subgroup.closure_univ", "continuous_within_at.mem_closure", "free_group.red.sizeof_of_step", "multiset.union_def", "subring.mem_to_submonoid", "inv_le_inv''", "subgroup.mem_gpowers", "set.left_inv_on.eq", "multiset.fold_distrib", "ring_hom.map_range", "list.filter_nil", "nnreal.coe_zero", "pell.pell_zd_add", "real.exp_log", "finsupp.lmap_domain_apply", "lipschitz_with.iff_le_add_mul", "with_zero.coe_add", "nnreal.nsmul_coe", "cardinal.powerlt_succ", "int.add_mod_mod", "lipschitz_with.of_le_add_mul", "mul_left_comm", "turing.tape.right\:2080_nth", "nat.mod_eq_of_lt", "category_theory.iso.conj_Aut_trans", "nat.bitwise_zero_left", "category_theory.arrow.hom_mk'_right", "finset.prod_ite", "list.concat_append", "composition.disjoint_range", "measure_theory.integral_dirac", "filter.germ.coe_pos", "dvd_of_mul_right_dvd", "list.perm.symm", "lt_add_of_pos_of_lt'", "finset.prod_range_div'", "ring_equiv.coe_add_equiv_refl", "local_equiv.target_subset_preimage_source", "nat.min_fac_sq_le_self", "abstract_completion.uniform_continuous_map", "infi_apply", "has_deriv_at.smul", "primrec.list_map", "smul_pow", "category_theory.limits.biproduct.lift_desc", "nat.partrec.of_eq", "mul_lt_mul_of_neg_right", "nat.dvd_add_left", "turing.list_blank.head_map", "vector_span_empty", "lt_of_add_lt_add_left", "real.mk_eq", "category_theory.non_preadditive_abelian.add_comm", "mv_polynomial.pderivative_C", "category_theory.limits.cones.postcompose_equivalence_inverse", "generalized_continued_fraction.of_terminated_at_n_iff_succ_nth_int_fract_pair_stream_eq_none", "finset.eq_of_card_le_one_of_sum_eq", "ideal.map.is_maximal", "filter.germ.const_comp_tendsto", "seq.head_cons", "has_sum_iff_tendsto_nat_of_summable_norm", "equiv.fun_unique_symm_apply", "category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_inv", "complex.tanh_eq_sinh_div_cosh", "list.erase_comm", "bor_eq_false_eq_eq_ff_and_eq_ff", "category_theory.graded_object.shift_functor_obj_apply", "category_theory.non_preadditive_abelian.neg_add_self", "has_fpower_series_at.coeff_zero", "nat.partrec.code.encode_lt_comp", "multiset.rel.mono", "linear_map.ker_std_basis", "polynomial.ite_le_nat_degree_coeff", "ordinal.lt_power_of_limit", "list.mem_map", "category_theory.monoidal_category.right_unitor_tensor", "real.rpow_lt_rpow_iff", "measure_theory.simple_func.const_apply", "nat.even.sub", "ennreal.add_right_inj", "topological_space.second_countable_topology_induced", "list.kerase_cons_eq", "hash_map.valid.contains_aux_iff", "nat.xgcd_aux_rec", "integral_closure_idem", "complex.cos_square", "mem_closure_of_continuous2", "wseq.head_some_of_nth_some", "category_theory.differential_object.hom.comp_f", "list.nil_sublist", "vadd_right_injective", "category_theory.equivalence.adjointify_\[Eta]_\[CurlyEpsilon]", "one_one_equiv.congr_left", "list.nodup_bind", "nnnorm_smul", "list.insert.def", "principal_seg.lt_top", "minimal_polynomial.unique", "measure_theory.ae_restrict_iff", "erased.map_out", "multiset.ndinter_subset_left", "linear_equiv.to_Module_iso'_inv", "add_mul_self_eq", "ideal.map_supr", "set.Icc_union_Icc_eq_Icc", "sup_Inf_eq", "measure_theory.with_density_apply", "polynomial.leading_coeff_pow", "tactic.abel.unfold_smul", "finset.sum_cancels_of_partition_cancels", "filter.tendsto_iff_ptendsto", "set.ball_image_iff", "isometric.coe_add_right", "plift.down_inj", "has_fpower_series_on_ball.uniform_geometric_approx", "is_comm_applicative.commutative_map", "isometric.inv_apply_self", "nat.modeq.dvd_of_modeq", "ulift.zero_down", "equiv.perm.sign_eq_of_is_swap", "polynomial.map_prod", "pgame.zero_lt_star", "differentiable_within_at_const", "multiset.subset_erase_dup'", "mul_le_mul_left'", "complex.deriv_cosh", "false_iff_true", "monotone.mul'", "nat.le_sub_left_iff_add_le", "zorn.chain_insert", "ideal.map_radical_le", "is_conj_trans", "ordinal.lt_mul_of_limit", "gaussian_int.nat_cast_nat_abs_norm", "finite_dimensional_bot", "closure_image_mem_nhds_of_uniform_inducing", "euclidean_domain.eq_div_of_mul_eq_right", "multiset.union_le_add", "filter.eventually_eq.is_local_min_on_iff", "submodule.comap_top", "qpf.fix.rec_unique", "finsupp.not_mem_support_iff", "false_implies_iff", "pell.eq_of_xn_modeq", "finsupp.emb_domain_notin_range", "setoid.trans", "lucas_lehmer.X.bit0_snd", "nat.succ_div", "neg_neg_sub_neg", "category_theory.functor.map_cone_inv_\[Pi]", "finset.pi.cons_ne", "homeomorph.image_symm", "traversable.map_traverse", "strict_weak_order.etrans", "is_closed_Ici", "topological_fiber_bundle_core.local_triv_at_ext_to_local_homeomorph", "cardinal.omega_pos", "has_deriv_within_at_iff_tendsto_slope", "int.bit_zero", "strict_mono.le_iff_le", "add_eq_zero_iff_neg_eq", "mv_polynomial.coeff_monomial", "filter.generate_empty", "quotient.ind\:2082'", "nat.lt_add_of_pos_right", "asymptotics.is_o.trans'", "abs_lt", "eq_inv_mul_iff_mul_eq", "set.Icc_diff_both", "nat.lt_succ_iff_lt_or_eq", "set.sum_indicator_subset_of_eq_zero", "list.func.mem_get_of_le", "submonoid.localization_map.mk'_mul_eq_mk'_of_mul", "monotone_closure", "linarith.int.coe_nat_mul_bit0", "filter.tendsto_at_top_add_right_of_le", "module.direct_limit.of_f", "finset.attach_image_val", "is_min_on.sup", "typevec.append_fun_comp'", "not_and", "measure_theory.lintegral_tsum", "nnreal.rpow_le_rpow_of_exponent_ge", "filter.ultrafilter_ultrafilter_of'", "add_subgroup.mem_map", "ideal.map_Inf", "le_zero_iff_eq", "has_fderiv_at.smul_const", "nnnorm_sum_le", "ennreal.inv_zero", "list.erasep_cons_of_neg", "topological_space.opens.mem_coe", "circle_deg1_lift.iterate_monotone", "fraction_map.exists_reduced_fraction", "polynomial.C_bit1", "setoid.sUnion_classes", "ring.fractional_ideal.val_eq_coe", "filter.frequently_or_distrib", "circle_deg1_lift.lt_translation_number_of_forall_add_lt", "Top.subsheaf_to_Types_sheaf_condition", "fin.cases_succ", "cau_seq.le_of_eq_of_le", "mv_polynomial.map_id", "is_topological_fiber_bundle.is_open_map_proj", "free_group.map_one", "composition_as_set.ext_iff", "int.lt_add_of_le_of_pos", "real.pi_gt_31415", "convex_hull_eq_union", "lucas_lehmer.X.nat_coe_fst", "linear_equiv.of_injective_endo_to_fun", "filter.eventually.prod_inr_nhds", "category_theory.limits.biprod.map_eq_map'", "abs_add", "linear_equiv_matrix_symm_one", "isometry.ediam_image", "measure_theory.l1.simple_func.of_simple_func_zero", "nnreal.div_self", "category_theory.limits.pullback_cone.mk_\[Pi]_app_left", "inner_product_geometry.angle_self", "add_subgroup.map_supr", "stream.nth_interleave_right", "localization_map.eq_mk'_iff_mul_eq", "fin.coe_two", "of_digits_modeq'", "add_sub_add_right_eq_sub", "eq_comm", "add_con.lift_on_beta", "measure_theory.ae_eq_fun.smul_mk", "mem_closure", "decidable.by_contradiction", "is_coprime.of_mul_right_right", "asymptotics.is_o.symm", "relation.refl_trans_gen_iff_eq", "uniform_space.completion.induction_on", "category_theory.limits.cofork.coequalizer_ext", "many_one_reducible.mk", "subsemiring.prod_mono", "add_lt_add", "embedding_subtype_coe", "pos_of_mul_pos_right", "category_theory.preadditive.epi_of_cancel_zero", "holor.slice_eq", "add_submonoid.localization_map.of_add_equiv_of_dom_eq", "padic_int.norm_lt_one_add", "mvqpf.fix.ind", "cardinal.min_eq", "times_cont_diff_const", "complex.I_mul", "stream.iterate_eq", "convex_hull_ediam", "vector.m_of_fn_pure", "computable.cond", "nat.sqrt_succ_le_succ_sqrt", "submodule.mem_span_singleton_self", "power_series.constant_coeff_X", "add_equiv.refl_apply", "category_theory.split_mono.id", "measure_theory.ae_eq_fun.coe_fn_const", "option.get_or_else_of_ne_none", "set.mem_Ioo_or_eq_left_of_mem_Ico", "buffer.lt_aux_2", "category_theory.category_of_elements.\[Pi]_map", "free_abelian_group.lift_comp", "lt_trichotomy", "complex.of_real_one", "measure_theory.ae_eq_fun.coe_fn_pos_part", "ordinal.CNF_zero", "simple_graph.adj_matrix_mul_apply", "eq_iff_eq_cancel_right", "filter.tendsto.congr", "is_compact.is_closed", "polynomial.degree_div_lt", "primrec.list_cases", "structure_groupoid.local_invariant_prop.lift_prop_within_at_of_lift_prop_at_of_mem_nhds", "submodule.comap_zero", "polynomial.degree_pos_of_root", "nat.add_left_cancel", "set.mem_range_self", "add_submonoid.mrange_inl'", "max.right_comm", "affine_map.line_map_vadd_neg", "ctop.mem_nhds_to_topsp", "cau_seq.inv_apply", "smooth_at.times_cont_mdiff_at", "inv_unique", "measure_theory.measure_Union", "derive_fintype.finset_above.mem_union_right", "list.eq_nil_iff_forall_not_mem", "filter.join_pure", "pi.add_apply", "add_monoid_hom.coe_snd", "cau_seq.completion.mk_eq_zero", "nhds_within_eq_nhds_within", "nat.prime_def_lt'", "add_equiv.map_sub", "is_coprime.pow_right", "inv_nonpos", "has_fderiv_within_at.const_mul", "nat.dist_eq_sub_of_le_right", "set.finite.dinduction_on", "int.neg_eq_neg_one_mul", "bool.bnot_bor", "ring.fractional_ideal.coe_span_singleton", "pequiv.trans_single_of_eq_none", "finset.eq_empty_of_forall_not_mem", "pos_num.cast_bit1", "has_deriv_at_inv", "filter.eventually.curry", "is_closed_iff_nhds", "is_unit.coe_lift_right", "num.cast_le", "category_theory.category_of_elements.from_comma_obj", "algebra.smul_def''", "ennreal.lt_top_of_mul_lt_top_right", "complex.norm_sq_zero", "interval_integral.fderiv_within_integral_of_tendsto_ae", "padic.of_rat_div", "finset.sum_le_sum_of_subset", "quadratic_form.smul_apply", "list.unzip_cons", "real.arccos_inj", "ennreal.of_real_zero", "set.preimage_sub_const_Ioc", "matrix.head_val'", "filter.order_bot.at_bot_eq", "real.rpow_le_rpow_of_exponent_ge", "div_fpow", "complex.two_sin", "add_submonoid.coe_infi", "turing.to_partrec.step_normal_eval", "category_theory.monoidal.functor_category.tensor_obj_map", "list.minimum_mem", "topological_space.opens.mk_inf_mk", "structure_groupoid.local_invariant_prop.lift_prop_on_of_mem_maximal_atlas", "complex.of_real_add", "segment_eq_Icc", "set.Ioo_subset_Ioo_union_Ico", "deriv_log'", "equiv.sum_congr_apply", "continuous_linear_map.op_norm_zero_iff", "has_strict_fderiv_at.implicit_to_local_homeomorph_apply_ker", "linear_map.proj_std_basis_same", "list.Ico.length", "list.mem_of_mem_head'", "list.prod_map_hom", "continuous_linear_map.le_op_norm_of_le", "submonoid.ext", "nat.factors_add_two", "finset.filter_false", "category_theory.nat_iso.of_components.hom_app", "continuous_multilinear_map.map_add", "free_add_monoid.lift_restrict", "encodable.encode_some", "mjoin_map_pure", "mul_lt_iff_lt_one_left'", "cfilter.of_equiv_val", "is_semiring_hom.comp", "matrix.cons_mul", "wseq.destruct_congr", "interval_integrable.smul", "nat.one_lt_fact", "list.drop_take", "linear_map.ker_le_ker_comp", "list.bag_inter_sublist_left", "ne_of_ne_of_eq", "nat.coprime.coprime_mul_right", "real.neg_one_lt_div_sqrt_one_add", "list.perm.foldl_eq", "is_integral_of_is_scalar_tower", "finset.filter_insert", "measure_theory.measure.smul_apply", "znum.add_zero", "add_submonoid.localization_map.add_equiv_of_localizations_right_neg", "inv_lt_inv_of_neg", "ideal.add_mem_iff_right", "inf_top_eq", "well_founded.not_lt_min", "mul_equiv.coe_mk", "function.semiconj.surj_on_image", "ennreal.sub_sub_cancel", "filter_basis.mem_filter_of_mem", "circle_deg1_lift.dist_map_map_zero_lt", "commute.units_inv_left_iff", "list.nil_map\:2082", "bounded_continuous_function.bounded_range", "rel_embedding.of_monotone_coe", "list.Ico.not_mem_top", "Cauchy.dense_inducing_pure_cauchy", "composition_as_set.lt_length'", "category_theory.limits.prod.lift_fst_assoc", "matrix.tail_transpose", "complex.sin_nat_mul_pi", "continuous_linear_equiv.equiv_of_right_inverse_symm_apply", "polynomial.roots_zero", "matrix.update_row_transpose", "ennreal.coe_nat_lt_coe", "free_comm_ring.map_of", "mul_right_bound", "submodule.mem_right_iff_eq_zero_of_disjoint", "measure_theory.simple_func.fin_meas_supp.iff_lintegral_lt_top", "asymptotics.is_O_with_snd_prod", "set.inj_on.left_inv_on_inv_fun_on", "lipschitz_with.add", "uniform_space.uniform_continuous_quotient_lift", "prime_multiset.coe_pnat_of_prime", "composition.size_up_to_index_le", "relator.rel_or", "category_theory.limits.pullback.hom_ext", "category_theory.functor.equiv_unit_iso", "bilin_form.coe_fn_mk", "times_cont_diff_on.differentiable_on", "cardinal.univ_id", "squeeze_zero_norm", "circle_deg1_lift.coe_mul", "linear_map.ker_comp", "set.bUnion_insert", "topological_fiber_bundle_core.mem_local_triv'_source", "polynomial.mem_map_range", "polynomial.card_roots_X_pow_sub_C", "tsum_comm", "AddCommGroup.kernel_iso_ker_over_hom_left_to_fun_val", "pi.zero_comp", "continuous_linear_map.lmul_right_norm", "padic_val_rat.pow", "free_semigroup.lift_of", "finsupp.support_mul", "metric.continuous_within_at_iff", "multiset.nodup_cons", "euclidean_domain.zero_div", "pos_num.cast_succ", "category_theory.limits.binary_bicone.to_cocone_\[Iota]_app_right", "linear_map.pair_fst_snd", "cau_seq.completion.inv_mul_cancel", "nat.dvd_sub", "finset.smul_sum", "continuous_linear_equiv.eq_symm_apply", "closed_embedding.continuous", "homeomorph.self_comp_symm", "interior_inter", "computable.map_decode_iff", "list.Ico.inter_consecutive", "list.not_perm_nil_cons", "list.array_eq_of_fn", "nat.subtype.of_nat_surjective_aux", "algebra.tensor_product.tmul_pow", "continuous_I_symm", "subgroup.coe_Inf", "int.neg_succ_of_nat_mul_sub_nat_nat", "isometric.apply_inv_self", "structure_groupoid.local_invariant_prop.lift_prop_on_congr_iff", "category_theory.monoidal_of_has_finite_products.associator_hom", "ring_hom.map_zero", "mv_polynomial.single_eq_C_mul_X", "abstract_completion.uniform_continuous_compare_equiv_symm", "omega.update_eq_of_ne", "magma.free_semigroup.of_mul_assoc_right", "list.sublists_aux_eq_foldr.aux", "finset.pi_empty", "localization_map.sec_spec", "convex_cone.map_map", "has_strict_deriv_at.sub", "image_sub_lt_mul_sub_of_deriv_lt", "rat.nonneg_mul", "polynomial.map_ne_zero", "set.Iic_subset_Iio_union_Icc", "nnreal.of_real_zero", "circle_deg1_lift.coe_inj", "subgroup.comap_top", "mv_polynomial.iter_to_sum_C_X", "mvqpf.Wrepr_W_mk", "finsupp.dim_eq", "seq.zip_with_nth_none'", "pow_dvd_pow_iff", "convex.translate", "vsub_set_singleton", "ordinal.lift_succ", "tangent_bundle.times_cont_mdiff_at_proj", "affine_subspace.sup_direction_le", "fderiv_within.comp", "set.empty_not_nonempty", "primrec\:2082.const", "ennreal.zero_lt_sub_iff_lt", "multiset.powerset_aux_eq_map_coe", "differentiable_id", "int.le_add_of_sub_left_le", "upper_bounds_singleton", "add_lie", "continuous.smul", "padic_norm_z.pow", "znum.mul_to_int", "path_component_symm", "is_measurable_closure", "tangent_map_comp", "continuous_at_of_strict_mono_surjective", "submonoid.comap_strict_mono_of_surjective", "multiset.map_filter_map_of_inv", "filter.eventually.mp", "ordinal.infinite_pigeonhole_set", "filter.prod_map_seq_comm", "is_local_max.comp_continuous_on", "filter.limsup_eq_infi_supr_of_nat", "hyperreal.infinite_neg_mul_infinite_pos", "wseq.lift_rel_join.lem", "modeq_nine_digits_sum", "nnreal.rpow_le_rpow_iff", "multiset.ndinsert_zero", "subalgebra.mem_to_submodule", "submonoid.localization_map.lift_mul_left", "submonoid.one_mem", "finset.mem_union_left", "infi_or", "fin.pred_succ", "nat.gcd_le_right", "ring_hom.id_apply", "times_cont_mdiff.comp_times_cont_mdiff_on", "category_theory.biprod.unipotent_upper_inv", "category_theory.limits.cocones.forget_map", "galois_coinsertion.u_l_eq", "is_unit_map_iff", "add_subgroup.ext", "finsupp.support_smul", "cardinal.mk_emptyc", "cau_seq.mk_to_fun", "complex.ext", "with_bot.coe_le", "dist_add_add_le_of_le", "ne_self_iff_false", "category_theory.curry_natural_right", "is_compact.compl_mem_sets_of_nhds_within", "tangent_bundle.smooth_on_proj", "list.exists_of_erasep", "Set.omega_zero", "inter_mem_nhds_within", "nnreal.sub_self", "finset_is_basis_of_span_eq_top_of_card_eq_findim", "coe_frobenius_equiv", "module.direct_limit.of.zero_exact", "is_closed_Union", "linear_map.disjoint_inl_inr", "CommRing.colimits.quot_neg", "linear_map.coe_mk", "free_abelian_group.induction_on'", "commute.eq", "contracting_with.edist_efixed_point_lt_top", "fintype.mem_pi_finset", "nat.cast_sub", "differentiable_on.snd", "is_R_or_C.of_real_zero", "bool.eq_ff_of_ne_tt", "filter.germ.coe_comp_tendsto", "primrec.id", "units.inv_mul_eq_iff_eq_mul", "computation.return_def", "real.cos_pi_div_two", "matrix.neg_dot_product", "turing.TM2.stmts\:2081_trans", "wseq.seq_destruct_think", "relation.refl_trans_gen_closed", "submonoid.localization_map.mk'_mul_cancel_right", "asymptotics.is_O_with_of_le", "set.inj_on.bij_on_image", "set.ne_insert_of_not_mem", "is_compl.inf_right_eq_bot_iff", "algebra.adjoin_eq_range", "presented_group.to_group.of", "cardinal.mk_pempty", "semiconj_by.add_left", "forall_congr", "typevec.drop_append1", "set.inter_compl_self", "let_value_eq", "function.bij_on_periodic_pts", "norm_num.nat_cast_ne", "bdd_below_insert", "function.injective.ne", "submodule.ne_bot_iff", "nat.mem_rfind", "finset.mk_coe", "equiv.prod_assoc_sym_apply", "category_theory.non_preadditive_abelian.add_neg_self", "set.preimage_sUnion", "simple_graph.mem_edge_set", "matrix.zero_mul", "set.seq_def", "list.count_le_of_sublist", "multilinear_map.norm_image_sub_le_of_bound", "valuation.is_equiv.map", "Mon.colimits.cocone_naturality_components", "ordinal.add_absorp", "zero_nsmul", "skew_adjoint_matrices_lie_subalgebra_equiv_transpose_apply", "set.preimage_preimage", "turing.tape.write_nth", "is_R_or_C.of_real_re", "ordinal.lt_sub", "abs_eq", "with_one.lift_coe", "add_monoid_hom.eq_lift_of_surjective", "nat.modeq.modeq_and_modeq_iff_modeq_mul", "measure_theory.simple_func.restrict_mono", "list.sum_map_mul_right", "multiset.disjoint_of_le_right", "rat.mul_self_denom", "eq_zero_of_right_cancel_add_self", "finset.mem_of_mem_inter_left", "measure_theory.measure.restrict_add", "subgroup.normal.mem_comm", "pythagorean_triple.ne_zero_of_coprime", "cardinal.finset_card_lt_omega", "measure_theory.lintegral_zero_measure", "compact_iff_ultrafilter_le_nhds", "cardinal.mk_sUnion_le", "polynomial.eval_mul", "zmod.prod_Ico_one_prime", "AddGroup.zero_apply", "strict_mono.injective", "has_fderiv_within_at.has_fderiv_at", "finmap.mem_erase", "fintype.bijective_bij_inv", "hyperreal.not_infinite_iff_exist_lt_gt", "nhds_left_sup_nhds_right'", "add_units.add_right_inj", "measure_theory.lintegral_mono_ae", "fderiv_within_inv", "nat.primes.coe_pnat_inj", "lower_bounds_mono_set", "sum_card_order_of_eq_card_pow_eq_one", "set.image2_image2_right", "is_basis.mk_eq_dim", "matrix.col_smul", "category_theory.functor.op_hom_obj", "category_theory.equivalence.refl_inverse", "linear_recurrence.sol_space_dim", "int.prime.dvd_nat_abs_of_coe_dvd_pow_two", "finset.insert_union", "polynomial.eval\:2082_pow", "with_bot.none_eq_bot", "nat.succ_add_sub_one", "list.sum_repeat", "ordinal.is_normal.le_self", "nat.div2_val", "Cauchy.monotone_gen", "list.sum_of_fn", "is_R_or_C.re_eq_add_conj", "polynomial.coeff_map", "is_local_min.max", "category_theory.nat_trans.ext", "cardinal.nat_cast_inj", "sup_bot_eq", "cau_seq.completion.of_rat_mul", "finset.prod_univ_sum", "multiset.powerset_len_aux_eq_map_coe", "int.coe_nat_succ", "lucas_lehmer.\[Omega]_unit_coe", "differentiable_on_snd", "polynomial.map_sub", "cardinal.aleph'_succ", "category_theory.functor.id_comp", "vector.id_traverse", "typevec.append_fun_id_id", "circle_deg1_lift.translation_number_mul_of_commute", "measure_theory.tendsto_lintegral_filter_of_dominated_convergence", "group.conjugates_of_set_mono", "ring_hom.eq_of_eq_on_sdense", "multiset.prod_add", "int.sub_nonneg_of_le", "basic_smooth_bundle_core.times_cont_mdiff_at_proj", "mem_right_add_coset_iff", "mv_polynomial.C_mul", "nonempty_interior_of_Union_of_closed", "measure_theory.l1.norm_eq", "one_div_neg_one_eq_neg_one", "real.sqrt_pos", "list.mem_inter_of_mem_of_mem", "polynomial.eval_map", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_inv_comp_assoc", "Inf_range", "list.keys_kerase", "real.Sup_def", "eventually_eq_nhds_within_iff", "measurable.smul", "list.permutations_aux_nil", "nat.pos_iff_ne_zero", "matrix.cons_val'", "int.coe_nat_eq_coe_nat_iff", "ring_hom.map_pow", "gcd_one_right", "int.bodd_zero", "set.finite_empty", "list.kreplace_nodupkeys", "finset.singleton_inter_of_not_mem", "subring.prod_mem", "category_theory.limits.colimit.post_desc", "list.map_lookup_eq_find", "multiset.mem_range", "times_cont_diff_within_at.differentiable_within_at'", "complex.arg_neg_I", "nat.one_succ_zero", "metric.diam_union", "times_cont_mdiff_on.comp'", "directed_of_sup", "filter.gc_map_comap", "int.neg_succ_of_nat_div", "matrix.empty_mul", "int.test_bit_lnot", "wseq.equiv.refl", "unique_diff_on_Icc", "zsqrtd.neg_re", "computation.map_ret", "list.lex.imp", "category_theory.over.post_obj", "category_theory.functor.sum_map_inr", "category_theory.limits.image.map_comp", "measurable_space.comap_mono", "canonically_ordered_semiring.pow_le_one", "computation.exists_of_lift_rel_right", "list.foldl_argmax\:2082_eq_none", "pow_sub", "homeomorph.embedding", "has_deriv_at.lhopital_zero_at_bot_on_Iio", "dif_eq_if", "submodule.subtype_eq_val", "ennreal.is_open_Ico_zero", "list.Ico.succ_singleton", "finset.subset_union_elim", "filter.tendsto_at_top_at_top_of_monotone'", "category_theory.monoidal_category.tensor_right_tensor_inv_app", "commute.cast_nat_mul_right", "add_right_neg", "int.div_mul_le", "hyperreal.infinitesimal_def", "linear_equiv.map_add", "polynomial.splits'", "lcm_mul_right", "option.is_some_none", "pnat.xgcd_type.step_is_special", "linear_equiv.ext", "set.Iic_subset_Iic_union_Icc", "add_subgroup.normal.comap", "smooth_neg", "list.argmin_nil", "has_deriv_within_at_const", "ennreal.top_ne_of_real", "polynomial.degree_normalize", "iff_iff_implies_and_implies", "gaussian_int.to_complex_eq_zero", "polynomial.div_by_monic_zero", "continuous_multilinear_map.uncurry0_curry0", "adjoin_root.algebra_map_eq", "padic.coe_sub", "finset.erase_ssubset", "many_one_degree.add_le'", "list.perm.sum_eq'", "continuous_within_at_Ico_iff_Ici", "equivariant_projection_condition", "polynomial.dvd_iff_mod_by_monic_eq_zero", "filter.eventually_le.is_local_min", "list.perm_of_mem_permutations_aux", "set.finite_singleton", "times_cont_diff_on.congr_mono", "times_cont_diff.continuous_linear_map_comp", "add_lt_of_lt_sub_right", "category_theory.functor.to_cone_\[Pi]_app", "nat.sub_eq_of_eq_add", "set.univ_pi_eq_empty", "complex.sin_add_pi", "quot.eqv_gen_sound", "convex_on.add", "mul_le_mul_right'", "nat.mul_pow", "dioph.xn_dioph", "affine.simplex.circumcenter_eq_affine_combination_of_points_with_circumcenter", "complex.norm_sq_conj", "fin.pred_one", "norm_num.nat_cast_one", "multiset.foldr_swap", "padic_int.norm_sub_mod_part", "lipschitz_with.of_dist_le'", "set.inter_compl_nonempty_iff", "minimal_polynomial.dvd", "dfinsupp.mk_zero", "Inf_singleton", "zmod.cast_one", "omega.nat.holds_is_diff", "multiset.card_eq_one", "measure_theory.measure.measurable_map", "filter.extraction_of_frequently_at_top'", "function.comp_update", "metric.Hausdorff_dist_le_of_mem_dist", "complex.sub_conj", "minimal_polynomial.zero", "linear_independent.repr_eq_single", "circle_deg1_lift.coe_pow", "commute.pow_pow", "ideal.comap_le_iff_le_map", "stream.cycle_singleton", "ereal.neg_inj", "emetric.diam_insert", "int.to_nat_le", "measure_theory.measure.one_le_haar_outer_measure_self", "nat.div_lt_self'", "submodule.bot_coe", "finset.filter_eq", "multiset.fold_union_inter", "quotient.fin_choice_eq", "div_le_div_of_le_left", "bdd_below.mono", "dvd_mul_right", "submonoid.localization_map.lift_eq", "power_series.coeff_one", "padic_norm_e.norm_int_lt_one_iff_dvd", "roption.bind_defined", "homological_complex.homology_obj", "zsqrtd.norm_nonneg", "finset.mono_of_fin_unique", "functor.map_equiv_symm_apply", "applicative.ext", "complex.of_real_im", "add_equiv.map_neg", "zero_lt_mul_left", "finsupp.monotone_to_fun", "filter.tendsto_at_top", "real.cos_neg_of_pi_div_two_lt_of_lt", "holor.mul_right_distrib", "set.left_inv_on.inj_on", "set.preimage_add_const_Ico", "nat.rfind_zero_none", "nat.one_ne_bit0", "has_fderiv_at_iff_has_deriv_at", "bilin_form.mem_is_pair_self_adjoint_submodule", "continuous_norm", "set.piecewise_compl", "prod.snd_sub", "filter.tendsto_at_bot_of_add_bdd_below_left", "metric.continuous_iff'", "measure_theory.measure.join_eq_bind", "set.univ_prod_univ", "category_theory.over.mk_hom", "le_neg_iff_add_nonpos", "nat.partrec.code.encode_code_eq", "linear_equiv.to_equiv_injective", "measurable_dist", "mvqpf.liftr_map", "mv_power_series.constant_coeff_zero", "mul_left_bound", "hyperreal.is_st_trans_real", "multiplicity.min_le_multiplicity_add", "bdd_above.union", "primorial_succ", "list.disjoint_comm", "lipschitz_with.edist_iterate_succ_le_geometric", "real.Sup_empty", "padic.coe_one", "one_div_le_one_div_of_neg_of_le", "nat.le_rec_on_injective", "ultrafilter_extend_eq_iff", "lt_inv'", "real.arcsin_nonpos", "metric.bounded_ball", "is_R_or_C.of_real_inv", "topological_space.compacts.equiv_to_fun_val", "list.sublists_aux\:2081_append", "polynomial.nat_degree_X_sub_C", "real.sin_pi_div_two_sub", "pnat.xgcd_type.reduce_v", "has_sum_iff_has_sum_of_ne_zero_bij", "eq_tt_of_not_eq_ff", "cardinal.le_mk_iff_exists_subset", "cardinal.cantor_function_aux_succ", "set.dual_Ioc", "nnreal.coe_pos", "list.index_of_argmin", "polynomial.eisenstein_criterion_aux.is_unit_of_nat_degree_eq_zero_of_forall_dvd_is_unit", "set.Iic_subset_Iio", "category_theory.limits.colimit.desc_extend", "multiset.choose_spec", "topological_space.mem_nhds_of_is_topological_basis", "complex.tan_neg", "has_fderiv_at_filter.add", "mv_power_series.constant_coeff_one", "set.union_diff_distrib", "ideal.mem_leading_coeff_nth_zero", "isometry.ediam_range", "multiset.coe_fold_r", "finset.fold_image", "int.neg_of_nat_mul_neg_succ_of_nat", "euclidean_geometry.exists_dist_eq_iff_exists_dist_orthogonal_projection_eq", "nat.cast_add", "linear_map.to_continuous_linear_map\:2081_coe", "setoid.eqv_gen_le", "free_add_semigroup.add_seq", "string.str_ne_str_left", "structure_groupoid.eq_on_source", "hyperreal.eq_of_is_st_real", "mul_left_surjective", "multiset.powerset_cons", "affine_subspace.vadd_mem_mk'", "pnat.factor_multiset_le_iff'", "submodule.span_mul_span", "disjoint.mono", "encodable.encodek2", "set.surj_on.comap_nonempty", "is_null_measurable.union_null", "real.cos_nonneg_of_neg_pi_div_two_le_of_le_pi_div_two", "generalized_continued_fraction.terminated_at_iff_part_denom_none", "continuous_sigma", "gmultiples_subset", "subgroup.list_prod_mem", "polynomial.degree_mul'", "div_lt_div_of_neg_of_lt", "many_one_equiv.symm", "add_submonoid.coe_Inf", "multiplicative.is_monoid_hom", "asymptotics.is_O_with_const_mul_self", "no_bot", "cardinal.ord_eq", "measure_theory.integrable_neg_iff", "add_submonoid.localization_map.lift_mk'", "polynomial.map_expand_pow_char", "eq_mul_of_inv_mul_eq", "finset.prod_nonneg", "free_monoid.lift_symm_apply", "forall_not_of_not_exists", "ordered_add_comm_group.lt_of_add_lt_add_left", "dense_embedding.mk'", "filter.eventually.curry_nhds", "continuous_multilinear_map.unit_le_op_norm", "dist_le_tsum_dist_of_tendsto", "measure_theory.measure.finite_at_filter.measure_mono", "ring_hom.map_one", "finsupp.subtype_domain_neg", "asymptotics.is_o_comm", "set.one_nonempty", "has_strict_fderiv_at.image_mem_to_local_homeomorph_target", "ideal.map_infi_comap_of_surjective", "nat.bit_val", "generalized_continued_fraction.numerators_stable_of_terminated", "list.exists_of_mem_map", "char_p.char_ne_one", "list.lookup_all_eq_lookup", "lucas_lehmer.residue_eq_zero_iff_s_mod_eq_zero", "category_theory.preimage_map", "filter.eventually_le.eventually_le_nhds", "list.foldr_reverse", "fintype.exists_pair_of_one_lt_card", "denumerable.of_equiv_of_nat", "mjoin_map_mjoin", "multiset.forall_of_pairwise", "ordinal.is_normal.le_set", "has_strict_fderiv_at.implicit_to_local_homeomorph_fst", "nat.mod_def_aux", "ennreal.add_lt_top", "multiset.le_cons_self", "uniform_inducing.mk'", "nat.sub_le_left_of_le_add", "ennreal.le_inv_iff_mul_le", "subalgebra.pow_mem", "well_founded.fix_F_eq", "irrational.of_add_rat", "finsupp.finite_le_nat", "generalized_continued_fraction.terminated_at_iff_part_num_none", "subring.comap_inf", "localization_map.lift_surjective_iff", "right_ord_continuous.map_cinfi", "asymptotics.is_O_with.smul", "and.rotate", "times_cont_diff_within_at.comp'", "pi.inv_apply", "list.sublist.append_right", "le_of_inv_le_inv", "measure_theory.simple_func.add_apply", "int.add_pos_of_pos_of_nonneg", "category_theory.limits.pushout_cocone.condition", "measure_theory.l1.norm_of_fun", "roption.mem_some_iff", "mvpfunctor.comp.get_mk", "Top.sheaf_condition.fork_X", "seq_map_assoc", "nhds_within_le_of_mem", "poly_equiv_tensor.to_fun_linear_mul_tmul_mul_aux_1", "vector_span_eq_span_vsub_set_right_ne", "bilin_form.sub_right", "ennreal.coe_pow", "times_cont_mdiff_at.times_cont_mdiff_within_at", "ordinal.unbounded_range_of_sup_ge", "euclidean_geometry.dist_eq_iff_dist_orthogonal_projection_eq", "submonoid.localization_map.mul_equiv_of_localizations_right_inv", "gold_mul_gold_conj", "has_deriv_at.rpow_of_one_le", "add_equiv.apply_symm_apply", "filter.lift_lift_same_eq_lift", "or_not", "free_abelian_group.lift.add", "int.coe_nat_abs_eq_normalize", "category_theory.under.limit_\[Pi]_app", "set.singleton.is_mul_hom", "submodule.inf_coe", "polynomial.C_mul'", "category_theory.functor.map_injective", "gronwall_bound_\[CurlyEpsilon]0_\[Delta]0", "list.not_mem_of_not_mem_cons", "ordinal.one_le_iff_pos", "alg_hom.injective_iff", "is_R_or_C.abs_abs", "filter.le_seq", "computable.comp\:2082", "deriv_ccosh", "add_monoid.mem_closure_union_iff", "continuous_linear_map.coe_fst'", "with_zero.inv_zero", "composition.monotone_size_up_to", "mul_action.of_quotient_stabilizer_mem_orbit", "submonoid.coe_copy", "primrec.ulower_down", "dioph.dioph_fn_iff_pfun", "add_subgroup.mem_Sup_of_mem", "subalgebra.mem_coe", "pgame.add_le_add_left", "convex.linear_image", "zsqrtd.le_trans", "setoid.sup_eq_eqv_gen", "differentiable_within_at.exp", "abs_pos_of_pos", "algebra.adjoin_union", "except_t.run_bind", "roption.eq_none_iff", "dvd_mul_sub_mul", "add_submonoid.map_le_of_le_comap", "set.finite.union", "monotone_and", "infi_prod", "eq_of_abs_sub_eq_zero", "multiset.nodup_of_nodup_map", "finset.filter_congr", "ennreal.rpow_le_rpow", "int.mul_mod_right", "uniform_continuous_of_tendsto_zero", "simple_graph.neighbor_finset_eq_filter", "constr_range", "char_p.sum_two_squares", "complex.arg_of_real_of_nonneg", "with_one.some_eq_coe", "nat.sub_lt_sub_add_sub", "turing.partrec_to_TM2.succ_ok", "continuous_linear_map.lmul_left_right_is_bounded_bilinear", "basic_smooth_bundle_core.smooth_proj", "subsemiring.mem_top", "category_theory.limits.span_map_fst", "is_lub_cSup", "set.right_inv_on.congr_right", "list.func.length_add", "tsum_le_tsum", "finset.mem_sigma", "tsum_eq_zero_of_not_summable", "nat.le_pred_of_lt", "if_true_left_eq_or", "semiconj_by.zero_left", "lie_algebra.of_associative_algebra_hom_comp", "lt_of_neg_lt_neg", "list.alternating_sum_singleton", "int.nat_abs_dvd_abs_iff", "topological_space.is_open_generated_countable_inter", "is_seq_compact.subseq_of_frequently_in", "field.closure_subset_iff", "card_lt_card_of_injective_of_not_mem", "set.seq_singleton", "rat.continuous_abs", "ring.fractional_ideal.mul_inv_cancel_iff", "is_bounded_bilinear_map_smul_right", "mvqpf.const.map_mk", "finsupp.mem_frange", "measure_theory.borel_le_lebesgue_measurable", "norm_num.int_mod", "sup_le_iff", "ring.direct_limit.of_sub", "mul_lt_one_of_nonneg_of_lt_one_left", "filter.inf_principal_eq_bot", "mul_ite", "set.Union_subset_Union", "ideal.comap_ne_bot_of_root_mem", "measure_theory.l1.pos_part_to_fun", "filter.ne_bot.ne", "list.rotate'_eq_take_append_drop", "measure_theory.simple_func.fin_meas_supp.integrable", "filter.infi_sets_eq_finite'", "dist_bdd_within_interval", "list.count_erase_of_ne", "t2_iff_ultrafilter", "disjoint.comm", "filter.Liminf_principal", "bdd_above_union", "bounded_continuous_function.continuous_evalf", "subsemiring.sum_mem", "min_sub", "local_homeomorph.mdifferentiable.symm", "matrix.vec_mul_vec_empty", "iff.comm", "compl_top", "add_submonoid.le_def", "finset.sum_powerset_insert", "continuous_within_at_Ioi_iff_Ici", "onote.repr_add", "equiv.to_iso_inv", "set.mem_Iio", "add_right_inj", "is_local_max_on.comp_antimono", "mv_polynomial.is_noetherian_ring_fin_0", "dist_triangle4", "finset.map_inter", "mul_div_cancel", "mul_equiv.to_CommMon_iso_hom", "turing.partrec_to_TM2.K'.elim_update_aux", "inv_mul_cancel", "filter.eventually_le.is_local_min_on", "piecewise_ae_eq_restrict", "supr_le", "pnat.coprime_one", "mul_action.of_quotient_stabilizer_mk", "list.count_repeat", "measure_theory.l1.simple_func.norm_eq'", "dfinsupp.sum_finset_sum_index", "differentiable_on.sum", "polynomial.coe_aeval_eq_eval", "finset.eq_empty_iff_forall_not_mem", "submonoid.localization_map.lift_surjective_iff", "zorn.chain.image", "formal_multilinear_series.bound_of_lt_radius", "measure_theory.tendsto_integral_filter_of_dominated_convergence", "zmod.cast_nat_cast", "eq.congr_right", "fixed_points.f_le_inf_of_fixed_points", "add_submonoid.closure_le", "real.rpow_add", "inner_sub_right", "asymptotics.is_O_with_neg_right", "finset.coe_inj", "add_submonoid.exists_list_of_mem_closure", "dist_sub_sub_le_of_le", "list.perm.append_cons", "tsum_geometric_two'", "convex.inter", "pgame.add_left_neg_le_zero", "Top.presheaf.germ_exist", "continuous_on_fst", "int.neg_add_lt_left_of_lt_add", "mvpfunctor.W_map_W_mk", "submodule.inner_left_of_mem_orthogonal", "zsqrtd.sq_le_add_mixed", "loc_path_connected_of_bases", "comp_comp_symm_mem_uniformity_sets", "measure_theory.ae_eq_fun.edist_eq_coe'", "complex.inv_I", "filter.has_basis_infi_principal_finite", "subring.coe_to_submonoid", "order_topology_of_nhds_abs", "is_add_unit.add_lift_right_neg", "fintype.prod_unique", "list.erase_dupkeys_cons", "one_le_pow_of_one_le", "bool.bxor_left_comm", "Mon_.id_hom", "category_theory.arrow.hom_mk_left", "interior_univ", "bool.band_left_comm", "finset.sum_union_inter", "zsqrtd.nonneg_smul", "multiset.mem_powerset_len_aux", "is_measurable.subtype_image", "filter.eventually_eq.is_local_max_iff", "finset.min'_lt_max'", "matrix.transpose_transpose", "with_top.one_eq_coe", "equiv.perm.same_cycle_inv", "mdifferentiable_at.mdifferentiable_within_at", "closed_embedding.closed_iff_preimage_closed", "euclidean_geometry.angle_eq_left", "local_homeomorph.of_set_to_local_equiv", "is_basis.equiv_fun_symm_apply", "multiset.erase_dup_eq_self", "is_compact.finite_measure", "rel.core_mono", "mv_polynomial.is_homogeneous_X", "list.prod_join", "filter.tendsto.mono_right", "tactic.ring_exp.inverse_pf", "filter.comap_sup", "omega.sat_empty", "differentiable_on.csin", "pth_root_frobenius", "nat.succ_pred_prime", "subgroup.coe_one", "orthogonal_projection_mem", "tactic.ring_exp.mul_p_pf_zero", "mem_non_zero_divisors_iff_ne_zero", "mul_equiv.refl_apply", "is_min_on.of_is_local_min_on_of_convex_on_Icc", "category_theory.functor.right_adjoint_of_is_equivalence", "list.lookup_cons_ne", "norm_add_mul_self", "Class.mem_hom_right", "pfun.lift_eq_coe", "is_local_min_on.is_local_min", "measure_theory.measure.haar.index_elim", "submonoid.localization_map.exists_of_sec_mk'", "summable_zero", "finset.exists_smaller_set", "category_theory.comonad.coalgebra.EilenbergMoore_to_category_struct_comp", "real.one_rpow", "complex.of_real_eq_zero", "initial_seg.antisymm.aux", "real.log_mul", "continuous_of_discrete_topology", "real.sin_nat_mul_pi", "composition.of_fn_blocks_fun", "is_adic_complete.subsingleton", "is_min_on.of_is_local_min_of_convex_univ", "is_R_or_C.of_real_to_complex", "category_theory.functor.const.op_obj_unop_inv_app", "real.le_Sup", "nnreal.sub_le_iff_le_add", "nnreal.coe_mk", "real.totally_bounded_Ico", "polynomial.expand_expand", "multiset.mem_sort", "filter.mem_mul", "con.lift_mk'", "set.prod_nonempty_iff", "subgroup.mem_Sup_of_directed_on", "is_measurable_inr_image", "ennreal.sub_le_of_sub_le", "quadratic_form.proj_apply", "subgroup.map_le_iff_le_comap", "free_group.to_group.mk", "polynomial.eq_prod_roots_of_separable", "zmod.inv_mul_of_unit", "nat.sub_lt", "half_le_harmonic_double_sub_harmonic", "with_top.is_glb_Inf'", "norm_num.bit1_succ", "dioph.dioph_fn_compn", "measure_theory.simple_func.range_comp_subset_range", "is_measurable.diff", "differentiable_on.smul_const", "measure_theory.outer_measure.of_content_preimage", "has_mfderiv_within_at.mfderiv_within", "continuous_of_rat", "is_compact.Inf_mem", "category_theory.limits.pushout.inl_desc", "category_theory.equivalence.cancel_counit_inv_right_assoc'", "bool.to_bool_or", "rat.cast_sub", "is_scalar_tower.smul_left_comm", "linarith.eq_of_eq_of_eq", "category_theory.monad_hom.id_comp", "category_theory.limits.pullback.lift_snd", "reader_t.ext", "matrix.transpose_smul", "has_deriv_within_at.csinh", "nat.partrec.merge'", "times_cont_diff_on_fderiv_within_apply", "set.preimage_const_sub_Ioi", "tendsto_subseq_of_frequently_bounded", "nndist_eq_nnnorm", "imp_true_iff", "reflect_lt", "int.gcd_eq_zero_iff", "affine_subspace.direction_top", "multiset.rel_map_right", "complex.abs_sub", "submonoid.map_comap_eq_of_surjective", "add_con.eq", "set.Inter_subset_of_subset", "antilipschitz_with.uniform_embedding", "infi_le_of_le", "tendsto_prod_uniformity_fst", "linear_independent_smul", "sup_idem", "mul_equiv.map_inv", "fin.update_snoc_last", "circle_deg1_lift.tendsto_translation_number", "real.pi_lt_31416", "list.nth_of_fn", "submodule.closed_complemented.is_closed", "continuous_within_at_iff_ptendsto_res", "is_lub.unique", "nhds_pi", "uniform_space.completion.uniform_continuous_map\:2082", "set.Icc_subset_Iic_iff", "int.of_nat_eq_of_nat_iff", "sub_add_eq_sub_sub", "polynomial.eval_comp", "cardinal.mk_range_eq", "ordinal.not_succ_is_limit", "category_theory.quotient.functor_obj_as", "complex.cos_int_mul_two_pi_add_pi", "norm_num.min_fac_helper.n_pos", "local_homeomorph.mdifferentiable.symm_comp_deriv", "measure_theory.outer_measure.sup_apply", "padic_seq.norm_eq_pow_val", "fin.snoc_cast_succ", "function.left_inverse.eq_right_inverse", "dfinsupp.sum_apply", "real.tan_lt_tan_of_lt_of_lt_pi_div_two", "is_local_min_on.inter", "continuous.I_extend", "add_subgroup.mem_gmultiples", "finmap.disjoint_union_left", "prime_spectrum.subset_zero_locus_iff_subset_vanishing_ideal", "tendsto_at_top_mul_left'", "nnreal.rpow_mul", "sylow.one_mem_vectors_prod_eq_one", "has_fderiv_at_inv", "set.empty_union", "category_theory.monoidal_of_has_finite_coproducts.right_unitor_hom", "function.iterate_fixed", "equiv.perm.sign_eq_sign_of_equiv", "localization.mk_eq_mk'", "normed_field.exists_lt_norm", "omega.coeffs.val_map_div", "nhds_within_Ici_ne_bot", "category_theory.limits.limit.cone_morphism_hom", "lt_add_of_sub_left_lt", "set.insert_pi", "function.uncurry_bicompl", "with_top.nat_induction", "omega.nat.preform.sat_or", "ring_equiv.map_zero", "unique.subsingleton_unique'", "matrix.ext", "linarith.int.coe_nat_bit1", "option.eq_none_of_is_none", "category_theory.limits.cones.whiskering_equivalence_functor", "wseq.lift_rel.symm", "multilinear_map.map_piecewise_smul", "set.Ioo_eq_empty", "mul_inv_cancel_right", "semidirect_product.left_inl", "finset.sum_subset_zero_on_sdiff", "ordinal.univ_umax", "list.split_wrt_composition_join", "to_mul_injective", "ideal.is_maximal_iff_is_maximal_disjoint", "UniformSpace.coe_id", "composition.ones_size_up_to", "convex.neg", "geom_series_def", "smooth_on_fst", "bounded_continuous_function.continuous_eval", "subgroup.gc_map_comap", "category_theory.comma.iso_mk_inv_left", "filter.le_of_map_le_map_inj'", "primrec.list_head'", "category_theory.limits.cokernel_cofork.app_zero", "bit1_lt_bit1", "bounded_continuous_function.neg_apply", "matrix.to_lin_apply", "computation.orelse_think", "ring_hom.coe_range_restrict", "distrib_mul_action_hom.map_add", "nat.not_even_one", "category_theory.limits.pair_obj_right", "category_theory.whiskering_right_obj_obj", "list.length_pmap", "euclidean_geometry.orthogonal_projection_of_nonempty_of_complete_eq", "list.minimum_concat", "nonpos_of_mul_nonneg_right", "inv_mul_eq_of_eq_mul", "set.nmem_set_of_eq", "zmod.val_min_abs_zero", "free_ring.induction_on", "simple_add_group_of_surjective", "function.is_periodic_pt.eq_zero_of_lt_minimal_period", "nat.lt_add_of_sub_lt_right", "if_eq_of_eq_true", "normed_ring.inverse_add_nth_order", "finite_field.expand_card", "category_theory.discrete.equiv_of_equivalence_to_fun", "set.compl_Ici", "nat.partrec.of_primrec", "continuous_linear_map.coe_fst", "iff_false", "multiset.fold_erase_dup_idem", "zsqrtd.not_sq_le_succ", "category_theory.equivalence.unit_inverse", "of_add_zero", "local_equiv.trans_target'", "submodule.infi_colon_supr", "pequiv.to_matrix_injective", "derivation.map_add", "continuous_multilinear_map.op_norm_neg", "nat.sqrt_add_eq", "interval_integral.deriv_integral_of_tendsto_ae_right", "punit.one_eq", "add_localization.add_equiv_of_quotient_symm_add_monoid_of", "category_theory.abelian.pseudoelement.pseudo_surjective_of_epi", "multiset.coe_filter_map", "algebraic_closure.adjoin_monic.algebra_map", "classical.axiom_of_choice", "tactic.group.gpow_trick", "set.union_singleton", "subsemiring.multiset_sum_mem", "dense_inducing.extend_unique_at", "rel_embedding.is_total", "list.chain.induction", "measure_theory.simple_func.map_restrict_of_zero", "measure_theory.compl_mem_ae_iff", "dfinsupp.sub_apply", "computable.vector_nth'", "linear_map.range_le_iff_comap", "add_subgroup.closure_mono", "metric.pos_of_mem_ball", "pow_zero", "list.mem_insert_iff", "submodule.prod_sup_prod", "filter.at_bot_ne_bot", "list.sublists'_nil", "submodule.coe_to_add_subgroup", "concave_on.translate_left", "auto.not_or_eq", "finset.center_mass_insert", "polynomial.map_mul", "int.even_neg", "differentiable_on.rpow", "turing.list_blank.tail_cons", "is_R_or_C.bit0_re", "uniform_embedding_def'", "alist.mem_keys", "ulift.neg_down", "nat.partrec.code.exists_code", "bernoulli_two", "category_theory.limits.pullback.lift_fst", "int.lor_bit", "add_con.ker_eq_lift_of_injective", "semidirect_product.ext_iff", "int.bodd_one", "lipschitz_with.prod", "pfunctor.M.cases_on_mk", "set.preimage_const_add_Ico", "has_strict_fderiv_at.mem_implicit_to_local_homeomorph_source", "riesz_extension", "differentiable.sin", "equiv.id_traverse", "option_t.run_monad_lift", "asymptotics.is_O.prod_left_fst", "list.prefix_refl", "lower_bounds_insert", "matrix.mul_vec_diagonal", "has_deriv_at.ccosh", "Top.presheaf.stalk_pushforward.id", "eq_mul_of_mul_inv_eq", "relation.eqv_gen_iff_of_equivalence", "with_top.coe_mul", "sub_self", "linear_map.map_le_map_iff'", "nnreal.coe_nonneg", "zero_vadd", "left_neg_eq_right_neg", "algebra.subset_adjoin", "polynomial.monic_normalize", "polynomial.div_def", "inner_product_geometry.angle_sub_eq_angle_sub_rev_of_norm_eq", "divp_eq_divp_iff", "filter.sInter_mem_sets_of_finite", "le_of_forall_sub_le", "polynomial.eval_zero", "category_theory.limits.pullback_cone.of_cone_X", "set.piecewise_range_comp", "add_group.mclosure_subset", "card_fiber_eq_of_mem_range", "roption.assert_defined", "seq_eq_bind_map", "is_coprime.is_unit_of_dvd", "filter.map_binfi_eq", "category_theory.types_id_apply", "is_add_subgroup.add_mem_cancel_right", "ring_hom.snd_comp_prod", "category_theory.limits.prod.associator_naturality", "joined_in.refl", "affine_subspace.sup_direction_lt_of_nonempty_of_inter_empty", "finsupp.swap_mem_antidiagonal_support", "turing.tape.mk'_left", "mem_nhds_within_insert", "iterated_deriv_within_eq_equiv_comp", "function.support_infi", "list.le_eq_not_gt", "supr_neg", "linear_map.ker_cod_restrict", "add_monoid_hom.coprod_comp_inr", "nat.cast_ne_zero", "coe_coe", "subalgebra.list_prod_mem", "set.dual_Iio", "composition.to_composition_as_set_blocks", "nat.pow_dvd_pow_iff_le_right'", "metric.Hausdorff_dist_triangle", "filter.infi_sup_right", "finset.finite_to_set", "padic_val_nat_of_not_dvd", "convex.segment_subset", "is_basis.det_self", "multiset.filter_add_filter", "nonote.repr_power", "linear_map.span_singleton_eq_range", "continuous_iff_sequentially_continuous", "int.add_mul_mod_self", "measurable_subtype_coe", "filter.eventually_ge_at_top", "zsqrtd.conj_im", "is_open_map.of_inverse", "multiset.sum_zero", "lcm_one_left", "filter.eventually_eq.is_local_extr_on_iff", "is_R_or_C.abs_add", "nat.mul_sub_div", "linear_action_act_smul", "false_and", "local_equiv.inv_fun_as_coe", "category_theory.comma_morphism.ext_iff", "submodule.prod_map_fst", "cardinal.mk_emptyc_iff", "filter.germ.const_le", "complex.inv_zero", "category_theory.limits.kernel_is_iso_comp_hom", "ordinal.cof_univ", "equiv.inv_fun_as_coe", "add_submonoid.mrange_inr'", "primrec.pair", "list.cons_sublist_cons", "gcd_dvd_gcd", "filter.frequently_at_bot", "uniform_continuous_of_continuous", "list.keys_cons", "asymptotics.is_o_neg_left", "set.preimage_const_mul_Ico", "pythagorean_triple.even_odd_of_coprime", "set.disjointed_subset", "irrational_rat_sub_iff", "pell.eq_of_xn_modeq_lem3", "ennreal.lt_sub_iff_add_lt", "is_glb.lower_bounds_eq", "sum.inr.inj_iff", "nat.fact_inj", "inducing.continuous", "exists_max_ideal_of_mem_nonunits", "free_ring.coe_of", "stream.mem_of_mem_odd", "matrix.det_adjugate_of_is_unit", "model_with_corners.unique_diff", "pnat.coe_inj", "infi_unit", "real.exists_exp_eq_of_pos", "list.sum_take_map_length_lt2", "measure_theory.simple_func.ext", "fract_zero", "add_monoid_hom.eq_int_cast", "cont_t.monad_lift_bind", "nat.coprime.coprime_mul_left", "cardinal.mul_eq_max_of_omega_le_left", "pgame.lt_of_mk_le", "add_group_with_zero_nhd.exists_Z_half", "add_sub_div_two_lt", "nat.modeq.modeq_of_dvd_of_modeq", "roption.bind_map", "vsub_vadd_comm", "pnat.mk_bit1", "int.succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul", "padic_norm_z.le_one", "wseq.head_terminates_iff", "nat.le_mul_of_pos_right", "submonoid.localization_map.lift_of_comp", "filter.infi_ne_bot_of_directed'", "sub_nonneg_of_le", "pSet.equiv.ext", "multiset.antidiagonal_coe", "set.disjoint_disjointed", "bounded_continuous_function.ext", "palindrome.append_reverse", "lt_of_pow_lt_pow", "ceil_add_int", "linear_map.comap_prod_prod", "is_min_filter.sup", "inner_product_geometry.norm_eq_of_angle_sub_eq_angle_sub_rev_of_angle_ne_pi", "linear_map.is_linear_map_prod_iso", "category_theory.functor.map_iso_hom", "set.Inter_pos", "finset.coe_injective", "le_mul_iff_one_le_left'", "char_matrix_apply_nat_degree_le", "is_open.unique_mdiff_within_at", "function.injective.has_left_inverse", "category_theory.abelian.exact_iff'", "euclidean_domain.dvd_gcd", "inner_product_geometry.angle_add_angle_sub_add_angle_sub_eq_pi", "submodule.linear_proj_of_is_compl_comp_subtype", "list.rel_of_sorted_cons", "set.compl_univ_iff", "matrix.transpose_col", "has_deriv_within_at.log", "principal_ideal_ring.factors_spec", "real.is_conjugate_exponent_iff", "measurable_from_nat", "ennreal.mul_right_mono", "abs_of_nonpos", "AddCommGroup.free_obj_coe", "finset.sum_range_succ'", "hyperreal.is_st_inv", "Sup_univ", "set.image_add_right'", "le_max_right_of_le", "mv_polynomial.eq_zero_or_eq_zero_of_mul_eq_zero", "linear_independent_iff'", "metric.mem_nhds_iff", "choose_le_succ_of_lt_half_left", "has_sum.mul_left", "list.sublists_len_zero", "map_lift_comp_preserves_products_iso_hom_assoc", "finset.image_preimage", "convex_segment", "prod.fst_add_snd", "lipschitz_with.comp", "add_con.ker_lift_injective", "category_theory.limits.wide_pullback_shape.wide_cospan_map", "forall_or_distrib_right", "add_monoid_hom.map_int_module_smul", "local_ring.is_unit_one_sub_self_of_mem_nonunits", "asymptotics.is_O_norm_norm", "has_deriv_within_at.liminf_right_slope_le", "simple_group_of_surjective", "ideal.comap_id", "dim_submodule_le", "metric.tendsto_locally_uniformly_iff", "has_deriv_at_filter.scomp", "set.right_mem_Ico", "module.direct_limit.of.zero_exact_aux", "complex.equiv_real_prod_apply", "ideal.zero_ne_one_of_proper", "polynomial.multiplicity_X_sub_C_finite", "filter.principal_le_iff", "set.preimage_add_const_Ioc", "computation.parallel_promises", "has_deriv_at.log", "finset.prod_const_one", "Top.subsheaf_to_Types_presheaf", "erased.out_mk", "is_max_on.of_is_local_max_on_of_concave_on", "exists_associated_mem_of_dvd_prod", "zmod.legendre_sym_eq_zero_iff", "tensor_product.tmul_neg", "not_imp_of_and_not", "eq_of_linear_independent_of_span_subtype", "lt_of_one_div_lt_one_div", "eventually_eventually_eq_nhds", "continuous_on_of_locally_uniform_approx_of_continuous_on", "primrec.vector_nth'", "monoid_hom.inr_apply", "with_bot.lattice_eq_DLO", "list.mfoldr_append", "complex.arg_le_pi", "set.up_down", "local_equiv.trans_source''", "coe_int_of_digits", "ennreal.tendsto_coe_nnreal_nhds_top", "cardinal.mk_pnat", "list.append_eq_cons_iff", "buffer.append_list_mk_buffer", "measurable_space.is_measurable_bot_iff", "semiconj_by.inv_right'", "is_extr_filter.neg", "one_add_one_eq_two", "fintype.card_punit", "multiset.Ico.filter_le", "function.is_periodic_pt_zero", "filter.map_lift_eq2", "list.disjoint_of_disjoint_append_left_left", "onote.NF_below_of_nat", "turing.list_blank.append_mk", "linear_independent_comp_subtype", "domain_mvt", "padic_norm.nonarchimedean", "nat.fib_mono", "real.Inf_empty", "is_local_extr.fderiv_eq_zero", "structure_groupoid.local_invariant_prop.lift_prop_within_at_indep_chart_aux", "real.has_deriv_at_rpow", "csupr_const", "is_glb_univ", "if_t_t", "filter.tendsto.nnrpow", "cardinal.le_powerlt", "equiv.cast_apply", "set.nonempty_interval", "nat.one_div_lt_one_div", "nnreal.div_pow", "mem_nhds_within_Ici_iff_exists_Ico_subset'", "list.smul_prod", "has_deriv_within_at.ccos", "category_theory.limits.id_zero_equiv_iso_zero_apply_hom", "list.foldl_eq_of_comm'", "mv_power_series.constant_coeff_comp_C", "pos_num.of_to_nat", "dense_inducing.comap_nhds_ne_bot", "filter.eventually_eq.has_strict_fderiv_at_iff", "tensor_product.tmul_smul", "filter.tendsto.prod_map", "continuous_linear_map.coe_equiv_prod_of_surjective_of_is_compl", "category_theory.comma.map_left_obj_hom", "linear_pmap.map_smul", "pnat.gcd_a'_coe", "localization_map.mk'_mul_cancel_left", "mv_polynomial.eval\:2097_apply", "linear_map.sup_range_inl_inr", "turing.TM1to1.tr_tape_mk'", "measure_theory.ae_eq_fun.pos_part_mk", "list.scanr_aux_cons", "is_bounded_linear_map.is_O_sub", "measure_theory.measure.le_sum", "mv_polynomial.sum_to_iter_Xl", "complex.I_sq", "list.alternating_sum_nil", "finset.prod_comm", "int.neg_add", "set.union_diff_left", "category_theory.limits.binary_bicone.to_cocone_\[Iota]_app_left", "turing.tape.write_move_right_n", "add_right_eq_self", "complex.of_real_div", "real.exp_list_sum", "nat.primrec'.add", "int.lt_div_iff_mul_lt", "totally_bounded_iff_filter", "monoid_hom.cancel_left", "category_theory.limits.fork.condition", "is_open_map.continuous_on_image_of_left_inv_on", "ordinal.le_add_right", "has_sum_of_subseq_of_summable", "path.continuous", "ordinal.cof_cof", "is_unit_of_mul_eq_one", "set.update_preimage_pi", "is_preconnected_sUnion", "nonempty_of_trunc", "subring.map_supr", "int.mul_le_of_le_div", "padic_seq.lift_index_left_left", "continuous_sum_rec", "filter.has_basis.le_iff", "category_theory.evaluation_uncurried_map", "finset.Ico.filter_le_of_top_le", "set.mk_preimage_prod_right", "multiset.union_comm", "add_subgroup.coe_smul", "function.surj_inv_eq", "list.dvd_prod", "filter.mem_seq_sets_def", "finset.univ_map_embedding", "minimal_polynomial.degree_pos", "int.le_of_lt_add_one", "continuous_linear_map.coprod_apply", "one_fpow", "set.left_mem_interval", "add_submonoid.map_comap_le", "has_deriv_at_filter_neg", "topological_space.opens.map_id_inv_app", "linear_map.proj_pi", "add_commute.units_neg_right", "pfunctor.M.dest_corec", "add_group.mem_closure", "rat.mul_one", "measure_theory.simple_func.map_preimage", "has_sum.has_sum_compl_iff", "semiconj_by.neg_one_left", "stream.iterate_id", "ring_hom.cancel_left", "option_t.ext", "subsemiring.range_snd", "multiset.subset_ndunion_right", "cau_seq.mul_equiv_zero'", "add_monoid_hom.lift_of_surjective_comp_apply", "fderiv_const_mul", "supr_eq_top", "initial_seg.lt_or_eq_apply_left", "is_measurable_insert", "is_compact.exists_Inf_image_eq", "add_submonoid.localization_map.map_comp_map", "unique_mdiff_within_at_iff", "with_zero.coe_lt_coe", "has_strict_fderiv_at.smul_algebra", "disjoint.ne", "localization_map.mk'_eq_iff_eq", "presented_group.closure_rels_subset_ker", "mvpfunctor.W_cases", "primrec.of_equiv", "set.univ_subtype", "singleton_charted_space_one_chart", "pi.comp_zero", "finset.countable_to_set", "Pi.uniformity", "prod.id_prod", "set.forall_not_of_sep_empty", "mjoin_map_map", "finset.sum_preimage_of_bij", "stream.mem_of_mem_even", "quotient.ind'", "nat.partrec'.head", "category_theory.limits.pullback.condition", "set.indicator_zero'", "alist.perm_union", "polynomial.derivative_one", "category_theory.limits.mono_factorisation_zero_m", "finite_dimensional.findim_of_field", "pgame.neg_zero", "continuous_multilinear_curry_right_equiv_apply", "ext_chart_at_coe_symm", "add_submonoid.localization_map.lift_id", "partrec.vector_m_of_fn", "measure_theory.measure.Inf_caratheodory", "cauchy_of_totally_bounded_of_ultrafilter", "classical.by_contradiction", "span_points_nonempty", "subring.multiset_sum_mem", "free_monoid.lift_apply", "norm_eq_infi_iff_inner_eq_zero", "ennreal.tendsto.const_mul", "add_con.rel_eq_coe", "nat.partrec.code.rfind_prim", "fin.prod_univ_succ", "tendsto_inv_nhds_within_Ioi", "typevec.drop_fun_comp", "vector.map_nil", "rat.nonneg_antisymm", "nnreal.summable_of_le", "valuation.is_equiv.comap", "polynomial.eval_X", "setoid.eqv_gen_mono", "circle_deg1_lift.inf_apply", "complex.continuous.inv", "real.arcsin_sin", "finsupp.multiset_sum_sum_index", "multiset.coe_foldl", "set.Iio_def", "ennreal.exists_inv_nat_lt", "matrix.tail_val'", "continuous_linear_equiv.map_add", "category_theory.limits.biprod.inr_fst", "differentiable_within_at_fst", "real.Lp_add_le", "complex.sin_pi_div_two", "function.embedding.schroeder_bernstein", "div_pow_le", "polynomial.root_or_root_of_root_mul", "list.append_subset_of_subset_of_subset", "is_complete.is_closed", "list.length_sublists_len", "direct_sum.mk_add", "deriv_inv", "fpow_add", "category_theory.limits.types.filtered_colimit.r_ge", "free_abelian_group.hom_equiv_symm_apply", "category_theory.limits.cocones.precompose_equivalence_functor", "filter.le_Limsup_of_le", "real.rpow_lt_one_of_one_lt_of_neg", "free_abelian_group.lift.of", "real.volume_singleton", "continuous_linear_map.continuous", "mul_action_hom.ext_iff", "open_add_subgroup.coe_add_subgroup_le", "semiconj_by.conj_mk", "finsupp.on_finset_apply", "seq.dropn_tail", "pgame.impartial.le_zero_iff", "submodule.comap_smul", "sym2.eq_swap", "open_embedding.continuous_at_iff", "add_subgroup.normal_in_normalizer", "category_theory.limits.pushout_cocone.is_colimit.hom_ext", "int.le_add_of_neg_le_sub_right", "topological_space.opens.inter_eq", "relation.refl_trans_gen_lift", "le_mul_iff_one_le_right", "roption.ext", "function.surjective.infi_comp", "max_lt_max", "list.last_singleton", "set.Ico_\:2124_card", "typevec.append_fun_comp_id", "polynomial.sum_C_mul_X_eq", "alg_equiv.mk_apply", "is_least.cInf_eq", "mv_polynomial.algebra_map_eq", "hyperreal.infinite_pos_iff_infinite_neg_neg", "irrational.div_cases", "list.disjoint_append_right", "principal_ideal_ring.ne_zero_of_mem_factors", "finset.sdiff_union_distrib", "onote.sub_NF_below", "add_submonoid.localization_map.add_equiv_of_localizations_right_neg_apply", "asymptotics.is_O.prod_left_snd", "measure_theory.lintegral_infi", "homeomorph.to_local_homeomorph_coe", "psigma.elim_val", "norm_num.sub_nat_neg", "partial_order.ext", "nat.not_lt_zero", "category_theory.cocones_map", "padic_norm.zero_of_padic_norm_eq_zero", "exists_int_pow_near'", "pequiv.single_mul_single", "submodule.comap_inf", "emetric.tendsto_locally_uniformly_iff", "poly.ext", "add_monoid_hom.map_gsmul", "deriv_const_add", "circle_deg1_lift.units_coe", "set.Ico_subset_Icc_self", "deriv_id", "equiv.subtype_equiv_codomain_symm_apply_ne", "list.infix_of_prefix", "normed_field.nnnorm_one", "Set.eq_empty", "is_local_min_on.comp_continuous_on", "vadd_comm", "set.mem_image2_iff", "primrec.of_nat", "interior_closed_ball'", "list.nth_le_append_right_aux", "cauchy_iff'", "mul_action.mem_orbit", "has_deriv_at_filter_iff_tendsto_slope", "multiset.coe_map", "is_closed_Icc", "primrec.list_concat", "and_eq_of_eq_true_left", "image_sub_le_mul_sub_of_deriv_le", "finset.card_sdiff", "affine_subspace.mem_direction_iff_eq_vsub_left", "category_theory.sum.inl__obj", "matrix.scalar_inj", "convex.mul_sub_lt_image_sub_of_lt_deriv", "category_theory.over.mk_right", "cardinal.add_le_add_right", "Gromov_Hausdorff.eq_to_GH_space", "principal_seg.lt_le_top", "fraction_map.mk'_num_denom", "nnreal.div_div_eq_mul_div", "is_min_filter.is_extr", "nat.exists_mul_self", "multiset.nodup_erase_dup", "filter.univ_mem_sets'", "left_ord_continuous.id", "lucas_lehmer.\[Omega]_pow_eq_one", "function.semiconj.eq", "inducing.continuous_on_iff", "list.mem_lookup", "isometric.coe_mul", "summable.summable_of_eq_zero_or_self", "measure_theory.simple_func.sup_apply", "pgame.lt_mk_of_le", "le_rfl", "abs_eq_zero", "filter.frequently_top", "measure_theory.lebesgue_length_Icc", "bot_sup_eq", "is_local_extr_on.congr", "nhds_list", "measurable.edist", "turing.TM1to1.tr_tape'_move_left", "nnreal.le_inv_iff_mul_le", "category_theory.abelian.pseudoelement.pseudo_apply_aux", "indicator_ae_eq_restrict", "continuous_subtype_is_closed_cover", "dim_span_of_finset", "pnat.xgcd_type.reduce_reduced", "continuous_if'", "int.eq_zero_or_eq_zero_of_mul_eq_zero", "inv_of_eq_inv", "category_theory.Comonad.coassoc_func_app", "measure_theory.induced_outer_measure_eq_extend'", "measure_theory.integral_div", "nndist_triangle_right", "measure_theory.ae_all_iff", "cauchy_seq.tendsto_lim", "ennreal.continuous_at_const_mul", "inv_inv'", "cau_seq.complete", "local_equiv.left_inv_on", "unique_diff_on_Ici", "continuous_linear_map.has_sum_of_summable", "eq_of_nhds_eq_nhds", "exists_rat_btwn", "ring.fractional_ideal.mul_generator_self_inv", "stream.nth_inits", "list.erase_eq_erasep", "nat.pow_lt_pow_of_lt_right", "ordinal.typein.principal_seg_coe", "bdd_above.inter_of_left", "add_submonoid.localization_map.add_neg", "list.perm.inter_right", "convex_hull_singleton", "tsum_comm'", "convex.linear_preimage", "wseq.bind_congr", "finset.attach_insert", "rat.le_trans", "implies_of_if_pos", "submonoid.mem_closure_singleton", "has_fderiv_at_const", "finsupp.comap_domain_apply", "submonoid.mrange_inr", "fin.cases_zero", "free_group.equivalence_join_red", "mul_semiring_action_hom.comp_id", "affine_subspace.direction_bot", "nat.bodd_succ", "nat.primrec'.idv", "real.log_lt_log", "set.nonempty.image_const", "units.mul_inv_eq_iff_eq_mul", "associates.out_dvd_iff", "finset.union_comm", "category_theory.limits.biprod.total", "multiset.disjoint_of_subset_right", "generalized_continued_fraction.zeroth_numerator_eq_h", "free_add_monoid.closure_range_of", "cardinal.add_def", "closure_union", "uniform_continuous_comap'", "ideal.map_eq_top_or_is_maximal_of_surjective", "pgame.equiv_trans", "set.Icc_diff_Ioo_same", "times_cont_mdiff_on.times_cont_mdiff_on_tangent_map_within", "inv_fpow", "real.sin_sq_add_cos_sq", "wseq.bisim_o.imp", "measure_theory.integrable.induction", "category_theory.functor.equiv_inverse", "is_min_filter.filter_inf", "category_theory.nat_trans.pi_app", "metric.tendsto_nhds", "associates.mk_eq_mk_iff_associated", "gpow_one_add", "list.nth_modify_nth_eq", "polynomial.smul_C", "pmf.has_sum_coe_one", "filter.bind_def", "has_deriv_within_at.sum", "padic_int.val_eq_coe", "perfect_closure.one_def", "pequiv.trans_symm", "isometric.point_reflection_dist_self_real", "cardinal.le_one_iff_subsingleton", "submodule.eq_bot_iff", "nat.mul_div_right", "reader_t.run_map", "normal_iff_eq_add_cosets", "hash_map.find_insert_eq", "int.mem_range_iff", "is_R_or_C.norm_sq_eq_abs", "seq.eq_or_mem_of_mem_cons", "path.map_coe", "matrix.reindex_mul", "multiset.coe_erase", "linear_map.coprod_inl", "nnreal.lt_of_real_iff_coe_lt", "pnat.xgcd_type.reduce_a", "principal_seg.coe_fn_mk", "simple_graph.dot_product_adj_matrix", "cardinal.ord_injective", "non_contradictory_intro", "CommRing.coe_of", "ite_apply", "bucket_array.mem_as_list", "distrib_mul_action_hom.comp_apply", "subring.range_fst", "int.le_to_nat", "ordinal.typein_lt_typein", "filter.has_basis.mem_iff", "Top.presheaf.pushforward_eq_eq", "list.mem_bag_inter", "set.maps_to.union", "set.mem_of_eq_of_mem", "set.Union_subset", "imp_congr_right", "normal_of_eq_cosets", "mv_polynomial.exists_degree_lt", "is_open_lt'", "local_homeomorph.trans_of_set'", "rel_embedding.is_asymm", "category_theory.limits.coprod.associator_naturality", "filter.limsup_le_limsup", "mem_of_is_seq_closed", "galois_connection.le_u_l", "rat.nonneg_add", "times_cont_diff_at_fst", "category_theory.limits.cofork.\[Pi]_eq_app_one", "free_add_magma.map_add", "is_min_filter.min", "mv_polynomial.C_injective", "ordinal.mul_div_le", "mul_lt_mul_left", "category_theory.iso.refl_hom", "fin.mod_def", "set.Iic_diff_Iic", "finite_dimensional.findim_fintype_fun_eq_card", "real.mul_rpow", "set.image_Inter_subset", "matrix.row_mul_vec", "asymptotics.is_O_fst_prod'", "ordinal.one_add_omega", "ordered_cancel_comm_monoid.char_zero_of_inj_zero", "gaussian_int.to_complex_im", "list.perm.sum_eq", "equiv.apply_eq_iff_eq", "subgroup.gpowers_eq_closure", "category_theory.limits.prod.map_snd_assoc", "is_group_hom.mul", "ennreal.not_top_le_coe", "hash_map.contains_aux_iff", "measure_theory.integrable_at_filter.inf_of_right", "norm_smul", "finite_dimensional.findim_fin_fun", "function.surjective.has_right_inverse", "list.pairwise_iff_nth_le", "nhds_within_prod", "nat.cast_injective", "concave_on_iff_div", "fin.cast_lt_cast_succ", "lie_algebra.equiv.trans_apply", "measure_theory.l1.simple_func.dense_range", "category_theory.limits.limit.id_pre", "add_equiv.map_add", "monad_lift_refl", "nonempty_inter", "binfi_le", "initial_seg.unique_of_extensional", "mul_action.mem_fixed_points", "strict_mono.top_preimage_top", "formal_multilinear_series.comp_along_composition_apply", "set.finite.exists_finset_coe", "hash_map.find_iff", "list.forall\:2082_cons_right_iff", "topological_space.is_topological_basis_of_subbasis", "order_bot.ext_bot", "cardinal.sum_const_eq_lift_mul", "category_theory.limits.equivalence_preserves_zero_morphisms", "continuous_linear_map.coe_mk", "cardinal.ne_zero_iff_nonempty", "continuous_linear_map.range_prod_le", "contracting_with.to_lipschitz_with", "linear_recurrence.geom_sol_iff_root_char_poly", "ennreal.tendsto_coe_sub", "minimal_polynomial.degree_ne_zero", "coeff_scale_roots", "finsupp.erase_ne", "category_theory.limits.cocones.precompose_equivalence_counit_iso", "iterated_fderiv_succ_apply_left", "real.cos_eq_zero_iff", "int.nat_abs_pos_of_ne_zero", "local_equiv.eq_of_eq_on_source_univ", "int.mod_add_cancel_right", "left_add_coset_equiv_rel", "add_monoid_hom.snd_comp_inl", "has_strict_fderiv_at.restrict_scalars", "edist_eq_coe_nnnorm_sub", "num.cast_succ", "has_strict_fderiv_at.iterate", "ordinal.card_mul", "set.restrict_apply", "swap_id_rel", "times_cont_diff_on.add", "filter.comap_prod", "is_unit.unit_spec", "mul_semiring_action_hom.map_mul", "ordinal.CNF_snd_lt", "opposite.unop_injective", "nat.pow_eq_mul_pow_sub", "nat.le_div_iff_mul_le'", "differentiable.const_smul_algebra", "set.left_inv_on.comp", "list.filter_cons_of_neg", "emetric.Hausdorff_edist_image", "continuous_linear_equiv.skew_prod_apply", "omega.coeffs.val_between_map_div", "norm_num.min_fac_helper_4", "submodule.comap_mono", "compl_sup_eq_top", "strict_mono_id", "submodule.neg_mem", "category_theory.over.creates_connected.raised_cone_lowers_to_original", "set.univ_neg", "category_theory.limits.colimit.map_post", "vector_span_eq_span_vsub_set_left", "free_monoid.lift_of_comp_eq_map", "norm_num.adc_bit0_bit0", "pgame.ne_of_lt", "matrix.is_unit_det_of_right_inverse", "is_path_connected.joined_in", "set_coe.ext_iff", "category_theory.equivalence.counit_functor", "set.countable_Union_Prop", "set.seq_seq", "ring_hom.map_int_cast", "polynomial.coe_monomial", "equiv.point_reflection_self", "convex_on_pow", "finset.sum_const_nat", "lipschitz_with.of_le_add_mul'", "category_theory.limits.image.factor_map", "multiset.prod_ne_zero", "real.exp_sum", "set.image_add_const_Icc", "nat.choose_zero_right", "rel_embedding.eq_preimage", "fintype.card_prod", "list.sublists'_eq_sublists", "multiset.to_finset_sum_count_eq", "rat.coe_int_denom", "finset.map_subtype_subset", "pSet.resp.eval_val", "CommGroup.one_apply", "set.pi_def", "nnreal.coe_bit1", "lists'.subset_def", "wseq.of_mem_append", "max_mul_of_nonneg", "abstract_completion.uniform_continuous_coe", "free_add_semigroup.pure_seq", "wseq.lift_rel_o.swap", "exists_forall_ge_and", "units.map_id", "continuous_linear_equiv.comp_differentiable_within_at_iff", "Icc_mem_nhds_within_Ioi", "mv_polynomial.induction_on'", "tactic.ring_exp.prod_to_sum_pf", "filter.tendsto_at_top_principal", "set.set_coe_eq_subtype", "equiv.sum_empty_apply_inl", "encodable.decode_zero", "decidable.mul_le_mul_right", "uniform_continuous.sub", "with_bot.coe_bit1", "topological_space.is_open_Union_countable", "set.mem_univ_pi", "cardinal.nat_cast_lt", "computation.length_bind", "filter.eventually_eq_of_left_inv_of_right_inv", "finset.length_sort", "finset.sum_sum_elim", "function.injective.of_comp", "matrix.special_linear_group.coe_to_GL", "submodule.top_smul", "nat.add_comm", "set.Ioo_inter_Ioo", "ideal.eq_radical_of_eq_jacobson", "multiset.zero_sigma", "nat.pos_of_bit0_pos", "is_open_map.restrict", "polynomial.splitting_field_aux.exists_lift", "nat.gcd_dvd_left", "Class.of_Set.inj", "convex.mul_sub_le_image_sub_of_le_deriv", "pow_mul_comm", "pmf.ext", "cardinal.powerlt_zero", "summable.has_sum_iff_tendsto_nat", "subring.ext'_iff", "filter.order_top.at_top_eq", "list.argmin_le_of_mem", "submodule.mem_span_singleton", "inner_add_sub_eq_zero_iff", "bex_imp_distrib", "linear_map.trace_eq_matrix_trace", "tendsto_neg_nhds_within_Ioi_neg", "norm_unit_eq_one", "wseq.head_cons", "direct_sum.of_neg", "measure_theory.simple_func.integral_eq_sum_filter", "linear_map.injective_iff_surjective", "category_theory.quotient.lift.is_lift_hom", "prod_X_sub_smul.eval", "primrec.nat_lt", "wseq.exists_of_lift_rel_left", "topological_space.opens.op_map_comp_obj", "mv_polynomial.eval\:2082_assoc", "le_inf_iff", "holor.holor_index_cons_decomp", "edist_le_of_edist_le_geometric_two_of_tendsto", "is_local_min.fderiv_eq_zero", "units.coe_mul_left", "list.last_cons_cons", "measure_theory.integral_union", "encodable.decode_unit_succ", "nat.mem_list_primes_of_dvd_prod", "cardinal.add_eq_left_iff", "nat.lt_of_sub_lt_sub_right", "partrec.bind_decode2_iff", "measure_theory.l1.integral_add", "emetric.Hausdorff_edist_closure\:2082", "ring.fractional_ideal.coe_inv_of_nonzero", "continuous_linear_map.prod_apply", "nat.lt_of_sub_eq_succ", "inv_le_self", "complex.abs_cast_nat", "matrix.row_apply", "semidirect_product.map_inl", "add_submonoid.closure_eq_of_le", "finsupp.map_range_multiset_sum", "uniformly_extend_exists", "multiset.ndunion_le_union", "algebra.subring_coe_algebra_map_hom", "eq_zero_of_left_cancel_add_self", "int.cast_bit1", "to_bool_true_eq_tt", "polynomial.div_X_C", "fin.coe_coe_eq_self", "nnreal.div_lt_one_of_lt", "is_R_or_C.one_im", "finset.piecewise_insert", "list.map_fst_zip", "equiv.perm.subtype_perm_one", "list.reverse_cons'", "mv_polynomial.dim_R", "derivation.map_sub", "isometry.antilipschitz", "emetric.diam_eq_zero_iff", "local_homeomorph.restr_coe_symm", "padic_int.cast_pow", "is_compact.elim_finite_subcover_image", "lt_add_of_nonneg_of_lt", "semidirect_product.mul_left", "finsupp.filter_add", "quotient.mk_out", "subring.list_sum_mem", "ordinal.pred_le", "is_Z_bilin.tendsto_zero_left", "padic_norm_z.one", "subgroup.closure_empty", "div_mul_left", "linear_map.mk_continuous_of_exists_bound_coe", "multiplicity.mul", "submonoid.exists_list_of_mem_closure", "filter.map_compose", "ennreal.div_one", "id_restr_groupoid_mem", "ring_hom.map_pth_root", "measure_theory.lebesgue_length_subadditive", "category_theory.biprod.inl_of_components", "category_theory.limits.pushout.inl_desc_assoc", "uniform.continuous_iff'_left", "normalize_gcd", "list.perm_ordered_insert", "mv_polynomial.coeff_add", "tensor_product.lcurry_apply", "pfunctor.M.head_succ", "Inf_sup_Inf", "multiset.prod_eq_foldl", "commute.mul_fpow", "associated_one_of_mul_eq_one", "nat.partrec.code.fixed_point\:2082", "int.cast_max", "set.compl_bUnion", "multiset.fold_cons_left", "pos_num.add_one", "category_theory.limits.types.jointly_surjective", "computation.lift_rel_think_right", "multiset.length_ndinsert_of_not_mem", "has_strict_deriv_at.has_deriv_at", "with_top.top_ne_one", "asymptotics.is_O.sub", "closure_closure", "rat.mul_assoc", "wseq.exists_of_mem_join", "list.disjoint_iff_ne", "complex.of_real_cpow", "multiset.Ico.card", "algebra.surjective_algbera_map_iff", "set.indicator_compl", "nat.partrec'.vec_iff", "sq_sub_sq", "turing.blank_extends.above_of_le", "canonically_ordered_semiring.mul_le_mul", "list.perm_insert_swap", "bitvec.to_fin_le_to_fin_of_le", "min_eq_left", "nat.div_le_of_le_mul", "category_theory.graded_object.comap_equiv_functor", "nat.min_fac_le_of_dvd", "differentiable.prod", "prod_mk_prod", "real.cos_pi_div_thirty_two", "real.sinh_eq", "topological_space.open_nhds.map_id_obj'", "commute.cast_int_mul_self", "Sup_apply", "monoid.mem_closure_union_iff", "category_theory.limits.cocone_morphism.ext_iff", "convex_cone.mem_mk", "sub_lt_sub_iff_right", "is_add_group_hom.neg_iff_ker", "measure_theory.measure_mono_ae", "stream.drop_append_stream", "local_homeomorph.inv_image_trans_target", "filter.seq_assoc", "polynomial.eval_eq_sum", "matrix.smul_cons", "multiset.map_id", "category_theory.limits.image.map_hom_mk'_\[Iota]", "ideal.mem_span_insert'", "polynomial.div_eq_zero_iff", "le_mul_of_one_le_left", "category_theory.uncurry_eq", "filter.comap_infi", "deriv_within_const_mul", "list.mem_append_right", "set.maps_to.image_subset", "subtype.coe_prop", "uniform.continuous_within_at_iff'_left", "function.semiconj.inj_on_range", "neg_neg_iff_pos", "complex.cos_zero", "perfect_closure.frobenius_mk", "set.image_sub_const_Ico", "equiv_equiv_iso_hom", "intermediate_value_univ\:2082", "derivation.coe_injective", "formal_multilinear_series.congr", "dfinsupp.support_map_range", "one_div_one", "list.map_id", "irrational.of_rat_sub", "hyperreal.infinite_neg_iff_infinitesimal_inv_neg", "fpow_eq_zero", "matrix.cons_val_zero'", "rat.mk_num_ne_zero_of_ne_zero", "finsupp.single_mem_supported", "norm_num.one_succ", "finset.image_bind_filter_eq", "subring.range_subtype", "lt_top_iff_ne_top", "list.nth_le_take", "nat.mod_le", "ring_hom.map_ne_zero", "finset.image_insert", "transitive_many_one_reducible", "ordinal.card_lt_nat", "matrix.row_empty", "set.disjoint_union_right", "nat.add_le_add_right", "submodule.le_div_iff", "measure_theory.measure.haar.index_mono", "typevec.cases_nil_append1", "set.mem_Ioi", "finset.map_eq_image", "finset.bind_empty", "category_theory.limits.prod_map_comp_id", "free_abelian_group.map_of", "add_semiconj_by.map", "set.mem_diff", "is_integral_trans_aux", "setoid.empty_not_mem_classes", "equiv.prod_congr_symm", "decidable.mul_le_mul_left", "function.injective_of_partial_inv", "quadratic_form.lin_mul_lin_apply", "submonoid.mem_powers", "ennreal.add_sub_self'", "ulift.rec.constant", "pgame.le_def_lt", "finset.nat.mem_antidiagonal", "encodable.Union_decode2", "is_lub_singleton", "set.range_ite_subset", "pos_num.cast_one", "con.con_gen_of_con", "compl_le_of_compl_le", "polynomial.zero_is_root_of_coeff_zero_eq_zero", "filter.mem_zero", "set.finite_range_const", "category_theory.preadditive.sub_comp_assoc", "polynomial.map_nat_cast", "joined_in.joined", "subalgebra.res_top", "cInf_Ici", "norm_add_square_eq_norm_square_add_norm_square_iff_inner_eq_zero", "finset.sum_bind", "metric.mem_ball_comm", "bilin_form.mem_self_adjoint_submodule", "poly_equiv_tensor.to_fun_alg_hom_apply_tmul", "is_compl.right_le_iff", "add_con.sup_def", "measurable_zero", "subgroup.coe_inf", "galois_coinsertion.l_injective", "set.union_neg", "continuous_linear_map.coe_prod_map", "ordinal.zero_CNF", "linear_map.ext_iff", "set.indicator_le_self'", "finset.Ico.filter_lt_of_top_le", "mv_polynomial.coeff_neg", "is_add_submonoid.finset_sum_mem", "compl_infi", "exists_eq_mul_right_of_dvd", "continuous_multilinear_map.op_norm_smul_le", "commute.one_right", "set.nonempty.add", "free_group.prod.unique", "true_eq_false_of_false", "differentiable_at_id'", "norm'_def", "eq_center_mass_card_le_dim_succ_of_mem_convex_hull", "list.sublists_len_sublist_of_sublist", "complex.abs_re_div_abs_le_one", "polynomial.degree_mul", "generalized_continued_fraction.succ_succ_nth_convergent'_aux_eq_succ_nth_convergent'_aux_squash_seq", "primrec.fst", "rat.sqrt_nonneg", "free_semigroup.mul_bind", "list.head_append", "category_theory.as_iso_inv", "with_top.coe_lt_top", "category_theory.prod_preserves_connected_limits.forget_cone_X", "relation.eq_comp", "topological_space.opens.comap_val", "category_theory.quotient.lift.is_lift_inv", "nat.pow_lt_iff_lt_left", "cardinal.eq_of_add_eq_add_left", "category_theory.iso.eq_comp_inv", "ennreal.coe_add", "asymptotics.is_O_with.mono", "matrix.empty_eq", "ennreal.coe_lt_top", "bitraversable.tsnd_comp_tfst", "ordinal.nat_cast_div", "ennreal.lt_iff_exists_rat_btwn", "field.closure_mono", "dfinsupp.filter_apply", "finset.insert_singleton_comm", "list.foldl_assoc_comm_cons", "ordered_comm_group.lt_of_mul_lt_mul_left", "finset.sum_range_one", "mul_div_cancel_of_invertible", "cardinal.card_typein_out_lt", "pythagorean_triple.coprime_of_coprime", "le_generate_from", "pfun.preimage_univ", "with_top.none_lt_some", "polynomial.derivative_add", "finset.sum_range_id_mul_two", "list.inter_cons_of_mem", "pequiv.ext_iff", "finset.add_sum_diff_singleton", "pnat.coprime_coe", "list.nth_le_of_fn'", "multiset.sum_map_zero", "relation.refl_trans_gen_mono", "ideal.comap_Inf", "supr_exists", "cardinal.lift_two_power", "infi_infi_eq_left", "function.embedding.coe_sigma_mk", "pfun.ext", "is_integral.is_algebraic", "bilin_form.lin_mul_lin_comp_right", "finset.range_mono_of_fin", "onote.NF_below.oadd", "polynomial.C_eq_int_cast", "measure_theory.outer_measure.of_content_opens", "zsqrtd.norm_nat_cast", "classical.skolem", "ring_equiv.map_ne_one_iff", "tactic.ring_exp.mul_p_pf_sum", "ordinal.log_lt", "nat.coprime.gcd_mul", "lucas_lehmer.two_lt_q", "polynomial.eval\:2082_zero", "category_theory.types_comp_apply", "int.neg_le_sub_right_of_le_add", "continuous_linear_equiv.coe_apply", "category_theory.limits.fork.app_zero_left_assoc", "mv_polynomial.aeval_def", "category_theory.functor.comp_map", "array.read_map", "with_top.coe_ne_top", "zsqrtd.divides_sq_eq_zero_z", "differentiable_within_at.continuous_within_at", "seq.cons_append", "times_cont_mdiff_within_at.mdifferentiable_within_at", "function.inv_fun_surjective", "is_closed.cSup_mem", "nat.bit1_ne_bit0", "prime_spectrum.subset_zero_locus_iff_le_vanishing_ideal", "category_theory.limits.biproduct.\[Iota]_\[Pi]_assoc", "add_units.neg_add_eq_iff_eq_add", "cfilter.coe_mk", "ordinal.le_omin", "measure_theory.measure.smul_to_outer_measure", "list.ilast_eq_last'", "set.mem_of_indicator_ne_zero", "direct_sum.to_group_neg", "ordinal.lift_lt", "add_monoid_hom.ext_nat", "add_con.add_con_gen_mono", "has_fderiv_within_at.restrict_scalars", "filter.has_basis.inf_principal", "list.mem_argmin_iff", "dite_comp_equiv_update", "pfun.preimage_subset_dom", "max_le", "list.modify_nth_eq_take_drop", "game.add_zero", "ennreal.of_real_le_of_real_iff", "zero_le_bit0", "nat.exists_coprime'", "list.chain'_singleton", "measure_theory.lebesgue_to_outer_measure", "units.ne_zero", "cardinal.aleph'_nat", "equiv.arrow_congr_trans", "set.monotone_inter", "linear_equiv.eq_of_linear_map_eq", "real.cos_two_pi", "complex.abs_nonneg", "monoid_hom.coe_prod_map", "measure_theory.ae_eq_fun.is_add_subgroup", "set.interval_of_not_ge", "bilin_form.to_matrix_comp_left", "multiset.mem_ndinsert_of_mem", "eq_rec_compose", "continuous_linear_equiv.comp_has_strict_fderiv_at_iff", "galois_connection.u_Inf", "commute.fpow_fpow", "dfinsupp.mk_smul", "euclidean_geometry.dist_orthogonal_projection_ne_zero_of_not_mem", "ne.symm", "sesq_form.add_right", "pnat.xgcd_type.start_v", "bounded_continuous_function.abs_diff_coe_le_dist", "complex.is_cau_seq_im", "free_add_magma.lift_of", "closed_embedding.is_closed_map", "multiset.coe_sum", "uniformity_basis_edist_le'", "category_theory.comma.map_left_comp_hom_app_left", "ennreal.one_to_nnreal", "category_theory.functor.inv_inv", "bilin_form.ortho_smul_left", "int.eq_neg_of_eq_neg", "ring_hom.map_multiset_prod", "semidirect_product.inr_injective", "add_monoid_hom.map_closure", "measure_theory.simple_func.const_lintegral_restrict", "filter.eventually_eq.trans", "linear_map.map_eq_top_iff", "filter.Sup_sets_eq", "zsqrtd.coe_nat_val", "asymptotics.is_o_zero", "int.nat_abs_neg", "set.Inter_univ", "quadratic_form.polar_smul_right", "opposite.unop_sub", "powers_hom_apply", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_apply_ker", "equiv.sum_comm_apply", "with_zero.div_one", "fin.coe_of_nat_eq_mod", "function.comp_apply", "inner_product_space.of_core.norm_eq_sqrt_inner", "list.lookup_erase_dupkeys", "list.reverse_append", "set.nonempty_of_not_subset", "int.add_one_le_iff", "summable_iff_vanishing", "decidable.le_iff_lt_or_eq", "emetric.inf_edist_le_inf_edist_of_subset", "multiset.induction_on", "pnat.gcd_eq_right_iff_dvd", "complex.cosh_zero", "dioph.or_dioph", "times_cont_diff_at.prod_map'", "emetric.Hausdorff_edist_zero_iff_closure_eq_closure", "fintype.sum_apply", "structure_groupoid.lift_prop_within_at_univ", "set.Ico_diff_left", "is_cau_seq.cauchy\:2083", "category_theory.monoidal_category.left_unitor_product_aux", "set.not_subset", "lipschitz_with.nndist_le", "compact_Union", "filter.Limsup_principal", "category_theory.coyoneda_map_app", "seq.of_stream_append", "interval_integral.integral_neg", "polynomial.degree_map'", "linarith.mul_zero_eq", "emetric.Hausdorff_edist_empty", "add_comm_group.is_Z_bilin.sub_right", "incomp_iff_eq", "Lim_spec", "seq.coinduction2", "pgame.nim.zero_first_loses", "list.join_join", "polynomial.expand_inj", "mv_polynomial.total_degree_le_degrees_card", "subtype.irreducible_space", "finset.supr_union", "semiconj_by.div_right", "pow_unbounded_of_one_lt", "matrix.special_linear_group.det_coe_fun", "unique_factorization_domain.unique", "nat.lxor_left_inj", "abstract_completion.inverse_compare", "is_basis.repr_range", "multiset.coe_le", "list.forall_mem_append", "to_bool_ff", "pgame.relabel_move_right'", "Ico_mem_nhds_within_Ici", "submodule.smul_le_smul", "simple_continued_fraction.coe_to_generalized_continued_fraction", "add_units.coe_neg", "option_t.run_bind", "subgroup.closure_le", "pgame.mk_lt_of_le", "nhds_within_Iio_self_ne_bot", "has_fpower_series_on_ball.tendsto_uniformly_on'", "filter.tendsto_at_top_of_add_const_left", "add_monoid_hom.flip_apply", "finsupp.finite_lt_nat", "AddCommGroup.free_map_coe", "list.mem_product", "is_R_or_C.I_to_real", "relation.join_of_single", "filter.eventually_eq.mfderiv_within_eq", "list.head'_map", "finset.comp_inf_eq_inf_comp_of_is_total", "euclidean_domain.dvd_mod_iff", "ordinal.is_normal.trans", "gold_sq", "measure_theory.measure.haar.echaar_sup_le", "unique_diff_within_at.mono", "filter.tendsto_pure_pure", "equiv.psigma_equiv_sigma_apply", "list.subperm.exists_of_length_lt", "multiset.card_repeat", "supr_eq_supr_finset'", "set.finite.preimage", "add_semiconj_by.zero_right", "additive.is_add_hom", "equiv.refl_trans", "tensor_algebra.hom_ext", "con.con_gen_eq", "filter.frequently_iff_forall_eventually_exists_and", "commute.inv_left_iff", "category_theory.limits.binary_cofan.\[Iota]_app_left", "turing.tr_reaches_rev", "filter.principal_is_measurably_generated_iff", "closure_subtype", "omega.nat.preterm.val_sub", "category_theory.iso.trans_assoc", "is_noetherian_of_quotient_of_noetherian", "ereal.coe_real_le", "function.support_mul", "category_theory.limits.coprod.desc_comp_comp_assoc", "polynomial.eval\:2082_add", "vector.nth_cons_succ", "linear_equiv.finite_dimensional", "affine.simplex.eq_circumcenter_of_dist_eq", "subset_tangent_cone_prod_right", "prod_map", "add_monoid_algebra.single_zero_mul_apply", "complete_space_iff_is_complete_univ", "fin.cast_le_injective", "polynomial.zero_le_degree_iff", "znum.zero_add", "int.cast_one", "affine_combination_mem_affine_span", "primrec\:2082.of_eq", "nat.modeq.modeq_of_modeq_mul_right", "nat.test_bit_lxor", "geom_sum_mul", "is_R_or_C.norm_sq_add", "finset.pi.cons_same", "is_R_or_C.is_cau_seq_re", "contracting_with.one_sub_K_ne_top", "finset.coe_inter", "vector.nth_mem", "measure_theory.simple_func.mem_range_of_measure_ne_zero", "complex.exp_eq_exp_iff_exists_int", "add_subgroup.normal.mem_comm", "set.infinite_iff_frequently_cofinite", "submodule.coe_is_compl_equiv_proj_symm_apply", "list.drop_nil", "finset.max_of_mem", "complex.of_real_tan", "nat.one_lt_pow'", "linear_pmap.mk_span_singleton_apply", "list.pairwise.imp\:2082", "formal_multilinear_series.apply_composition_ones", "Kuratowski_embedding.embedding_of_subset_isometry", "list.take_all_of_le", "continuous_linear_map.has_deriv_within_at", "set.mem_insert", "category_theory.preadditive.sum_comp_assoc", "asymptotics.is_O_neg_right", "set.indicator_range_comp", "submodule.coe_injective", "filter.extraction_of_eventually_at_top", "exists_lt_of_lt_csupr", "set.pairwise_on_eq_iff_exists_eq", "complex.of_real_exp_of_real_re", "equiv.perm.is_cycle_swap_mul", "filter.tendsto_inf_right", "category_theory.limits.types.coprod_desc", "is_greatest.cSup_eq", "dfinsupp.mk_neg", "padic_seq.add_eq_max_of_ne", "is_bounded_linear_map.lim_zero_bounded_linear_map", "category_theory.preimage_iso_hom", "matrix.from_blocks_to_blocks", "dfinsupp.erase_apply", "category_theory.iso.conj_pow", "list.range'_append", "smooth_manifold_with_corners.mem_maximal_atlas_of_mem_atlas", "stream.take_theorem", "category_theory.under.post_map_right", "has_deriv_within_at.sqrt", "rel_embedding.is_antisymm", "one_div_mul_cancel", "nnnorm_add_le", "Inf_mem_closure", "Group.ext", "cardinal.eq_of_add_eq_add_right", "set.preimage_neg_Ico", "set.mem_image_iff_bex", "ennreal.infi_ennreal", "is_basis.constr_apply", "category_theory.limits.cocone.of_pushout_cocone_\[Iota]", "pnat.gcd_mul_lcm", "multiset.to_finset_inter", "polynomial.map_pow", "set.bUnion_mono", "and_eq_of_eq_false_left", "set.nonempty.image2", "pequiv.symm_refl", "pgame.turn_bound_of_left", "matrix.from_blocks_multiply", "ordinal.dvd_add", "real.continuous_at_rpow_of_ne_zero", "measure_theory.extend_Union_le_tsum_nat'", "peirce", "with_top.is_lub_Sup", "one_lt_mul_of_le_of_lt'", "nat.dvd_gcd_iff", "asymptotics.is_O_with.comp_tendsto", "or_false", "set.Iio_subset_Iio", "mvqpf.Wequiv.refl", "to_topological_space_subtype", "one_le_inv", "category_theory.under.id_right", "computation.results_thinkN_ret", "set.preimage_image_eq", "alist.not_mem_empty", "add_monoid_hom.gclosure_preimage_le", "option.iget_mem", "algebra.algebra_ext", "iff_iff_and_or_not_and_not", "real.sin_sub", "nat.choose_one_right", "generalized_continued_fraction.comp_exact_value_correctness_of_stream_eq_some", "emetric.mem_ball", "le_mul_of_one_le_right'", "nat.psub_eq_some", "monotonicity.exists", "ennreal.zero_to_nnreal", "matrix.from_blocks_smul", "continuous.edist", "add_submonoid.localization_map.to_map_injective", "category_theory.iso.cancel_iso_hom_right_assoc", "add_submonoid.mem_inf", "affine_map.line_map_linear", "finsupp.lmap_domain_id", "padic_int.zmod_congr_of_sub_mem_max_ideal", "category_theory.abelian.pseudoelement.zero_morphism_ext", "quot.lift_on\:2082_mk", "polynomial.X_mul", "exists_pos_bound_of_bound", "set.left_inv_on.eq_on", "affine_map.coe_homothety_hom", "option.bind_eq_none", "category_theory.limits.cocone.w", "mat_poly_equiv_coeff_apply_aux_2", "ordinal.sub_le_self", "submonoid.localization_map.mk'_eq_iff_eq_mul", "neg_le_sub_iff_le_add'", "list.sublist_cons", "has_sum.tendsto_sum_nat", "submonoid.coe_subtype", "list.forall\:2082_take_append", "set.image3_congr", "ring_commutator.commutator", "le_Inf_iff", "pgame.add_move_right_inr", "category_theory.nat_trans.op_id", "set.preimage_const_mul_Ici", "pgame.right_wins_of_equiv", "set.image_preimage_inter", "complex.ext_abs_arg", "midpoint_neg_neg", "category_theory.equivalence.inv_fun_map", "linear_map.comap_cod_restrict", "multiset.add_bind", "category_theory.limits.cone.category_to_category_struct_id_hom", "compact_of_totally_bounded_is_closed", "has_strict_fderiv_at_snd", "int.shiftr_eq_div_pow", "set.Ici_inter_Ici", "generalized_continued_fraction.part_denom_eq_s_b", "open_embedding.open_target", "pow_two_nonneg", "has_fderiv_within_at_const", "add_con.lift_coe", "is_local_max_on.sup", "lipschitz_with.prod_snd", "convex_cone.comap_comap", "category_theory.limits.cokernel_is_iso_comp_inv", "pell.x_increasing", "set.countable_of_injective_of_countable_image", "continuous_ulift_down", "ideal.map_top", "int.sub_pos_of_lt", "real.has_deriv_at_rpow_of_pos", "continuous_linear_map.id_comp", "le_add_of_neg_add_le_left", "has_deriv_at_filter.sub", "with_zero.inv_one", "exists_pos_rat_lt", "filter.mem_generate_iff", "affine_map.comp_id", "real.sinh_zero", "power_series.coeff_X_pow", "polynomial.exists_separable_of_irreducible", "times_cont_diff_zero_fun", "is_extr_filter.congr", "cardinal.lift_lt", "ordinal.has_succ_of_is_limit", "local_homeomorph.continuous_at_symm", "linear_map.has_deriv_within_at", "subsemiring.coe_to_add_submonoid", "generalized_continued_fraction.zeroth_convergent'_eq_h", "category_theory.monad_hom.comp_id", "function.injective.eq_iff'", "ennreal.ne_top_of_mul_ne_top_right", "dioph.dioph_fn_comp2", "div_eq_iff_mul_eq", "rat.num_denom", "ideal.map_mul", "set.surj_on.mono", "monoid_hom.normal_ker", "is_strict_weak_order_of_is_order_connected", "set.mem_sep", "primrec.nat_mul", "list_all_iff_forall", "ennreal.inv_mul_cancel", "add_right_comm", "nat.sub_add_comm", "units.inv_mul_of_eq", "category_theory.monoidal_category.tensor_right_obj", "nnreal.tendsto_inverse_at_top_nhds_0_nat", "is_closed_proj_of_compact", "set.sep_set_of", "category_theory.monoidal.tensor_hom_app", "list.pairwise_sublists", "measure_theory.simple_func.monotone_eapprox", "has_fderiv_within_at.const_sub", "list.mem_enum_from", "list.Ico.filter_lt_of_ge", "cardinal.mk_compl_eq_mk_compl_finite", "real.borel_eq_generate_from_Ioo_rat", "category_theory.functor_to_types.naturality", "array.rev_list_foldr", "measure_theory.ae_map_iff", "omega.term.val_neg", "semiconj_by.fpow_right", "measure_theory.measure.regular.map", "id_map'", "affine_subspace.not_mem_bot", "differentiable_within_at.neg", "matrix.diagonal_neg", "fintype.sum_pow_mul_eq_add_pow", "linear_map.to_matrix_of_equiv", "max.left_comm", "submodule.mem_Sup_of_directed", "multiset.countp_cons_of_neg", "ennreal.two_ne_top", "function.injective.iterate", "linear_independent_singleton", "inducing.prod_mk", "filter.has_basis.comap", "add_subgroup.coe_to_add_submonoid", "ordinal.add_mul_limit_aux", "category_theory.action_as_functor_obj", "homological_complex.image_to_kernel_map_condition_assoc", "category_theory.comonad.coalgebra.EilenbergMoore_to_category_struct_id", "continuous_multilinear_map.uncurry_right_apply", "disjoint.eq_bot", "finset.affine_combination_indicator_subset", "ennreal.infi_mul_right", "real.tendsto_exp_at_top", "approximates_linear_on.closed_ball_subset_target", "derivation.commutator_apply", "linear_map.supr_range_std_basis_le_infi_ker_proj", "multiset.mem_erase_of_nodup", "initial_seg.le_lt_apply", "subtype.eq", "is_closed_map_smul_of_ne_zero", "relator.left_unique_of_rel_eq", "list.disjoint_singleton", "units.dvd_mul_left", "is_noetherian_span_of_finite", "pi.one_apply", "int.mod_eq_mod_iff_mod_sub_eq_zero", "polynomial.eq_zero_of_eq_zero", "free_group.red.step.diamond", "category_theory.faithful.of_comp_eq", "category_theory.limits.limit.map_post", "circle_deg1_lift.lt_iterate_pos_iff", "classical.some_spec", "nat.div_le_of_le_mul'", "nat.mod_self", "quotient_add_group.lift_mk'", "uniform_space.separation_quotient.uniform_continuous_lift", "nat.shiftl_succ", "nat.le_zero_iff", "smul_neg", "hyperreal.infinitesimal_add", "Ico_mem_nhds_within_Ioi", "real.abs_cos_le_one", "mem_closure_iff_frequently", "nat.size_bit0", "surj_on_Ici_of_monotone_surjective", "linear_independent.image", "finset.prod_pow", "top_unique", "enorm.map_sub_le", "isometric.to_equiv_inj", "continuous_linear_equiv.differentiable", "real.sinh_sub", "associated.trans", "normed_ring.inverse_add_norm", "uniform_space.separation_quotient.map_unique", "category_theory.monoidal_category.unitors_equal.cells_6'", "int.lcm_one_right", "real.totally_bounded_Ioo", "times_cont_mdiff_id", "list.singleton_perm", "add_submonoid.top_prod", "ite_mul_zero_right", "int.modeq.modeq_mul", "wseq.lift_rel_destruct_iff", "neg_involutive", "real.exp_sub", "int.le_total", "div_le_div", "algebraic_geometry.structure_presheaf_in_CommRing_map_to_fun", "bdd_above.insert", "mul_inv_eq_one", "nat.add_mod_left", "finset.val_le_iff", "ring_hom.coe_srange_restrict", "dfinsupp.support_filter", "ordinal.dvd_antisymm", "category_theory.limits.eq_zero_of_mono_cokernel", "free_semigroup.traverse_pure'", "subtype.forall", "nnnorm_indicator_eq_indicator_nnnorm", "list.perm_append_left_iff", "list.forall_mem_cons'", "submodule.orthogonal_disjoint", "differentiable_on.congr", "submodule.prod_equiv_of_is_compl_symm_apply_right", "affine_map.line_map_apply", "multiset.antidiagonal_map_fst", "finset.Ico.pred_singleton", "finset.sum_range_id", "ennreal.coe_mono", "finset.cons_val", "finset.prod_nat_pow", "add_submonoid.coe_subset_coe", "category_theory.fork_\[Iota]_comp_cofork_\[Pi]", "stream.interchange", "nat.partrec.code.pair_prim", "is_local_extr.on", "linear_independent_inl_union_inr'", "nat.div_mul_div_le_div", "not_nontrivial_iff_subsingleton", "min_eq_neg_max_neg_neg", "uniform_add_group.mk'", "generalized_tube_lemma", "mv_polynomial.is_homogeneous.mul", "coe_not_mem_range_equiv_symm", "measure_theory.inner_content_mono'", "category_theory.limits.limit.cone_point_unique_up_to_iso_inv_comp", "dioph.add_dioph", "seq_bind_eq", "equiv.forall\:2082_congr", "image_norm_le_of_norm_deriv_right_lt_deriv_boundary", "has_strict_fderiv_at.local_inverse_continuous_at", "fraction_map.eq_zero_of_num_eq_zero", "lt_add_of_pos_of_lt", "finmap.erase_union_singleton", "category_theory.monoidal.Mon_functor_category_equivalence_inverse", "list.chain'.imp", "semidirect_product.right_hom_comp_inr", "list.mem_of_mem_filter", "guard_true", "continuous_linear_map.is_O_id", "category_theory.non_preadditive_abelian.mono_of_zero_kernel", "quotient_add_group_saturate", "local_homeomorph.continuous_within_at_iff_continuous_within_at_comp_right", "unique_diff_on_Ico", "affine_map.map_vadd", "measurable_space.is_measurable_sup", "infi_union", "inner_sum_smul_sum_smul_of_sum_eq_zero", "parallelogram_law", "measure_theory.l1.simple_func.lintegral_edist_to_simple_func_lt_top", "category_theory.reflective.comparison_ess_surj_aux", "prod_eq_generate_from", "eq_lim_at_left_extend_from_Ioo", "pnat.prime.ne_one", "infi_comm", "set.Union_union_distrib", "matrix.det_update_column_add", "omega.coeffs.val_except_add_eq", "is_connected_connected_component", "mul_aut.mul_apply", "omega.coeffs.val_except_update_set", "complete_space_extension", "nat.not_prime_iff_min_fac_lt", "filter.germ.coe_zero", "real.arcsin_zero", "summable.sub", "equiv.perm.sign_aux_eq_sign_aux2", "continuous_within_at_Ioc_iff_Iic", "ring_equiv.map_eq_one_iff", "char.eq_of_veq", "group.closure_mono", "free_group.reduce.not", "int.neg_of_sign_eq_neg_one", "infinite.exists_subset_card_eq", "list.map_length_split_wrt_composition_aux", "neg_add_rev", "nat.pow_left_strict_mono", "dif_neg", "nat.decreasing_induction_trans", "category_theory.arrow.has_lift.ext", "function.iterate_add", "subalgebra.srange_le", "typevec.last_fun_split_fun", "holor.cprank_max_mul", "category_theory.non_preadditive_abelian.comp_sub", "set.mem_compl_iff", "if_neg", "asymptotics.is_O_const_mul_left_iff'", "list.filter_true", "ennreal.zero_rpow_def", "complex.eta", "free_monoid.map_of", "is_connected_singleton", "category_theory.preadditive.comp_sub", "polynomial.sum_monomial_eq", "primrec.of_eq", "monoid_hom.mem_range", "int.of_nat_add_neg_succ_of_nat_of_lt", "is_compact.measure_zero_of_nhds_within", "inv_mul_self", "mvpfunctor.liftp_iff", "galois_connection.le_u", "measurable.snd", "deriv_rpow", "polynomial.mem_degree_le", "submonoid.closure_le", "nat.bit0_le_bit", "list.length_foldr_permutations_aux2'", "category_theory.over.construct_products.cones_equiv_inverse_obj_2", "ennreal.coe_pos", "dual_pair.is_basis", "nat.sub_le_sub_right_iff", "path.source", "znum.gcd_to_nat", "is_cau_geo_series", "mv_power_series.monomial_zero_eq_C_apply", "computation.destruct_map", "lie_algebra.equiv.symm_apply_apply", "add_units.val_coe", "power_series.X_prime", "multiplicity.finite_of_finite_mul_right", "continuous_linear_map.antilipschitz_of_uniform_embedding", "zsqrtd.sqrtd_re", "pfunctor.approx.approx_eta", "formal_multilinear_series.change_origin_summable_aux1", "function.is_fixed_pt.iterate", "fact_zero_lt_one", "affine_subspace.coe_affine_span_singleton", "ennreal.coe_lt_coe_nat", "topological_space.is_topological_basis_of_open_of_nhds", "finite_dimensional.finset_card_le_findim_of_linear_independent", "add_con.add_ker_mk_eq", "tendsto_comp_of_locally_uniform_limit_within", "le_cInf", "finset.union_insert", "pfunctor.M.ext", "add_le_add", "matrix.std_basis_matrix_add", "category_theory.limits.is_limit.cone_points_iso_of_equivalence_inv", "exists_eq_right'", "measure_theory.ae_eq_fun.coe_fn_add", "category_theory.adjunction.hom_equiv_naturality_left_symm", "linear_map.to_affine_map_linear", "real.exp_multiset_sum", "linear_pmap.domain_sup", "asymptotics.is_O.mul", "induced_inf", "circle_deg1_lift.commute_int_add", "subgroup.one_mem", "complex.zero_im", "submodule.span_induction", "mdifferentiable_within_at.congr_of_eventually_eq", "subalgebra.to_submodule_inj", "finset.disjoint_insert_right", "constr_add", "measure_theory.tendsto_measure_Inter", "dist_triangle4_right", "lists'.of_to_list", "fderiv_within_inter", "ext_chart_at_continuous_on_symm", "prime_spectrum.vanishing_ideal_univ", "tendsto_nhds_within_congr", "multiset.card_pmap", "ennreal.pow_lt_top", "list.mem_erase_of_nodup", "finset.card_pi", "submodule.le_def'", "submodule.add_eq_sup", "option.lift_or_get_none_right", "continuous_linear_equiv.norm_symm_pos", "Set.singleton_inj", "list.pairwise_filter_map_of_pairwise", "Module.monoidal_category.hom_apply", "iterated_fderiv_within_apply_eq_iterated_deriv_within_mul_prod", "mem_pair_self_adjoint_matrices_submodule", "is_compact.union", "list.map_ret_sublist_sublists", "infi_eq_infi_finset'", "polynomial.nat_degree_restriction", "nnreal.of_real_le_iff_le_coe", "local_equiv.left_inv", "has_fderiv_within_at.mul", "polynomial.C_bit0", "category_theory.coe_inv_hom_id", "complex.differentiable_sin", "mul_div_cancel'", "affine.simplex.monge_plane_def", "typevec.last_append1", "measurable_space.dynkin_system.generate_inter", "finite_dimensional.findim_eq_card_basis'", "equiv.const_vadd_zero", "ordinal.mul_add_one", "turing.tape.mk'_head", "finset.inf_union", "nonpos_of_neg_nonneg", "affine_subspace.bot_coe", "list.perm_lookmap", "complex.sub_im", "add_submonoid.comap_id", "multiset.count_filter", "finsupp.map_domain_id", "equiv.comp_map", "con.induction_on\:2082", "cSup_intro'", "category_theory.sum.swap_map_inr", "measure_theory.measure.haar.index_pos", "lipschitz_with.uncurry", "fin_enum.mem_to_list", "homological_complex.graded_homology_map", "primrec.nat_cases'", "is_subgroup.mul_mem_cancel_left", "primrec.vector_to_list", "nat.two_mul_odd_div_two", "subspace.convex", "int.nat_abs_of_nonneg", "finset.superset.trans", "local_homeomorph.trans_of_set", "mul_action_hom.comp_id", "polynomial.coeff_comp_degree_mul_degree", "cSup_mem_closure", "uniform_space.completion.uniform_continuous_extension\:2082", "wseq.drop.aux_none", "subsemiring.top_prod", "measure_theory.simple_func.restrict_empty", "monoid_hom.map_iterate_frobenius", "set.image_sub_const_Ioi", "matrix.cons_eq_zero_iff", "lt_one_div", "wseq.mem_append_left", "mfderiv_zero_of_not_mdifferentiable_at", "le_supr'", "dense_inducing.prod", "continuous_on_neg", "algebra.to_comap_apply", "polynomial.degree_lt_eq_span_X_pow", "neg_nsmul", "d_array.ext", "znum.cmp_to_int", "mul_self_eq_mul_self_iff", "finset.card_attach", "finset.sum_pair", "polynomial.monic_X_pow_add", "rel.image_mono", "category_theory.prod_comp_fst", "rat.cast_mul_of_ne_zero", "finset.mem_singleton", "times_cont_mdiff_within_at_iff", "tactic.ring.horner_neg", "category_theory.limits.\[Iota]_colim_map", "multiset.cons_inter_of_pos", "pos_num.cast_le", "category_theory.sum.associator_obj_inl_inr", "int.pred_self_lt", "with_bot.inf_eq_min", "localization_map.comap_map_of_is_prime_disjoint", "lift_nhds_right", "interval_integral.integral_has_fderiv_at_of_tendsto_ae", "continuous_linear_map.lipschitz", "emetric.diam_ball", "complex.abs_ne_zero", "add_monoid_hom.coe_mk'", "metric.inductive_limit_dist_eq_dist", "tendsto_at_bot_add_tendsto_right", "category_theory.abelian.pseudoelement.apply_zero", "not_top_lt", "adjoin_root.is_root_root", "free_group.sum.mul", "function.injective.sum_map", "list.suffix_of_suffix_length_le", "isometric.apply_symm_apply", "bilin_form.smul_apply", "measurable.subtype_coe", "real.sinh_surjective", "mem_residual", "continuous_within_at_const", "is_local_max_on.on_subset", "finset.dvd_sum", "compact_iff_totally_bounded_complete", "cau_seq.one_not_equiv_zero", "znum.cast_le", "add_submonoid.localization_map.lift_eq_iff", "is_path_connected_iff_eq", "list.subperm_append_left", "list.modify_nth_tail_modify_nth_tail_le", "generalized_continued_fraction.part_denom_none_iff_s_none", "is_open.preimage", "unique_factorization_domain.exists_mem_factors_of_dvd", "wseq.cons_congr", "list.nth_append", "relation.transitive_join", "continuous_within_at.tendsto_nhds_within_image", "finset.mem_filter", "list.nodup_nil", "set.Ioo_def", "is_submonoid_Union_of_directed", "uniform_space.completion.coe_mul", "filter.le_Liminf_of_le", "set.directed_on_Union", 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"set.subset_preimage_image", "turing.to_partrec.code.pred_eval", "quotient_ring_saturate", "measure_theory.ae_eq_symm", "set.finite.bdd_below_bUnion", "dioph.const_dioph", "pfunctor.fst_map", "linear_map.snd_prod", "function.embedding.equiv_of_fintype_self_embedding_to_embedding", "submodule.annihilator_eq_top_iff", "metric.bounded.ediam_ne_top", "prime_multiset.coe_nat_injective", "set.Iic_inter_Iic", "subsemiring.closure_empty", "dist_add_right", "submodule.coe_smul", "interval_integral.integral_of_le", "matrix.map_sub", "set.mk_mem_prod", "polynomial.map_mod_by_monic", "add_assoc", "function.commute.left_bij_on_fixed_pts_comp", "dense_inducing.extend_unique", "two_mul", "local_homeomorph.trans_refl", "measure_theory.extend_mono", "norm_algebra_map_eq", "mv_polynomial.total_degree_zero", "state_t.run_bind", "category_theory.iso.symm_inv", "measure_theory.measure.finite_at_nhds_within", "polynomial.nat_degree_pos_of_aeval_root", "smul_prod", "set.not_mem_of_not_mem_sUnion", "filter.ext'", "real.range_sin", "real.rpow_def_of_nonneg", "nat.lt_asymm", "category_theory.abelian.coimages.coimage_strong_epi_mono_factorisation_to_mono_factorisation_I", "pequiv.mem_iff_mem", "filter.lift'_inf_powerset", "add_subgroup.add_mem", "metric.uniformity_eq_comap_nhds_zero", "measurable_sum", "submodule.smul_induction_on", "tendsto_inv_nhds_within_Ioi_inv", "summable.mul_left", "norm_indicator_eq_indicator_norm", "subring.Inf_to_submonoid", "module.End.eigenspace_eval\:2082_polynomial_degree_1", "function.commute.iterate_left", "subsemiring.mem_to_submonoid", "norm_num.lt_one_bit0", "finset.filter_true", "filter.tendsto_at_bot_of_add_const_left", "pnat.coprime.gcd_mul_right_cancel", "path.extend_one", "times_cont_diff_within_at.continuous_within_at'", "primrec.list_index_of", "set.bInter_eq_Inter", "emetric.mem_iff_ind_edist_zero_of_closed", "dvd_add_right", "polynomial.prime_X_sub_C", "measurable.min", "nonempty_empty", "abs_sub_le", "set.countable_iff_exists_injective", "filter.germ.lift_rel_const_iff", "wseq.mem_cons_of_mem", "finset.inf_le", "polynomial.div_mod_by_monic_unique", "list.rotate'_length", "list.take_nil", "set.bij_on.inter", "omega.term.val_div", "mul_right_eq_self", "matrix.transpose_mul", "add_units.lift_right_neg_add", "le_iff_exists_add", "inv_lt_inv", "free_add_monoid.lift_eval_of", "ennreal.inv_lt_top", "tactic.ring_exp.pow_p_pf_one", "pos_of_mul_neg_left", "units.one_sub_coe", "ring_hom.injective_iff_ker_eq_bot", "finset.prod_add_prod_le", "deriv_add_const", "linear_map.findim_range_add_findim_ker", "opposite.op_zero", "primrec.sum_inr", "int.zero_ne_neg_of_ne", "set.preimage_const_mul_Ioo_of_neg", "algebra.adjoin_eq_span", "pgame.impartial.not_first_loses", "polynomial.exists_irreducible_of_nat_degree_ne_zero", "le_max_left_of_le", "supr_of_empty", "category_theory.bifunctor.map_comp_id", "finsupp.emb_domain_apply", "convex_ball", "linear_map.range_comp_le_range", "set.Ioc_subset_Ioc_left", "exists_ne", "category_theory.types_hom", "ge_mem_nhds", "real.Sup_le", "polynomial.coeff_smul", "norm_num.div_eq", "primrec.fin_val", "rat.coe_nat_eq_mk", "primrec.fin_app", "zmod.sum_two_squares", "computation.head_empty", "nat.exists_prime_and_dvd", "nat.zero_lxor", "has_strict_fderiv_at.comp", "function.update_eq_self", "equiv.perm.ne_and_ne_of_swap_mul_apply_ne_self", "has_ftaylor_series_up_to_on.has_fderiv_within_at", "free_group.red.step.cons", "zorn.chain_closure_empty", "topological_fiber_bundle_core.local_triv_at_symm_fst", "inv_lt_one_iff_one_lt", "complex.neg_im", "metric.Hausdorff_dist_closure", "list.pw_filter_nil", "norm_snd_le", "category_theory.differential_object.zero_f", "matrix.col_mul_vec", "composition.one_le_blocks", "real.tan_inj_of_lt_of_lt_pi_div_two", "multiset.eq_repeat_of_mem", "ideal.is_prime.radical", "equiv.perm.cycle_of_apply_self", "multiset.sub_le_self", "induced_infi", "turing.list_blank.append_assoc", "topological_space.open_nhds.map_obj", "affine_map.coe_mul", "except_t.goto_mk_label", "is_greatest_singleton", "wseq.map_think", "ordinal.is_limit_iff_omega_dvd", "list.chain_lt_range'", "punit.zero_eq", "set.disjoint_iff", "eq_of_sub_eq_zero", "is_R_or_C.of_real_nat_cast", "list.nil_infix", "euclidean_domain.dvd_lcm_right", "emetric.diam_le_iff_forall_edist_le", "add_subgroup.add_mem_cancel_right", "continuous_linear_equiv.symm_symm_apply", "linear_map.sub_mem_ker_iff", "nat.partrec'.tail", "ctop.realizer.of_equiv_\[Sigma]", "CommRing.colimits.quot_mul", "list.perm_nil", "nat.dvd_add_self_left", "encodable.Union_decode2_disjoint_on", "int.mul_def", "omega.coeffs.val_between_sub", "sequentially_complete.set_seq_sub_aux", "nat.bodd_add_div2", "complex.dist_eq", "dense_inducing.extend_eq", "measure_theory.outer_measure.zero_caratheodory", "nat.partrec.code.eval_curry", "eq_of_zero_eq_one", "denumerable.raise_lower", "nat.add_mul_div_right", "real.arctan_one", "eq.congr_left", "pSet.equiv_iff_mem", "has_strict_fderiv_at.map_implicit_function_of_complemented_eq", "compact_open_separated_add", "finsupp.hom_ext", "num_is_root_scale_roots_of_aeval_eq_zero", "list.mem_diff_iff_of_nodup", "lucas_lehmer.X.\[Omega]_mul_\[Omega]b", "exists_int_lt", "filter.map_congr", "holor.slice_add", "category_theory.limits.equalizer.iso_source_of_self_inv", "is_noetherian_ring.well_founded_dvd_not_unit", "localization_map.mem_coe_submodule", "set.maps_to.iterate", "equiv.sigma_preimage_equiv_symm_apply_fst", "real.sqrt_eq_rpow", "differentiable.csinh", "pequiv.trans_assoc", "primrec.option_bind", "set_of_is_preconnected_eq_of_ordered", "measure_theory.lintegral_map", "category_theory.adjunction.left_triangle", "prime_spectrum.gc_set", "stream.zip_eq", "dfinsupp.subtype_domain_neg", "polynomial.is_unit_C", "finset.Ico.eq_empty_of_le", "times_cont_diff_on_const", "subgroup.mem_sup_right", "true_iff_false", "set.indicator_nonneg", "tfae_mem_nhds_within_Iic", "stream.all_def", "principal_seg.coe_coe_fn", "equiv.nontrivial", "cauchy_nhds", "qpf.Wequiv.abs'", "measurable_inv_iff", "finset.disjoint_of_subset_left", "set.Ico_subset_Ico_union_Ico", "set.image_mul_right_Icc", "sum.elim_injective", "lists.to_of_list", "ennreal.tsum_supr_eq", "option.orelse_none", "relation.equivalence_join_refl_trans_gen", "smooth_left_mul", "measure_theory.outer_measure.of_content_caratheodory", "list.count_eq_zero_of_not_mem", "emetric.inf_edist_le_inf_edist_add_edist", "nat.test_bit_lor", "sub_eq_zero_of_eq", "is_path_connected_iff", "prod.fst_mul", "polynomial.continuous", "ennreal.coe_nat_ne_top", "dfinsupp.mk_add", "edist_mem_uniformity", "polynomial.is_root_of_aeval_algebra_map_eq_zero", "pell.is_pell_mul", "dvd_of_mul_left_dvd", "polynomial.ne_zero_of_ne_zero_of_monic", "add_subgroup.prod_mono_left", "metric.sum.one_dist_le", "category_theory.limits.zero_of_source_iso_zero", "int.modeq.modeq_mul_left'", "ideal.eq_jacobson_iff_not_mem", "mdifferentiable_within_at.congr", "exists_unique.exists2", "measure_theory.l1.simple_func.coe_neg", "computable.succ", "neg_concave_on_iff", "simple_graph.mem_neighbor_finset", "computation.results_thinkN", "ideal.comap_radical", "ext_chart_preimage_mem_nhds_within", "closure_Ioc", "measure_theory.outer_measure.is_caratheodory_inter", "ring.fractional_ideal.mul_right_mono", "measure_theory.integrable_on_of_bounded", "imp_eq_of_eq_false_left", "exists_add_lt_and_pos_of_lt", "and_assoc", "powers.one_mem", "lucas_lehmer_sufficiency", "subring.closure_univ", "isometric.coe_to_affine_map", "linear_equiv.map_eq_zero_iff", "sesq_form.sub_right", "filter.frequently_imp_distrib", "setoid.nonempty_of_mem_partition", "mul_eq_one_iff'", "homological_complex.kernel_map_comp", "continuous_subtype_val", "set.singleton_one", "add_commute.refl", "zmod.units_pow_card_sub_one_eq_one", "ideal.mul_assoc", "free_abelian_group.of_mul", "one_le_div_of_neg", "multiset.singleton_disjoint", "nat.bit1_lt", "imp_self", "uniform_space.has_basis_nhds_prod", "list.all_iff_forall", "norm_num.zero_succ", "category_theory.limits.epi_image_of_epi", "max_lt", "is_local_max.on", "ptendsto_nhds", "filter.tendsto_snd", "is_extr_on.inter", "free_group.prod_mk", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_inv", "list.any_iff_exists_prop", "circle_equiv_symm_apply", "set.disjoint_diff", "category_theory.fully_faithful_cancel_right_inv_app", "stream.tail_map", "ideal.quotient.zero_ne_one_iff", "int.add_lt_add", "ideal.mul_le_inf", "add_semiconj_by.neg_neg_symm", "int.distrib_right", "cardinal.mk_image_eq_of_inj_on_lift", "measurable.mono", "emetric.exists_edist_lt_of_inf_edist_lt", "list.nodup.sublist_ext", "is_bounded_linear_map.comp", "ordinal.is_normal.nfp_le_fp", "ennreal.exists_pos_sum_of_encodable", "has_fpower_series_on_ball.tendsto_locally_uniformly_on", "add_subgroup.bot_normal", "int.sub_nat_nat_add_add", "fintype.card_ulift", "nonneg_of_mul_nonpos_right", "divp_left_inj", "submodule.smul_mono_right", "real.mk_lt", "associates.is_unit_iff_eq_one", "is_lub_Icc", "rat.zero_mk", "group.conj_mem_conjugates_of_set", "real.differentiable_cosh", "category_theory.limits.cocones.ext_inv_hom", "algebra.id.smul_eq_mul", "fin.snoc_update", "div_nonneg", "turing.partrec_to_TM2.tr_ret_respects", "strict_mono.order_dual", "ring_invo.map_eq_zero_iff", "add_comm_group.direct_limit.of_sub", "set.seq_subset", "circle_deg1_lift.translation_number_map_id", "submonoid.localization_map.lift_mk'", "norm_num.rat_cast_div", "function.commute.inv_on_fixed_pts_comp", "int.le_of_neg_le_neg", "nat.modeq.mod_modeq", "finset.weighted_vsub_of_point_apply", "polynomial.coeff_mul", "finmap.replace_to_finmap", "omega.int.preform.sat_of_implies_of_sat", "strict_mono.monotone", "complex.abs_I", "tactic.ring_exp.div_pf", "quotient_map.continuous_iff", "affine_map.coe_zero", "nat.add_pos_right", "cardinal.zero_lt_bit0", "mvpfunctor.W_dest'_W_mk", "pgame.lt_of_le_of_lt", "int.neg_succ_of_nat_add_neg_succ_of_nat", "set.singleton_def", "multiset.pi.cons_same", "wseq.ret_bind", "function.bij_on_pts_of_period", "subgroup.coe_coe", "int.nat_abs_add_le", "multiples.self_mem", "has_fpower_series_on_ball.coeff_zero", "list.le_argmax_of_mem", "measure_theory.measure.regular_haar_measure", "measure_theory.le_infi_lintegral", "con.coe_eq", "turing.list_blank.exists_cons", "mdifferentiable_within_at.comp", "tactic.ring.horner_mul_horner", "free_group.join_red_of_step", "is_local_extr_on_const", "measure_theory.simple_func.sup_eq_map\:2082", "equiv.symm_trans_apply", "Class.powerset_hom", "circle_deg1_lift.iterate_pos_eq_iff", "prod.map_fst'", "cardinal.mul_le_mul_right", "multiset.powerset_len_aux_cons", "function.left_inverse.surjective", "monoid_hom.coe_of", "nhds_within_Ioc_eq_nhds_within_Iic", "multiset.card_pos", "finite_dimensional.complete", "typevec.typevec_cases_cons\:2082_append_fun", "hyperreal.infinitesimal_neg_iff_infinite_neg_inv", "eq_of_forall_dist_le", "mem_groupoid_of_pregroupoid", "con.le_def", "mvqpf.corecF_eq", "is_closed.preimage", "sym2.other_is_mem_other", "equiv.perm.disjoint_mul_comm", "category_theory.limits.image.map_id", "list.mem_singleton_self", "add_le_of_le_of_nonpos'", "ideal.coeff_zero_mem_comap_of_root_mem", "set.maps_to_empty", "nat.mod_two_of_bodd", "list.perm_insertion_sort", "set.nonempty.inr", "alist.keys_insert", "right_mem_segment", "vector_allp_nil", "Module.Mon_Module_equivalence_Algebra.functor_map_to_fun", "matrix.transpose_nonsing_inv", "tactic.abel.subst_into_smulg", "symmetric_symmetrize_rel", "zsqrtd.divides_sq_eq_zero", "false_ne_true", "finset.inj_on_of_surj_on_of_card_le", "category_theory.limits.cones.whiskering_equivalence_counit_iso", "real.sqrt_le_left", "holor.cast_type", "generalized_continued_fraction.convergents'_aux_stable_of_terminated", "has_strict_fderiv_at.sub_const", "ordinal.sub_le", "finset.sum_Ico_eq_sum_range", "multiset.prod_repeat", "power_series.coeff_inv_aux", "ideal.map_mono", "forall_congr_eq", "derivation.smul_to_linear_map_coe", "int.sign_one", "matrix.alg_hom.map_det", "nat.dist.triangle_inequality", "int.neg_lt_neg", "irrational.rat_sub", "real.inner_le_Lp_mul_Lq", "list.find_some", "closed_under_restriction_iff_id_le", "circle_deg1_lift.translation_number_eq_of_semiconj", "associates.factor_set.sup_add_inf_eq_add", "seq.join_cons_nil", "isometric.preimage_symm", "comp.seq_mk", "category_theory.adjunction.right_triangle", "int.div_lt_iff_lt_mul", "filter.has_basis.exists_iff", "semiquot.mem_map", "pos_num.min_fac_aux_to_nat", "of_digits_eq_foldr", "list.bind_singleton", "ereal.neg_def", "set.bUnion_union", "is_least_Icc", "padic_norm_z.norm_p", "mem_nhds_iff_exists_Ioo_subset'", "set.singleton_union", "wseq.cons_append", "add_monoid_hom.cancel_right", "mvqpf.const.mk_get", "has_strict_fderiv_at.smul_const", "lie_algebra.orthogonal.Pso_inv", "has_fderiv_at.comp", "continuous_linear_equiv.continuous_on", "measure_theory.eventually_eq_dirac'", "is_R_or_C.norm_sq_mul", "ordinal.sub_eq_zero_iff_le", "gt_of_ge_of_gt", "ennreal.rpow_one", "abstract_completion.compare_coe", "multiset.rel_zero_left", "list.is_nil_iff_eq_nil", "list.chain'.cons'", "set.subset_pi_eval_image", "int.nat_abs_mul_self'", "structure_groupoid.local_invariant_prop.lift_prop_within_at_of_lift_prop_at", "multiset.sup_zero", "pSet.resp.refl", "ennreal.not_lt_zero", "add_magma.free_add_semigroup.induction_on", "nat.sub_mul_mod", "tendsto_pow_at_top_nhds_0_of_lt_1", "ring.subset_closure", "polynomial.eval_unique", "mul_div_cancel_left", "mv_polynomial.degrees_monomial_eq", "nat.fact_ne_zero", "stream.nth_unfolds_head_tail", "category_theory.limits.bicone.to_cone_X", "add_submonoid.localization_map.of_add_equiv_of_localizations_apply", "pnat.coprime.symm", "int.not_even_one", "topological_space.nhds_mk_of_nhds", "set.Icc_subset_Icc_union_Icc", "add_submonoid.map_inl", "ordinal.le_total", "cardinal.bit1_eq_self_iff", "cancel_factors.cancel_factors_eq", "category_theory.comma.comp_right", "supr_subtype", "nat.bit0_inj", "measure_theory.measure.haar.mem_prehaar_empty", "affine.triangle.altitude_eq_monge_plane", "complex.cos_pi_div_two_sub", "int.sub_lt_sub_left", "finset.image_eq_empty", "Module.Mon_Module_equivalence_Algebra.inverse_map_hom", "set.nonempty_iff_univ_nonempty", "matrix.transpose_apply", "poly.proj_eval", "mv_polynomial.sum_to_iter_Xr", "local_homeomorph.tendsto_symm", "list.nth_update_nth_ne", "finset.mem_univ", "subtype.val_injective", "category_theory.limits.biproduct.map_eq_map'", "roption.bind_dom", "set.Ioc_subset_Ioo_right", "nat.min_fac_eq_one_iff", "option.some_bind", "emetric.diam_empty", "is_coprime.of_mul_add_right_right", "ideal.mul_eq_bot", "nat.lt_iff_add_one_le", "algebra.adjoin_le", "list.map_of_fn", "cardinal.powerlt_omega_le", "continuous_linear_equiv.map_sub", "set.Icc_subset_Ico_iff", "zsqrtd.le_antisymm", "category_theory.limits.biprod.inr_map_assoc", "nat.mul_self_le_mul_self_iff", "metric.is_open_ball", "finset.union_sdiff_distrib", "times_cont_diff.comp", "filter.tendsto_at_bot_add_nonpos_left", "nat.sub_lt_right_iff_lt_add", "add_magma.free_add_semigroup.map_add", "subtype.equiv_iff", "gronwall_bound_x0", "mv_polynomial.C_add", "category_theory.quotient.lift_obj", "with_top.add_lt_add_iff_right", "finite_field.forall_pow_eq_one_iff", "set.Icc_union_Ioc_eq_Icc", "dense_inducing.extend_eq_at", "tendsto_at_top_mul_left", "valuation.map_neg", "finset.bind_singleton_eq_self", "eq_true_of_not_eq_false", "category_theory.Monad.Monad_Mon_equiv_functor", "Icc_mem_nhds_within_Iic", "set.inter_singleton_nonempty", "monoid_hom.coe_range", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_self", "function.commute.iterate_pos_lt_of_map_lt", "continuous_multilinear_map.op_norm_zero_iff", "nat.coprime.gcd_mul_left_cancel", "fin_enum.mem_pi", "add_monoid_hom.coprod_unique", "is_local_min.min", "measure_theory.simple_func.map_coe_ennreal_restrict", "primrec.nat_div_mod", "zmod.nat_coe_zmod_eq_zero_iff_dvd", "differentiable_on_inv", "nat.choose_eq_fact_div_fact", "circle_deg1_lift.lt_map_map_zero", "finset.prod_range_reflect", "linear_action_add_act", "function.equiv.is_equivalence", "add_submonoid.le_comap_map", "adjoin_root.lift_of", "contracting_with.apriori_edist_iterate_efixed_point_le", "add_monoid_hom.coe_mul_left", "list.filter_map_nil", "unique_factorization_domain.induction_on_prime", "ordinal.le_add_left", "is_min_filter.max", "tsum_prod'", "nat.shiftl'_sub", "set.sUnion_subset_sUnion", "times_cont_diff_on.differentiable_on_iterated_fderiv_within", "lie_algebra.endo_algebra_bracket", "imp_iff_right", "free_group.reduce.red", "measurable_nnnorm", "category_theory.limits.is_colimit.cocone_points_iso_of_nat_iso_hom", "linear_equiv.prod_apply", "continuous_linear_map.uniform_embedding_of_bound", "skew_adjoint_matrices_lie_subalgebra_equiv_apply", "int.sign_mul", "free_add_semigroup.traverse_pure", "poly.add_eval", "zmod.cast_int_cast'", "unit_of_invertible_val", "span_le_span_iff", "local_homeomorph.eq_on_source.trans'", "equiv.arrow_congr_symm", "zmod.neg_val", "ideal.eq_top_of_unit_mem", "complex.norm_real", "fin_enum.finset.mem_enum", "wseq.destruct_tail", "nat.totient_pos", "set.bUnion_univ", "ennreal.tendsto_to_real", "category_theory.faithful_reflects_epi", "inv_le_iff_one_le_mul", "zmod.val_zero", "fin.val_eq_coe", "emetric.closeds.edist_eq", "filter.lift_infi'", "gaussian_int.to_complex_div_im", "uniform_continuous\:2082_def", "infi_image", "measure_theory.ae_eq_fun.comp\:2082_mk_mk", "geom_sum_Ico", "padic_int.ext", "direct_sum.mk_zero", "category_theory.limits.cones.postcompose_obj_X", "tactic.ring_exp.pow_pp_pf_prod", "matrix.minor_cons_row", "pnat.xgcd_type.reduce_special", "filter.tendsto_principal_principal", "formal_multilinear_series.min_radius_le_radius_add", "abs_sub_round", "nat.lt_size_self", "is_R_or_C.inv_re", "finsupp.single_eq_zero", "linear_pmap.to_fun_eq_coe", "sym2.rel_bool_spec", "measure_theory.l1.simple_func.dense_inducing", "semidirect_product.lift_inl", "rat.add_comm", "commute.self_cast_nat_mul", "complex.conj_im", "ordinal.power_is_limit_left", "well_founded.lt_succ_iff", "real.inv_rpow", "finset.coe_preimage", "cardinal.lift_max", "multiset.bind_add", "set.card_singleton", "category_theory.eq_of_comp_right_eq", "uniform_embedding_subtype_val", "divp_eq_one_iff_eq", "category_theory.sum_comp_inl", "topological_fiber_bundle_core.local_triv'_inv_fst", "false_or", "pgame.left_moves_mk", "deriv.lhopital_zero_nhds_left", "list.append_subset_iff", "sup_inf_le", "list_all_cons", "smul_comm", "matrix.subsingleton_of_empty_right", "finsupp.induction\:2082", "add_con.ker_lift_range_eq", "tactic.ring_exp.pow_pf_c_c", "int.coe_nat_zero", "finset.mem_of_mem_erase", "exists_or_distrib", "typevec.comp_id", "list.rel_foldr", "structure_groupoid.local_invariant_prop.lift_prop_id", "right_ord_continuous.map_infi", "measure_theory.measure.haar.prehaar_self", "cardinal.aleph_idx_le", "of_digits_append", "algebra.adjoin_le_iff", "primrec.encode_iff", "finset.erase_eq_of_not_mem", "Mod.comap_obj_X", "function.const_comp", "list.nth_range", "setoid.inf_iff_and", "fin.nat_find_mem_find", "units.unit_of_nearby_coe", "mv_polynomial.coeff_X'", "nhds_within_ext_chart_target_eq", "ring.fractional_ideal.span_singleton_fractional", "finset.eq_one_of_prod_eq_one", "galois_coinsertion.strict_mono_l", "finset.sum_subtype_of_mem", "filter.tendsto_map", "function.right_inverse_surj_inv", "ball_subset_of_comp_subset", "add_div_eq_mul_add_div", "set.abs_sub_left_of_mem_interval", "primrec.list_inth", "bool.dichotomy", "list.map_add_range'", "category_theory.equivalence.cancel_unit_right_assoc", "set.inter_subset_inter_right", "real.cos_sq_le_one", "prod.inv_mk", "power_series.order_monomial_of_ne_zero", "category_theory.monoidal_category.right_unitor_inv_naturality", "algebraic_geometry.PresheafedSpace.ext", "mem_path_component_self", "measure_theory.extend_union", "commute.fpow_self", "category_theory.non_preadditive_abelian.neg_sub'", "padic_norm_e.zero", "ennreal.to_real_add", "euclidean_geometry.dist_set_eq_iff_dist_orthogonal_projection_eq", "list.cons_append", "monotone_comp_rel", "has_fderiv_within_at.prod", "list.erase_sublist", "relation.trans_gen.head", "nat.bodd_zero", "filter.mem_Sup_sets", "real.continuous_sin", "inner_product_geometry.angle_neg_right", "composition_card", "set.finite.of_fintype", "complex.abs_eq_zero", "real.of_rat_sub", "set.inter_diff_self", "times_cont_diff_at.add", "list.insert_of_not_mem", "open_subgroup.ext_iff", "turing.tape.mk'_right", "linear_independent.inl_union_inr", "asymptotics.is_o.congr_of_sub", "string.iterator.zero_lt_length_next_to_string_of_has_next", "multiset.zero_add", "multiset.sections_cons", "Ioo_mem_nhds_within_Ioi", "is_coprime.mul_dvd", "zsqrtd.le_of_add_le_add_left", "multiset.mem_attach", "compact_univ", "measure_theory.l1.simple_func.dense_embedding", "monotonicity.const", "continuous_subtype_nhds_cover", "ordinal.CNF_foldr", "complex.exp_sub", "times_cont_diff_on.continuous_on_iterated_fderiv_within", "lucas_lehmer.s_mod_mod", "filter.push_pull", "uniformity_le_symm", "asymptotics.is_o_const_smul_right", "ideal.eval\:2082_C_mk_eq_zero", "set.inj_on.inv_fun_on_image", "list.join_repeat_nil", "set.univ_nonempty", "omega.coeffs.val_between_nil", "finset.prod_sum", "multiset.fold_add", "continuous_iff_ultrafilter", "filter.frequently_iff", "add_monoid_hom.fst_comp_prod", "list.sum_take_of_fn", "Set.mem_inter", "ideal.sup_mul_left_self", "polynomial.splits_id_iff_splits", "finite_dimensional.of_finite_basis", "reflexive_one_one_reducible", "filter.add_zero", "mv_polynomial.iter_to_sum_C_C", "real.has_deriv_at_log_of_pos", "mdifferentiable_id", "nat.primrec'.sub", "compl_inf", "mul_left_eq_self", "multiset.to_finset_subset", "category_theory.limits.binary_bicone.to_cone_X", "finset.mem_image_of_mem", "nat.cast_id", "nnreal.geom_mean_le_arith_mean3_weighted", "state_t.run_monad_lift", "has_ftaylor_series_up_to_on.congr", "equiv.psigma_equiv_sigma_symm_apply", "CommRing.free_obj_coe", "gronwall_bound_K0", "affine_map.coe_one", "is_local_extr.comp_continuous", "decidable.not_ball", "measurable_space.gc_comap_map", "with_one.coe_ne_one", "euclidean_geometry.orthogonal_projection_eq_self_iff", "group.closure_subset_iff", "power_series.coeff_succ_mul_X", "dense_inter_of_open_right", "add_subgroup.map_bot", "ordinal.mul_lt_mul_iff_left", "implicit_function_data.left_map_implicit_function", "complex.abs_div", "fin.le_iff_coe_le_coe", "fpow_le_iff_le", "function.support_sub", "polynomial.mod_by_monic_X", "category_theory.limits.prod.map_fst_assoc", "int.add_le_of_le_sub_right", "typevec.diag_sub_val", "pell.n_lt_a_pow", "nat.coprime_one_left_iff", "category_theory.limits.zero_of_epi_comp", "equiv.has_sum_iff_of_support", "algebra.comap_top", "measurable_space.is_measurable_generate_from", "is_min_filter.sub", "pgame.lt_zero", "or_iff_left_of_imp", "complex.sin_pi", "cau_seq.abv_pos_of_not_lim_zero", "pgame.le_of_equiv_of_le", "pnat.one_coe", "map_cInf_of_continuous_at_of_monotone", "complex.log_I", "module.gsmul_eq_smul", "dense_inducing.extend_Z_bilin", "multiset.filter_eq_nil", "free_abelian_group.mul_def", "generalized_continued_fraction.of_h_eq_floor", "set.bij_on_Union", "dioph.dioph_comp2", "wseq.to_list'_map", "measure_theory.ae_eq_fun.quotient_out'_eq_coe_fn", "deriv_within_mul", "measure_theory.measure.dirac_apply", "is_least_union_iff", "geom_series\:2082_self", "neg_add_le_right_of_le_add", "complex.sin_neg", "inner_product_space.of_core.inner_smul_right", "rel.preimage_univ", "bool.ff_eq_to_bool_iff", "nat.coprime.gcd_right", "filter.mem_sets_of_eq_bot", "real.nnnorm_coe_nat", "open_embedding_inl", "padic.coe_mul", "norm_num.add_bit1_bit1", "equiv.coe_mul_left", "differentiable_within_at.pow", "list.tfae_cons_of_mem", "finset.sup_empty", "polynomial.degree_eq_degree_of_associated", "le_of_forall_ge_of_dense", "has_sum_subtype_iff_indicator", "set.preimage_coe_coe_diagonal", "finset.sum_product'", "uniform_continuous\:2082_curry", "isometry.right_inv", "complex.re_add_im", "fin.find_min'", "ordinal.mul_pos", "is_coprime.mul_right", "one_le_two", "add_submonoid.mem_infi", "set.Ioc_diff_right", "multiset.cons_subset", "dist_le_of_le_geometric_two_of_tendsto", "ennreal.of_real_one", "compact_compact_separated", "filter.image_coe_mem_sets", "is_local_max_on.fderiv_within_nonpos", "continuous_inf_dom_left", "zero_eq_dist", "local_equiv.maps_to", "is_cyclic.exists_monoid_generator", "category_theory.limits.biprod.braiding_map_braiding_assoc", "closure_Ioi", "finsupp.mem_supported", "add_submonoid.comap_infi", "infi_and", "set.finite.coe_to_finset", "submonoid.localization_map.sec_spec'", "list.nth_le_drop'", "finset.mem_bind", "nat.succ_le_iff", "pos_num.cast_add", "measure_theory.simple_func.fin_meas_supp.pair", "smooth_right_mul", "list.erase_cons_tail", "times_cont_mdiff_within_at.mono", "complex.sinh_conj", "smooth.prod_map", "is_greatest.bdd_above", "mfderiv_within_inter", "continuous_linear_equiv.times_cont_diff_within_at_comp_iff", "continuous_within_at.tendsto", "cardinal.univ_umax", "list.length_lookmap", "category_theory.monoidal_of_has_finite_coproducts.tensor_obj", "ennreal.le_inv_iff_le_inv", "module.direct_limit.induction_on", "multiset.sup_cons", "category_theory.limits.prod.hom_ext", "neg_add_le_left_of_le_add", "category_theory.under.comp_right", "list.sum_hom_rel", "equiv.symm_trans_swap_trans", "div_ne_zero", "cardinal.add_eq_right_iff", "add_submonoid.coe_supr_of_directed", "list.append_eq_has_append", "finite_field.card'", "linear_pmap.left_le_sup", "rel.core_id", "cau_seq.zero_lim_zero", "nat.prime_two", "circle_deg1_lift.translation_number_translate", "int.to_nat_lt_to_nat", "set.insert_diff_of_mem", "localization.induction_on\:2082", "matrix.from_blocks_add", "nat.le_of_succ_le", "pgame.move_right_mk", "linear_independent_monoid_hom", "subgroup.prod_mono_left", "function.is_periodic_pt.sub", "vsub_left_injective", "cauchy_pure", "cardinal.lt_omega", "is_bounded_linear_map.differentiable_at", "nhds_def", "compl_le_compl_iff_le", "is_bounded_bilinear_map_mul", "omega.coeffs.val_between_eq_of_le", "submonoid.prod_bot_sup_bot_prod", "onote.NF.below_of_lt'", "is_measurable.compl_iff", "filter.const_eventually_eq'", "list.pairwise_filter", "tendsto.max", "zsqrtd.one_im", "nhds_basis_opens", "submodule.eta", "lt_max_iff", "con.ext'_iff", "nat.primrec'.comp\:2082", "infi_pos", "category_theory.limits.coprod_desc_inl_inr", "fin.succ_le_succ_iff", "pow_two_pos_of_ne_zero", "algebra.restrict_scalars_equiv_apply", "metric.tendsto_nhds_within_nhds_within", "category_theory.iso.hom_eq_inv", "set.range_comp_subset_range", "ennreal.ne_top_of_mul_ne_top_left", "finset.prod_preimage", "bdd_above_Ico", "or.comm", "one_one_equiv.le_congr_left", "stream.even_interleave", "filter.map.is_monoid_hom", "ideal.eq_bot_or_top", "submodule.mem_span_insert'", "mul_geom_sum", "structure_groupoid.compatible", "alist.insert_singleton_eq", "cardinal.mk_bounded_set_le", "sum.traverse_map", "convex_empty", "finset.coe_mem", "finset.fold_map", "affine_subspace.affine_span_coe", "add_subgroup.mem_comap", "localization_map.ring_equiv_of_ring_equiv_eq_map", "measurable.nnnorm", "is_coprime.mul_add_left_right_iff", "prod.fst_mul_snd", "CommRing.free_map_coe", "finset.inf_def", "coe_not_mem_range_equiv", "linear_map.quotient_inf_equiv_sup_quotient_symm_apply_left", "exists_eq_left", "omega.int.valid_of_unsat_not", "Sup_insert", "padic.of_rat_one", "list.count_append", "list.ne_nil_of_mem", "real.add_lt_add_iff_left", "dioph.lt_dioph", "real.exp_ne_zero", "add_submonoid.localization_map.eq_of_eq", "tensor_product.smul_tmul", "tendsto_uniformly.continuous", "is_linear_map.map_neg", "differentiable_on.mul_const", "matrix.scalar.commute", "galois_connection.l_u_le", "bdd_below_iff_subset_Ici", "emetric.mem_closure_iff_inf_edist_zero", "concave_on.le_on_segment'", "set.inj_on.comp", "complex.lim_re", "galois_connection.l_sup", "euclidean_geometry.angle_eq_angle_of_angle_eq_pi", "wseq.mem_think", "list.mem_union_right", "pSet.lift_mem_embed", "measure_theory.integrable_zero", "convex.mem_Icc", "add_submonoid.comap_map_comap", "category_theory.functor_to_types.hom_inv_id_app_apply", "continuous_linear_map.differentiable", "metric.bounded.subset", "mvpfunctor.W_mk_eq", "traversable.mfoldl_map", "polynomial.next_coeff_of_pos_nat_degree", "pfunctor.iget_map", "ennreal.lt_iff_exists_real_btwn", "finset.subset_range_sup_succ", "zsqrtd.le_total", "subgroup.gpowers_subset", "mul_le_mul_of_nonneg_left", "Module.Mon_Module_equivalence_Algebra.inverse_obj_mul", "convex_on_univ_of_deriv2_nonneg", "filter.prod_map_map_eq", "real.sqr_sqrt", "ordinal.power_le_power_left", "cau_seq.lim_mul", "antilipschitz_with.of_subsingleton", "mul_lt_mul''''", "metric.nonempty_closed_ball", "is_min_filter.bicomp_mono", "int.gcd_dvd_left", "fintype.left_inverse_bij_inv", "list.index_of_inj", "smul_eq_zero", "cau_seq.exists_lt", "contracting_with.dist_le_of_fixed_point", "list.foldl_eq_foldr", "divp_mul_cancel", "free_group.one_bind", "order_bot.lower_bounds_univ", "has_deriv_at.smul_const", "ennreal.one_lt_two", "neg_add_lt_iff_lt_add_right", "continuous_linear_equiv.injective", "ordinal.add_omega_power", "submodule.coe_mk", "subtype.map_comp", "filter.tendsto_comap", "finset.inf_empty", "bool.cond_ff", "times_cont_diff_on_succ_iff_has_fderiv_within_at", "pell.xz_succ_succ", "submonoid.localization_map.eq_mk'_iff_mul_eq", "univ_unique", "eq_top_iff", "submodule.prod_map_snd", "isometric.mul_apply", "is_noetherian_ring.exists_irreducible_factor", "linear_map.range_prod_le", "semidirect_product.mul_right", "associated_normalize", "holor.mul_assoc0", "nat.prime.pow_not_prime", "polynomial.prod_X_sub_C_next_coeff", "coe_I_zero", "has_sum_le", "category_theory.biproduct.column_nonzero_of_iso'", "int.mul_mod", "finset.singleton_subset_set_iff", "hyperreal.infinite_pos_iff_infinite_of_pos", "interval_integral.integral_has_fderiv_within_at", "cardinal.aleph_is_normal", "set.inter_subset_right", "le_of_tendsto'", "measure_theory.to_measure_apply", "nnreal.zero_rpow", "matrix.dot_product_diagonal'", "ring.fractional_ideal.sup_eq_add", "bool.to_nat_le_to_nat", "multiset.sub_eq_fold_erase", "add_con.map_of_surjective_eq_map_gen", "padic_seq.norm_eq", "multiset.erase_dup_singleton", "of_not_imp", "finset.prod_range_one", "enat.with_top_equiv_lt", "list.length_injective", "div_le_iff_of_nonneg_of_le", "turing.partrec_to_TM2.tr_normal_respects", "list.map_filter_map_of_inv", "submodule.sup_orthogonal_of_is_complete", "list.lex.append_right", "set.ext_iff", "hyperreal.coe_bit0", "quadratic_form.to_matrix_smul", "finset.card_bind_le", "circle_deg1_lift.map_nat_add", "cardinal.add_le_add_left", "asymptotics.is_O_with.sub_is_o", "convex_hull_to_cone_is_least", "int.zero_add", "lie_algebra.direct_sum.bracket_apply", "multiset.nat.mem_antidiagonal", "measure_theory.outer_measure.mono'", "pmf.tsum_coe", "finset.comp_sup_eq_sup_comp_of_is_total", "submonoid.prod_mono", "list.erase_cons_subperm_cons_erase", "category_theory.limits.fork.of_\[Iota]_app_zero", "has_fderiv_within_at.add_const", "has_mfderiv_within_at_inter", "equiv.apply_symm_apply", "measure_theory.measure.regular.smul", "finset.card_erase_of_mem", "finset.sum_centroid_weights_eq_one_of_nonempty", "nat.land_assoc", "mvqpf.fix.mk_dest", "pow_gcd_card_eq_one_iff", "tsum_eq_sum", "finset.mem_map_of_mem", "lie_zero", "derivation.coe_fn_coe", "multiset.fold_singleton", "is_local_extr_on.inter", "push_neg.not_implies_eq", "wseq.lift_rel_flatten", "exists_mem_ne_zero_of_ne_bot", "int.to_nat_zero_of_neg", "has_strict_fderiv_at.to_local_homeomorph_coe", "with_top.le_coe", "local_homeomorph.restr_open_source", "multiset.rel.add", "padic_int.mk_units_eq", "Cauchy.pure_cauchy_dense", "cardinal.mk_range_le", "associates.prod_le_prod", "has_deriv_at.cos", "bit0_pos", "stream.mem_cons_of_mem", "nat.lt_of_lt_pred", "qpf.fix.ind_rec", "ring.direct_limit.of_one", "list.exists_le_of_sum_le", "nat.mul_dvd_mul_iff_left", "continuous_dist", "polynomial.continuous_on", "smul_inv", "category_theory.biprod.of_components_fst", "set.lt_eq_ssubset", "pow_le_one_of_le_one", "lipschitz_with.edist_lt_top", "set.nonempty_Ico_sdiff", "free_ring.lift_comp_of", "filter.tendsto.comp", "filter.lift'_mono", "order.sequence_of_cofinals.monotone", "irrational_add_rat_iff", "exists_lt_mul_self", "nat.mul_lt_mul_of_pos_right", "irrational.of_mul_rat", "valuation.map_neg_one", "category_theory.limits.biprod.inr_snd_assoc", "opposite.op_neg", "prime_spectrum.zero_locus_empty_of_one_mem", "mul_self_lt_mul_self", "measurable_space.is_measurable_Inf", "div_self_of_invertible", "uniform_continuous_subtype_mk", "category_theory.limits.types.terminal_from", "quadratic_form.polar_smul_left", "ideal.le_comap_mul", "set.image2_empty_right", "div_mul_right", "mv_polynomial.mem_restrict_degree", "half_add_self", "zorn.zorn_subset", "submonoid.map_bot", "not_forall_of_exists_not", "set.preimage_id'", "multiset.mem_cons_self", "lie_algebra.equiv.of_subalgebra_apply", "polynomial.differentiable_at", "eq_of_nhds_ne_bot", "finset.sup_lt_iff", "polynomial.eq_X_add_C_of_degree_eq_one", "char.vne_of_ne", "sequential_closure_subset_closure", "pow_succ'", "cardinal.one_le_bit0", "compact_open_separated_mul", "fin.lt_def", "nat.coprime.gcd_left", "int.coe_nat_lt_coe_nat_of_lt", "measure_theory.simple_func.fin_meas_supp.of_lintegral_lt_top", "fderiv_within_sum", "nat.mul_succ", "real.continuous_rpow_aux1", "nnnorm_eq_zero", "category_theory.comma.id_left", "upper_bounds_Ioc", "bilin_form.is_adjoint_pair.mul", "convex_cone.salient_of_blunt", "bilin_form.is_adjoint_pair.smul", "powers_hom_symm_apply", "equiv.set.sum_compl_symm_apply_of_mem", "finset.fold_insert_idem", "uniform_space.completion.continuous_extension", "measure_theory.ae_eq_fun.neg_mk", "lt_irrefl", "finset.subtype_map_of_mem", "add_commute.left_comm", "gsmul_one", "zmod.legendre_sym_eq_one_or_neg_one", "finset.fold_union_empty_singleton", "measure_theory.integrable_of_dominated_convergence", "dist_partial_sum_le_of_le_geometric", "set.ball_insert_iff", "list.length_enum", "dense_inducing.mk'", "char_poly_degree_eq_dim", "list.Ico.pred_singleton", "units.zero_lt", "zorn.super_of_not_max", "subtype.range_coe_subtype", "filter.lift'_pure", "prod.snd_one", "set.diff_subset_comm", "nat.rfind_opt_spec", "lcm_units_coe_right", "upper_bounds_insert", "holor.cprank_max_upper_bound", "integral_domain.to_is_integral_domain", "num.add_to_nat", "norm_eq_infi_iff_inner_le_zero", "complex.nat_cast_im", "principal_seg.of_element_top", "hyperreal.infinite_of_infinitesimal_inv", "category_theory.arrow.lift_mk'_right_assoc", "set.image_add_const_Ico", "is_max_on.inf", "matrix.det_zero_of_column_eq", "semiquot.mem_blur'", "functor.map_equiv_apply", "pos_num.pred_to_nat", "set.eq_on.image_eq", "digits_lt_base'", "eq_add_cosets_of_normal", "is_preconnected_closed_iff", "field.subset_closure", "smooth_mul", "computation.terminates_of_mem", "pgame.nim.sum_first_wins_iff_neq", "category_theory.discrete.nat_iso_inv_app", "filter.ne_bot.nonempty_of_mem", "is_order_right_adjoint_Sup", "list.perm_repeat", "nat.bit0_succ_eq", "game.le_antisymm", "quotient.exists_rep", "lucas_lehmer.X.coe_nat", "structure_groupoid.local_invariant_prop.lift_prop_within_at_congr_iff_of_eventually_eq", "inf_sup_self", "onote.zero_mul", "int.neg_mul_comm", "category_theory.limits.biprod.braiding_map_braiding", "ordinal.succ_inj", "filter.comap_eq_of_inverse", "add_units.is_add_unit_add_add_units", "inv_involutive", "differentiable_at.neg", "ring_equiv.map_eq_zero_iff", "linarith.int.coe_nat_mul_one", "int.neg_neg_of_nat_succ", "set.inter_right_comm", "wseq.exists_of_lift_rel_right", "option.bind_assoc", "localization_map.ring_equiv_of_ring_equiv_eq", "category_theory.zero_mul_inv", "vector.to_list_injective", "is_greatest_Ioc", "fin.cons_succ", "measure_theory.integral_nonneg_of_ae", "fin.cast_succ_injective", "equiv.bijective", "nonneg_add_comm_group.nonneg_total_iff", "convex.norm_image_sub_le_of_norm_fderiv_le", "category_theory.limits.walking_pair.swap_symm_apply_ff", "measure_theory.measure.conj_conj", "abs_inv", "norm_num.adc_one_one", "mdifferentiable_at_atlas_symm", "category_theory.functor.map_iso_trans", "primrec\:2082.right", "measure_theory.integrable_on.mono", "is_measurable.sUnion", "polynomial.eval\:2082_eq_sum", "iff_false_left", "joined_in.mono", "times_cont_mdiff_at.prod_map'", "circle_deg1_lift.lt_map_of_nat_lt_translation_number", "lt_supr_iff", "one_div_lt_one_div_of_lt", "ennreal.to_real_rpow", "ordinal.type_eq_zero_iff_empty", "set.preimage_const_add_Iio", "imp_not_comm", "filter.map_sub_at_top_eq_nat", "int.mul_lt_mul_of_neg_right", "quotient_add_group.coe_zero", "nsmul_add_comm'", "real.exp_neg", "measure_theory.simple_func.mem_range", "filter.germ.const_top", "with_top.some_le_some", "opposite.unop_eq_zero_iff", "finmap.keys_singleton", "generalized_continued_fraction.continuants_aux_stable_step_of_terminated", "has_fderiv_at.sub", "nat.pred_lt", "set.Union_neg", "finmap.keys_replace", "submodule.linear_proj_of_is_compl_idempotent", "subgroup.le_normalizer_of_normal", "category_theory.comma.fst_map", "list.nil_kunion", "has_deriv_at_filter.is_O_sub", "hyperreal.is_st_st_of_is_st", "abs_pos_of_neg", "zsqrtd.muld_val", "category_theory.prod_id_snd", "continuous_within_at.congr", "is_local_min_on.comp_mono", "approximates_linear_on.surj_on_closed_ball", "Mod.assoc_flip", "complex.cosh_of_real_re", "filter.map_inf'", "finmap.lift_on_to_finmap", "homological_complex.d_squared", "real.sin_nonpos_of_nonnpos_of_neg_pi_le", "computation.terminates_congr", "supr_eq_of_tendsto", "category_theory.limits.cofork.is_colimit.hom_ext", "frontier_le_subset_eq", "continuous_linear_map.coe_coprod", "list.take'_nil", "int.mod_sub_cancel_right", "set.sigma_to_Union_surjective", "modeq_digits_sum", "with_top.add_eq_top", "subgroup.multiset_prod_mem", "int.neg_succ_of_nat_mod", "tangent_map_chart_symm", "generalized_continued_fraction.of_correctness_at_top_of_terminates", "nat.choose_succ_right_eq", "directed.rel_sequence", "measure_theory.measure.restrict_Union", "con.mul_ker_mk_eq", "ring_hom.coe_add_monoid_hom_injective", "multiset.coe_foldr", "ennreal.to_nnreal_sum", "nnreal.coe_ne_zero", "finsupp.sum_neg", "linear_independent.mono", "real.rpow_eq_zero_iff_of_nonneg", "add_subgroup.coe_bot", "equiv.set.union_apply_right", "structure_groupoid.local_invariant_prop.lift_prop_at_of_mem_maximal_atlas", "linear_map.std_basis_apply", "mv_polynomial.smul_eval", "finsupp.prod_single_index", "pgame.add_congr", "bernoulli_four", "ennreal.mul_Sup", "qpf.liftp_iff'", "times_cont_diff_on_succ_iff_fderiv_within", "equiv.perm.sign_inv", "cardinal.sup_le", "filter.tendsto.basis_both", "subsemiring.coe_bot", "nat.lt_of_le_and_ne", "vsub_sub_vsub_cancel_right", "cau_seq.lim_zero_sub_rev", "polynomial.coe_eval\:2082_ring_hom", "premetric.metric_quot_dist_eq", "function.embedding.refl_apply", "measurable_space.map_infi", "equiv.subtype_congr_right_mk", "set.mem_interval_of_le", "filter.frequently.exists", "nnreal.coe_div", "ereal.le_neg_of_le_neg", "gcd_assoc", "local_homeomorph.continuous_on_iff_continuous_on_comp_right", "lt_of_le_not_le", "nat.bit1_inj", "zero_smul", "multiset.disjoint_of_nodup_add", "div_lt_div_iff", "fin.is_some_find_iff", "le_top", "times_cont_mdiff.prod_mk", "nat.cast_two", "associates.prod_mono", "zorn.chain_succ", "ideal.exists_coeff_ne_zero_mem_comap_of_non_zero_divisor_root_mem", "cmp_compares", "free_add_magma.map_of", "is_min_on.sub", "nat.partrec'.of_prim", "euclidean_domain.gcd_eq_gcd_ab", "or_eq_of_eq_false_right", "nat.partrec.code.evaln_mono", "min_le_min", "euclidean_domain.div_zero", "equiv.mul_left_symm", "comp_le_comp_left_of_monotone", "euclidean_geometry.reflection_reflection", "function.semiconj\:2082.id_left", "nsmul_sub", "eq_zero_of_mul_self_add_mul_self_eq_zero", "is_measurable_Ici", "asymptotics.is_O.congr_right", "convex_halfspace_im_lt", "free_magma.traverse_pure", "real.sin_pi_div_four", "sum.elim_inr", "mv_polynomial.total_degree_rename_le", "mv_polynomial.pderivative_eq_zero_of_not_mem_vars", "differentiable_on.sin", "interval_integral.norm_integral_eq_norm_integral_Ioc", "computation.think_mem", "is_unit_iff_forall_dvd", "list.kreplace_self", "ne.def", "multiset.to_list_zero", "num.cast_bit0", "affine_map.coe_homothety_affine", "nat.sub_zero", "fin.update_cons_zero", "neg_inj", "subtype.tag_irrelevant", "of_iff_true", "zsqrtd.add_def", "deriv_zero_of_not_differentiable_at", "antilipschitz_with.to_right_inv_on'", "omega.nat.holds_nonneg_consts", "list.traverse_eq_map_id", "cardinal.mk_image_eq_lift", "is_R_or_C.norm_sq_eq_def'", "pnat.prime.not_dvd_one", "list.subperm_cons_diff", "is_compl.to_order_dual", "finset.sum_add_distrib", "affine_subspace.mem_inf_iff", "measure_theory.simple_func.integral_eq_integral", "category_theory.abelian.pseudoelement.pseudo_injective_of_mono", "holor.cprank_max_nil", "continuous_linear_map.differentiable_within_at", "cardinal.aleph_idx.init", "list.map_concat", "filter.map_eq_bot_iff", "set.image_add_left'", "polynomial.degree_mul_le", "finset.surj_on_of_inj_on_of_card_le", "hyperreal.infinite_pos_of_tendsto_top", "multiset.count_le_of_le", "ultrafilter_is_open_basic", "has_fderiv_within_at.const_add", "array.mem_rev_list_aux", "zorn.chain_closure_closure", "num.shiftr_to_nat", "ring_hom.eq_lift_of_surjective", "is_compl.antimono", "category_theory.limits.cokernel_comp_is_iso_inv", "category_theory.cokernel_zero_of_nonzero_to_simple", "finset.piecewise_univ", "complex.abs_im_div_abs_le_one", "padic_seq.ne_zero_iff_nequiv_zero", "asymptotics.is_O.prod_left", "lt_or_le", "or_true", "qpf.supp_eq_of_is_uniform", "normalize_coe_units", "ennreal.lt_iff_exists_nnreal_btwn", "add_subgroup.coe_inf", "turing.tape.nth_zero", "polynomial.X_sub_C_mul_remove_factor", "list.forall\:2082_drop", "nat.cast_eq_zero", "computation.lift_rel_congr", "nat.multiplicity_eq_card_pow_dvd", "sum.swap_swap_eq", "measurable.is_glb", "list.nth_range'", "turing.pointed_map.map_pt", "neg_add_cancel_left", "not_imp_not", "add_lt_add_right", "cardinal.zero_power", "int.eq_mul_div_of_mul_eq_mul_of_dvd_left", "subring.closure_eq_of_le", "continuous_linear_map.op_norm_comp_le", "int.mod_nonneg", "continuous_linear_map.coe_cod_restrict", "set.image_image", "pnat.gcd_eq", "add_submonoid.localization_map.map_comp", "subgroup.coe_inv", "lcm_one_right", "list.map_filter_eq_foldr", "le_total", "complex.linear_map.coe_re", "locally_finite_iff_exists_realizer", "multiset.bind_assoc", "dfinsupp.mem_support_to_fun", "sub_lt_of_sub_lt", "topological_space.opens.supr_s", "complex.of_real_sin_of_real_re", "list.rel_perm_imp", "multiset.ndunion_le_add", "category_theory.limits.is_equivalence_preserves_zero_morphisms", "filter.Limsup_le_Limsup_of_le", "mv_polynomial.monic_monomial_eq", "nat.coprime.gcd_mul_left_cancel_right", "set.insert_nonempty", "continuous_on_inv", "roption.ret_eq_some", "matrix.special_linear_group.ext", "measure_theory.ae_eq_fun.induction_on\:2083", "wseq.of_list_cons", "localization_map.mk'_mul_cancel_right", "nnreal.add_halves", "monotone.const_mul", "ring.direct_limit.of_neg", "add_monoid_algebra.coe_algebra_map", "complex.norm_rat", "inner_mul_inner_self_le", "exists_lt_of_cinfi_lt", "category_theory.limits.pushout_cocone.mk_X", "bilin_form.coe_fn_congr", "ideal.is_maximal.is_prime", "subtype.coe_eta", "has_fderiv_at.neg", "cardinal.sup_lt_ord_of_is_regular", "multiset.bind_bind", "uniform_space.uniform_continuous_quotient_mk", "submodule.sum_smul_mem", "vsub_left_cancel_iff", "finset.card_le_one_of_subsingleton", "list.tendsto_insert_nth", "rel_iso.apply_symm_apply", "finset.sdiff_subset_sdiff", "generalized_continued_fraction.ext_iff", "traversable.foldr_map", "submonoid.mem_sup", "cardinal.lift_eq_nat_iff", "ordinal.type_out", "ordinal.cof_le_card", "is_local_extr.comp_antimono", "units.mul_left_eq_zero", "measure_theory.simple_func.lintegral_sum", "inv_div_left", "set.univ_inv", "normal_of_compact_t2", "list.prod_hom", "continuous.continuous_at", "int.lt_sub_right_of_add_lt", "list.subperm.countp_le", "has_strict_deriv_at_neg", "fintype.univ_bool", "fderiv_smul_algebra_const", "set.image_preimage_subset", "category_theory.monoidal_functor.comp_\[CurlyEpsilon]_is_iso", "set.surj_on.inter", "measurable_space.le_map_comap", "nat.modeq.modeq_mul_right'", "measure_theory.simple_func.bind_apply", "category_theory.limits.pushout_cocone.mk_inl", "roption.ext'", "set.indicator_finset_sum", "nat.div_div_div_eq_div", "finsupp.smul_single", "add_submonoid.localization_map.ext", "order.mem_ideal_of_cofinals", "wseq.lift_rel_destruct", "associates.prod_top", "nat.dvd_of_pow_dvd", "Set.ext", "measure_theory.integral_add_compl", "computation.equiv.equivalence", "add_submonoid.forall", "real.exp_pos", "zmod.pow_div_two_eq_neg_one_or_one", "polynomial.derivative_eval\:2082_C", "free_group.red.exact", "continuous_quotient_mk", "mul_div_mul_right", "nat.partrec.code.evaln_complete", "measurable_space.generate_from_sup_generate_from", "nat.prime.multiplicity_one", "add_submonoid.coe_prod", "has_fderiv_within_at.continuous_within_at", "has_deriv_at_filter.const_add", "list.chain_singleton", "list.map_erase", "filter.tendsto_iff_rtendsto'", "category_theory.equivalence.pow_one", "continuous_extend_from", "interior_mem_uniformity", "finset.filter_union_right", "uniform_continuous_uniformly_extend", "list.mem_insert_nth", "digits_zero_succ", "sym_sesq_form.ortho_sym", "polynomial.coeff_nat_degree_eq_zero_of_degree_lt", "polynomial.fderiv_within", "interval_integral.integral_smul", "digits_len_le_digits_len_succ", "with_zero.coe_mul", "mvqpf.const.get_map", "int.eq_of_mul_eq_mul_right", "functor.comp.applicative_comp_id", "Set.mem_insert", "submodule.mem_sup'", "filter.ptendsto_iff_rtendsto", "turing.partrec_to_TM2.head_main_ok", "ennreal.add_ne_top", "has_fderiv_within_at.nhds_within", "game.add_assoc", "filter.rcomap'_compose", "wseq.lift_rel_think_left", "dfinsupp.prod_map_range_index", "cardinal.mul_lt_omega", "subsemiring.map_le_iff_le_comap", "bounded_continuous_function.norm_eq", "quotient_group.eq", "and_not_self", "path.of_line_mem", "continuous_linear_map.has_strict_fderiv_at", "mul_equiv.to_equiv_symm", "znum.cast_inj", "alt_sesq_form.self_eq_zero", "int.zero_shiftl", "Set.mem_Union", "int.units_pow_two", "category_theory.adjunction.cones_iso_component_hom_app", "preorder_hom.ext", "joined_in.target_mem", "add_submonoid.localization_map.mk'_eq_iff_mk'_eq", "is_compact.exists_is_lub", "set.bUnion_empty", "ennreal.coe_nonneg", "commute.units_inv_right_iff", "submonoid.mem_inf", "int.nat_abs_of_neg_succ_of_nat", "finset.Ico.subset", "add_lt_add_iff_right", "omega.nat.sub_subst_equiv", "nhds_within_Iic_self_ne_bot", "norm_norm", "list.update_nth_length", "category_theory.limits.biproduct.\[Iota]_\[Pi]_ne", "measure_theory.simple_func.restrict_preimage_singleton", "is_group_hom.comp", "mul_equiv.coe_symm_mk", "ennreal.le_div_iff_mul_le", "pgame.winner_cases", "add_submonoid.coe_comap", "nat.add_div_eq_of_add_mod_lt", "typevec.cases_cons_append1", "complex.sin_add", "category_theory.arrow.lift.fac_left", "computation.think_equiv", "times_cont_mdiff_on_id", "equiv.neg_symm", "finmap.keys_union", "tendsto_finset_prod", "measure_theory.regular_conj_iff", "pos_num.mul_to_nat", "uliftable.up_down", "nat.zero_of_test_bit_eq_ff", "with_zero.zero_le", "subgroup.map_map", "ideal.quotient.eq_zero_iff_mem", "set.down_up", "irrational.rat_add", "filter.mem_or_compl_mem_of_ultrafilter", "denumerable.denumerable_list_aux", "monotone_gfp", "sub_sub_sub_cancel_right", "padic_norm_z.padic_norm_z_of_int", "char.zero_lt_d800", "rat.denom_neg_eq_denom", "function.injective.nontrivial", "decidable.forall_or_distrib_left", "polynomial.splitting_field_aux.succ", "multiset.ndinsert_of_mem", "Lim_nhds", "finset.not_mem_sdiff_of_mem_right", "continuous_linear_map.range_prod_eq", "associates.out_top", "real.cos_int_mul_two_pi_add_pi", "finset.center_mass_subset", "tangent_bundle.smooth_at_proj", "cardinal.mk_compl_eq_mk_compl_finite_lift", "inner_product_geometry.angle_zero_right", "free_group.red.to_append_iff", "mul_self_eq_zero", "list.range'_sublist_right", "equiv.tsum_eq_tsum_of_support", "nat.cast_dvd_char_zero", "polynomial.has_strict_deriv_at", "multiset.disjoint_left", "list.maximum_eq_none", "algebra_map_isometry", "associates.eq_of_factors_eq_factors", "cluster_pt_iff", "bot_inf_eq", "complex.smul_re", "abelianization.commutator_subset_ker", "le_div_iff_of_neg", "le_sup_left", "hyperreal.is_st_neg", "div_lt_one", "finset.inter_eq_inter_of_sdiff_eq_sdiff", "measure_theory.measure.finite_at_filter.integrable_at_filter_of_tendsto", "Mod.id_hom'", "nat.modeq.modeq_add_cancel_right", "fderiv_within_const_add", "lt_mul_of_one_lt_right'", "finset.weighted_vsub_empty", "free_group.pure_bind", "list.sublists'_aux_eq_sublists'", "function.semiconj.inverses_right", "inner_product_geometry.angle_neg_left", "pred_ne_self", "omega.coeffs.val_between_set", "padic_seq.not_equiv_zero_const_of_nonzero", "circle_deg1_lift.translation_number_eq_of_tendsto\:2080", "subring.in_closure.rec_on", "equiv.coe_fn_injective", "lucas_lehmer.X.nat_coe_snd", "ext_chart_at_source", "ordinal.power_pos", "nat.dvd_add_right", "measure_theory.lintegral_const_mul", "affine_subspace.le_def'", "finsupp.range_restrict_dom", "alist.lookup_insert", "tendsto_indicator_of_monotone", "filter.eventually_le.trans_eq", "finset.powerset_len_mono", "bool.coe_to_bool", "is_local_min.has_deriv_at_eq_zero", "convex.mem_Ioo", "associates.quotient_mk_eq_mk", "nat.mul_dvd_of_dvd_div", "typevec.eq_of_drop_last_eq", "measurable_space.comap_generate_from", "has_fderiv_at.comp_has_deriv_within_at", "topological_space.compacts.ext", "polynomial.coeff_C_mul", "finsupp.prod_subtype_domain_index", "measure_theory.measure.restrict_empty", "list.insert_nth_remove_nth_of_ge", "fintype.card_le_one_iff", "pfunctor.M.bisim", "times_cont_diff_on_zero", "ideal.map_id", "computable.sum_inl", "list.append_left_inj", "prime_multiset.coe_nat_prime", "rat.denom_div_eq_of_coprime", "monoid_algebra.single_one_comm", "polynomial.is_unit_or_eq_zero_of_separable_expand", "and.imp_right", "bounded_std_simplex", "int.div_pos_of_pos_of_dvd", "mul_left_cancel_iff", "cardinal.lift_lift", "metric.ediam_le_of_forall_dist_le", "pfunctor.comp_map", "smooth.neg", "is_scalar_tower.algebra_map_apply", "filter.germ.coe_coe_ring_hom", "measure_theory.measure.le_iff'", "path.cast_coe", "set.mem_Inter_of_mem", "enorm.ext", "set.inter_assoc", "nat.prime.multiplicity_fact", "le_generate_from_iff_subset_is_open", "category_theory.eq_whisker", "is_R_or_C.int_cast_im", "nat.gcd_rec", "finset.image_empty", "filter.Liminf_le_Liminf", "list.maximum_concat", "computable.of_option", "set.bijective_iff_bij_on_univ", "metric.to_inductive_limit_commute", "category_theory.whisker_left_id", "submonoid.closure_univ", "list.alternating_prod_eq_finset_prod", "matrix.head_zero", "monoid_algebra.single_one_mul_apply", "monotone.iterate_le_of_le", "continuous_linear_map.op_norm_smul_le", "ring_equiv.coe_add_equiv", "nat.primrec.cases", "mv_polynomial.as_sum", "directed_of_inf", "filter.mem_pure_sets", "nnreal.div_add_div_same", "finset.sup_insert", "sub_left_inj", "max_le_add_of_nonneg", "submonoid.prod_mem", "associates.factors_mono", "inf_eq_bot_iff_le_compl", "int.eq_mul_of_div_eq_right", "padic_val_nat_one", "multiset.map_add", "is_max_filter.congr", "associates.mk_mul_mk", "linear_equiv.dim_eq", "multiset.eq_union_right", "metric.diam_ball", "polynomial.degree_le_mul_left", "category_theory.of_type_functor_obj", "continuous_linear_map.curry_uncurry_left", "bitraversable.tfst_tsnd", "finset.bdd_below", "fintype.card_fun", "isometric.coe_neg", "is_coprime.prod_right", "ordinal.type_le", "alg_hom.coe_mk", "nat.bit1_succ_eq", "category_theory.eq_of_comp_left_eq", "submodule.fg_bot", "tensor_product.comm_tmul", "csupr_le_csupr", "subgroup.mem_comap", "differentiable_at_inv", "hyperreal.zero_iff_infinitesimal_real", "pell.yz_succ_succ", "eventually_nhds_within_of_eventually_nhds", "int.add_mul_div_right", "continuous_mul_left", "nnreal.div_def", "ordinal.mul_sub", "is_measurable.insert", "times_cont_diff_within_at.times_cont_diff_on", "category_theory.iso.to_equiv_comp", "multiset.coe_sigma", "nat.sub_one", "polynomial.degree_derivative_lt", "list.nodup_erase_of_nodup", "real.cos_nonpos_of_pi_div_two_le_of_le", "is_compact.exists_forall_ge", "is_local_min.comp_continuous", "map_bind", "filter.join_le", "mv_power_series.coeff_inv_of_unit", "circle_deg1_lift.dist_map_zero_lt_of_semiconj", "list.foldr_join", "mv_polynomial.homogeneous_component_is_homogeneous", "fin_enum.pi.mem_enum", "equiv.sigma_equiv_prod_symm_apply", "ennreal.le_of_forall_epsilon_le", "set.Ico_disjoint_Ico", "real.arctan_tan", "isometric.const_vadd_zero", "list.nth_le_update_nth_eq", "list.reverse_revzip", "submodule.map_smul'", "ite_cast", "pequiv.single_apply_of_ne", "filter.has_basis.uniform_continuous_iff", "cluster_pt_principal_iff", "ennreal.zero_rpow_of_neg", "computation.lift_rel.symm", "ennreal.pow_pos", "local_equiv.refl_coe", "mem_of_is_glb_of_is_closed", "affine.simplex.ext", "euclidean_geometry.orthogonal_projection_fn_eq", "list.prod_singleton", "list.mfoldl_eq_foldl", "is_unit.mul_right_eq_zero", "convex_convex_hull", "cardinal.lift_univ", "list.cons_head_tail", "filter.tendsto_lift'_powerset_mono", "nat.lt_two_pow", "mem_interior", "ctop.coe_mk", "tendsto_pow_at_top_at_top_of_one_lt", "multiset.zero_ndinter", "has_deriv_at_real_of_complex", "has_deriv_within_at.add", "local_of_surjective", "card_order_of_eq_totient_aux\:2082", "abs_le_abs", "is_R_or_C.abs_re_div_abs_le_one", "eq_false", "filter.ptendsto'_def", "hash_map.valid.find_aux_iff", "list.sublists'_aux_append", "not.imp", "category_theory.sum.associator_map_inl_inl", "set.union_inter_distrib_left", "differentiable.rpow_of_one_le", "category_theory.limits.prod.triangle", "continuous_linear_map.coe_apply", "add_submonoid.localization_map.sec_spec'", "padic_seq.norm_nonneg", "prime_multiset.prod_smul", "add_submonoid.map_bot", "fin.succ_pos", "ordinal.card_succ", "nat.add_sub_of_le", "category_theory.comonad.coalgebra.hom.ext", "category_theory.monad.forget_creates_colimits.commuting", "inv_eq_iff_mul_eq_one", "Inf_pair", "category_theory.limits.pullback_cone.mk_snd", "quotient_add_group.open_coe", "is_closed_Union_of_locally_finite", "continuous_smul", "half_lt_self", "mvqpf.cofix.bisim'", "vector.traverse_eq_map_id", "is_preirreducible.image", "zsqrtd.smul_val", "multilinear_map.restr_norm_le", "filter.map_add", "add_monoid_hom.inr_apply", "polynomial.coeff_nat_degree_succ_eq_zero", "polynomial.degree_X_pow", "polynomial.leading_coeff_add_of_degree_eq", "deriv_cosh", "subgroup.conjugates_of_set_subset_normal_closure", "mv_polynomial.induction_on", "cau_seq.bounded'", "hyperreal.infinite_neg_add_not_infinite_pos", "equiv.perm.disjoint_comm", "function.commute.iterate_pos_eq_iff_map_eq", "inv_lt'", "cardinal.mk_Iio_real", "ordinal.type_add", "pi.single_eq_same", "int.mul_div_mul_of_pos_left", "is_min_filter.inf", "inner_product_geometry.angle_nonneg", "ennreal.inv_top", "uniform_space.completion.continuous_coe", "finset.bUnion_union", "polynomial.eval\:2082_list_prod_noncomm", "finsupp.supported_comap_lmap_domain", "measure_theory.to_outer_measure_apply", 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"univ_separated_iff", "filter.eventually.exists_mem", "filter.hyperfilter_ne_bot", "lie_algebra.equiv.refl_apply", "tendsto_const_div_at_top_nhds_0_nat", "matrix.is_unit_iff_is_unit_det", "polynomial.coeff_expand", "finset.insert.comm", "measure_theory.ae_eq_fun.edist_mk_mk'", "filter.eventually.prod_inr", "algebraic_closure.to_splitting_field_eval_X_self", "category_theory.over.construct_products.cones_equiv_inverse_obj_X", "mul_lt_mul_left_of_neg", "differentiable_neg", "continuous_finset_sum", "finset.insert_union_distrib", "nnreal.rpow_sub", "list.rotate_length", "monotonicity.imp", "formal_multilinear_series.change_origin_summable_aux2", "tactic.ring_exp.add_overlap_pf", "inf_uniformity", "norm_num.add_bit0_bit1", "ideal.mk_ker", "submodule.liftq_mkq", "finset.prod_Ico_id_eq_fact", "pequiv.to_matrix_trans", "seq1.join_map_ret", "num.zneg_to_znum_neg", "algebraic_geometry.PresheafedSpace.restrict_presheaf", "set.preimage_sub_const_Iic", "euclidean_domain.lcm_dvd_iff", "gaussian_int.to_complex_neg", "convex.subset_to_cone", "category_theory.limits.limit.hom_iso_hom", "category_theory.nat_iso.naturality_2", "is_open_interior", "units.max_coe", "times_cont_diff.neg", "set.sUnion_singleton", "mv_polynomial.coeff_C_mul", "not_imp_comm", "ball_mono", "strict_weak_order.not_lt_of_equiv", "units.coe_pow", "real.coe_fib_eq'", "primrec.fin_succ", "matrix.col_empty", "function.bijective_iff_has_inverse", "finset.Ico_\:2124.mem", "computable.sum_cases", "int.modeq.modeq_add", "is_bounded_bilinear_map.is_O_comp", "pell.x_sub_y_dvd_pow", "to_mul_of_mul", "tactic.ring_exp.mul_pf_prod_c", "polynomial.coeff_mul_C", "exists_int_gt", "wseq.equiv.equivalence", "subsingleton_of_zero_eq_one", "list.foldr_with_index_aux_eq_foldr_with_index_aux_spec", "computation.lift_rel_aux.ret_right", "dist_sub_sub_le", "is_least.nonempty", "continuous_linear_map.coe_injective", "mem_nhds_within_Ici_iff_exists_Icc_subset", "measure_theory.outer_measure.is_caratheodory_sum", "geom_gold_conj_is_sol_fib_rec", "qpf.cofix.dest_corec", "complex.arg_eq_arg_iff", "nat.cond_to_bool_mod_two", "function.involutive_iff_iter_2_eq_id", "cardinal.mul_def", "of_digits_zmodeq'", "disjoint_nested_nhds", "stream.corec_eq", "alg_hom.coe_monoid_hom_injective", "nnreal.pow_arith_mean_le_arith_mean_pow", "filter.map_inf", "matrix.nonsing_inv_mul", "is_coprime.of_prod_left", "ring.fractional_ideal.eq_zero_iff", "nnreal.coe_pow", "measurable_const_smul_iff", "primrec\:2082.unpaired", "nat.pow_dvd_pow_iff_le_right", "metric.finite_approx_of_totally_bounded", "ring.fractional_ideal.map_mul", "add_monoid_hom.map_nsmul", "onote.mul_zero", "mv_power_series.trunc_one", "algebra.subring_algebra_map_apply", "linear_map.std_basis_ne", "list.perm_iff_count", "fraction_map.lift_mk'", "wseq.nth_mem", "free_group.prod.of", "nat.add_lt_of_lt_sub_left", "list.pairwise.imp_of_mem", "Mod.comp_hom", "multiset.ndunion_eq_union", "add_subgroup.closure_induction", 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"zsqrtd.sq_le_cancel", "function.right_inverse.left_inverse", "set.surjective_iff_surj_on_univ", "affine_subspace.span_empty", "is_compl.le_left_iff", "category_theory.monoidal_category.right_unitor_product_aux", "nonneg_of_mul_nonpos_left", "continuous_linear_map.neg_apply", "int.sqrt_nonneg", "norm_num.dvd_eq_int", "subgroup.center_normal", "matrix.special_linear_group.mul_val", "is_unit.dvd_mul_right", "multiset.erase_le_iff_le_cons", "measure_theory.lebesgue_length_mono", "mv_polynomial.vars_monomial", "multiset.card_pi", "nat.gcd_dvd_gcd_mul_left", "open_add_subgroup.coe_subset", "topological_fiber_bundle_core.local_triv_symm_fst", "continuous_of_locally_uniform_approx_of_continuous", "finset.sum_subtype", "nat.add_assoc", "category_theory.over.construct_products.cones_equiv_inverse_map_hom", "principal_seg.coe_coe_fn'", "is_complete.complete_space_coe", "int.mul_neg_eq_neg_mul_symm", "gpow_coe_nat", "set.inf_eq_inter", "category_theory.limits.cone_of_cocone_left_op_\[Pi]_app", 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"finsupp.map_range_single", "neg_eq_iff_neg_eq", "bernoulli_def", "dioph.ne_dioph", "category_theory.non_preadditive_abelian.lift_map", "enorm.map_zero", "hyperreal.inv_epsilon_eq_omega", "ring_hom.coe_monoid_hom_injective", "category_theory.limits.prod_map_id_comp", "direct_sum.to_group.unique", "add_equiv.to_AddMon_iso_hom", "multiset.singleton_eq_singleton", "pgame.lt_congr", "deriv_div_const", "filter.eventually_eq.eq_of_nhds", "alg_equiv_iso_Algebra_iso_hom", "rel.dom_inv", "quot.induction_on\:2082", "computation.lift_eq_iff_equiv", "monotone.mul_const", "decidable.imp_iff_not_or", "finset.filter_subset", "pfun.core_mono", "con.ker_lift_mk", "con.Sup_eq_con_gen", "directed.mono_comp", "multiset.inf_cons", "is_seq_compact.is_compact", "cau_seq.completion.of_rat_one", "finset.mono_of_fin_injective", "pythagorean_triple.gcd_dvd", "measure_theory.integrable_on_finset_union", "inner_product_geometry.norm_sub_square_eq_norm_square_add_norm_square'", "exists_nhds_square", "finset.prod_sigma", "category_theory.limits.is_terminal.mono_from", "finsupp.lmap_domain_disjoint_ker", "smooth_right_add", "ite_eq_mem_std_simplex", "is_bounded_linear_map.times_cont_diff", "uniform_space.completion.extension_unique", "measure_theory.outer_measure.supr_apply", "finset.image_to_finset", "cardinal.denumerable_iff", "Cauchy.uniform_embedding_pure_cauchy", "nat.prime.multiplicity_mul", "has_fderiv_at.of_local_left_inverse", "times_cont_mdiff_on.prod_map", "poly.one_eval", "char_poly_monic_of_nontrivial", "is_add_submonoid_Union_of_directed", "deriv.comp", "category_theory.limits.coprod.hom_ext", "convex_cone.mem_top", "tactic.abel.term_add_term", "continuous_multilinear_map.norm_map_init_le", "measure_theory.measure_ne_top", "opposite.op_sub", "padic_int.zmod_repr_lt_p", "add_subgroup.comap_comap", "generalized_continued_fraction.squash_seq_nth_of_lt", "vector.nth_map", "continuous_multilinear_map.uncurry_curry_left", "emetric.ball_eq_empty_iff", "mvfunctor.liftr_def", "le_refl", "pequiv.single_mul_single_of_ne", "euclidean_domain.xgcd_val", "list.sublists_len_aux_eq", "list.nodup_of_fn", "list.subset_cons_of_subset", "of_digits_digits_append_digits", "set.set_of_exists", "dfinsupp.ext", "list.repeat_subset_singleton", "le_csupr", "tt_band", "continuous_linear_map.coe_snd", "filter.has_basis.sup", "primrec.unpair", "finset.singleton_iff_unique_mem", "add_eq_of_eq_sub'", "ennreal.sub_zero", "setoid.Sup_def", "strict_mono.mul_const", "normed_space.norm_le_dual_bound", "le_trans", "gaussian_int.norm_nonneg", "decidable.of_not_not", "multiset.foldr_zero", "le_of_eq", "nat.choose_zero_succ", "continuous_stone_cech_extend", "eqv_lt_iff_eq", "finsupp.filter_apply_pos", "int.lt.intro", "supr_le_iff", "nhds_basis_uniformity", "disjoint_sup_right", "category_theory.discrete.functor_map", "nat.gcd_gcd_self_left_right", "list.perm.subset", "is_measurable.bUnion", "zsqrtd.norm_int_cast", "has_deriv_at.has_deriv_within_at", "nnreal.add_sub_cancel'", "linear_map.one_app", "is_noetherian_of_surjective", "metric.Hausdorff_dist_le_of_inf_dist", "mul_lt_of_le_one_of_lt", "linear_independent_le_dim", "dvd.intro", "finmap.lookup_empty", "subgroup.comap_infi", "is_closed_frontier", "mul_action.eq_inv_smul_iff", "sub_lt", "measurable.piecewise", "mvfunctor.id_map'", "measure_theory.l1.simple_func.add_to_simple_func", "list.pairwise_join", "div_eq_of_eq_mul", "add_con.comp_mk'_apply", "num.dvd_to_nat", "finset.sum_smul", "interval_integrable.symm", "uniform_space.completion.continuous_map", "ring.direct_limit.exists_of", "localization_map.eq_iff_exists", "interior_Ico", "nat.lt_sub_left_iff_add_lt", "int.neg_mul_eq_neg_mul", "is_bounded_linear_map.continuous", "finmap.induction_on\:2083", "semilattice_inf.ext_inf", "has_fderiv_at.sum", "is_min_on.is_local_min", "cau_seq.ext", "local_homeomorph.source_preimage_target", "add_submonoid.localization_map.eq_mk'_iff_add_eq", "list.nat.antidiagonal_zero", 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"polynomial.nat_degree_comp", "finite_dimensional.dim_lt_omega", "category_theory.whisker_left_id'", "mem_nhds_within", "multiset.traverse_map", "list.update_nth_eq_take_cons_drop", "function.inv_fun_on_neg", "times_cont_diff_at_inverse", "monoid_algebra.equivariant_of_linear_of_comm_apply", "list.mem_tails", "filter.tendsto.lim_eq", "znum.cast_zero'", "qpf.liftp_iff", "is_open_map.id", "finset.le_min'", "tactic.ring_exp.mul_pp_pf_prod_gt", "dist_triangle_left", "computation.map_parallel", "matrix.nonsing_inv_right_left", "mem_span_insert_exchange", "is_connected_range", "real.exp_log_eq_abs", "normed_ring.inverse_add", "tendsto_order", "nat.zero_test_bit", "add_comm_group.is_Z_bilin.neg_right", "prod_mk_mem_comp_rel", "left_inverse_pth_root_frobenius", "wseq.bind_ret", "tendsto_comp_of_locally_uniform_limit", "affine_map.homothety_apply", "ideal.le_map_of_comap_le_of_surjective", "principal_seg.equiv_lt_apply", "continuous_on.preimage_closed_of_closed", "edist_le_range_sum_edist", "many_one_equiv.congr_right", "set.image_eq_range", "tsum_geometric_nnreal", "is_add_subgroup.eq_trivial_iff", "list.subperm.count_le", "is_local_min.sub", "list.length_merge_sort", "set.preimage_const_mul_Ioi_of_neg", "pnat.one_le", "list.disjoint_right", "category_theory.limits.pullback_cone.of_cone_\[Pi]", "Ioc_mem_nhds_within_Iic", "sub_add_add_cancel", "is_glb_singleton", "Set.mem_map", "has_fderiv_within_at.iterate", "finset.card_empty", "alist.mem_replace", "monotone_of_monotone_nat", "typevec.drop_fun_of_subtype", "adic_completion.range_eval", "nat.gcd_succ", "zmod.wilsons_lemma", "differentiable_at.smul_algebra_const", "set.finite.summable", "monotone.map_inf_le", "eq_of_uniformity_inf_nhds_of_is_separated", "is_mul_hom.mul", "neg_of_mul_pos_left", "is_linear_map.is_linear_map_smul", "is_max_on_iff", "measure_theory.measure.to_outer_measure_le", "dvd_iff_dvd_of_dvd_sub", "computation.terminates_parallel.aux", "is_local_min_on.add", "list.left_unique_forall\:2082", "with_top.lt_iff_exists_coe_btwn", "int.nonneg_of_neg_nonpos", "neg_one_lt_gold_conj", "metric.continuous_iff", "equiv.arrow_congr'_refl", "eq_zero_of_add_self_right_cancel", "of_digits_singleton", "polynomial.derivative_map", "mv_polynomial.homogeneous_component_eq_zero'", "nat.pow_lt_pow_succ", "complex.continuous_im", "topological_space.mem_basis_subset_of_mem_open", "topological_space.opens.le_def", "add_zero", "list.sublists_cons_perm_append", "has_strict_deriv_at_pow", "inner_product_space.of_core.inner_add_right", "category_theory.monoidal_category.tensoring_right_obj", "free_group.mul_bind", "associated.refl", "filter.infi_sets_induct", "metric.mem_uniformity_dist", "convex_iff_segment_subset", "ordinal.CNF_rec_ne_zero", "int.cast_two", "asymptotics.is_O_with.prod_left_fst", "nnreal.coe_min", "int.zero_mod", "frontier_Ico", "nat.pow_dvd_of_le_of_pow_dvd", "mul_equiv.to_fun_apply", "finset.bind_mono", "category_theory.limits.kernel_fork.condition", "submonoid.localization_map.mul_inv_right", "category_theory.comma.map_right_comp_hom_app_left", "initial_seg.eq", "poly_equiv_tensor_symm_apply_tmul", "directed.sequence_mono", "dfinsupp.subtype_domain_apply", "pi_Lp.add_apply", "dlist.to_list_cons", "list.zip_nil_right", "multiset.count_smul", "omega.coeffs.forall_val_dvd_of_forall_mem_dvd", "has_lt.lt.gt", "fin.val_zero'", "ordinal.one_power", "set.bInter_pair", "closed_embedding_of_continuous_injective_closed", "ctop.realizer.of_equiv_F", "not_lt_bot", "nat.div2_bit0", "string.iterator.length_next_to_string_next", "linear_map.range_range_restrict", "alist.mem_of_perm", "order_top.ext_top", "zsqrtd.nonnegg_cases_right", "multiset.add_inter_distrib", "if_congr", "continuous_linear_equiv.has_fderiv_within_at", "semiconj_by.cast_nat_mul_right", "is_extr_on.elim", "lucas_lehmer.\[Omega]_pow_formula", "forall_elim_eq_right", "roption.mem_bind", "pgame.domineering.move_right_smaller", "free_ring.lift_of", "asymptotics.is_O.const_mul_right'", "rat.eq_iff_mul_eq_mul", "unique_factorization_domain.integrally_closed", "polynomial.roots_mul", "finsupp.map_domain_injective", "pell.x_sub_y_dvd_pow_lem", "differentiable_at.inv", "measure_theory.l1.simple_func.neg_part_to_simple_func", "joined_in.source_mem", "rat.denom_div_cast_eq_one_iff", "has_deriv_within_at.neg", "polynomial.map_monic_ne_zero", "list.nodup_repeat", "computation.lift_rel_rec.lem", "field.mem_closure", "filter.mem_lift'", "nat.zero_lt_one_add", "alg_equiv.to_Algebra_iso_hom", "setoid.Inf_def", "galois_connection.upper_bounds_l_image_subset", "is_submonoid.coe_mul", "submonoid.map_le_map_iff_of_injective", "not_lt_of_le", "category_theory.limits.is_colimit.unique_up_to_iso_hom", "mul_aut.conj_apply", "real.sqrt_two_add_series_zero_nonneg", "has_fderiv_at.fst", "set.inter_eq_Inter", "le_mul_of_inv_mul_le_left", "con.ker_eq_lift_of_injective", "finset.univ_inter", "mul_one", "asymptotics.is_o_norm_norm", "category_theory.non_preadditive_abelian.sub_zero", "list.choose_mem", "infinite.exists_not_mem_finset", "multiset.coe_add", "monotone.order_dual", "unique_mdiff_within_at.eq", "filter.ultrafilter_of_ultrafilter", "equiv.perm.gpow_apply_eq_self_of_apply_eq_self", "metric.mk_uniformity_basis_le", "well_founded.has_min", "convex.norm_image_sub_le_of_norm_deriv_le", "linear_independent.insert", "nat.le_mul_self", "set.nonempty.fst", "normal.exists_is_splitting_field", "matrix.one_map", "array.read_write_of_ne", "composition.size_up_to_length", "is_local_extr.elim", "metric.closed_ball_diff_ball", "compact_empty", "computation.get_thinkN", "equiv.point_reflection_symm", "composition.single_length", "finset.sum_sub_distrib", "nat.nsmul_eq_mul", "set.indicator_of_not_mem", "with_bot.bot_lt_some", "list.map_append", "add_monoid_hom.eq_on_closure", "ennreal.div_lt_iff", "zorn.chain.total_of_refl", "has_deriv_at.neg", "real.cosh_eq", "int.gcd_div_gcd_div_gcd", "list.sublist.reverse", "add_monoid_hom.iterate_map_sub", "gaussian_int.to_complex_def'", "category_theory.comma.map_right_map_left", "measure_theory.outer_measure.of_function_caratheodory", "int.succ_neg_succ", "emetric.continuous_inf_edist", "traversable.traverse_id", "set.nonempty_Iio", "sub_le_sub_iff", "filter.tendsto.dist", "bot_unique", "fpow_inj", "pgame.mk_add_move_right_inr", "nat.neg_one_pow_eq_one_iff_even", "dvd_add_left", "add_localization.add_equiv_of_quotient_add_monoid_of", "multiset.attach_cons", "quadratic_form.ext", "category_theory.over.construct_products.cones_equiv_functor_map_hom", "measure_theory.integral_zero", "add_lt_of_nonpos_of_lt", "padic_int.irreducible_p", "dfinsupp.erase_def", "pgame.impartial.first_wins_symm", "true_ne_false", "set.image2_singleton_right", "polynomial.mem_roots", "homeomorph.is_O_congr", "module_ext", "semidirect_product.inv_left", "continuous.prod_mk", "nat.eq_zero_or_pos", "ennreal.rpow_eq_pow", "nat.pred_lt_pred", "nat.bit1_lt_bit0_iff", "int.bitwise_diff", "Limsup_eq_of_le_nhds", "complex.of_real_tan_of_real_re", "mul_semiring_action_hom.coe_polynomial", "complex.conj_eq_zero", "structure_groupoid.local_invariant_prop.lift_prop_on_of_lift_prop", "add_submonoid.exists", "polynomial.is_coprime_map", "ennreal.bit0_eq_zero_iff", "function.injective_of_partial_inv_right", "continuous_multilinear_map.cons_smul", "dim_fun'", "category_theory.functor.cones_map_app", "real.sqrt_eq_iff_sqr_eq", "ring.fractional_ideal.inv_nonzero", "tsum_fintype", "linear_independent.repr_eq", "polynomial.degree_one", "mfderiv_const", "nat.choose_symm_half", "quadratic_form.map_neg", "group.mclosure_subset", "filter.is_ultrafilter.eventually_imp", "nat.coprime_mul_iff_right", "measure_theory.integrable.integrable_on", "finite_of_linear_independent", "irreducible_component_subset_connected_component", "mul_semiring_action_hom.ext_iff", "list.mem_fin_range", "roption.bind_eq_bind", "category_theory.limits.bicone.to_cone_\[Pi]_app", "has_sum_geometric_of_lt_1", "le_of_tendsto_of_tendsto'", "continuous_linear_equiv.units_equiv_aut_apply", "submodule.le_orthogonal_orthogonal", "continuous_linear_map.bounds_bdd_below", "eq_of_incomp", "measure_theory.ae_eq_fun.coe_fn_zero", "monoid_algebra.coe_algebra_map", "uniform_embedding_of_rat", "alist.empty_entries", "polynomial.separable.is_coprime", "is_subring_Union_of_directed", "measure_theory.lintegral_rw\:2082", "equiv.perm.swap_mul_eq_mul_swap", "is_R_or_C.abs_inv", "lucas_lehmer.X.X_card", "measure_theory.measure_diff", "submonoid.le_comap_map", "sylow.exists_prime_order_of_dvd_card", "ennreal.to_nnreal_pos_iff", "cardinal.mk_image_le_lift", "set.finite.summable_compl_iff", "if_pos", "equiv.perm.support_swap_mul_eq", "prod.fst_sum", "is_subring.coe_subtype", "multiset.sub_zero", "measure_theory.is_left_invariant_inner_content", "mul_neg_geom_sum", "continuous_generated_from", "finmap.disjoint_empty", "ennreal.one_to_real", "set.image_inter_subset", "is_measurable.empty", "category_theory.reassoc_of", "complex.inv_re", "monoid_algebra.single_pow", "complex.exp_log", "linear_equiv.is_unit_det", "is_compl.sup_inf", "set.powerset_mono", "sym2.mem_iff", "set.subset_compl_singleton_iff", "fract_fract", "to_lin_to_matrix", "is_integral_alg_hom", "continuous_linear_map.ext", "mvqpf.liftp_iff", "fin.le_coe_last", "set.mem_sep_iff", "filter.germ.coe_le", "mv_polynomial.homogeneous_component_eq_zero", "tangent_map_within_congr", "list.ne_nil_of_length_eq_succ", "is_separated_of_separated_space", "set.nonempty.right", "int.bitwise_and", "rat.uniform_space_eq", "nat.lt_succ_iff", "cauchy.comap", "asymptotics.is_O_with.congr_left", "is_extr_on.on_subset", "matrix.is_unit_det_transpose", "cardinal.mk_set_le", "measurable_mul", "bilin_form.is_adjoint_pair_id", "tangent_map_within_proj", "quadratic_form.lin_mul_lin_self_pos_def", "set.Ioi_subset_Ioc_union_Ici", "mvqpf.liftr_iff", "local_homeomorph.trans_self_symm", "int.div_nonpos", "differentiable_within_at.cosh", "category_theory.non_preadditive_abelian.comp_add", "cardinal.omega_is_regular", "ennreal.exists_nat_gt", "cardinal.mk_list_eq_sum_pow", "submodule.mem_map", "ennreal.to_real_eq_to_real", "lt_min", "filter.at_top_ne_bot", "emetric.tendsto_nhds", "differentiable_on.ccosh", "digits_zero_zero", "dioph.dom_dioph", "real.is_lub_Sup", "decidable.not_and_distrib", "add_neg_of_neg_of_nonpos'", "well_founded.eq_iff_not_lt_of_le", "UniformSpace.extension_comp_coe", "is_add_unit.lift_right_neg_add", "monoid_hom.ext_iff", "nat.bodd_one", "normed_algebra.norm_one", "multiset.inf_zero", "metric.completion.eq_of_dist_eq_zero", "pi.algebra_map_apply", "turing.list_blank.nth_mk", "finset.empty_sdiff", "dfinsupp.single_eq_of_ne", "mv_power_series.coeff_X", "tangent_map_chart", "homeomorph.is_closed_map", "padic_int.zmod_congr_of_sub_mem_span", "qpf.supp_map", "bex.imp_right", "left_inverse_neg_add_add_right", "add_semiconj_by.neg_right", "int.add_le_add_three", "complex.tan_eq_sin_div_cos", "omega.coeffs.val_between_add", "tendsto_nhds", "measure_theory.lebesgue_outer_Icc", "multiset.powerset_aux'_nil", "finsupp.prod_comm", "continuous_nndist", "complex.abs_cpow_inv_nat", "asymptotics.is_o_const_mul_left_iff", "linear_independent_of_finite", "AddCommGroup.colimits.quot_neg", "finsupp.supported_univ", "subgroup.mul_mem", "category_theory.functor.op_inv_map", "filter.tendsto.sup", "lt_add_of_lt_of_pos'", "vsub_mem_vsub_set", "nnreal.coe_sum", "add_units.mk_semiconj_by", "is_R_or_C.rat_cast_im", "convex_cone.coe_inf", "complex.is_cau_seq_re", "associates.prod_coe", "induced_compose", "submodule.map_sup", "ring_hom.codomain_trivial_iff_range_eq_singleton_zero", "finmap.disjoint.symm", "function.inv_fun_on_eq'", "erased.pure_def", "is_bounded_linear_map.differentiable_within_at", "composition.sigma_eq_iff_blocks_eq", "nat.dist_add_add_right", "times_cont_mdiff_on_iff", "int.eq_coe_or_neg", "hash_map.find_erase", "complex.cosh_sub", "hyperreal.epsilon_eq_inv_omega", "category_theory.preadditive.neg_comp_assoc", "metric.cauchy_iff", "continuous_within_at_iff_continuous_at_restrict", "is_closed.closed_embedding_subtype_coe", "filter.eventually.eventually_nhds", "finmap.union_empty", "local_homeomorph.eventually_right_inverse'", "nhds_within_empty", "lt_iff_le_not_le", "category_theory.monoidal.associator_inv_apply", "polynomial.div_by_monic_eq_of_not_monic", "filter.frequently_sup", "num.mem_of_znum'", "nat.coprime.gcd_mul_right_cancel_right", "set.ord_connected_interval", "bit1_nsmul", "multiset.erase_dup_eq_zero", "int.gcd_comm", "function.inv_fun_on_pos", "monoid_hom.fst_comp_inl", "measure_theory.measure.haar_outer_measure_of_is_open", "stream.map_map", "embedding.prod_mk", "submonoid.localization_map.of_mul_equiv_of_mul_equiv_apply", "set.mem_inter_eq", "div_le_iff_of_neg", "equiv.sigma_congr_right_apply", "list.mfoldl_with_index_eq_mfoldl_enum", "multiset.sup_union", "pnat.factor_multiset_one", "nonempty_psigma", "composition.index_exists", "is_compact.tendsto_subseq'", "ordinal.lift.principal_seg_top'", "measure_theory.l1.edist_eq", "exists_eq", "local_homeomorph.of_set_coe", "set.preimage_sub_const_Ico", "real.div_sqrt_one_add_lt_one", "of_to_bool_ff", "free_group.red.step.cons_left_iff", "asymptotics.is_o.def'", "times_cont_mdiff_on_symm_of_mem_maximal_atlas", "finite_dimensional.span_of_finite", "finset.Ico.filter_Ico_bot", "and_self_left", "measure_theory.l1.simple_func.eq_iff'", "is_open_map_add_left", "set.right_mem_Ioc", "tendsto_inv_nhds_within_Iio", "finmap.keys_erase", "fin.pred_inj", "ge_of_eq", "subsemiring.zero_mem", "dfinsupp.prod_zero_index", "monad_map_refl", "function.Sup_div_semiconj", "list.mem_filter_map", "has_strict_fderiv_at.implicit_to_local_homeomorph_of_complemented_apply", "mem_gmultiples", "multiset.repeat_succ", "matrix.induction_on", "monotone_Inf_of_monotone", "cardinal.mk_preimage_of_subset_range", "polynomial.nat_degree_X_sub_C_le", "dfinsupp.mk_apply", "has_mfderiv_at.mdifferentiable_at", "nat.le_lt_antisymm", "category_theory.nat_trans.vcomp_eq_comp", "is_glb.infi_eq", "function.commute.id_left", "category_theory.limits.cone.whisker_\[Pi]", "has_deriv_within_at.const_smul", "finset.empty_union", "polynomial.coe_add", "top_inf_eq", "real.geom_mean_le_arith_mean2_weighted", "nat.lt_succ_sqrt", "submonoid.localization_map.of_mul_equiv_of_mul_equiv", "filter.le_pure_iff", "isometric.to_real_linear_equiv_symm_apply", "is_measurable.inter", "category_theory.limits.cone.w", "exists_eq_mul_left_of_dvd", "seq.join_append", "submodule.mem_map_of_mem", "emetric.uniform_embedding_iff", "equiv.perm.is_cycle_cycle_of", "continuous_linear_equiv.to_span_nonzero_singleton_homothety", "padic_norm.mul", "circle_deg1_lift.translation_number_le_of_le_add_nat", "multiset.powerset_coe'", "measure_theory.l1.lintegral_edist_to_fun_lt_top", "set.piecewise_eq_of_mem", "int.sub_mul", "function.is_periodic_pt.minimal_period_dvd", "monoid_algebra.single_mul_apply_aux", "free_add_semigroup.traverse_add'", "category_theory.cones_obj", "localization_map.lift_of_comp", "lagrange.interpolate_sub", "lie_algebra.orthogonal.is_unit_PD", "composition_as_set.boundary_length", "uniform_space.completion.dense_inducing_coe", "is_conj_refl", "computation.lift_rel_rec", "int.mul_lt_mul'", "set.countable.insert", "uniform.tendsto_nhds_left", "bounded_continuous_function.norm_const_le", "floor_eq_iff", "distrib_mul_action_hom.comp_id", "equiv.one_def", "measure_theory.lintegral_liminf_le", "bool.to_bool_true", "measurable.ennreal_of_real", "Set.regularity", "emetric.mk_uniformity_basis_le", "ennreal.tsum_mul_right", "multiset.card_erase_lt_of_mem", "finset.sdiff_empty", "subtype.restrict_injective", "lt_add_iff_pos_right", "matrix.diagonal_mul_diagonal", "pgame.numeric.lt_move_right", "emetric.empty_or_nonempty_of_Hausdorff_edist_ne_top", "emetric.uniform_embedding_iff'", "nat.partrec.ppred", "cardinal.mk_bounded_set_le_of_omega_le", "computation.map_id", "set.surj_on_Union", "traversable.comp_sequence", "real.two_pi_pos", "filter.ne_bot.map", "matrix.smul_empty", "int.ne_neg_of_ne", "padic_norm_z.padic_norm_z_eq_padic_norm_e", "add_units.eq_neg_add_iff_add_eq", "set.mem_powerset_iff", "is_R_or_C.eq_conj_iff_re", "convex_hyperplane", "pfunctor.M.cases_mk", "mv_polynomial.map_eval\:2082", "category_theory.eq_to_iso_refl", "set.image_mul_prod", "set.disjointed_induct", "seq.mem_rec_on", "complex.div_I", "is_add_hom.add", "list.perm_append_singleton", "mv_polynomial.rename_C", "set.Union_image_left", "is_min_on.comp_antimono", "complex.linear_map.coe_of_real", "filter.tendsto_at_bot_at_bot_of_monotone", "pythagorean_triple.classification", "tactic.ring.horner_mul_const", "unique_factorization_domain.irreducible_factors", "mul_eq_one_iff_eq_inv", "of_real_norm_eq_coe_nnnorm", "category_theory.pi.comap_id_inv_app", "real.continuous_at_rpow", "hyperreal.st_eq_Sup", "list.forall_mem_inter_of_forall_right", "fract_add_floor", "mv_power_series.mul_inv_of_unit", "filter.forall_sets_nonempty_iff_ne_bot", "linear_map.continuous_of_finite_dimensional", "real.le_Inf", "bit1_pos", "pell.is_pell_conj", "decidable.lt_or_eq_of_le", "lucas_lehmer.\[Omega]_pow_eq_neg_one", "set.mem_univ", "is_glb.Inf_eq", "list.prefix_iff_eq_take", "list.func.get_nil", "relation.refl_trans_gen.head_induction_on", "list.to_finset_card_le", "int.mod_lt", "turing.TM1to1.tr_supports", "has_strict_fderiv_at_id", "matrix.empty_val'", "add_pow", "measure_theory.ae_eq_fun.integrable_mk", "bilin_form.lin_mul_lin_apply", "real.continuous_sinh", "function.sometimes_eq", "localization_map.lift_injective_iff", "complex.is_cau_abs_exp", "char_p.exists", "set.sInter_union_sInter", "rel.preimage_inter", "localization_map.sec_spec'", "le_one_div", "list.nth_le_map", "is_min_filter_const", "nat.add_sub_eq_max", "is_compact.finite_compact_cover", "AddCommGroup.colimits.quot_zero", "nat.succ_sub_succ", "trans", "list.mem_sublists", "int.mul_mod_mul_of_pos", "add_comm_group.is_Z_bilin.comp_hom", "eq_tt_eq_not_eq_ff", "ring_hom.eq_on_sclosure", "subgroup.mul_mem_cancel_left", "list.le_count_iff_repeat_sublist", "except_t.run_map", "semimodule.nsmul_eq_smul", "rat.exists_mul_self", "measure_theory.outer_measure.is_caratheodory_Union_nat", "galois_coinsertion.u_supr_l", "relation.refl_trans_gen.trans", "int.mul_div_mul_of_pos", "order_embedding.acc", "equiv.option_equiv_sum_punit_none", "monoid_hom.map_units_inv", "uniformly_extend_of_ind", "algebra.is_algebraic_trans", "list.length_pos_of_ne_nil", "rat.coe_int_eq_mk", "multilinear_map.curry_right_apply", "set.bInter_mono'", "real.differentiable_cos", "fderiv_within_univ", "Sup_union", "is_add_subgroup.mem_trivial", "cardinal.mk_Ico_real", "ctop.realizer.is_open", "multiset.pmap_eq_map_attach", "algebraic_closure.exists_of_step", "convex.norm_image_sub_le_of_norm_has_fderiv_within_le", "continuous_linear_map.uncurry_left_norm", "set.ord_connected_sInter", "tangent_bundle_model_space_coe_chart_at_symm", "has_strict_fderiv_at.approximates_deriv_on_nhds", "le_ceil", "mem_closure_iff_cluster_pt", "bsupr_le_supr", "set.diff_inter_self", "bitraversable.id_tfst", "add_right_iterate", "has_ftaylor_series_up_to.zero_eq'", "real.cos_bound", "neg_le_neg", "turing.TM2to1.add_bottom_nth_succ_fst", "monoid_algebra.zero_mul", "dfinsupp.single_eq_same", "list.func.mem_get_of_ne_zero", "hyperreal.is_st_st_of_exists_st", "set.union_eq_self_of_subset_right", "list.sublists_aux_ne_nil", "turing.TM2to1.tr_stmts\:2081_run", "complex.continuous_linear_map.of_real_isometry", "ring.direct_limit.lift_neg", "gold_conj_irrational", "convex_halfspace_re_lge", "pSet.mem.congr_right", "supr_true", "continuous_multilinear_map.curry_right_norm", "category_theory.monad.forget_creates_limits.lifted_cone_X", "padic_seq.stationary", "zero_le_mul_left", "div_add'", "prime.div_or_div", "submodule.map_subtype_top", "nnreal.zero_le_coe", "pnat.xgcd_type.flip_a", "circle_deg1_lift.le_iterate_of_add_int_le_map", "eq_Icc_cInf_cSup_of_connected_bdd_closed", "submodule.mem_annihilator'", "category_theory.abelian.images.image_strong_epi_mono_factorisation_to_mono_factorisation_e", "function.semiconj.maps_to_periodic_pts", "nhds_within_eq", "is_group_hom.one_ker_inv'", "euclidean_geometry.angle_eq_zero_of_angle_eq_pi_left", "set.ord_connected_Ico", "div_sub'", "list.qsort_cons", "category_theory.forget_obj_eq_coe", "commute.units_gpow_left", "is_R_or_C.abs_eq_zero", "nat.sub_le_self", "affine.simplex.sum_monge_point_weights_with_circumcenter", "mem_right_add_coset", "commute.pow_self", "simple_graph.irrefl", "complex.exp_inj_of_neg_pi_lt_of_le_pi", "finset.image_filter", "pfun.ext'", "category_theory.monoidal_category.unitors_equal.cells_14", "category_theory.monoidal_category.tensor_left_tensor_hom_app", "category_theory.limits.is_initial.epi_to", "set.finite.is_compact", "geom_sum_Ico_mul_neg", "nat.dvd_prime", "list.lex.to_ne", "generalized_continued_fraction.zeroth_denominator_eq_one", "equiv.subtype_preimage_apply", "linear_pmap.snd_apply", "finsupp.map_domain_finset_sum", "real.exp_log_of_neg", "set.ssubset_def", "submodule.inner_right_of_mem_orthogonal", "nsmul_le_nsmul_of_le_right", "div_le_iff'", "asymptotics.is_O_of_le", "tensor_product.smul_zero", "basic_smooth_bundle_core.mem_chart_source_iff", "order_of_eq_prime", "differentiable.comp_differentiable_on", "multiset.sub_inter", "real.rpow_int_cast", "vector_span_range_eq_span_range_vsub_left", "function.involutive.injective", "emetric.countable_closure_of_compact", "map_Inf_of_continuous_at_of_monotone'", "except_t.run_monad_lift", "turing.tape.move_left_right", "list.eq_of_sum_take_eq", "measure_theory.simple_func.supr_approx_apply", "set.maps_to_bInter_bInter", "category_theory.eq_of_comp_left_eq'", "semiquot.is_pure_of_subsingleton", "set.subset_sUnion_of_mem", "equiv.symm_apply_apply", 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"free_monoid.of_def", "free_semigroup.map_mul'", "submonoid.subset_closure", "measure_theory.ae_eq_fun.integrable_coe_fn", "is_basis_empty", "list.mem_attach", "add_equiv.to_AddCommMon_iso_inv", "add_units.coe_zero", "gpow_mul", "set.range_nonempty_iff_nonempty", "mdifferentiable_within_at_iff", "function.semiconj.maps_to_pts_of_period", "matrix.std_basis_matrix_zero", "not_tendsto_nhds_of_tendsto_at_top", "set.Ici_singleton_of_top", "list.mem_bind_of_mem", "affine.simplex.monge_point_eq_smul_vsub_vadd_circumcenter", "polynomial.monic_X_sub_C", "induced_order_topology", "fderiv_within_const_smul_algebra", "set.mem_bInter", "circle_deg1_lift.forall_map_sub_of_Icc", "finset.pi_subset", "measure_theory.ae_eq_fun.edist_add_right", "list.filter_subset", "is_local_min_on.has_fderiv_within_at_nonneg", "finset.sum_apply_dite", "asymptotics.is_O_with.const_mul_right", "span_int_eq", "list.mem_erasep_of_neg", "metric.ball_subset_interior_closed_ball", "add_monoid_hom.map_mclosure", "monoid_hom.coe_to_hom_units", "polynomial.derivative_eval", "submodule.map_mono", "iff.elim_left", "neg_eq_iff_add_eq_zero", "mul_max_of_nonneg", "has_sum.sigma", "differentiable_within_at_univ", "qpf.corecF_eq", "nat.mul_left_eq_self_iff", "composition.embedding_injective", "is_open.is_G\[Delta]", "gaussian_int.norm_sq_div_sub_div_lt_one", "list.map_sublists'_aux", "pfunctor.M.iselect_eq_default", "directed_comp", "times_cont_mdiff_on_congr", "category_theory.comma.iso_mk_hom_right", "cau_seq.neg_lim_zero", "enorm.max_map", "polynomial.nat_degree_zero", "matrix.update_row_apply", "multiset.filter_map_cons_none", "add_submonoid.coe_copy", "add_left_cancel_iff", "function.left_inverse.iterate", "linear_map.lsmul_apply", "Sup_le_Sup", "filter.has_antimono_basis.tendsto", "finset.mem_univ_val", "measure_theory.tsum_measure_preimage_singleton", "differentiable_at.sqrt", "nat.add_eq_one_iff", "subgroup.normal_closure_mono", "list.suffix_insert", "homeomorph.comp_continuous_iff", "right_coset_assoc", "measure_theory.measure.count_apply_infinite", "list.join_split_wrt_composition_aux", "int.neg_nonneg_of_nonpos", "function.comp.left_id", "proof_irrel", "differentiable_on.log", "nnreal.of_real_add", "uniformity_eq_symm", "convex_cone.mem_coe", "hyperreal.lt_of_pos_of_infinitesimal", "mvpfunctor.M.bisim\:2080", "measure_theory.simple_func.supr_eapprox_apply", "complex.inv_def", "list.Ico.eq_cons", "submonoid.localization_map.symm_comp_of_mul_equiv_of_localizations_apply", "polynomial.leading_coeff_prod'", "add_units.eq_iff", "is_R_or_C.abs_two", "mv_polynomial.mem_restrict_degree_iff_sup", "linear_recurrence.mk_sol_eq_init", "filter.low_scores", "category_theory.limits.cone_morphism.ext_iff", "norm_num.adc_one_bit0", "finset.sdiff_inter_self", "category_theory.limits.prod.lift_map", "filter.prod_inf_prod", "fin.succ_inj", "denumerable.lower_raise", "polynomial.continuous_at", "polynomial.unique_separable_of_irreducible", "nonempty.congr", "add_self_eq_zero", "generalized_continued_fraction.continuants_stable_of_terminated", "linarith.int.coe_nat_mul_zero", "decidable.not_and_iff_or_not", "matrix.vec_mul_diagonal", "nat.div2_bit1", "set.preimage_surjective", "list.sublist_or_mem_of_sublist", "multiplicity.eq_some_iff", "ball_and_distrib", "formal_multilinear_series.id_apply_ne_one", "category_theory.limits.equalizer.lift_\[Iota]", "set.image2_right", "complex.int_cast_im", "pSet.mem_image", "submodule.inf_comap_le_comap_add", "lt_div_iff_of_neg'", "finsupp.span_eq_map_total", "subring.le_def", "nat.le_find_greatest", "finset.prod_insert_one", "hash_map.valid.erase", "abstract_completion.continuous_coe", "con.mk'_ker", "measure_theory.measure.haar.chaar_sup_le", "filter.frequently_supr", "local_equiv.image_inter_source_eq", "ring_hom.comp_assoc", "enat.with_top_equiv_symm_top", "nat.test_bit_land", "free_group.sum.of", "image.is_add_submonoid", "derive_fintype.finset_in.mem_mk", "submonoid.map_surjective_of_surjective", "has_deriv_within_at.const_sub", "span_gcd", "polynomial.degree_ne_of_nat_degree_ne", "array.rev_list_length", "disjoint.mono_left", "finmap.ext_iff", "complex.sin_pi_sub", "category_theory.iso.refl_conj", "function.is_partial_inv_left", "differentiable_on.cexp", "lucas_lehmer.s_mod_nonneg", "multiset.coe_eq_coe", "filter.is_bounded_bot", "fin.val_two", "rel.image_id", "measure_theory.l1.of_fun_smul", "finset.union_sdiff_self", "nat.primrec'.mkpair", "finset.Ico.self_eq_empty", "set.bUnion_range_preimage_singleton", "polynomial.separable_prod_X_sub_C_iff", "submodule.ker_liftq_eq_bot", "padic.valuation_zero", "fin.succ_above_zero", "le_add_iff_nonneg_left", "ordinal.cof_bsup_le_lift", "list.disjoint_cons_left", "times_cont_diff_within_at.continuous_within_at", "pythagorean_triple.mul_is_classified", "norm_le_zero_iff", "multiset.eq_zero_iff_forall_not_mem", "continuous_on.continuous_at", "coinduced_bot", "neg_add_eq_zero", "has_sum_nat_add_iff", "cau_seq.lim_mul_lim", "mat_poly_equiv_coeff_apply_aux_1", "galois_coinsertion.u_inf_l", "measure_theory.measure.haar_measure_pos_of_is_open", "topological_space.opens.comap_comp", "finset.prod_Ico_eq_prod_range", "is_R_or_C.int_cast_re", "zorn.chain.mono", "commute.div_left", "multiset.le_zero", "nnreal.inv_pow", "nat.cast_mul", "quotient_add_group.ker_lift_mk'", "open_embedding.to_local_equiv_coe", "circle_deg1_lift.map_fract_sub_fract_eq", "abs_inner_div_norm_mul_norm_eq_one_iff", "int.exists_mul_self", "mv_polynomial.degrees_prod", "pfunctor.M.dest_mk", "mem_connected_component", "cardinal.bit1_le_bit0", "one_le_of_inv_le_one", "list.lookup_cons_eq", "measurable_pi_apply", "cardinal.succ_le", "finset.prod_ite_eq", "ordinal.lift_umax", "ordinal.card_le_card", "has_sum_geometric_of_abs_lt_1", "continuous_linear_equiv.units_equiv_to_continuous_linear_map", "convergent_eqv_pure", "metric.emetric_closed_ball_nnreal", "polynomial.eval_sub", "add_submonoid.closure_univ", "lim_nhds_within_id", "quadratic_form.associated_apply", "continuous_linear_equiv.symm_apply_eq", "function.injective.prod_map", "add_con.ext'_iff", "is_preconnected_empty", "pgame.neg_neg", "sub_nonpos_of_le", "topological_group.regular_space", "turing.tape.map_mk'", "le_floor", "or.imp_left", "measure_theory.outer_measure.trim_eq", "exp_neg_inv_glue.smooth", "equiv.ring_equiv_apply", "finsupp.of_multiset_apply", "finset.eq_empty_of_not_nonempty", "linarith.lt_of_eq_of_lt", "rat.coe_nat_denom", "subalgebra.val_apply", "units.mul_inv'", "set.singleton.is_add_hom", "free_monoid.lift_comp_of", "monoid_hom.comp_to_functor", "nat.le_of_add_le_add_left", "ring_invo.to_fun_eq_coe", "dfinsupp.support_erase", "set.bUnion_range", "is_ring_hom.map_zero", "int.div_lt_of_lt_mul", "ordinal.div_eq_zero_of_lt", "free_add_magma.traverse_eq", "CpltSepUniformSpace.coe_of", "is_unit_of_mul_is_unit_right", "set.univ_mul_univ", "set.maps_to.inter_inter", "finset.disjoint_iff_disjoint_coe", "equiv.perm.inv_def", "multiset.disjoint_ndinsert_right", "quot.lift_indep_pr1", "submonoid.localization_map.mul_equiv_of_mul_equiv_mk'", "finset.inter_insert_of_not_mem", "principal_seg.coe_fn_to_rel_embedding", "exists_swap", "order_of_dvd_card_univ", "cau_seq.completion.mk_neg", "category_theory.comma.map_left_id_hom_app_right", "eq_zero_of_ne_zero_of_mul_eq_zero", "traversable.fold_map_hom_free", "finset.mem_of_mem_insert_of_ne", "div_mul_eq_mul_div_comm", "set.inj_on_Union_of_directed", "finset.centroid_weights_apply", "inv_mul_lt_iff_lt_mul", "multiset.coe_attach", "dist_eq_norm_vsub", "has_strict_fderiv_at.neg", "complex.tan_of_real_im", "semiconj_by.inv_symm_left'", "free_abelian_group.one_def", "computation.get_mem", "local_homeomorph.restr_to_local_equiv", "int.abs_div_le_abs", "category_theory.mono_of_mono", "has_ftaylor_series_up_to_on.prod", "nat.bit1_ne_one", "convex_on_exp", "pgame.equiv_nim_grundy_value", "linear_map.mk\:2082_apply", "affine_map.linear_map_vsub", "deriv.lhopital_zero_nhds_right", "add_localization.induction_on\:2082", "int.le_sub_right_of_add_le", "ordinal.card_univ", "function.mem_support", "zorn.exists_maximal_of_chains_bounded", "differentiable_at.prod_map", "localization_map.is_integer_mul", "list.nodup_map_iff", "complex.exp_multiset_sum", "pmf.coe_bind_apply", "stream.tail_cons", "real.exp_injective", "complex.norm_sq_one", "is_open_induced", "cauchy_seq_of_edist_le_geometric", "int.coe_nat_ne_coe_nat_iff", "ordinal.lift_le", "enat.coe_inj", "times_cont_diff_on.continuous_on_iterated_deriv_within", "sub_lt_sub_right", "constr_smul", "ordinal.add_lt_add_iff_left", "structure_groupoid.local_invariant_prop.lift_prop_on_chart_symm", "list.count_cons", "exists_true_iff_nonempty", "monotone_mul_right_of_nonneg", "category_theory.limits.parallel_pair_map_right", "setoid.mk_classes_classes", "submonoid.powers_eq_closure", "midpoint_sub_right", "list.indexes_values_eq_filter_enum", "generalized_continued_fraction.exists_s_b_of_part_denom", "em", "turing.list_blank.map_mk", "supr_const", "filter.frequently_at_top", "multiset.powerset_len_mono", "list.nth_concat_length", "equiv.perm.eq_inv_iff_eq", "bilin_form.is_skew_adjoint_iff_neg_self_adjoint", "matrix.reindex_lie_equiv_symm_apply", "is_cau_series_of_abv_cau", "direct_sum.to_group_zero", "complex.uniform_continuous_of_real", "roption.bind_none", "list.chain'_map", "ennreal.coe_max", "list.nth_le_mem", "min_eq_right", "omega.coeffs.val_nil", "computation.eq_of_ret_mem", "vector.traverse_def", "finset.inter_val", "finset.nonempty_of_prod_ne_one", "ordinal.is_normal.lt_nfp", "subring.coe_Sup_of_directed_on", "convex_on.exists_ge_of_center_mass", "list.sublist_append_of_sublist_right", "monoid_hom.map_range", "free_magma.mul_seq", "subtype.range_val_subtype", "Set.Union_singleton", "fin.div_def", "uniform_space.completion.uniform_continuous_completion_separation_quotient_equiv_symm", "category_theory.limits.is_limit.lift_cone_morphism_hom", "measure_theory.integrable.mono'", "abs_lt_of_lt_of_neg_lt", "nat.add_mul_mod_self_left", "monoid_hom.map_exists_left_inv", "int.coe_nat_dvd_left", "has_deriv_at.comp", "ring_equiv.to_monoid_hom_refl", "padic_norm.triangle_ineq", "nat.coprime.gcd_mul_right_cancel", "lists.of_to_list", "list.split_wrt_composition_aux_cons", "partrec.sum_cases", "submodule.ext'_iff", "is_add_unit.map", "submodule.smul_mem_iff", "mdifferentiable_within_at.mfderiv_within", "nnreal.is_greatest_Lp", "ring.fractional_ideal.one_mem_one", "filter.eq_binfi_of_mem_sets_iff_exists_mem", "is_conj_one_right", "list.exists_mem_cons_iff", "set_of_is_preconnected_subset_of_ordered", "mul_action.mem_fixed_points_iff_card_orbit_eq_one", "continuous_linear_equiv.one_le_norm_mul_norm_symm", "list.mem_lookup_kunion", "wseq.mem_of_mem_dropn", "cardinal.infinite_iff", "multiplicity.get_one_right", "metric.ball_union_sphere", "inner_product_geometry.sin_angle_sub_add_angle_sub_rev_eq_sin_angle", "local_equiv.symm_image_inter_target_eq", "encodable.mem_decode2'", "sym2.map_id", "uniform_space.separation_quotient.lift_mk", "uniform_space.completion.coe_add", "category_theory.limits.limit_iso_limit_curry_comp_lim_hom_\[Pi]_\[Pi]", "ideal.comap_comap", "linear_map.comp_smul", "times_cont_diff_iff_iterated_deriv", "list.sublist.append", "has_fderiv_within_at.comp", "add_units.coe_add", "add_submonoid.localization_map.lift_of_comp", "power_series.coeff_monomial'", "int.le_add_of_nonneg_right", "finset.union_inter_cancel_right", "filter.range_mem_map", "set.Icc_inter_Icc", "lt_add_of_lt_of_nonneg", "wseq.dropn_cons", "norm_num.add_bit1_bit0", "totally_bounded_preimage", "exists_imp_distrib", "multiset.map_mk_eq_map_mk_of_rel", "commute.left_comm", "encodable.length_sorted_univ", "complex.abs_abs", "measure_theory.ae_eq_fun.inv_mk", "tendsto_nhds_within_iff_subtype", "associated_zero_iff_eq_zero", "bitvec.add_lsb_eq_twice_add_one", "linear_map.cod_restrict_apply", "filter.is_countably_generated.filter_basis_filter", "measure_theory.measure.count_apply_lt_top", "subring.mem_bot", "min_le_max", "sum_range_choose", "fintype.coe_image_univ", "algebraic_geometry.LocallyRingedSpace.id_val", "list.argmax_singleton", "nat.add_left_comm", "free_group.map.one", "semidirect_product.hom_ext", "finset.prod_induction", "polynomial.eval_int_cast", "category_theory.limits.coequalizer.iso_target_of_self_hom", "rel_embedding.collapse_F.lt", "bilin_form.to_matrix_comp", "measure_theory.integrable_zero_measure", "local_of_nonunits_ideal", "one_div_lt_one_div_of_neg_of_lt", "list.kunion_cons", "mul_action_hom.id_apply", "measure_theory.l1.simple_func.zero_to_simple_func", "nat.add_sub_cancel_right", "disjoint_nhds_at_top", "set.Inter_subset_Inter2", "differentiable_within_at.smul_algebra_const", "nat.modeq.symm", "cancel_factors.cancel_factors_le", "lt_of_lt_of_incomp", "nonempty_psum", "prime_spectrum.zero_locus_bot", "is_group_hom.inv_ker_one'", "convex.mono_of_deriv_nonneg", "matrix.mul_neg", "equiv.add_equiv_apply", "not_nonempty_iff_imp_false", "measure_theory.integrable_on.right_of_union", "measure_theory.coe_to_outer_measure", "decidable_eq_inr_neg", "linear_map.disjoint_ker'", "measure_theory.lintegral_congr_ae", "bot_lt_iff_ne_bot", "has_strict_fderiv_at.eventually_left_inverse", "has_mfderiv_at.continuous_at", "list.nodup_join", "linear_map.zero_apply", "contracting_with.tendsto_iterate_efixed_point", "category_theory.limits.is_image.fac_lift_assoc", "tensor_product.map_tmul", "gcd_zero_left", "rel_embedding.is_trichotomous", "le_of_sup_eq", "enat.get_le_get", "traversable.to_list_map", "dvd_add_iff_left", "padic_val_rat.defn", "nat.mod_def", "tactic.ring2.horner_expr.cseval_of_csexpr", "tangent_bundle_model_space_topology_eq_prod", "pnat.gcd_rel_left", "is_group_hom.map_one", "is_measurable.diff_null", "list.forall_mem_of_forall_mem_union_right", "int.eq_of_mod_eq_of_nat_abs_sub_lt_nat_abs", "trunc.induction_on\:2082", "exists_eq_left'", "onote.zero_add", "topological_space.opens.gi_choice_val", "free_semigroup.map_of", "measure_theory.tendsto_lintegral_norm_of_dominated_convergence", "category_theory.monoidal_category.unitors_equal.cells_6", "pi.smul_apply'", "eventually_norm_pow_le", "gaussian_int.norm_pos", "is_G\[Delta]_univ", "multiset.sum_add", "is_unit_of_dvd_unit", "finsupp.support_subtype_domain", "tactic.ring_exp.add_pf_sum_overlap_zero", "ordinal.one_eq_type_unit", "computable.of_eq", "int.lt_div_add_one_mul_self", "polynomial.splitting_field_aux.algebra_map_succ", "measure_theory.measure.restrict_apply_eq_zero", "is_open_sUnion", "add_submonoid.closure_eq", "is_bounded_bilinear_map.continuous_right", "powers_eq_gpowers", "seq.mem_cons_of_mem", "finset.sum_nonneg", "homeomorph.to_local_homeomorph_coe_symm", "ennreal.tendsto.mul_const", "category_theory.limits.zero_of_to_zero", "filter.is_basis.filter_eq_generate", "joined_in.symm", "Set.map_fval", "strict_mono.mul", "linear_map.findim_le_findim_of_injective", "has_deriv_at.lhopital_zero_right_on_Ico", "omega.nat.val_canonize", "finset.attach_eq_univ", "add_submonoid.map_map", "pgame.mk_le_mk", "function.left_inverse.comp", "measure_theory.ae_eq_fun.coe_fn_le", "list.perm.subperm", "sub_mul_add_eq_of_mul_add_eq_mul_add", "Group.one_apply", "nat.add_le_to_le_sub", "euclidean_domain.lcm_zero_right", "le_sup_right", "set.preimage_neg_Ioi", "padic_val_rat_of_nat", "irrational_sqrt_two", "finset.prod_union_inter", "homological_complex.comm", "matrix.to_bilin_form_apply", "subsemiring.mk'_to_submonoid", "Sup_le_Sup_of_subset_instert_bot", "linear_equiv.lie_conj_apply", "computation.think_bind", "multiset.sub_le_sub_right", "rat.denom_one", "turing.TM2to1.supports_run", "bounded_continuous_function.arzela_ascoli", "category_theory.limits.prod_comparison_inv_natural", "sylow.mem_fixed_points_mul_left_cosets_iff_mem_normalizer", "strict_mono.mul_monotone", "times_cont_mdiff.times_cont_mdiff_at", "uniform_continuous\:2082.uniform_continuous", "rel_iso.coe_one", "abs_max_sub_max_le_abs", "nat.sub_lt_succ", "measure_theory.lintegral_supr", "filter.germ.induction_on", "rank_finset_sum_le", "bitvec.bits_to_nat_to_bool", "measure_theory.le_inner_content", "list.reverse_foldl", "continuous_linear_map.smul_right_one_eq_iff", "measure_theory.simple_func.lintegral_map", "mv_polynomial.map_monomial", "list.mem_split", "function.support_div", "mv_polynomial.pderivative_mul", "lower_bounds_union", "subring.mem_map", "finsupp.to_multiset_strict_mono", "implies_of_if_neg", "equiv.arrow_congr_refl", "int.div_eq_zero_of_lt", "enorm.finite_norm_eq", "list.extractp_eq_find_erasep", "lie_self", "submodule.span_eq_of_le", "measure_theory.norm_set_integral_le_of_norm_le_const", "dim_fin_fun", "measure_theory.simple_func.lintegral_eq_lintegral", "mem_closure_iff_seq_limit", "deriv_sqrt", "finsupp.to_finset_to_multiset", "quotient_map_quotient_mk", "set.finite_range_ite", "bernoulli_three", "deriv_const_mul", "prime_spectrum.comap_as_ideal", "category_theory.limits.image.iso_strong_epi_mono_inv_comp_mono", "is_local_max.inf", "free_comm_ring.map_subtype_val_restriction", "list.length_pos_iff_ne_nil", "polynomial.aeval_alg_hom", "equiv.nonempty_iff_nonempty", "int.add_mod_self", "matrix.diag_apply", "pfunctor.M.nth_of_bisim", "is_noetherian_submodule_left", "filter.eventually_eq.prod_mk", "omega.clauses.unsat_nil", "padic_polynomial_dist", "set.preimage_const_sub_Ico", "nat.cases_succ", "linear_map.continuous_on_pi", "padic_int.appr_spec", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_obj_X_map", "category_theory.abelian.pseudoelement.pseudo_apply_mk", "magma.free_semigroup.map_mul", "polynomial.is_noetherian_ring", "is_bounded_bilinear_map.is_O", "equiv.swap_core_swap_core", "filter.eventually.congr", "nat.div_zero", "matrix_equiv_tensor.left_inv", "nat.choose_two_right", "equiv.prod_sum_distrib_apply_left", "unique_diff_on.inter", "is_irrefl.swap", "typevec.subtype_val_nil", "int.shiftl_eq_mul_pow", "finset.mem_powerset_len", "polynomial.nat_degree_eq_zero_iff_degree_le_zero", "submodule.map_inl", "real.cos_sub_cos", "equiv.sum_pempty_apply_inl", "polynomial.integral_normalization_coeff_degree", "semiconj_by.units_coe_iff", "ennreal.div_add_div_same", "iff_not_self", "equiv.perm.sign_aux_mul", "AddCommGroup.kernel_iso_ker_hom_comp_subtype", "field.direct_limit.mul_inv_cancel", "nat.cast_pred", "mv_polynomial.coe_one", "matrix.adjugate_mul", "category_theory.monoidal_of_has_finite_products.tensor_obj", "pfunctor.liftp_iff'", "submonoid.le_def", "localization_map.ring_equiv_of_ring_equiv_eq_map_apply", "has_ftaylor_series_up_to_on.continuous_on", "encodable.decode_prod_val", "continuous_within_at_of_locally_uniform_approx_of_continuous_within_at", "nat.gcd_gcd_self_right_left", "div_lt_div_left", "function.is_periodic_pt.const_mul", "measure_theory.ae_eq_fun.lift_rel_mk_mk", "category_theory.limits.types.prod", "list.foldr_append", "mod_mem_iff", "ordinal.min_eq", "set.Inter_inter_distrib", "polynomial.coeff_monomial", "list.any_cons", "set.preimage_const_mul_Ioc", "abs_mul_self", "valuation.comap_comp", "char_p.char_is_prime_of_pos", "measure_theory.measure.map_mul_right_eq_self", "affine_subspace.direction_inf", "generalized_continued_fraction.ext", "le_cSup_of_le", "sub_neg_eq_add", "commute.pow_right", "set.bInter_range", "pos_num.cast_to_znum", "filter.image_mem_map", "nat.prime.one_lt", "is_subgroup.mem_center", "set.set_of_mem_eq", "category_theory.le_of_hom", "le_binfi", "equiv.eq_symm_apply", "finsupp.smul_sum", "category_theory.limits.biproduct.map_eq", "partrec.fix", "uniform_space.uniformity_quotient", "polynomial.degree_pos_of_irreducible", "list.pairwise_lt_range", "zmod.card", "set.singleton_seq", "list.find_indexes_eq_map_indexes_values", "hyperreal.infinite_neg_mul_of_infinite_pos_not_infinitesimal_neg", "list.head_add_tail_sum'", "partrec.nat_cases_right", "stream.tail_iterate", "traversable.traverse_eq_map_id'", "pfunctor.M.children_mk", "ordinal.type_ne_zero_iff_nonempty", "filter.map_inj", "list.perm.swap'", "prime_multiset.prod_zero", "category_theory.iso.cancel_iso_inv_right", "isometric.symm_apply_apply", "structure_groupoid.local_invariant_prop.lift_prop_within_at_indep_chart", "quotient_add_group.range_ker_lift_injective", "set.inter_univ", "pnat.factor_multiset_le_iff", "inducing_of_inducing_compose", "monotone.iterate_ge_of_ge", "category_theory.limits.types.sigma", "subgroup.comap_comap", "znum.cast_succ", "inner_self_eq_zero", "is_measurable_Ioc", "measurable_space.comap_bot", "list.reverse_nil", "multiset.zero_disjoint", "filter.lift_inf", "lists.is_list_of_mem", "seq.of_list_cons", "forall_lt_iff_le'", "neg_neg_of_pos", "inner_product_space.of_core.inner_comm", "nat.even_add", "category_theory.functor.map_arrow_obj_right", "lim_nhds_id", "is_preconnected.intermediate_value", "power_series.inv_of_unit_eq'", "partrec\:2082.comp", "category_theory.limits.cocones.ext_hom_hom", "circle_deg1_lift.pow_mono", "ring_hom.eq_of_eq_on_set_top", "finset.card_sigma", "ordinal.pred_eq_iff_not_succ", "concave_on.le_on_segment", "finset.ne_insert_of_not_mem", "linear_equiv.conj_comp", "primrec.const", "local_equiv.refl_restr_target", "ordinal.zero_power'", "primrec.list_reverse", "continuous_linear_map.lmul_right_apply", "mfderiv_within_subset", "cardinal.prop_eq_two", "category_theory.concrete_category.mono_of_injective", "filter.add_mem_add", "submonoid.forall", "primrec.list_append", "ordinal.succ_pred_iff_is_succ", "rel_iso.map_sup", "turing.TM2to1.add_bottom_head_fst", "set.disjoint_right", "category_theory.limits.prod_map_id_comp_assoc", "semiquot.is_pure_iff", "one_div_le_neg_one", "linear_map.proj_apply", "euclidean_geometry.dist_affine_combination", "exists_integral_multiple", "semiquot.is_pure.mono", "order_of_dvd_iff_pow_eq_one", "padic_val_rat.min_le_padic_val_rat_add", "set.pairwise_disjoint.subset", "eq_univ_of_nonempty_clopen", "nat.pow_one", "neg_nonneg", "real.tanh_zero", "subgroup.prod_mem", "pos_num.one_sub'", "finset.nat.card_antidiagonal", "exists_mem_ne_zero_of_dim_pos", "polynomial.separable_X_sub_C", "nat.le_antisymm", "one_div_pow", "times_cont_diff_within_at_univ", "quot.induction_on", "normed_field.norm_inv", "smooth_iff", "filter.inf_ne_bot_iff", "galois_connection.is_glb_l", "filter.tendsto.prod_mk", "category_theory.monad.forget_map", "ordering.ite_eq_gt_distrib", "has_deriv_within_at.mono", "pSet.mem.ext", "real.le_of_forall_epsilon_le", "adjoin_root.lift_root", "multiset.fold_eq_foldr", "false_of_a_eq_not_a", "basic_smooth_bundle_core.times_cont_mdiff_on_proj", "complex.sin_zero", "valuation.comap_on_quot_eq", "add_submonoid.comap_top", "pgame.first_wins_of_equiv_iff", "finsupp.to_multiset_single", "local_equiv.source_inter_preimage_inv_preimage", "bdd_above_Icc", "sub_lt_sub_of_lt_of_le", "multiset.nodup_pmap", "category_theory.limits.biprod.lift_desc", "multiset.nodup_of_nodup_cons", "nat.sub_mono_right_strict", "asymptotics.is_O_with.const_mul_left", "prod.mk_sub_mk", "localization_map.lift_eq_iff", "pi_Lp.aux_uniformity_eq", "seq.map_append", "ideal.is_maximal.exists_inv", "with_zero.mul_left_inv", "circle_deg1_lift.map_sub_int", "real.mul_pos", "multiset.ndinsert_of_not_mem", "equiv.perm.pow_apply_eq_self_of_apply_eq_self", "bool.bor_inl", "cont_t.run_with_cont_t", "list.sublist_of_cons_sublist", "matrix.special_linear_group.ext_iff", "multiset.of_mem_filter", "qpf.id_map", "edist_le_Ico_sum_edist", "turing.TM2to1.tr_supports", "list.mem_range", "upper_bounds_Ioo", "list.insert_nth_remove_nth_of_le", "differentiable_on.cosh", "isometry_emetric_iff_metric", "differentiable_within_at.iterate", "le_nhds_of_Limsup_eq_Liminf", "pgame.nim_add_nim_equiv", "set.finite.compact_bUnion", "isometric.range_coe", "fpow_zero", "submodule.orthogonal_gc", "circle_deg1_lift.tendsto_translation_number\:2080", "num.add_zero", "set.ord_connected_Ioc", "set.disjoint.union_left", "eq_add_neg_iff_add_eq", "ideal.is_jacobson_localization", "linear_map.ker_id", "units.mul_left_dvd", "pow_eq_mod_order_of", "linear_action_smul_act", "set.preimage_kern_image", "with_top.coe_Sup", "semiconj_by.sub_right", "set.range_inclusion", "finsupp.sum_smul_index", "list.filter_map_filter_map", "category_theory.non_preadditive_abelian.image.fac_assoc", "int.lt_of_add_lt_add_right", "category_theory.graded_object.comap_eq_hom_app", "is_integral_mul", "measure_theory.outer_measure.Inf_gen_nonempty2", "category_theory.limits.coequalizer.\[Pi]_desc", "metric.mem_ball'", "finset.monotone_preimage", "is_basis.dual_lin_independent", "continuous_at.prod", "has_deriv_at.const_mul", "linear_equiv.to_Module_iso_hom", "bounded_continuous_function.dist_set_exists", "ennreal.to_nnreal_add", "ordinal.le_power_self", "associated_mul_left_cancel", "inf_sup_left", "asymptotics.is_o.tendsto_0", "fintype.card_sigma", "has_fderiv_at_filter_id", "power_series.trunc_add", "znum.bit1_of_bit1", "complex.cos_two_pi", "affine_independent_iff_linear_independent_vsub", "ctop.realizer.nhds_F", "asymptotics.is_o.comp_tendsto", "ordinal.is_normal.deriv_fp", "category_theory.ev_coev_assoc", "monotone.map_infi2_le", "is_add_group_hom.sub", "list.length_erasep_of_mem", "not_and_of_not_left", "equiv.forall_congr_left'", "list.func.get_pointwise", "tendsto_at_top_add_tendsto_left", "set.not_disjoint_iff", "is_local_min.comp_continuous_on", "complex.continuous_sin", "filter.liminf_eq_supr_infi", "has_fderiv_at.snd", "int.lt_of_neg_lt_neg", "rat.zero_ne_one", "fract_coe", "is_complete_of_complete_image", "continuous_linear_map.is_bounded_linear_map", "affine_subspace.ext_of_direction_eq", "pfunctor.supp_eq", "has_strict_fderiv_at.differentiable_at", "category_theory.limits.pushout_cocone.of_cocone_\[Iota]", "nat.lxor_bit", "category_theory.curry_id_eq_coev", "field.direct_limit.exists_inv", "linarith.le_of_eq_of_le", "polynomial.exists_finset_roots", "set.Icc_subset_Ici_self", "finset.union_distrib_left", "nat.lt_of_sub_pos", "nat.primrec.mul", "pfun.compl_dom_subset_core", "primrec.ulower_up", "ordinal.lift_is_limit", "free_ring.coe_add", "filter.eventually_eq.is_max_filter_iff", "category_theory.limits.cone_left_op_of_cocone_\[Pi]_app", "nonempty_sigma", "abstract_completion.extend_def", "finset.eq_weighted_vsub_subset_iff_eq_weighted_vsub_subtype", "homeomorph.quotient_map", "affine_subspace.direction_eq_vector_span", "function.support_add", "category_theory.functor.left_adjoint_of_is_equivalence", "ordinal.cof_eq", "vector3.cons_head_tail", "category_theory.comma.map_right_id_inv_app_left", "list.erase_dup_eq_self", "nhds_left_sup_nhds_right", "measure_theory.integrable.neg", "abs_of_pos", "ideal.is_prime.comap", "rel_iso.inv_apply_self", "vector.eq_nil", "affine_map.add_linear", "subring.coe_mul", "cardinal.lift_ord", "is_add_group_hom.injective_iff_trivial_ker", "circle_deg1_lift.transnum_aux_seq_zero", "measure_theory.norm_set_integral_le_of_norm_le_const'", "finset.subset_union_left", "category_theory.non_preadditive_abelian.lift_sub_lift", "finsupp.single_left_inj", "finset.card_eq_one", "filter.tendsto_at_top_of_add_bdd_above_right", "turing.TM2to1.tr_eval", "eq_affine_combination_of_mem_affine_span", "eq.symm", "add_comm_group.direct_limit.lift_of", "mv_polynomial.total_degree_finset_prod", "times_cont_diff_at_snd", "tactic.abel.zero_smul", "applicative_transformation.preserves_map", "category_theory.monad.algebra.hom.ext", "ctop.realizer.mem_interior_iff", "set.image_diff_preimage", "ideal.is_maximal_of_is_integral_of_is_maximal_comap", "mul_nonneg_of_nonpos_of_nonpos", "mul_lt_of_lt_one_of_lt'", "complex.one_cpow", "rat.num_nonneg_iff_zero_le", "cardinal.mul_eq_left", "pnat.bit0_le_bit0", "category_theory.currying_inverse_map_app_app", "list.sublist.trans", "topological_group.t2_space", "matrix.det_transpose", "submonoid.localization_map.of_mul_equiv_of_dom_id", "convex_cone.salient_iff_not_flat", "mul_le_mul_of_nonneg_right", "real.arccos_nonneg", "strict_mono.add_const", "nhds_eq_uniformity", "filter.exists_lt_of_tendsto_at_top", "set.image_univ", "infi_false", "finset.fold_op_rel_iff_or", "has_groupoid_of_pregroupoid", "category_theory.limits.cones.ext_inv_hom", "div_right_comm", "fixed_points.minpoly.irreducible", "finsupp.prod_zero_index", "int.even_coe_nat", "multiset.Ico.filter_lt", "is_separated_iff_induced", "norm_sub_square_eq_norm_square_add_norm_square", "polynomial.roots_multiset_prod", "metric.continuous_within_at_iff'", "extend_from_extends", "submodule.convex", "affine_subspace.vsub_right_mem_direction_iff_mem", "measure_theory.measure_empty", "int.to_nat_coe_nat_add_one", "complex.abs_two", "ennreal.forall_ennreal", "hensels_lemma", "galois_coinsertion.l_le_l_iff", "ring.exists_list_of_mem_closure", "or_of_or_of_imp_right", "coinduced_mono", "ennreal.of_real_ne_top", "continuous_linear_equiv.symm_equiv_of_inverse", "category_theory.limits.map_pair_right", "differentiable_at.log", "submodule.coe_neg", "nat.lt_or_ge", "nat.sqrt_lt_self", "ring.image_closure", "real.has_deriv_at_rpow_of_neg", "add_group_with_zero_nhd.add_Z", "finsupp.subtype_domain_add", "category_theory.comonad.forget_obj", "gsmul_eq_mul'", "finset.sum_comm", "zsqrtd.decompose", "int.mod_self", "nonempty_ulift", "linear_independent_Union_of_directed", "real.one_lt_exp_iff", "has_deriv_at.sin", "magma.free_semigroup.lift_mul", "differentiable_within_at.add_const", "tactic.ring_exp.add_pf_sum_lt", "hyperreal.infinite_iff_infinite_neg", "euclidean_geometry.orthogonal_projection_def", "interior_subset_closure", "dvd_mul_left", "pgame.turn_bound_of_right", "lie_algebra.morphism.range_bracket", "ordinal.is_normal.refl", "finset.card_image_of_inj_on", "option.get_or_else_some", "max_self", "convex_cone.ext", "vadd_vsub_vadd_cancel_left", "int.not_even_bit1", "polynomial.nat_degree_one", "equiv.sum_compl_apply_symm_of_pos", "pythagorean_triple.eq", "list.mem_keys_kinsert", "monotone.map_sup", "linear_equiv.arrow_congr_trans", "alist.insert_entries_of_neg", "ordinal.cof_add", "submonoid.comap_inf", "finset.image_bind", "dfinsupp.prod_neg_index", "turing.list_blank.tail_mk", "metric.diam_closed_ball", "smooth_iff_proj_smooth", "list.mem_permutations_aux2", "int.div_one", "prod.snd_add", "neg_le_abs_self", "continuous_linear_map.differentiable_on", "finset.disjoint_bind_left", "free_group.sum.inv", "add_subgroup.mem_center_iff", "abs_one_div", "nat.lt_sub_right_of_add_lt", "list.erasep_append_right", "times_cont_mdiff_within_at.congr_of_eventually_eq", "set.disjoint_of_subset", "eq_orthogonal_projection_fn_of_mem_of_inner_eq_zero", "filter.eventually.and", "finset.bUnion_finset_image", "filter.supr_join", "times_cont_diff_on.ftaylor_series_within", "ring_equiv.is_integral_domain", "subsemiring.coe_subset_coe", "convex.combo_self", "znum.le_to_int", "free_ring.coe_neg", "iter_deriv_pow", "category_theory.sum.inr__obj", "computation.terminates_of_lift_rel", "buffer.to_list_append_list", "subsemiring.comap_inf", "padic_seq.val_eq_iff_norm_eq", "finset.map_map", "add_monoid_algebra.zero_mul", "free_add_magma.traverse_pure'", "ennreal.tsum_eq_supr_sum", "algebra.adjoin_algebra_map'", "finset.mono_of_fin_singleton", "add_monoid_hom.coe_fst", "local_ring.is_unit_or_is_unit_one_sub_self", "set.fmap_eq_image", "partrec.nat_elim", "generalized_continued_fraction.squash_seq_succ_n_tail_eq_squash_seq_tail_n", "primrec.option_get", "is_lub_of_mem_nhds", "function.right_inverse_iff_comp", "measure_theory.ae_eq_fun.coe_fn_pair", "matrix.transpose_empty_rows", "sum.swap_right_inverse", "is_add_monoid_hom.comp", "is_coprime.mul_right_iff", "hyperreal.is_st_add", "real.sqrt_two_add_series_two", "multiset.rel_cons_left", "wseq.nil_append", "exists_extension_norm_eq", "finmap.mem_insert", "nat.not_pos_pow_dvd", "nat.lor_comm", "has_fpower_series_on_ball.neg", "interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_right", "set.Iic_def", "not_iff_not", "set.set_compr_eq_eq_singleton", "norm_num.min_fac_helper_2", "category_theory.id_of_comp_left_id", "asymptotics.is_o.prod_left", "category_theory.evaluation_map_app", "direct_sum.of_sub", "finset.max_eq_none", "ring_hom.ker_eq_comap_bot", "fintype.card_equiv", "nonote.repr_mul", "ring_hom.ext_int", "int.neg_ne_zero_of_ne", "set.diff_singleton_eq_self", "num.of_znum_to_nat", "polynomial.separable.injective_of_prod_X_sub_C", "add_pow_char_pow", "cardinal.finset_card", "measure_theory.measure.sum_bool", "ennreal.pow_eq_top", "fin.pred_above_succ_above", "finsupp.prod_fintype", "linear_independent_Union_finite_subtype", "filter.tendsto.sub", "interval_integral.integral_has_deriv_at_left", "inv_nonneg", "int.test_bit_zero", "nat.coprime.pow_left", "differentiable_at.fst", "emetric.Hausdorff_edist_self", "ordinal.lt_power_succ_log", "adjoin_root.adjoin_root_eq_top", "Top.presheaf_to_Top_obj", "measurable.indicator", "cauchy.map", "bounded_continuous_function.smul_apply", "primrec.list_head", "equiv.sum_compl_apply_inl", "sym2.eq_iff", "zsqrtd.eq_zero_or_eq_zero_of_mul_eq_zero", "category_theory.functor.map_inv", "category_theory.non_preadditive_abelian.lift_map_assoc", "span_nat_eq_add_group_closure", "category_theory.limits.cospan_right", "turing.list_blank.tail_map", "is_bounded_linear_map_prod_iso", "is_glb.mono", "list.map_eq_foldr", "filter.is_bounded_principal", "matrix.diagonal_dot_product", "is_R_or_C.abs_abs_sub_le_abs_sub", "category_theory.adjunction.functoriality_unit'_app_hom", "alist.lookup_union_right", "quotient.choice_eq", "fin.cast_succ_lt_succ", "div_lt_div_of_lt", "free_group.map_mul", "mdifferentiable_at_id", "is_open_mul_right", "add_submonoid.localization_map.add_mk'_zero_eq_mk'", "direct_sum.to_module_lof", "units_eq_one", "poly_equiv_tensor.right_inv", "measure_theory.measure.eventually_cofinite", "linear_map.is_unit_iff", "finset.singleton_inter_of_mem", "direct_sum.mk_smul", "mem_nhds_within_Iio_iff_exists_mem_Ico_Ioo_subset", "zmod.cast_mul'", "list.Ico.map_sub", "cardinal.mk_le_of_surjective", "submodule.mem_annihilator", "category_theory.prod.snd_obj", "set.union_distrib_Inter_left", "set.mem_Iic", "inv_mul_le_of_le_mul", "cardinal.ord_omega", "multiplicity.pow_dvd_of_le_multiplicity", "set.maps_to_univ", "linear_independent.image_subtype", "complex.cos_add_pi", "int.mul_div_cancel", "typevec.last_fun_from_append1_drop_last", "Sup_le", "list.forall\:2082.mp", "subring.mem_mk'", "measure_theory.measure.count_apply_finite", "has_strict_fderiv_at.mul", "submodule.add_mem_iff_right", "is_measurable_closed_ball", "pSet.equiv.trans", "roption.mem_map", "eventually_ne_of_tendsto_norm_at_top", "function.commute.iterate_iterate", "nat.one_le_of_lt", "list.lex.ne_iff", "category_theory.under.hom_mk_left", "is_glb_lt_iff", "units.mul_left_inj", "ennreal.supr_mul", "complex.norm_sq_nonneg", "le_of_mul_le_mul_left'", "is_R_or_C.of_real_pow", "one_div_lt_neg_one", "is_open.frontier_eq", "znum.cast_neg", "wseq.tail_of_seq", "linear_equiv_matrix_apply", "nat.size_pos", "preorder_hom.coe_id", "tfae_mem_nhds_within_Ici", "set.univ_pi_eq_empty_iff", "category_theory.limits.wide_pullback_shape.wide_cospan_obj", "circle_deg1_lift.dist_map_zero_lt_of_semiconj_by", "polynomial.leading_coeff_X_pow", "num.to_nat_inj", "convex_hull_subset_union", "finset.fold_union_inter", "mv_polynomial.pderivative_zero", "int.pred_succ", "is_measurable.disjointed", "mv_polynomial.smul_eq_C_mul", "set.forall_of_forall_insert", "ordinal.mul_add_div", "add_comm_group.direct_limit.lift_unique", "zsqrtd.norm_mul", "int.nat_abs_add_neg", "convex_cone.smul_mem", "nat.gcd_eq_left_iff_dvd", "gsmul_int_int", "cau_seq.is_cau", "dfinsupp.erase_add_single", "is_const_of_fderiv_eq_zero", "midpoint_zero_add", "enorm.eq_zero_iff", "ne_of_gt", "set.Ioo_union_Ici_eq_Ioi", "associates.unique'", "is_local_extr_on.neg", "complex.equiv_real_prod_symm_im", "poly.zero_eval", "set.countable_empty", "prime_spectrum.comap_comp", "nat.coprime_one_right", "set.bij_on.maps_to", "list.nodup_middle", "not_non_contradictory_iff_absurd", "lower_bounds_mono_mem", "affine_independent_embedding_of_affine_independent", "list.not_nodup_cons_of_mem", "dist_le_of_approx_trajectories_ODE", "generalized_continued_fraction.int_fract_pair.nth_stream_fr_lt_one", "minimal_polynomial.root", "associated_one_iff_is_unit", "linear_map.has_deriv_at_filter", "pow_two", "ring_hom.map_rat_cast", "polynomial.root_multiplicity_eq_multiplicity", "category_theory.image_to_kernel_map_zero_right", "typevec.drop_fun_rel_last", "algebra.eq_top_iff", "continuous_linear_map.infi_ker_proj", "monoid_hom.mem_mrange", "dist_smul", "option_t.goto_mk_label", "is_integral_of_surjective", "emetric.Hausdorff_edist_self_closure", "polynomial.nat_degree_prod'", "has_sum.has_sum_iff_compl", "two_nsmul", "setoid.Sup_eq_eqv_gen", "polynomial.degree_pos_of_aeval_root", "add_comm_group.direct_limit.lift_neg", "vadd_assoc", "composition.index_embedding", "topological_space.opens.inclusion_open_embedding", "category_theory.monoidal_category.tensoring_right_map_app", "dite_apply", "finset.disjoint_union_left", "measure_theory.integrable_congr'", "pell.pell_val", "nhds_basis_opens'", "submonoid.coe_infi", "list.perm.subperm_right", "ordinal.nat_cast_pos", "linear_map.range_eq_top_of_cancel", "list.index_of_cons_ne", "stream.nth_interleave_left", "multiplicative.normal_subgroup_iff", "set.univ_inter", "multiplicity.neg", "linear_map.lflip_apply", "category_theory.adjunction.counit_naturality_assoc", "set.to_finset_empty", "edist_le_of_edist_le_geometric_of_tendsto\:2080", "finset.map_inj", "local_equiv.restr_eq_of_source_subset", "nat.add_self_ne_one", "set.Icc_diff_Ico_same", "metric.sphere_disjoint_ball", "set.sUnion_empty", "set.image_const_add_Iic", "multiplicity.finite_mul_iff", "is_R_or_C.smul_im", "category_theory.curry.obj_map_app", "category_theory.lax_monoidal_functor.comp_to_functor", "fintype.card_eq", "trunc.lift_beta", "function.equiv.trans", "submodule.one_le", "mem_closure_of_is_lub", "abs_dist", "antilipschitz_with.injective", "equiv.perm.disjoint_one_right", "and_true", "or.imp", "add_con.Inf_def", "continuous_linear_map.coe_zero'", "nat.pow_le_pow_of_le_right", "cardinal.add_eq_self", "enat.lt_add_one_iff_lt", "decidable.not_and_not_right", "composition_as_set.lt_length", "ennreal.lt_of_real_iff_to_real_lt", "linear_map.range_mkq_comp", "linear_equiv.of_bijective_apply", "submodule.coe_prod_equiv_of_is_compl", "local_equiv.prod_symm", "compare_reals.compare_uc_symm", "is_measurable_le'", "uniform_space.completion.coe_one", "list.maximum_nil", "category_theory.non_preadditive_abelian.\[CapitalDelta]_\[Sigma]_assoc", "multiplicity.multiplicity_eq_zero_of_not_dvd", "multiset.prod_singleton", "affine.simplex.eq_monge_point_of_forall_mem_monge_plane", "list.bind_append", "finset.fold_max_le", "euclidean_geometry.orthogonal_projection_orthogonal_projection", "ring_hom.map_frobenius", "category_theory.limits.walking_pair.equiv_bool_apply_right", "category_theory.curry_uncurry", "tendsto_inv_nhds_within_Iio_inv", "topological_space.nhds_generate_from", "local_homeomorph.trans_source'", "function.semiconj.comp_left", "fderiv_within_smul_algebra_const", "real.sin_lt_sin_of_le_of_le_pi_div_two", "real.differentiable_at_sinh", "category_theory.pi.comap_eval_iso_eval_hom_app", "linear_map.to_matrix_id", "omega.nat.holds_nonneg_consts_core", "filter.ne_bot.mul", "sup_inf_self", "ennreal.supr_add_supr", "cardinal.mk_prod", "finset.filter_ssubset", "measurable_space.comap_sup", "dioph.reindex_dioph", "list.func.nil_pointwise", "with_zero.lift_unique", "category_theory.monoidal_category.unitors_equal.cells_1_2", "rel_embedding.is_symm", "is_subgroup.subset_normalizer", "polynomial.nat_degree_pos_iff_degree_pos", "euclidean_geometry.exists_unique_dist_eq_of_insert", "one_not_mem_nonunits", "ring_hom.ker_eq", "equiv.swap_self", "structure_groupoid.local_invariant_prop.lift_prop_on_mono", "category_theory.limits.types.filtered_colimit.is_colimit_eq_iff", "exists_approx_preimage_norm_le", "real.sin_le_sin_of_le_of_le_pi_div_two", "int.dvd_sub_of_mod_eq", "cardinal.extend_function", "compact_space_of_finite_subfamily_closed", "equiv.to_local_equiv_symm_coe", "equiv.neg_def", "matrix.mul_assoc", "nat.mem_factors_iff_dvd", "continuous.nndist", "decidable.lt_or_le", "null_is_null_measurable", "set.disjoint_compl", "pell.pell_zd_sub", "real.cos_add_pi_div_two", "relation.refl_trans_gen.cases_head_iff", "magma.free_semigroup.of_mul", "polynomial.nat_degree_pow'", "abstract_completion.dense'", "add_monoid_hom.eq_nat_cast", "left_inverse_add_right_neg_add", "equiv.has_sum_iff", "pnat.coprime.factor_eq_gcd_right_right", "filter.tendsto_at_bot_at_top", "prod.mk_vsub_mk", "free_group.quot_lift_mk", "ideal.is_open_of_open_subideal", "is_closed.cInf_mem", "add_neg_of_nonpos_of_neg", "constr_basis", "differentiable_on.smul_algebra_const", "metric.sphere_union_ball", "finite_dimensional.findim_eq_card_basis", "multiset.erase_cons_head", "category_theory.abelian.pseudoelement.zero_eq_zero", "closure_singleton", "disjoint_span_singleton", "supr_le_supr2", "int.shiftr_coe_nat", "subgroup.coe_gpow", "set.preimage_neg_Ioo", "pequiv.trans_refl", "closure_eq_interior_union_frontier", "topological_space.opens.map_iso_refl", "set.Icc_union_Ioo_eq_Ico", "category_theory.curry_eq", "composition.to_composition_as_set_boundaries", "multiset.foldr_add", "tendsto_zero_iff_norm_tendsto_zero", "con.ext", "dfinsupp.subtype_domain_add", "padic.mk_eq", "list.rel_append", "set.mem_compl_singleton_iff", "linear_equiv.symm_trans", "ideal.comap_ne_bot_of_integral_mem", "bilin_form.ext", "asymptotics.is_o.smul_is_O", "interval_integral.integral_const'", "multiset.Ico.filter_le_of_bot", "psigma.ext", "inner_add_add_self", "ideal.is_maximal_iff", "complex.uniform_continuous_abs", "hash_map.insert_lemma", "hyperreal.infinitesimal_zero", "quotient.lift_on_beta", "int.cast_nonneg", "measure_theory.simple_func.forall_range_iff", "set.nonempty_Ici", "list.forall\:2082.flip", "set.univ_subset_iff", "set.bot_eq_empty", "ennreal.rpow_le_one", "setoid.rel_iff_exists_classes", "option.get_some", "category_theory.comonad.coalgebra.hom.ext_iff", "linear_map.quotient_inf_equiv_sup_quotient_apply_mk", "measurable_norm", "rat.inv_def", "linear_independent.repr_range", "rank_comp_le1", "measure_theory.measure.le_lift_linear_apply", "turing.partrec_to_TM2.split_at_pred_eq", "polynomial.degree_derivative_eq", "measure_theory.outer_measure.of_content_interior_compacts", "real.one_le_rpow_of_pos_of_le_one_of_nonpos", "wseq.head_nil", "category_theory.iso.conj_Aut_gpow", "has_sum.mul_right", "submodule.bot_smul", "ordering.compares.inj", "is_basis.to_matrix_apply", "mul_lt_of_lt_of_lt_one'", "submodule.add_mem_iff_left", "or_imp_distrib", "bilin_form.neg_left", "category_theory.limits.types.coprod_inl", "fintype.card_option", "list.foldl_append", "units.coe_inv'", "matrix.from_blocks_diagonal", "nnreal.summable_comp_injective", "int.bit0_val", "finset.prod_pos", "pos_num.div'_to_nat", "set.prod_inter_prod", "int.gcd_dvd_gcd_mul_right_right", "continuous_linear_equiv.differentiable_on", "ennreal.div_le_iff_le_mul", "cardinal.powerlt_omega", "group.mclosure_inv_subset", "measure_theory.measure.finite_at_filter.mono", "prod_charted_space_chart_at", "le_one_div_of_neg", "normalize_eq_zero", "prime_two_or_dvd_of_dvd_two_mul_pow_self_two", "add_commute.map", "list.mem_or_eq_of_mem_update_nth", "and.left_comm", "linarith.lt_of_lt_of_eq", "has_deriv_at.deriv", "cau_seq.lim_zero_congr", "norm_num.ne_zero_neg", "singleton_has_groupoid", "differentiable_on_of_locally_differentiable_on", "exists_extension_of_le_sublinear", "algebra.adjoin_int", "units.mul_inv", "ideal.radical_pow", "int.coe_nat_pow", "initial_seg.trans_apply", "convex.smul_preimage", "measure_theory.inner_content_Sup_nat", "free_add_semigroup_free_add_magma_add", "monoid_hom.map_mul_eq_one", "tactic.ring_exp.add_pf_sum_z", "list.drop_take_succ_eq_cons_nth_le", "t2_iff_nhds", "real.rpow_nonneg_of_nonneg", "complex.of_real_bit0", "list.unzip_zip_left", "subgroup.subset_closure", "ordinal.sub_zero", "filter.map_div_at_top_eq_nat", "typevec.nil_fun_comp", "stream.mem_append_stream_right", "finmap.mem_to_finmap", "finite_dimensional.exists_nontrivial_relation_of_dim_lt_card", "subring.one_mem", "is_min_on.min", "znum.dvd_to_int", "complex.mul_inv_cancel", "topological_space.tendsto_nhds_generate_from", "free_group.red.church_rosser", "nat.div2_zero", "set.indicator_compl_add_self", "zmod.cast_id", "nat.mul_ne_zero", "continuous.pow", "set.union_empty", "nat.partrec'.map", "edist_nndist", "nat.sqrt_le_add", "filter.lift_principal2", "measure_theory.simple_func.piecewise_compl", "matrix.cons_val_succ'", "sum.lex_wf", "edist_add_add_le", "finset.sum_range_zero", "mv_polynomial.C_neg", "cSup_insert", "ennreal.coe_Sup", "complex.is_cau_seq_conj", "id.map_eq", "padic_int.inv_mul", "id.def", "zmod.cast_sub'", "polynomial.eval_smul'", "matrix.special_linear_group.to_GL_mul", "nat.eq_zero_of_mul_eq_zero", "nonpos_of_mul_nonneg_left", "linear_map.fun_congr_left_id", "tendsto_uniformly_on.continuous_on", "real.sin_le_one", "cauchy_seq_of_le_geometric", "derive_fintype.finset_above.mem_cons_self", "category_theory.limits.cone_of_cone_uncurry_X", "enat.get_zero", "finsupp.support_eq_empty", "traversable.map_eq_traverse_id", "nat.pos_of_dvd_of_pos", "pell.yn_ge_n", "complex.cos_add_pi_div_two", "finset.sup_eq_supr", "nat.le_mkpair_left", "ring_hom.to_fun_eq_coe", "bounded_continuous_function.coe_le_coe_add_dist", "list.map_cons", "nat.add_mod_of_add_mod_lt", "convex_on.le_on_segment", "mul_one_div_cancel", "function.is_periodic_pt.minimal_period_pos", "finmap.union_assoc", "local_homeomorph.of_set_trans_of_set", "affine_map.id_linear", "quotient_group.ker_mk", "real.convex_iff_is_preconnected", "left_ord_continuous.comp", "pos_num.one_add", "finsupp.card_to_multiset", "wseq.destruct_nil", "set.image_diff", "metric.mem_closed_ball_self", "partrec.of_eq_tot", "list.eq_nil_of_subset_nil", "finmap.extract_eq_lookup_erase", "list.erase_dup_append", "continuous_multilinear_map.sub_apply", "cardinal.le_add_right", "commute.geom_sum\:2082_mul_add", "is_asymm.is_irrefl", "homological_complex.image_to_kernel_map_comp_kernel_map", "finset.max_of_nonempty", "option.bind_eq_some", "pythagorean_triple.classified", "set.image_inv", "nnreal.of_real_one", "filter.is_cobounded.mk", "measure_theory.to_measure_to_outer_measure", "filter.eventually_le.antisymm", "add_subgroup.map_sup", "is_bounded_bilinear_map_comp", "linear_map.map_add\:2082", "has_ftaylor_series_up_to_on.of_le", "times_cont_diff_on.prod", "multilinear_map.ext", "free_magma.map_mul", "cluster_pt.of_nhds_le", "Module.monoidal_category.left_unitor_naturality", "filter.is_countably_generated.exists_antimono_seq'", "subgroup.pow_mem", "continuous_multilinear_map.curry_right_apply", "num.bitwise_to_nat", "affine.simplex.monge_point_mem_affine_span", "local_equiv.trans_target''", "topological_space.opens.coe_comap", "add_submonoid.closure_union", "filter.mul_mem_mul", "polynomial.mod_by_monic_eq_sub_mul_div", "nat.modeq.modeq_mul_right", "lists'.to_list_cons", "matrix.mul_vec_mul_vec", "set.preimage_add_right_zero'", "comp_mem_uniformity_sets", "array.mem_to_list", "is_basis.to_matrix_self", "closure_of_rat_image_lt", "nnreal.eq", "finsupp.lt_wf", "add_aut.one_apply", "set.snd_image_prod_subset", "left_distrib", "exists.elim", "t2_iff_is_closed_diagonal", "setoid.sup_def", "cauchy_iff", "pgame.lt_of_le_mk", "filter.monotone_mem_sets", "set.image_inter_on", "has_ftaylor_series_up_to_succ_iff_right", "measure_theory.l1.simple_func.coe_zero", "polynomial.monic_integral_normalization", "list.countp_le_of_sublist", "list.rel_filter", "multiset.antidiagonal_zero", "gaussian_int.norm_mod_lt", "multiset.Ico.self_eq_zero", "ennreal.mem_Ioo_self_sub_add", "int.bit1_nonneg", "compact_pi_infinite", "ring_equiv.to_Ring_iso_hom", "and_eq_of_eq_false_right", "bool.coe_sort_tt", "finsupp.supported_mono", "enat.coe_add_get", "pi.neg_apply", "one_gsmul", "rat.floor_def", "subrel_val", "function.equiv.symm", "ordinal.omega_le_of_is_limit", "filter.tendsto_finset_range", "to_bool_true", "finset.product_eq_bind", "nhds_within_mono", "set.image_neg_Ioc", "list.take_cons", "is_path_connected.image", "set.Icc_union_Ioi_eq_Ici", "dfinsupp.sum_add", "semidirect_product.right_hom_eq_right", "power_series.order_monomial", "convex_hull_exists_dist_ge2", "has_fderiv_at_filter.tendsto_nhds", "not_of_not_not_not", "norm_num.mul_bit0_bit0", "isometry_subsingleton", "complex.div_re", "cardinal.ord_univ", "filter.tendsto_at_bot_add_nonpos_right'", "filter.tendsto_if", "list.count_cons_self", "filter.tendsto.mul", "set.Ioc_subset_Ioo_union_Icc", "finset.min'_singleton", "nat.dist_succ_succ", "set.nmem_singleton_empty", "nat.add_mod", "bool.forall_bool", "ideal.map_le_iff_le_comap", "option.eq_some_of_is_some", "measure_theory.simple_func.le_sup_lintegral", "mv_polynomial.eval_C", "complex.arg_cos_add_sin_mul_I", "linear_map.coe_equiv_prod_of_surjective_of_is_compl", "inv_eq_zero", "pythagorean_triple.is_classified_of_normalize_is_primitive_classified", "measure_theory.measure.add_apply", "generalized_continued_fraction.succ_nth_convergent_eq_squash_gcf_nth_convergent", "matrix.mul_sum", "generalized_continued_fraction.int_fract_pair.succ_nth_stream_eq_none_iff", "add_semiconj_by.units_neg_right_iff", "category_theory.limits.zero_of_target_iso_zero", "pell.xn_modeq_x2n_add", "matrix.transpose_sub", "padic_seq.norm_zero_iff", "finsupp.prod_sum_index", "associated_of_dvd_dvd", "units.mul_neg", "monoid_hom.range_top_of_surjective", "charted_space_core.open_target", "times_cont_mdiff_top", "uniform_continuous.continuous", "mvqpf.comp.mk_get", "multiset.to_finset_zero", "pythagorean_triple.is_primitive_classified_of_coprime_of_odd_of_pos", "multiset.join_cons", "nat.prime_iff_prime", "add_units.coe_add_left", "infi_split_single", "order_of_le_of_pow_eq_one", "int.coe_nat_add", "continuous_linear_equiv.map_smul", "has_deriv_at_gronwall_bound", "nndist_eq_zero", "complex.sin_conj", "cardinal.mk_union_le", "edist_eq_coe_nnnorm", "set.countable_set_of_finite_subset", "Cauchy.uniform_continuous_extend", "equiv.sum_compl_apply_symm_of_neg", "fpow_pos_of_pos", "tactic.abel.term_add_const", "set.empty_def", "buffer.write_eq_write'", "int.ne_zero_of_gcd", "ennreal.coe_one", "fderiv_const_sub", "real.angle.coe_add", "multiset.inter_le_left", "list.mfoldr_nil", "continuous.continuous_on", "convex.strict_mono_of_deriv_pos", "fixed_points.minpoly.monic", "has_sum_geometric_of_norm_lt_1", "set.preimage_const", "alg_hom.comp_apply", "pgame.one_right_moves", "direct_sum.of_zero", "category_theory.functor.right_unitor_hom_app", "is_add_monoid_hom.map_add", "polynomial.units_coeff_zero_smul", "computation.head_think", "int.coe_nat_inj'", "polynomial.C_1", "differentiable_at.const_smul", "submonoid.coe_eq_coe", "nat.bitwise_bit", "int.add_lt_add_of_lt_of_le", "sub_sub_assoc_swap", "list.nth_len_le", "finset.card_image_of_injective", "asymptotics.is_O_with.triangle", "lt_div_iff'", "subgroup.mem_map", "finset.nonempty_iff_ne_empty", "continuous_linear_map.differentiable_at", "I_symm_zero", "bifunctor.id_snd", "ge_iff_le", "finset.bind_image", "associates.factors_mk", "non_contradictory_em", "finset.sdiff_subset", "int.one_shiftl", "rat.cast_nonpos", "zorn.chain.directed_on", "filter.has_basis_self", "hyperreal.zero_of_infinitesimal_real", "measure_theory.tsum_measure_le_measure_univ", "char_matrix_apply_ne", "is_R_or_C.of_real_bit0", "equiv.injective", "differentiable.add", "filter.mem_at_bot", "category_theory.limits.wide_pushout_shape.wide_span_obj", "eq_equivalence", "dfinsupp.sum_subtype_domain_index", "magma.free_semigroup.of_mul_assoc", "affine.simplex.face_eq_mk_of_point", "filter.tendsto_at_bot_at_bot_of_monotone'", "is_bounded_bilinear_map.continuous_left", "module.gsmul_eq_smul_cast", "ideal.quotient.lift_mk", "ennreal.top_to_real", "measure_theory.outer_measure.is_caratheodory_empty", "fin.mk_coe", "lagrange.nat_degree_basis", "polynomial.is_unit_iff_degree_eq_zero", "complex.equiv_real_prod_symm_re", "is_lub_of_is_lub_of_tendsto", "borel_eq_top_of_encodable", "Icc_zero_one_symm", "int.bit_coe_nat", "smooth_at_fst", "pfunctor.M.cases_on_mk'", "mdifferentiable_within_at.has_mfderiv_within_at", "int.mod_mod", "measure_theory.simple_func.coe_piecewise", "measure_theory.outer_measure.le_sum_caratheodory", "linear_map.coe_quotient_inf_to_sup_quotient", "pfun.preimage_def", "polynomial.prime_X", "dif_ctx_congr", "linear_map.zero_comp", "emetric.exists_ball_subset_ball", "matrix.linear_equiv_matrix_comp", "function.surjective.exists\:2082", "nat.bitwise_bit_aux", "list.rotate_mod", "padic_seq.norm_mul", "primrec.nat_strong_rec", "nnreal.rpow_le_rpow_of_exponent_le", "prime_spectrum.zero_locus_univ", "not_iff_comm", "mv_polynomial.pderivative_C_mul", "differentiable.inv", "polynomial.leading_coeff_map", "is_preconnected_Iio", "nat.le_induction", "int.abs_eq_nat_abs", "differentiable_at.div", "sub_sub_self", "finset.prod_subtype_eq_prod_filter", "implicit_function_data.to_local_homeomorph_apply", "ball_0_eq", "hyperreal.infinite_neg_add_not_infinite", "linear_independent.unique", "unique_diff_on_Icc_zero_one", "Module.Mon_Module_equivalence_Algebra.ring_neg", "int.mul_zero", "set.Ico_subset_Ioo_left", "nnreal.mul_div_cancel", "multiplicity.multiplicity_sub_of_gt", "category_theory.comonad_hom.assoc", "forall_and_distrib", "add_units.add_neg_of_eq", "quadratic_form.isometry.map_app", "coinduced_supr", "computation.mem_map", "list.mem_sections", "decidable.not_or_of_imp", "measure_theory.integrable.integrable_on'", "continuous_linear_map.pi_zero", "pnat.prime_two", "true_or", "matrix.neg_mul_vec", "filter.mem_cofinite", "int.sub_nat_nat_add", "finset.coe_singleton", "real.cos_add", "is_basis_of_span_eq_top_of_card_eq_findim", "finset.prod_eq_prod_Ico_succ_bot", "continuous.max", "cardinal.le_add_left", "multiplicity.finite_int_iff", "structure_groupoid.lift_prop_on_univ", "polynomial.degree_le_eq_span_X_pow", "measure_theory.ae_eq_fun.inv_to_germ", "has_strict_deriv_at.to_local_left_inverse", "lucas_lehmer.X.units_card", "ultrafilter_extend_extends", "edist_ne_top", "basic_smooth_bundle_core.coe_chart_at_symm_fst", "mul_self_inj_of_nonneg", "localization.r_of_eq", "game.not_le", "nat.prime.dvd_choose_add", "finset.mul_prod_diff_singleton", "simple_graph.adj_matrix_mul_self_apply_self", "abstract_completion.funext", "real.young_inequality_of_nonneg", "finset.sup_def", "filter.eventually.exists", "is_mul_hom.inv", "int.to_add_pow", "list.pairwise_append_comm", "exists_false", "real.Sup_le_ub", "sub_le_iff_le_add", "rat.div_num_denom", "pgame.impartial.lt_zero_iff", "times_cont_mdiff_within_at_top", "denumerable.decode_eq_of_nat", "fintype.card_subtype_lt", "algebra.adjoin_empty", "Set.subset_iff", "finmap.lookup_eq_none", "continuous_within_at.prod_map", "is_R_or_C.im_to_real", "lfp_lfp", "monoid_hom.coe_snd", "Top.subpresheaf_to_Types_map_val", "zmod.inv_zero", "prod.neg_mk", "fin.exists_iff", "infi_subtype", "multiset.pmap_congr", "principal_seg.irrefl", "isometric.coe_const_vadd", "padic_val_rat.le_padic_val_rat_add_of_le", "fintype.eq_of_subsingleton_of_prod_eq", "multiplicity.unique", "associates.le_mul_left", "has_fderiv_at_filter.const_add", "category_theory.limits.bicone.to_binary_bicone_snd", "set.image_zero", "sub_lt_of_abs_sub_lt_left", "uniform_inducing.inducing", "list.nodupkeys.eq_of_mk_mem", "mv_power_series.mul_assoc", "ennreal.sub_eq_of_add_eq", "nat.eq_of_lt_succ_of_not_lt", "filter.realizer.of_equiv_\[Sigma]", "category_theory.functor.op_inv_obj", "push_neg.classical.implies_iff_not_or", "real.differentiable_at_cosh", "mv_polynomial.exists_finset_rename", "relation.refl_trans_gen_of_equivalence", "pgame.lt_of_equiv_of_lt", "ennreal.of_real_lt_top", "commute.add_right", "one_smul", "is_extr_filter.comp_mono", "add_submonoid.copy_eq", "poly.mul_eval", "hyperreal.infinite_iff_infinite_abs", "mvqpf.fix.rec_eq", "int.neg_succ_of_nat_add_of_nat", "Mon.coe_of", "cauchy_seq_of_edist_le_geometric_two", "finset.summable_compl_iff", "list.find_nil", "pgame.zero_add_equiv", "finset.card_le_univ", "list.func.eq_get_of_mem", "list.index_of_le_length", "semiconj_by.map", "ennreal.ne_top_of_tsum_ne_top", "matrix.neg_mul", "prime_multiset.factor_multiset_prod", "finset.fin_range_card", "edist_triangle_right", "category_theory.limits.is_image.iso_ext_hom", "mem_map_sets_iff'", "set.Ici_inter_Iio", "continuous_multilinear_curry_right_equiv_symm_apply", "add_subgroup.comap_infi", "has_deriv_at.sqrt", "relator.rel_forall_of_right_total", "list.kreplace_of_forall_not", "list.nil_append", "infi_subtype'", "isometric.add_right_to_equiv", "real.arccos_zero", "not_bounded_iff", "quotient_group.coe_one", "enat.lt_wf", "ring_hom.mul_def", "category_theory.limits.cocones.precompose_obj_X", "multiplicity.get_multiplicity_self", "free_add_monoid.lift_symm_apply", "category_theory.action_category.\[Pi]_map", "order_of_le_card_univ", "polynomial.degree_coe_units", "model_with_corners_prod_coe_symm", "nonpos_of_mul_nonpos_left", "list.take_zero", "nat.fact_mul_pow_le_fact", "list.alternating_prod_singleton", "set.mul_subset_mul", "complex.tanh_of_real_re", "ennreal.coe_nat_lt_coe_nat", "rat.cast_coe_int", "measure_theory.simple_func.coe_add", "nat.mul_mod_right", "multiset.erase_dup_subset", "category_theory.over.creates_connected.raise_cone_\[Pi]_app", "set.Icc_eq_empty", "abs_zero", "category_theory.limits.cones.functoriality_map_hom", "tactic.ring_exp.sum_congr", "complex.abs_conj", "add_submonoid.nsmul_mem", "multiset.nodup_bind", "ordinal.one_ne_zero", "mul_inv'", "continuous_on.comp'", "finsupp.disjoint_lsingle_lsingle", "stream.drop_map", "padic_val_nat.div'", "category_theory.comma.snd_map", "measure_theory.integrable_at_filter.inf_ae_iff", "deriv.lhopital_zero_right_on_Ioo", "is_coprime.add_mul_left_right", "cardinal.power_le_power_left", "category_theory.sum.inr__map", "bdd_below.union", "free_group.map_pure", "le_implies_le_of_le_of_le", "algebra_compatible_smul", "function.support_binop_subset", "measure_theory.measure.restrict_compl_add_restrict", "matrix.vec_mul_vec_eq", "stream.drop_const", "euclidean_domain.gcd_zero_left", "nat.eq_sqrt", "linear_equiv.map_neg", "well_founded.induction", "nat.modeq.trans", "AddCommGroup.as_hom_injective", "mul_eq_mul_prime_pow", "function.is_periodic_pt.is_fixed_pt", "real.uniform_continuous_add", "opposite.unop_add", "add_subgroup.neg_mem", "circle_deg1_lift.map_le_of_map_zero", "is_closed.Icc_subset_of_forall_exists_gt", "add_monoid_hom.ext", "normalize_eq_normalize", "with_top.coe_one", "add_pow_char_of_commute", "real.tendsto_exp_div_pow_at_top", "list.bex_cons", "continuous_multilinear_curry_fin1_apply", "category_theory.arrow.w", "ne_zero_iff_of_associated", "ennreal.one_half_lt_one", "real.differentiable_sinh", "lcm_dvd_lcm_mul_right_right", "is_R_or_C.of_real_to_real", "pell.y_increasing", "affine_subspace.self_mem_mk'", "quotient_group.card_preimage_mk", "measure_theory.measure.restrict_Union_apply", "category_theory.limits.colimit.\[Iota]_cocone_morphism", "add_submonoid.localization_map.mk'_self", "polynomial.degree_map_eq_of_injective", "ideal.span_singleton_one", "measure_theory.measure.haar_outer_measure_exists_compact", "category_theory.curry_injective", "wseq.flatten_think", "set.mem_Icc_Ico_Ioc_Ioo_of_subset_of_subset", "tendsto_coe_nat_real_at_top_iff", "set.maps_to_Union", "monoid_algebra.mul_def", "differentiable.cosh", "polynomial.monic_X_add_C", "strict_mono.bot_preimage_bot", "set.image3_congr'", "relation.iff_comp", "list.unzip_right", "is_add_group_hom.mem_ker", "of_eq_true", "associates.exists_mem_multiset_le_of_prime", "finset.empty_inter", "semiquot.mem_univ", "associates.mk_le_mk_iff_dvd_iff", "set.preimage_eq_core", "set.mem_Iic_Iio_of_subset_of_subset", "polynomial.coeff_to_subring", "computable_pred.rice\:2082", "hash_map.mem_erase", "free_abelian_group.induction_on", "one_one_reducible.disjoin_right", "list.Ico.filter_lt_of_le_bot", "nat.coprime_mul_iff_left", "galois_connection.u_l_u_eq_u", "add_submonoid.monotone_comap", "finset.sum_insert_zero", "multiset.rec_on_0", "list.perm.erase", "int.add_nonpos", "category_theory.adjunction.cones_iso_component_inv_app", "add_submonoid.localization_map.mk'_spec", "ideal.mul_mono", "hyperreal.lt_of_st_lt", "category_theory.monoidal.tensor_obj_obj", "contracting_with.edist_efixed_point_le'", "connected_space_iff_connected_component", "category_theory.monad.forget_creates_colimits.\[Gamma]_app", "eq.trans_le", "has_deriv_at.differentiable_at", "finset.empty_val", "category_theory.non_preadditive_abelian.neg_def", "list.kunion_nodupkeys", "with_zero.lift_zero", "wseq.tail_nil", "ordinal.sub_is_limit", "add_submonoid.localization_map.add_neg_right", "is_strict_order.swap", "computation.map_think", "polynomial.degree_C_mul_X_pow_le", "set.finite_image_iff", "cardinal.omega_le_bit0", "filter.le_map_comap_of_surjective'", "ring_hom.range_top_iff_surjective", "add_pos", "div_eq_iff", "matrix.special_linear_group.inv_apply", "mvqpf.liftp_preservation_iff_uniform", "submodule.span_singleton_eq_range", "set.to_finset_card", "has_strict_deriv_at.of_local_left_inverse", "mv_polynomial.is_homogeneous_monomial", "filter.principal_singleton", "summable.sigma'", "enat.add_lt_add_iff_left", "rel.comp_left_id", "add_subgroup.normal.mem_comm_iff", "pfunctor.M.truncate_approx", "ite_mul_zero_left", "rat.zero_add", "algebra.tensor_product.congr_symm_apply", "filter.comap_lift_eq2", "one_le_bit1", "sum_range_sub_sum_range", "ordinal.power_is_normal", "filter.tendsto.is_cobounded_under_ge", "category_theory.limits.equalizer.condition", "pgame.mk_add_move_left_inr", "inv_eq_iff", "finset.sum_image", "set.Ioi_subset_Ici", "polynomial.derivative_C", "is_irreducible_iff_sInter", "rel_iso.cof.aux", "nat.one_lt_bit0_iff", "free_group.reduce.min", "le_add_right", "lt_mul_iff_one_lt_right", "deriv_within_csinh", "add_submonoid.localization_map.add_equiv_of_localizations_symm_eq_add_equiv_of_localizations", "subring.closure_empty", "ideal.jacobson_top", "free_group.red.refl", "matrix.from_blocks_apply\:2081\:2081", "orthogonal_projection_def", "set.right_inv_on.eq_on", "measure_theory.ae_eq_fun.pair_eq_mk", "measure_theory.outer_measure.le_trim_iff", "strict_weak_order.esymm", "matrix.to_linear_equiv_apply", "set.mem_image2", "set.diff_eq_empty", "multiset.add_sub_cancel_left", "sub_div'", "primrec.vector_to_list_iff", "category_theory.limits.limit.cone_point_unique_up_to_iso_inv_comp_assoc", "measure_theory.all_ae_of_real_f_le_bound", "category_theory.sum.inverse_associator_map_inr_inl", "polynomial.degree_div_by_monic_lt", "is_R_or_C.smul_re'", "wseq.equiv.symm", "nat.shiftl'_ne_zero_left", "list.perm.foldr_eq", "eq_iff_le_not_lt", "forall_le_or_exists_lt_sup", "is_order_connected.neg_trans", "con.lift_funext", "int.mul_nonneg_of_nonpos_of_nonpos", "zmod.card_units_eq_totient", "map_ne_zero_of_mem_non_zero_divisors", "polynomial.nat_degree_remove_factor", "computable.pred", "of_digits_modeq", "add_monoid_hom.normal_ker", "equiv.coe_vadd_const_symm", "except_t.run_monad_map", "submonoid.map_inl", "sesq_form.ext", "category_theory.limits.is_limit.hom_iso_hom", "padic_norm.padic_norm_p_lt_one_of_prime", "pell.y_dvd_iff", "set.maps_to.iterate_restrict", "free_add_magma.traverse_add", "real.cosh_add", "has_deriv_within_at.prod", "div_le_div_right", "dense_inducing.nhds_eq_comap", "cardinal.power_le_max_power_one", "local_homeomorph.trans_source", "ideal.mem_span_insert", "multiset.cons_eq_cons", "enat.with_top_equiv_symm_le", "multiset.to_finset_eq_empty", "dfinsupp.sum_zero_index", "padic_norm_z.nonarchimedean", "sub_le_of_abs_sub_le_right", "mv_polynomial.eval\:2082_add", "nnreal.tendsto.sub", "inner_product_space.of_core.inner_add_add_self", "int.coe_nat_lt", "ring_hom.map_srange", "finset.prod_eq_multiset_prod", "le_of_forall_le", "zmod.int_coe_zmod_eq_zero_iff_dvd", "set.mul_comm", "le_sub_right_of_add_le", "real.log_pos_iff", "mdifferentiable_at.continuous_at", "real.sqrt_one", "is_compact.adherence_nhdset", "has_strict_deriv_at.scomp", "mv_polynomial.eval\:2082_C", "hyperreal.exists_st_iff_not_infinite", "localization_map.lift_id", "circle_deg1_lift.translate_pow", "category_theory.functor.map_iso_symm", "submodule.linear_proj_of_is_compl_range", "real.rpow_eq_pow", "filter.map_inf_le", "list.perm.erase_dup", "cardinal.mk_range_eq_of_injective", "exists_rat_near", "nat.eq_zero_of_dvd_of_lt", "subspace.closed_complemented_iff_has_closed_compl", "list.pairwise_pw_filter", "times_cont_diff_id", "nat.not_succ_le_self", "pequiv.of_set_symm", "real.arccos_neg_one", "exists_nhds_split_inv", "turing.list_blank.ext", "category_theory.uncurry_natural_left", "eq_mul_inv_of_mul_eq", "multiplicity.multiplicity_add_of_gt", "multiset.le_ndunion_left", "submonoid.map_supr", "int.gcd_self", "set.sUnion_pair", "category_theory.abelian.image_eq_image", "add_lt_add_of_le_of_lt", "equiv.perm.sign_bij_aux_mem", "wseq.nth_tail", "measure_theory.outer_measure.diff_null", "set.maps_to_bUnion_bUnion", "submodule.map_top", "set.Ioo_union_Icc_eq_Ioc", "times_cont_diff_on_top_iff_fderiv_within", "list.lookmap_cons_some", "ring_hom.iterate_map_one", "vsub_set_finite_of_finite", "nat.commute_cast", "finset.disjoint_sdiff_inter", "has_fderiv_at_filter.congr_of_eventually_eq", "add_submonoid.localization_map.of_add_equiv_of_localizations_comp", "measure_theory.measure.finite_at_filter.inf_ae_iff", "sup_compl_eq_top", "monoid_hom.mrange_top_of_surjective", "cau_seq.of_near", "set.Inter_lt_succ", "topological_space.Union_basis_of_is_open", "mv_power_series.coeff_zero_X", "inv_mul_lt_of_lt_mul", "category_theory.is_iso.iso.inv_inv", "cau_seq.cauchy_seq", "finset.card_image_le", "ennreal.to_real_pos_iff", "equiv.perm.of_subtype_subtype_perm", "int.modeq.mod_coprime", "mv_polynomial.eval\:2082_cast_comp", "hyperreal.infinite_pos_def", "nat.add_pos_iff_pos_or_pos", "sum.exists", "ennreal.one_ne_top", "hyperreal.coe_le_coe", "Sup_eq_top", "homeomorph.is_open_preimage", "filter.tendsto_comap'_iff", "list.disjoint_nil_left", "Top.coe_of", "ordinal.le_succ_of_is_limit", "left_inverse_sub_add_left", "buffer.lt_aux_1", "decidable.not_iff", "nat.gcd_zero_right", "submodule.le_comap_mkq", "irrational.inv", "measure_theory.ae_eq_fun.smul_to_germ", "finset.Ico.image_const_sub", "invertible_unique", "semiconj_by.units_inv_symm_left", "mvpfunctor.M.dest_eq_dest'", "list.enum_map_fst", "category_theory.functor.pentagon", "set.Icc_subset_Ico_union_Icc", "pfun.preimage_as_subtype", "ordinal.log_le_log", "polynomial.div_wf_lemma", "padic_int.mk_zero", "free_group.to_group.unique", "hyperreal.infinite_pos_mul_of_not_infinitesimal_pos_infinite_pos", "of_irreducible_map", "circle_deg1_lift.map_add_int", "local_equiv.image_source_eq_target", "mvpfunctor.const.mk_get", "category_theory.adjunction.hom_equiv_naturality_left", "findim_eq_zero_of_dim_eq_zero", "nnreal.coe_Inf", "omega.unsat_of_unsat_eq_elim", "list.perm.nodup_iff", "set.sUnion_insert", "submodule.closed_complemented_bot", "isometric.coe_eq_to_equiv", "sub_add_eq_add_sub", "nat.dist_pos_of_ne", "set.sInter_pair", "list.take_append_drop", "free_semigroup.traverse_mul'", "nat.bit1_eq_succ_bit0", "computation.terminates_parallel", "primrec.list_rec", "eq_bot_mono", "classical.nonempty_pi", "continuous_multilinear_map.curry0_apply", "metric.Hausdorff_edist_ne_top_of_nonempty_of_bounded", "norm_num.one_add", "closure_eq_inter_uniformity", "set.prod_singleton", "continuous_linear_equiv.fderiv", "mvpfunctor.M.bisim_lemma", "closure_Iio'", "vector.nth_zero", "real.deriv_cos", "finset.inter_subset_inter_right", "int.shiftr_add", "nat.prime.ne_zero", "ordinal.wf", "cardinal.mk_union_add_mk_inter", "filter.eventually.exists_forall_of_at_top", "real.is_conjugate_exponent.pos", "geom_sum", "equiv.set.union_apply_left", "complex.of_real_tanh", "int.exists_eq_neg_of_nat", "id_rel_subset", "submodule.comap_bot", "matrix.update_column_ne", "category_theory.functor.const_comp_hom_app", "set.finite_lt_nat", "fderiv_within_sub", "circle_deg1_lift.translation_number_eq_of_tendsto\:2080'", "category_theory.arrow.has_lift.ext_iff", "has_deriv_within_at.smul", "category_theory.limits.equalizer.lift_\[Iota]_assoc", "abs_one", "add_halves'", "list.all_iff_forall_prop", "omega.coeffs.val_between_neg", "category_theory.limits.cokernel_zero_iso_target_hom", "discrete_valuation_ring.has_unit_mul_pow_irreducible_factorization.of_ufd_of_unique_irreducible", "category_theory.discrete.equivalence_inverse", "int.nat_abs_dvd", "filter.realizer.bot_\[Sigma]", "not_injective_infinite_fintype", "abs_norm_sub_norm_le", "set.inj_on.congr", "quadratic_form.coe_fn_add", "convex.to_cone_is_least", "is_basis.repr_ker", "list.mem_cons_of_mem", "eq_sub_iff_add_eq", "subsemiring.prod_bot_sup_bot_prod", "rat.mk_eq", "matrix.diag_one", "summable.indicator", "measure_theory.simple_func.map_integral", "function.semiconj.maps_to_preimage", "primrec_rel.comp\:2082", "is_monoid_hom.of_mul", "with_top.zero_lt_top", "rat.mk_eq_zero", "composition.sigma_pi_composition_eq_iff", "submonoid.mem_top", "matrix.from_blocks_apply\:2081\:2082", "normed_ring.tsum_geometric_of_norm_lt_1", "int.neg_add_cancel_right", "denumerable.prod_nat_of_nat", "ennreal.mul_lt_top", "list.map_tail", "finset.disj_union_eq_union", "dist_nndist", "nnreal.of_real_pos", "has_fderiv_within_at.sum", "turing.to_partrec.step_normal.is_ret", "le_infi", "turing.pointed_map.head_map", "mv_power_series.mul_inv", "num.cast_lt", "has_strict_deriv_at.has_strict_fderiv_at_equiv", "category_theory.limits.mono_factorisation_zero_e", "nat.dvd_of_mul_dvd_mul_left", "mv_polynomial.is_homogeneous.total_degree", "lower_bounds_Ioo", "list.map_join", "add_con.trans", "computation.map_congr", "fpow_sub", "euclidean_geometry.angle_le_pi", "has_deriv_at_iff_is_o_nhds_zero", "bool.bnot_true", "int.mul_nonneg", "linear_map.ker_le_range_iff", "category_theory.non_preadditive_abelian.sub_add", "prime_multiset.coe_pnat_prime", "continuous_Sup_dom", "eq_Icc_of_connected_compact", "int.le.elim", "finsupp.filter_apply_neg", "hash_map.valid.as_list_nodup", "abstract_completion.continuous_map\:2082", "mem_of_mem_perms_of_list", "measure_theory.simple_func.map_coe_nnreal_restrict", "nhds_within_Icc_eq_nhds_within_Iic", "filter.const_eventually_eq", "real.abs_sin_le_one", "asymptotics.is_O.sum", "affine.simplex.sum_centroid_weights_with_circumcenter", "zmod.nat_cast_surjective", "quot.eq", "list.argmax_eq_some_iff", "finset.sum_const_zero", "finset.inter_distrib_left", "category_theory.limits.types.prod_snd", "ennreal.coe_inv", "semidirect_product.right_hom_comp_map", "list.is_prefix.trans", "pos_of_neg_neg", "submonoid.mem_map", "function.commute.iterate_pos_le_iff_map_le'", "con.map_of_surjective_eq_map_gen", "set.image_add_right", "pgame.one_move_left", "bilin_form.ortho_smul_right", "with_zero.mul_comm", "category_theory.limits.functor_category_colimit_cocone_X", "finset.min_of_nonempty", "filter.tendsto_at_bot_add_nonpos_left'", "finset.inter_comm", "alg_equiv.coe_ring_equiv", "finsupp_lequiv_direct_sum_symm_lof", "fin.tail_init_eq_init_tail", "category_theory.monoidal_functor.map_left_unitor", "nat.cast_nonneg", "num.sub_to_nat", "pequiv.mem_of_set_self_iff", "module.direct_limit.totalize_apply", "mdifferentiable_chart", "matrix.one_apply", "list.cons_subset", "structure_groupoid.chart_mem_maximal_atlas", "ordinal.succ_zero", "set.Iic_union_Ico_eq_Iio", "mul_nonpos_of_nonneg_of_nonpos", "filter.principal_univ", "ff_bxor", "list.range_sublist", "neg_smul", "int.sub_nat_nat_of_sub_eq_succ", "has_strict_fderiv_at.local_inverse_apply_image", "modeq_mersenne", "set.interval_of_not_le", "category_theory.simple.ext", "set.ssubset_insert", "real.rpow_sub", "znum.cast_mul", "continuous_within_at.neg", "complex.exp_neg", "interior_compl", "filter.tendsto.nnnorm", "lie_algebra.equiv.symm_trans_apply", "set.univ_prod", "fintype.sum_extend_by_zero", "padic_int.unit_coeff_spec", "subsingleton.measurable", "lagrange.interpolate_neg", "decidable.ne_iff_lt_or_gt", "add_con.lift_mk'", "set.bex_insert_iff", "submodule.coe_is_compl_equiv_proj_apply", "list.length_map_accumr\:2082", "lt_of_sub_neg", "differentiable_on.iterate", "int.gcd_dvd_gcd_mul_left", "cardinal.aleph_idx_aleph'", "has_strict_deriv_at.to_local_inverse", "finset.nonempty.mono", "has_fderiv_at_iff_tendsto", "measure_theory.measure_bUnion_le", "list.subset.refl", "computable_pred.to_re", "is_closed_le", "turing.TM2.stmts\:2081_supports_stmt_mono", "multiset.inter_add_distrib", "set.pure_def", "differentiable_within_at.fst", "set.subset_inter", "real.zero_lt_one", "int.lcm_zero_right", "int.of_nat_succ", "set.zero_mem_zero", "category_theory.iso.trans_hom", "category_theory.nat_trans.ext_iff", "typevec.last_fun_of_subtype", "left_inv_eq_right_inv", "finset.range_one", "function.is_periodic_pt.map", "mv_polynomial.is_homogeneous.coeff_eq_zero", "semiquot.mem_pure_self", "filter.eventually_le.is_min_filter", "dioph.mul_dioph", "finset.mem_range", "nat.prime.multiplicity_pow", "list.Ico.succ_top", "category_theory.monad.forget_creates_limits.cone_point_A", "bitvec.to_bool_add_lsb_mod_two", "nat.le_of_dvd", "computable.nat_div2", "is_submonoid.pow_mem", "affine_subspace.span_points_subset_coe_of_subset_coe", "list.to_finset_nil", "option.none_orelse", "is_group_hom.injective_iff_trivial_ker", "measure_theory.simple_func.mul_apply", "tensor_product.lift.unique", "int.le_of_sub_nonneg", "ball_eq_of_symmetry", "filter.tendsto_infi'", "vector.mmap_nil", "forall_3_true_iff", "Set.omega_succ", "cau_seq.const_inv", "heq.trans", "finset.filter_or", "quotient_add_group.injective_ker_lift", "set.inclusion_self", "fderiv_add", "power_series.constant_coeff_inv", "units.eq_mul_inv_iff_mul_eq", "floor_one", "times_cont_mdiff_on.mdifferentiable_on", "mv_power_series.coeff_mul_C", "computation.terminates_map_iff", "nat.with_bot.add_eq_zero_iff", "metric.closed_ball_mem_nhds", "category_theory.limits.kernel_fork.app_one", "rel.preimage_comp", "finset.sum_nat_cast", "complex.of_real_sub", "ennreal.one_lt_coe_iff", "local_homeomorph.mdifferentiable.trans", "multiset.disjoint_iff_ne", "nhds_within_Ioo_eq_nhds_within_Ioi", "pell.pell_zd_im", "fin.eq_mk_iff_coe_eq", "nat.bodd_bit1", "is_min_on.on_subset", "add_commute.symm_iff", "metric.completion.dist_comm", "homological_complex.homology_map_id", "finset.Ico.image_sub", "push_neg.not_exists_eq", "submonoid.comap_map_eq_of_injective", "mersenne_pos", "local_equiv.eq_on_source_refl", "enat.to_with_top_zero", "set.prod_mono", "polynomial.degree_pow_le", "function.injective.comap_subsingleton", "category_theory.functor.congr_hom", "list.ball_cons", "abs_sub", "continuous_linear_map.coe_mul", "continuous_pi", "mvpfunctor.W_path_cases_on_eta", "free_group.red.step.cons_bnot", "push_neg.not_or_eq", "add_aut.mul_def", "prod.fst_one", "differentiable.rpow", "subgroup.mul_mem_cancel_right", "measure_theory.integrable_smul_iff", "roption.map_bind", "finset.insert_ne_empty", "set.image_const_add_Ico", "ennreal.zero_eq_coe", "finset.union_sdiff_of_subset", "set.add_image_prod", "category_theory.forget_map_eq_coe", "bdd_below_Ioi", "nat.div_mul_div", "primrec_rel.comp", "submodule.mem_orthogonal", "quotient.out_eq", "list.foldl_hom", "enat.coe_zero", "list.qsort_nil", "polynomial.monomial_mul_monomial", "measure_theory.ae_eq_fun.mk_sub", "set.range_eq_Union", "ge_of_tendsto'", "set.Inter_const", "int.sum_two_squares_of_two_mul_sum_two_squares", "polynomial.map_map", "lie_add_group_core.to_lie_add_group", "neg_mul_eq_mul_neg", "band_ff", "nat.lt_add_right", "filter.frequently_at_top'", "seq.map_comp", "homeomorph.range_coe", "ideal.disjoint_closure_singleton_iff_not_mem", "measure_theory.outer_measure.trim_sum_ge", "set.neg_mem_neg", "int.div_dvd_div", "mvqpf.cofix.ext", "complex.cos_add", "add_monoid_hom.comp_apply", "set.Icc_subset_Ioo", "topological_fiber_bundle_core.is_topological_fiber_bundle", "equiv.right_inverse_symm", "list.cons_ne_nil", "list.all_nil", "pow_lt_pow", "has_fderiv_at.sub_const", "supr_eq_if", "le_of_nat_ceil_le", "set.prod_subset_prod_iff", "multiset.map_zero", "interior_Icc", "submodule.disjoint_span_singleton", "ennreal.add_left_inj", "finset.subset.antisymm_iff", "localization_map.integer_normalization_coeff", "rat.inv_mul_cancel", "mul_action.mem_stabilizer_iff", "bifunctor.comp_fst", "is_subgroup.coe_inv", "measure_theory.integrable_on_zero", "category_theory.comonad_hom.comp_id", "add_submonoid.mrange_inl", "finsupp.sigma_support", "category_theory.limits.pullback_cone.mk_\[Pi]_app", "list.perm.fold_op_eq", "functor.comp.pure_seq_eq_map", "if_false_right_eq_and", "power_series.coeff_mul_C", "category_theory.ev_coev", "model_with_corners.mdifferentiable", "complex.re_sq_le_norm_sq", "measure_theory.simple_func.lintegral_mono", "list.pw_filter_subset", "filter.comap_Sup", "times_cont_mdiff_on.congr", "open_embedding.comp", "set.bInter_subset_bInter_left", "category_theory.eq_to_hom_trans", "cardinal.succ_zero", "emetric.Hausdorff_edist_zero_iff_eq_of_closed", "submonoid.localization_map.mul_equiv_of_localizations_symm_apply", "computable.vector_cons", "complex.log_re", "mv_polynomial.rename_id", "complex.differentiable_at_exp", "continuous_inr", "real.ball_eq_Ioo", "has_fderiv_at_filter.neg", "category_theory.limits.kernel_comp_is_iso_hom_comp_kernel_\[Iota]", "infi_le_infi_const", "is_R_or_C.abs_one", "sub_eq_neg_add", "poly_equiv_tensor.to_fun_linear_mul_tmul_mul", "pnat.gcd_dvd_left", "is_unit.mul_right_dvd", "mvpfunctor.W_dest'_W_mk'", "complex.cosh_sub_sinh", "filter.ne_bot.add", "hyperreal.infinite_pos_neg_of_infinite_neg", "filter.tendsto_inf_left", "linear_map.range_le_bot_iff", "is_local_extr_on.comp_antimono", "finset.mem_erase", "computation.mem_of_promises", "free_ring.coe_eq", "abs_dist_sub_le", "metric.uniform_continuous_inf_dist_pt", "computation.le_stable", "category_theory.limits.is_limit.cone_points_iso_of_nat_iso_inv", "set.preimage_const_add_Ioo", "turing.tr_eval_rev", "order_separated", "measure_theory.ae_eq_fun.integrable_zero", "asymptotics.is_o.add_is_O_with", "int.dvd_of_pow_dvd", "set.subset_empty_iff", "exists_Ico_subset_of_mem_nhds", "dense_inter_of_open_left", "norm_sub_pow_two", "continuous_linear_map.pi_apply", "category_theory.single_obj.map_hom_comp", "cau_seq.le_of_le_of_eq", "times_cont_diff_on_univ", "is_basis.iff_det", "int.coe_nat_bit1", "fin.one_pos", "pequiv.trans_eq_none", "measure_theory.simple_func.coe_neg", "fin.mk_bit0", "free_semigroup.lift_of_mul", "principal_seg.init_iff", "nat.exists_eq_add_of_le", "polynomial.coeff_one_zero", "function.surjective.nontrivial", "div_le_iff_of_neg'", "complex.norm_sq_neg", "set.comp_piecewise", "iterated_deriv_eq_iterate", "lt_iff_lt_of_le_iff_le'", "category_theory.monoidal.right_unitor_hom_apply", "pnat.coe_nat_factor_multiset", "dfinsupp.subtype_domain_sub", "pequiv.single_mul_single_right", "prod.fst_injective", "set.prod_union", "tendsto_const_nhds", "multiset.fold_zero", "uniformity_basis_edist_le", "fintype.card_le_one_iff_subsingleton", "category_theory.over.iterated_slice_equiv_functor", "mv_polynomial.pderivative_monomial_mul", "ordinal.power_lt_omega", "pfunctor.liftp_iff", "le_inv_iff_mul_le_one", "is_coprime.mul_add_left_left_iff", "category_theory.monad.forget_creates_limits.new_cone_X", "mvqpf.liftr_map_last", "category_theory.eq_to_iso_trans", "mul_equiv.map_prod", "submodule.linear_proj_of_is_compl_ker", "list.kerase_kerase", "subsemiring.mul_mem", "topological_space.opens.open_embedding_of_le", "smul_zero", "localization.mul_equiv_of_quotient_mk", "subgroup.normal_closure_le_normal", "nonote.repr_sub", "matrix.diagonal_mul", "mv_polynomial.degrees_neg", "complex.arg_eq_arg_neg_sub_pi_of_im_neg_of_re_neg", "filter.has_basis.cauchy_seq_iff", "composition_as_set.ext", "set.range_id", "exists_lt_of_lt_cSup", "times_cont_diff_iff_continuous_differentiable", "mem_skew_adjoint_matrices_lie_subalgebra", "nhds_within_Iio_ne_bot'", "cInf_le", "continuous_multilinear_map.op_norm_le_bound", "category_theory.nat_iso.of_components.app", "linear_equiv.symm_apply_apply", "is_compact.exists_is_greatest", "homeomorph.coinduced_eq", "gaussian_int.to_complex_div_re", "free_abelian_group.sub_bind", "is_linear_map.is_linear_map_add", "dual_pair.coeffs_lc", "has_deriv_within_at.limsup_slope_norm_le", "nat.fact_succ", "add_left_cancel", "hofer", "list.traverse_nil", "is_lub_le_iff", "or_iff_not_imp_left", "int.dvd_nat_abs", "multiset.erase_add_left_pos", "exists_unique_iff_exists", "set.preimage_inter_range", "group.conjugates_of_set_subset_normal_closure", "add_lt_of_lt_of_neg'", "filter.eventually_supr", "filter.has_basis.ex_mem", "category_theory.limits.kernel_iso_of_eq_refl", "finset.sdiff_inter_distrib_right", "differentiable_at.add", "hyperreal.st_neg", "measure_theory.integrable.congr'", "linear_map.range_smul'", "plift.rec.constant", "submodule.mem_infi", "ennreal.rpow_lt_rpow_of_exponent_lt", "is_local_extr_on.is_local_extr", "ring_equiv.map_mul", "filter.at_top_countable_basis", "complex.norm_sq_sub", "is_R_or_C.conj_to_complex", "ordinal.zero_eq_lift_type_empty", "finite_dimensional.exists_relation_sum_zero_pos_coefficient_of_dim_succ_lt_card", "associates.one_eq_mk_one", "subgroup.prod_top", "subsemiring.closure_union", "filter.map_swap_eq_comap_swap", "category_theory.curry_eq_iff", "asymptotics.is_O_with_norm_norm", "mv_polynomial.coeff_map", "ennreal.sub_supr", "add_monoid_hom.lift_of_surjective_comp", "filter.has_basis.cauchy_iff", "turing.TM2to1.stk_nth_val", "category_theory.abelian.pseudoelement.mono_of_zero_of_map_zero", "mv_polynomial.coeff_mul_X'", "free_group.red.step.to_group", "units.inv_unique", "nat.gcd_mul_right", "exists_pempty", "concave_on.comp_affine_map", "inducing.nhds_eq_comap", "bxor_coe_iff", "int.eq_zero_of_nat_abs_eq_zero", "alg_equiv.map_sum", "is_open.unique_diff_on", "algebraic_closure.span_eval_ne_top", "ring_equiv.to_CommRing_iso_inv", "multiset.le_induction_on", "not_lt_zero'", "is_add_group_hom.injective_iff", "matrix.map_add", "deriv_within_sub_const", "digits_zero", "category_theory.core.comp_hom", "lucas_lehmer.X.mul_fst", "nat.sqrt_le", "quotient.induction_on\:2083'", "real.cos_arcsin_nonneg", "differentiable.mul", "category_theory.Monad.to_Mon_X", "uniformity_basis_edist", "order_bot.bdd_below", "add_submonoid.localization_map.mk'_spec'", "nnreal.rpow_zero", "differentiable_on.sqrt", "has_deriv_at.add", "heq_of_eq", "lt_mem_sets_of_Limsup_lt", "max_neg_neg", "mul_div_cancel_of_imp", "multilinear_map.mk_continuous_norm_le", "zsqrtd.add_re", "filter.eventually_lift'_powerset_forall", "add_semiconj_by.units_neg_symm_left_iff", "list.pairwise_of_pairwise_cons", "multiset.sub_le_iff_le_add", "submodule.comap_subtype_eq_top", "subtype.restrict_apply", "continuous_at.iterate", "multiset.pmap_zero", "equiv_of_is_basis_comp", "measure_theory.measure.haar.is_left_invariant_index", "set.surj_on.image_eq_of_maps_to", "filter.inf_ne_bot_iff_frequently_left", "finset.mem_mk", "is_measurable.univ", "set.sep_mem_eq", "free_abelian_group.map_add", "initial_seg.init'", "metric.bounded_union", "is_least_Ico", "submodule.linear_proj_of_is_compl_apply_right'", "times_cont_diff.has_strict_fderiv_at", "eq_bot_iff_dim_eq_zero", "times_cont_diff_at.continuous_linear_map_comp", "has_fderiv_at_filter.snd", "matrix.update_column_transpose", "list.map_eq_map_iff", "ideal.comap_ne_bot_of_algebraic_mem", "has_fpower_series_on_ball.sum", "list.concat_eq_append", "set.preimage_range_inter", "nhds_is_closed", "set.prod_insert", "monoid_hom.eq_of_eq_on_mdense", "linear_equiv_matrix_apply'", "lipschitz_with.uniform_continuous", "multiset.sum_eq_foldl", "circle_deg1_lift.coe_one", "list.countp_cons_of_pos", "zmod.legendre_sym_two", "category_theory.functor.triangle", "list.chain'_map_of_chain'", "prod.mk_mul_mk", "dim_of_field", "submonoid.prod_top", "category_theory.equivalence.cancel_counit_inv_right_assoc", "cauchy_map_iff_exists_tendsto", "category_theory.discrete.id_def", "set.eq_sep_of_subset", "list.perm.bag_inter", "affine_subspace.vsub_left_mem_direction_iff_mem", "set.mul_singleton", "linear_map.comp_apply", "polynomial.expand_eq_map_domain", "sum_le_has_sum", "max_eq_left_of_lt", "subgroup.coe_subset_coe", "mfderiv_eq_fderiv", "supr_bot", "pfunctor.M.head_eq_head'", "multiset.subset_iff", "nhds_within_eq_map_subtype_coe", "wseq.think_congr", "holor.sum_unit_vec_mul_slice", "wseq.dropn_add", "filter.mul_assoc", "denumerable.sigma_of_nat_val", "finmap.lookup_list_to_finmap", "computation.results_think", "category_theory.uncurry_natural_right", "not_bex", "real.abs_exp", "deriv_const_sub", "free_group.to_group.of_eq", "nat.dist_mul_right", "ideal.bot_mul", "complex.continuous_of_real", "int.induction_on", "set.exists_finite_iff_finset", "euclidean_geometry.reflection_involutive", "le_gronwall_bound_of_liminf_deriv_right_le", "category_theory.yoneda_obj_map", "exists_const", "homological_complex.comm_at", "cInf_lt_of_lt", "polynomial.coeff_inv_units", "concave_on.convex_lt", "finset.inf_insert", "list.eq_of_mem_repeat", "turing.partrec_to_TM2.pred_ok", "function.surjective.range_eq", "mv_power_series.mul_zero", "category_theory.preimage_id", "real.sin_arccos", "ulift.add_down", "multiset.map_le_map", "linear_equiv.symm_conj_apply", "continuous_linear_map.subtype_val_apply", "set.Ico_\:2115_card", "pfun.dom_eq", "semidirect_product.left_inr", "zero_smul_set", "rel_iso.cof", "finset.attach_val", "algebra.subring_coe_algebra_map", "set.mem_image_iff_of_inverse", "iterated_fderiv_within_zero_apply", "set.dual_Ioo", "multiset.zero_bind", "mv_polynomial.monomial_zero", "multiset.inf_mono", "tendsto_multiset_sum", "sum.map_inr", "padic.coe_div", "eq_inv_smul_iff", "fixed_points.f_le_Inf_of_fixed_points", "add_localization.add_equiv_of_quotient_mk'", "list.to_finset_val", "asymptotics.is_O.trans_is_o", "linear_independent_subtype_disjoint", "mem_Icc_of_mem_std_simplex", "subring.coe_map", "category_theory.functor.right_unitor_inv_app", "real.le_sqrt'", "has_fderiv_within_at.const_smul_algebra", "polynomial.monic.degree_eq_zero_iff_eq_one", "list.reverse_prefix", "continuous_on.add", "add_submonoid.dense_induction", "matrix.to_lin_zero", "znum.zneg_bit1", "finset.bind_insert", "real.rpow_add'", "one_lt_mul", "list.nth_le_nth", "complex.conj_neg_I", "with_zero.mul_le_mul_left", "nat.dist_comm", "is_add_group_hom.map_sub", "set.bInter_image", "neg_one_pow_eq_or", "has_deriv_at_real_of_complex_aux", "finset.card_singleton_inter", "affine_independent_subtype_of_affine_independent", "set.mul_union", "nat.sub_succ", "finset.mem_attach_fin", "submodule.is_principal.mem_iff_generator_dvd", "smodeq.top", "category_theory.quotient.sound", "int.sub_neg_of_lt", "is_open_map.nhds_le", "measure_theory.inner_content_empty", "finset.inf_singleton", "semiconj_by.cast_int_mul_cast_int_mul", "exists_has_deriv_within_at_eq_of_lt_of_gt", "inf_of_le_right", "circle_deg1_lift.tendsto_translation_number\:2080'", "int.coe_nat_ne_zero", "char_p.char_is_prime", "measure_theory.integrable_norm_iff", "polynomial.is_unit_of_is_unit_leading_coeff_of_is_unit_map", "seq.dropn_add", "turing.partrec_to_TM2.move_ok", "emetric.second_countable_of_separable", "tensor_product.curry_apply", "nat.eq_zero_or_eq_succ_pred", "category_theory.monoidal_category.left_unitor_product_aux_square", "punit.inf_eq", "is_add_group_hom.zero_iff_ker_neg", "set.left_mem_Ioo", "list.prefix_cons_inj", "asymptotics.is_O_with.add_is_o", "continuous_linear_map.comp_zero", "int.le_neg_of_le_neg", "category_theory.category_of_elements.from_comma_map", "ulower.ext", "deriv_within_const_smul", "isometry.dist_eq", "abs_mul_abs_self", "set.countable_iff_exists_inj_on", "lucas_lehmer.X.ext", "irreducible_of_associated", "typevec.fst_diag", "add_submonoid.localization_map.mk'_eq_of_eq", "open_embedding.open_iff_image_open", "localization.mk_eq_mk'_apply", "ext_chart_at_source_mem_nhds", "roption.mem_eq", "category_theory.limits.cofork.of_cocone_\[Iota]", "localization_map.integer_normalization_aeval_eq_zero", "function.surjective.of_comp", "setoid.injective_iff_ker_bot", "circle_deg1_lift.translation_number_pow", "set.monotone_image", "algebraic_geometry.structure_sheaf.is_locally_fraction_pred", "ennreal.inv_lt_iff_inv_lt", "category_theory.monad.free_obj_A", "pow_eq_one_iff", "filter.eventually_eq.comp\:2082", "circle_deg1_lift.le_translation_number_of_add_le", "times_cont_diff.comp_times_cont_diff_on", "lie_algebra.matrix_trace_commutator_zero", "premetric.dist_nonneg", "filter.mem_comap_sets", "has_deriv_at.add_const", "ordinal.cof_omega", 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"measurable_generate_from", "cardinal.mul_le_mul", "computable_pred.computable_iff", "hyperreal.coe_bit1", "model_with_corners.mdifferentiable_on_symm", "formal_multilinear_series.comp_partial_sum", "imp_congr_ctx_eq", "compact_diff", "gpow_add", "set.bInter_univ", "int.test_bit_lxor", "generalized_continued_fraction.convergents'_aux_stable_step_of_terminated", "Set.mem_empty", "complex.exp_eq_exp_re_mul_sin_add_cos", "scale_roots_aeval_eq_zero", "real.arccos_neg", "commute.units_gpow_right", "min_le_add_of_nonneg_left", "submodule.quotient.mk'_eq_mk", "asymptotics.is_O.add_is_o", "formal_multilinear_series.comp_coeff_zero'", "ordinal.card_eq_nat", "category_theory.limits.alternative_cone_\[Pi]", "enat.add_left_cancel_iff", "has_strict_fderiv_at.sub", "measure_theory.ae_eq_fun.coe_fn_inv", "filter.lift_infi", "le_add_of_sub_left_le", "measurable_to_nat", "set.maps_to_preimage", "monoid_hom.map_ne_zero", "pfunctor.W.mk_dest", 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"list.tfae_cons_cons", "ordinal.lift_id'", "nat.sub_mod_eq_zero_of_mod_eq", "piecewise_ae_eq_restrict_compl", "real.differentiable_at_sin", "nat.pred_le", "list.modify_nth_eq_update_nth", "list.disjoint_of_disjoint_cons_left", "continuous_linear_map.deriv_within", "ordinal.power_is_limit", "nat.dist_zero_left", "rel_iso.to_rel_embedding_eq_coe", "nat.subtype.lt_succ_iff_le", "zmod.cast_pow", "real.sin_neg_of_neg_of_neg_pi_lt", "dlist.to_list_concat", "asymptotics.is_O_const_mul_right_iff", "principal_ideal_ring.is_maximal_of_irreducible", "structure_groupoid.mem_maximal_atlas_of_mem_atlas", "mv_polynomial.ker_eval\:2097", "measure_theory.measure.haar.is_left_invariant_prehaar", "add_sub_cancel'", "continuous_linear_equiv.differentiable_within_at", "int.ne_of_nat_ne_nonneg_case", "neg_preimage_closure", "monotone.map_is_greatest", "is_add_subgroup.add_mem_cancel_left", "linear_equiv.eq_bot_of_equiv", "differentiable_within_at.smul_const", "tactic.ring_exp.simple_pf_prod_neg_one", "lists'.mem_def", "matrix.trace_transpose", "alist.mem_union", "ordinal.one_dvd", "differentiable_within_at.ccos", "linear_map.sum_apply", "power_series.X_pow_dvd_iff", "measure_theory.l1.add_to_fun", "set.indicator_le", "homeomorph.coe_eq_to_equiv", "nat.decreasing_induction_succ", "free_magma.lift_mul", "omega.nat.preterm.val_var", "frobenius_nat_cast", "category_theory.biprod.unipotent_lower_inv", "category_theory.limits.cokernel.condition", "polynomial.eval\:2082_bit1", "mem_of_nhds", "right_ord_continuous.map_Inf", "ennreal.to_real_mul_to_real", "hyperreal.is_st_symm_real", "smul_le_smul_of_nonneg", "finset.eq_empty_or_nonempty", "tactic.ring_exp.exp_congr", "multiset.filter_map_eq_map", "asymptotics.is_O_self_const_mul'", "cardinal.prod_mk", "list.mem_sections_length", "local_equiv.to_fun_as_coe", "int.lnot_bit", "list.erase_dup_nil", "zorn.max_chain_spec", "cau_seq.const_add", "dvd_add_iff_right", "real.sin_eq_zero_iff_cos_eq", "is_compact.induction_on", "algebra.id.map_eq_self", "ring_equiv.to_Ring_iso_inv", "cau_seq.le_of_exists", "category_theory.iso.inv_comp_eq", "function.surjective.range_comp", "measure_theory.outer_measure.ext", "topological_space.opens.empty_eq", "if_false_left_eq_and", "chart_at_self_eq", "continuous_linear_map.has_strict_deriv_at", "mul_semiring_action_hom.coe_fn_coe", "units.mk0_coe", "zmod.euler_criterion", "imp_eq_of_eq_false_right", "norm_num.mul_neg_pos", "multiset.map_cons", "tendsto_iff_norm_tendsto_zero", "homeomorph.comp_continuous_on_iff", "linear_map.finite_dimensional_of_surjective", "ideal.is_prime.mem_or_mem_of_mul_eq_zero", "polynomial.comp_zero", "category_theory.currying_inverse_obj_map_app", "list.repeat_succ", "category_theory.limits.cocone.category_to_category_struct_comp_hom", "ordinal.mul_le_mul_left", "onote.repr_one", "znum.neg_zero", "linear_map.is_linear", "finsupp.prod_neg_index", "measure_theory.measure.ext", "finset.singleton_val", "subring.coe_one", "dim_mul_dim", "finset.prod_range_induction", "free_group.reduce.sound", "formal_multilinear_series.radius_neg", "interval_integral.integral_add", "submodule.eq_zero_of_bot_submodule", "list.pw_filter_sublist", "stream.interleave_eq", "multiset.inter_le_ndinter", "is_open_sInter", "differentiable_at.smul_algebra", "int.coe_nat_le_coe_nat_iff", "tactic.ring_exp.mul_coeff_pf_mul_one", "finmap.lookup_erase", "convex.center_mass_mem", "inf_le_right'", "has_sum.prod_fiberwise", "set.Ioc_subset_Ioi_self", "differentiable_at_const", "is_local_extr.comp_continuous_on", "ennreal.add_eq_top", "linear_map.pi_zero", "turing.TM2.step_supports", "add_neg_eq_of_eq_add", "filter.tendsto.not_tendsto", "real.cos_neg", "has_strict_deriv_at.neg", "multiset.product_add", "finset.sum_apply", "pSet.subset.congr_left", "continuous_iff_continuous_at", "measure_theory.ae_eq_fun.comp\:2082_eq_mk", "continuous_quot_mk", "add_submonoid.mem_carrier", "functor.const.ext", "int.to_nat_sub_of_le", "fintype.prod_dvd_of_coprime", 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"multiplicity.is_greatest'", "multiset.nodup_of_le", "functor.comp.comp_map", "set.image_add_const_Iic", "is_topological_fiber_bundle.continuous_proj", "linear_equiv.findim_eq", "function.embedding.coe_subtype", "filter.tendsto_congr'", "fin.coe_zero", "mv_polynomial.degrees_sum", "finset.inter_bind", "times_cont_mdiff_within_at.prod_map", "asymptotics.is_O_refl_left", "cardinal.lt_succ_self", "subsemiring.mem_comap", "category_theory.comma.map_right_id_hom_app_left", "matrix.zero_dot_product'", "local_equiv.eq_on_source.symm_eq_on", "monotonicity.true", "vector_space.dual_dim_eq", "dfinsupp.prod_single_index", "ideal.comap_is_prime", "tangent_cone_mono_nhds", "nat.partrec'.bind", "pnat.mk_le_mk", "asymptotics.is_O_zero_right_iff", "subgroup.coe_subtype", "pow_le_pow_of_le_one", "category_theory.faithful.of_iso", "list.chain'.tail", "dif_pos", "list.count_cons'", "pgame.one_left_moves", "rel.mem_core", "decidable.not_not", "set.Icc_subset_Ico_right", "continuous_at_fst", "finmap.lookup_to_finmap", "set.set_of_forall", "is_R_or_C.I_re", "int.mul_neg_succ_of_nat_neg_succ_of_nat", "units.neg_neg", "has_deriv_within_at.deriv_within", "mem_perms_of_list_iff", "gaussian_int.mod_four_eq_three_of_nat_prime_of_prime", "category_theory.is_equivalence.fun_inv_map", "finset.univ_sigma_univ", "turing.to_partrec.code.nil_eval", "monoid_hom.ext", "lt_one_div_of_neg", "list.scanr_cons", "measure_theory.l1.simple_func.of_simple_func_add", "is_add_subgroup.mem_norm_comm_iff", "filter.limsup_congr", "iff_false_right", "set.subset_image_compl", "is_lub.cSup_eq", "subsemiring.comap_infi", "coe_I_one", "finset.weighted_vsub_eq_weighted_vsub_of_point_of_sum_eq_zero", "complex.exists_extension_norm_eq", "image_le_of_liminf_slope_right_lt_deriv_boundary", "category_theory.limits.diagram_of_cones.cone_points_map", "set.indicator_congr", "pnat.coprime.gcd_mul_right_cancel_right", "submonoid.mem_infi", "category_theory.limits.has_limit.iso_of_nat_iso_hom_\[Pi]_assoc", 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"cardinal.increasing_cantor_function", "cau_seq.completion.mk_eq_mk", "real.exists_sin_eq", "multiplicity.finite_mul", "and.swap", "strict_mono_of_deriv_pos", "is_noetherian_ring_of_ring_equiv", "polynomial.degree_map", "has_fderiv_within_at.mono", "conj_mul", "has_fderiv_at_filter_snd", "list.append_right_inj", "open_add_subgroup.is_open", "iff_true_intro", "measure_theory.ae_eq_fun.coe_fn_sub", "nat.strong_rec_on_beta'", "is_glb.union", "composition.sum_blocks_fun", "linear_independent_comp_subtype_disjoint", "computation.ret_mem", "is_greatest.upper_bounds_eq", "multiset.eq_repeat", "is_Hausdorff.subsingleton", "list.nodup_attach", "equiv.swap_apply_right", "approximates_linear_on.inverse_approx_map_contracts_on", "is_total_preorder.swap", "wseq.destruct_join", "equiv.subtype_preimage_symm_apply_coe_neg", "int.lt_of_add_lt_add_left", "set.maps_to.comp", "valuation.mem_supp_iff", "is_closed_eq", "linarith.int.coe_nat_bit0", "finite_dimensional.cardinal_mk_le_findim_of_linear_independent", "category_theory.Monad.to_Mon_mul", "set.image_subset_range", "measure_theory.outer_measure.empty'", "is_local_extr_on.comp_mono", "list.take_while_append_drop", "fderiv_smul_algebra", "set.indicator_compl_add_self_apply", "measure_theory.outer_measure.of_content_eq_infi", "multiset.to_finset_val", "computation.map_comp", "submodule.span_smul", "add_con.lift_apply_mk'", "multiset.map_eq_map_of_bij_of_nodup", "circle_deg1_lift.translate_inv_apply", "nat.zero_mul", "finset.coe_map_subset_range", "cardinal.mk_univ", "ideal.span_singleton_eq_span_singleton", "has_strict_fderiv_at.eq_implicit_function", "upper_bounds_mono_set", "det_of_card_zero", "monoid_hom.coprod_comp_inr", "ideal.mem_span_singleton", "filter.not_frequently", "finset.univ_sum_single", "lfp_le", "pgame.le_zero", "associates.is_unit_mk", "ring_equiv.map_neg", "int.sub_le_sub", "nnreal.sub_add_cancel_of_le", "nnreal.rpow_lt_rpow", "with_zero.lift_coe", "finset.sdiff_eq_self_of_disjoint", "submodule.mul_bot", "pgame.add_move_left_inl", "mdifferentiable_at.congr_of_eventually_eq", "asymptotics.is_o.const_mul_left", "uniform_space.comap_quotient_eq_uniformity", "lie_algebra.orthogonal.PD_inv", "function.iterate_pred_comp_of_pos", "mul_self_lt_mul_self_iff", "polynomial.eval\:2082_sum", "category_theory.limits.fork.\[Iota]_eq_app_zero", "localization.ring_equiv_of_quotient_symm_mk'", "Top.presheaf.stalk_functor_obj", "list.Ico.filter_lt_of_succ_bot", "ideal.mul_mono_right", "ordinal.lift_type_le", "isometric.add_right_symm", "filter.eventually_or_distrib_left", "nat.add_succ", "list.nth_le_append_right", "sub_pow_char_pow", "power_series.monomial_eq_mk", "submodule.closed_complemented_top", "category_theory.over.construct_products.cones_equiv_counit_iso_2", "submodule.map_subtype_embedding_eq", "set.bUnion_subset_bUnion_left", "category_theory.prod.symmetry_hom_app", "multiset.to_finsupp_support", "infi_eq_bot", "multiset.count_add", "metric.uniformity_basis_dist_inv_nat_pos", "ring.fractional_ideal.ext", "stream.nth_const", "alg_equiv.coe_alg_hom", "fib_rec_char_poly_eq", "filter.liminf_le_limsup", "tendsto_right_nhds_uniformity", "ideal.comap_eq_top_iff", "with_zero.zero_mul", "primrec.bnot", "floor_lt", "real.arcsin_one", "int.to_add_gpow", "composition.size_up_to_le", "nat.le_mul_of_pos_left", "add_subgroup.ext'", "abstract_completion.uniform_continuous_extend", "eventually_eventually_nhds", "polynomial.mem_nth_roots", "formal_multilinear_series.le_radius_of_bound", "infi_inf", "turing.blank_extends.trans", "equiv.coe_add_right", "ideal.exists_sub_mem", "nat_ceil_mono", "polynomial.derivative_mul", "multiset.revzip_powerset_aux_lemma", "free_abelian_group.of_mul_of", "category_theory.monad.free_map_f", "int.of_nat_nat_abs_of_nonpos", "free_abelian_group.neg_seq", "measurable.subtype_mk", "category_theory.discrete.functor_map_id", "filter.rmap_sets", "continuous_within_at.image_closure", "nat.size_le_size", 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"complex.continuous_exp", "quot.lift_beta", "inv_smul_smul'", "add_commute.neg_neg_iff", "int.mul_neg_of_neg_of_pos", "vector.cons_tail", "typevec.const_append1", "uniform_continuous_iff", "emetric.diam_pos_iff", "finset.coe_subset", "ennreal.lt_inv_iff_lt_inv", "pairwise.pairwise_on", "mv_power_series.ext", "finsupp.support_filter", "onote.mul_nat_eq_mul", "filter.prod_def", "affine_map.coe_add", "trans_rel_right", "has_strict_fderiv_at.mem_to_local_homeomorph_source", "subring.coe_subset_coe", "free_semigroup.traverse_pure", "differentiable_on.csinh", "hyperreal.infinitesimal_pos_iff_infinite_pos_inv", "injective_of_lt_imp_ne", "int.sub_lt_sub_of_le_of_lt", "ordinal.lt_mul_succ_div", "category_theory.uncurry_injective", "finite_field.card_image_polynomial_eval", "nat.le_of_pred_lt", "floor_nonneg", "pfun.dom_iff_graph", "measure_theory.l1.simple_func.coe_pos_part", "filter.realizer.principal_F", "list.ordered_insert_nil", "local_homeomorph.of_set_trans", "filter.infi_principal_finset", "ennreal.top_ne_coe", "ennreal.inv_inv", "category_theory.limits.pair_obj_left", "concave_on_real_of_slope_mono_adjacent", "with_top.none_le", "is_local_min_on.min", "add_units.coe_hom_apply", "setoid.inf_def", "pmf.summable_coe", "ultrafilter_converges_iff", "fin.init_update_cast_succ", "is_max_filter.comp_tendsto", "fin.one_val", "nat.dvd_sub_mod", "fintype.prod_sum_type", "option.some_orelse'", "list.head_mem_head'", "filter.Limsup_eq_infi_Sup", "bounded_continuous_function.norm_le", "le_antisymm'", "nat.min_fac_has_prop", "finset.eq_weighted_vsub_of_point_subset_iff_eq_weighted_vsub_of_point_subtype", "linear_independent_iff", "add_lt_of_nonpos_of_lt'", "contracting_with.one_sub_K_pos'", "filter.tendsto.liminf_eq", "multiset.add_sigma", "ordinal.is_normal.le_set'", "local_equiv.refl_symm", "lucas_lehmer.X.bit0_fst", "category_theory.limits.biprod.map_fst_assoc", "multiset.to_finsupp_add", "local_equiv.eq_on_source.source_inter_preimage_eq", "add_units.add_neg_eq_iff_eq_add", "gpowers_subset", "bool.of_to_bool_iff", "multiset.add_left_cancel", "padic_int.p_dvd_of_norm_lt_one", "ideal.quotient.nontrivial", "ennreal.zero_sub", "is_local_extr.neg", "stream.tail_drop", "encodable.subtype.encode_eq", "geom_sum_inv", "free_add_semigroup.traverse_pure'", "set.Ioc_union_Icc_eq_Ioc", "denumerable.of_nat_nat", "times_cont_diff_at.sub", "iff_of_true", "one_div_mul_one_div_rev", "set.image_const_add_Ioi", "mdifferentiable_at_const", "dvd_or_coprime", "computation.bind_assoc", "option.bex_ne_none", "int.bit1_pos", "polynomial.degree_div_by_monic_le", "ordinal.enum_lt", "measure_theory.measure.lintegral_join", "order_embedding.map_lt_iff", "set.countable_prod", "category_theory.limits.fork.of_cone_\[Pi]", "mv_power_series.X_dvd_iff", "uniformity_prod_eq_prod", "dfinsupp.single_add", "finset.weighted_vsub_of_point_vadd_eq_of_sum_eq_one", "galois_connection.monotone_u", "set.Ioo_subset_Iio_self", "with_bot.coe_nsmul", "is_open_map_mul_right", "set.inter_singleton_eq_empty", "lagrange.interpolate_zero", "continuous_ultrafilter_extend", "complex.cpow_nat_inv_pow", "valuation.map_zero", "lt_add_of_neg_lt_sub_left", "approximates_linear_on.inverse_approx_map_maps_to", "is_add_subgroup.sub_mem", "power_series.monomial_zero_eq_C", "partrec.sum_cases_left", "ring_hom.coe_mul", "free_magma.lift_unique", "differentiable_within_at.has_fderiv_within_at", "equiv.perm.sign_refl", "algebra.mul_smul_comm", "deriv_sinh", "has_deriv_at.lhopital_zero_nhds", "finset.not_mem_union", "category_theory.limits.prod.symmetry", "tendsto_at_top_of_geom_lt", "polynomial.nat_degree_pos_of_eval\:2082_root", "add_units.coe_mk_of_add_eq_zero", "category_theory.limits.image.map_\[Iota]", "emetric.Hausdorff_edist_triangle", "list.erase_dup_subset", "filter.tendsto_at_bot_add_left_of_ge'", "turing.TM2.stmts\:2081_self", "asymptotics.is_O_iff", "galois_connection.is_glb_u_image", "semiconj_by.add_right", "pow_add", "category_theory.monoidal_of_has_finite_coproducts.right_unitor_inv", "CommGroup.ext", "list.pairwise_pair", "category_theory.nat_trans.hcomp_app", "real.is_cau_seq_iff_lift", "finset.sdiff_eq_filter", "cardinal.mk_preimage_of_injective_of_subset_range_lift", "div_ne_zero_iff", "filter.generate_eq_generate_inter", "valuation.map_eq_of_sub_lt", "category_theory.limits.coprod.braiding_inv", "list.perm_merge_sort", "embedding_of_embedding_compose", "int.neg_lt_sub_right_of_lt_add", "tactic.ring_exp.mul_pp_pf_prod_lt", "measure_theory.outer_measure.coe_supr", "decidable.of_not_imp", "ordinal.mul_omega", "bit1_pos'", "fract_lt_one", "open_add_subgroup.coe_inf", "rtendsto_nhds", "times_cont_diff.differentiable_iterated_deriv", "set.Inter_subset_Inter", "category_theory.sum.associator_map_inr", "ennreal.max_mul", "rat.mul_def", "list.tail_subset", "is_coprime.mul_add_right_left_iff", "ring_invo.coe_ring_equiv", "string.str_ne_str_right", "has_deriv_at.scomp_has_deriv_within_at", "set.indicator_apply", "ordinal.succ_pos", "category_theory.iso.to_equiv_symm_fun", "deriv_sub", "Top.stalk_to_fiber_germ", "mv_polynomial.is_integral_domain_fin_zero", "subsemiring.mem_Sup_of_directed_on", "pell.yz_sub", "pythagorean_triple.symm", "polynomial.root_mul_right_of_is_root", "fin.cast_succ_fin_succ", "metric.mem_nhds_within_iff", "finset.Ico.diff_left", "int.test_bit_succ", "continuous_linear_map.norm_id_field'", "finset.coe_map", "equiv.sum_assoc_apply_in2", "interval_integral.integral_const_of_cdf", "matrix.det_eq_one_of_card_eq_zero", "continuous_within_at.prod", "ring.in_closure.rec_on", "times_cont_mdiff_at_snd", "filter.rcomap_compose", "fraction_map.comap_is_algebraic_iff", "list.sublists_concat", "asymptotics.is_O.congr_of_sub", "complex.cpow_def", "fract_floor", "free_group.red.append_append", "roption.dom_iff_mem", "min_le_add_of_nonneg_right", "add_submonoid.multiset_sum_mem", "list.reverse_sublist_iff", "complex.cos_sub", "auto.not_and_eq", "function.embedding.equiv_symm_to_embedding_trans_to_embedding", "list.erase_subperm", "int.shiftl_sub", "unique_uniformity_of_compact_t2", "sub_smul", "monoid_hom.cancel_right", "mem_uniformity_edist", "equiv.perm.cycle_of_inv", "list.foldr_map", "uniform_continuous\:2082.comp", "set.add_empty", "emetric.tendsto_uniformly_on_iff", "function.left_inverse_iff_comp", "nat.primrec'.mul", "sub_add_cancel", "dvd_neg", "submodule.restrict_scalars_bot", "set.mem_singleton_iff", "homeomorph.symm_to_local_homeomorph", "canonically_ordered_semiring.pow_pos", "int.div_sign", "stream.interleave_tail_tail", "set.range_const_subset", "with_bot.bot_add", "list.range_core_range'", "category_theory.unop_unop_obj", "filter.eventually_principal", "nat.partrec.code.eval_part", "affine_map.homothety_def", "ideal.mul_mono_left", "partrec.nat_iff", "padic_norm_e.is_rat", "nat.add_mod_right", "rat.denom_ne_zero", "set.mem_inter", "measurable_space.map_inf", "eq.subst", "add_equiv.map_ne_zero_iff", "free_magma.mul_bind", "is_closed_of_closure_subset", "submodule.subset_span", "measure_theory.lintegral_mono", "neg_le_sub_left_of_le_add", "set.card_image_of_injective", "is_local_extr_on.elim", "eq_one_of_right_cancel_mul_self", "padic_norm_e.neg", "complex.of_real_fpow", "nat.le_of_add_le_add_right", "add_subgroup.mem_Inf", "dioph.div_dioph", "finset.sum_const", "is_add_unit_zero", "euclidean_geometry.orthogonal_projection_fn_vsub_mem_direction_orthogonal", "nat.partrec.code.rec_prim'", "int.one_nonneg", "le_one_of_one_le_inv", "list.keys_kreplace", "matrix.mul_one", "mul_lt_right'", "free_group.prod.mul", "tactic.ring2.horner_expr.cseval_mul_const", "bilin_form.comp_right_comp_left", "perfect_closure.nat_cast", "finset.prod_ne_zero_iff", "smul_assoc", "set.finite.sUnion", "nonempty.elim_to_inhabited", "is_compact.elim_finite_subfamily_closed", "set.prod_preimage_eq", "pi.const_one", "con.lift_coe", "affine_map.coe_mk'", "category_theory.limits.colimit.map_desc", "nhds_within_has_basis", "setoid.classes_mk_classes", "differentiable_within_at_inter'", "dfinsupp.support_subtype_domain", "finset.filter_not", "set.sUnion_subset", "affine.simplex.face_points", "add_monoid_hom.map_sum", "lt_mul_of_one_lt_right", "num.to_of_nat", "filter.germ.coe_coe_add_hom", "add_submonoid.coe_Sup_of_directed_on", "Mod.id_hom", "fin.of_nat_eq_coe", "category_theory.limits.colimit.\[Iota]_map_assoc", "pell.matiyasevic", "fin.coe_pred", "filter.at_bot_basis'", "multiset.smul_sum", "rat.num_ne_zero_of_ne_zero", "differentiable_on.div", "set.inj_on.image_Inter_eq", "has_sum_of_bounded_monoid_hom_of_summable", "set.range_comp", "mul_aut.coe_one", "continuous_multilinear_curry_fin0_apply", "polynomial.nat_degree_separable_eq_card_roots", "deriv_within_div_const", "nhds_within_Iic_ne_bot", "measure_theory.outer_measure.smul_dirac_apply", "int.to_nat_of_nonneg", "list.length_split_lt", "enorm.finite_edist_eq", "sub_right_le_of_le_add", "local_equiv.target_inter_inv_preimage_preimage", "ennreal.tsum_coe_ne_top_iff_summable", "unique_diff_on_Iio", "Algebra.coe_of", "omega.int.univ_close_of_unsat_clausify", "emetric.cauchy_seq_iff_nnreal", "Top.presheaf.pushforward.id_inv_app'", "nhds_infi", "is_compl.disjoint_right_iff", "exp_neg_inv_glue.pos_of_pos", "classical.epsilon_spec_aux", "dense_Union_interior_of_closed", "self_le_inv", "subring.coe_Inf", "is_max_filter.bicomp_mono", "add_le_add_iff_left", "category_theory.iso.op_inv", "category_theory.functor.map_arrow_map_right", "exp_neg_inv_glue.f_aux_deriv_pos", "continuous_linear_map.lmul_left_right_apply", "nat.primes.coe_nat_inj", "zsqrtd.coe_nat_re", "derivation.leibniz", "mem_closure2", "exists_norm_eq_infi_of_complete_convex", "set.diff_subset_diff_left", "valuation.map_add_of_distinct_val", "with_top.op_sum", "measure_theory.l1.simple_func.coe_neg_part", "fin.forall_fin_succ", "submonoid.localization_map.mul_mk'_one_eq_mk'", "int.ne_of_lt", "smooth_within_at.times_cont_mdiff_within_at", "category_theory.limits.coprod.inl_desc", "finset.prod_Ico_consecutive", "norm_num.int_cast_ne", "stream.inits_eq", "submodule.liftq_apply", "category_theory.limits.inv_prod_comparison_map_fst", "subring.coe_mk'", "prime_spectrum.zero_locus_empty", "list.length_reverse", "submonoid.localization_map.inv_inj", "differentiable.div", "monoid_hom.range_top_iff_surjective", "set.union_preimage_subset", "generalized_continued_fraction.int_fract_pair.stream_is_seq", "monotone_lam", "perfect_closure.induction_on", "left_ord_continuous.order_dual", "set.finite.map", "filter.tendsto.mul_mul", "monoid_hom.inv_apply", "mul_semiring_action_hom.map_add", "cardinal.le_mul_right", "category_theory.over.map_obj_hom", "category_theory.functor.associator_hom_app", "composition.single_embedding", "gpow_neg_succ_of_nat", "pell.xn_one", "znum.to_of_int", "ennreal.continuous_coe", "measure_theory.l1.eq_iff", "direct_sum.mk_injective", "sub_eq_of_eq_add", "generalized_continued_fraction.first_numerator_eq", "frontier_closed_ball", "array.rev_list_reverse_aux", "not_bdd_above_iff'", "int.div2_bit", "multiplicity.multiplicity_add_eq_min", "filter.map_at_bot_eq_of_gc", "parallelogram_law_with_norm", "nat.pred_eq_ppred", "upper_bounds_empty", "dense_Inter_of_open", "set.Ico_disjoint_Ico_same", "ordinal.div_def", "hyperreal.infinitesimal_of_tendsto_zero", "category_theory.iso.hom_congr_trans", "category_theory.limits.prod_right_unitor_hom_naturality", "nhds_within_Ioi_ne_bot", "roption.mem_map_iff", "ordinal.is_limit_add_iff", "int.add_nonneg", "finset.prod_eq_zero", "submodule.disjoint_iff_comap_eq_bot", "filter.inf_principal", "tendsto_nhds_within_mono_left", "multiset.to_finset_map", "set.preimage_const_mul_Iio", "deriv_pow", "list.join_split_wrt_composition", "set.set_of_true", "multiset.powerset_len_aux_perm", "category_theory.limits.cones.whiskering_equivalence_inverse", "primrec.nat_iterate", "function.support_max", "is_linear_map.is_linear_map_sub", "nhds_within_basis_open", "multiset.coe_nil_eq_zero", "znum.abs_to_nat", "cardinal.mk_subtype_mono", "real.cos_eq_one_iff", "submonoid.closure_eq_of_le", "nat.sub_eq_psub", "list.Ico.chain'_succ", "pgame.add_right_neg_le_zero", "quadratic_form.add_apply", "zorn.succ_increasing", "filter.le_of_ultrafilter", "set.singleton_smul", "stream.nth_drop", "dense_Inter_of_open_nat", "inv_mul_lt_iff_lt_mul_right", "linear_map.smul_right\:2097_apply", "rat.div_mk_div_cancel_left", "metric.bounded_of_finite", "measure_theory.integrable_on.add_measure", "linear_pmap.map_neg", "pell.xy_coprime", "list.of_fn_zero", "generalized_continued_fraction.of_correctness_of_terminates", "dense_range.closure_range", "measure_theory.simple_func.bind_const", "pgame.subsequent.right_move", "complex.of_real_inv", "is_open_uniformity", "equiv.perm.same_cycle.symm", "submonoid.localization_map.symm_comp_of_mul_equiv_of_localizations_apply'", "ordinal.mul_zero", "submodule.findim_lt", "free_abelian_group.add_seq", "multiset.powerset_aux'_perm", "padic_seq.norm_neg", "category_theory.has_hom.hom.op_unop", "times_cont_diff_groupoid_prod", "composition.blocks_length", "set.inv_mem_inv", "list.lookmap_id'", "multiset.nodup_powerset_len", "con.Inf_def", "continuous_linear_equiv.symm_apply_apply", "ennreal.add_halves", "bdd_above_Iio", "alg_equiv.apply_symm_apply", "list.iota_eq_reverse_range'", "add_localization.r_eq_r'", "interior_union_is_closed_of_interior_empty", "fin.prod_univ_cast_succ", "complex.mul_conj", "submodule.linear_proj_of_is_compl_apply_eq_zero_iff", "measure_theory.lintegral_dirac", "with_top.coe_bit1", "cardinal.sup_lt_of_is_regular", "deriv_within.scomp", "quotient.eq'", "category_theory.exp_comparison_natural_right", "list.perm_cons_append_cons", "is_extr_filter.filter_mono", "has_deriv_within_at.mul_const", "nat.sub_lt_left_iff_lt_add", "int.add_left_cancel", "function.inv_fun_neg", "monotone_lfp", "card_trivial", "add_units.neg_add_of_eq", "exists_Ico_subset_of_mem_nhds'", "polynomial.eval_smul", "filter.germ.abs_def", "computable.list_reverse", "finsupp.sub_single_one_add", "equiv.perm.swap_induction_on", "ennreal.sub_right_inj", "cau_seq.const_neg", "measure_theory.outer_measure.comap_apply", "borel_eq_top_of_discrete", "dvd_trans", "has_fderiv_at.has_deriv_at", "nonzero_of_invertible", "category_theory.equivalence.equivalence_mk'_unit", "abs_abs_sub_le_abs_sub", "is_least_univ", "ceil_lt_add_one", "metric.continuous_at_iff", "neg_vsub_eq_vsub_rev", "sym_bilin_form.is_refl", "floor_add_int", "commute.mul_right", "matrix.det_adjugate_of_cancel", "stream.mem_cycle", "formal_multilinear_series.change_origin_summable_aux_j_injective", "model_with_corners.unique_diff_preimage_source", "set.surj_on_Inter_Inter", "nat.zero_min", "is_measurable_Iio", "padic_int.coe_one", "coe_sort_tt", "pos_num.succ'_pred'", "add_submonoid.mrange_fst", "valuation.ext", "set.dual_Ico", "ordinal.succ_le_succ", "finsupp.support_map_range", "category_theory.iso.symm_mk", "continuous_linear_map.uniform_continuous", "monotone.div_const", "not_congr", "add_comm_group.direct_limit.lift_add", "valuation.comap_id", "category_theory.limits.colimit.pre_id", "submodule.lt_def", "multiplicity.multiplicity_le_multiplicity_iff", "polynomial.to_subring_one", "dense_embedding.to_embedding", "fixed_points.minpoly.eval\:2082", "neg_eq_neg_one_mul", "times_cont_mdiff_within_at_iff_times_cont_mdiff_on_nhds", "onote.oadd_lt_oadd_1", "infi_le_infi_of_subset", "series_ratio_test", "continued_fraction.convergents_eq_convergents'", "Ioo_mem_nhds", "tendsto_abs_at_top_at_top", "list.foldl_reverse", "ideal.mul_comm", "subsemiring.le_def", "zorn.zorn_partial_order\:2080", "uniform.tendsto_congr", "ordered_ring.mul_nonneg", "interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae", "bot_le", "imp_iff_not_or", "irrational.of_rat_mul", "cardinal.mk_finset_eq_mk", "emetric.exists_edist_lt_of_Hausdorff_edist_lt", "pos_num.cast_mul", "finset.sum_univ_pi", "rel.image_univ", "units.coe_gpow'", "fin.heq_ext_iff", "lie_algebra.special_linear.E_trace_zero", "list.drop_suffix", "polynomial.monic_map_iff", "real.cos_arcsin", "list.length_tail", "znum.cast_pos", "functor.comp.map_pure", "linear_equiv.coe_uncurry", "affine_subspace.direction_inf_of_mem_inf", "ennreal.mul_div_cancel", "matrix.one_apply_eq", "turing.TM2to1.tr_respects_aux\:2081", "category_theory.limits.is_limit.cone_point_unique_up_to_iso_hom_comp", "inv_zero", "euclidean_domain.gcd_eq_left", "equiv.perm.disjoint.symm", "vector3.insert_fs", "one_one_reducible.of_equiv", "polynomial.comp_one", "pgame.not_le_lt", "vector_span_eq_span_vsub_set_left_ne", "complex.differentiable_cos", "list.sublist.erase", "is_open_iff_nhds", "bilin_form.to_matrix_apply", "submodule.mkq_apply", "infi_eq_dif", "continuous_linear_map.smul_comp", "finset.mem_of_subset", "ordinal.is_normal.le_iff", "category_theory.unop_unop_map", "isometric.eq_symm_apply", "set.right_mem_Ioo", "power_series.order_eq", "linear_map.quotient_inf_equiv_sup_quotient_symm_apply_eq_zero_iff", "filter.is_countably_generated_iff_exists_antimono_basis", "function.surjective.iterate", "min_max_distrib_right", "monoid_hom.comp_assoc", "pell.pell_eqz", "nhds_cons", "multiset.cons_product", "ideal.neg_mem_iff", "rat.coe_cast_hom", "add_monoid_hom.map_exists_right_neg", "pell.xn_modeq_x4n_sub", "measure_theory.l1.coe_smul", "ulift.down_up", "complex.of_real_sin", "set.subset.rfl", "prod.smul_fst", "polynomial.eval\:2082_mul_noncomm", "complex.continuous_mul", "list.not_mem_keys_kerase", "emetric.totally_bounded_iff", "is_compl.disjoint_left_iff", "ring_hom.sclosure_preimage_le", "pow_two_sub_pow_two", "continuous_at.inv", "category_theory.limits.biprod.map_snd_assoc", "finsupp.sum_smul_index'", "exists_elim_eq_right", "inner_sub_left", "ennreal.coe_eq_zero", "filter.frequently_const", "primrec.decode", "measure_theory.measure_zero_iff_ae_nmem", "bdd_below_empty", "int.mul_assoc", "free_magma.mul_map_seq", "list.reverse_singleton", "finset.subset_insert", "real.volume_interval", "smodeq.symm", "padic_val_nat_eq_factors_count", "measure_theory.lebesgue_length_Ioo", "subtype.mem", "ideal.top_mul", "of_digits_lt_base_pow_length'", "list.erasep_subset", "mul_neg_geom_series", "base_pow_length_digits_le", "finset.sort_sorted_lt", "Top.sheaf_condition.w", "is_coprime.of_mul_add_left_left", "set.image2_subset", "mv_power_series.ext_iff", "field.ring_closure_subset", "one_div_lt", "asymptotics.is_O_const_one", "finsupp.supported_eq_span_single", "add_sub_cancel", "free_group.red.cons_nil_iff_singleton", "int.coe_nat_sub", "local_homeomorph.image_inter_source_eq", "ennreal.of_real_eq_coe_nnreal", "is_unit_of_dvd_one", "onote.oadd_mul_NF_below", "ereal.neg_le", "real.has_deriv_at_sin", "function.left_inverse.comp_eq_id", "finset.singleton_inj", "finset.weighted_vsub_of_point_erase", "polynomial.degree_add_C", "category_theory.monoidal_functor.id_\[Mu]_is_iso", "filter.has_basis.tendsto_right_iff", "matrix.mul_add", "fin.coe_cast_le", "measure_theory.ae_eq_fun.induction_on", "vector.nth_of_fn", "directed_of_chain", "set.Union_subset_Union_const", "asymptotics.is_o_zero_right_iff", "local_homeomorph.mdifferentiable.comp_symm_deriv", "subalgebra.zero_mem", "pow_card_eq_one", "submonoid.map_id", "has_fderiv_within_at_fst", "finset.piecewise_empty", "bitraversable.comp_tfst", "complex.abs_inv", "real.cos_two_neg", "finset.card_eq_sum_ones", "list.ordered_insert_count", "set.preimage_const_of_mem", "polynomial.mod_eq_self_iff", "submodule.annihilator_mono", "multiset.rel_map_left", "ring.direct_limit.lift_one", "filter.tendsto.congr_uniformity", "add_subgroup.prod_top", "abstract_completion.map_comp", "znum.cast_zneg", "finmap.union_comm_of_disjoint", "heq.symm", "metric.diam_union'", "filter.not_ne_bot", "bilin_form.is_adjoint_pair_zero", "is_unit_of_mul_is_unit_left", "enat.add_lt_add_right", "prime_spectrum.zero_locus_singleton_zero", "polynomial.has_fderiv_within_at", "ctop.realizer.tendsto_nhds_iff", "interval_integral.integral_has_deriv_at_of_tendsto_ae_right", "category_theory.monoidal_category.unitors_equal.cells_8", "nnreal.dist_eq", "finset.exists_le_of_sum_le", "category_theory.limits.coprod.inl_desc_assoc", "submonoid.coe_one", "prod.snd_surjective", "ordinal.rel_iso_enum'", "linear_equiv.range", "fderiv_within_neg", "normal_add_subgroup_of_add_comm_group", "add_monoid_hom.comp_id", "polynomial.monic_prod_of_monic", "continuous_list_sum", "enat.add_one_le_iff_lt", "filter.has_basis.tendsto_left_iff", "affine.simplex.point_eq_affine_combination_of_points_with_circumcenter", "exists_prop_of_true", "local_homeomorph.symm_to_local_equiv", "filter.frequently_low_scores", "zsqrtd.sq_le_smul", "finset.nonempty.bex", "nat.primrec'.head", "category_theory.lax_monoidal_functor.comp_\[Mu]", "linear_equiv_matrix_id", "add_submonoid.closure_induction", "function.is_periodic_pt.eq_of_apply_eq_same", "is_absolute_value.sub_abv_le_abv_sub", "nat.left_distrib", "inf_right_idem", "measure_theory.measure.comap_apply", "basic_smooth_bundle_core.times_cont_mdiff_proj", "metric.closure_ball_subset_closed_ball", "times_cont_mdiff_within_at.prod_map'", "nat.cast_succ", "abstract_completion.map_unique", "measure_theory.ae_eq_fun.induction_on\:2082", "nat.mul_le_mul_of_nonneg_right", "uniform_inducing.uniform_continuous", "add_monoid_algebra.single_mul_apply_aux", "set.mem_one", "semiquot.pure_le", "free_abelian_group.lift.unique", "filter.tendsto.norm", "affine.simplex.dist_circumcenter_eq_circumradius'", "encodable.encode_sigma_val", "with_top.add_lt_add_iff_left", "eq_mp_rfl", "simple_graph.complete_graph_is_regular", "subtype.dist_eq", "closure_Iic", "ordinal.power_le_of_limit", "set.restrict_eq", "gaussian_int.to_complex_inj", "list.perm_comp_forall\:2082", "infi_sigma", "num.lt_iff_cmp", "int.sign_mul_nat_abs", "polynomial.nat_degree_pow", "classical.indefinite_description", "add_submonoid.localization_map.ext_iff", "ideal.quotient.is_integral_domain_iff_prime", "add_monoid_hom.coe_of", "nat.odd_mul_odd", "digits_of_lt", "polynomial.C_eq_nat_cast", "add_submonoid.closure_eq_mrange", "alg_hom.map_prod", "ennreal.coe_lt_one_iff", "add_magma.free_add_semigroup.lift_of", "power_series.trunc_one", "list.cons_union", "smooth_on_const", "polynomial.degree_lt_degree_mul_X", "dfinsupp.map_range_apply", "submonoid.mem_closure", "direct_sum.component.lof_self", "isometric.point_reflection_dist_self'", "category_theory.limits.colimit.\[Iota]_pre", "measure_theory.measure.finite_at_filter.filter_mono", "eckmann_hilton.one", "bxor_tt", "ordinal.cof_eq'", "set.diff_diff_right", "fderiv_const_smul_algebra", "sesq_form.neg_right", "min_left_comm", "filter.frequently_cofinite_iff_infinite", "commute.sub_left", "traversable.foldr_to_list", "uniform_continuous_snd", "real.arcsin_nonneg", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_is_iso_comp_inv", "list.bag_inter_nil_iff_inter_nil", "uniform_space.complete_of_cauchy_seq_tendsto", "is_local_max_on.congr", "computation.equiv.trans", "measure_theory.finite_at_filter_of_finite", "units.coe_mul_right", "computation.equiv.refl", "semiconj_by.inv_inv_symm_iff", "bdd_below_union", "finset.insert_erase", "tactic.ring_exp.add_pf_z_sum", "lie_algebra.orthogonal.is_unit_Pso", "nnreal.add_sub_cancel", "set.mem_to_finset_val", "homeomorph.homeomorph_mk_coe", "has_strict_fderiv_at.to_implicit_function_of_complemented", "geom_gold_is_sol_fib_rec", "equiv.perm.sign_surjective", "if_false", "bifunctor.fst_comp_fst", "continuous_multilinear_map.uncurry_curry_right", "mul_lt_mul_right'", "filter.tendsto_iff_comap", "int.modeq.gcd_a_modeq", "measurable.const_smul", "max_choice", "polynomial.expand_eq_C", "category_theory.functor.prod_obj", "submodule.restrict_scalars_carrier", "nndist_edist", "list.revzip_map_snd", "continuous_map.coe_continuous", "nhds_within_Icc_eq_nhds_within_Ici", "lt_ceil", "filter.sets_iff_generate", "infi_empty", "uniform_space.completion.dense\:2082", "not_iff_self", "localization_map.map_smul", "add_monoid_hom.map_nat_cast_smul", "fintype.sum_bool", "mem_closure_iff", "inner_product_geometry.norm_sub_square_eq_norm_square_add_norm_square_sub_two_mul_norm_mul_norm_mul_cos_angle", "linear_independent.injective", "continuous_inv", "list.kerase_nodupkeys", "set.zero_nonempty", "abs_by_cases", "ring.fractional_ideal.coe_map", "nat.mkpair_unpair'", "and_iff_left_iff_imp", "ordinal.is_normal.limit_le", "continuous_linear_equiv.of_bijective_apply_symm_apply", "frobenius_mul", "palindrome.of_reverse_eq", "finset.nonempty_of_sum_ne_zero", "fin.coe_one'", "set.preimage_add_const_Ici", "measure_theory.outer_measure.is_left_invariant_of_content", "turing.to_partrec.code.exists_code.comp", "iff_eq_eq", "filter.Ioi_mem_at_top", "card_eq_card_quotient_mul_card_subgroup", "div_eq_one_iff_eq", "complex.rat_cast_im", "rat.cast_commute", "times_cont_diff.prod", "polynomial.roots_list_prod", "metric.diam_pair", "category_theory.iso_whisker_left_inv", "vector.mmap_cons", "infi_const", "has_deriv_at.comp_has_deriv_within_at", "equiv.swap_inv", "euclidean_geometry.dist_square_eq_dist_square_add_dist_square_iff_angle_eq_pi_div_two", "pnat.add_coe", "monotone_Sup_of_monotone", "rel_embedding.map_inf_le", "game.le_trans", "free_monoid.hom_map_lift", "supr_sigma", "submonoid.localization_map.inv_unique", "alist.to_finmap_eq", "padic_int.coe_neg", "char_p.eq", "norm_sum_le", "omega.coeffs_reduce_correct", "nat.pow_lt_pow_of_lt_left", "category_theory.limits.image_mono_iso_source_hom_self", "monoid_hom.coprod_apply", "topological_space.opens.local_homeomorph_subtype_coe_source", "ordinal.le_div", "omega.nat.implies_neg_elim", "ordinal.mul_succ", "lucas_lehmer.s_mod_lt", "int.div_mul_cancel", "filter.ne_bot.comap_of_image_mem", "AddGroup.ext", "local_homeomorph.continuous_at_iff_continuous_at_comp_right", "subtype.preconnected_space", "is_unit.smul_eq_zero", "pow_bit0", "nat.fact_pos", "linear_map.supr_range_std_basis_eq_infi_ker_proj", "dist_edist", "list.chain'_cons'", "nnreal.of_real_of_nonpos", "category_theory.limits.cofork.right_app_one_assoc", "finset.exists_max_image", "ordinal.le_of_mul_le_mul_left", "lt_of_mul_lt_mul_right'", "dif_ctx_simp_congr", "smul_add_hom_apply", "list.modify_nth_tail_modify_nth_tail_same", "free_semigroup.mul_map_seq", "ring_hom.coe_comp", "mul_comm", "measure_theory.measure.restrict_add_restrict_compl", "span_nat_eq", "nat.shiftl_add", "multiset.rec_on_cons", "category_theory.limits.prod.map_snd", "list.mem_keys_kunion", "pythagorean_triple.is_primitive_classified_of_coprime_of_zero_left", "add_submonoid.list_sum_mem", "multiset.erase_subset", "rel_iso.bijective", "cardinal.pow_cast_right", "subalgebra.ext_iff", "int.gcd_eq_right", "list.mem_map_of_mem", "isometry.diam_range", "finset.supr_singleton", "edist_triangle_left", "lie_algebra.orthogonal.is_unit_PB", "equiv.swap_comp_apply", "times_cont_mdiff_iff", "ordinal.mul_lt_mul_of_pos_left", "free_group.red.length", "forall_or_of_or_forall", "polynomial.not_is_unit_X", "set.not_mem_of_mem_compl", "measurable_space.dynkin_system.has_compl_iff", "padic.cast_eq_of_rat_of_int", "equiv.arrow_congr'_trans", "finset.center_mass_filter_ne_zero", "nat.cast_one", "pequiv.eq_some_iff", "finset.prod_bij_ne_one", "pell.pell_zd_succ", "set.interval_subset_interval_iff_le", "polynomial.card_roots", "pgame.impartial.add_self", "nnreal.geom_mean_le_arith_mean_weighted", "zsqrtd.coe_int_add", "circle_deg1_lift.tendsto_translation_number_aux", "zmod.val_one_eq_one_mod", "finset.singleton_disjoint", "has_strict_fderiv_at.of_local_left_inverse", "sub_self_div_two", "le_of_not_lt", "polynomial.finset_sum_coeff", "list.nil_suffix", "le_neg", "filter.tendsto.neg", "complex.cpow_eq_pow", "category_theory.iso.symm_self_id", "tendsto_inf_principal_nhds_iff_of_forall_eq", "subgroup.coe_mul", "add_commute.units_of_coe", "ordinal.deriv_is_normal", "continuous_within_at.mem_closure_image", "real.sqrt_le_sqrt", "is_compl.of_eq", "inv_mul_cancel_right'", "matrix.to_lin_neg", "is_extr_filter.comp_antimono", "finset.singleton_ne_empty", "function.mem_pts_of_period", "pth_root_eq_iff", "euclidean_domain.xgcd_aux_P", "list.length_erase_of_mem", "omega.symmod_eq", "finset.eq_of_subset_of_card_le", "zero_scale_roots", "nat.sqrt_aux_2", "finset.image_id", "continuous_multilinear_map.add_apply", "list.take'_left", "finsupp.sum_sub", "list.lookup_kunion_left", "list.Ico.self_empty", "list.subperm.length_le", "euclidean_domain.zero_mod", "has_fderiv_at_filter.const_sub", "le_gfp", "polynomial.coeff_zero", "continuous_linear_map.range_coe", "polynomial.coeff_zero_eq_eval_zero", "ennreal.bit1_ne_zero", "category_theory.functor.hom_pairing_map", "bool.bxor_ff_right", "zero_open_separated_add", "real.lb_le_Inf", "nnreal.rpow_lt_rpow_iff", "category_theory.prod_preserves_connected_limits.\[Gamma]\:2082_app", "turing.TM2to1.add_bottom_nth_snd", "ennreal.tsum_coe_eq", "list.mem_insert_self", "category_theory.iso.hom_congr_comp", "rel_embedding.coe_fn_to_embedding", "uniform_continuous.comp", "category_theory.currying_unit_iso_inv_app_app_app", "multiset.map_pmap", "cau_seq.completion.cau_seq_zero_ne_one", "mv_polynomial.degrees_one", "is_connected.image", "rel_embedding.well_founded_iff_no_descending_seq", "polynomial.separable.of_pow'", "gaussian_int.to_complex_def\:2082", "has_fderiv_at.has_fderiv_within_at", "category_theory.monoidal.right_unitor_inv_app", "with_bot.bot_lt_coe", "filter.comap_lift'_eq", "direct_sum.ext_iff", "emetric.mk_uniformity_basis", "ennreal.top_ne_zero", "add_monoid_algebra.of_apply", "filter.mem_map_seq_iff", "monoid.subset_closure", "matrix.vec_mul_cons", "multiset.singleton_inj", "int.of_add_mul", "eq_inv_of_mul_eq_one", "infinite.of_surjective", "set.image_eq", "pos_num.mod'_to_nat", "nat.fib_pos", "function.injective.summable_iff", "is_local_min.has_fderiv_at_eq_zero", "list.nth_le_map'", "matrix.transpose_one", "asymptotics.is_o_pow_pow", "linear_equiv.to_Module_iso'_hom", "finsupp.emb_domain_zero", "add_submonoid.multiples_subset", "centroid_mem_affine_span_of_cast_card_ne_zero", "set.singleton_zero", "set.preimage_mul_left_one", "is_glb_le_is_lub", "option.some_injective", "ideal.map_quotient_self", "multiset.rel_flip", "pgame.impartial.no_good_right_moves_iff_first_loses", "multiset.subset_zero", "is_closed_map_sigma_mk", "continuous_linear_map.smul_right_norm", "decidable.not_not_iff", "list.mem_ext", "dfinsupp.support_zip_with", "measure_theory.ae_eq_trans", "add_subgroup.ext'_iff", "category_theory.functor.comp_obj", "subspace.coe_prod_equiv_of_closed_compl", "with_zero.some_eq_coe", "set.Union_subset_Union2", "finset.coe_sdiff", "measure_theory.measure.lt_iff'", "set.image_inv_Ioo_0_left", "submodule.forall", "finset.some_mem_insert_none", "mul_semiring_action_hom.coe_fn_coe'", "int.units_eq_one_or", "total_of", "vector_span_image_eq_span_vsub_set_left_ne", "free_group.closure_subset", "list.nodup_iff_nth_le_inj", "div_pos", "metric.Hausdorff_dist_closure\:2082", "list.minimum_cons", "continuous_inv_of_strict_mono_equiv", "finset.exists_intermediate_set", "power_series.map_id", "is_basis_span", "function.support_comp_eq", "real.differentiable_at_exp", "Mod.regular_X", "to_bool_tt", "div_mul_le_div_mul_of_div_le_div", "function.support_supr", "wseq.dropn_of_seq", "set.Ioo_subset_Ioo_left", "measure_theory.integral_empty", "ennreal.summable", "set.union_insert", "composition.eq_ones_iff", "inner_zero_right", "turing.TM2to1.tr_respects", "measure_theory.l1.simple_func.integral_eq_lintegral", "le_supr", "int.neg_of_nat_mul_of_nat", "zmod.coe_to_nat", "finmap.lookup_union_left_of_not_in", "category_theory.preimage_iso_inv", "finsupp.map_range_apply", "option.guard_eq_some", "zero_eq_mul", "ennreal.coe_nat", "equiv.to_pequiv_trans", "le_of_sub_nonneg", "norm_num.int_cast_bit0", "category_theory.limits.image.\[Iota]_zero'", "generalized_continued_fraction.squash_seq_eq_self_of_terminated", "continuous_multilinear_map.map_piecewise_smul", "turing.tape.mk'_left_right\:2080", "circle_deg1_lift.iterate_mono", "lower_bounds_singleton", "add_monoid_algebra.mul_single_zero_apply", "comp_le_uniformity", "multiset.subset_erase_dup", "zsqrtd.mul_conj", "subset_comp_self", "free_add_magma.map_add'", "list.index_of_nil", "eq_rec_heq", "power_series.le_order_add", "approximates_linear_on.inj_on", "pnat.lcm_dvd", "is_basis.det_apply", "set.maps_to.coe_restrict_apply", "multiset.subset_of_le", "int.modeq.modeq_and_modeq_iff_modeq_mul", "prod.snd_neg", "linear_equiv.trans_refl", "seq.not_mem_nil", "vector_all_iff_forall", "associated_mul_right_cancel", "multiplicity.finset.prod", "list.nth_of_fn_aux", "set.interval_subset_interval_left", "set.compl_empty_iff", "znum.zneg_zneg", "add_monoid_hom.mclosure_preimage_le", "measure_theory.measure.map_dirac", "category_theory.limits.walking_pair.equiv_bool_apply_left", "nat.prime_def_min_fac", "int.lt.dest", "padic.of_rat_add", "real.rpow_le_one_of_one_le_of_nonpos", "polynomial.splits_of_splits_id", "polynomial.eval_div_by_monic_pow_root_multiplicity_ne_zero", "turing.list_blank.nth_zero", "nat.add_le_add", "linear_map.continuous_iff_is_closed_ker", "category_theory.tensoring_right_monoidal_to_lax_monoidal_functor_\[Mu]_app", "bucket_array.foldl_eq", "cast_heq", "matrix.cons_transpose", "measure_theory.exists_is_measurable_superset_iff_measure_eq_zero", "finset.sdiff_disjoint", "ordinal.typein_enum", "measurable.sub_nnreal", "metric.ball_disjoint_same", "list.map_map", "metric.ball_subset_ball", "set.union_inter_distrib_right", "ideal.map_map", "category_theory.monoidal_category.triangle_assoc_comp_right_inv", "is_extr_filter.filter_inf", "finset.sum_fin_eq_sum_range", "polynomial.nat_degree_C", "nnreal.coe_prod", "list.diff_eq_foldl", "linear_map.fun_left_id", "inv_smul_eq_iff", "mvpfunctor.liftp_iff'", "add_submonoid.localization_map.map_add_right", "times_cont_diff_add", "multiset.revzip_powerset_aux_perm", "zsqrtd.norm_eq_one_iff", "nat.add_mod_eq_add_mod_left", "is_subgroup.mem_norm_comm", "map_Sup_of_continuous_at_of_monotone", "category_theory.functor_to_types.map_inv_map_hom_apply", "int.div_eq_iff_eq_mul_right", "vsub_eq_zero_iff_eq", "list_all_map", "ordinal.fintype_card", "primrec.vector_cons", "list.perm.kunion", "rat.le_refl", "linear_map.comap_le_comap_iff", "computable.option_map", "is_local_min.inf", "real.cos_one_le", "ennreal.inv_pos", "set.image_id'", "submodule.infi_orthogonal", "finmap.disjoint_union_right", "list.forall\:2082_map_left_iff", "set.Ico_inter_Ico", "set.subset_Union", "multiset.count_zero", "lie_act", "set.union_def", "roption.mem_some", "polynomial.X_pow_sub_C_ne_zero", "stream.mem_interleave_right", "multiset.ndinter_eq_inter", "int.to_nat_zero", "int.coe_nat_succ_pos", "category_theory.eq_curry_iff", "measure_theory.outer_measure.trim_add", "finset.sum_range_reflect", "continuous_within_at_univ", "set.Ioc_union_Ioc_right", "mul_lt_mul_of_pos_right", "real.sqrt_two_add_series_succ", "norm_num.from_nat_pow", "mem_perms_of_finset_iff", "tactic.ring.horner_horner", "function.semiconj.commute", "if_congr_prop", "eq_false_of_or_eq_false_left", "polynomial.support_zero", "nonneg_le_nonneg_of_squares_le", "dist_sub_left", "add_monoid_hom.coe_to_real_linear_map", "mul_le_iff_le_one_right'", "set.surj_on.left_inv_on_of_right_inv_on", "list.mem_erase_iff_of_nodup", "subtype.preimage_coe_eq_preimage_coe_iff", "subring.mem_comap", "forall_swap", "filter.mem_map_sets_iff", "is_preirreducible.closure", "int.lt_iff_add_one_le", "has_fderiv_at_filter.sum", "mul_eq_zero_comm", "filter.bind_inf_principal", "finset.Ico.union_consecutive", "equiv.coe_ulift_symm", "primrec.option_get_or_else", "ring_equiv.local_ring", "computation.results.mem", "valuation.supp_quot", "int.nat_abs_gcd", "set.pi_if", "equiv.trans_refl", "list.prod_eq_foldr", "add_units.coe_mk", "nat.one_mul", "filter.prod_infi_left", "con.lift_range", "ennreal.mul_lt_of_lt_div", "function.is_periodic_pt.add", "tendsto_indicator_of_antimono", "typevec.repeat_eq_append1", "mul_action.smul_inv_smul", "filter.realizer.ne_bot_iff", "abs_inner_le_norm", "real.rpow_le_one", "local_equiv.image_eq_target_inter_inv_preimage", "finset.disjoint_left", "free_abelian_group.lift.sub", "is_local_min_on.has_fderiv_within_at_eq_zero", "ideal.ker_le_comap", "category_theory.equivalence.symm_unit_iso", "ordinal.div_le_of_le_mul", "matrix.is_unit_det_of_left_inverse", "subsemiring.closure_sUnion", "nat.coprime.gcd_eq_one", "finset.filter_union_filter_neg_eq", "cardinal.zero_lt_bit1", "mul_lt_mul_left'", "category_theory.limits.kernel.\[Iota]_of_mono", "category_theory.is_iso.hom_inv_id", "nat.primrec'.if_lt", "filter.lift'_bot", "cardinal.mul_eq_left_iff", "Top.stalk_to_fiber_surjective", "metric.mem_closure_range_iff_nat", "subsemiring.closure_le", "measure_theory.lintegral_sub", "ordinal.mul_lt_omega", "finset.prod_eq_one", "Module.monoidal_category.triangle", "separated_iff_t2", "list.mfoldr_with_index_eq_mfoldr_enum", "set.preimage_image_preimage", "set.union_subset_union", "semiquot.map_def", "int.cast_commute", "algebra.mem_top", "real.rpow_def_of_neg", "list.tendsto_cons_iff", "turing.TM2to1.tr_respects_aux\:2082", "nat.exists_most_significant_bit", "cardinal.mk_Union_eq_sum_mk", "quadratic_form.associated_left_inverse", "sym2.rel.symm", "generalized_continued_fraction.squash_seq_nth_of_not_terminated", "times_cont_mdiff_on.continuous_on", "metric.ball_eq_empty_iff_nonpos", "nat.eq_zero_of_mul_le", "differentiable.neg", "is_open_ne", "uniformity_basis_edist_inv_nat", "list.naturality", "monoid_hom.map_closure", "affine.simplex.points_with_circumcenter_eq_circumcenter", "bilin_form.smul_left", "finset.sdiff_sdiff_self_left", "asymptotics.is_o.const_mul_right'", "pow_dvd_pow", "lcm_units_coe_left", "finset.prod_piecewise", "inner_smul_self_left", "linear_pmap.map_add", "strict_mono.mul_const'", "finsupp.filter_sum", "nat.is_unit_iff", "mv_polynomial.map_map", "list.exists_lt_of_sum_lt", "complex.cos_pi", "list.func.get_eq_default_of_le", "smooth_left_add", "pgame.impartial.neg_equiv_self", "emetric.nonempty_compacts.is_closed_in_closeds", "multiset.cons_inj_right", "asymptotics.is_O_with_congr", "is_R_or_C.conj_bit1", "inv_mul_le_left_of_le_mul", "num.add_of_nat", "list.mem_permutations_of_perm_lemma", "multiset.card_add", "wseq.tail_cons", "int.even_sub", "metric.diam_triple", "mul_neg_one", "pnat.xgcd_type.flip_y", "norm_image_sub_le_of_norm_deriv_le_segment'", "irrational.mul_cases", "int.normalize_coe_nat", "ennreal.mul_supr", "list.perm.union", "surreal.not_le", "midpoint_def", "continued_fraction.coe_to_simple_continued_fraction", "set.left_inv_on.congr_left", "ordinal.dvd_zero", "snum.bit_one", "has_le.le.ge", "submodule.mem_supr_of_directed", "set.subset_preimage_univ", "list.lex.not_nil_right", "multiset.mem_filter", "cardinal.mk_int", "mdifferentiable_on_of_locally_mdifferentiable_on", "num.lt_to_nat", "finsupp.nat_sub_apply", "add_monoid_hom.map_range", "cardinal.one_power", "padic_val_rat.finite_int_prime_iff", "emetric.uniformity_has_countable_basis", "normed_field.continuous_on_inv", "category_theory.non_preadditive_abelian.neg_neg", "finset.fold_insert", "polynomial.alg_hom_eval\:2082_algebra_map", "finset.weighted_vsub_apply", "list.rel_foldl", "complex.uniform_continuous_mul", "list.length_permutations_aux2", "finset.prod_image", "rat.mul_comm", "list.take'_length", "list.func.length_sub", "add_con.refl", "turing.TM2to1.tr_normal_run", "units.coe_lt_coe", "group_separation_rel", "rat.mul_add", "real.arccos_le_pi", "monoid_hom.map_eq_zero", "prime_spectrum.zero_locus_Union", "seq.of_list_nil", "writer_t.goto_mk_label", "finsupp.prod_map_domain_index", "measure_theory.simple_func.mem_range_self", "list.disjoint_of_subset_left", "padic_val_rat.one", "computable.comp", "lucas_lehmer.X.add_snd", "ideal.bot_prime", "hash_map.valid.replace_aux", "linear_equiv.refl_trans", "monotone.is_lub_image_le", "localization_map.eq_iff_eq", "filter.is_countably_generated_binfi_principal", "option.none_bind", "dvd_zero", "deriv_within_cosh", "submodule.quot_hom_ext", "subring.Inf_to_add_subgroup", "continuous_sub", "direction_affine_span", "emetric.mem_ball_comm", "list.countp_cons_of_neg", "int.bodd_neg_of_nat", "neg_le_iff_add_nonneg", "le_add_of_nonneg_left", "is_scalar_tower.to_alg_hom_apply", "div_eq_div_iff", "finite_dimensional.eq_top_of_findim_eq", "nhds_eq_nhds_iff", "list.func.get_neg", "Class.inter_hom", "cardinal.mk_list_eq_mk", "multiset.filter_union", "computable_pred.halting_problem", "tactic.ring_exp.exp_to_prod_pf", "nnreal.mul_div_cancel'", "ideal.mem_image_of_mem_map_of_surjective", "nat.gcd_gcd_self_left_left", "alist.ext", "int.to_nat_add_one", "category_theory.functor.equiv_functor_obj", "linear_map.dom_restrict_apply", "ring_hom.map_sclosure", "cardinal.le_mk_iff_exists_set", "mem_affine_span_iff_mem_of_affine_independent", "cluster_pt.of_inf_left", "measure_theory.l1.simple_func.norm_to_simple_func", "matrix.map_mul", "is_compl.le_right_iff", "nat.psub_eq_none", "ordinal.add_left_cancel", "list.inter_subset_left", "equiv.trans_to_embedding", "linear_map.map_coe_ker", "ring.direct_limit.of.zero_exact_aux", "continuous_linear_map.op_norm_nonneg", "function.support_prod_subset", "set.image_compl_subset", "set.inter_union_distrib_left", "is_bounded_bilinear_map.differentiable", "nat.mul_eq_one_iff", "polynomial.separable_one", "composition.ones_blocks", "is_basis.equiv_fun_total", "Module.Mon_Module_equivalence_Algebra.inverse_obj_X", "finset.fold_sup_bot_singleton", "is_basis.injective", "category_theory.quotient.comp_left", "finset.prod_bij'", "equiv.set.image_apply", "generalized_continued_fraction.convergents_stable_of_terminated", "setoid.eqv_classes_of_disjoint_union", "polynomial.of_irreducible_expand_pow", "polynomial.coeff_mul_monomial_zero", "setoid.eq_iff_classes_eq", "category_theory.limits.biprod.inl_fst_assoc", "finsupp.support_sup", "cau_seq.bounded", "Ico_mem_nhds_within_Iic", "category_theory.is_iso.inv_hom_id_assoc", "encodable.mem_decode2", "module.End.eigenspace_div", "option.ball_ne_none", "is_glb_of_is_lub_of_tendsto", "int.modeq.modeq_add_fac", "finset.sum_comp", "measure_theory.l1.integral_sub", "list.sublists_aux_cons_append", "category_theory.limits.types.prod_lift", "set.countable_iff_exists_surjective_to_subtype", "set.Ioo_self", "category_theory.monoidal.associator_hom_app", "max_le_max", "add_subgroup.normal_of_comm", "measure_theory.l1.simple_func.smul_to_simple_func", "fin.coe_add_nat", "finsupp.total_comp", "primrec_pred.of_eq", "category_theory.limits.is_image.iso_ext_inv", "matrix.diagonal_one", "isometric.point_reflection_dist_self", "list.nth_eq_some", "measure_theory.simple_func.coe_const", "nat.factors_lemma", "nat.partrec'.nil", "bool.not_ff", "uniform_space.completion.coe_zero", "measure_theory.measure.restrict\:2097_apply", "dvd_sub_pow_of_dvd_sub", "linear_map.curry_uncurry_left", "primrec.list_foldl", "list.count_singleton", "metric.closed_ball_diff_sphere", "lt_mul_of_inv_mul_lt", "mvqpf.fix.ind_aux", "approximates_linear_on.continuous_on", "ideal.span_singleton_eq_top", "mv_polynomial.pderivative_add", "neg_one_lt_zero", "matrix.cons_vec_mul", "deriv.neg", "filter.tendsto.is_bounded_under_le", "nnreal.le_of_forall_epsilon_le", "metric.to_glue_commute", "linear_equiv.mk_apply", "ceil_pos", "has_deriv_at.of_local_left_inverse", "measure_theory.outer_measure.add_apply", "polynomial.X_dvd_iff", "category_theory.limits.biproduct.\[Iota]_\[Pi]_ne_assoc", "category_theory.comonad_hom.id_comp", "isometric.add_left_symm", "add_localization.r_of_eq", "list.sum_range_succ'", "associates.prod_le", "neg_le_of_neg_le", "polynomial.coeff_coe", "embedding.map_nhds_eq", "lcm_assoc", "stream.mem_cons", "measure_theory.measure.regular.inner_regular_eq", "category_theory.limits.limit.lift_map", "uniform_inducing.dense_inducing", "tendsto_locally_uniformly_on.mono", "category_theory.functor.pi_obj", "alg_equiv.trans_apply", "int.bitwise_or", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_inv_assoc", "is_clopen_diff", "heq.elim", "subsemiring.coe_comap", "homological_complex.homology_map_comp", "complex.equiv_lim_aux", "mul_inv_rev'", "finsupp.smul_apply'", "tendsto_iff_edist_tendsto_0", "differentiable_on.const_smul_algebra", "measure_theory.measure.join_map_map", "measure_theory.outer_measure.Inf_gen_nonempty1", "nat.le_total", "finset.Ico.succ_singleton", "summable.has_sum", "measure_theory.integral_const", "finsupp_lequiv_direct_sum_single", "multiset.le_count_iff_repeat_le", "times_cont_diff_within_at.differentiable_within_at", "filter.germ.quot_mk_eq_coe", "real.cos_nat_mul_two_pi", "metric.inf_edist_ne_top", "pos_num.lt_to_nat", "metric.proper_image_of_proper", "summable.prod_symm", "local_homeomorph.refl_source", "measurable_space.generate_from_le", "category_theory.comma.map_right_id_hom_app_right", "with_bot.well_founded_lt", "true_and", "list.perm_cons_erase", "int.lt_of_add_one_le", "category_theory.types_comp", "uniform_space.completion.map_id", "topological_space.open_nhds.op_map_id_obj", "bool.bxor_comm", "filter.mem_prod_same_iff", "summable_geometric_of_lt_1", "algebraic_geometry.SheafedSpace.comp_base", "set.finite_univ", "subsemiring.map_map", "filter.is_bounded_le_of_top", "is_open.unique_mdiff_on", "finset.disjoint_empty_left", "multiset.add_product", "has_fpower_series_on_ball.sub", "ideal.map_sup", "semiquot.pure_is_pure", "emetric.tendsto_uniformly_iff", "filter.prod_bot", "preorder_hom.coe_inj", "local_ring.eq_maximal_ideal", "has_fderiv_at_filter.sub", "contracting_with.apriori_edist_iterate_efixed_point_le'", "ennreal.mul_lt_mul_left", "nat.lcm_dvd", "pell.is_pell_pell_zd", "nat.prime.ne_one", "eq_bot_iff", "multiset.Ico.nodup", "option.bind_eq_none'", "measurable.dist", "int.coe_cast_ring_hom", "dvd_add_self_left", "one_div_fpow", "finset.insert_val'", "complex.deriv_cos'", "zsqrtd.nonnegg_pos_neg", "set.bUnion_singleton", "polynomial.degree_to_subring", "fintype.card_pempty", "polynomial.irreducible_of_degree_eq_one_of_monic", "set.maps_to_image", "tsum_eq_zero_add", "filter.eventually_eq.exists_mem", "omega.int.univ_close_of_valid", "map_eq_bind_pure_comp", "is_add_group_hom.zero_ker_neg'", "padic_norm_z.norm_p_pow", "asymptotics.is_O_norm_left", "multiset.mem_union", "nat.lt_le_antisymm", "nhds_translation_add_neg", "many_one_degree.of_le_of", "int.sub_right_le_of_le_add", "algebraic_geometry.LocallyRingedSpace.comp_val", "computable\:2082.part", "filter.is_bounded.is_bounded_under", "eq.ge", "nat.exists_dvd_of_not_prime", "differentiable_within_at.add", "times_cont_diff_fst", "has_fderiv_at_boundary_of_tendsto_fderiv", "znum.of_nat_cast", "padic.coe_inj", "int.mul_le_mul_of_nonneg_right", "padic_norm_z.norm_one", "int.of_nat_div", "category_theory.monoidal_category.right_assoc_tensor_obj", "int.dist_eq", "zmod.cast_nat_cast'", "free_abelian_group.pure_seq", "metric.glue_dist_glued_points", "int.add_mul_mod_self_left", "multiset.exists_mem_of_ne_zero", "znum.to_int_inj", "forall_prop_of_true", "abs_nonpos_iff", "exists_ratio_has_deriv_at_eq_ratio_slope'", "pgame.zero_le", "half_pos", "interval_integral.integral_sub_linear_is_o_of_tendsto_ae", "linear_map.mk_continuous_norm_le", "finset.Ico.zero_bot", "ordinal.log_def", "list.reverse_cons", "tactic.ring.horner_mul_horner_zero", "multiset.sum_map_mul_left", "measure_theory.measure.coe_zero", "asymptotics.is_O_with.add", "pow_ne_zero'", "div_pos_of_neg_of_neg", "prod.smul_mk", "is_min_filter.comp_mono", "measure_theory.integrable.smul", "equiv.subtype_equiv_codomain_apply", "bounded_continuous_function.uniform_continuous_comp", "mul_nonpos_of_nonpos_of_nonneg", "category_theory.limits.mono_factorisation.ext", "ordinal.nat_cast_succ", "alg_hom.map_add", "ordinal.mul_ne_zero", "ordinal.add_succ", "primrec\:2082.uncurry", "padic_int.coe_sub", "submodule.mem_span_insert", "category_theory.over.map_map_left", "is_max_on.add", "summable_iff_cauchy_seq_finset", "is_basis.smul", "measure_theory.tendsto_integral_of_dominated_convergence", "sum.lex_acc_inr", "bounded_continuous_function.sub_apply", "is_coprime.add_mul_left_right_iff", "commute.gpow_gpow_self", "sylow.one_mem_fixed_points_rotate", "ennreal.is_open_ne_top", "prime_spectrum.mem_vanishing_ideal", "differentiable_within_at.has_deriv_within_at", "wseq.lift_rel.swap_lem", "algebra.lmul'_apply", "num.le_iff_cmp", "fin.succ_above_below", "measure_theory.measure.measurable_of_measurable_coe", "zsqrtd.of_int_re", "lie_algebra.equiv.one_apply", "cardinal.prod_ne_zero", "nat.max_succ_succ", "rat.lt_one_iff_num_lt_denom", "real.uniform_continuous_neg", "complex.of_real_inj", "cInf_mem_closure", "filter.mem_bind_sets", "vadd_vsub_vadd_cancel_right", "dist_neg_neg", "finset.bind_singleton", "filter.eventually_eq.deriv_within_eq", "finset.compl_eq_univ_sdiff", "list.drop_sum_join", "rat.cast_sub_of_ne_zero", "le_sup_left_of_le", "commute.units_inv_left", "equiv.forall_congr'", "is_R_or_C.im_le_abs", "gt_mem_nhds", "is_subgroup.coe_gpow", "multiset.sub_add_inter", "quot.exact", "inf_infi", "nnreal.rpow_add", "finset.sdiff_subset_self", "num.succ_to_nat", "is_compl.sup_eq_top", "metric.ball_half_subset", "multiset.count_eq_one_of_mem", "galois_insertion.l_infi_of_ul_eq_self", "ge.le", "finset.min_insert", "category_theory.differential_object.comp_f", "num.cast_zero", "filter.map_eq_of_inverse", "finset.sum_subtype_map_embedding", "wseq.dropn_nil", "multiset.inter_eq_zero_iff_disjoint", "multiset.attach_map_val", "computation.get_eq_of_promises", "cardinal.aleph'_zero", "fin.mem_find_iff", "asymptotics.is_o.const_mul_right", "int.add_assoc", "set.pairwise_on.mono", "list.not_mem_keys", "discrete_valuation_ring.aux_pid_of_ufd_of_unique_irreducible", "ordinal.sup_le", "linear_map.ker_eq_bot_iff_range_eq_top", "free_ring.coe_one", "zero_fpow", "typevec.append_fun_comp", "nhds_translation_mul_inv", "stream.nth_even", "has_sum_geometric_two", "filter.comap_add_comap_le", "pmf.map_id", "times_cont_diff_on.of_le", "is_valid_char_range_2", "free_abelian_group.lift.zero", "measure_theory.lintegral_smul_measure", "ennreal.tsum_sigma", "abs_inner_div_norm_mul_norm_le_one", "set.preimage_mul_const_Ico", "submodule.quotient_equiv_of_is_compl_apply_mk_coe", "congr_arg2", "filter.has_basis.le_basis_iff", "multiset.coe_bind", "measure_theory.measure_eq_infi", "zsqrtd.nonneg_mul_lem", "semidirect_product.inl_injective", "matrix.special_linear_group.mul_apply", "affine_independent_iff_indicator_eq_of_affine_combination_eq", "finset.sum_div", "sylow.mem_vectors_prod_eq_one", "geom_lt", "filter.comap_inf_principal_ne_bot_of_image_mem", "filter.germ.coe_neg", "multiset.join_zero", "category_theory.limits.prod_comparison_natural_assoc", "wseq.exists_of_mem_bind", "ideal.span_mono", "matrix.std_basis_eq_basis_mul_basis", "subtype.image_preimage_val", "category_theory.limits.limit.cone_morphism_\[Pi]", "function.is_fixed_pt.eq", "nat.mul_div_cancel_left'", "pos_num.cast_to_int", "measure_theory.simple_func.fin_meas_supp.lintegral_lt_top", "multiplicative.is_group_hom", "add_submonoid.localization_map.of_add_equiv_of_dom_apply", "unique.forall_iff", "linear_map.bound_of_continuous", "int.lt_add_one_iff", "emetric.ball_zero", "category_theory.limits.as_factor_thru_image", "multiset.disjoint_cons_right", "bex_congr", "encodable.axiom_of_choice", "vector.ext", "auto.not_not_eq", "local_homeomorph.symm_target", "set.mem_bInter_iff", "rel.image_subset_iff", "tendsto_one_div_add_at_top_nhds_0_nat", "ennreal.Ico_eq_Iio", "is_conj_symm", "semiconj_by.units_coe", "times_cont_diff_top", "set.preimage_const_mul_Ioi", "polynomial.coe_norm_unit", "category_theory.adjunction.eq_hom_equiv_apply", "nnreal.inv_inv", "set.diff_empty", "units.inv_mul", "complex.continuous_linear_map.of_real_norm", "set.nonempty.inl", "topological_space.opens.map_comp_obj_unop", "array.read_map\:2082", "continuous_linear_map.norm_map_tail_le", "set.mem_Ioo", "differentiable_at.comp", "gaussian_int.nat_cast_real_norm", "set.finite.image2", "submodule.add_mem", "sesq_form.smul_right", "subsemiring.top_prod_top", "nat.lor_assoc", "int.le_of_sub_nonpos", "ennreal.coe_le_one_iff", "list.nth_le_index_of", "set.singleton_add", "set.pairwise_on_univ", "frobenius_sub", "left_coset_mem_left_coset", "le_sub", "fpow_le_one_of_nonpos", "has_deriv_within_at.pow", "reader_t.run_read", "metric.ball_disjoint", "rat.cast_inv_of_ne_zero", "fpow_neg_one", "category_theory.limits.nonzero_image_of_nonzero", "finsupp.supr_lsingle_range", "polynomial.roots_map", "smul_mul'", "ennreal.rpow_eq_top_iff", "enat.coe_one", "list.subset_append_of_subset_right", "primrec.of_nat_iff", "real.log_lt_log_iff", "local_equiv.restr_coe_symm", "dense_Inter_of_G\[Delta]", "smooth_at_snd", "punit.mul_eq", "is_coprime.pow", "set.card_fintype_insert'", "units.mul_left_symm", "ennreal.coe_nnreal_eq", "sub_left_le_of_le_add", "int.exists_gcd_one'", "is_bounded_bilinear_map.is_bounded_linear_map_right", "holor_index.cast_type", "padic_seq.norm_one", "measure_theory.integrable_on.mono_set_ae", "nat.fact_eq_one", "multiset.erase_le_erase", "nnreal.one_div_div", "real.arcsin_neg_one", "multiset.fold_cons'_left", "set.image_insert_eq", "category_theory.limits.cocones.functoriality_map_hom", "finset.sigma_mono", "ring.direct_limit.lift_unique", "category_theory.monad.forget_creates_limits.lifted_cone_is_limit_lift_f", "max_comm", "mul_semiring_action_hom.ext", "nat.div_pos", "filter.disjoint_iff", "compact_range", "bdd_above_insert", "mv_power_series.coeff_trunc", 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"list.forall\:2082_cons", "ring_equiv.map_add", "add_monoid_hom.eq_on_neg", "alist.keys_singleton", "filter.rmap_compose", "algebra.commutes", "set.image_preimage_eq", "lt_iff_not_ge", "cardinal.mk_cardinal", "continuous_linear_map.coe_sub", "dist_triangle4_left", "list.drop_add", "filter.has_basis_binfi_principal", "add_le_of_le_neg_add", "ideal.mul_left_self_sup", "finset.range_succ", "nat.find_greatest_eq_zero", "category_theory.limits.cocone.extend_\[Iota]", "tendsto_add_one_pow_at_top_at_top_of_pos", "pgame.numeric_neg", "equiv.add_right_symm", "inv_mul_cancel_of_invertible", "is_add_group_hom.mk'", "cau_seq.const_inj", "lucas_lehmer.int.coe_nat_pow_pred", "Set.mem_prod", "list.nth_le_range", "nontrivial_iff", "enorm.map_sub_rev", "wseq.lift_rel_cons", "submonoid.localization_map.lift_left_inverse", "nat.find_min'", "ordinal.not_zero_is_limit", "cardinal.powerlt_le", "con.ker_rel", "pfunctor.id_map", "lie_algebra.special_linear.E_diag_zero", "rel_iso.coe_coe_fn", 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"nat.sub_min", "Module.Mon_Module_equivalence_Algebra.ring_zero", "finset.mem_pi", "asymptotics.is_O_one_of_tendsto", "quadratic_form.associated_is_sym", "asymptotics.is_O_with_self_const_mul", "local_homeomorph.mdifferentiable.mdifferentiable_at_symm", "algebra.adjoin_eq_ring_closure", "finsupp.total_comap_domain", "nat.le_rec_on_self", "category_theory.epi_from_simple_zero_of_not_iso", "submonoid.ext'_iff", "dim_add_dim_split", "Hausdorffification.lift_comp_of", "monoid_hom.map_list_prod", "submonoid.localization_map.ext_iff", "fderiv_smul_const", "add_subgroup.gmultiples_eq_closure", "list.enum_map_snd", "set.preimage_bUnion", "emetric.complete_of_cauchy_seq_tendsto", "with_top.coe_inf", "set.image_pair", "mv_polynomial.ne_zero_iff", "measure_theory.lintegral_nnnorm_zero", "matrix.mul_vec_empty", "set.monotone_prod", "infi_and'", "local_homeomorph.is_o_congr", "list.minimum_eq_coe_iff", "sub_sub", "irrational.rat_mul", "list.forall\:2082.imp", "polynomial.degree_sub_lt", 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"continuous_linear_map.equiv_prod_of_surjective_of_is_compl_to_linear_equiv", "decidable.le_imp_le_of_lt_imp_lt", "turing.partrec_to_TM2.tr_list_ne_Cons", "set.Icc_subset_interval'", "is_add_monoid_hom.map_nsmul", "set.Inter_neg", "ideal.mem_comap", "times_cont_mdiff_at.of_succ", "eq_true_intro", "interval_integral.integral_has_fderiv_at", "free_add_semigroup.add_map_seq", "gpow_zero", "alist.union_entries", "multiset.not_nodup_pair", "generalized_continued_fraction.nth_of_eq_some_of_succ_nth_int_fract_pair_stream", "finset.erase_subset_erase", "list.mem_erase_dup", "list.subperm_cons", "is_irreducible_singleton", "int.shiftr_neg", "turing.TM1.stmts\:2081_self", "bitraversable.tsnd_tfst", "bitvec.of_fin_le_of_fin_of_le", "gsmul_mul'", "set.preimage_neg_Iio", "list.reverse_inj", "continuous_linear_map.mul_apply", "turing.reaches\:2081.to\:2080", "list.lookmap_none", "ordinal.is_normal.lt_iff", "simple_graph.mul_adj_matrix_apply", "subsemiring.coe_Inf", "category_theory.prod.fst_map", "monoid_algebra.lift_apply", "int.one_mul", "mul_left_cancel", "complex.abs_zero", "int.sub_le_of_sub_le", "affine.simplex.circumcenter_circumradius_unique_dist_eq", "real.pi_upper_bound_start", "measure_theory.is_right_invariant_conj", "set.ord_connected.dual", "polynomial.pow_root_multiplicity_dvd", "function.cSup_div_semiconj", "real.has_deriv_at_log", "dec_em", "infi_Prop_eq", "subring.coe_comap", "set.inter_subset", "nine_dvd_iff", "continuous_finset_prod", "deriv_within_id", "ring.mem_closure", "nat.eq_of_dist_eq_zero", "subset_comp_self_of_mem_uniformity", "filter.ultrafilter.eq_iff_val_le_val", "finmap.lookup_erase_ne", "eq_one_of_mul_self_right_cancel", "power_series.order_zero", "emetric.nhds_basis_closed_eball", "omega.nat.univ_close_of_unsat_neg_elim_not", "implicit_function_data.prod_fun_apply", "unique_diff_within_at_inter", "convex_on_const", "subring.subset_closure", "differentiable_within_at.restrict_scalars", "punit.le", "cardinal.nat_cast_pow", "edist_le_zero", "ring.fractional_ideal.map_id", "submodule.quotient.mk_eq_zero", "ring_equiv.map_neg_one", "computable.vector_of_fn'", "decidable.not_forall_not", "measurable_of_measurable_union_cover", "enat.with_top_equiv_zero", "category_theory.kernel_zero_of_nonzero_from_simple", "Top.id_app", "mul_aut.one_def", "times_cont_diff_within_at.sum", "nat.lcm_zero_right", "omega.pred_mono_2", "category_theory.mono_to_simple_zero_of_not_iso", "measurable.comp", "list.sublist_append_of_sublist_left", "multiset.induction", "uniform_embedding_translate", "ring.is_noetherian_of_zero_eq_one", "filter.tendsto_add_at_top_iff_nat", "has_deriv_at.sinh", "of_digits_zmod", "cardinal.zero_le", "multiset.add_sub_cancel", "rat.mul_denom_eq_num", "differentiable_within_at.log", "punit.Inf_eq", "multiplicity.finite_nat_iff", "function.update_comm", "nhds_bot", "dense_inducing.self_sub_closure_image_preimage_of_open", "list.perm_nodupkeys", "pell.xn_succ_succ", "tangent_map_within_id", "real.uniform_continuous_abs", "category_theory.action_category.\[Pi]_obj", "category_theory.equivalence.pow_minus_one", "nat.dvd_add", "multiset.sum_eq_foldr", "fintype.exists_univ_list", "finset.abs_sum_le_sum_abs", "list.length_rotate", "subsingleton.is_measurable", "subsemiring.ext'", "not_not", "wseq.nth_of_seq", "linear_map.fst_prod", "local_homeomorph.trans_to_local_equiv", "category_theory.sum.swap_obj_inr", "uniform_space.separation_quotient.map_mk", "category_theory.limits.coprod.braiding_hom", "finset.singleton_nonempty", "int.sub_eq_zero_iff_eq", "multiset.count_bind", "subsemiring.coe_top", "category_theory.limits.lim_map_\[Pi]", "int.land_bit", "add_subgroup.coe_comap", "disjoint_nhds_at_bot", "set.sInter_empty", "ring.direct_limit.polynomial.exists_of", "int.sign_eq_div_abs", "add_submonoid.localization_map.map_left_cancel", "euclidean_geometry.dist_orthogonal_projection_eq_zero_iff", "submodule.eq_top_iff'", "tactic.ring_exp.negate_pf", "ring_hom.not_one_mem_ker", "is_unit_zero_iff", "multiset.rel_eq_refl", "stream.map_const", "disjoin_le", "set.image_Union", "submodule.quotient.mk_add", "measure_theory.l1.simple_func.norm_eq", "discrete_valuation_ring.not_a_field", "pgame.relabel_move_right", "nonneg_of_mul_nonneg_right", "multilinear_map.map_add_univ", "approximates_linear_on.lipschitz", "sub_eq_of_eq_add'", "real.continuous_at_rpow_of_pos", "units.coe_mk0", "equiv.prod_comm_symm", "pos_of_mul_neg_right", "matrix.one_apply_ne", "is_unit.dvd_mul_left", "continued_fraction.coe_to_generalized_continued_fraction", "num.cast_succ'", "dist_le_of_le_geometric_of_tendsto", "mdifferentiable_on_atlas", "divp_eq_iff_mul_eq", "geom_sum_mul_add", "iff_of_eq", "set.preimage_mul_preimage_subset", "distrib_mul_action_hom.coe_fn_coe'", "mv_polynomial.degrees_pow", "convex_iff_forall_pos", "nat.gcd_dvd_right", "tactic.ring2.correctness", "stream.append_approx_drop", "list.eq_nil_of_map_eq_nil", "pos_num.pred'_succ'", "pfunctor.M.corec_unique", "real.exp_eq_one_iff", "measure_theory.ae_eq_fun.comp_to_germ", "polynomial.degree_map_eq_of_leading_coeff_ne_zero", "category_theory.monoidal_category.id_tensor_comp", "eq_inv_of_eq_inv", "direct_sum.to_group_of", "zsqrtd.conj_mul", "fin.mk.inj_iff", "list.cons_perm_iff_perm_erase", "filter.has_basis.lift'", "measure_theory.measure.haar.prehaar_nonneg", "sym2.is_diag_iff_proj_eq", "alg_hom.coe_to_ring_hom", "filter.mem_join_sets", "is_extr_on_dual_iff", "nat.discriminate", "padic_norm_e.zero_def", "continuous_linear_map.comp_assoc", "list.repeat_count_eq_of_count_eq_length", "topological_space.is_open_of_is_topological_basis", "add_submonoid.range_subtype", "inner_product_geometry.angle_eq_zero_iff", "nat.eq_zero_of_double_le", "mem_tangent_cone_of_segment_subset", "div_lt_iff_of_neg'", "contracting_with.dist_fixed_point_le", "mv_polynomial.total_degree_mul", "finset.inf_coe", "fpow_neg_mul_fpow_self", "list.mem_of_mem_inter_left", "ordinal.lift_omega", "nat.bit0_le", "continuous_linear_equiv.coe_coe", "well_founded.recursion", "euclidean_geometry.inner_weighted_vsub", "has_fderiv_within_at_inter'", "euclidean_geometry.dist_reflection_eq_of_mem", "is_add_submonoid.multiple_subset", "category_theory.functor.comp_id", "map_supr_of_continuous_at_of_monotone'", "set.pi_eq_empty", "free_add_magma.lift_unique", "list.permutations_aux2_snd_cons", "mul_inv_cancel", "set.finite.bdd_below", "submodule.one_eq_map_top", "is_connected.union", "linear_map.mk_continuous_coe", "nat.add_lt_add_right", "measure_theory.integral_congr_ae", "nat.size_shiftl'", "int.nat_abs_of_nat_core", "submodule.bot_mul", "digits_aux_def", "add_submonoid.localization_map.of_add_equiv_of_localizations_eq_iff_eq", "dist_vadd_cancel_left", "is_subgroup.mem_norm_comm_iff", "filter.liminf_const", "is_irreducible.is_connected", "finsupp.erase_same", "multiset.cons_inj_left", "ordinal.succ_ne_zero", "category_theory.functor.map_inv_hom", "Set.mem_diff", "filter.infi_principal_fintype", "hyperreal.infinite_pos_add_not_infinite_neg", "uniform_space.completion.coe_eq", "inner_product_geometry.angle_smul_left_of_pos", "set.coe_embedding_of_subset_apply", "list.pairwise_lt_range'", "finsupp.le_iff", "ring_equiv.symm_to_ring_hom_apply_to_ring_hom_apply", "free_group.map.mk", "generalized_continued_fraction.squash_gcf_nth_of_lt", "is_max_filter.sup", "multiplicity.unique'", "category_theory.limits.cocone_left_op_of_cone_\[Iota]_app", "cardinal.aleph'_lt", "le_lfp", "localization_map.lift_comp", "free_abelian_group.map_sub", "continuous_linear_equiv.comp_has_fderiv_within_at_iff", "implicit_function_data.to_local_homeomorph_coe", "polynomial.irreducible_of_degree_eq_one", "nnreal.coe_inv", "magma.free_semigroup.induction_on", "filter.tendsto_at_top_of_monotone_of_filter", "units.mul_right_eq_zero", "bool.bor_assoc", "holor.slice_unit_vec_mul", "measure_theory.integrable.max_zero", "hyperreal.infinite_pos_mul_infinite_pos", "typevec.const_iff_true", "complex.sinh_add", "padic_seq.equiv_zero_of_val_eq_of_equiv_zero", "band_self", "linear_map.uniform_continuous_of_bound", "nnreal.arith_mean_le_rpow_mean", "nat.mul_mod_left", "dfinsupp.smul_apply", "or_eq_of_eq_false_left", "wseq.lift_rel.equiv", "finsupp.erase_single_ne", "nat.prime.multiplicity_le_multiplicity_choose_add", "continuous_at_iff_ultrafilter", "inv_eq_one", "continuous_linear_equiv.antilipschitz", "vsub_right_injective", "alg_equiv.map_sub", "Set.ext_iff", "is_preorder.swap", "measure_theory.integrable_on.indicator", "set.preimage_const_mul_Icc", "stream.head_even", "mv_polynomial.eval_assoc", "lie_group_core.to_topological_group", "times_cont_mdiff_at_iff_times_cont_diff_at", "polynomial.eval\:2082_one", "multiset.to_finset_add", "int.nonpos_of_neg_nonneg", "polynomial.degree_div_X_lt", "category_theory.limits.prod_map_id_id", "lcm_dvd_iff", "matrix_equiv_tensor.right_inv", "exists_exists_and_eq_and", "rat.mk_denom_ne_zero_of_ne_zero", "measure_theory.simple_func.lintegral_add", "polynomial.coe_X", "const_smul_hom_apply", "is_unit_of_map_unit", "local_equiv.trans_self_symm", "measure_theory.simple_func.approx_comp", "ennreal.tendsto.div_const", "list.func.length_set", "padic_norm_z.eq_of_norm_add_lt_right", "embedding.continuous", "int.cast_coe_nat'", "is_closed_map_smul_of_unit", "category_theory.limits.cones.whiskering_equivalence_unit_iso", "measurable_one", "nat.coe_cast_add_monoid_hom", "right_ord_continuous.map_inf", "multiplicative.is_submonoid", "nat.pow_mul", "ennreal.pow_le_pow", "int.coe_nat_inj", "pequiv.bot_apply", "complex.abs_neg", "enat.sup_eq_max", "circle_deg1_lift.translation_number_of_map_pow_eq_add_int", "filter.tendsto_at_top_embedding", "structure_groupoid.id_mem_maximal_atlas", "filter.map_supr", "linear_map.smul_right_apply", "fderiv_within_smul_algebra", "list.disjoint_of_disjoint_cons_right", "list.mem_filter_of_mem", "nat.cast_inj", "lt_add_of_neg_add_lt", "is_compact.bdd_above", "matrix.from_blocks_one", "finset.prod_bind", "category_theory.limits.image.fac_lift_assoc", "mul_div_comm", "continuous_linear_map.comp_smul", "pgame.zero_le_add_left_neg", "prod.snd_zero", "zero_mem_nonunits", "antilipschitz_with.add_lipschitz_with", "differentiable_on_id", "computable.list_of_fn", "asymptotics.is_O_with.trans_le", "mem_nhds_within_iff_exists_mem_nhds_inter", "filter.eventually_eq.is_local_max_on_iff", "function.left_inverse_of_surjective_of_right_inverse", "list.subperm.trans", "pfun.mem_core", "asymptotics.is_O.mono", "neg_sub", "int.nat_abs_bit1_nonneg", "onote.NF_below.mono", "nat.le.dest", "measurable_from_top", "normalize_eq_normalize_iff", "add_submonoid.localization_map.map_eq", "submonoid.localization_map.map_right_cancel", "function.support_subset_iff", "dist_zero_right", "wseq.dropn_think", "measure_theory.extend_Union", "nndist_self", "traversable.length_to_list", "bundle_trivialization.coe_fst", "nat.pow_right_injective", "measure_theory.simple_func.induction", "cauchy_seq_of_controlled", "nat.eq_or_lt_of_le", "finset.sum_erase", "cardinal.lift_inj", "nonempty_subtype", "set.mem_prod", "multiset.prod_map_one", "interval_integral.integral_has_deriv_within_at_of_tendsto_ae_right", "polynomial.coeff_neg", "list.nth_le_singleton", "category_theory.limits.image.fac_assoc", "topological_fiber_bundle_core.mem_local_triv_source", "nat.even_div", "category_theory.concrete_category.hom_ext", "set.sum_indicator_subset", "finite_dimensional.findim_mul_findim", "ring_hom.srange_top_iff_surjective", "con.mul", "tendsto_if_nhds_within", "int.eq_nat_abs_of_zero_le", "finset.prod_empty", "ordinal.card_one", "le_mul_of_le_of_one_le", "rat.cast_round", "measure_theory.simple_func.coe_zero", "pgame.one_left_wins", "nat.gcd_comm", "dense_inducing.continuous_extend", "fixed_points.sup_le_f_of_fixed_points", "finset.exists_pos_of_sum_zero_of_exists_nonzero", "is_unit.ne_zero", "nat.mul_right_inj", "set.mem_Ici", "set.nonempty_Ioc", "zmod.pow_totient", "nat.xgcd_aux_fst", "unique_factorization_domain.irreducible_iff_prime", "list.nodup_range", "nat.dvd_lcm_left", "linear_pmap.Sup_le", "finsupp.mem_support_iff", "list.alternating_prod_nil", "is_unit.mul", "cardinal.bit1_ne_zero", "has_deriv_at_pow", "poly_equiv_tensor.left_inv", "times_cont_diff_groupoid_zero_eq", "generalized_continued_fraction.coe_to_generalized_continued_fraction", "polynomial.eval\:2082_nat_cast", "and_iff_right", "commute.neg_one_left", "continuous_linear_equiv.symm_comp_self", "category_theory.graded_object.comap_equiv_counit_iso", "finset.mem_sdiff", "set.surj_on_Inter", "category_theory.sum.inverse_associator_map_inr_inr", "is_linear_map.map_zero", "stream.mem_map", "finsupp.zero_apply", "measurable_space.map_top", "local_equiv.symm_source", "set.preimage_mul_const_Icc", "is_measurable.const", "ideal.map_comap_of_surjective", "differentiable_pow", "mul_le_of_le_of_le_one'", "filter.eventually_of_forall", "ideal.mem_radical_of_pow_mem", "has_fderiv_within_at.sub", "affine_map.coe_mk", "set.Ioo_union_Ico_eq_Ioo", "metric.nhds_basis_closed_ball", "list.perm_of_mem_permutations", "semilattice_sup.ext_sup", "nat.gcd_mul_left_right", "category_theory.limits.coprod.desc_comp_comp", "setoid.eqv_gen_idem", "associates.eq_of_mul_eq_mul_left", "linear_equiv.of_submodules_apply", "pos_div_pow_pos", "lipschitz_with.mk_one", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_obj_one_app", "pfun.preimage_inter", "ennreal.mem_Iio_self_add", "multiplicity.finite_def", "nnreal.coe_eq_zero", "differentiable_on_congr", "add_monoid_hom.mrange_top_iff_surjective", "nat.exists_dvd_of_not_prime2", "sum_le_tsum", "set.ord_connected_empty", "category_theory.prod_id", "function.injective.ne_iff", "nat.le_sqrt", "complex.sinh_mul_I", "complex.abs_abs_sub_le_abs_sub", "composition_as_set.blocks_sum", "ideal.pow_le_pow", "list.filter_sublist", "category_theory.monoidal.Mon_functor_category_equivalence.inverse_obj_X_obj", "algebra.gc", "add_localization.add_equiv_of_quotient_symm_mk", "local_equiv.symm_symm", "finsupp.sum_finset_sum_index", "measure_theory.integrable_at_filter.eventually", "filter.binfi_sup_left", "neg_of_mul_neg_left", "basic_smooth_bundle_core.chart_source", "category_theory.arrow.lift.fac_right", "finset.case_strong_induction_on", "tensor_product.lid_tmul", "abs_of_nonneg", "measure_theory.l1.integrable", "ordinal.zero_div", "gfp_le", "uniform_embedding_set_inclusion", "local_homeomorph.right_inv", "seq.mem_map", "is_connected.Icc_subset", "continuous_multilinear_map.ratio_le_op_norm", "lucas_lehmer.X.bit1_fst", "uniform_space.uniform_continuous_quotient", "nat.gcd_dvd_gcd_of_dvd_right", "list.tfae_singleton", "filter.tendsto_at_bot_of_monotone_of_subseq", "subgroup.coe_pow", "category_theory.limits.cocone_left_op_of_cone_X", "measurable_space.generate_from_le_iff", "turing.TM0to1.tr_respects", "free_group.red.step.bnot_rev", "Kuratowski_embedding.isometry", "subsemiring.map_bot", "multiset.union_le_iff", "multiset.lt_iff_cons_le", "complex.continuous_cosh", "free_semigroup.lift_unique", "finset.fold_empty", "linear_map.llcomp_apply", "ultrafilter_pure_injective", "ordinal.div_aux", "rat.continuous_mul", "primrec.sum_inl", "list.perm.diff_right", "smooth_on.add", "multiset.filter_map_zero", "list.insert_nth_nil", "category_theory.Monad.to_of_mon_end_iso_hom_app_to_nat_trans_app", "one_le_div", "real.sqrt_eq_zero", "filter.tendsto_iff_eventually", "nndist_nnnorm_nnnorm_le", "computation.lift_rel_mem_cases", "add_subgroup.center_normal", "perfect_closure.eq_iff", "is_lub.insert", "partrec.option_cases_right", "affine_map.coe_smul", "int.lt_add_of_sub_right_lt", "set.sUnion_union", "pnat.le_of_dvd", "multiplicity.eq_top_iff_not_finite", "differentiable_within_at.snd", "measure_theory.is_right_invariant_conj'", "is_partial_order.swap", "le_supr_iff", "mul_lt_iff_lt_one_right'", "finset.card_range", "times_cont_diff_on_iff_continuous_on_differentiable_on", "differentiable_at.pow", "finset.card_le_one_iff", "fact.pow.pos", "set.mem_zero", "category_theory.whiskering_left_map_app_app", "finset.sum_Ico_add", "real.one_le_rpow", "pgame.impartial.winner_cases", "finsupp.lsum_single", "list.append_assoc", "nat.land_comm", "stream.tail_eq_drop", "category_theory.limits.cokernel_iso_of_eq_refl", "finsupp.total_emb_domain", "submodule.fg_mul", "set.indicator_comp_of_zero", "nat.succ_ne_self", "norm_le_gronwall_bound_of_norm_deriv_right_le", "nsmul_neg_comm", "implicit_function_data.implicit_function_has_strict_fderiv_at", "set.enumerate_inj", "uniformity_lift_le_swap", "ring_hom.map_sum", "measure_theory.outer_measure.f_Union", "pgame.nonmoves_nonempty", "rel_iso.mul_apply", "frobenius_one", "seq.map_cons", "image_norm_le_of_norm_deriv_right_lt_deriv_boundary'", "neg_square", "add_monoid_hom.map_exists_left_neg", "list.of_fn_succ", "unique_diff_on_Ioo", "local_homeomorph.of_set_target", "map_lift_comp_preserves_products_iso_hom", "local_equiv.eq_on_source.eq_on", "measurable.nnreal_of_real", "bitraversable.tsnd_eq_snd_id", "matrix.adjugate_apply", "mv_polynomial.eval_prod", "neg_inv", "is_scalar_tower.restrict_base_apply", "is_Z_bilin.tendsto_zero_right", "complex.abs_exp_sub_one_sub_id_le", "sesq_form.ortho_zero", "function.commute.iterate_iterate_self", "omega.int.unsat_of_clauses_unsat", "norm_nonneg", "power_series.coeff_zero_X", "category_theory.abelian.app_hom", "fderiv_within_const_apply", "ordinal.mul_lt_omega_power", "local_equiv.symm_target", "real.continuous.inv", "has_deriv_within_at.iterate", "metric.mem_closure_iff_inf_dist_zero", "lt_inf_iff", "function.involutive.bijective", "cardinal.mk_union_of_disjoint", "ordinal.pred_lt_iff_is_succ", "category_theory.comonad_hom.ext", "subring.list_prod_mem", "isometric.symm_symm", "list.reverse_concat", "linear_map.comp_der_apply", "adjoin_root.lift_comp_of", "segment_translate_preimage", "not_not_intro", "int.le_of_add_le_add_left", "nat.mod_two_ne_one", "isometric.point_reflection_apply", "neg_lt_neg_iff", "not_iff_not_of_iff", "list.maximum_cons", "module.End.ker_eval\:2082_ring_hom_noncomm_unit_polynomial", "fixed_points.Sup_le_f_of_fixed_points", "category_theory.limits.is_colimit.of_nat_iso.hom_of_cocone_of_hom", "free_abelian_group.of_one", "convex_on_real_of_slope_mono_adjacent", "category_theory.functor_to_types.comp", "linear_pmap.sup_apply", "subsemiring.coe_one", "set.image_sub_const_Ioo", "finset.Ico.filter_le_of_le_bot", "list.rel_join", "category_theory.monoidal.functor_category.tensor_hom_app", "num.of_nat'_eq", "set.image_sub_const_Iio", "pequiv.symm_symm", "real.rpow_lt_rpow_of_exponent_lt", "submodule.smul_mem_span_smul_of_mem", "real.bounded_iff_bdd_below_bdd_above", "submodule.span_univ", "convex_cone.salient_of_positive_cone", "list.perm.mem_iff", "continuous_linear_map.coe_coe", "neg_ne_zero", "decidable.em", "monoid_hom.comp_apply", "galois_connection.u_infi", "set.image2_congr'", "decidable.not_forall", "inner_product_geometry.angle_neg_self_of_nonzero", "category_theory.currying_functor_map_app", "measure_theory.l1.simple_func.integral_eq_norm_pos_part_sub", "set.inter_def", "pnat.gcd_det_eq", "filter.has_basis.prod'", "filter.limsup_eq", "is_closed_sigma_iff", "formal_multilinear_series.id_apply_one", "subring.coe_inf", "asymptotics.is_O.mul_is_o", "polynomial.C_neg", "complex.norm_nat", "pfunctor.approx.truncate_eq_of_agree", "cardinal.bit0_lt_bit0", "nat.subtype.succ_le_of_lt", "measure_theory.measure.conj_apply", "list.not_nodup_pair", "composition_as_set.length_lt_card_boundaries", "list.perm_append_comm", "exists_dual_vector'", "submonoid.localization_map.mul_equiv_of_localizations_symm_eq_mul_equiv_of_localizations", "punit_eq", "lagrange.eq_of_eval_eq", "dist_le_of_approx_trajectories_ODE_of_mem_set", "fin.comp_init", "semiconj_by.inv_symm_left_iff", "set.image2_left", "inv_lt_zero", "linear_map.comp_coe", "encodable.encode_prod_val", "has_deriv_within_at_fpow", "mv_power_series.X_def", "nat.choose_succ_succ", "finsupp.map_domain_comap_domain", "int.mod_zero", "continuous.add", "set.interval_subset_interval", "circle_deg1_lift.map_add_nat", "list.pmap_eq_map_attach", "power_series.X_eq", "sym2.map_comp", "preserves_products_iso_hom_\[Pi]_assoc", "int.bit_neg_succ", "subring.gsmul_mem", "polynomial.monic_one", "add_subgroup.forall", "set.quot_mk_range_eq", "list.argmin_eq_some_iff", "ennreal.Lp_add_le", "add_subgroup.coe_zero", "list.prod_range_succ'", "subspace.coe_continuous_linear_proj_of_closed_compl", "category_theory.pi.comap_comp_inv_app", "is_closed_ge'", "differentiable_at.sub_const", "add_monoid_hom.inl_apply", "category_theory.limits.coprod.associator_inv", "semiconj_by.neg_left", "ordinal.one_le_iff_ne_zero", "matrix.det_mul", "polynomial.C_eq_algebra_map", "nat.modeq.pow_totient", "not_bdd_below_iff'", "asymptotics.is_O_with.congr'", "category_theory.limits.biprod.braiding'_hom", "wseq.not_mem_nil", "tensor_product.lift_mk_compr\:2082", "category_theory.limits.cocones.functoriality_obj_X", "seq.zip_with_nth_none", "tensor_product.assoc_tmul", "real.log_neg_eq_log", "pequiv.of_set_eq_some_self_iff", "mul_lt_of_lt_of_le_one", "filter.Limsup_bot", "set.Ioi_diff_Ici", "cardinal.mul_le_max_of_omega_le_left", "isometry.uniform_embedding", "finset.infi_singleton", "free_group.red.red_iff_irreducible", "finset.mono_of_fin_zero", "polynomial.coeff_coe_units_zero_ne_zero", "finsupp.map_domain_sum", "nat.add_pos_left", "segment_eq_interval", "ring.fractional_ideal.mem_singleton_mul", "algebra.is_integral_trans", "nat.modeq.modeq_mul_left", "zsqrtd.mul_re", "is_open_diff", "turing.to_partrec.cont.then_eval", "measure_theory.measure.haar_outer_measure_lt_top_of_is_compact", "pi.single_eq_of_ne", "category_theory.epi_of_epi", "poly.neg_eval", "imp_eq_of_eq_true_right", "nnreal.one_rpow", "mdifferentiable_on.congr_mono", "is_open_map.prod", "setoid.eqv_gen_of_setoid", "category_theory.sum.inverse_associator_obj_inl", "ring_hom.lift_of_surjective_comp_apply", "continuous_within_at_id", "int.cast_neg", "pfunctor.M.approx_mk", "polynomial.X_pow_mul", "ideal.quotient.exists_inv", "list.index_of_lt_length", "rel_supr_tsum", "asymptotics.is_o.prod_left_fst", "subtype.exists", "differentiable.restrict_scalars", "ring_hom.map_geom_series", "eq_of_div_eq_one", "pnat.bit1_le_bit0", "algebra.map_top", "list.zip_nil_left", "free_group.red.step.append_right", "mv_polynomial.coe_add", "ring.fractional_ideal.span_fractional_iff", "cmp_using_eq_eq", "neg_neg", "real.Inf_of_not_bdd_below", "ordinal.power_add", "real.cosh_zero", "submodule.prod_comap_inl", "ennreal.sum_eq_top_iff", "finset.union_self", "finsupp.support_zero", "has_deriv_at.continuous_at", "multiset.zero_subset", "pgame.le_iff_neg_ge", "add_con.inf_def", "set.subset.trans", "isometry.diam_image", "intermediate_value_Icc", "locally_compact_of_compact_nhds", "equiv.const_vadd_add", "category_theory.graded_object.comap_equiv_unit_iso", "right_ord_continuous.map_is_least", "list.length_sublists'", "lt_add_of_lt_of_pos", "inv_of_inv_of", "zmod.nat_coe_eq_nat_coe_iff", "measure_theory.simple_func.range_zero", "matrix.mul_zero", "finset.Ico.insert_succ_bot", "cSup_lower_bounds_eq_cInf", "add_semiconj_by.units_neg_right", "add_subgroup.is_open_of_mem_nhds", "unique_mdiff_within_at.inter'", "filter.tendsto.is_bounded_under_ge", "dfinsupp.induction\:2082", "nat.find_spec", "eq_neg_of_add_eq_zero", "is_closed_singleton", "convex_on.le_on_segment'", "monoid_hom.coprod_comp_inl", "exists_unique.elim2", "topological_space.opens.map_comp_obj'", "closed_embedding_of_embedding_closed", "setoid.is_partition_classes", "list.modify_nth_length", "primrec\:2082.option_some_iff", "valuation.on_quot_comap_eq", "finsupp.order_embedding_to_fun_apply", "is_R_or_C.norm_sq_to_complex", "submonoid.coe_inf", "uniformity_basis_edist'", "option.mem_def", "exists_Ioc_subset_of_mem_nhds", "polynomial.separable.of_mul_left", "add_subgroup.le_normalizer_of_normal", "category_theory.nat_iso.cancel_nat_iso_hom_left", "linear_map.map_sum", "euclidean_geometry.orthogonal_projection_fn_mem", "finset.disjoint_filter_filter", "submodule.ker_subtype", "monotone.map_infi_le", "set.Ici_diff_Ioi", "lt_iff_le_and_ne", "normalize_eq", "has_fderiv_at.comp_has_fderiv_within_at", "nat.dvd_add_self_right", "list.func.get_set_eq_of_ne", "nat.pow_zero", "dense_range.equalizer", "generalized_continued_fraction.continuants_recurrence_aux", "category_theory.category_of_elements.\[Pi]_obj", "set.countable_pi", "zero_eq_inv", "category_theory.equivalence.inverse_counit", "pfunctor.W.dest_mk", "real.pi_lt_sqrt_two_add_series", "list.chain_of_pairwise", "nat.partrec.none", "bool.bor_left_comm", "list.sublist.antisymm", "nat.sqrt_eq_zero", "ideal.factors_decreasing", "metric.uniform_continuous_on_iff", "set.bij_on.inj_on", "cardinal.cantor_function_le", "is_basis.coord_fun_eq_repr", "has_fderiv_at.mul", "localization_map.lift_eq", "associates.eq_of_mul_eq_mul_right", "has_mfderiv_at.comp_has_mfderiv_within_at", "squeeze_zero'", "mv_polynomial.coeff_mul", "submodule.sup_mul", "category_theory.iso.hom_congr_symm", "pnat.gcd_a_eq", "is_min_on.neg", "cardinal.cantor'", "measure_theory.ae_eq_fun.integrable.add", "metric.cauchy_seq_iff'", "equiv.set.univ_apply", "free_magma.traverse_mul", "cau_seq.completion.mk_add", "local_ring.is_unit_of_mem_nonunits_one_sub_self", "local_homeomorph.to_fun_eq_coe", "uniform.continuous_on_iff'_left", "nat.mod_two_eq_zero_or_one", "is_closed_connected_component", "list.chain'_cons", "is_glb.bdd_below", "mv_polynomial.eq_zero_of_eval_eq_zero", "cardinal_lift_le_dim_of_linear_independent", "uniform_space.has_seq_basis", "polynomial.degree_X", "tendsto_pow_at_top_nhds_0_of_abs_lt_1", "dense_inducing.closure_range", "cardinal.le_min", "pfunctor.M.is_path_cons'", "commute.neg_right", "real.rpow_def_of_nonpos", "add_subgroup.coe_subset_coe", "add_monoid_hom.id_apply", "direct_sum.lof_apply", "alg_hom.map_sub", "is_add_group_hom.zero_iff_ker_neg'", "category_theory.limits.biprod.hom_ext", "is_closed_sInter", "category_theory.adjunction.functoriality_unit_app_hom", "iff_def'", "finset.image_subset_image", "ordinal.zero_dvd", "nat.succ_inj'", "measure_theory.simple_func.coe_restrict", "category_theory.limits.biproduct.desc_eq", "nat.prime.dvd_of_dvd_pow", "dual_pair.dual_lc", "real.sqrt_inv", "wseq.lift_rel_nil", "and.right_comm", "filter.germ.coe_sub", "nat.pred_inj", "continuous_linear_equiv.comp_continuous_on_iff", "finset.sum_ite", "generalized_continued_fraction.int_fract_pair.exists_succ_nth_stream_of_fr_zero", "nonempty.exists", "nat.primrec'.cons", "continuous.iterate", "has_strict_fderiv_at.const_mul", "measure_theory.simple_func.integral_neg", "lcm_eq_zero_iff", "polynomial.separable_X", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_le'", "zmod.inv_coe_unit", "local_equiv.image_trans_source", "has_fderiv_at.restrict_scalars", "minimal_polynomial.aeval", "perfect_closure.mk_add_mk", "submonoid.monotone_map", "commute.inv_inv_iff", "tactic.abel.const_add_term", "ordinal.lift_one", "times_cont_mdiff_within_at.comp'", "nat.cast_pow", "roption.get_or_else_some", "is_R_or_C.im_to_complex", "add_submonoid.localization_map.eq_iff_exists", "qpf.is_lawful_functor", "measure_theory.outer_measure.trim_eq_infi'", "is_compact.tendsto_subseq", "option.none_bind'", "rat.le_floor", "additive.is_add_subgroup_iff", "edist_le_tsum_of_edist_le_of_tendsto", "eq_of_forall_le_iff", "eq_inv_of_mul_left_eq_one", "nat_degree_scale_roots", "category_theory.eq_to_hom_map", "push_neg.not_not_eq", "function.update_comp_eq_of_not_mem_range", "set.exists_of_ssubset", "category_theory.iso.cancel_iso_hom_left", "int.sign_eq_one_of_pos", "mem_nhds_within_Ioi_iff_exists_Ioo_subset", "nnreal.coe_le_coe", "option.ne_none_iff_is_some", "dim_pos", "is_greatest.mono", "is_basis.repr_eq_single", "well_founded.well_founded_iff_has_min", "continuous_linear_map.fderiv", "finset.sum_eq_zero_iff_of_nonpos", "array.ext", "Sup_eq_supr", "nat.div_lt_iff_lt_mul'", "smooth_manifold_with_corners.compatible_of_mem_maximal_atlas", "category_theory.limits.zero_of_from_zero", "isometric.coe_to_real_linear_equiv_of_map_zero", "category_theory.limits.cocones.whiskering_equivalence_counit_iso", "array.write_eq_write'", "is_coprime.prod_left_iff", "enat.with_top_equiv_coe", "pnat.xgcd_type.rq_eq", "category_theory.preadditive.epi_iff_cancel_zero", "embedding.continuous_on_iff", "fin.val_one", "filter.inf_ne_bot_iff_frequently_right", "measurable_space.monotone_map", "list.append_inj", "list.nodupkeys.pairwise_ne", "nat.mod_add_mod", "linear_dependent_iff", "submonoid.localization_map.map_mul_left", "ulift.mul_down", "finset.card_congr", "list.unzip_revzip", "zsqrtd.mul_pos", "pow_boole", "ennreal.inner_le_Lp_mul_Lq", "measurable_fst", "subring.multiset_prod_mem", "multiset.powerset_len_zero_left", "uniform_continuous_of_rat", "pgame.equiv_congr_right", "ite_eq_tt_distrib", "int.sub_nat_self", "measure_theory.measure.haar.prehaar_mono", "mv_power_series.coeff_monomial", "dfinsupp.prod_add_index", "decidable.or_iff_not_and_not", "mvpfunctor.const.get_map", "category_theory.Monad.Mon_to_Monad_obj", "convex_halfspace_re_le", "measure_theory.l1.simple_func.to_simple_func_of_simple_func", "equiv.arrow_congr_comp", "list.length_scanl", "add_submonoid.localization_map.lift_spec", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_hom_assoc", "zmod.val_min_abs_def_pos", "pgame.le_of_lt", "submonoid.comap_comap", "abs_sub_abs_le_abs_sub", "cardinal.mk_image_eq_of_inj_on", "strict_weak_order.not_lt_of_equiv'", "fintype.card_eq_sum_ones", "finset.sum_mul_sum", "subgroup.mem_closure_singleton", "seq1.bind_ret", "primrec.option_map\:2081", "add_monoid_hom.iterate_map_zero", "measure_theory.integral_indicator", "measure_theory.l1.measurable", "pow_le_max_of_min_le", "free_comm_ring.exists_finite_support", "opposite.equiv_to_opposite_symm_apply", "finsupp.lmap_domain_comp", "fin.val_zero", "differentiable_on.ccos", "linear_map.to_pmap_apply", "localization_map.mk'_self", "category_theory.nat_iso.trans_app", "polynomial.of_mem_support_derivative", "principal_seg.cod_restrict_apply", "le_inv_of_neg", "fin.last_val", "measure_theory.measure.zero_le", "category_theory.functor.const.obj_obj", "open_add_subgroup.ext", "add_monoid_hom.range_top_iff_surjective", "sub_add_sub_cancel'", "linear_map.add_apply", "submodule.coe_eq_zero", "real.image_Icc", "add_submonoid.mrange_inr", "padic_norm_z.eq_of_norm_add_lt_left", "two_dvd_bit0", "adic_completion.eval_apply", "complex.continuous_cos", "multiset.coe_filter", "nat.div_lt_iff_lt_mul", "cast_eq", "equiv.perm.card_support_swap_mul", "continuous_multilinear_map.mk_pi_field_apply", "con.refl", "roption.coe_none", "finset.filter_subset_filter", "cardinal.ord_le", "list.lookmap_cons_none", "fin.ext", "set.surj_on_Union_Union", "ordinal.le_add_sub", "topological_space.opens.map_comp_inv_app", "is_R_or_C.abs_sub_le", "add_submonoid.mem_sup", "finset.disjoint_iff_inter_eq_empty", "coe_frobenius_equiv_symm", "of_add_to_add", "interval_integral.integral_has_strict_deriv_at_of_tendsto_ae_right", "ennreal.some_eq_coe", "unique_mdiff_on.unique_diff_on", "set.preimage_mul_const_Ici", "set.Ioi_inter_Ioi", "fixed_points.minpoly.ne_one", "category_theory.limits.binary_cofan.is_colimit.hom_ext", "ring_hom.coe_one", "finsupp.lsingle_apply", "ring_hom.range_top_of_surjective", "and.congr_right_iff", "cardinal.ord_zero", "ordinal.ord_cof_eq", "eq_sub_iff_add_eq'", "dioph.reindex_dioph_fn", "stream.const_eq", "ordinal.div_add_mod", "set.coe_inclusion", "right_ord_continuous.map_cInf", "mem_nhds_within_Iic_iff_exists_Icc_subset", "ring.fractional_ideal.fractional_inf", "unique_mdiff_on.smooth_bundle_preimage", "dvd_lcm_right", "inner_product_geometry.cos_angle_sub_add_angle_sub_rev_eq_neg_cos_angle", "convex_hull_exists_dist_ge", "list.prod_erase", "matrix.special_linear_group.det_coe_matrix", "set.finite.finite_subsets", "zorn.chain.total", "asymptotics.is_O_with_iff", "continuous_multilinear_curry_fin0_symm_apply", "measure_theory.measure.finite_at_filter.filter_sup", "ordinal.sub_eq_of_add_eq", "Module.range_eq_top_of_epi", "real.sin_square", "category_theory.is_iso.hom_inv_id_assoc", "real.is_conjugate_exponent.nonneg", "list.perm.kerase", "submonoid.powers_subset", "measurable_supr", "measure_theory.l1.norm_eq_norm_to_fun", "typevec.append_fun_inj", "filter.frequently_true_iff_ne_bot", "cardinal.lift_succ", "add_subgroup.gc_map_comap", "category_theory.monoidal_category.left_assoc_tensor_map", "or_eq_of_eq_true_left", "measure_theory.inner_content_exists_compact", "int.add_assoc_aux2", "upper_bounds_Iio", "category_theory.functor.sum_obj_inl", "add_submonoid.multiples_eq_closure", "ennreal.top_rpow_def", "fin.le_last", "add_con.induction_on\:2082", "is_coprime.of_mul_add_right_left", "set.prod_univ_range_eq", "filter.rcomap'_sets", "category_theory.limits.functor_category_limit_cone_\[Pi]_app_app", "alg_equiv.map_one", "real.sin_arctan", "equiv.add_left_symm", "subalgebra.sum_mem", "linear_map.coprod_inl_inr", "ennreal.bot_eq_zero", "list.forall\:2082_nil_right_iff", "quotient_map.continuous", "nat.gcd_eq_right", "set.countable_encodable", "filter.tendsto_at_bot_of_monotone_of_filter", "category_theory.limits.cone.functor_w", "neg_one_gsmul", "compl_le_iff_compl_le", "sum.naturality", "set.sInter_image", "cardinal.lt_lift_iff", "mfderiv_within_id", "simple_graph.trace_adj_matrix", "multiset.mem_sub_of_nodup", "exists_unique.unique", "finset.sort_eq", "multiset.card_antidiagonal", "exists_nat_pow_near", "int.eq_one_of_dvd_one", "set.range_smul_range", "multiset.bind_hcongr", "polynomial.comp_eq_sum_left", "list.map_eq_map", "add_subgroup.sub_mem", "gcd_dvd_gcd_mul_right", "int.le_of_dvd", "asymptotics.is_o_id_const", "associates.prod_add", "list.mem_iff_nth", "pequiv.bot_trans", "dim_span_le", "finset.val_eq_zero", "multiset.count_eq_zero_of_not_mem", "weighted_vsub_mem_vector_span", "mv_polynomial.rename_rename", "Sup_inter_le", "fderiv_sum", "inner_product_space.of_core.inner_mul_inner_self_le", "padic_norm.add_eq_max_of_ne", "mv_polynomial.C_sub", "subsingleton.set_cases", "mul_min_of_nonneg", "linear_map.range_smul", "exists_ratio_deriv_eq_ratio_slope", "coe_sort_ff", "pos_num.cast_sub'", "inv_add_inv", "category_theory.category_of_elements.comp_val", "times_cont_mdiff.times_cont_mdiff_tangent_map", "has_deriv_within_at.rpow_of_one_le", "list.mem_lookup_kunion_middle", "is_lub_univ", "game.add_comm", "measure_theory.integrable_add", "commute.gpow_left", "nnreal.div_self_le", "int.le_mul_of_div_le", "dioph.abs_poly_dioph", "asymptotics.is_O_neg_left", "inf_compl_eq_bot", "ring.fractional_ideal.le_iff", "linear_map.exists_right_inverse_of_surjective", "complex.tendsto_inv", "roption.map_id'", "ordinal.power_zero", "inf_le_inf", "mv_polynomial.map_X", "multiset.le_smul_erase_dup", "list.to_finset_cons", "add_monoid_hom.prod_unique", "filter.eventually_eq_principal", "ennreal.sub_lt_sub_self", "deriv_sin", "alg_hom.map_mul", "submodule.span_zero", "category_theory.under.post_obj", "category_theory.comonad.coalgebra.EilenbergMoore_to_category_struct_to_has_hom_hom", "zsqrtd.nonneg_mul", "metric.emetric_ball_nnreal", "pnat.xgcd_type.reduce_b", "imp_of_not_imp_not", "measure_theory.l1.smul_to_fun", "has_strict_deriv_at_id", "filter.rcomap'_rcomap'", "opposite.unop_eq_iff_eq_op", "add_submonoid.coe_eq_coe", "seq.of_stream_cons", "turing.blank_rel.symm", "multiset.filter_map_cons_some", "is_subgroup.mem_trivial", "filter.eventually_true", "polynomial.map_div", "onote.NF.zero_of_zero", "differentiable_within_at_inter", "turing.TM1to0.tr_supports", "differentiable_within_at.congr_mono", "category_theory.limits.prod_comparison_inv_natural_assoc", "finset.sum_bij_ne_zero", "nnreal.continuous_at_rpow", "prod_X_sub_smul.smul", "real.sqrt_eq_zero_of_nonpos", "subgroup.mem_normalizer_iff", "finset.map_to_finset", "category_theory.limits.colimit.pre_map", "commute.cast_nat_mul_self", "finsupp.support_add_eq", "free_group.red.antisymm", "asymptotics.is_O.smul_is_o", "local_homeomorph.restr_open_to_local_equiv", "inv_lt", "mvpfunctor.comp.get_map", "mdifferentiable_within_at_univ", "tendsto_order_unbounded", "composition.ones_embedding", "subring.closure_eq", "additive.is_add_subgroup", "rel_iso.to_equiv_injective", "add_units.neg_add_cancel_left", "add_div'", "list.nodupkeys_iff_pairwise", "category_theory.over.id_left", "roption.to_of_option", "list.sublist_suffix_of_union", "multiset.mem_of_mem_erase", "traversable.foldl.unop_of_free_monoid", "eq_of_uniformity_inf_nhds", "measurable_space.induction_on_inter", "fin.cast_succ_lt_last", "equiv.Pi_congr_left'_symm_apply", "monoid_hom.coe_of_mdense", "linear_equiv.map_ne_zero_iff", "exists_deriv_eq_slope", "valuation.supp_quot_supp", "ring_char.eq", "inner_product_space.of_core.abs_inner_le_norm", "exists_ratio_has_deriv_at_eq_ratio_slope", "multilinear_map.add_apply", "turing.TM1to0.tr_eval", "finset.piecewise_insert_of_ne", "deriv_within_log'", "with_bot.coe_zero", "segment_symm", "measure_theory.simple_func.integral_sub", "continuous.tendsto", "nat.mul_div_le_mul_div_assoc", "cau_seq.sub_apply", "lipschitz_with.continuous", "exists_norm_eq_infi_of_complete_subspace", "finsupp.support_subset_iff", "ring_hom.map_prod", "convex_on.convex_epigraph", "subring.add_mem", "inner_product_geometry.cos_angle_add_angle_sub_add_angle_sub_eq_neg_one", "pos_num.cast_to_num", "multiset.coe_subset", "list.unzip_left", "mem_left_add_coset", "archimedean_iff_rat_le", "vector_space.eval_ker", "category_theory.under.w", "Gromov_Hausdorff.HD_below_aux1", "matrix.det_permute", "ennreal.coe_inv_le", "cardinal.mk_univ_real", "ennreal.coe_tsum", "primrec.comp", "multiset.exists_cons_of_mem", "is_open_Iio", "plift.up_down", "category_theory.over.construct_products.cones_equiv_inverse_2", "nat.div_eq_self", "padic.cast_eq_of_rat", "interval_integral.deriv_within_integral_of_tendsto_ae_right", "differentiable_on_pow", "set.union_subset_iff", "finset.prod_range_eq_prod_fin", "onote.NF_below_zero", "complex.sub_re", "mem_nhds_within_Ioi_iff_exists_Ioo_subset'", "continuous_linear_map.add_comp", "generalized_continued_fraction.zero_le_of_denom", "semimodule.restrict_scalars_smul_def", "nat.partrec.code.rec_computable", "nat.modeq.modeq_of_modeq_mul_left", "simple_graph.transpose_adj_matrix", "iterated_fderiv_succ_eq_comp_right", "dim_le_of_submodule", "div_le_div'", "add_left_eq_self", "polynomial.irreducible_of_eisenstein_criterion", "list.ext_le", "category_theory.limits.image.as_\[Iota]", "is_min_on_iff", "measurable_id", "inv_mul_cancel_left'", "zero_eq_edist", "fin.of_nat_zero", "summable_sum", "set.bInter_insert", "div_zero", "vadd_left_cancel_iff", "convex_halfspace_lt", "asymptotics.is_o.of_const_mul_right", "bilin_form.neg_apply", "matrix.dot_product_empty", "real.log_neg", "pfunctor.approx.head_succ'", "compl_inf_eq_bot", "ring_hom.iterate_map_neg", "dim_fun", "free_abelian_group.add_bind", "lt_mul_of_one_le_of_lt'", "finset.prod_subtype_of_mem", "category_theory.functor_to_types.hcomp", "list.cons_ne_self", "submonoid.localization_map.map_mul_right", "category_theory.limits.biproduct.hom_ext'", "category_theory.equivalence.functor_map_inj_iff", "is_local_min_on.comp_antimono", "filter.tendsto_finset_preimage_at_top_at_top", "primrec.vector_of_fn'", "set.Ioo_subset_Ioo", "polynomial.coeff_smul'", "real.sinh_add", "set.infinite_univ", "category_theory.limits.prod.symmetry_assoc", "subgroup.forall", "affine_subspace.not_le_iff_exists", "nnreal.inv_zero", "matrix.special_linear_group.to_lin_mul", "fderiv_within_mul_const", "computation.thinkN_mem", "linear_equiv.map_smul", "free_abelian_group.zero_seq", "subgroup.is_open_of_open_subgroup", "continuous_multilinear_map.zero_apply", "zsqrtd.bit1_im", "list.func.nil_sub", "equiv.inv_def", "multiset.mem_erase_dup", "cardinal.power_le_power_right", "pgame.wf_subsequent", "norm_num.int_div", "mul_lt_mul_of_neg_left", "is_max_filter.min", "nat.not_mem_of_lt_Inf", "uniform_space.first_countable_topology", "cardinal.lift_le", "finset.coe_insert", "antilipschitz_with.mul_le_edist", "ordinal.div_le", "ring_hom.functions_ext", "galois_connection.monotone_intro", "ordinal.le_log", "normed_field.punctured_nhds_ne_bot", "algebra.tensor_product.alg_hom_of_linear_map_tensor_product_apply", "ideal.unit_mul_mem_iff_mem", "isometric.point_reflection_fixed_iff", "semimodule.eq_zero_of_zero_eq_one", "measure_theory.outer_measure.map_apply", "decidable.eq_or_lt_of_le", "category_theory.limits.bicone_\[Iota]_\[Pi]_self", "real.tendsto_exp_neg_at_top_nhds_0", "mv_polynomial.coeff_sub", "set.image2_union_right", "list.mem_inits", "has_fderiv_at.fderiv", "neg_one_smul", "generalized_continued_fraction.denom_eq_conts_b", "category_theory.limits.binary_fan.\[Pi]_app_left", "sub_right_lt_of_lt_add", "convex_cone.add_mem", "filter.frequently.mono", "linear_equiv.of_submodule_symm_apply", "irrational.sub_rat", "ring_equiv.symm_trans", "multiset.le_ndinter", "convex_std_simplex", "is_closed.closure_eq", "category_theory.limits.prod.symmetry'_assoc", "bdd_above.inter_of_right", "add_monoid_hom.eq_on_mclosure", "filter.tendsto_Ixx_class_principal", "int.eq_of_sub_eq_zero", "encodable.decode_unit_zero", "is_R_or_C.of_real_eq_zero", "pgame.mk_add_move_right_inl", "nat.shiftl'_add", "uniform_continuous_neg", "add_semiconj_by.add_left", "submonoid.closure_eq_mrange", "ulift.one_down", "Module.ker_eq_bot_of_mono", "filter.sup_sets_eq", "ennreal.sub_le_sub_add_sub", "category_theory.monoidal_category.left_unitor_product_aux_triangle", "ideal.eq_bot_of_prime", "is_measurable.union", "affine_subspace.mem_coe", "alg_hom.comp_id", "list.pairwise.imp", "multiplicity.pow'", "nat.partrec.code.curry_inj", "quotient_group.eq_class_eq_left_coset", "isometric.coe_to_homeomorph", "tendsto_uniformly.comp", "pfun.preimage_subset_core", "multiset.mem_powerset_aux", "ennreal.tsum_geometric", "complex.of_real_pow", "real.cos_le_one", "category_theory.monoidal.Mon_functor_category_equivalence.functor_map_app_hom", "times_cont_mdiff.prod_map", "is_group_hom.one_iff_ker_inv", "nat.partrec.code.encode_lt_prec", "linear_equiv.of_submodules_symm_apply", "finset.sum_mono_set", "add_monoid_hom.eq_of_eq_on_dense", "function.embedding.cod_restrict_apply", "add_sub_comm", "submodule.one_mul", "summable_of_norm_bounded_eventually", "ordinal.unbounded_of_unbounded_Union", "linear_pmap.right_le_sup", "lie_subalgebra.mem_coe", "equiv.perm.cycle_of_pow_apply_self", "coe_fn_coe_trans", "int.nat_abs_div", "measure_theory.ae_eq_fun.one_def", "finsupp.subtype_domain_finsupp_sum", "nat.choose_eq_zero_of_lt", "composition_as_set.to_composition_blocks", "ne_bot_of_le_ne_bot", "hyperreal.is_st_Sup", "polynomial.leading_coeff_mul_X_pow", "nsmul_one", "times_cont_diff_within_at.mono", "computation.not_terminates_empty", "ultrafilter_is_closed_basic", "pi_Lp.lipschitz_with_equiv", "monoid.closure_subset", "is_closed_induced_iff", "convex_halfspace_im_lge", "zero_lt_one'", "set.compl_univ", "set.Iic_singleton_of_bot", "filter.eventually_eq.trans_le", "subsemiring.nsmul_mem", "nat.le_rec_on_trans", "omega.nat.univ_close_of_valid", "real.sin_square_pi_over_two_pow", "add_sub_add_left_eq_sub", "continuous_Sup_rng", "affine.simplex.altitude_def", "finset.mem_insert_self", "subgroup.closure_eq", "norm_num.subst_into_mul", "one_half_pos", "padic_norm_e.norm_int_le_one", "char_matrix_apply_eq", "auto.not_implies_eq", "filter.is_countably_generated.subseq_tendsto", "measurable_infi", "filter.is_bounded_top", "list.perm.union_right", "set.inv_preimage", "emetric.totally_bounded_iff'", "nnreal.lt_inv_iff_mul_lt", "roption.pure_eq_some", "le_of_tendsto_of_tendsto", "setoid.eq_of_mem_classes", "has_strict_fderiv_at.mem_implicit_to_local_homeomorph_of_complemented_source", "ordinal.zero_mul", "multiset.Ico.map_add", "monotonicity.not", "nat.sub_lt_self", "equiv.sum_prod_distrib_apply_right", "ordinal.sub_self", "category_theory.nat_iso.cancel_nat_iso_inv_right_assoc", "enat.to_with_top_coe'", "div_eq_zero_iff", "nat.rfind_min'", "asymptotics.is_O_with_const_const", "frobenius_pth_root", "turing.to_partrec.code.ok.zero", "differentiable_at.deriv_within", "set.Ioi_subset_Ioi_iff", "ring_hom.coe_range", "min_lt_min", "category_theory.adjunction.hom_equiv_naturality_right_symm", "znum.cast_bitm1", "dense_inducing.closure_image_nhds_of_nhds", "category_theory.limits.bicone.to_binary_bicone_inl", "asymptotics.is_O_with.prod_left_snd", "composition_as_set.card_boundaries_pos", "list.infix_of_mem_join", "power_series.order_finite_of_coeff_ne_zero", "sum.uniformity", "set.Icc_eq_empty_iff", "locally_finite.realizer.to_locally_finite", "inv_gold", "asymptotics.is_o.is_O", "polynomial.eval_neg", "list.length_revzip", "tsum_geometric_of_norm_lt_1", "open_subgroup.coe_injective", "int.dist_cast_real", "is_R_or_C.norm_sq_one", "cardinal.mul_eq_max", "ring_hom.map_nat_cast", "sub_le_self_iff", "filter.tendsto.eventually", "neg_lie", "ordinal.omin_le", "function.support_sup", "list.lookup_kunion_right", "is_compact.image_of_continuous_on", "antisymm", "equiv.perm.exists_gpow_eq_of_is_cycle", "opposite.op_unop", "polynomial.div_by_monic_eq_div", "ennreal.mul_le_mul_left", "zmod.cast_val", "measure_theory.measure.add_le_add", "submodule.linear_eq_on", "zorn.zorn_subset\:2080", "nat.even_mul", "is_R_or_C.abs_neg", "not_of_iff_false", "category_theory.limits.prod_map_map", "set.Icc_subset_Ioi_iff", "category_theory.limits.colimit.cocone_\[Iota]", "num.cmp_swap", "matrix.mul_adjugate", "submonoid.localization_map.mul_equiv_of_localizations_left_inv_apply", "set.inter_neg", "filter.pmap_res", "list.forall_mem_of_fn_iff", "cSup_Iic", "category_theory.monoidal.Mon_functor_category_equivalence.unit_iso_hom_app_hom_app", "mul_aut.one_apply", "list.init_append_last'", "category_theory.monoidal_category.right_unitor_product_aux_square", "monoid_hom.mrestrict_apply", "filter.germ.const_le_iff", "Ioi_mem_nhds", "equiv.swap_apply_self", "finset.sorted_zero_eq_min'", "gaussian_int.to_complex_sub", "asymptotics.is_O.const_mul_right", "category_theory.limits.prod_map_comp_id_assoc", "wseq.exists_dropn_of_mem", "nat.prime.coprime_pow_of_not_dvd", "set.Icc_subset_Ioo_iff", "is_compl.inf_eq_bot", "real.sin_two_pi", "subtype.coind_injective", "finsupp.smul_apply", "category_theory.quotient.lift_map", "lt_imp_lt_of_le_imp_le", "pi_eq_sum_univ", "continuous_on.preimage_open_of_open", "int.sub_nat_nat_add_left", "ordinal.is_normal.bsup", "set.bUnion_subset_bUnion_right", "generalized_continued_fraction.le_of_succ_succ_nth_continuants_aux_b", "groupoid_of_pregroupoid_le", "affine_span_nonempty", "category_theory.limits.cone_of_cocone_left_op_X", "prod.snd_mul", "mul_comm_div'", "bounded_lattice.ext", "nonneg_of_mul_nonneg_left", "typevec.id_eq_nil_fun", "commute.neg_one_right", "ordinal.one_CNF", "mul_div_cancel_of_imp'", "asymptotics.is_O_with.weaken", "seq.nil_append", "filter.ptendsto_def", "linear_equiv.conj_id", "list.cons_subset_cons", "padic_seq.norm_nonzero_of_not_equiv_zero", "int.modeq.modeq_mul_left", "is_min_on.localize", "option.get_of_mem", "deriv_within_const", "polynomial.splits_of_splits_of_dvd", "continuous_linear_equiv.is_O_sub_rev", "finmap.lookup_union_right", "length_perms_of_list", "filter.eventually.frequently", "is_closed_map_mul_right", "category_theory.prod.snd_map", "le_of_span_le_span", "list.mem_sublists_len_self", "mvqpf.Wrepr_equiv", "path.target", "add_submonoid.localization_map.lift_left_inverse", "nat.prime_dvd_prime_iff_eq", "complex.differentiable_at_sinh", "times_cont_diff_on.fderiv_within", "submodule.mem_supr_of_mem", "real.cos_pi_div_four", "quot.induction_on\:2083", "setoid.symm'", "perfect_closure.mk_zero", "circle_deg1_lift.mul_apply", "finset.mem_map'", "ennreal.bit1_eq_top_iff", "polynomial.degree_nonneg_iff_ne_zero", "complex.arg_eq_arg_neg_add_pi_of_im_nonneg_of_re_neg", "fin.find_eq_none_iff", "state_t.run_map", "int.mul_lt_mul", "pnat.mod_coe", "category_theory.non_preadditive_abelian.image.fac", "dense", "matrix.det_permutation", "omega.coeffs.val_set", "asymptotics.is_O_bot", "onote.NF.below_of_lt", "category_theory.arrow.lift_mk'_left_assoc", "filter.realizer.top_F", "category_theory.iso.symm_eq_iff", "div_div_eq_div_mul", "continuous_linear_equiv.map_neg", "category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom_assoc", "continuous_linear_equiv.self_comp_symm'", "neg_mul_eq_neg_mul", "finset.prod_preimage_of_bij", "image_le_of_liminf_slope_right_le_deriv_boundary", "le_of_neg_of_one_div_le_one_div", "submonoid.coe_ssubset_coe", "category_theory.limits.is_limit.of_nat_iso.cone_of_hom_fac", "complex.cos_conj", "asymptotics.is_O_with.congr_const", "le_add_of_nonneg_of_le", "turing.partrec_to_TM2.unrev_ok", "embedding.closure_eq_preimage_closure_image", "quotient.ind\:2082", "ennreal.top_sub_coe", "add_submonoid.localization_map.map_mk'", "set.mem_powerset", "is_R_or_C.abs_conj", "category_theory.adjunction.equiv_homset_right_of_nat_iso_symm_apply", "list.perm.filter_map", "cardinal.card_ord", "list.func.get_map", "pnat.gcd_comm", "galois_connection.id", "complex.cpow_neg", "lie_algebra.orthogonal.JB_transform", "eq_pos_center_mass_card_le_dim_succ_of_mem_convex_hull", "infi_emptyset", "complex.I_mul_I", "measure_theory.is_left_invariant_conj", "finset.coe_image_subset_range", "multiset.disjoint.symm", "quadratic_form.pos_def.add", "tendsto_nhds_within_mono_right", "set.image2_singleton", "is_null_measurable.Union_nat", "int.mul_self_le_mul_self", "submonoid.localization_map.map_eq", "generalized_continued_fraction.pair.coe_to_generalized_continued_fraction_pair", "Cauchy.mem_uniformity'", "linear_map.mem_ker", "modeq_three_digits_sum", "adic_completion.eval_comp_of", "filter.ext_iff", "euclidean_geometry.dist_square_eq_dist_square_add_dist_square_sub_two_mul_dist_mul_dist_mul_cos_angle", "mv_polynomial.eval_unique", "cardinal.mk_Ioo_real", "int.coe_nat_dvd", "norm_num.clear_denom_mul", "ennreal.of_real_to_real_le", "alist.perm_lookup", "multiset.card_singleton", "ideal.comap_mono", "multiplicative.is_submonoid_iff", "set.image_smul", "finset.inf_eq_inter", "linear_map.std_basis_same", "finset.prod_pair", "monotone.const_add", "is_R_or_C.of_real_one", "mv_power_series.coeff_C", "filter.liminf_eq_supr_infi_of_nat", "submonoid.mem_Sup_of_directed_on", "num.cast_one", "measure_theory.inner_content_pos", "lt_of_le_of_ne", "topological_space.opens.to_Top_map", "id_rel_sub_separation_relation", "continuous_within_at.continuous_at", "measure_theory.measure.haar.echaar_mono", "rel_iso.symm_apply_rel", "localization.mk_eq_monoid_of_mk'", "norm_num.clear_denom_lt", "multiset.map_filter_map", "interval_integral.deriv_integral_right", "bounded_continuous_function.arzela_ascoli\:2082", "midpoint_add_self", "bdd_above.mono", "filter.has_basis.to_has_basis", "mdifferentiable_on.comp", "differentiable_at_inverse", "int.of_nat_add_neg_succ_of_nat_of_ge", "subalgebra.map_le", "finmap.mem_of_lookup_eq_some", "filter.tendsto_iff_ptendsto_univ", "add_subgroup.gmultiples_subset", "fin_enum.nodup_to_list", "subgroup.mem_infi", "equiv.image_compl", "geom_series_zero", "quotient_map.id", "forall_const", "finset.mem_subtype", "ideal.eq_top_of_is_unit_mem", "multiset.bind_map_comm", "inner_div_norm_mul_norm_eq_one_of_ne_zero_of_pos_mul", "convex.translate_preimage_right", "reader_t.run_pure", "multiset.Ico.not_mem_top", "finset.bInter_inter", "ordinal.add_is_limit", "polynomial.coeff_X_one", "metric.bounded_empty", "unique_factorization_domain.exists_reduced_factors'", "set.insert_diff_singleton", "set.Icc_subset_Icc", "Mod.comap_map_hom", "category_theory.limits.pullback_cone.mk_\[Pi]_app_right", "int.lt_succ", "list.nil_diff", "monoid_algebra.mul_apply_antidiagonal", "option.get_mem", "finset.sum_hom_rel", "linear_equiv_matrix'_apply", "tactic.ring.horner_atom", "monotone.mem_lower_bounds_image", "with_one.ne_one_iff_exists", "finset.inf_eq_infi", "filter.eventually_lt_of_lt_liminf", "tendsto_at_top_mul_right", "fp.float.zero.valid", "smul_algebra_smul_comm", "lt_of_add_lt_add_right", "tendsto_locally_uniformly.tendsto_comp", "category_theory.prod.sectl_map", "algebra.tensor_product.mul_assoc'", "summable.add_compl", "totally_bounded.image", "multilinear_map.zero_apply", "gpow_one", "option_t.run_map", "ennreal.coe_indicator", "pos_num.add_succ", "ennreal.sum_lt_top", "finsupp.mul_sum", "loc_path_connected_of_is_open", "zorn.zorn_partial_order", "add_semiconj_by.neg_right_iff", "linear_map.ker_eq_top", "pfunctor.M.ichildren_mk", "finset.sum_Ico_eq_sub", "measure_theory.outer_measure.is_caratheodory_compl", "decidable.not_lt", "is_scalar_tower.algebra_comap_eq", "seq.zip_with_nth_some", "eq_add_neg_of_add_eq", "one_lt_mul'", "generalized_continued_fraction.int_fract_pair.exists_succ_nth_stream_of_gcf_of_nth_eq_some", "continuous_within_at.add", "multiset.exists_mem_of_rel_of_mem", "measurable_space.map_comp", "multiset.nodup_map_on", "submodule.sup_smul", "cauchy_seq_iff_tendsto", "mv_polynomial.total_degree_C", "contracting_with.exists_fixed_point'", "is_add_unit_add_unit", "filter.germ.lift_pred_coe", "contracting_with.fixed_point_unique", "associates.factors_le", "category_theory.monad.free_obj_a", "inv_gold_conj", "cau_seq.add_apply", "max_eq_neg_min_neg_neg", "tsum_mul_left", "linear_map.inr_injective", "category_theory.functor.const.map_app", "monotone.map_is_least", "set.preimage_mul_const_Ico_of_neg", "is_R_or_C.norm_sq_of_real", "circle_deg1_lift.translation_number_eq_rat_iff", "submonoid.mem_bot", "inv_lt_of_inv_lt", "category_theory.limits.epi_of_epi_image", "filter.ptendsto_of_ptendsto'", "eq_min", "add_monoid_hom.snd_comp_prod", "commute.self_cast_int_mul_cast_int_mul", "le_inf", "submonoid.map_sup", "rel_iso.coe_fn_injective", "le_cSup", "nhds_eq_comap_uniformity_aux", "is_closed_le'", "valuation.is_equiv.symm", "zmod.cast_self", "refl_bilin_form.ortho_sym", "divp_assoc", "filter.lift'_le", "list.length_map", "set.Ioc_union_Ioc_symm", "mv_polynomial.is_integral_domain_fintype", "monoid_algebra.one_def", "subgroup.top_prod_top", "linear_independent.repr_ker", "structure_groupoid.local_invariant_prop.lift_prop_at_chart", "rat.neg_def", "and.imp_left", "deriv_within_sinh", "function.semiconj.bij_on_range", "measure_theory.simple_func.integral_congr", "linear_equiv.coe_fn_to_continuous_linear_equiv_of_continuous", "category_theory.comma.snd_obj", "category_theory.limits.biproduct.\[Iota]_\[Pi]", 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"category_theory.limits.coprod_map_id_comp_assoc", "free_group.inv_bind", "interior_mono", "generalized_continued_fraction.of_terminated_at_iff_int_fract_pair_seq1_terminated_at", "measure_theory.ae_eq_fun.mk_eq_mk", "subtype.symm", "convex.sum_mem", "finset.disjoint_filter", "lie_algebra.orthogonal.so_indefinite_equiv_apply", "category_theory.functor.map_iso_refl", "ordinal.mod_zero", "is_lub.supr_eq", "ennreal.measurable_of_measurable_nnreal_nnreal", "list.chain_cons", "exists_has_deriv_within_at_eq_of_gt_of_lt", "ring.fractional_ideal.fractional_sup", "set.sUnion_eq_bUnion", "nat.subtype.lt_succ_self", "polynomial.degree_monomial_le", "mjoin_pure", "list.subperm_append_right", "multiset.le_cons_erase", "left_inverse_add_left_sub", "homeomorph.compact_preimage", "deriv_within_add_const", "norm_num.lt_one_bit1", "bounded_continuous_function.dist_le_two_norm", "set.univ_pi_nonempty_iff", "list.nodupkeys.eq_of_fst_eq", "metric.bounded.finite_measure", "metric.inf_dist_le_Hausdorff_dist_of_mem", "valuation.ne_zero_iff", "list.nodup_product", "finset.sup_mono_fun", "finset.insert_inter_of_mem", "padic.complete'", "wseq.seq_destruct_cons", "functor.comp.seq_assoc", "free_add_monoid.map_comp", "multiset.add_sub_of_le", "linear_order.concave_on_of_lt", "differentiable_at.prod", "neg_injective", "monoid_hom.fst_comp_inr", "inner_product_geometry.angle_smul_right_of_neg", "linear_independent.comp", "pgame.numeric_one", "order_top.upper_bounds_univ", "times_cont_mdiff_on.smooth_on", "ennreal.le_tsum", "int.nat_abs_bit0_step", "list.range'_subset_right", "real.tan_pi_div_four", "real.exp_zero", "gpow_mul'", "is_compact.exists_Sup_image_eq", "decidable.not_iff_not", "add_submonoid.localization_map.of_add_equiv_of_localizations_eq", "add_submonoid.mem_Inf", "list.drop_left'", "set.left_mem_Ioc", "list.drop_take_succ_join_eq_nth_le", "matrix.reindex_apply", "differentiable_within_at.sinh", "category_theory.limits.biprod.desc_eq", 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"category_theory.sum_comp_inr", "equiv.swap_apply_left", "summable.compl_add", "isometric.ext", "con.con_gen_le", "finsupp.disjoint_iff", "category_theory.functor.const.unop_functor_op_obj_map", "nat.prime.not_dvd_mul", "linear_equiv.coe_to_add_equiv", "is_compact.is_lub_Sup", "monoid.closure_mono", "category_theory.nat_trans.comp_app", "polynomial.degree_erase_lt", "filter.germ.map_coe", "units.coe_mk", "inner_self_nonneg", "order_top.bdd_above", "monoid_hom.gclosure_preimage_le", "continuous_linear_equiv.equiv_of_inverse_apply", "int.two_dvd_ne_zero", "I_extend_range", "analytic_at.continuous_at", "dim_fun_eq_lift_mul", "le_div_iff'", "set.subsingleton.mono", "turing.TM0.step_supports", "homeomorph.to_local_homeomorph_target", "topological_space.opens.comap_mono", "le_of_eq_or_lt", "subsemiring.prod_mem", "convex.affine_preimage", "complex.abs_exp_of_real", "fpow_strict_mono", "add_equiv.map_eq_zero_iff", "filter.tendsto_inf", "generalized_continued_fraction.fib_le_of_continuants_aux_b", "infi_le_infi", "asymptotics.is_O_self_const_mul", "linear_map.comap_map_eq_self", "multiset.attach_ndinsert", "cardinal.lt_omega_iff_fintype", "is_measurable_Ico", "set.image_mul_right", "category_theory.equivalence.refl_counit_iso", "list.last'_is_none", "span_int_eq_add_group_closure", "finset.insert_def", "many_one_equiv_refl", "stream.nth_of_bisim", "category_theory.abelian.pseudoelement.exact_of_pseudo_exact", "nat.bodd_mul", "add_group.closure_eq_mclosure", "affine.simplex.monge_point_eq_affine_combination_of_points_with_circumcenter", "has_deriv_at.lhopital_zero_left_on_Ioo", "set.mem_Ioo_or_eq_right_of_mem_Ioc", "with_zero.lt_of_mul_lt_mul_left", "subsemiring.closure_induction", "add_monoid_algebra.mul_apply", "nat.partrec.code.encode_lt_rfind'", "unique_diff_within_at.eq_deriv", "finset.coe_bind", "ordinal.nat_cast_lt", "set.Ico_diff_Iio", "add_comm_group.direct_limit.induction_on", "int.lt_irrefl", "nnreal.of_real_coe", "nat.primrec'.of_eq", "category_theory.equiv_relation", "cardinal.add_lt_omega_iff", "multiset.Ico.filter_le_of_le", "mul_aut.conj_symm_apply", "add_submonoid.localization_map.mk'_eq_iff_eq", "divp_divp_eq_divp_mul", "hyperreal.not_infinite_pos_of_infinite_neg", "category_theory.pi.comap_obj", "not_iff", "filter.tendsto.eventually_interval_integrable", "TopCommRing.coe_of", "polynomial.zero_div_by_monic", "has_sum_fintype", "nat.div_eq_iff_eq_mul_right", "metric.uniformity_basis_edist", "nat.mul_mod", "semiquot.mem_bind", "cau_seq.equiv_lim", "seq1.map_join'", "submodule.quotient.mk_eq_mk", "is_add_subgroup.coe_neg", "category_theory.limits.kernel_zero_iso_source_inv", "list.foldl_cons", "unique_diff_on_univ", "interval_integrable.neg", "finset.induction_on", "prod.map_fst", "lower_bounds_empty", "fin.cons_zero", "list.perm.bind_right", "nat.div_mul_cancel", "has_strict_deriv_at.mul", "alg_hom.comp_algebra_map", "add_commute.add_left", "norm_fst_le", "category_theory.monoidal_category.unitors_equal.cells_4'", "category_theory.comonad.cofree_obj_a", "set.mul_mem_mul", "nat.primrec'.tail", "irreducible_iff_of_associated", "multiset.lift_beta", "int.eq_one_of_mul_eq_one_right", "subring.prod_mono", "multiset.mem_ndinter", "finset.centroid_def", "polynomial.mod_by_monic_eq_mod", "subgroup.coe_map", "set.finite.bdd_above_bUnion", "Sup_inf_Sup", "monoid_hom.coe_mk'", "polynomial.separable_map", "add_pow_char_pow_of_commute", "compl_singleton_mem_nhds", "one_lt_div_of_neg", "category_theory.abelian.pseudoelement.zero_of_map_zero", "nat.le_add_of_sub_le_left", "list.erase_dup_sublist", "mv_power_series.map_comp", "hyperreal.gt_of_neg_of_infinitesimal", "enat.with_top_equiv_symm_zero", "finsupp.support_zip_with", "list.concat_eq_reverse_cons", "trace_eq_neg_char_poly_coeff", "ideal.radical_eq_jacobson_iff_radical_quotient_eq_jacobson_bot", "measurable_space.ext", "category_theory.limits.cokernel_iso_of_eq_trans", "with_top.mul_coe", "multiset.nat.card_antidiagonal", "finset.sum_union", "le_nhds_iff_adhp_of_cauchy", "mv_polynomial.is_integral_domain_fin", "measure_theory.outer_measure.is_caratheodory_iff_le'", "has_deriv_within_at.smul_const", "computation.lift_rel_think_left", "list.insert_nth_comm", "abs_nonneg", "ring_hom.srestrict_apply", "category_theory.limits.prod.associator_inv", "measure_theory.ae_add_measure_iff", "nnreal.Lp_add_le", "real.exp_add", "state_t.run_get", "equiv.smul_def", "topological_space.compacts.bot_val", "continuous_linear_map.times_cont_diff", "polynomial.nat_degree_to_subring", "interval_integral.integral_has_strict_fderiv_at_of_tendsto_ae", "multiset.filter_map_filter_map", "has_fderiv_within_at_univ", "dist_le_of_trajectories_ODE_of_mem_set", "category_theory.monad.forget_creates_limits.\[Gamma]_app", "nat.pred_le_pred", "ring.closure_mono", "set.disjoint_disjointed'", "set.image_eq_preimage_of_inverse", "ring.fractional_ideal.is_principal_iff", "tangent_bundle.times_cont_mdiff_within_at_proj", "filter.eventually_le.trans", "finset.inter_subset_inter", "omega.mul_symdiv_eq", "rat_inv_continuous_lemma", "list.kerase_keys_subset", "nat.zero_mod", "function.surjective.forall\:2083", "padic.exi_rat_seq_conv_cauchy", "category_theory.limits.prod.braiding_inv", "coe_sort_coe_trans", "fin.coe_fin_le", "cardinal.aleph_idx.initial_seg_coe", "functor.comp.functor_comp_id", "wseq.destruct_terminates_of_nth_terminates", "set_has_maximal_iff_noetherian", "lists'.mem_of_subset", "finset.prod_inter_mul_prod_diff", "floor_sub_int", "list.length_join", "localization_map.exist_integer_multiples_of_finset", "group.normal_closure_subset", "dioph.inject_dummies", "nnreal.has_sum_geometric", "finsupp.sum_map_range_index", "with_top.mul_def", "polynomial.degree_sum_le", "ODE_solution_unique_of_mem_set", "mv_polynomial.eval\:2082_comp_left", "bounded_continuous_function.add_apply", "set.preimage_add_const_Ioo", "set.diff_subset_diff", "measure_theory.measure.haar.chaar_sup_eq", "boole_mul", "matrix.map_apply", "filter.tendsto.basis_right", "primrec\:2082.swap", "continuous_linear_equiv.skew_prod_symm_apply", "encodable.length_le_encode", "category_theory.eq_to_iso.inv", "function.semiconj.comp_eq", "unique_mdiff_on.unique_diff_on_inter_preimage", "order_dual.dual_lt", "computable.option_bind", "complex.of_real_cosh", "zmod.val_cast_nat", "localization_map.coeff_integer_normalization_mem_support", "submonoid.mem_nhds_one", "polynomial.div_X_add", "finset.sup_le_iff", "asymptotics.is_o.congr_right", "rank_zero", "measurable_nndist", "tactic.ring_exp.pow_e_pf_exp", "category_theory.eq_to_hom_refl", "multiset.nodup_product", "nat.add_sub_add_right", "vector.map_cons", "omega.term.val_sub", "rel_embedding.is_strict_total_order'", "norm_num.bit0_succ", "set.bij_on.to_local_equiv_target", "one_lt_fpow", "continuous_inclusion", "true_equivalence", "formal_multilinear_series.le_comp_radius_of_summable", "with_top.coe_le_coe", "cardinal.two_le_iff'", "dfinsupp.single_zero", "le_bsupr", "deriv.neg'", "differentiable_within_at.const_mul", "list.mem_to_finset", "measure_theory.measure_Union_le", "cancel_factors.cancel_factors_lt", "is_open_bInter", "filter.strict_mono_subseq_of_id_le", "fin.coe_succ", "set.mem_or_mem_of_mem_union", "continuous_if", "polynomial.degree_le_mono", "tensor_product.lift.tmul'", "add_monoid_hom.fst_comp_inl", "category_theory.eq_to_hom_app", "has_deriv_at.exp", "affine_map.homothety_mul", "lie_algebra.orthogonal.mem_so", "encodable.skolem", "closure_eq_cluster_pts", "affine_map.ext", "tendsto_uniformly_on_univ", "asymptotics.is_O_with.symm", "ideal.exists_maximal", "mem_closure_of_is_glb", "list.last_congr", "polynomial.coeff_sum", "num.ppred_to_nat", "subsemiring.mem_closure_iff", "nat.mul_pos", "continuous_multilinear_map.continuous_eval", "decidable.not_iff_comm", "Ico_mem_nhds_within_Iio", "nndist_smul", "add_submonoid.localization_map.map_units", "measure_theory.integrable_on_union", "add_group_with_zero_nhd.nhds_eq", "char.ne_of_vne", "list.eq_of_sublist_of_length_eq", "filter.sInter_comap_sets", "ordinal.mul_is_limit_left", "real.arsinh_sinh", "finset.prod_eq_zero_iff", "monoid_hom.coe_mrange_restrict", "category_theory.limits.bicone.to_cocone_\[Iota]_app", "matrix.cons_zero_zero", "omega.coeffs.val_sub", "polynomial.splits_prod", "linear_map.prod_eq_sup_map", "is_open_gt'", "filter.mem_infi_sets", "pgame.add_comm_equiv", "stream.nth_zero_iterate", "list.take_sum_join", "le_supr_of_le", "finset.filter_ne", "galois_connection.u_unique", "linear_map.coe_fn_congr", "emetric.nhds_eq", "nat.decreasing_induction_self", "real.sqrt_eq_iff_mul_self_eq", "continuous_on.integrable_on_compact", "set.inter_diff_assoc", "sub_ne_zero", "filter.ptendsto'_of_ptendsto", "turing.blank_rel.trans", "encodable.decode2_inj", "lt_add_of_nonneg_of_lt'", "filter.binfi_sets_eq", "add_comm", "list.to_finset_surjective", "fintype.sum_fiberwise", 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"inner_eq_norm_mul_self_add_norm_mul_self_sub_norm_sub_mul_self_div_two", "pnat.xgcd_type.qp_eq", "list.infix_refl", "is_compl_top_bot", "option.map_some", "formal_multilinear_series.comp_partial_sum_target_tendsto_at_top", "fin.coe_fin_lt", "with_zero.mul_inv_rev", "matrix.tail_zero", "rat.mk_ne_zero_of_ne_zero", "add_right_injective", "multiset.map_const", "set.subset_sUnion_of_subset", "smooth.inv", "set.Ioc_union_Ioc", "category_theory.yoneda_evaluation_map_down", "nnreal.pow_eq_zero", "subgroup.map_supr", "iff.trans", "monoid_hom.lift_of_surjective_comp_apply", "fin.succ_rec_on_succ", "ennreal.coe_rpow_of_nonneg", "subring.coe_add", "fintype.of_equiv_card", "list.sublists_len_succ_cons", "continuous_linear_equiv.ext\:2081", "isometric.add_right_apply", "add_submonoid.localization_map.add_equiv_of_localizations_left_neg", "mul_div_assoc'", "option.map_id'", "omega.int.is_nnf_push_neg", "lie_subalgebra.mem_coe'", "nat.div_mod_unique", "category_theory.coyoneda_obj_map", "le_antisymm", "with_zero.mul_div_cancel", "cardinal_mk_eq_cardinal_mk_field_pow_dim", "filter.tendsto_at_bot_of_add_bdd_below_right'", "mul_lt_mul_of_le_of_lt", "finset.fold_op_rel_iff_and", "set.Ico_subset_Iio_self", "int.nonneg_of_pos", "measure_theory.ae_eq_fun.ext", "is_open_add_left", "category_theory.nat_trans.id_hcomp_app", "norm_num.nat_div", "is_ring_hom.comp", "submodule.map_mul", "gold_add_gold_conj", "ext_chart_at_continuous_at", "list.chain_split", "deriv_csinh", "equiv.sigma_preimage_equiv_apply", "associates.le_of_mul_le_mul_right", "category_theory.functor.map_presheaf_obj_X", "geom_series_one", "computable.vector_of_fn", "dist_pos", "monoid_hom.map_mrange", "nat.primrec'.prim_iff\:2081", "mv_power_series.inv_of_unit_eq'", "int.sign_neg_one", "nat.bit1_le_bit0_iff", "nat.modeq.modeq_add_cancel_left", "set.Ico_union_Ici_eq_Ici", "dioph.sub_dioph", "ring.fractional_ideal.span_singleton_mul_span_singleton", "list.sorted_nil", "times_cont_diff_on.prod_map", "ordinal.lift_cof", "matrix.update_column_self", "submodule.restrict_scalars_top", "filter.eventually_map", "mv_polynomial.monomial_mul", "multiset.erase_dup_zero", "nat.le_add_right", "exists_nhds_quarter", "differentiable_within_at.const_smul", "of_digits_zmodeq", "subgroup.normal_closure_normal", "has_fpower_series_on_ball.add", "linear_map.deriv", "polynomial.induction_on", "ennreal.to_real_add_le", "differentiable_on.cos", "alist.lookup_to_alist", "is_preconnected_Ioo", "asymptotics.is_o.congr_left", "int.shiftl_coe_nat", "local_equiv.prod_coe", "interval_integrable.refl", "category_theory.discrete.nat_iso_hom_app", "linear_map.equiv_prod_of_surjective_of_is_compl_apply", "measurable.prod_mk", "function.embedding.equiv_to_embedding_trans_symm_to_embedding", "fderiv_neg", "nhds_inf", "inv_image.trans", "measure_theory.simple_func.eapprox_comp", "metric.bounded_iff_subset_ball", "filter.binfi_sup_right", "ennreal.top_ne_one", "rat.mk_pnat_num", "filter.eventually_eq.div", "CommGroup.coe_of", "deriv_within_fpow", "irrational.of_inv", "with_one.lift_unique", "complex.continuous_linear_map.im_norm", "category_theory.limits.is_colimit.comp_cocone_point_unique_up_to_iso_hom", "lucas_lehmer.X.closed_form", "differentiable_within_at.cexp", "polynomial.coeff_mul_degree_add_degree", "complex.tanh_zero", "inf_le_inf_right", "continuous_multilinear_map.norm_map_cons_le", "list.subset_append_right", "submodule.smul_mem", "formal_multilinear_series.comp_along_composition_norm", "pgame.nim.sum_first_loses_iff_eq", "rat.mul_nonneg", "one_sub_gold", "mul_equiv.map_ne_one_iff", "cauchy_seq_of_dist_le_of_summable", "zero_pow", "finmap.mem_union", "is_coprime.add_mul_right_right", "finmap.insert_entries_of_neg", "metric.compact_iff_seq_compact", "zorn.chain_chain_closure", "mv_polynomial.mem_support_not_mem_vars_zero", "semidirect_product.range_inl_eq_ker_right_hom", "set.inter_Inter", "is_local_min_on.congr", "real.sin_add", "sub_lt_sub_left", "complex.continuous_re", "set.image_one", "lie_mem_left", "nat.div_lt_self", "int.bit0_pos", "finsupp.total_single", "rat.zero_mk_pnat", "category_theory.Monad.Monad_Mon_equiv_unit_iso", "continuous_linear_equiv.units_equiv_aut_symm_apply", "times_cont_diff_within_at.prod_map'", "measure_theory.integrable.add", "linear_map.range_comp", "tsum_nonneg", "category_theory.whiskering_left_obj_obj", "differentiable.snd", "min_mul_of_nonneg", "list.length_split_wrt_composition_aux", "exists_unique.exists", "is_bounded_bilinear_map.has_strict_fderiv_at", "decidable.or_iff_not_imp_left", "category_theory.limits.types.prod_map", "pnat.xgcd_type.flip_v", "category_theory.cancel_mono", "add_equiv.to_add_monoid_hom_apply", "set.nonempty_of_ssubset'", "lists'.to_of_list", "lt_mul_of_one_lt_of_lt", "nat.lcm_zero_left", "normed_field.tendsto_inv", "eq_neg_iff_add_eq_zero", "differentiable_on_fst", "complex.one_im", "add_group_with_zero_nhd.neg_Z", "is_preconnected.Icc_subset", "convex.mem_Ioc", "int.neg_succ_of_nat_eq'", "padic_val_nat.mul", "finset.prod_subtype", "polynomial.separable_iff_derivative_ne_zero", "stream.inits_core_eq", "subsemiring.list_sum_mem", "list.mem_traverse", "real.cos_pos_of_neg_pi_div_two_lt_of_lt_pi_div_two", "category_theory.iso.symm_self_conj", "list.zip_cons_cons", "differentiable.exp", "disjoint.sup_left", "measure_theory.measure.haar.prehaar_mem_haar_product", "mdifferentiable_on.mono", "isometric.point_reflection_symm", "filter.exists_ultrafilter_iff", "add_subgroup.multiset_sum_mem", "int.eq_coe_of_zero_le", "int.even_pow", "multiset.card_le_of_le", "differentiable_at.sub", "to_topological_space_mono", "ideal.map_eq_bot_iff_le_ker", "disjoint_iff", "is_coprime.map", "category_theory.limits.colimit.\[Iota]_desc", "list.tendsto_cons'", "pgame.le_zero_iff_zero_le_neg", "metric.dist_le_diam_of_mem'", "category_theory.limits.cokernel_image_\[Iota]_hom", "prime_spectrum.basic_open_open", "succ_dvd_or_succ_dvd_of_succ_sum_dvd_mul", "min_choice", "matrix.cramer_is_linear", "computation.lift_rel.swap", "is_R_or_C.nat_cast_im", "mul_self_sub_mul_self_eq", "localization_map.ext", "norm_num.zero_adc", "with_zero.zero_lt_coe", "holor.cprank_max_add", "category_theory.limits.biprod.lift_eq", "is_compact.uniform_continuous_on_of_continuous'", "category_theory.arrow.mk_hom", "list.nth_mem", "powers.self_mem", "mvqpf.cofix.mk_dest", "times_cont_diff_within_at.neg", "polynomial.coeff_X_pow_self", "submonoid.comap_le_comap_iff_of_surjective", "turing.reaches.to\:2080", "is_unit.mul_left_inj", "inner_product_geometry.norm_add_square_eq_norm_square_add_norm_square_iff_angle_eq_pi_div_two", "zero_lt_bit0", "quot.factor_mk_eq", "metric.uniform_continuous_iff", "category_theory.limits.limit.lift_\[Pi]", "cardinal.ord_nat", "mv_polynomial.is_homogeneous_C", "norm_num.clear_denom_simple_div", "continuous.comp", "fin.find_eq_some_iff", "nat.bit0_ne_one", "power_series.order_mul_ge", "multiset.map_congr", "turing.list_blank.cons_bind", "filter.pure_sets", "surj_on_Icc_of_monotone_surjective", "is_local_extr.deriv_eq_zero", "has_deriv_at_filter_iff_tendsto", "znum.zneg_bitm1", "list.zip_append", "filter.Liminf_bot", "list.chain'_split", "zmod.legendre_sym_eq_one_iff", "add_submonoid.gc_map_comap", "right_ord_continuous.order_dual", "wseq.lift_rel_map", "nat.size_eq_zero", "ring_hom.coe_of", "set.diff_inter", "zmod.le_div_two_iff_lt_neg", "emetric.diam_mono", "has_strict_fderiv_at.add", "mul_div_assoc", "equiv.swap_core_self", "ennreal.sum_lt_top_iff", "metric.completion.coe_isometry", "setoid.comap_eq", "mul_divp_cancel", "category_theory.epi_iff_surjective", "measurable.nndist", "has_ftaylor_series_up_to.has_fderiv_at", "ordinal.add_le_add_left", "nat.bit0_ne_bit1", "tsum_le_tsum_of_inj", "multiset.coe_sub", "function.uncurry_def", "generalized_continued_fraction.int_fract_pair.seq1_fst_eq_of", "category_theory.limits.binary_cofan.mk_\[Iota]_app_left", "computation.of_results_bind", "sup_lt_iff", "ne.intro", "lagrange.eq_interpolate", "bitraversable.tsnd_comp_tsnd", "nat.Inf_eq_zero", "measure_theory.simple_func.integral_add_measure", "div_div_eq_mul_div", "finset.prod_insert_of_eq_one_if_not_mem", "int.neg_inj", "rat.add_assoc", "con.inf_def", "ideal.mul_eq_inf_of_coprime", "submodule.prod_coe", "ring_hom.iterate_map_smul", "free_group.inv_mk", "mv_polynomial.eval\:2082_neg", "equiv.coe_prod_congr", "category_theory.Monad.of_to_mon_end_iso_inv_app_hom", "onote.eq_of_cmp_eq", "emetric.inf_edist_le_edist_of_mem", "differentiable_within_at.smul", "equiv.perm.sign_bij_aux_surj", "one_lt_bit1", "div_eq_mul_inv", "continuous_linear_map.coe_prod", "measure_theory.integrable_at_filter.filter_mono", "poly.sumsq_nonneg", "nat.partrec'.part_iff\:2081", "derive_fintype.finset_above.mem_cons_of_mem", "ideal.mem_jacobson_iff", "linear_map.span_inl_union_inr", "list.foldr_eq_of_comm'", "min_assoc", "measure_theory.ae_eq_refl", "formal_multilinear_series.comp_assoc", "Top.presheaf.pushforward.id_hom_app", "deriv_rpow_of_one_le", "quadratic_eq_zero_iff_of_discrim_eq_zero", "approximates_linear_on.inverse_approx_map_dist_self", "closure_induced", "is_extr_on.localize", "linear_map.comp_eq_id_comm", "cardinal.ord_le_type", "function.surjective.sigma_map", "ordinal.card_typein", "antilipschitz_with.to_right_inv_on", "pgame.grundy_value_zero", "filter.comap_has_basis", "list.concat_cons", "imp_or_distrib", "ordinal.limit_rec_on_zero", "nat.lxor_zero", "int.neg_neg_of_pos", "measure_theory.outer_measure.coe_smul", "multiset.le_add_right", "filter.high_scores", "turing.tape.map_mk\:2082", "set.prod_range_range_eq", "uniformly_extend_spec", "continuous_linear_equiv.subsingleton_or_norm_symm_pos", "set.inj_on.mono", "cauchy_seq_of_le_geometric_two", "int.lt_of_sub_one_le", "dfinsupp.support_sum", "pfunctor.M.corec_def", "local_homeomorph.prod_trans", "filter.tendsto_at_bot_pure", "fin.cast_succ_cast_lt", "continuous_linear_map.norm_id_le", "num.dvd_iff_mod_eq_zero", "add_neg_le_iff_le_add", "cardinal.nat_succ", "seq1.join_cons", "equiv.perm.sign_aux_swap", "complex.sin_of_real_im", "computation.results_ret", "category_theory.monoidal_category.left_unitor_nat_iso_hom_app", "category_theory.limits.colimit.\[Iota]_post", "with_top.one_ne_top", "category_theory.limits.image_mono_iso_source_inv_\[Iota]", "pgame.nim.nim_def", "nat.partrec.code.const_inj", "coe_affine_span", "continuous_linear_map.map_sub", "is_add_group_hom.neg_ker_zero", "dioph.and_dioph", "is_totally_disconnected_empty", "set.countable_encodable'", "stream.interleave_even_odd", "ideal.mem_of_one_mem", "filter.seq_mono", "linear_map.inr_apply", "geom_sum\:2082_mul_add", "complex.norm_sq_eq_abs", "real.sin_bound", "category_theory.bifunctor.diagonal", "multilinear_map.uncurry_right_apply", "ring_hom.eq_of_eq_on_set_dense", "set.eq_on.inj_on_iff", "monoid_algebra.lift_unique", "nat.find_greatest_spec", "finsupp.bot_eq_zero", "differentiable_at.differentiable_within_at", "units.to_Aut_hom", "list.zip_map_right", "measure_theory.integral_non_integrable", "complex.norm_sq_div", "is_compact.inter_left", "finset.mem_image", "multiset.filter_map_some", "Top.presheaf_to_Type_obj", "ennreal.sub_infi", "padic_val_rat.neg", "polynomial.monic_X", "add_commute.eq", "submodule.fg_prod", "is_preconnected.Iio_cSup_subset", "local_homeomorph.refl_target", "int.prime.dvd_mul", "filter.eventually_le.is_local_max", "fintype.card_perm", "add_subgroup.is_open_of_open_add_subgroup", "finsupp.order_iso_multiset_symm_apply", "list.Ico.bag_inter_consecutive", "mul_eq_mul_of_div_eq_div", "quadratic_form.add_lin_mul_lin", "has_deriv_at_filter.neg", "category_theory.adjunction.monad_\[Mu]_app", "roption.mem_to_option", "units.val_coe", "norm_num.add_bit0_bit0", "has_fderiv_within_at.comp_has_deriv_within_at", "nat.dist_eq_sub_of_le", "int_prod_range_nonneg", "submodule.mk_eq_zero", "ordinal.lift.principal_seg_top", "nat.sub_add_min_cancel", "finsupp.range_total", "measurable_of_continuous_on_compl_singleton", "finset.erase_dup_eq_self", "category_theory.functor.op_map", "list.suffix_or_suffix_of_suffix", "category_theory.adjunction.left_triangle_components_assoc", "int.div2_val", "encodable.decode_sum_val", "matrix.mul_mul_left", "polynomial.map_mod", "cardinal.two_le_iff", "ennreal.sup_eq_max", "monoid_hom.map_mul_inv", "multiset.powerset_len_coe", "multiset.card_powerset_len", "mem_closure_iff_nhds_basis", "submonoid.coe_coe", "finset.nat.antidiagonal_zero", "free_comm_ring.is_supported_one", "matrix.col_vec_mul", "inv_one", "asymptotics.is_O_const_const", "int.sub_mod", "Gromov_Hausdorff.to_GH_space_continuous", "measure_theory.simple_func.norm_integral_le_integral_norm", "set.Icc_subset_Ici_iff", "list.append_inj_right'", "mul_left_iterate", "finset.sdiff_eq_self", "smul_lt_smul_of_pos", "ennreal.to_real_le_of_le_of_real", "mem_own_left_add_coset", "metric.tendsto_uniformly_iff", "roption.get_eq_of_mem", "continuous_linear_equiv.comp_fderiv_within", "turing.TM2.stmts_trans", "list.perm_inv_core", "roption.of_option_eq_get", "measure_theory.outer_measure.of_function_le", "closure_minimal", "nat.zero_ne_bit0", "vector.to_list_mk", "cardinal.mk_sum_compl", "linear_map.ker_id_sub_eq_of_proj", "multilinear_map.map_smul_univ", "one_lt_two", "generalized_continued_fraction.of_correctness_of_nth_stream_eq_none", "ring_hom.map_geom_series\:2082", "linear_independent_subtype", "CommRing.colimits.quot_zero", "finset.insert_sdiff_of_mem", "filter.frequently_Sup", "submodule.span_image", "zsqrtd.sq_le_mul", "add_subgroup.coe_supr_of_directed", "category_theory.limits.cokernel_cofork.condition_assoc", "units.inv_mul'", "le_add_of_neg_add_le_right", "filter.tendsto_at_top_mono'", "qpf.comp_map", "set.univ_add_univ", "local_homeomorph.refl_local_equiv", "summable_of_norm_bounded", "filter.eventually_eq.times_cont_mdiff_at_iff", "finset.exists_ne_one_of_prod_ne_one", "cardinal.lift_down", "fin.succ_above_above", "has_fpower_series_on_ball.has_fpower_series_at", "nnreal.div_add_div", "cardinal.lift_lt_univ'", "is_R_or_C.of_real_fpow", "finsupp.support_on_finset_subset", "znum.cast_add", "measure_theory.measure.haar_outer_measure_eq_infi", "category_theory.limits.epi_of_target_iso_zero", "pythagorean_triple.is_classified_of_is_primitive_classified", "set.indicator_self_add_compl", "mv_polynomial.sum_homogeneous_component", "list.filter_cons_of_pos", "nhds_contain_boxes_of_compact", "multiset.erase_lt", "ordered_ring.mul_lt_mul_of_pos_right", "multiset.countp_pos", "quotient_add_group.coe_add", "list.mem_diff_of_mem", "zmod.cast_hom_apply", "polynomial.to_subring_zero", "is_path_connected.subset_path_component", "multiset.count_pos", "turing.tr_reaches", "lt_mul_of_inv_mul_lt_left", "finset.union_sdiff_self_eq_union", "multiset.mem_singleton_self", "cardinal.sup_le_sum", "add_monoid_hom.coprod_apply", "finset.min'_lt_max'_of_card", "set.image_surjective", "int.modeq.trans", "uniformity_comap", "frobenius_def", "filter.at_top_finset_eq_infi", "open_embedding_inr", "three_dvd_iff", "normed_ring.inverse_one_sub_nth_order", "ideal.comap_jacobson_of_surjective", "sum.lex_inr_inl", "mem_comp_comp", "add_submonoid.coe_bot", "category_theory.constant_of_preserves_morphisms", "is_R_or_C.norm_sq_eq_def", "ring.direct_limit.of_zero", "asymptotics.is_o_iff", "pgame.grundy_value_add", "uniformity_basis_edist_nnreal", "list.mem_singleton", "category_theory.equivalence.cancel_unit_right", "has_deriv_within_at.congr_mono", "pi_Lp.neg_apply", "smooth_pow", "abs_abs", "polynomial.eval\:2082_sub", "complex.continuous_tan", "contract_left_apply", "set.compl_inv", "filter.tendsto.prod_mk_nhds", "set.mem_sUnion_of_mem", "real.continuous_mul", "filter.prod_comm", "finsupp.sum_comm", "set.countable_iff_exists_surjective", "zmod.cast_sub", "cfilter.mem_to_filter_sets", "list.Ico.filter_le_of_le", "min_max_distrib_left", "Iio_mem_nhds", "nat.pow_dvd_pow", "heq.subst", "direct_sum.single_eq_lof", "nat.bit_lt_bit0", "alist.lookup_erase", "submonoid.localization_map.mul_inv", "times_cont_diff_on_iff_continuous_on_differentiable_on_deriv", "hyperreal.infinite_neg_mul_of_not_infinitesimal_pos_infinite_neg", "stream.even_cons_cons", "fintype.pi_finset_subset", "continuous_on_extend_from", "filter.eventually_eq.mul", "measure_theory.measure.haar.nonempty_Inter_cl_prehaar", "has_strict_deriv_at.sum", "measure_theory.simple_func.integrable_iff_fin_meas_supp", "open_add_subgroup.mem_nhds_zero", "pairwise_disjoint_on_bool", "times_cont_mdiff_on_snd", "neg_add_lt_left_of_lt_add", "multiset.bind_cons", "units.mul_lift_right_inv", "add_submonoid.coe_ssubset_coe", "semiquot.get_mem", "nat.even_zero", "mul_action_hom.to_quotient_apply", "nsmul_zero", "d_array.ext'", "decidable.not_imp", "list.join_eq_nil", "category_theory.limits.prod.map_iso_inv", "list.func.get_add", "nat.succ_injective", "pmf.pure_bind", "measure_theory.l1.simple_func.of_simple_func_sub", "linarith.int.coe_nat_one_mul", "cardinal.add_le_add", "category_theory.equivalence.cancel_counit_inv_right", "metric.inf_dist_nonneg", "tendsto_at_top_infi_nat", "filter.mem_at_top", "tendsto_neg", "list.index_of_cons_self", "continuous_on.continuous_within_at", "int.pred_nat_succ", "complex.of_real_rat_cast", "finset.mem_fin_range", "fin.sum_univ_succ", "one_div_nonpos", "inner_add_right", "multiset.coe_join", "finset.choose_property", "inf_comm", "riesz_extension.step", "omega.nat.preform.holds_constant", "concave_on.smul", "cau_seq.const_le", "classical.exists_true_of_nonempty", "associated.symm", "list.sublists_aux\:2081_concat", "list.index_of_argmax", "finset.image_subset_iff", "list.forall\:2082_length_eq", "filter_basis.eq_infi_principal", "subsemiring.mem_supr_of_directed", "real.exp_lt_exp", "computation.equiv_of_mem", "local_equiv.prod_source", "abs_le_of_le_of_neg_le", "linear_map.prod_apply", "continuous_linear_map.has_fderiv_at_filter", "category_theory.curry_natural_left", "tendsto_swap_uniformity", "pell.xy_modeq_yn", "cluster_pt.of_le_nhds", "category_theory.limits.cokernel_not_mono_of_nonzero", "submodule.findim_quotient_add_findim", "subsemiring.Inf_to_submonoid", "int.of_nat_add", "edist_triangle4", "zsqrtd.bit0_im", "ctop.realizer.is_basis", "is_G\[Delta]_Inter_of_open", "partrec.rfind_opt", "multilinear_map.map_sum_finset", "set.mem_of_mem_inter_right", "is_add_subgroup.of_add_neg", "option.orelse_none'", "cauchy_seq_tendsto_of_complete", "alg_hom.commutes", "distrib_three_right", "roption.eta", "has_mfderiv_within_at.mono", "tactic.ring_exp.prod_congr", "mv_polynomial.eval\:2082_monomial", "prime_spectrum.subset_vanishing_ideal_zero_locus", "div_le_div_right_of_neg", "matrix.diagonal_apply_ne'", "model_with_corners_self_coe", "magma.free_semigroup.map_of", "is_trichotomous.swap", "nat.zero_shiftl", "submodule.mem_bot", "pSet.equiv.eq", "order_top.tendsto_at_top_nhds", "inv_le_of_inv_le", "formal_multilinear_series.comp_along_composition_nnnorm", "euclidean_geometry.orthogonal_projection_linear", "discrete_valuation_ring.unit_mul_pow_congr_unit", "sup_of_le_left", "add_subgroup.bot_sum_bot", "measure_theory.l1.of_fun_to_fun", "fixed_points.minpoly.irreducible_aux", "linear_map.subtype_comp_cod_restrict", "cardinal.le_sup", "is_bounded_bilinear_map_smul", "hyperreal.infinite_mul_of_not_infinitesimal_infinite", "cardinal.mk_compl_eq_mk_compl_infinite", "irrational_neg_iff", "set.finite.exists_finset", "relation.refl_trans_gen.symmetric", "free_group.map.id", "localization.mk_one_eq_of", "is_compact.compl_mem_sets", "real.rpow_mul", "continuous_linear_equiv.comp_times_cont_diff_within_at_iff", "ring_equiv.injective", "emetric.inf_edist_closure", "implies.trans", "category_theory.limits.kernel_comp_is_iso_inv", "filter.is_cobounded_bot", "submodule.smul_bot", "function.is_fixed_pt.left_of_comp", "exists_elim_eq_left", "add_subgroup.coe_mk", "hyperreal.not_infinite_pos_add_infinite_neg", "vector.remove_nth_insert_nth_ne", 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"has_fderiv_at.iterate", "fin.snoc_last", "ring_hom.prod_map_def", "dense_sUnion_interior_of_closed", "semiconj_by.mul_right", "sesq_form.smul_left", "submodule.dim_sup_add_dim_inf_eq", "rel.preimage_union", "linear_equiv.trans_symm", "is_scalar_tower.of_algebra_map_eq", "primrec.succ", "measure_theory.simple_func.piecewise_empty", "pgame.turn_bound_ne_zero_of_right_move", "list.nth_update_nth_eq", "category_theory.functor.left_op_map", "set.eq_of_Ico_disjoint", "polynomial.monic_map", "add_one_gsmul", "traversable.pure_transformation_apply", "set.subset_bInter", "list.sum_singleton", "sequentially_complete.le_nhds_of_seq_tendsto_nhds", "matrix.sum_mul", "is_lub.union", "complex.continuous_linear_map.of_real_coe", "succ_ne_self", "ordinal.add_le_add_iff_left", "multiset.sum_map_mul_right", "mv_polynomial.sum_mv_polynomial_eq_zero", "isometric.add_left_to_equiv", "dist_le_range_sum_of_dist_le", "list.forall_mem_of_forall_mem_union_left", "polynomial.degree_le_zero_iff", 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"bilin_form.is_adjoint_pair_iff_comp_left_eq_comp_right", "composition.length_sigma_composition_aux", "Module.monoidal_category.right_unitor_naturality", "generalized_continued_fraction.zeroth_convergent_eq_h", "subgroup.coe_infi", "set.abs_sub_le_of_subinterval", "uniform_continuous_dist", "add_aut.coe_mul", "int.sub_self", "local_homeomorph.restr_source'", "mfderiv_within_univ", "lie_gsmul", "submodule.exists_of_lt", "omega.int.val_canonize", "polynomial.nat_degree_X_le", "dense_range.induction_on\:2082", "filter.frequently.mem_of_closed", "nat.gcd_zero_left", "wseq.map_nil", "list.drop_append", "nnreal.has_sum_iff_tendsto_nat", "mul_equiv.trans_apply", "free_group.red.step.append_left", "forall_lt_iff_le", "multiset.zero_product", "zsqrtd.bit0_re", "push_neg.not_le_eq", "stream.map_iterate", "is_bounded_bilinear_map.fderiv", "lipschitz_with.restrict", "finite_field.sum_pow_lt_card_sub_one", "polynomial.sum_over_range'", "disjoint_self", "isometric.coe_vadd_const_symm", 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"list.perm.inter_left", "convex_on_of_deriv_mono", "has_sum_ite_eq", "fin.cons_self_tail", "measure_theory.simple_func.map_preimage_singleton", "int.bitwise_xor", "list.take_prefix", "polynomial.mul_comp", "div_two_sub_self", "subtype.preirreducible_space", "set.bUnion_subset_Union", "dlist.of_list_to_list", "string.lt_iff_to_list_lt", "irrational.of_pow", "finset.subset.antisymm", "int.lcm_zero_left", "ring_hom.comp_id", "homological_complex.kernel_map_id", "differentiable_const", "ennreal.tsum_comm", "submodule.infi_coe", "differentiable_within_at.prod", "multiset.disjoint_cons_left", "pnat.eq_one_of_lt_two", "algebra.tensor_product.rid_tmul", "nnreal.rpow_nat_inv_pow_nat", "filter.is_basis.mem_filter_iff", "real.continuous_cos", "lucas_lehmer.X.left_distrib", "set.bdd_below_bdd_above_iff_subset_interval", "category_theory.differential_object.hom.ext_iff", "not_and_self_iff", "multiset.revzip_powerset_aux'", "add_monoid_hom.map_multiset_sum", "apply_dite", "roption.map_some", 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"list.perm.product_right", "mul_action_hom.id_comp", "or_iff_right_of_imp", "add_submonoid.mem_nhds_zero", "int.nat_abs_add_nonneg", "times_cont_diff_on_of_locally_times_cont_diff_on", "fderiv_within_subset", "localization_map.map_comp", "is_group_hom.mk'", "fderiv_within.comp_deriv_within", "game.zero_add", "pell.is_pell_one", "AddCommMon.coe_of", "padic_int.unit_coeff_coe", "add_semiconj_by.conj_mk", "matrix.to_linear_equiv_symm_apply", "Gromov_Hausdorff.candidates_b_dist_mem_candidates_b", "measure_theory.to_outer_measure_eq_induced_outer_measure", "fintype.univ_pempty", "is_basis_singleton_one", "finset.filter_empty", "is_closed_compl_iff", "function.curry_uncurry", "contracting_with.fixed_point_lipschitz_in_map", "supr_union", "set.sup_eq_union", "is_unit.lift_right_inv_mul", "ideal.map_sup_comap_of_surjective", "push_neg.not_lt_eq", "is_glb_Ioc", "real.arctan_lt_pi_div_two", "complex.has_deriv_at_exp", "category_theory.monoidal_category.unitors_equal.cells_1_7", "encodable.encode_inl", "omega.forall_mem_repeat_zero_eq_zero", "measure_theory.ae_eq_fun.mk_coe_fn", "galois_insertion.l_supr_of_ul_eq_self", "tendsto_locally_uniformly_on.tendsto_comp", "localization_map.mul_mk'_eq_mk'_of_mul", "tsum_neg", "with_bot.some_le_some", "filter.ultrafilter_of_spec", "list.monotone_sum_take", "nat.sub_induction", "zero_dvd_iff", "inv_injective'", "lim_norm", "add_sub_cancel'_right", "summable.sigma", "nat.partrec'.idv", "continuous.comp_continuous_on", "associates.irreducible_mk_iff", "matrix.cramer_apply", "typevec.append_prod_append_fun", "matrix.row_mul_col_apply", "subgroup.normal_comap", "norm_num.nat_cast_bit0", "finset.sigma_preimage_mk", "ennreal.bot_lt_iff_ne_bot", "iterated_deriv_within_zero", "measure_theory.measure.join_dirac", "finset.coe_erase", "commute.inv_inv'", "nhds_nhds_eq_uniformity_uniformity_prod", "category_theory.is_equivalence.inv_fun_id_inv_comp", "lie_subalgebra.ext_iff", "polynomial.as_sum", "submodule.map_inr", 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"filter.has_basis.sInter_sets", "map_nhds_subtype_coe_eq", "padic_int.mod_part_nonneg", "matrix.special_linear_group.to_GL_one", "real.sqrt_zero", "nat.rfind_min", "asymptotics.is_O_with.sub", "submodule.mem_top", "set.finite.mem_to_finset", "cardinal.mk_subset_ge_of_subset_image", "subgroup.normal.comap", "set.preimage_const_mul_Ioc_of_neg", "list.range_succ_eq_map", "finset.prod_comp", "submodule.prod_inf_prod", "nat.mul_zero", "add_submonoid.mem_map", "sigma.ext", "finset.coe_empty", "alg_hom.ext", "ennreal.mul_le_iff_le_inv", "category_theory.limits.biprod.map_snd", "polynomial.is_splitting_field.finite_dimensional", "ring_hom.map_one_ne_zero", "filter.eventually_eq.fderiv_eq", "fintype.card_subtype_le", "computation.eq_thinkN", "polynomial.map_monic_eq_zero_iff", "additive.is_add_group_hom", "of_irreducible_mul", "is_basis.total_repr", "erased.out_inj", "mem_nhds_iff_exists_Ioo_subset", "submodule.is_principal.eq_bot_iff_generator_eq_zero", "exists_nhds_split", "alg_hom.id_apply", "continuous_on.congr", "ordinal.zero_lt_one", "mul_inv_of_self", "nat.bodd_div2_eq", "filter.ne_bot.comap_of_range_mem", "multiset.mem_to_finset", "matrix.update_row_self", "ennreal.has_sum_coe", "finsupp.single_apply", "add_submonoid.closure_Union", "finset.sum_boole", "category_theory.currying_functor_obj_obj", "differentiable_on.const_mul", "set.preimage_mul_const_Iic", "set.Union_subset_iff", "filter.ne_bot_of_le", "matrix.mul_adjugate_apply", "mul_self_le_mul_self_iff", "complex.differentiable_at_cos", "left_coset_right_coset", "filter.has_basis.prod_self", "set.fst_image_prod_subset", "affine.simplex.sum_points_with_circumcenter", "structure_groupoid.trans", "char_p.exists_unique", "set.mem_mul", "W.depth_pos", "dvd.elim", "polynomial.leading_coeff_prod", "indicator_union_eventually_eq", "polynomial.leading_coeff_of_injective", "finsupp.total_apply", "list.sublists_aux_cons_eq_sublists_aux\:2081", "array.read_write", "semidirect_product.map_right", "category_theory.limits.biprod.inr_snd", "Mod.comap_obj_act", "set.image_subset_image_iff", "unique_mdiff_on_iff_unique_diff_on", "measure_theory.ae_eq_fun.mk_to_germ", "free_semigroup.traverse_eq", "list.erasep_of_forall_not", "pequiv.symm_bot", "bool.coe_sort_ff", "formal_multilinear_series.partial_sum_continuous", "units.mk_semiconj_by", "has_fderiv_at_snd", "finset.insert_subset", "padic_int.norm_int_lt_one_iff_dvd", "closure_inter_subset_inter_closure", "list.dvd_sum", "list.update_nth_eq_nil", "rat.le_antisymm", "tendsto_neg_nhds_within_Iio_neg", "multiset.coe_eq_zero", "hyperreal.not_infinitesimal_of_infinite", "computable.fst", "real.is_conjugate_exponent.ne_zero", "topological_space.opens.gc", "filter.principal_empty", "num.cast_pos", "list.rotate_length_mul", "ennreal.mul_rpow_of_ne_zero", "finite_dimensional.exists_is_basis_finset", "nat.sqrt_aux_1", "max_mul_mul_le_max_mul_max", "equiv.sum_congr_symm", "differentiable_within_at_id", "ideal.sup_mul", "finsupp.comap_smul_apply", "deriv_within_subset", "computable_pred.computable_of_one_one_reducible", "category_theory.prod.inverse_associator_map", "set.Ioc_subset_Ioc_union_Ioc", "interval_integral.integral_sub_integral_sub_linear_is_o_of_tendsto_ae_left", "finset.sum_nsmul", "complex.continuous_inv", "nnreal.inv_pos", "int.lt_neg_of_lt_neg", "filter.has_basis.mem_of_mem", "max_zero_sub_eq_self", "multiset.disjoint_add_right", "list.rel_of_chain_cons", "times_cont_diff_on_congr", "filter.has_basis_infi_principal", "euclidean_geometry.reflection_symm", "is_compact.exists_is_least", "finsupp.map_range_finset_sum", "times_cont_mdiff_on.prod_mk", "zmod.pow_card_sub_one_eq_one", "multiset.sections_add", "set.ord_connected_iff", "subsemiring.mem_Inf", "computation.bind_ret", "metric.completion.mem_uniformity_dist", "fpow_mul'", "ideal.comap_map_comap", "metric.uniform_embedding_iff", "ennreal.lt_add_right", "AddCommGroup.colimits.quot_add", "list.foldl_map'", "multilinear_map.map_zero", "rel_iso.map_rel_iff", "measure_theory.measure_congr", "list.mem_permutations", "primrec\:2082.curry", "int.mul_le_mul_of_nonpos_right", "equiv.empty_sum_apply_inr", "continuous_within_at_snd", "associates.normalize_out", "wseq.map_join", "linarith.eq_of_not_lt_of_not_gt", "prime_multiset.prod_of_prime", "filter.realizer.of_equiv_F", "is_bounded_linear_map_prod_multilinear", "supr_singleton", "set.indicator_finset_bUnion", "one_add_gsmul", "finset.sum_empty", "set.image_inter", "lucas_lehmer.order_ineq", "ideal.le_radical", "complex.rat_cast_re", "cauchy_seq.mem_entourage", "category_theory.monoidal_category.unitors_equal.cells_10_13", "add_commute.units_neg_left", "function.surjective.comp", "and_comm", "order.cofinal.above_mem", "nnreal.lt_sub_iff_add_lt", "add_aut.inv_def", "is_local_min_on.fderiv_within_nonneg", "mvpfunctor.Wp_ind", "measure_theory.measure.measurable_coe", "left_inverse_neg", "bifunctor.fst_snd", "distrib_mul_action_hom.ext", "polynomial.multiplicity_finite_of_degree_pos_of_monic", "measure_theory.measure.haar.is_left_invariant_chaar", "int.zero_lt_one", "int.sub_le_sub_right", "decidable.and_iff_not_or_not", "list.mem_iff_nth_le", "filter.tendsto.div", "polynomial.root_X_sub_C", "commute.refl", "dfinsupp.single_apply", "affine.triangle.orthocenter_mem_altitude", "computation.bind_congr", "polynomial.degree_pos_induction_on", "exists_gpow_eq_one", "mul_inv_eq_iff_eq_mul", "dual_pair.coeffs_apply", "category_theory.abelian.pseudoelement.zero_morphism_ext'", "preimage_equivalence", "open_add_subgroup.mem_coe_opens", "le_nhds_of_cauchy_adhp_aux", "real.rpow_one", "is_local_max.neg", "differentiable_at.smul", "multiset.sum_map_add", "imp_congr", "multiset.mem_ndinsert", "inner_sum", "subgroup.subset_normal_closure", "has_mfderiv_within_at.union", "finset.not_mem_erase", "finsupp.unique_single", "list.ilast'_mem", "normal_separation", "ideal.le_comap_sup", "free_abelian_group.neg_bind", "continuous_multilinear_map.map_smul", "dfinsupp.sum_map_range_index", "finset.range_eq_Ico", "Gromov_Hausdorff.totally_bounded", "matrix.mul_val_succ", "ennreal.one_rpow", "is_unit_of_add_is_unit_right", "submonoid.coe_comap", "concave_on_iff_convex_hypograph", "finset.sum_attach", "irrational.of_fpow", "nnreal.div_one", "prod.fst_surjective", "list.not_eq_key", "subring.forall", "encodable.decode_option_zero", "trichotomous_of", "function.support_min", "primrec\:2082.nat_iff'", "vector.naturality", "metric.bounded_iff_mem_bounded", "subgroup.normal_in_normalizer", "typevec.append_fun_comp_split_fun", "ordinal.lt_mul_div_add", "cSup_union", "ennreal.nhds_of_ne_top", "multiset.filter_map_map", "open_subgroup.ext", "isometry.isometric_on_range_apply", "mvpfunctor.M.bisim'", "add_monoid_hom.map_real_smul", "category_theory.limits.parallel_pair_obj_zero", "complete_space_coe_iff_is_complete", "irreducible.separable", "list.func.map_add_map", "matrix.cons_nonzero_iff", "is_bounded_le_nhds", "category_theory.limits.coprod_map_map", "list.eq_nil_of_prefix_nil", "finsupp.inf_apply", "monotone.add_strict_mono", "list.find_mem", "continuous_snd", "is_integral_of_noetherian", "list.inter_subset_right", "encodable.sorted_univ_nodup", "nat.shiftr_add", "list.map_nil", "order.cofinal_meets_ideal_of_cofinals", "adjoin_root.eval\:2082_root", "linear_map.std_basis_eq_single", "prod.smul_snd", "add_subgroup.normal_comap", "equiv.forall_congr", "tendsto_inv_zero_at_top", "sub_one_lt_floor", "structure_groupoid.local_invariant_prop.lift_prop_within_at_inter", "pos_num.add_to_nat", "pequiv.inj", "has_deriv_within_at.union", "induced_mono", "finset.card_pos", "convex_interval", "is_preconnected.union", "finsupp.filter_zero", "set.inter_eq_self_of_subset_left", "complex.differentiable_at_sin", "tendsto_at_top_supr", "set.ne_empty_iff_nonempty", "bilin_form.sub_left", "finmap.keys_ext", "pgame.nim.exists_move_left_eq", "tendsto_const_uniformity", "set.subset_inter_iff", "matrix.one_mul", "real.of_rat_lt", "nnreal.rpow_sub'", "mul_neg_of_neg_of_pos", "smul_lie", "has_sum_mul_left_iff", "le_sub_left_of_add_le", "bdd_above_iff_subset_Iic", "one_div_neg", "set.Union_union", "nat.partrec.code.of_nat_code_eq", "int.gcd_dvd_gcd_of_dvd_right", "list.bind_eq_bind", "lie_algebra.equiv.symm_symm", "gaussian_int.to_complex_zero", "ring_hom.map_iterate_pth_root", "matrix.transpose_map", "category_theory.limits.biprod.symmetry_assoc", "finset.card_eq_zero", "add_neg", "card_vector", "mem_left_add_coset_left_add_coset", "category_theory.Monad.of_Mon_func", "category_theory.limits.equalizer.fork_\[Iota]", "pnat.xgcd_type.flip_w", "mul_right_inj'", "is_topological_fiber_bundle_snd", "real.cos_pi", "norm_sum_le_of_le", "two_ne_zero'", "real.Lp_add_le_of_nonneg", "ennreal.rpow_nat_cast", "times_cont_diff_within_at.comp", "set.piecewise_empty", "filter.tendsto_Ixx_class_of_subset", "bounded_continuous_function.equicontinuous_of_continuity_modulus", "free_group.map.of", "linear_action_act_add", "mul_pow", "submodule.range_mkq", "multiset.sum_cons", "filter.germ.const_lt", "ordinal.lift_type_fin", "norm_sub_le_of_le", "not_prime_zero", "nhds_top_order", "real.is_conjugate_exponent.sub_one_ne_zero", "deriv_within_congr", "affine.simplex.eq_circumradius_of_dist_eq", "ordinal.le_sup", "pgame.add_lt_add_right", "cardinal.sum_lt_prod", "list.product_cons", "finsupp.supported_empty", "multiset.le_inter_iff", "list.lt_eq_not_ge", "finsupp.single_injective", "uniform_continuous_of_const", "real.one_lt_rpow", "is_max_on.sup", "polynomial.nat_degree_nat_cast", "commute.mul_gpow", "Gromov_Hausdorff.HD_candidates_b_dist_le", "linear_map.map_comap_eq_self", "set.compl_bInter", "sub_sub_sub_cancel_left", "not.imp_symm", "polynomial.map_add", "subspace.closed_complemented_of_quotient_finite_dimensional", "set.image_const_sub_Ioc", "fintype.well_founded_of_trans_of_irrefl", "generalized_continued_fraction.of_one_le_nth_part_denom", "is_R_or_C.of_real_sub", "filter.principal_le_lift'", "list.filter_map_cons", "is_local_min.bicomp_mono", "infi_univ", "continuous_linear_map.proj_ker_of_right_inverse_comp_inv", "nat.case_strong_induction_on", "equiv.coe_add_left", "equiv.subsingleton", "set.ord_connected.inter", "derivation.map_neg", "complex.bit0_re", "function.support_comp_subset", "direct_sum.of_smul", "add_con.to_add_submonoid_inj", "bool.to_bool_and", "rel.preimage_id", "neg_dvd_of_dvd", "principal_seg.top_eq", "is_extr_filter_const", "multiset.Ico.filter_le_of_top_le", "subgroup.is_open_mono", "fintype.prod_fiberwise", "intermediate_value_Icc'", "local_homeomorph.ext", "pSet.mem.congr_left", "alist.perm_erase", "set.nonempty_def", "local_homeomorph.eq_on_source.symm_eq_on_target", "ordinal.not_succ_of_is_limit", "int.mul_div_cancel_of_mod_eq_zero", "equiv.perm.eq_swap_of_is_cycle_of_apply_apply_eq_self", "traversable.fold_map_map", "equiv.sum_comm_symm", "fpow_add_one", "sub_le_sub_right", "convex_on.comp_linear_map", "nat.bit_lt_bit", "int.bodd_add", "submodule.range_fst", "Top.continuous_prelocal_pred", "add_units.add_neg", "traversable.foldl.of_free_monoid_comp_free_mk", "gold_pos", "complex.cpow_neg_one", "minimal_polynomial.degree_le_of_ne_zero", "equiv.perm.is_conj_swap", "has_deriv_at_interval_left_endpoint_of_tendsto_deriv", "turing.TM1to1.step_aux_move", "associates.mul_mono", "complex.ext_iff", "category_theory.iso.self_symm_conj", "findim_top", "inv_mul_cancel_left", "nat.not_two_dvd_bit1", "finsupp.zip_with_apply", "semiquot.eq_mk_of_mem", "int.lt_mul_of_div_lt", "nat.sub_one_sub_lt", "category_theory.limits.biprod.inl_map", "real.differentiable_sin", "add_monoid_hom.mrange_eq_map", "sup_left_comm", "mv_power_series.coeff_index_single_self_X", "tangent_cone_mono", "polynomial.nat_degree_prod_le", "int.neg_pos_of_neg", "filter.mem_principal_sets", "measure_theory.simple_func.pair_preimage", "tactic.ring_exp.base_to_exp_pf", "add_monoid_hom.neg_apply", "formal_multilinear_series.comp_partial_sum_target_subset_image_comp_partial_sum_source", "int.add_mul_div_left", "is_R_or_C.I_mul_I_of_nonzero", "finset.max_eq_sup_with_bot", "matrix.cons_val_fin_one", "measure_theory.simple_func.fin_meas_supp.map", "measure_theory.l1.simple_func.of_simple_func_to_simple_func", "div_pow", "submodule.span_span", "set.ord_connected_Iic", "Mod.regular_act", "pos_num.to_nat_to_int", "subalgebra.res_inj", "submonoid.localization_map.mul_equiv_of_mul_equiv_eq_map", "mv_polynomial.rename_eq", "rel_embedding.cod_restrict_apply", "category_theory.limits.coprod.symmetry'", "algebraic_geometry.PresheafedSpace.id_base", "list.chain'.rel_head", "padic_norm_e.is_norm", "circle_deg1_lift.commute_nat_add", "primrec.nat_mod", "ordinal.lt_succ_self", "le_infi_iff", "rel.core_univ", "filter.comap_map", "dist_add_add_le", "polynomial.exists_root_of_degree_eq_one", "int.dvd_lcm_right", "mul_dvd_mul_iff_right", "not_or", "left_ord_continuous.iterate", "category_theory.limits.cocone_of_cone_left_op_X", "continuous_linear_map.map_add", "written_in_ext_chart_model_space", "computable\:2082.comp", "reader_t.goto_mk_label", "times_cont_diff_within_at.of_le", "algebraic_geometry.PresheafedSpace.as_coe", "norm_num.sle_one_bit1", "measurable_iff_le_map", "inner_div_norm_mul_norm_eq_one_iff", "finset.center_mass_mem_convex_hull", "filter.germ.const_min", "list.func.equiv_refl", "measure_theory.measure.restrict_sum", "real.cosh_neg", "polynomial.irreducible_of_irreducible_map", "mvfunctor.liftp_def", "sub_floor_div_mul_nonneg", "category_theory.monoidal.Mon_functor_category_equivalence.functor_obj_obj_X", "deriv_within_pow", "set.preimage_mul_const_Ioo_of_neg", "lie_algebra.special_linear.E_apply_one", "bounded_continuous_function.norm_def", "list.rotate'_rotate'", "bernoulli_zero", "to_bool_iff", "module.direct_limit.lift_of", "deriv_const'", "emetric.diam_le_of_forall_edist_le", "bit0_le_bit0", "pgame.numeric_add", "Sup_eq_bot", "multilinear_map.curry_uncurry_right", "isometric.trans_apply", "real.iter_deriv_exp", "zero_pow_eq_zero", "smooth.add", "complex.linear_map.coe_im", "nhds_within_univ", "linear_map.coprod_inr", "free_group.to_group.mul", "inv_pow", "measure_theory.ae_eq_fun.edist_eq_coe", "vector.continuous_remove_nth", "nat.cast_add_one_pos", "category_theory.under.mk_hom", "multiset.mem_antidiagonal", "list.continuous_insert_nth", "computable_pred.not", "continuous_linear_map.smul_right_one_one", "interval_integral.measure_integral_sub_linear_is_o_of_tendsto_ae_of_ge'", "group.gpowers_eq_closure", "submonoid.localization_map.eq'", "cardinal.le_sum", "category_theory.equivalence.fun_inv_id_assoc_inv_app", "deriv_within.neg", "nat.zero_eq_mul", "typevec.append1_drop_last", "multiplicity.not_finite_iff_forall", "measure_theory.simple_func.lintegral_eq_of_measure_preimage", "category_theory.limits.colimit.comp_cocone_point_unique_up_to_iso_hom", "add_submonoid.zero_mem", "matrix.diagonal_apply_eq", "multiset.nodup_cons_of_nodup", "seq.destruct_eq_cons", "cau_seq.add_pos", "left_eq_inf", "zmod.exists_pow_two_eq_neg_one_iff_mod_four_ne_three", "multiset.disjoint_of_subset_left", "multiset.mem_coe", "measure_theory.ae_eq_fun.pair_mk_mk", "mul_le_one'", "lucas_lehmer.X.neg_snd", "has_fpower_series_at.sub", "category_theory.monoidal_functor.id_to_lax_monoidal_functor_to_functor", "filter.eventually_eq.eq_of_nhds_within", "function.semiconj\:2082.eq", "finsupp.comap_smul_single", "function.surjective.image_surjective", "function.semiconj.iterate_left", "sup_inf_right", "associates.dvd_eq_le", "sup_apply", "real.mk_eq_mk", "asymptotics.is_O.trans_le", "filter.tendsto_neg_at_bot_at_top", "affine_subspace.vadd_mem_of_mem_direction", "rat.cast_add_of_ne_zero", "filter.mem_traverse_sets_iff", "dioph.of_no_dummies", "tactic.interval_cases.mem_set_elems", "nhds_bind_nhds_within", "list.func.sub_nil", "is_compl.symm", "with_zero.ne_zero_iff_exists", "finset.range_zero", "edist_le_of_edist_le_geometric_two_of_tendsto\:2080", "euclidean_geometry.orthogonal_projection_fn_mem_orthogonal", "measure_theory.inner_content_comap", "category_theory.limits.cones.forget_map", "order.le_cof", "cardinal.mk_Ioi_real", "category_theory.pi.comp_apply", "finset.sum_eq_zero_iff_of_nonneg", "min_mul_max", "scale_roots_aeval_eq_zero_of_aeval_mk'_eq_zero", "int.mul_lt_of_lt_div", "cardinal.ord_is_limit", "category_theory.over.construct_products.cones_equiv_functor_obj_X", "filter.tendsto_at_top_add_right_of_le'", "affine.simplex.circumcenter_mem_affine_span", "equiv.sigma_preimage_equiv_symm_apply_snd_fst", "category_theory.limits.cokernel.\[Pi]_desc_assoc", "disjoint.sup_right", "int.mod_eq_zero_of_dvd", "cancel_factors.sub_subst", "div_le_div_of_le", "list.pairwise_singleton", "eq_of_fin_equiv", "localization_map.lift_left_inverse", "comp_le_uniformity3", "filter.bot_prod", "polynomial.lcoeff_apply", "con.induction_on", "finite_dimensional.findim_pos", "finset.min_singleton", "tsum_mul_right", "composition_as_set.boundary_zero", "continuous.continuous_within_at", "mvqpf.id_map", "abs_div", "subsemiring.Inf_to_add_submonoid", "convex.mem_to_cone'", "list.prod_ne_zero", "category_theory.preadditive.epi_of_cokernel_zero", "cardinal.is_inaccessible.mk", "lt_add_of_neg_add_lt_right", "pfunctor.M.bisim'", "cardinal.le_iff_exists_add", "linarith.int.coe_nat_mul_bit1", "multiset.map_single_le_powerset", "alg_hom.comp_assoc", "add_equiv.to_fun_apply", "partrec.cond", "equiv.perm.sign_bij", "add_comm_group.direct_limit.directed_system", "int.le_add_of_neg_le_sub_left", "measure_theory.measure_lt_top", "real.angle.coe_sub", "category_theory.limits.pullback_cone.mk_X", "nat.cast_dvd", "is_cau_geo_series_const", "finset.erase_insert_subset", "finset.prod_hom", "norm_num.sle_bit1_bit0", "nat.div_dvd_of_dvd", "lebesgue_number_lemma_sUnion", "set.piecewise_insert_self", "nat.sub_cancel", "strict_mono.comp", "measure_theory.ae_eq_fun.coe_fn_edist", "mvqpf.cofix.ext_mk", "finset.filter_val", "filter.eventually_lift'_powerset'", "cardinal.cantor", "linear_independent_iff_not_smul_mem_span", "linear_map_algebra_module.smul_apply", "int.modeq.modeq_neg", "finsupp.of_multiset_strict_mono", "category_theory.limits.prod.lift_fst", "filter.map_comap_le", "set.insert_diff_self_of_not_mem", "add_submonoid.mem_sup_right", "set.maps_to_bUnion", "list.sublists_aux\:2081_eq_sublists_aux", "fderiv_within_id'", "inv.is_group_hom", "list.length_range'", "category_theory.limits.kernel_fork.condition_assoc", "topological_space.opens.is_basis_iff_cover", "ennreal.mul_ne_top", "continuous_linear_map.norm_id", "neg_pos_of_neg", "add_monoid_hom.coprod_inl_inr", "measure_theory.measure.zero_to_outer_measure", "nat.succ_sub", "units.eq_iff", "pgame.relabel_move_left", "category_theory.limits.cocones.equivalence_of_reindexing_functor_obj", "real.cos_inj_of_nonneg_of_le_pi", "category_theory.uncurry_curry", "real.deriv_exp", "measure_theory.measure.le_iff", "has_deriv_at.sum", "algebraic_closure.adjoin_monic.is_integral", "is_add_group_hom.map_zero", "finset.subset_insert_iff", "bool.bxor_bnot_bnot", "has_ftaylor_series_up_to_on.differentiable_on", "algebra.is_algebraic_of_finite", "category_theory.bifunctor.map_id", "set.bij_on_Inter_of_directed", "seq1.bind_assoc", "commute.inv_right", "matrix.empty_mul_empty", "list.inter_cons_of_not_mem", "ennreal.to_real_of_real'", "omega.nat.neg_free_neg_elim_core", "lt_inv", "isometry.vadd_vsub", "is_integral_of_mem_closure", "finset.Ico.filter_lt", "set.empty_prod", "differentiable_within_at.mul", "multiset.nodup_map", "nat.pow_dvd_pow_iff", "affine_subspace.mk'_eq", "monoid_hom.iterate_map_inv", "int.add_lt_add_of_le_of_lt", "inv_div", "category_theory.limits.walking_pair.swap_apply_left", "finset.sum_map", "category_theory.functor.hom_obj", "category_theory.sum.inverse_associator_obj_inr_inl", "image_range_order_of", "nat.sub.right_comm", "category_theory.nat_iso.app_inv", "set.Iio_subset_Iic_iff", "measure_theory.measure.haar.chaar_mem_haar_product", "mul_inv_lt_of_lt_mul'", "list.countp_append", "not_and_of_not_or_not", "many_one_equiv.trans", "category_theory.monad.forget_creates_colimits.cocone_point_A", "nat.one_lt_iff_ne_zero_and_ne_one", "neq_of_not_iff", "subset_interior_iff_nhds", "filter.lift'_principal", "ideal.integral_closure.eq_bot_of_comap_eq_bot", "finsupp.coe_leval'", "finset.sort_sorted", "pnat.gcd_one", "equiv.refl_apply", "fin.one_lt_succ_succ", "monotone.mem_upper_bounds_image", "list.unzip_zip", "dist_le_tsum_of_dist_le_of_tendsto\:2080", "matrix.cons_val_succ", "sym2.elems_iff_eq", "is_preconnected.mem_intervals", "list.enum_from_map_fst", "pi.one_comp", "norm_num.lt_bit0_bit0", "wseq.lift_rel_append", "submodule.smul_le", "findim_span_le_card", "bilin_form.comp_apply", "gsmul_eq_mul", "monotone.mul_const'", "subgroup.prod_mono_right", "bilin_form.is_adjoint_pair.eq", "nat.modeq.coprime_of_mul_modeq_one", "function.has_right_inverse.surjective", "filter.lift_assoc", "sub_lt_sub_iff_left", "pequiv.mem_single", "uniform_space.completion.uniform_inducing_coe", "continuous_linear_map.sum_apply", "rank_comp_le2", "uniform_space.completion.uniform_embedding_coe", "has_deriv_within_at.has_fderiv_within_at", "gcd_dvd_gcd_mul_left_right", "ite_mul", "list.foldr_hom", "nat.coprime.coprime_mul_left_right", "fin.coe_coe_of_lt", "algebra.is_algebraic_iff", "le_iff_eq_or_lt", "mul_le_of_le_one_right", "list.take_left'", "subsemiring.map_supr", "fin.tail_update_succ", "finset.min_of_mem", "nat.rfind_opt_mono", "ordinal.enum_typein", "cardinal.mk_compl_finset_of_omega_le", "algebra.tensor_product.ext", "cinfi_le", "continuous_infi_dom", "list.take_append", "category_theory.monoidal_category.left_unitor_tensor_inv", "polynomial.eval_nat_cast", "union_upper_bounds_subset_upper_bounds_inter", "composition.ones_length", "complex.uniform_continuous_inv", "ideal.span_singleton_mul_left_unit", "interval_integral.norm_integral_le_abs_integral_norm", "relation.trans_gen.head'", "asymptotics.is_O_with_neg_left", "linear_independent_bUnion_of_directed", "option.mem_to_list", "le_mul_iff_one_le_left", "with_top.coe_eq_one", "hyperreal.ne_zero_of_infinite", "differentiable_at.has_fderiv_at", "nat.primrec'.unpair\:2081", "set.compl_set_of", "submonoid.mem_supr_of_mem", "continuous.prod_map", "topological_space.opens.union_eq", "filter.frequently_imp_distrib_right", "multiset.cons_union_distrib", "option.lift_or_get_none_left", "mul_lt_mul_right_of_neg", "alist.lookup_insert_ne", "finsupp.single_finset_sum", "set.Ioi_subset_Ioi", "nat.add_lt_of_lt_sub_right", "add_monoid_hom.ext_iff", "times_cont_diff_within_at_snd", "primrec.list_foldr", "neg_lt_of_neg_lt", "add_submonoid.localization_map.of_add_equiv_of_dom_id", "times_cont_mdiff_on.comp", "function.comp_const", "category_theory.limits.cokernel_is_iso_comp_hom", "map_nhds_induced_eq", "inner_zero_left", "nat.mul_sub_right_distrib", "free_add_semigroup.lift_of_add", "semiconj_by.units_inv_symm_left_iff", "one_le_fpow_of_nonneg", "finset.sort_to_finset", "has_fpower_series_at.analytic_at", "polynomial.monic.leading_coeff", "unique_factorization_domain.no_factors_of_no_prime_factors", "local_homeomorph.symm_image_inter_target_eq", "add_add_neg_cancel'_right", "ordinal.typein_injective", "vsub_set_subset_vector_span", "filter.germ.lt_def", "nat.le_of_sub_eq_zero", "set.mem_union_left", "filter.mem_top_sets_iff_forall", "bot_eq_top_of_dim_eq_zero", "monoid_hom.eq_of_eq_on_mtop", "compl_Inf", "subtype.forall'", "is_R_or_C.abs_to_real", "padic_seq.stationary_point_spec", "multiset.Ico.filter_lt_of_top_le", "is_R_or_C.is_cau_seq_im", "has_deriv_within_at.has_deriv_at", "nhds_subtype", "pnat.mk_bit0", "trans_rel_left", "is_closed_separation_rel", "is_monoid_hom.comp", "int.neg_succ_lt_zero", "dvd_iff_dvd_digits_sum", "continuous_at.prod_map'", "list.maximum_mem", "list.nth_update_nth_of_lt", "one_le_inv'", "primrec.list_join", "nat.gcd_dvd_gcd_mul_right", "ordinal.pos_iff_ne_zero", "mem_comp_rel", "filter.germ.map_const", "has_deriv_within_at_pow", "measurable_iff_comap_le", "finset.max_singleton", "multiset.count_eq_zero", "has_le.le.le_or_lt", "multiset.bind_congr", "seq.append_assoc", "deriv_within_cos", "computation.tail_ret", "denumerable.raise'_chain", "list.pairwise.iff", "finset.mem_of_mem_inter_right", "differentiable_within_at.div_const", "computable_pred.computable_iff_re_compl_re", "primrec.vector_head", "submonoid.localization_map.mk'_eq_of_eq", "ulift.sub_down", "tensor_product.mk_compr\:2082_inj", "filter.push_pull'", "nhds_within_prod_eq", "bifunctor.comp_snd", "filter.is_cobounded_ge_of_top", "option.mem_unique", "monoid_hom.coprod_inl_inr", "multilinear_map.curry_left_apply", "free_group.reduce.cons", "nat.div_eq_sub_div", "induced_iff_nhds_eq", "complex.continuous_abs", "nat.eq_mul_of_div_eq_right", "category_theory.evaluation_uncurried_obj", "differentiable_at.fderiv_within", "finset.sum_inter_add_sum_diff", "has_deriv_at_filter.const_sub", "has_fpower_series_on_ball.continuous_on", "continuous_linear_map.deriv", "pgame.first_wins_of_equiv", "function.embedding.ext", "dvd_refl", "list.func.length_pointwise", "mvqpf.cofix.bisim_rel", "subgroup.mem_Inf", "nat.zero_div", "set.finite.convex_hull_eq", "gsmul_coe_nat", "equiv.sum_compl_apply_inr", "int.sub_nat_nat_sub", "set.pair_eq_singleton", "zero_linear_action", "ennreal.rpow_neg_one", "inv_mul_le_right_of_le_mul", "fintype.card_eq_one_iff", "is_add_group_hom.neg_iff_ker'", "is_compact.inter", "ideal.leading_coeff_nth_mono", "ennreal.has_sum", "multiset.count_union", "polynomial.derivative_monomial", "list.func.forall_val_of_forall_mem", "filter.tendsto.integral_sub_linear_is_o_ae", "continuous_within_at.union", "finmap.mem_keys", "isometric.coe_to_real_linear_equiv_of_map_zero_symm", "ring.fractional_ideal.right_inverse_eq", "set.mem_Ici_Ioi_of_subset_of_subset", "int.le_add_of_sub_right_le", "filter.ultrafilter_map", "category_theory.limits.cokernel_\[Pi]_comp_cokernel_is_iso_comp_hom", "tactic.ring_exp.add_overlap_pf_zero", "list.revzip_map_fst", "finmap.mem_singleton", "nat.size_bit", "measurable_of_measurable_on_compl_singleton", "norm_indicator_le_norm_self", "ennreal.exists_nat_mul_gt", "ring_hom.coe_snd", "finset.inter_singleton_of_mem", "differentiable.sqrt", "submonoid.coe_mul", "cardinal.cantor_function_aux_nonneg", "hash_map.valid.idx_enum", "category_theory.monoidal_category.right_unitor_nat_iso_hom_app", "category_theory.over.construct_products.cones_equiv_functor_obj_\[Pi]_app", "real.sqrt_two_add_series_lt_two", "multilinear_map.map_sub", "function.right_inverse.comp", "ordinal.cof_sup_le", "prod.snd_vadd", "category_theory.currying_inverse_obj_obj_map", "set.image_subset", "pgame.turn_bound_ne_zero_of_left_move", "set.preimage_const_add_Iic", "and_self", "additive.simple_add_group_iff", "galois_insertion.l_sup_u", "primrec\:2082.nat_iff", "multiset.ndinter_subset_right", "category_theory.abelian.coimages.coimage.fac", "linear_pmap.map_zero", "punit_eq_punit", "is_open_Ioi", "nat.primrec'.pred", "set.Ioc_union_Ioc_union_Ioc_cycle", "is_local_min_on.max", "seq.map_id", "uniformity_lift_le_comp", "approximates_linear_on.inverse_approx_map_fixed_iff", "cauchy.mono'", "ring_hom.ext", "finset.prod_eq_single", "interval_integral.deriv_integral_left", "list.perm.cons_inv", "eventually_countable_forall", "add_subgroup.prod_mono", "tactic.ring_exp.pow_p_pf_cons", "linear_equiv.conj_trans", "submodule.map_comap_subtype", "category_theory.functor.const.op_obj_op_inv_app", "real.is_conjugate_exponent.mul_eq_add", "ennreal.tendsto_at_top", "submonoid.localization_map.epic_of_localization_map", "list.eq_repeat", "category_theory.functor.map_cocone_\[Iota]", "ordinal.lt_limit", "continuous_left_of_strict_mono_surjective", "zmod.cast_zero", "nat.coprime.coprime_mul_right_right", "isometric.point_reflection_midpoint_left", "onote.scale_power_aux", "pequiv.single_trans_of_mem", "roption.mem_assert", "submodule.fg_iff_finite_dimensional", "category_theory.limits.cones.postcompose_equivalence_counit_iso", "set.inter_inv", "is_compact.prod", "filter.map_infi_eq", "set.bij_on.surj_on", "category_theory.adjunction.functoriality_counit'_app_hom", "nnreal.pow_ne_zero", "valuation.map_add_supp", "norm_num.add_pos_neg_pos", "is_local_max.fderiv_eq_zero", "submodule.sup_eq_range", "one_div_le_one_div_of_le", "measure_theory.monotone_lintegral", "set.exists_range_iff'", "continuous_add_left", "iterated_deriv_within_eq_iterate", "list.sorted_merge_sort", "set.union_prod", "power_series.order_one", "polynomial.separable.of_pow", "rel_iso.map_top", "infi_subtype''", "int.of_nat_one", "linear_map.fun_left_comp", "finsupp.multiset_map_sum", "category_theory.comma.fst_obj", "cSup_le", "nat.min_zero", "pgame.add_zero_equiv", "set.indicator_le_self", "finsupp.erase_single", "multiset.nodup_filter_map", "times_cont_mdiff_at_const", "commute.symm", "rel_iso.refl_apply", "open_add_subgroup.neg_mem", "multiset.rel_add_left", "turing.reaches\:2080.single", "subring.range_snd", "list.eq_iff_join_eq", "complex.tan_arg", "nat.prime_iff_prime_int", "filter.is_bounded_ge_of_bot", "fderiv_mul_const", "function.iterate_mul", "submonoid.bot_prod_bot", "set.diagonal_eq_range", "open_embedding.continuous_inv_fun", "num.to_nat_to_int", "le_sub_iff_add_le", "partrec.option_some_iff", "nonempty_plift", "equiv.perm.is_cycle_swap_mul_aux\:2082", "list.mmap_with_index_aux_spec_cons", "multiplicity_eq_zero_of_coprime", "continuous_multilinear_map.curry0_uncurry0", "matrix_equiv_tensor_apply_std_basis", "ennreal.div_lt_top", "rel.mem_preimage", "multilinear_map.cons_smul", "list.traverse_cons", "gfp_induct", "add_group_with_zero_nhd.nhds_zero_eq_Z", "limit_zero_of_norm_tendsto_zero", "is_bounded_linear_map.add", "measure_theory.measure.haar.prehaar_sup_eq", "mem_nhds_within_Ioi_iff_exists_Ioc_subset", "nat.eq_zero_of_gcd_eq_zero_left", "finset.prod_congr", "smooth_within_at.prod_map", "cardinal.bit0_le_bit1", "is_absolute_value.abv_div", "prime_spectrum.mem_zero_locus", "multiset.powerset_aux_perm", "interval_integral.integral_has_fderiv_within_at_of_tendsto_ae", "left_ord_continuous.lt_iff", "has_strict_fderiv_at.const_smul", "polynomial.coeff_to_subring'", "real.differentiable_exp", "multiset.prod_map_mul", "submodule.comap_liftq", "filter.Liminf_eq_supr_Inf", "multiset.not_mem_zero", "category_theory.limits.pushout_cocone.of_cocone_X", "id.pure_eq", "rel_embedding.is_well_order", "list.length_eq_zero", "quotient.induction_on\:2082", "nat.div_mul_le_self", "set.surj_on_iff_surjective", "multiset.count_erase_of_ne", "cardinal.mk_subtype_le_of_subset", "metric.completion.dist_triangle", "ordinal.lt_bsup", "continuous_iff_continuous_on_univ", "zsqrtd.nonneg_add_lem", "add_monoid_hom.single_apply", "list.mem_keys_kerase_of_ne", "multiset.abs_sum_le_sum_abs", "subsingleton_iff", "mul_inv_le_iff_le_mul'", "set.union_subset", "interval_integral.integral_has_strict_fderiv_at", "int.modeq.modeq_add_cancel_right", "dense_inducing_pure", "set.inter_comm", "int.le.intro_sub", "real.cos_add_two_pi", "finset.inter_left_comm", "subtype.preimage_coe_nonempty", "finite_dimensional.exists_nontrivial_relation_sum_zero_of_dim_succ_lt_card", "filter.eventually_le_congr", "list.sublist_of_cons_sublist_cons", "rel_iso.apply_inv_self", "heq_iff_eq", "category_theory.initial_mono", "continuous_linear_map.proj_apply", "set.interval_of_le", "turing.partrec_to_TM2.split_at_pred_ff", "finsupp.sum_mul", "measure_theory.simple_func.pair_preimage_singleton", "category_theory.limits.limit.hom_ext", "set.nonempty_inter_iff_exists_right", "list.erasep_sublist", "mv_polynomial.eval_monomial", "nat.mul_right_eq_self_iff", "multiset.smul_prod", "is_basis.mk_range_eq_dim", "finset.insert_singleton_self_eq", "units.coe_le_coe", "polynomial.expand_C", "category_theory.left_adjoint_preserves_epi", "ennreal.mul_div_cancel'", "multiplicity.finite_iff_dom", "multiset.sort_eq", "tensor_algebra.lift_comp_\[Iota]", "add_equiv.to_equiv_symm", "subgroup.closure_mono", "finmap.induction_on\:2082", "list.perm_comp_perm", "topological_space.opens.map_id_hom_app", "normed_space.double_dual_bound", "typevec.eq_nil_fun", "pell.yn_one", "mv_power_series.coeff_zero_mul_X", "smul_sub", "generalized_continued_fraction.continuants_aux_recurrence", "list.take'_eq_take", "dim_range_of_surjective", "times_cont_diff_on_iff_ftaylor_series", "inner_product_geometry.cos_angle", "has_fderiv_at.const_smul_algebra", "list.pairwise.chain'", "int.eq_zero_of_sign_eq_zero", "ideal.coeff_zero_mem_comap_of_root_mem_of_eval_mem", "mul_sub_left_distrib", "ideal.comap_ne_top", "mem_nhds_uniformity_iff_left", "char_poly_monic", "lt_mul_of_one_lt_left'", "matrix.adjugate_zero", "complex.is_cau_exp", "int.neg_of_nat_of_succ", "filter.tendsto_def", "category_theory.whisker_left_comp", "wseq.nth_add", "bool.bxor_bnot_right", "bool.band_elim_right", "finset.convex_hull_eq", "option.eq_none_iff_forall_not_mem", "is_unit.mk0", "continuous_within_at.mono", "set.preimage_mul_const_Iio", "lt_mul_of_le_of_one_lt", "list.disjoint_of_disjoint_append_left_right", "localization_map.to_map_injective", "num.cast_sub'", "turing.partrec_to_TM2.copy_ok", "alt_bilin_form.self_eq_zero", "multiset.bind_def", "differentiable_on.continuous_on", "ordinal.power_ne_zero", "classical.epsilon_singleton", "quadratic_form.map_add_self", "asymptotics.is_O.smul", "turing.tr_eval'", "continuous_multilinear_map.op_norm_nonneg", "category_theory.induced_functor_map", "continuous_linear_map.proj_ker_of_right_inverse_apply_idem", "linear_pmap.sup_h_of_disjoint", "category_theory.single_obj.to_End_def", "uniform_space.completion.uniform_continuous_coe", "complex.cosh_sq_sub_sinh_sq", "sum.inr_ne_inl", "real.tan_zero", "cardinal.mk_preimage_of_injective", "finset_is_basis_of_linear_independent_of_card_eq_findim", "primrec\:2082.encode_iff", "nat.le_three_of_sqrt_eq_one", "deriv_within_sum", "nat.primrec.cases1", "eq_or_lt_of_le", "alg_hom.map_neg", "summable_of_absolute_convergence_real", "metric.continuous_on_iff", "submodule.restrict_scalars'_injective", "padic_seq.not_lim_zero_const_of_nonzero", "ideal.is_prime.mem_of_pow_mem", "valuation.map_sub_le_max", "geom_series_mul_neg", "deriv_within_rpow_of_one_le", "inf_le_left", "finset.card_def", "category_theory.limits.pullback_cone.condition_assoc", "circle_deg1_lift.translation_number_conj_eq'", "list.chain_iff_nth_le", "alist.ext_iff", "matrix.diag_transpose", "not_or_distrib", "finset.sum_lt_sum", "list.lookup_all_length_le_one", "list.maximum_eq_coe_iff", "equiv.perm.mem_iff_of_subtype_apply_mem", "list.sublist_append_right", "deriv_within_sqrt", "set.union_eq_compl_compl_inter_compl", "subsingleton_or_nontrivial", "bilin_form.mul_to_matrix", "linear_equiv.coe_fn_to_continuous_linear_equiv_of_continuous_symm", "convex_cone.comap_id", "matrix.cons_vec_mul_vec", "mul_right_injective", "zmod.val_add", "divp_inv", "finset.bind_val", "stream.length_take", "tendsto_inverse_at_top_nhds_0_nat", "composition_as_set_card", "list.rel_perm", "ordinal.infinite_pigeonhole", "set.indicator_rel_indicator", "measure_theory.integrable.smul_measure", "perfect_closure.zero_def", "is_add_unit_of_add_is_add_unit_left", "cau_seq.const_pos", "localization.mul_equiv_of_quotient_monoid_of", "Class.mem_hom_left", "list.perm_ext", "complex.mul_im", "has_deriv_at_filter.mono", "submonoid.mem_comap", "option.some_ne_none", "set.mem_Icc", "tensor_product.congr_tmul", "alg_equiv.surjective", "zmod.val_min_abs_eq_zero", "free_add_semigroup.map_of", "metric.totally_bounded_of_finite_discretization", "differentiable_within_at.comp", 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DirectedEdge["padic_norm_e.norm_rat_le_one", "congr"], DirectedEdge["padic_norm_e.norm_rat_le_one", "int.coe_nat_le"], DirectedEdge["padic_norm_e.norm_rat_le_one", "norm_zero"], DirectedEdge["padic_norm_e.norm_rat_le_one", "eq.trans"], DirectedEdge["padic_norm_e.norm_rat_le_one", "not_false_iff"], DirectedEdge["padic_norm_e.norm_rat_le_one", "rat.cast_one"], DirectedEdge["omega.nat.implies_neg_elim_core", "and.imp"], DirectedEdge["omega.nat.implies_neg_elim_core", "congr"], DirectedEdge["omega.nat.implies_neg_elim_core", "congr_arg"], DirectedEdge["omega.nat.implies_neg_elim_core", "not_and_distrib"], DirectedEdge["omega.nat.implies_neg_elim_core", "not_le"], DirectedEdge["omega.nat.implies_neg_elim_core", "iff.symm"], DirectedEdge["omega.nat.implies_neg_elim_core", "or.comm"], DirectedEdge["omega.nat.implies_neg_elim_core", "eq.trans"], DirectedEdge["omega.nat.implies_neg_elim_core", "omega.nat.le_and_le_iff_eq"], DirectedEdge["hash_map.entries_empty", "hash_map.mk_as_list"], DirectedEdge["hash_map.keys_empty", "hash_map.entries_empty"], DirectedEdge["has_deriv_within_at.div", "one_mul"], DirectedEdge["has_deriv_within_at.div", "congr"], DirectedEdge["has_deriv_within_at.div", "tactic.ring.const_add_horner"], DirectedEdge["has_deriv_within_at.div", "mul_neg_eq_neg_mul_symm"], DirectedEdge["has_deriv_within_at.div", "has_deriv_at_inv"], DirectedEdge["has_deriv_within_at.div", "mul_assoc"], DirectedEdge["has_deriv_within_at.div", "neg_zero"], DirectedEdge["has_deriv_within_at.div", "has_deriv_within_at.mul"], DirectedEdge["has_deriv_within_at.div", "function.comp_app"], DirectedEdge["has_deriv_within_at.div", "tactic.ring.horner_add_horner_lt"], DirectedEdge["has_deriv_within_at.div", "norm_num.one_succ"], DirectedEdge["has_deriv_within_at.div", "add_zero"], DirectedEdge["has_deriv_within_at.div", "zero_add"], DirectedEdge["has_deriv_within_at.div", "zero_mul"], DirectedEdge["has_deriv_within_at.div", "tactic.ring.horner_neg"], DirectedEdge["has_deriv_within_at.div", "neg_mul_eq_neg_mul_symm"], DirectedEdge["has_deriv_within_at.div", "tactic.ring.horner_mul_const"], DirectedEdge["has_deriv_within_at.div", "norm_num.subst_into_add"], DirectedEdge["has_deriv_within_at.div", "sub_eq_add_neg"], DirectedEdge["has_deriv_within_at.div", "div_eq_inv_mul"], DirectedEdge["has_deriv_within_at.div", "eq.trans"], DirectedEdge["has_deriv_within_at.div", "congr_arg"], DirectedEdge["has_deriv_at.div", "has_deriv_within_at.div"], DirectedEdge["deriv_within_div", "has_deriv_within_at.div"], DirectedEdge["differentiable_within_at.div", "has_deriv_within_at.div"], DirectedEdge["list.perm_singleton", "list.perm_repeat"], DirectedEdge["list.perm.eq_singleton", "list.perm_singleton"], DirectedEdge["measure_theory.simple_func.neg_part_map_norm", "measure_theory.simple_func.pos_part_map_norm"], DirectedEdge["cau_seq.pos_add_lim_zero", "sub_eq_add_neg"], DirectedEdge["cau_seq.pos_add_lim_zero", "abs_lt"], 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DirectedEdge["commute.geom_sum\:2082_mul_add", "pow_succ"], DirectedEdge["commute.geom_sum\:2082_mul_add", "finset.sum_congr"], DirectedEdge["commute.geom_sum\:2082_mul_add", "mul_assoc"], DirectedEdge["commute.geom_sum\:2082_mul_add", "add_assoc"], DirectedEdge["commute.geom_sum\:2082_mul_add", "commute.eq"], DirectedEdge["commute.geom_sum\:2082_mul_add", "finset.mul_sum"], DirectedEdge["commute.geom_sum\:2082_mul_add", "nat.sub_sub"], DirectedEdge["commute.geom_sum\:2082_mul_add", "nat.add_sub_of_le"], DirectedEdge["geom_sum\:2082_mul_comm", "commute.geom_sum\:2082_mul_add"], DirectedEdge["is_asymm.is_irrefl", "asymm"], DirectedEdge["is_strict_weak_order_of_is_order_connected", "is_asymm.is_irrefl"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "category_theory.limits.image.ext"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "homological_complex.kernel_map_condition"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "eq.trans"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "category_theory.limits.equalizer.hom_ext"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "congr_arg"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "congr"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "eq_self_iff_true"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "homological_complex.image_map_\[Iota]"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map", "homological_complex.image_to_kernel_map_condition_assoc"], DirectedEdge["homological_complex.image_to_kernel_map_comp_kernel_map_assoc", "homological_complex.image_to_kernel_map_comp_kernel_map"], DirectedEdge["finset.max_of_nonempty", "finset.max_of_mem"], DirectedEdge["finset.max_eq_none", "finset.max_of_nonempty"], DirectedEdge["option.bind_eq_some", "eq.trans"], DirectedEdge["option.bind_eq_some", "congr_arg"], DirectedEdge["option.bind_eq_some", "eq_false_intro"], DirectedEdge["option.bind_eq_some", "funext"], DirectedEdge["option.bind_eq_some", "congr"], DirectedEdge["option.bind_eq_some", "iff_false_intro"], DirectedEdge["option.bind_eq_some", "iff_self"], DirectedEdge["option.bind_eq_some", "exists_eq_left'"], DirectedEdge["option.bind_eq_some", "false_and"], DirectedEdge["option.bind_eq_some", "option.some_bind"], DirectedEdge["nat.partrec.code.evaln_bound", "option.bind_eq_some"], DirectedEdge["nat.partrec.code.evaln_mono", "option.bind_eq_some"], DirectedEdge["nat.partrec.code.evaln_complete", "option.bind_eq_some"], DirectedEdge["nat.psub_eq_some", "option.bind_eq_some"], DirectedEdge["nat.partrec.code.evaln_sound", "option.bind_eq_some"], DirectedEdge["pythagorean_triple.classified", "int.gcd_one_left"], DirectedEdge["pythagorean_triple.classified", "or_self"], DirectedEdge["pythagorean_triple.classified", "mul_zero"], DirectedEdge["pythagorean_triple.classified", "eq_self_iff_true"], DirectedEdge["pythagorean_triple.classified", "norm_num.int_sub_hack"], DirectedEdge["pythagorean_triple.classified", "nat.pos_of_ne_zero"], DirectedEdge["pythagorean_triple.classified", "eq.trans"], DirectedEdge["pythagorean_triple.classified", "zero_mul"], DirectedEdge["pythagorean_triple.classified", "pow_one"], DirectedEdge["pythagorean_triple.classified", "sub_zero"], DirectedEdge["pythagorean_triple.classified", "mul_one"], DirectedEdge["pythagorean_triple.classified", "int.gcd_div_gcd_div_gcd"], DirectedEdge["pythagorean_triple.classified", "congr"], DirectedEdge["pythagorean_triple.classified", "congr_arg"], DirectedEdge["pythagorean_triple.classified", "pythagorean_triple.is_primitive_classified_of_coprime"], DirectedEdge["pythagorean_triple.classified", "norm_num.pow_bit0"], DirectedEdge["pythagorean_triple.classified", "one_mul"], 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DirectedEdge["add_subgroup.map_sup", "galois_connection.l_sup"], DirectedEdge["is_bounded_bilinear_map_comp", "zero_mul"], DirectedEdge["is_bounded_bilinear_map_comp", "one_mul"], DirectedEdge["is_bounded_bilinear_map_comp", "eq.trans"], DirectedEdge["is_bounded_bilinear_map_comp", "zero_lt_one"], DirectedEdge["is_bounded_bilinear_map_comp", "continuous_linear_map.op_norm_comp_le"], DirectedEdge["is_bounded_bilinear_map_comp", "eq.symm"], DirectedEdge["is_bounded_bilinear_map_comp", "tactic.ring.horner_mul_const"], DirectedEdge["is_bounded_bilinear_map_comp", "continuous_linear_map.ext"], DirectedEdge["continuous_linear_map.is_bounded_linear_map_comp_left", "is_bounded_bilinear_map_comp"], DirectedEdge["continuous_linear_map.is_bounded_linear_map_comp_right", "is_bounded_bilinear_map_comp"], DirectedEdge["linear_map.map_add\:2082", "linear_map.map_add"], DirectedEdge["has_ftaylor_series_up_to_on.of_le", "le_trans"], DirectedEdge["has_ftaylor_series_up_to_on_succ_iff_left", 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DirectedEdge["filter.is_countably_generated.exists_antimono_seq'", "filter.has_basis.mem_iff"], DirectedEdge["filter.is_countably_generated.exists_antimono_seq'", "iff_self"], DirectedEdge["uniform_space.complete_of_convergent_controlled_sequences", "filter.is_countably_generated.exists_antimono_seq'"], DirectedEdge["subgroup.gpow_mem", "subgroup.pow_mem"], DirectedEdge["continuous_multilinear_map.curry_uncurry_right", "continuous_multilinear_map.curry_right_apply"], DirectedEdge["num.bitwise_to_nat", "nat.binary_rec_eq"], DirectedEdge["num.bitwise_to_nat", "nat.binary_rec_zero"], DirectedEdge["num.bitwise_to_nat", "congr_fun"], DirectedEdge["num.bitwise_to_nat", "nat.bitwise_zero_right"], DirectedEdge["num.bitwise_to_nat", "nat.bitwise_zero_left"], DirectedEdge["num.bitwise_to_nat", "congr"], DirectedEdge["num.bitwise_to_nat", "nat.bitwise_zero"], DirectedEdge["num.bitwise_to_nat", "eq.symm"], DirectedEdge["num.bitwise_to_nat", "num.bit_to_nat"], DirectedEdge["num.bitwise_to_nat", "congr_arg"], DirectedEdge["num.lor_to_nat", "num.bitwise_to_nat"], DirectedEdge["num.ldiff_to_nat", "num.bitwise_to_nat"], DirectedEdge["num.land_to_nat", "num.bitwise_to_nat"], DirectedEdge["num.lxor_to_nat", "num.bitwise_to_nat"], DirectedEdge["affine.simplex.monge_point_mem_affine_span", "centroid_mem_affine_span_of_card_eq_add_one"], DirectedEdge["affine.simplex.monge_point_mem_affine_span", "finset.card_fin"], DirectedEdge["affine.simplex.monge_point_mem_monge_plane", "affine.simplex.monge_point_mem_affine_span"], DirectedEdge["affine.triangle.orthocenter_mem_affine_span", "affine.simplex.monge_point_mem_affine_span"], DirectedEdge["local_equiv.trans_target''", "local_equiv.trans_source''"], DirectedEdge["topological_space.opens.comap_comp", "topological_space.opens.coe_comap"], DirectedEdge["add_submonoid.closure_union", "galois_connection.l_sup"], DirectedEdge["filter.mul_mem_mul", "set.subset.refl"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "congr_fun"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "if_pos"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "congr_arg"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "congr"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "funext"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "sub_add_eq_sub_sub"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "if_neg"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "mul_zero"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "eq.trans"], DirectedEdge["polynomial.mod_by_monic_eq_sub_mul_div", "sub_zero"], DirectedEdge["polynomial.is_coprime_of_is_root_of_eval_derivative_ne_zero", "polynomial.mod_by_monic_eq_sub_mul_div"], DirectedEdge["polynomial.mod_by_monic_X_sub_C_eq_C_eval", "polynomial.mod_by_monic_eq_sub_mul_div"], DirectedEdge["polynomial.mod_by_monic_add_div", "polynomial.mod_by_monic_eq_sub_mul_div"], DirectedEdge["polynomial.dvd_iff_mod_by_monic_eq_zero", "polynomial.mod_by_monic_eq_sub_mul_div"], DirectedEdge["nat.modeq.modeq_mul", "nat.modeq.modeq_mul_right"], DirectedEdge["lists'.to_list_cons", "sigma.mk.inj_iff"], DirectedEdge["lists'.to_list_cons", "eq_self_iff_true"], DirectedEdge["lists'.to_list_cons", "eq.trans"], DirectedEdge["lists'.to_list_cons", "congr_arg"], DirectedEdge["lists'.to_list_cons", "congr"], DirectedEdge["lists'.mem_cons", "lists'.to_list_cons"], DirectedEdge["lists'.mem_of_subset'", "lists'.to_list_cons"], DirectedEdge["matrix.mul_vec_mul_vec", "eq.symm"], DirectedEdge["matrix.mul_vec_mul_vec", "funext"], DirectedEdge["matrix.mul_vec_mul_vec", "matrix.dot_product_assoc"], DirectedEdge["set.preimage_add_right_zero'", "set.preimage_add_right_zero"], DirectedEdge["set.preimage_add_right_zero'", "set.singleton_eq_singleton_iff"], DirectedEdge["set.preimage_add_right_zero'", "eq_self_iff_true"], DirectedEdge["set.preimage_add_right_zero'", "eq.trans"], DirectedEdge["set.preimage_add_right_zero'", "congr_arg"], DirectedEdge["set.preimage_add_right_zero'", "congr"], DirectedEdge["comp_mem_uniformity_sets", "monotone_comp_rel"], DirectedEdge["comp_mem_uniformity_sets", "filter.mem_lift'_sets"], DirectedEdge["comp_mem_uniformity_sets", "monotone_id"], DirectedEdge["comp_symm_of_uniformity", "comp_mem_uniformity_sets"], DirectedEdge["Cauchy.pure_cauchy_dense", "comp_mem_uniformity_sets"], DirectedEdge["tendsto_comp_of_locally_uniform_limit_within", "comp_mem_uniformity_sets"], DirectedEdge["mem_nhds_uniformity_iff_right", "comp_mem_uniformity_sets"], DirectedEdge["continuous_within_at_of_locally_uniform_approx_of_continuous_within_at", "comp_mem_uniformity_sets"], DirectedEdge["lebesgue_number_lemma_seq", "comp_mem_uniformity_sets"], DirectedEdge["lebesgue_number_lemma", "comp_mem_uniformity_sets"], DirectedEdge["comp_symm_mem_uniformity_sets", "comp_mem_uniformity_sets"], DirectedEdge["separated_equiv", "comp_mem_uniformity_sets"], DirectedEdge["Cauchy.Cauchy_eq", "comp_mem_uniformity_sets"], DirectedEdge["complete_space_extension", "comp_mem_uniformity_sets"], DirectedEdge["uniform_space.comap_quotient_le_uniformity", "comp_mem_uniformity_sets"], DirectedEdge["array.mem_to_list", "list.mem_reverse"], DirectedEdge["array.mem_to_list", "eq.symm"], DirectedEdge["array.mem_to_list", "array.rev_list_reverse"], DirectedEdge["array.mem_to_list", "array.mem_rev_list"], DirectedEdge["bucket_array.mem_as_list", "array.mem_to_list"], DirectedEdge["is_basis.to_matrix_self", "congr_fun"], DirectedEdge["is_basis.to_matrix_self", "eq_self_iff_true"], DirectedEdge["is_basis.to_matrix_self", "linear_equiv_matrix_apply"], DirectedEdge["is_basis.to_matrix_self", "eq_comm"], DirectedEdge["is_basis.to_matrix_self", "eq.trans"], DirectedEdge["is_basis.to_matrix_self", "linear_equiv.trans_apply"], DirectedEdge["is_basis.to_matrix_self", "module_equiv_finsupp_apply_basis"], DirectedEdge["is_basis.to_matrix_self", "if_congr"], DirectedEdge["is_basis.to_matrix_self", "matrix.ext"], 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DirectedEdge["char_poly_sub_diagonal_degree_lt", "add_sub_cancel"], DirectedEdge["bernoulli_two", "add_sub_cancel"], DirectedEdge["dvd_add_iff_left", "add_sub_cancel"], DirectedEdge["affine_map.decomp'", "add_sub_cancel"], DirectedEdge["free_group.red.cons_nil_iff_singleton", "free_group.red.step.cons_bnot_rev"], DirectedEdge["free_group.red.cons_nil_iff_singleton", "relation.refl_trans_gen.single"], DirectedEdge["free_group.red.cons_nil_iff_singleton", "free_group.red.church_rosser"], DirectedEdge["free_group.red.cons_nil_iff_singleton", "free_group.red.singleton_iff"], DirectedEdge["free_group.red.cons_nil_iff_singleton", "free_group.red.step.cons_bnot"], DirectedEdge["free_group.red.cons_nil_iff_singleton", "eq.symm"], DirectedEdge["free_group.red.cons_nil_iff_singleton", "free_group.red.cons_cons"], DirectedEdge["int.coe_nat_sub", "int.of_nat_sub"], DirectedEdge["modeq_mersenne", "int.coe_nat_sub"], DirectedEdge["pell.matiyasevic", "int.coe_nat_sub"], DirectedEdge["zmod.nat_abs_val_min_abs_neg", "int.coe_nat_sub"], DirectedEdge["padic_val_nat.div", "int.coe_nat_sub"], DirectedEdge["lucas_lehmer.residue_eq_zero_iff_s_mod_eq_zero", "int.coe_nat_sub"], DirectedEdge["has_strict_deriv_at_fpow", "int.coe_nat_sub"], DirectedEdge["pell.eq_pow_of_pell", "int.coe_nat_sub"], DirectedEdge["nat.modeq.modeq_iff_dvd'", "int.coe_nat_sub"], DirectedEdge["pell.dz_val", "int.coe_nat_sub"], DirectedEdge["int.add_mul_div_right", "int.coe_nat_sub"], DirectedEdge["pell.is_pell_nat", "int.coe_nat_sub"], DirectedEdge["pell.eq_of_xn_modeq_lem3", "int.coe_nat_sub"], DirectedEdge["pell.yn_modeq_a_sub_one", "int.coe_nat_sub"], DirectedEdge["local_homeomorph.image_inter_source_eq", "set.inter_subset_right"], DirectedEdge["edist_nndist", "ennreal.of_real_eq_coe_nnreal"], DirectedEdge["of_real_norm_eq_coe_nnnorm", "ennreal.of_real_eq_coe_nnreal"], DirectedEdge["ennreal.lt_iff_exists_add_pos_lt", "ennreal.of_real_eq_coe_nnreal"], DirectedEdge["is_unit_of_dvd_one", 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DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "inner_product_space.of_core.inner_smul_right"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "pow_one"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "tactic.ring.horner_neg"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "inner_product_space.of_core.inner_add_add_self"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "tactic.ring.horner_pow"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "congr"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "inner_product_space.of_core.inner_smul_left"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "one_mul"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "congr_arg"], DirectedEdge["inner_product_space.of_core.inner_mul_inner_self_le", "le_of_not_gt"], 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DirectedEdge["inner_product_space.of_core.abs_inner_le_norm", "tactic.ring.horner_atom"], DirectedEdge["inner_eq_norm_add_mul_self_sub_norm_mul_self_sub_norm_mul_self_div_two", "tactic.ring.horner_atom"], DirectedEdge["real.arccos_le_pi", "tactic.ring.horner_atom"], DirectedEdge["real.arcsin_nonneg", "tactic.ring.horner_atom"], DirectedEdge["gold_conj_neg", "tactic.ring.horner_atom"], DirectedEdge["is_bounded_bilinear_map_comp_multilinear", "tactic.ring.horner_atom"], DirectedEdge["real.sqrt_eq_rpow", "tactic.ring.horner_atom"], DirectedEdge["padic_val_nat_eq_factors_count", "tactic.ring.horner_atom"], DirectedEdge["formal_multilinear_series.change_origin_summable_aux1", "tactic.ring.horner_atom"], DirectedEdge["pnat.gcd_props", "tactic.ring.horner_atom"], DirectedEdge["exists_ratio_has_deriv_at_eq_ratio_slope'", "tactic.ring.horner_atom"], DirectedEdge["formal_multilinear_series.id_apply_one'", "tactic.ring.horner_atom"], DirectedEdge["int.modeq.modeq_add_cancel_left", "tactic.ring.horner_atom"], DirectedEdge["pell.pell_zd_succ_succ", "tactic.ring.horner_atom"], DirectedEdge["lucas_lehmer.X.right_distrib", "tactic.ring.horner_atom"], DirectedEdge["omega.rhs_correct_aux", "tactic.ring.horner_atom"], DirectedEdge["pnat.gcd_a'_coe", "tactic.ring.horner_atom"], DirectedEdge["lucas_lehmer.X.X_card", "tactic.ring.horner_atom"], DirectedEdge["euclidean_geometry.dist_square_smul_orthogonal_vadd_smul_orthogonal_vadd", "tactic.ring.horner_atom"], DirectedEdge["inner_product_geometry.norm_sub_square_eq_norm_square_add_norm_square_sub_two_mul_norm_mul_norm_mul_cos_angle", "tactic.ring.horner_atom"], DirectedEdge["nat.lt_of_test_bit", "tactic.ring.horner_atom"], DirectedEdge["polynomial.is_unit_of_self_mul_dvd_separable", "tactic.ring.horner_atom"], DirectedEdge["real.coe_fib_eq'", "tactic.ring.horner_atom"], DirectedEdge["continuous_linear_map.norm_map_tail_le", "tactic.ring.horner_atom"], DirectedEdge["mv_polynomial.pderivative_mul", "tactic.ring.horner_atom"], DirectedEdge["monotone.mem_lower_bounds_image", "set.ball_image_of_ball"], DirectedEdge["monotone.le_is_glb_image", "monotone.mem_lower_bounds_image"], DirectedEdge["is_glb.of_image", "monotone.mem_lower_bounds_image"], DirectedEdge["galois_connection.is_glb_u_image", "monotone.mem_lower_bounds_image"], DirectedEdge["with_one.ne_one_iff_exists", "with_one.coe_ne_one"], DirectedEdge["finset.inf_eq_infi", "finset.sup_eq_supr"], DirectedEdge["filter.infi_sets_induct", "finset.inf_eq_infi"], DirectedEdge["filter.infi_sup_left", "finset.inf_eq_infi"], DirectedEdge["filter.mem_infi_sets_finset", "finset.inf_eq_infi"], DirectedEdge["measure_theory.hahn_decomposition", "finset.inf_eq_infi"], DirectedEdge["filter.eventually_lt_of_lt_liminf", "exists_lt_of_lt_cSup"], DirectedEdge["filter.eventually_lt_of_lt_liminf", "filter.eventually.mono"], DirectedEdge["formal_multilinear_series.bound_of_lt_radius", "filter.eventually_lt_of_lt_liminf"], DirectedEdge["filter.eventually_lt_of_limsup_lt", 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DirectedEdge["fp.float.zero.valid", "sub_nonneg"], DirectedEdge["fp.float.zero.valid", "norm_num.subst_into_neg"], DirectedEdge["fp.float.zero.valid", "sub_nonneg_of_le"], DirectedEdge["fp.float.zero.valid", "pow_one"], DirectedEdge["fp.float.zero.valid", "nat.size_zero"], DirectedEdge["fp.float.zero.valid", "nat.le_mul_of_pos_left"], DirectedEdge["fp.float.zero.valid", "neg_zero"], DirectedEdge["fp.float.zero.valid", "eq.symm"], DirectedEdge["fp.float.zero.valid", "neg_mul_eq_neg_mul_symm"], DirectedEdge["fp.float.zero.valid", "int.coe_nat_le"], DirectedEdge["fp.float.zero.valid", "norm_num.one_succ"], DirectedEdge["fp.float.zero.valid", "tactic.ring.horner_add_horner_eq"], DirectedEdge["fp.float.zero.valid", "tactic.ring.add_neg_eq_sub"], DirectedEdge["fp.float.zero.valid", "int.coe_nat_zero"], DirectedEdge["smul_algebra_smul_comm", "smul_smul"], DirectedEdge["smul_algebra_smul_comm", "algebra.commutes"], DirectedEdge["smul_algebra_smul_comm", "algebra_compatible_smul"], DirectedEdge["smul_algebra_smul_comm", "eq.symm"], DirectedEdge["smul_algebra_smul_comm", "mul_smul"], DirectedEdge["is_bounded_bilinear_map_smul_algebra", "smul_algebra_smul_comm"], DirectedEdge["lt_of_add_lt_add_right", "lt_of_add_lt_add_left"], DirectedEdge["pell.eq_of_xn_modeq_lem3", "lt_of_add_lt_add_right"], DirectedEdge["enat.add_lt_add_iff_right", "lt_of_add_lt_add_right"], DirectedEdge["order_topology_of_nhds_abs", "lt_of_add_lt_add_right"], DirectedEdge["list.nth_range'", "lt_of_add_lt_add_right"], DirectedEdge["tendsto_locally_uniformly.tendsto_comp", "tendsto_comp_of_locally_uniform_limit"], DirectedEdge["tendsto_uniformly.tendsto_comp", "tendsto_locally_uniformly.tendsto_comp"], DirectedEdge["algebra.tensor_product.mul_assoc'", "congr_arg"], DirectedEdge["algebra.tensor_product.mul_assoc'", "eq_self_iff_true"], DirectedEdge["algebra.tensor_product.mul_assoc'", "eq.trans"], DirectedEdge["algebra.tensor_product.mul_assoc'", "forall_congr_eq"], 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DirectedEdge["equiv.perm.same_cycle_apply", "gpow_one"], DirectedEdge["subgroup.mem_closure_singleton", "gpow_one"], DirectedEdge["gpow_mul", "gpow_one"], DirectedEdge["gpow_one_add", "gpow_one"], DirectedEdge["equiv.perm.is_cycle_swap_mul_aux\:2081", "gpow_one"], DirectedEdge["gpow_add_one", "gpow_one"], DirectedEdge["option_t.run_map", "function.comp_app"], DirectedEdge["option_t.run_map", "congr_arg"], DirectedEdge["option_t.run_map", "eq.trans"], DirectedEdge["option_t.run_map", "eq.symm"], DirectedEdge["option_t.run_map", "bind_ext_congr"], DirectedEdge["option_t.run_map", "eq_self_iff_true"], DirectedEdge["option_t.run_map", "congr"], DirectedEdge["option_t.run_map", "option_t.run_pure"], DirectedEdge["ennreal.coe_indicator", "add_monoid_hom.map_indicator"], DirectedEdge["measure_theory.lintegral_eq_nnreal", "ennreal.coe_indicator"], DirectedEdge["pos_num.add_succ", "congr_arg"], DirectedEdge["pos_num.add_succ", "eq.trans"], DirectedEdge["pos_num.add_succ", "eq_self_iff_true"], DirectedEdge["pos_num.add_succ", "pos_num.one_add"], DirectedEdge["pos_num.add_succ", "congr"], DirectedEdge["pos_num.add_succ", "pos_num.add_one"], DirectedEdge["ennreal.sum_lt_top", "with_top.sum_lt_top"], DirectedEdge["measure_theory.simple_func.fin_meas_supp.lintegral_lt_top", "ennreal.sum_lt_top"], DirectedEdge["ennreal.to_nnreal_sum", "ennreal.sum_lt_top"], DirectedEdge["measure_theory.simple_func.fin_meas_supp_iff", "ennreal.sum_lt_top"], DirectedEdge["finsupp.mul_sum", "eq.trans"], DirectedEdge["finsupp.mul_sum", "finset.mul_sum"], DirectedEdge["finsupp.mul_sum", "congr"], DirectedEdge["finsupp.mul_sum", "congr_arg"], DirectedEdge["monoid_algebra.mul_apply_right", "finsupp.mul_sum"], DirectedEdge["polynomial.eval\:2082_mul_noncomm", "finsupp.mul_sum"], DirectedEdge["polynomial.map_mul", "finsupp.mul_sum"], DirectedEdge["polynomial.coeff_C_mul", "finsupp.mul_sum"], DirectedEdge["polynomial.eval\:2082_smul", "finsupp.mul_sum"], DirectedEdge["mv_polynomial.smul_eq_C_mul", 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DirectedEdge["is_open.is_connected_iff_is_path_connected", "loc_path_connected_of_is_open"], DirectedEdge["zorn.zorn_partial_order", "zorn.exists_maximal_of_chains_bounded"], DirectedEdge["zorn.zorn_partial_order", "le_trans"], DirectedEdge["zorn.zorn_partial_order\:2080", "zorn.zorn_partial_order"], DirectedEdge["zorn.zorn_subset", "zorn.zorn_partial_order"], DirectedEdge["add_semiconj_by.neg_right_iff", "add_neg_self"], DirectedEdge["add_semiconj_by.neg_right_iff", "neg_add_self"], DirectedEdge["add_semiconj_by.neg_right_iff", "add_semiconj_by.units_neg_right_iff"], DirectedEdge["add_semiconj_by.neg_right", "add_semiconj_by.neg_right_iff"], DirectedEdge["add_commute.neg_right_iff", "add_semiconj_by.neg_right_iff"], DirectedEdge["add_semiconj_by.neg_neg_symm_iff", "add_semiconj_by.neg_right_iff"], DirectedEdge["linear_map.ker_eq_top", "linear_map.ext"], DirectedEdge["linear_map.ker_eq_top", "linear_map.ker_zero"], DirectedEdge["linear_map.ker_eq_top", "eq.symm"], DirectedEdge["linear_map.ker_eq_top", "linear_map.mem_ker"], DirectedEdge["linear_map.ker_eq_top", "eq.subst"], DirectedEdge["linear_map.range_le_ker_iff", "linear_map.ker_eq_top"], DirectedEdge["linear_map.range_le_bot_iff", "linear_map.ker_eq_top"], DirectedEdge["pfunctor.M.ichildren_mk", "pfunctor.M.approx.P_mk"], DirectedEdge["pfunctor.M.ichildren_mk", "congr"], DirectedEdge["pfunctor.M.ichildren_mk", "congr_fun"], DirectedEdge["pfunctor.M.ichildren_mk", "pfunctor.M.ext'"], DirectedEdge["pfunctor.M.ichildren_mk", "eq.trans"], DirectedEdge["pfunctor.M.ichildren_mk", "funext"], DirectedEdge["finset.sum_Ico_eq_sub", "finset.sum_Ico_eq_add_neg"], DirectedEdge["geom_sum_Ico_mul", "finset.sum_Ico_eq_sub"], DirectedEdge["geom_sum_Ico", "finset.sum_Ico_eq_sub"], DirectedEdge["geom_sum_Ico_mul_neg", "finset.sum_Ico_eq_sub"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "compl_compl'"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "set.diff_eq"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "eq.trans"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "imp_congr_eq"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "forall_congr_eq"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "congr"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "imp_self"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl", "congr_arg"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_inter", "measure_theory.outer_measure.is_caratheodory_compl"], DirectedEdge["measure_theory.outer_measure.is_caratheodory_compl_iff", "measure_theory.outer_measure.is_caratheodory_compl"], DirectedEdge["decidable.not_lt", "decidable.le_of_not_lt"], DirectedEdge["decidable.not_lt", "not_lt_of_ge"], DirectedEdge["decidable.le_iff_le_iff_lt_iff_lt", "decidable.not_lt"], DirectedEdge["nat.mod_lt", "decidable.not_lt"], 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DirectedEdge["localization_map.mk'_mem_iff", "submodule.smul_mem"], DirectedEdge["ideal.is_jacobson_localization", "submodule.smul_mem"], DirectedEdge["linear_independent_of_span_eq_top_of_card_eq_findim", "submodule.smul_mem"], DirectedEdge["algebra.fg_trans", "submodule.smul_mem"], DirectedEdge["submodule.smul_le_right", "submodule.smul_mem"], DirectedEdge["finsupp.supported_eq_span_single", "submodule.smul_mem"], DirectedEdge["submodule.smul_mem_iff'", "submodule.smul_mem"], DirectedEdge["mv_polynomial.map_restrict_dom_eval\:2097", "submodule.smul_mem"], DirectedEdge["ideal.unit_mul_mem_iff_mem", "submodule.smul_mem"], DirectedEdge["submodule.span_mul_span", "submodule.smul_mem"], DirectedEdge["submodule.smul_assoc", "submodule.smul_mem"], DirectedEdge["submodule.exists_finset_of_mem_supr", "submodule.smul_mem"], DirectedEdge["polynomial.degree_le_eq_span_X_pow", "submodule.smul_mem"], DirectedEdge["submodule.mem_span_singleton", "submodule.smul_mem"], DirectedEdge["submodule.smul_mem_span_smul'", "submodule.smul_mem"], DirectedEdge["submodule.sum_smul_mem", "submodule.smul_mem"], DirectedEdge["submodule.exists_sub_one_mem_and_smul_eq_zero_of_fg_of_le_smul", "submodule.smul_mem"], DirectedEdge["has_fderiv_within_at.unique_diff_within_at", "submodule.smul_mem"], DirectedEdge["is_integral_of_mem_of_fg", "submodule.smul_mem"], DirectedEdge["fg_adjoin_singleton_of_integral", "submodule.smul_mem"], DirectedEdge["euclidean_geometry.exists_unique_dist_eq_of_insert", "submodule.smul_mem"], DirectedEdge["char_poly_sub_diagonal_degree_lt", "submodule.smul_mem"], DirectedEdge["submodule.convex", "submodule.smul_mem"], DirectedEdge["ring.fractional_ideal.fractional_mul", "submodule.smul_mem"], DirectedEdge["submodule.coe_supr_of_directed", "submodule.smul_mem"], DirectedEdge["ideal.mem_image_of_mem_map_of_surjective", "submodule.smul_mem"], DirectedEdge["ring.fractional_ideal.div_one", "submodule.smul_mem"], DirectedEdge["polynomial.degree_lt_eq_span_X_pow", "submodule.smul_mem"], DirectedEdge["ideal.eq_bot_or_top", "submodule.smul_mem"], DirectedEdge["ring.fractional_ideal.fractional_div_of_nonzero", "submodule.smul_mem"], DirectedEdge["submodule.neg_mem", "submodule.smul_mem"], DirectedEdge["submodule.span_smul", "submodule.smul_mem"], DirectedEdge["finsupp.span_eq_map_total", "submodule.smul_mem"], DirectedEdge["submodule.smul_mem_span_smul", "submodule.smul_mem"], DirectedEdge["euclidean_geometry.dist_square_smul_orthogonal_vadd_smul_orthogonal_vadd", "submodule.smul_mem"], DirectedEdge["algebra.adjoin_eq_span", "submodule.smul_mem"], DirectedEdge["ideal.mul_mem_left", "submodule.smul_mem"], DirectedEdge["submodule.smul_mem_span_smul_of_mem", "submodule.smul_mem"], DirectedEdge["submodule.fg_of_fg_map_of_fg_inf_ker", "submodule.smul_mem"], DirectedEdge["formal_multilinear_series.comp_along_composition_norm", "multilinear_map.mk_continuous_norm_le"], DirectedEdge["formal_multilinear_series.comp_along_composition_norm", "formal_multilinear_series.comp_along_composition_multilinear_bound"], DirectedEdge["formal_multilinear_series.comp_along_composition_norm", "norm_nonneg"], DirectedEdge["formal_multilinear_series.comp_along_composition_norm", "finset.prod_nonneg"], DirectedEdge["formal_multilinear_series.comp_along_composition_norm", "mul_nonneg"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "pgame.impartial.add_self"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "lt_of_le_of_ne"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "imp_of_not_imp_not"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "pgame.impartial.not_first_loses"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "congr"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "pgame.lt_def_le"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "pgame.add_move_left_inr"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "pgame.add_comm_equiv"], 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DirectedEdge["one_sub_gold", "norm_num.subst_into_add"], DirectedEdge["one_sub_gold", "lt_irrefl"], DirectedEdge["one_sub_gold", "norm_num.add_neg_pos_pos"], DirectedEdge["one_sub_gold", "not.intro"], DirectedEdge["one_sub_gold", "norm_num.add_pos_neg_neg"], DirectedEdge["one_sub_gold", "gold_add_gold_conj"], DirectedEdge["one_sub_gold", "add_zero"], DirectedEdge["one_sub_gold", "sub_neg_of_lt"], DirectedEdge["one_sub_gold", "norm_num.subst_into_neg"], DirectedEdge["one_sub_gold", "linarith.lt_of_lt_of_eq"], DirectedEdge["one_sub_gold", "neg_neg"], DirectedEdge["one_sub_gold", "sub_eq_zero_of_eq"], DirectedEdge["one_sub_gold", "tactic.ring.horner_atom"], DirectedEdge["one_sub_gold", "tactic.ring.horner_add_const"], DirectedEdge["one_sub_gold", "neg_zero"], DirectedEdge["one_sub_gold", "neg_eq_zero"], DirectedEdge["one_sub_gold", "zero_add"], DirectedEdge["one_sub_gold", "tactic.ring.zero_horner"], DirectedEdge["one_sub_gold", "tactic.ring.horner_add_horner_eq"], DirectedEdge["mul_equiv.map_ne_one_iff", "mul_equiv.map_eq_one_iff"], DirectedEdge["mul_equiv.map_ne_one_iff", "mt"], DirectedEdge["ring_equiv.map_ne_one_iff", "mul_equiv.map_ne_one_iff"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "real.dist_eq"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "eq.symm"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "metric.cauchy_seq_iff'"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "le_trans"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "le_abs_self"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "finset.sum_Ico_eq_sub"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "lt_of_le_of_lt"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "Exists.imp"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "cauchy_seq_of_tendsto_nhds"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "dist_le_Ico_sum_of_dist_le"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "dist_comm"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "has_sum.tendsto_sum_nat"], DirectedEdge["cauchy_seq_of_dist_le_of_summable", "trans_rel_right"], DirectedEdge["cauchy_seq_of_summable_dist", "cauchy_seq_of_dist_le_of_summable"], DirectedEdge["cauchy_seq_of_le_geometric", "cauchy_seq_of_dist_le_of_summable"], DirectedEdge["zero_pow", "zero_mul"], DirectedEdge["finite_field.pow_card", "zero_pow"], DirectedEdge["pow_lt_pow_of_lt_left", "zero_pow"], DirectedEdge["polynomial.coeff_zero_eq_eval_zero", "zero_pow"], DirectedEdge["matrix.det_zero", "zero_pow"], DirectedEdge["irrational_nrt_of_n_not_dvd_multiplicity", "zero_pow"], DirectedEdge["polynomial.nat_degree_pow", "zero_pow"], DirectedEdge["polynomial.nat_degree_pow'", "zero_pow"], DirectedEdge["asymptotics.is_o_pow_pow", "zero_pow"], DirectedEdge["padic_int.appr_spec", "zero_pow"], DirectedEdge["polynomial.eisenstein_criterion_aux.eval_zero_mem_ideal_of_eq_mul_X_pow", "zero_pow"], DirectedEdge["ennreal.inv_pow", "zero_pow"], DirectedEdge["polynomial.is_unit_or_eq_zero_of_separable_expand", "zero_pow"], DirectedEdge["mv_polynomial.eval_indicator_apply_eq_one", "zero_pow"], DirectedEdge["char_dvd_card_solutions_family", "zero_pow"], DirectedEdge["tactic.ring_exp.pow_p_pf_zero", "zero_pow"], DirectedEdge["zmod.legendre_sym_eq_pow", "zero_pow"], DirectedEdge["finmap.mem_union", "alist.mem_union"], DirectedEdge["finmap.disjoint_union_left", "finmap.mem_union"], DirectedEdge["is_coprime.add_mul_right_right", "is_coprime_comm"], DirectedEdge["is_coprime.add_mul_right_right", "is_coprime.add_mul_right_left"], DirectedEdge["is_coprime.mul_add_right_right", "is_coprime.add_mul_right_right"], DirectedEdge["is_coprime.add_mul_right_right_iff", "is_coprime.add_mul_right_right"], DirectedEdge["finmap.insert_entries_of_neg", "finmap.mem_to_finmap"], DirectedEdge["finmap.insert_entries_of_neg", "congr"], DirectedEdge["finmap.insert_entries_of_neg", "finmap.induction_on"], DirectedEdge["finmap.insert_entries_of_neg", "congr_arg"], DirectedEdge["finmap.insert_entries_of_neg", "list.perm_cons"], DirectedEdge["finmap.insert_entries_of_neg", "eq.trans"], DirectedEdge["finmap.insert_entries_of_neg", "multiset.coe_eq_coe"], DirectedEdge["finmap.insert_entries_of_neg", "alist.insert_entries_of_neg"], DirectedEdge["finmap.insert_entries_of_neg", "mt"], DirectedEdge["finmap.insert_entries_of_neg", "multiset.cons_coe"], DirectedEdge["finmap.insert_entries_of_neg", "alist.to_finmap_entries"], DirectedEdge["metric.compact_iff_seq_compact", "uniform_space.compact_iff_seq_compact"], DirectedEdge["metric.compact_iff_seq_compact", "emetric.uniformity_has_countable_basis"], DirectedEdge["tendsto_subseq_of_frequently_bounded", "metric.compact_iff_seq_compact"], DirectedEdge["zorn.chain_chain_closure", "zorn.chain_succ"], DirectedEdge["zorn.chain_chain_closure", "or.elim"], DirectedEdge["zorn.chain_chain_closure", "zorn.chain_closure_total"], DirectedEdge["zorn.max_chain_spec", "zorn.chain_chain_closure"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "finset.insert_eq_of_mem"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "finsupp.not_mem_support_iff"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "push_neg.not_not_eq"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "multiset.mem_union"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "finsupp.to_finset_to_multiset"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "eq.symm"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "finset.sup_insert"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "imp_of_not_imp_not"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "multiset.sup_eq_union"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "imp_congr_eq"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "congr"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "congr_arg"], DirectedEdge["mv_polynomial.mem_support_not_mem_vars_zero", "eq.trans"], DirectedEdge["mv_polynomial.pderivative_eq_zero_of_not_mem_vars", "mv_polynomial.mem_support_not_mem_vars_zero"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "imp_congr_ctx_eq"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "forall_true_iff"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "semidirect_product.ext"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "exists_imp_distrib"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "eq_comm"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "le_antisymm"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "monoid_hom.mem_range"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "semidirect_product.left_inl"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "congr"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "congr_arg"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "forall_congr_eq"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "congr_fun"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "eq.trans"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "eq_self_iff_true"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "semidirect_product.right_inl"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "forall_const"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "semidirect_product.right_hom_eq_right"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "funext"], DirectedEdge["semidirect_product.range_inl_eq_ker_right_hom", "monoid_hom.mem_ker"], DirectedEdge["set.inter_Inter", "set.Inter_const"], DirectedEdge["set.inter_Inter", "set.Inter_inter_distrib"], DirectedEdge["set.diff_Union", "set.inter_Inter"], DirectedEdge["is_local_min_on.congr", "is_min_filter.congr"], DirectedEdge["real.sin_add", "sub_zero"], DirectedEdge["real.sin_add", "complex.of_real_inj"], DirectedEdge["real.sin_add", "complex.of_real_mul"], DirectedEdge["real.sin_add", "congr"], DirectedEdge["real.sin_add", "mul_zero"], DirectedEdge["real.sin_add", "complex.cos_of_real_im"], DirectedEdge["real.sin_add", "eq.symm"], DirectedEdge["real.sin_add", "eq.trans"], DirectedEdge["real.sin_add", "complex.sin_add"], DirectedEdge["real.sin_add", "complex.of_real_cos"], DirectedEdge["real.sin_add", "complex.of_real_sin_of_real_re"], DirectedEdge["real.sin_add", "congr_arg"], DirectedEdge["real.sin_add", "complex.of_real_cos_of_real_re"], DirectedEdge["real.sin_add", "complex.add_re"], DirectedEdge["real.sin_add", "complex.of_real_add"], DirectedEdge["real.sin_add", "eq_self_iff_true"], DirectedEdge["real.sin_int_mul_pi", "real.sin_add"], DirectedEdge["inner_product_geometry.sin_angle_add_angle_sub_add_angle_sub_eq_zero", "real.sin_add"], DirectedEdge["real.sin_pi", "real.sin_add"], 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DirectedEdge["measure_theory.integral_non_integrable", "measure_theory.integral_undef"], DirectedEdge["measure_theory.integral_indicator", "measure_theory.integral_non_integrable"], DirectedEdge["measure_theory.integral_eq_lintegral_of_nonneg_ae", "measure_theory.integral_non_integrable"], DirectedEdge["measure_theory.integral_map_measure", "measure_theory.integral_non_integrable"], DirectedEdge["measure_theory.integral_const", "measure_theory.integral_non_integrable"], DirectedEdge["measure_theory.integral_congr_ae", "measure_theory.integral_non_integrable"], DirectedEdge["measure_theory.integral_smul_measure", "measure_theory.integral_non_integrable"], DirectedEdge["complex.norm_sq_div", "complex.norm_sq_inv"], DirectedEdge["complex.norm_sq_div", "complex.norm_sq_mul"], DirectedEdge["is_compact.inter_left", "is_compact.inter_right"], DirectedEdge["is_compact.inter_left", "eq.subst"], DirectedEdge["finset.mem_image", "multiset.mem_map"], DirectedEdge["finset.mem_image", "eq.trans"], 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DirectedEdge["finset.image_to_finset", "finset.mem_image"], DirectedEdge["finset.image_filter", "finset.mem_image"], DirectedEdge["finset.product_eq_bind", "finset.mem_image"], DirectedEdge["fintype.injective_iff_surjective", "finset.mem_image"], DirectedEdge["function.injective.map_at_top_finset_prod_eq", "finset.mem_image"], DirectedEdge["mem_image_univ_iff_mem_range", "finset.mem_image"], DirectedEdge["polynomial.degree_le_eq_span_X_pow", "finset.mem_image"], DirectedEdge["finset.bind_singleton", "finset.mem_image"], DirectedEdge["finset.mem_mul", "finset.mem_image"], DirectedEdge["sum_hom_units_eq_zero", "finset.mem_image"], DirectedEdge["finset.coe_image", "finset.mem_image"], DirectedEdge["fin.prod_univ_cast_succ", "finset.mem_image"], DirectedEdge["finset.sum_powerset_insert", "finset.mem_image"], DirectedEdge["finsupp.sigma_support", "finset.mem_image"], DirectedEdge["finset.mem_image_of_mem", "finset.mem_image"], DirectedEdge["finset.prod_cancels_of_partition_cancels", 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DirectedEdge["fintype.prod_sum_type", "finset.mem_image"], DirectedEdge["finset.image_union", "finset.mem_image"], DirectedEdge["finset.prod_sum", "finset.mem_image"], DirectedEdge["finset.Ico.image_const_sub", "finset.mem_image"], DirectedEdge["multiset.filter_map_some", "congr_arg"], DirectedEdge["multiset.filter_map_some", "list.filter_map_some"], DirectedEdge["multiset.filter_map_some", "quot.induction_on"], DirectedEdge["ennreal.sub_infi", "iff_self"], DirectedEdge["ennreal.sub_infi", "eq.trans"], DirectedEdge["ennreal.sub_infi", "congr_arg"], DirectedEdge["ennreal.sub_infi", "add_comm"], DirectedEdge["ennreal.sub_infi", "supr_le_iff"], DirectedEdge["ennreal.sub_infi", "ennreal.sub_le_iff_le_add"], DirectedEdge["ennreal.sub_infi", "congr"], DirectedEdge["ennreal.sub_infi", "eq_of_forall_ge_iff"], DirectedEdge["ennreal.sub_infi", "funext"], DirectedEdge["ennreal.sub_infi", "ennreal.infi_add"], DirectedEdge["ennreal.sub_infi", "forall_congr_eq"], DirectedEdge["measure_theory.measure_Inter_eq_infi_nat", "ennreal.sub_infi"], DirectedEdge["measure_theory.lintegral_infi_ae", "ennreal.sub_infi"], DirectedEdge["padic_val_rat.neg", "iff_false_intro"], DirectedEdge["padic_val_rat.neg", "and_true"], DirectedEdge["padic_val_rat.neg", "dif_neg"], DirectedEdge["padic_val_rat.neg", "not_true"], DirectedEdge["padic_val_rat.neg", "rat.num_neg_eq_neg_num"], DirectedEdge["padic_val_rat.neg", "false_and"], DirectedEdge["padic_val_rat.neg", "ne.def"], DirectedEdge["padic_val_rat.neg", "eq_self_iff_true"], DirectedEdge["padic_val_rat.neg", "rat.denom_neg_eq_denom"], DirectedEdge["padic_val_rat.neg", "not_false_iff"], DirectedEdge["padic_val_rat.neg", "dif_pos"], DirectedEdge["padic_val_rat.neg", "congr"], DirectedEdge["padic_val_rat.neg", "neg_zero"], DirectedEdge["padic_val_rat.neg", "congr_arg"], DirectedEdge["padic_val_rat.neg", "eq.trans"], DirectedEdge["padic_val_rat.neg", "multiplicity.neg"], DirectedEdge["padic_val_rat.neg", "not_not"], DirectedEdge["padic_val_rat.neg", "neg_eq_zero"], DirectedEdge["padic_norm.neg", "padic_val_rat.neg"], DirectedEdge["polynomial.monic_X", "polynomial.leading_coeff_X"], DirectedEdge["polynomial.irreducible_of_eisenstein_criterion", "polynomial.monic_X"], DirectedEdge["add_commute.left_comm", "add_commute.eq"], DirectedEdge["add_commute.right_comm", "add_commute.eq"], DirectedEdge["submodule.fg_prod", "set.finite.image"], DirectedEdge["submodule.fg_prod", "set.finite.union"], DirectedEdge["submodule.fg_prod", "submodule.fg_def"], DirectedEdge["submodule.fg_prod", "linear_map.span_inl_union_inr"], DirectedEdge["is_preconnected.Iio_cSup_subset", "is_preconnected.Ioi_cInf_subset"], DirectedEdge["int.prime.dvd_mul", "nat.prime.dvd_mul"], DirectedEdge["int.prime.dvd_mul", "int.nat_abs_mul"], DirectedEdge["int.prime.dvd_mul", "int.coe_nat_dvd_left"], DirectedEdge["int.prime.dvd_mul", "eq.symm"], DirectedEdge["prime_two_or_dvd_of_dvd_two_mul_pow_self_two", "int.prime.dvd_mul"], DirectedEdge["int.prime.dvd_mul'", "int.prime.dvd_mul"], DirectedEdge["filter.eventually_le.is_local_max", "filter.eventually_le.is_max_filter"], DirectedEdge["fintype.card_perm", "card_perms_of_finset"], DirectedEdge["fintype.card_perm", "eq.subst"], DirectedEdge["matrix.det_eq_one_of_card_eq_zero", "fintype.card_perm"], DirectedEdge["fintype.card_equiv", "fintype.card_perm"], DirectedEdge["matrix.adjugate_eq_one_of_card_eq_one", "fintype.card_perm"], DirectedEdge["add_subgroup.is_open_of_open_add_subgroup", "filter.mem_sets_of_superset"], DirectedEdge["add_subgroup.is_open_of_open_add_subgroup", "add_subgroup.is_open_of_mem_nhds"], DirectedEdge["add_subgroup.is_open_mono", "add_subgroup.is_open_of_open_add_subgroup"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "eq_self_iff_true"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "eq.trans"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "finsupp.to_multiset_to_finsupp"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "eq.symm"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "congr_arg"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "congr"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "finsupp.order_iso_multiset_apply"], DirectedEdge["finsupp.order_iso_multiset_symm_apply", "rel_iso.apply_symm_apply"], DirectedEdge["list.Ico.bag_inter_consecutive", "list.bag_inter_nil_iff_inter_nil"], DirectedEdge["list.Ico.bag_inter_consecutive", "list.Ico.inter_consecutive"], DirectedEdge["multiset.Ico.inter_consecutive", "list.Ico.bag_inter_consecutive"], DirectedEdge["mul_eq_mul_of_div_eq_div", "div_self"], DirectedEdge["mul_eq_mul_of_div_eq_div", "div_mul_eq_mul_div"], DirectedEdge["mul_eq_mul_of_div_eq_div", "mul_one"], DirectedEdge["mul_eq_mul_of_div_eq_div", "mul_comm"], DirectedEdge["mul_eq_mul_of_div_eq_div", "div_mul_cancel"], DirectedEdge["mul_eq_mul_of_div_eq_div", "div_mul_eq_mul_div_comm"], DirectedEdge["mul_eq_mul_of_div_eq_div", "eq.symm"], DirectedEdge["mul_eq_mul_of_div_eq_div", "mul_assoc"], DirectedEdge["quadratic_form.add_lin_mul_lin", "quadratic_form.ext"], DirectedEdge["has_deriv_at_filter.neg", "continuous_linear_map.one_apply"], DirectedEdge["has_deriv_at_filter.neg", "eq.trans"], DirectedEdge["has_deriv_at_filter.neg", "one_smul"], DirectedEdge["has_deriv_at_filter.neg", "has_fderiv_at_filter.has_deriv_at_filter"], DirectedEdge["has_deriv_at_filter.neg", "congr_arg"], DirectedEdge["has_deriv_at_filter.neg", "has_fderiv_at_filter.neg"], DirectedEdge["has_deriv_at_filter.neg", "continuous_linear_map.smul_right_apply"], DirectedEdge["has_deriv_at_filter.neg", "continuous_linear_map.neg_apply"], DirectedEdge["has_deriv_at_filter.neg", "congr"], DirectedEdge["has_deriv_at_filter_neg", "has_deriv_at_filter.neg"], DirectedEdge["has_deriv_at.neg", "has_deriv_at_filter.neg"], DirectedEdge["has_deriv_within_at.neg", "has_deriv_at_filter.neg"], DirectedEdge["has_deriv_at_filter.sub", "has_deriv_at_filter.neg"], DirectedEdge["roption.mem_to_option", "option.not_mem_none"], DirectedEdge["roption.mem_to_option", "dif_pos"], DirectedEdge["roption.mem_to_option", "option.mem_def"], DirectedEdge["roption.mem_to_option", "congr_arg"], DirectedEdge["roption.mem_to_option", "iff_true_intro"], DirectedEdge["roption.mem_to_option", "congr"], DirectedEdge["roption.mem_to_option", "mt"], DirectedEdge["roption.mem_to_option", "dif_neg"], DirectedEdge["roption.mem_to_option", "iff_false_intro"], DirectedEdge["roption.mem_to_option", "eq.trans"], DirectedEdge["roption.mem_to_option", "not_false_iff"], DirectedEdge["roption.mem_to_option", "Exists.fst"], DirectedEdge["roption.mem_to_option", "dif_ctx_congr"], DirectedEdge["roption.of_to_option", "roption.mem_to_option"], DirectedEdge["norm_num.add_bit0_bit0", "eq.trans"], DirectedEdge["norm_num.add_bit0_bit0", "congr_arg"], DirectedEdge["norm_num.add_bit0_bit0", "eq_self_iff_true"], DirectedEdge["norm_num.add_bit0_bit0", "add_left_comm"], DirectedEdge["norm_num.add_bit0_bit0", "eq.subst"], DirectedEdge["norm_num.add_bit0_bit0", "congr"], DirectedEdge["norm_num.add_bit0_bit0", "add_assoc"], DirectedEdge["real.tan_lt_tan_of_nonneg_of_lt_pi_div_two", "norm_num.add_bit0_bit0"], DirectedEdge["quadratic_eq_zero_iff_discrim_eq_square", "norm_num.add_bit0_bit0"], DirectedEdge["real.cos_one_le", "norm_num.add_bit0_bit0"], DirectedEdge["inner_product_geometry.sin_angle_sub_add_angle_sub_rev_eq_sin_angle", "norm_num.add_bit0_bit0"], DirectedEdge["inner_product_geometry.cos_angle_sub_add_angle_sub_rev_eq_neg_cos_angle", "norm_num.add_bit0_bit0"], DirectedEdge["euclidean_geometry.exists_unique_dist_eq_of_insert", "norm_num.add_bit0_bit0"], DirectedEdge["int.exists_sum_two_squares_add_one_eq_k", "norm_num.add_bit0_bit0"], DirectedEdge["bernoulli_three", "norm_num.add_bit0_bit0"], DirectedEdge["real.cos_two_neg", "norm_num.add_bit0_bit0"], DirectedEdge["real.sin_pos_of_pos_of_le_one", "norm_num.add_bit0_bit0"], DirectedEdge["exists_norm_eq_infi_of_complete_convex", "norm_num.add_bit0_bit0"], DirectedEdge["exp_neg_inv_glue.f_aux_deriv", "norm_num.add_bit0_bit0"], DirectedEdge["real.cos_bound", "norm_num.add_bit0_bit0"], DirectedEdge["pos_num.min_fac_to_nat", "norm_num.add_bit0_bit0"], DirectedEdge["pythagorean_triple.even_odd_of_coprime", "norm_num.add_bit0_bit0"], DirectedEdge["pythagorean_triple.coprime_classification", "norm_num.add_bit0_bit0"], DirectedEdge["pythagorean_triple.classification", "norm_num.add_bit0_bit0"], DirectedEdge["real.cos_pos_of_le_one", "norm_num.add_bit0_bit0"], DirectedEdge["real.pi_lt_3141593", "norm_num.add_bit0_bit0"], DirectedEdge["real.pi_gt_3141592", "norm_num.add_bit0_bit0"], DirectedEdge["complex.arg_cos_add_sin_mul_I", "norm_num.add_bit0_bit0"], DirectedEdge["inner_eq_norm_add_mul_self_sub_norm_sub_mul_self_div_four", "norm_num.add_bit0_bit0"], DirectedEdge["real.sin_bound", "norm_num.add_bit0_bit0"], DirectedEdge["real.pi_lt_315", "norm_num.add_bit0_bit0"], DirectedEdge["real.pi_gt_three", "norm_num.add_bit0_bit0"], DirectedEdge["modeq_three_digits_sum", "norm_num.add_bit0_bit0"], DirectedEdge["gold_conj_irrational", "norm_num.add_bit0_bit0"], DirectedEdge["gold_irrational", "norm_num.add_bit0_bit0"], DirectedEdge["bernoulli_four", "norm_num.add_bit0_bit0"], DirectedEdge["real.pi_lt_31416", "norm_num.add_bit0_bit0"], DirectedEdge["has_strict_deriv_at_inv", "norm_num.add_bit0_bit0"], DirectedEdge["real.pi_gt_31415", "norm_num.add_bit0_bit0"], DirectedEdge["complex.arg_le_pi", "norm_num.add_bit0_bit0"], DirectedEdge["real.pi_gt_314", "norm_num.add_bit0_bit0"], DirectedEdge["real.cos_lt_cos_of_nonneg_of_le_pi", "norm_num.add_bit0_bit0"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "congr_fun"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "continuous_linear_map.one_apply"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "eq_self_iff_true"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "continuous_linear_map.ext"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "congr"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "continuous_linear_map.coe_comp'"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "function.comp_app"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "congr_arg"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "has_fderiv_within_at.comp"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "continuous_linear_map.smul_right_apply"], DirectedEdge["has_fderiv_within_at.comp_has_deriv_within_at", "eq.trans"], DirectedEdge["convex.norm_image_sub_le_of_norm_has_fderiv_within_le", "has_fderiv_within_at.comp_has_deriv_within_at"], DirectedEdge["has_fderiv_at.comp_has_deriv_within_at", "has_fderiv_within_at.comp_has_deriv_within_at"], DirectedEdge["domain_mvt", "has_fderiv_within_at.comp_has_deriv_within_at"], DirectedEdge["nat.dist_eq_sub_of_le", "zero_add"], DirectedEdge["nat.dist_eq_sub_of_le", "nat.sub_eq_zero_of_le"], DirectedEdge["nat.dist_eq_sub_of_le", "nat.dist.def"], DirectedEdge["nat.dist_zero_left", "nat.dist_eq_sub_of_le"], DirectedEdge["nat.dist_eq_sub_of_le_right", "nat.dist_eq_sub_of_le"], DirectedEdge["nat.dist_pos_of_ne", "nat.dist_eq_sub_of_le"], DirectedEdge["int_prod_range_nonneg", "congr_arg"], DirectedEdge["int_prod_range_nonneg", "finset.card_range"], DirectedEdge["int_prod_range_nonneg", "congr"], DirectedEdge["int_prod_range_nonneg", "int.coe_nat_le"], DirectedEdge["int_prod_range_nonneg", "eq.symm"], DirectedEdge["int_prod_range_nonneg", "sub_nonneg"], DirectedEdge["int_prod_range_nonneg", "sub_nonpos"], DirectedEdge["int_prod_range_nonneg", "finset.ext"], DirectedEdge["int_prod_range_nonneg", "eq.trans"], DirectedEdge["int_prod_range_nonneg", "le_of_eq"], DirectedEdge["int_prod_range_nonneg", "int.coe_nat_lt"], DirectedEdge["int_prod_range_nonneg", "finset.mem_range"], DirectedEdge["int_prod_range_nonneg", "le_or_lt"], DirectedEdge["int_prod_range_nonneg", "finset.prod_nonneg_of_card_nonpos_even"], DirectedEdge["int_prod_range_nonneg", "le_trans"], DirectedEdge["int_prod_range_nonneg", "finset.prod_eq_zero"], DirectedEdge["int_prod_range_nonneg", "le_of_lt"], DirectedEdge["int_prod_range_nonneg", "finset.prod_nonneg"], DirectedEdge["int_prod_range_nonneg", "finset.mem_filter"], DirectedEdge["int_prod_range_nonneg", "sub_self"], DirectedEdge["int_prod_range_nonneg", "int.coe_nat_nonneg"], DirectedEdge["convex_on_fpow", "int_prod_range_nonneg"], DirectedEdge["submodule.mk_eq_zero", "subtype.ext_iff_val"], DirectedEdge["linear_equiv.eq_bot_of_equiv", "submodule.mk_eq_zero"], DirectedEdge["linear_map.is_compl_of_proj", "submodule.mk_eq_zero"], DirectedEdge["cardinal.lt_univ", 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DirectedEdge["submonoid.mem_supr_of_directed", "submonoid.le_def"], DirectedEdge["submonoid.mem_supr_of_directed", "le_supr"], DirectedEdge["submonoid.mem_supr_of_directed", "submonoid.one_mem"], DirectedEdge["submonoid.mem_supr_of_directed", "congr_arg"], DirectedEdge["submonoid.mem_supr_of_directed", "congr"], DirectedEdge["submonoid.coe_supr_of_directed", "submonoid.mem_supr_of_directed"], DirectedEdge["submonoid.mem_Sup_of_directed_on", "submonoid.mem_supr_of_directed"], DirectedEdge["finset.weighted_vsub_vadd_affine_combination", "vadd_eq_add"], DirectedEdge["finset.weighted_vsub_vadd_affine_combination", "affine_map.map_vadd"], DirectedEdge["finset.weighted_vsub_vadd_affine_combination", "finset.affine_combination_linear"], DirectedEdge["finset.weighted_vsub_vadd_affine_combination", "eq.symm"], DirectedEdge["eq_affine_combination_of_mem_affine_span", "finset.weighted_vsub_vadd_affine_combination"], 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"filter.inter_mem_inf_sets"], DirectedEdge["filter.prod_mem_prod", "filter.preimage_mem_comap"], DirectedEdge["dense_inducing.extend_Z_bilin", "filter.prod_mem_prod"], DirectedEdge["prod_mem_nhds_sets", "filter.prod_mem_prod"], DirectedEdge["complete_space_extension", "filter.prod_mem_prod"], DirectedEdge["nhds_le_uniformity", "filter.prod_mem_prod"], DirectedEdge["nhds_within_prod", "filter.prod_mem_prod"], DirectedEdge["is_closed_diagonal", "filter.prod_mem_prod"], DirectedEdge["filter.prod_map_map_eq", "filter.prod_mem_prod"], DirectedEdge["cauchy_of_totally_bounded_of_ultrafilter", "filter.prod_mem_prod"], DirectedEdge["add_subgroup.list_sum_mem", "add_submonoid.list_sum_mem"], DirectedEdge["subring.list_sum_mem", "add_subgroup.list_sum_mem"], DirectedEdge["zmod.cast_self", "char_p.cast_eq_zero"], DirectedEdge["char_p.eq", "char_p.cast_eq_zero"], DirectedEdge["char_p.cast_eq_mod", "char_p.cast_eq_zero"], DirectedEdge["polynomial.is_unit_or_eq_zero_of_separable_expand", "char_p.cast_eq_zero"], DirectedEdge["turing.tape.move_left_nth", "eq.symm"], DirectedEdge["turing.tape.move_left_nth", "turing.list_blank.tail_cons"], DirectedEdge["turing.tape.move_left_nth", "turing.list_blank.nth_zero"], DirectedEdge["turing.tape.move_left_nth", "eq.trans"], DirectedEdge["turing.tape.move_left_nth", "add_sub_cancel"], DirectedEdge["turing.tape.move_left_nth", "turing.list_blank.nth_succ"], DirectedEdge["turing.tape.move_left_nth", "turing.list_blank.head_cons"], DirectedEdge["turing.tape.move_right_nth", "turing.tape.move_left_nth"], DirectedEdge["gold_ne_zero", "ne_of_gt"], DirectedEdge["vector3.append_left", "congr"], DirectedEdge["vector3.append_left", "congr_fun"], DirectedEdge["vector3.append_left", "eq_self_iff_true"], DirectedEdge["vector3.append_left", "congr_arg"], DirectedEdge["vector3.append_left", "vector3.append_cons"], DirectedEdge["vector3.append_left", "vector3.cons_fs"], DirectedEdge["vector3.append_left", "eq.symm"], DirectedEdge["vector3.append_left", "eq_of_heq"], DirectedEdge["vector3.append_left", "vector3.cons_fz"], DirectedEdge["vector3.append_left", "eq.trans"], DirectedEdge["multiset.nodup_bind", "multiset.quot_mk_to_coe''"], DirectedEdge["tendsto_multiset_prod", "multiset.quot_mk_to_coe''"], DirectedEdge["tendsto_multiset_sum", "multiset.quot_mk_to_coe''"], DirectedEdge["multiset.nodup_sigma", "multiset.quot_mk_to_coe''"], DirectedEdge["continuous_multiset_sum", "multiset.quot_mk_to_coe''"], DirectedEdge["multiset.lt_cons_self", "multiset.quot_mk_to_coe''"], DirectedEdge["multiset.cons_inj_right", "multiset.quot_mk_to_coe''"], DirectedEdge["continuous_multiset_prod", "multiset.quot_mk_to_coe''"], DirectedEdge["multiset.exists_mem_of_ne_zero", "multiset.quot_mk_to_coe''"], DirectedEdge["eq_zero_of_one_div_eq_zero", "one_div_ne_zero"], DirectedEdge["multiset.antidiagonal_coe'", "multiset.revzip_powerset_aux_perm_aux'"], DirectedEdge["multiset.antidiagonal_map_fst", 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DirectedEdge["real.cos_pi", "not_false_iff"], DirectedEdge["real.cos_pi", "mul_zero"], DirectedEdge["real.cos_pi", "ne.def"], DirectedEdge["real.cos_pi", "zero_pow'"], DirectedEdge["has_deriv_within_at.sqrt", "real.cos_pi"], DirectedEdge["real.sin_add_pi", "real.cos_pi"], DirectedEdge["inner_product_geometry.cos_angle_sub_add_angle_sub_rev_eq_neg_cos_angle", "real.cos_pi"], DirectedEdge["complex.sin_arg", "real.cos_pi"], DirectedEdge["real.sin_int_mul_pi", "real.cos_pi"], DirectedEdge["real.cos_two_pi", "real.cos_pi"], DirectedEdge["real.exists_cos_eq", "real.cos_pi"], DirectedEdge["real.sin_two_pi", "real.cos_pi"], DirectedEdge["real.cos_int_mul_two_pi_add_pi", "real.cos_pi"], DirectedEdge["real.cos_pi_sub", "real.cos_pi"], DirectedEdge["real.cos_add_pi", "real.cos_pi"], DirectedEdge["real.sin_nat_mul_pi", "real.cos_pi"], DirectedEdge["complex.cos_pi", "real.cos_pi"], DirectedEdge["real.has_deriv_at_rpow_of_neg", "real.cos_pi"], DirectedEdge["real.sin_pi_sub", "real.cos_pi"], DirectedEdge["norm_sum_le_of_le", "finset.sum_le_sum"], DirectedEdge["norm_sum_le_of_le", "norm_sum_le"], DirectedEdge["norm_sum_le_of_le", "le_trans"], DirectedEdge["cauchy_seq_finset_of_norm_bounded", "norm_sum_le_of_le"], DirectedEdge["two_ne_zero'", "nat.cast_ne_zero"], DirectedEdge["two_ne_zero'", "nat.cast_one"], DirectedEdge["two_ne_zero'", "nat.cast_succ"], DirectedEdge["complex.re_eq_add_conj", "two_ne_zero'"], DirectedEdge["add_self_eq_zero", "two_ne_zero'"], DirectedEdge["complex.cosh_mul_I", "two_ne_zero'"], DirectedEdge["complex.two_cosh", "two_ne_zero'"], DirectedEdge["complex.two_sin", "two_ne_zero'"], DirectedEdge["complex.cos_square", "two_ne_zero'"], DirectedEdge["complex.sinh_mul_I", "two_ne_zero'"], DirectedEdge["real.pi_div_two_le_two", "two_ne_zero'"], DirectedEdge["complex.sinh_add", "two_ne_zero'"], DirectedEdge["complex.two_sinh", "two_ne_zero'"], DirectedEdge["real.cos_bound", "two_ne_zero'"], DirectedEdge["real.sinh_eq", "two_ne_zero'"], DirectedEdge["real.sin_bound", "two_ne_zero'"], DirectedEdge["real.two_le_pi", "two_ne_zero'"], DirectedEdge["complex.cosh_sub_sinh", "two_ne_zero'"], DirectedEdge["complex.two_cos", "two_ne_zero'"], DirectedEdge["half_add_self", "two_ne_zero'"], DirectedEdge["complex.cosh_add", "two_ne_zero'"], DirectedEdge["real.cos_pi_div_two", "two_ne_zero'"], DirectedEdge["real.one_le_pi_div_two", "two_ne_zero'"], DirectedEdge["complex.cosh_add_sinh", "two_ne_zero'"], DirectedEdge["ennreal.half_lt_self", "two_ne_zero'"], DirectedEdge["real.cosh_eq", "two_ne_zero'"], DirectedEdge["real.Lp_add_le_of_nonneg", "iff_true_intro"], DirectedEdge["real.Lp_add_le_of_nonneg", "abs_of_nonneg"], DirectedEdge["real.Lp_add_le_of_nonneg", "real.Lp_add_le"], DirectedEdge["real.Lp_add_le_of_nonneg", "finset.sum_congr"], DirectedEdge["real.Lp_add_le_of_nonneg", "add_nonneg"], DirectedEdge["real.Lp_add_le_of_nonneg", "congr_arg"], DirectedEdge["real.Lp_add_le_of_nonneg", "congr"], DirectedEdge["ennreal.rpow_nat_cast", "nat.cast_succ"], DirectedEdge["ennreal.rpow_nat_cast", "ennreal.coe_rpow_of_nonneg"], DirectedEdge["ennreal.rpow_nat_cast", "nat.cast_nonneg"], DirectedEdge["ennreal.rpow_nat_cast", "nat.cast_zero"], DirectedEdge["ennreal.rpow_nat_cast", "ennreal.top_pow"], DirectedEdge["ennreal.rpow_nat_cast", "eq.trans"], DirectedEdge["ennreal.rpow_nat_cast", "eq_self_iff_true"], DirectedEdge["ennreal.rpow_nat_cast", "pow_zero"], DirectedEdge["ennreal.rpow_nat_cast", "congr_arg"], DirectedEdge["ennreal.rpow_nat_cast", "ennreal.coe_pow"], DirectedEdge["ennreal.rpow_nat_cast", "nat.nat_zero_eq_zero"], DirectedEdge["ennreal.rpow_nat_cast", "congr"], DirectedEdge["ennreal.rpow_nat_cast", "ennreal.none_eq_top"], DirectedEdge["ennreal.rpow_nat_cast", "ennreal.rpow_zero"], DirectedEdge["ennreal.rpow_nat_cast", "ennreal.some_eq_coe"], DirectedEdge["ennreal.rpow_nat_cast", "nnreal.rpow_nat_cast"], DirectedEdge["ennreal.rpow_nat_cast", "ennreal.top_rpow_of_pos"], DirectedEdge["times_cont_diff_within_at.comp", "eq.symm"], DirectedEdge["times_cont_diff_within_at.comp", "times_cont_diff_on.comp"], DirectedEdge["times_cont_diff_within_at.comp", "eq.trans"], DirectedEdge["times_cont_diff_within_at.comp", "set.inter_subset_left"], DirectedEdge["times_cont_diff_within_at.comp", "mem_of_mem_nhds_within"], DirectedEdge["times_cont_diff_within_at.comp", "set.subset.antisymm"], DirectedEdge["times_cont_diff_within_at.comp", "nhds_within_mono"], DirectedEdge["times_cont_diff_within_at.comp", "set.insert_eq_of_mem"], DirectedEdge["times_cont_diff_within_at.comp", "set.insert_subset_insert"], DirectedEdge["times_cont_diff_within_at.comp", "set.inter_subset_right"], DirectedEdge["times_cont_diff_within_at.comp", "times_cont_diff_on.mono"], DirectedEdge["times_cont_diff_within_at.comp", "congr_arg"], DirectedEdge["times_cont_diff_within_at.comp", "filter.inter_mem_sets"], DirectedEdge["times_cont_diff_within_at.comp", "times_cont_diff_within_at.continuous_within_at'"], DirectedEdge["times_cont_diff_within_at.comp", "continuous_within_at.preimage_mem_nhds_within'"], DirectedEdge["times_cont_diff_within_at.comp", "le_refl"], DirectedEdge["times_cont_diff_within_at.comp", "congr"], DirectedEdge["times_cont_diff_within_at.comp", "set.image_subset_iff"], DirectedEdge["times_cont_diff_within_at.comp", "set.mem_inter_eq"], DirectedEdge["times_cont_diff_within_at.comp", "times_cont_diff_within_at.times_cont_diff_on"], DirectedEdge["times_cont_diff_within_at.comp", "iff_true_intro"], DirectedEdge["times_cont_diff_within_at.comp", "nhds_within_restrict''"], DirectedEdge["times_cont_diff_within_at.comp", "times_cont_diff_on.times_cont_diff_within_at"], DirectedEdge["times_cont_diff_within_at.comp", "set.mem_insert"], DirectedEdge["times_cont_diff_within_at.comp", "set.image_insert_eq"], DirectedEdge["times_cont_diff_at.comp", "times_cont_diff_within_at.comp"], DirectedEdge["times_cont_diff_within_at.prod_map'", "times_cont_diff_within_at.comp"], DirectedEdge["times_cont_diff.comp_times_cont_diff_within_at", "times_cont_diff_within_at.comp"], DirectedEdge["times_cont_diff_within_at.neg", "times_cont_diff_within_at.comp"], DirectedEdge["times_cont_diff_within_at.comp'", "times_cont_diff_within_at.comp"], DirectedEdge["times_cont_diff_within_at.add", "times_cont_diff_within_at.comp"], DirectedEdge["times_cont_diff_within_at_local_invariant_prop", "times_cont_diff_within_at.comp"], DirectedEdge["set.piecewise_empty", "if_congr"], DirectedEdge["set.piecewise_empty", "if_false"], DirectedEdge["set.piecewise_empty", "funext"], DirectedEdge["set.piecewise_empty", "congr"], DirectedEdge["set.piecewise_empty", "eq.trans"], DirectedEdge["set.piecewise_empty", "set.mem_empty_eq"], DirectedEdge["set.piecewise_empty", "congr_arg"], DirectedEdge["set.piecewise_empty", "eq_self_iff_true"], DirectedEdge["set.piecewise_empty", "iff.refl"], DirectedEdge["set.piecewise_empty", "congr_fun"], DirectedEdge["measure_theory.simple_func.piecewise_empty", "set.piecewise_empty"], DirectedEdge["filter.tendsto_Ixx_class_of_subset", "filter.eventually_of_forall"], DirectedEdge["filter.tendsto_Ixx_class_of_subset", "filter.tendsto_lift'_powerset_mono"], DirectedEdge["filter.tendsto_Ixx_class_of_subset", "prod.forall"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "dist_triangle_right"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "abs_dist"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "real.dist_eq"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "congr_arg"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "sub_zero"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "half_pos"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "congr"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "lt_of_le_of_lt"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "eq_self_iff_true"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "add_halves"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "le_trans"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "eq.trans"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "metric.tendsto_nhds_nhds"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "le_abs_self"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "metric.ball_mem_nhds"], DirectedEdge["bounded_continuous_function.equicontinuous_of_continuity_modulus", "add_lt_add"], DirectedEdge["free_group.map_pure", "free_group.map.of"], DirectedEdge["free_group.map.unique", "free_group.map.of"], DirectedEdge["free_group.to_group_eq_prod_map", "free_group.map.of"], DirectedEdge["mul_pow", "commute.all"], DirectedEdge["mul_pow", "commute.mul_pow"], DirectedEdge["nsmul_add", "mul_pow"], DirectedEdge["finite_field.sum_pow_units", "mul_pow"], DirectedEdge["real.sin_pi_over_two_pow_succ", "mul_pow"], DirectedEdge["formal_multilinear_series.comp_summable_nnreal", "mul_pow"], DirectedEdge["scale_roots_eval\:2082_eq_zero", "mul_pow"], DirectedEdge["real.cos_pi_over_two_pow", "mul_pow"], DirectedEdge["lucas_lehmer.X.closed_form", "mul_pow"], DirectedEdge["tactic.ring.horner_pow", "mul_pow"], DirectedEdge["ideal.is_prime_radical", "mul_pow"], DirectedEdge["complex.sin_sq_add_cos_sq", "mul_pow"], DirectedEdge["finset.prod_pow", "mul_pow"], DirectedEdge["normed_ring.inverse_add_norm_diff_nth_order", "mul_pow"], DirectedEdge["polynomial.integral_normalization_eval\:2082_eq_zero", "mul_pow"], DirectedEdge["real.pi_lt_sqrt_two_add_series", "mul_pow"], DirectedEdge["lucas_lehmer.\[Omega]_pow_formula", "mul_pow"], DirectedEdge["tactic.ring_exp.pow_pp_pf_prod", "mul_pow"], DirectedEdge["polynomial.expand_char", "mul_pow"], DirectedEdge["formal_multilinear_series.bound_of_lt_radius", "mul_pow"], DirectedEdge["submodule.range_mkq", "submodule.eq_top_iff'"], DirectedEdge["submodule.range_mkq", "quot.induction_on"], DirectedEdge["submodule.map_mkq_eq_top", "submodule.range_mkq"], DirectedEdge["multiset.sum_cons", "multiset.foldr_cons"], DirectedEdge["multiset.sum_map_add", "multiset.sum_cons"], DirectedEdge["multiset.prod_map_sum", "multiset.sum_cons"], DirectedEdge["finsupp.single_multiset_sum", "multiset.sum_cons"], DirectedEdge["finsupp.mem_support_multiset_sum", "multiset.sum_cons"], DirectedEdge["multiset.le_sum_of_subadditive", "multiset.sum_cons"], DirectedEdge["multiset.prod_map_add", "multiset.sum_cons"], DirectedEdge["multiset.sum_bind", "multiset.sum_cons"], DirectedEdge["multiset.sum_singleton", "multiset.sum_cons"], DirectedEdge["multiset.sum_map_mul_right", "multiset.sum_cons"], DirectedEdge["multiset.join_cons", "multiset.sum_cons"], DirectedEdge["multiset.sum_map_mul_left", "multiset.sum_cons"], DirectedEdge["multiset.card_join", "multiset.sum_cons"], DirectedEdge["multiset.count_bind", "multiset.sum_cons"], DirectedEdge["finsupp.multiset_sum_sum_index", "multiset.sum_cons"], DirectedEdge["multiset.dvd_sum", "multiset.sum_cons"], DirectedEdge["filter.germ.const_lt", "filter.germ.coe_lt"], DirectedEdge["filter.germ.const_lt", "filter.germ.lift_rel_const_iff"], DirectedEdge["filter.germ.const_lt", "iff.trans"], DirectedEdge["hyperreal.coe_lt_coe", "filter.germ.const_lt"], DirectedEdge["ordinal.lift_type_fin", "congr"], DirectedEdge["ordinal.lift_type_fin", "ordinal.lift_nat_cast"], DirectedEdge["ordinal.lift_type_fin", "ordinal.type_fin"], DirectedEdge["ordinal.lift_type_fin", "congr_arg"], DirectedEdge["ordinal.lift_type_fin", "eq.trans"], DirectedEdge["norm_sub_le_of_le", "add_le_add"], DirectedEdge["norm_sub_le_of_le", "le_trans"], DirectedEdge["norm_sub_le_of_le", "norm_sub_le"], DirectedEdge["not_prime_zero", "prime.ne_zero"], DirectedEdge["unique_factorization_domain.irreducible_iff_prime", "not_prime_zero"], DirectedEdge["nhds_top_order", "nhds_eq_order"], DirectedEdge["nhds_top_order", "iff_false_intro"], DirectedEdge["nhds_top_order", "not_top_lt"], DirectedEdge["nhds_top_order", "congr"], DirectedEdge["nhds_top_order", "eq_self_iff_true"], DirectedEdge["nhds_top_order", "congr_arg"], DirectedEdge["nhds_top_order", "infi_false"], DirectedEdge["nhds_top_order", "eq.trans"], DirectedEdge["nhds_top_order", "iff.trans"], DirectedEdge["nhds_top_order", "infi_top"], DirectedEdge["nhds_top_order", "set.mem_Iio"], DirectedEdge["nhds_top_order", "infi_congr_Prop"], DirectedEdge["nhds_top_order", "inf_top_eq"], DirectedEdge["nhds_top_order", "funext"], DirectedEdge["nhds_top_order", "set.mem_Ioi"], DirectedEdge["ennreal.nhds_top", "nhds_top_order"], DirectedEdge["real.is_conjugate_exponent.sub_one_ne_zero", "ne_of_gt"], DirectedEdge["real.is_conjugate_exponent.sub_one_ne_zero", "real.is_conjugate_exponent.sub_one_pos"], DirectedEdge["real.is_conjugate_exponent.sub_one_mul_conj", "real.is_conjugate_exponent.sub_one_ne_zero"], DirectedEdge["deriv_within_congr", "congr_arg"], DirectedEdge["deriv_within_congr", "fderiv_within_congr"], DirectedEdge["deriv_within_congr", "congr"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "affine.simplex.circumcenter_circumradius_unique_dist_eq"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "congr_arg"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "eq.trans"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "prod.ext_iff"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "eq_self_iff_true"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "forall_congr_eq"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "congr"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "forall_const"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "imp_congr_eq"], DirectedEdge["affine.simplex.eq_circumradius_of_dist_eq", "iff_true_intro"], DirectedEdge["ordinal.le_sup", "ordinal.omin_mem"], DirectedEdge["ordinal.iterate_le_nfp", "ordinal.le_sup"], DirectedEdge["ordinal.sup_le", "ordinal.le_sup"], DirectedEdge["ordinal.sup_succ", "ordinal.le_sup"], DirectedEdge["ordinal.cof_univ", "ordinal.le_sup"], DirectedEdge["pgame.add_lt_add_right", "eq.symm"], DirectedEdge["pgame.add_lt_add_right", "pgame.add_le_add_left"], DirectedEdge["pgame.add_lt_add_right", "pgame.add_le_add_right"], DirectedEdge["pgame.add_lt_add_right", "pgame.not_le"], DirectedEdge["pgame.add_lt_add_right", "pgame.add_right_neg_le_zero"], DirectedEdge["pgame.add_lt_add_right", "pgame.zero_le_add_right_neg"], DirectedEdge["pgame.add_lt_add_right", "pgame.le_of_relabelling"], DirectedEdge["pgame.add_lt_add_right", "pgame.le_trans"], DirectedEdge["pgame.add_lt_add_right", "mt"], DirectedEdge["pgame.lt_iff_sub_pos", "pgame.add_lt_add_right"], DirectedEdge["pgame.add_lt_add_left", "pgame.add_lt_add_right"], DirectedEdge["cardinal.sum_lt_prod", "iff.symm"], DirectedEdge["cardinal.sum_lt_prod", "not_le_of_lt"], DirectedEdge["cardinal.sum_lt_prod", "cardinal.mk_out"], DirectedEdge["cardinal.sum_lt_prod", "lt_of_not_ge"], DirectedEdge["cardinal.sum_lt_prod", "congr_arg"], DirectedEdge["cardinal.sum_lt_prod", "lt_of_le_of_lt"], DirectedEdge["cardinal.sum_lt_prod", "cardinal.ne_zero_iff_nonempty"], DirectedEdge["cardinal.sum_lt_prod", "classical.some_spec"], DirectedEdge["cardinal.sum_lt_prod", "eq.symm"], DirectedEdge["cardinal.sum_lt_prod", "funext"], DirectedEdge["cardinal.sum_lt_prod", "not_exists"], DirectedEdge["cardinal.sum_lt_prod", "ne_of_gt"], DirectedEdge["cardinal.sum_lt_prod", "eq.trans"], DirectedEdge["cardinal.sum_lt_prod", "function.inv_fun_surjective"], DirectedEdge["cardinal.sum_lt_prod", "cardinal.zero_le"], DirectedEdge["cardinal.sum_lt_prod", "congr_fun"], DirectedEdge["cardinal.sum_lt_prod", "not_forall"], DirectedEdge["cardinal.lt_power_cof", "cardinal.sum_lt_prod"], DirectedEdge["list.length_product", "list.product_cons"], DirectedEdge["list.product_nil", "list.product_cons"], DirectedEdge["finsupp.supported_empty", "finsupp.mem_supported'"], DirectedEdge["finsupp.supported_empty", "finsupp.ext"], DirectedEdge["finsupp.supported_empty", "eq.trans"], DirectedEdge["finsupp.supported_empty", "eq_self_iff_true"], DirectedEdge["finsupp.supported_empty", "congr_arg"], DirectedEdge["finsupp.supported_empty", "submodule.mem_bot"], DirectedEdge["finsupp.supported_empty", "forall_congr_eq"], DirectedEdge["finsupp.supported_empty", "not_false_iff"], DirectedEdge["finsupp.supported_empty", "forall_prop_of_true"], DirectedEdge["finsupp.supported_empty", "congr"], DirectedEdge["finsupp.supported_empty", "imp_congr_eq"], DirectedEdge["finsupp.supported_empty", "finsupp.zero_apply"], DirectedEdge["finsupp.supported_empty", "set.mem_empty_eq"], DirectedEdge["finsupp.supported_empty", "eq_bot_iff"], DirectedEdge["linear_independent_empty", "finsupp.supported_empty"], DirectedEdge["multiset.le_inter_iff", "le_inf_iff"], DirectedEdge["list.lt_eq_not_ge", "eq.symm"], DirectedEdge["list.lt_eq_not_ge", "eq.subst"], DirectedEdge["list.lt_eq_not_ge", "decidable.not_not_iff"], DirectedEdge["finsupp.single_injective", "finsupp.single_eq_same"], DirectedEdge["mv_polynomial.C_injective", "finsupp.single_injective"], DirectedEdge["finsupp.single_eq_single_iff", "finsupp.single_injective"], DirectedEdge["finsupp.ker_lsingle", "finsupp.single_injective"], DirectedEdge["uniform_continuous_of_const", "set.eq_univ_iff_forall"], DirectedEdge["uniform_continuous_of_const", "iff_true_intro"], DirectedEdge["uniform_continuous_of_const", "congr"], DirectedEdge["uniform_continuous_of_const", "le_trans"], DirectedEdge["uniform_continuous_of_const", "congr_arg"], DirectedEdge["uniform_continuous_of_const", "filter.map_le_iff_le_comap"], DirectedEdge["uniform_continuous_of_const", "filter.principal_univ"], DirectedEdge["uniform_continuous_of_const", "eq.trans"], DirectedEdge["uniform_continuous_of_const", "refl_le_uniformity"], DirectedEdge["uniform_continuous_of_const", "filter.comap_principal"], DirectedEdge["uniform_continuous_of_const", "le_top"], DirectedEdge["Cauchy.uniform_continuous_extend", "uniform_continuous_of_const"], DirectedEdge["uniform_continuous_const", "uniform_continuous_of_const"], DirectedEdge["uniform_space.separation_quotient.uniform_continuous_lift", "uniform_continuous_of_const"], DirectedEdge["abstract_completion.uniform_continuous_extend", "uniform_continuous_of_const"], DirectedEdge["real.one_lt_rpow", "eq.symm"], DirectedEdge["real.one_lt_rpow", 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DirectedEdge["seq.append_assoc", "seq.cons_append"], DirectedEdge["seq.append_assoc", "eq_self_iff_true"], DirectedEdge["seq.append_assoc", "seq.destruct_nil"], DirectedEdge["seq.append_assoc", "seq.nil_append"], DirectedEdge["seq.append_assoc", "congr"], DirectedEdge["seq.append_assoc", "seq.eq_of_bisim"], DirectedEdge["seq.append_assoc", "eq.trans"], DirectedEdge["seq.append_assoc", "congr_arg"], DirectedEdge["seq.append_assoc", "forall_congr_eq"], DirectedEdge["seq.append_assoc", "true_and"], DirectedEdge["seq1.bind_assoc", "seq.append_assoc"], DirectedEdge["seq1.join_join", "seq.append_assoc"], DirectedEdge["seq.join_append", "seq.append_assoc"], DirectedEdge["wseq.append_assoc", "seq.append_assoc"], DirectedEdge["deriv_within_cos", "differentiable_within_at.has_deriv_within_at"], DirectedEdge["deriv_within_cos", "has_deriv_within_at.deriv_within"], DirectedEdge["deriv_within_cos", "has_deriv_within_at.cos"], DirectedEdge["denumerable.raise'_chain", "nat.lt_succ_self"], DirectedEdge["denumerable.raise'_chain", "nat.le_add_left"], DirectedEdge["denumerable.raise'_sorted", "denumerable.raise'_chain"], DirectedEdge["list.pairwise.iff", "list.pairwise.iff_of_mem"], DirectedEdge["list.pairwise_filter", "list.pairwise.iff"], DirectedEdge["finset.mem_of_mem_inter_right", "finset.mem_inter"], DirectedEdge["finset.inter_subset_right", "finset.mem_of_mem_inter_right"], DirectedEdge["pgame.domineering.move_right_card", "finset.mem_of_mem_inter_right"], DirectedEdge["pgame.domineering.move_left_card", "finset.mem_of_mem_inter_right"], DirectedEdge["differentiable_within_at.div_const", "differentiable_within_at.const_mul"], DirectedEdge["differentiable_within_at.div_const", "iff_true_intro"], DirectedEdge["differentiable_within_at.div_const", "eq.trans"], DirectedEdge["differentiable_within_at.div_const", "div_eq_inv_mul"], DirectedEdge["differentiable_within_at.div_const", "congr"], DirectedEdge["differentiable_within_at.div_const", "congr_arg"], DirectedEdge["differentiable_within_at.div_const", "funext"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "and_true"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "partrec.merge"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "eq.trans"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "roption.mem_assert_iff"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "funext"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "roption.mem_some_iff"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "computable.to\:2082"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "exists_const"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "computable_pred.to_re"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "partrec.of_eq"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "computable_pred.not"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "congr"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "partrec.map"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "exists_and_distrib_right"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "decidable.em"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "roption.mem_map_iff"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "eq_iff_true_of_subsingleton"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "roption.eq_some_iff"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "bool.ff_eq_to_bool_iff"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "computable.const"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "exists_prop"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "bool.tt_eq_to_bool_iff"], DirectedEdge["computable_pred.computable_iff_re_compl_re", "congr_arg"], DirectedEdge["primrec.vector_head", "primrec.vector_to_list"], DirectedEdge["primrec.vector_head", 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DirectedEdge["filter.push_pull'", "inf_comm"], DirectedEdge["filter.push_pull'", "congr_arg"], DirectedEdge["filter.push_pull'", "congr"], DirectedEdge["filter.push_pull'", "eq.trans"], DirectedEdge["filter.push_pull'", "filter.push_pull"], DirectedEdge["is_closed_proj_of_compact", "filter.push_pull'"], DirectedEdge["nhds_within_prod_eq", "nhds_prod_eq"], DirectedEdge["nhds_within_prod_eq", "eq.symm"], DirectedEdge["nhds_within_prod_eq", "filter.prod_inf_prod"], DirectedEdge["nhds_within_prod_eq", "filter.prod_principal_principal"], DirectedEdge["nhds_within_prod", "nhds_within_prod_eq"], DirectedEdge["has_fderiv_at_boundary_of_tendsto_fderiv", "nhds_within_prod_eq"], DirectedEdge["continuous_within_at.prod_map", "nhds_within_prod_eq"], DirectedEdge["bifunctor.comp_snd", "congr"], DirectedEdge["bifunctor.comp_snd", "congr_fun"], DirectedEdge["bifunctor.comp_snd", "congr_arg"], DirectedEdge["bifunctor.comp_snd", "eq_self_iff_true"], DirectedEdge["bifunctor.comp_snd", 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DirectedEdge["has_fderiv_at_boundary_of_tendsto_fderiv", "differentiable_at.fderiv_within"], DirectedEdge["fderiv_within_inv", "differentiable_at.fderiv_within"], DirectedEdge["polynomial.fderiv_within", "differentiable_at.fderiv_within"], DirectedEdge["differentiable_at.deriv_within", "differentiable_at.fderiv_within"], DirectedEdge["finset.sum_inter_add_sum_diff", "congr"], DirectedEdge["finset.sum_inter_add_sum_diff", "congr_fun"], DirectedEdge["finset.sum_inter_add_sum_diff", "eq_self_iff_true"], DirectedEdge["finset.sum_inter_add_sum_diff", "if_t_t"], DirectedEdge["finset.sum_inter_add_sum_diff", "funext"], DirectedEdge["finset.sum_inter_add_sum_diff", "eq.symm"], DirectedEdge["finset.sum_inter_add_sum_diff", "finset.sum_piecewise"], DirectedEdge["finset.sum_inter_add_sum_diff", "eq.trans"], DirectedEdge["finset.sum_inter_add_sum_diff", "congr_arg"], DirectedEdge["finset.add_sum_diff_singleton", "finset.sum_inter_add_sum_diff"], DirectedEdge["has_deriv_at_filter.const_sub", "has_deriv_at_filter.neg"], DirectedEdge["has_deriv_at_filter.const_sub", "has_deriv_at_filter.const_add"], DirectedEdge["has_deriv_at.const_sub", "has_deriv_at_filter.const_sub"], DirectedEdge["has_deriv_within_at.const_sub", "has_deriv_at_filter.const_sub"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "continuous_const"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "formal_multilinear_series.partial_sum_continuous"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "filter.at_top_ne_bot"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "continuous.continuous_on"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "has_fpower_series_on_ball.tendsto_locally_uniformly_on'"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "continuous_id"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "tendsto_locally_uniformly_on.continuous_on"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "continuous.comp"], DirectedEdge["has_fpower_series_on_ball.continuous_on", "continuous.sub"], DirectedEdge["has_fpower_series_at.comp", "has_fpower_series_on_ball.continuous_on"], DirectedEdge["has_fpower_series_at.continuous_at", "has_fpower_series_on_ball.continuous_on"], DirectedEdge["formal_multilinear_series.continuous_on", "has_fpower_series_on_ball.continuous_on"], DirectedEdge["continuous_linear_map.deriv", "has_deriv_at.deriv"], DirectedEdge["continuous_linear_map.deriv", "continuous_linear_map.has_deriv_at"], DirectedEdge["pgame.first_wins_of_equiv", "pgame.lt_of_lt_of_equiv"], DirectedEdge["pgame.first_wins_of_equiv", "pgame.lt_of_equiv_of_lt"], DirectedEdge["pgame.nim.sum_first_loses_iff_eq", "pgame.first_wins_of_equiv"], DirectedEdge["pgame.equiv_nim_grundy_value", "pgame.first_wins_of_equiv"], DirectedEdge["pgame.first_wins_of_equiv_iff", "pgame.first_wins_of_equiv"], DirectedEdge["function.embedding.ext", "funext"], DirectedEdge["function.embedding.equiv_of_fintype_self_embedding_to_embedding", "function.embedding.ext"], DirectedEdge["function.embedding.equiv_symm_to_embedding_trans_to_embedding", "function.embedding.ext"], DirectedEdge["function.embedding.ext_iff", "function.embedding.ext"], DirectedEdge["function.embedding.equiv_to_embedding_trans_symm_to_embedding", "function.embedding.ext"], DirectedEdge["dvd_refl", "dvd.intro"], DirectedEdge["dvd_refl", "eq_self_iff_true"], DirectedEdge["dvd_refl", "congr"], DirectedEdge["dvd_refl", "eq.trans"], DirectedEdge["dvd_refl", "mul_one"], DirectedEdge["dvd_refl", "congr_arg"], DirectedEdge["zmod.cast_add'", "dvd_refl"], DirectedEdge["nat.gcd_mul_left_left", "dvd_refl"], DirectedEdge["zmod.cast_nat_cast'", "dvd_refl"], DirectedEdge["polynomial.splits_of_splits_id", "dvd_refl"], DirectedEdge["nat.gcd_gcd_self_right_left", "dvd_refl"], DirectedEdge["nat.min_fac_eq", "dvd_refl"], DirectedEdge["nat.pow_dvd_pow_iff_pow_le_pow", "dvd_refl"], DirectedEdge["discrete_valuation_ring.of_ufd_of_unique_irreducible", "dvd_refl"], DirectedEdge["multiplicity.get_one_right", "dvd_refl"], DirectedEdge["ideal.mem_jacobson_iff", "dvd_refl"], DirectedEdge["nat.dvd_prime", "dvd_refl"], DirectedEdge["adjoin_root.mk_self", "dvd_refl"], DirectedEdge["zmod.cast_mul'", "dvd_refl"], DirectedEdge["padic_int.p_dvd_of_norm_lt_one", "dvd_refl"], DirectedEdge["nat.gcd_eq_left", "dvd_refl"], DirectedEdge["nat.gcd_dvd", "dvd_refl"], DirectedEdge["irreducible_of_prime", "dvd_refl"], DirectedEdge["principal_ideal_ring.is_maximal_of_irreducible", "dvd_refl"], DirectedEdge["dvd_lcm_left", "dvd_refl"], DirectedEdge["pell.eq_of_xn_modeq_lem3", "dvd_refl"], DirectedEdge["char_p.char_is_prime_of_two_le", "dvd_refl"], DirectedEdge["fraction_map.is_unit_denom_of_num_eq_zero", "dvd_refl"], DirectedEdge["multiplicity.multiplicity_self", "dvd_refl"], DirectedEdge["zmod.cast_int_cast'", "dvd_refl"], DirectedEdge["gcd_dvd_gcd_mul_right_right", "dvd_refl"], DirectedEdge["nat.succ_div", "dvd_refl"], DirectedEdge["zmod.cast_one'", "dvd_refl"], DirectedEdge["euclidean_domain.gcd_dvd", "dvd_refl"], DirectedEdge["pell.yn_modeq_two", "dvd_refl"], DirectedEdge["dvd_add_self_right", "dvd_refl"], DirectedEdge["lcm_units_coe_left", "dvd_refl"], DirectedEdge["pell.eq_pow_of_pell", "dvd_refl"], DirectedEdge["dvd_lcm_right", "dvd_refl"], DirectedEdge["unique_factorization_domain.dvd_of_dvd_mul_left_of_no_prime_factors", "dvd_refl"], DirectedEdge["char_p.char_ne_one", "dvd_refl"], DirectedEdge["is_cyclic_of_card_pow_eq_one_le", "dvd_refl"], DirectedEdge["dvd_add_self_left", "dvd_refl"], DirectedEdge["zmod.cast_pow'", "dvd_refl"], DirectedEdge["nat.min_fac_aux_has_prop", "dvd_refl"], DirectedEdge["euclidean_domain.gcd_self", "dvd_refl"], DirectedEdge["finite_field.card", "dvd_refl"], DirectedEdge["associates.one_or_eq_of_le_of_prime", "dvd_refl"], DirectedEdge["gcd_zero_right", "dvd_refl"], DirectedEdge["nat.fact_dvd_fact", "dvd_refl"], DirectedEdge["char_p.cast_eq_zero", "dvd_refl"], DirectedEdge["padic_int.appr_spec", "dvd_refl"], DirectedEdge["nat.dvd_add_self_left", "dvd_refl"], DirectedEdge["lcm_eq_left_iff", "dvd_refl"], DirectedEdge["pow_dvd_pow_of_dvd", "dvd_refl"], DirectedEdge["padic_int.zmod_congr_of_sub_mem_max_ideal", "dvd_refl"], DirectedEdge["int.nat_abs_div", "dvd_refl"], DirectedEdge["gcd_same", "dvd_refl"], DirectedEdge["nat.prime.dvd_fact", "dvd_refl"], DirectedEdge["nat.prime_iff_prime", "dvd_refl"], DirectedEdge["lcm_dvd_lcm_mul_left", "dvd_refl"], DirectedEdge["pell.yn_modeq_a_sub_one", "dvd_refl"], DirectedEdge["gcd_zero_left", "dvd_refl"], DirectedEdge["lcm_dvd_lcm_mul_left_right", "dvd_refl"], DirectedEdge["lcm_dvd_lcm_mul_right", "dvd_refl"], DirectedEdge["gcd_dvd_gcd_mul_left", "dvd_refl"], DirectedEdge["pell.modeq_of_xn_modeq", "dvd_refl"], DirectedEdge["mul_dvd_mul_right", "dvd_refl"], DirectedEdge["ideal.is_local.mem_jacobson_or_exists_inv", "dvd_refl"], DirectedEdge["gcd_dvd_gcd_mul_right", "dvd_refl"], DirectedEdge["is_noetherian_ring.exists_irreducible_factor", "dvd_refl"], DirectedEdge["modeq_mersenne", "dvd_refl"], DirectedEdge["mul_dvd_mul_left", "dvd_refl"], DirectedEdge["multiplicity.multiplicity_pow_self", "dvd_refl"], DirectedEdge["int.gcd_eq_left", "dvd_refl"], DirectedEdge["multiplicity.get_multiplicity_self", "dvd_refl"], DirectedEdge["nat.dvd_one", "dvd_refl"], DirectedEdge["zmod.cast_sub'", "dvd_refl"], DirectedEdge["zsqrtd.divides_sq_eq_zero", "dvd_refl"], DirectedEdge["char_p.ring_char_ne_one", "dvd_refl"], DirectedEdge["zmod.nat_abs_val_min_abs_neg", "dvd_refl"], DirectedEdge["zero_dvd_iff", "dvd_refl"], DirectedEdge["lcm_dvd_lcm_mul_right_right", "dvd_refl"], DirectedEdge["multiplicity.one_right", "dvd_refl"], DirectedEdge["nat.dvd_add_self_right", "dvd_refl"], DirectedEdge["gcd_dvd_gcd_mul_left_right", "dvd_refl"], DirectedEdge["dvd_sub_pow_of_dvd_sub", "dvd_refl"], DirectedEdge["dvd_symm_of_irreducible", "dvd_refl"], DirectedEdge["lcm_same", "dvd_refl"], DirectedEdge["euclidean_domain.mod_self", "dvd_refl"], DirectedEdge["char_p.sum_two_squares", "dvd_refl"], DirectedEdge["gcd_eq_left_iff", "dvd_refl"], DirectedEdge["nat.pow_dvd_pow_of_dvd", "dvd_refl"], DirectedEdge["ideal.span_singleton_mul_right_unit", "dvd_refl"], DirectedEdge["list.func.length_pointwise", "congr"], DirectedEdge["list.func.length_pointwise", "congr_arg"], DirectedEdge["list.func.length_pointwise", "max_eq_left"], DirectedEdge["list.func.length_pointwise", "nat.max_succ_succ"], DirectedEdge["list.func.length_pointwise", "nat.zero_le"], DirectedEdge["list.func.length_pointwise", "list.length_map"], DirectedEdge["list.func.length_pointwise", "eq.trans"], DirectedEdge["list.func.length_pointwise", "max_eq_right"], DirectedEdge["list.func.length_add", "list.func.length_pointwise"], DirectedEdge["list.func.length_sub", "list.func.length_pointwise"], DirectedEdge["mvqpf.cofix.bisim_rel", "quot.factor_mk_eq"], 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