Multiset 📖 | CompOp | 1044 mathmath: Finset.val_strictMono, Polynomial.rightInverse_ofMultiset_roots, Multiset.dedup_ext, Cycle.toMultiset_eq_nil, Sym.toMultiset_zero, Multiset.Ico_sub_Ico_right, Multiset.powersetCardAux_eq_map_coe, Multiset.prod_zero, Finsupp.sum_toMultiset, UniqueFactorizationMonoid.factors_one, Nat.Partition.indiscrete_parts, IsAlgClosed.roots_eq_zero_iff_degree_nonpos, Multiset.add_zero, Polynomial.mem_aroots', Multiset.ndunion_le_union, Multiset.sub_le_self, Multiset.countable, Multiset.le_iff_subset, Multiset.product_cons, DFinsupp.toMultiset_sup, Multiset.coe_le, Finset.pimage_eq_image_filter, Multiset.coe_inter, Multiset.covBy_iff, Polynomial.roots_expand, Multiset.card_eq_zero, Multiset.zero_product, Finmap.lookup_eq_some_iff, WellFounded.cutExpand, MvPolynomial.degrees_monomial, Multiset.disjoint_finset_sum_left, Multiset.foldr_add, Multiset.coe_product, Multiset.toFinsupp_add, exists_associated_mem_of_dvd_prod, Multiset.erase_lt, Multiset.powersetCard_zero_left, Finsupp.toMultiset_strictMono, Multiset.Ico_sub_Ico_left, Multiset.le_singleton, Multiset.lcm_eq_zero_iff, Multiset.Nodup.notMem, Multiset.join_zero, CovBy.finset_val, Multiset.equivDFinsupp_symm_apply, Multiset.sup_eq_union, IsNonarchimedean.multiset_powerset_image_add, Multiset.add_inter_distrib, Multiset.attach_ndinsert, isConjRoot_iff_mem_minpoly_aroots, Cardinal.mk_multiset_of_nonempty, Multiset.toDFinsupp_support, ADEInequality.sumInv_pqr, Multiset.coe_subset, UniqueFactorizationMonoid.mem_normalizedFactors_iff, instInfiniteMultisetOfNonempty, Polynomial.mem_roots_sub_C', Sym.val_eq_coe, Multiset.dedup_eq_zero, Multiset.notMem_zero, Multiset.le_iff_count, Polynomial.aroots_X_sub_C, Multiset.powersetAux_perm_powersetAux', Multiset.powerset_coe', Multiset.union_le_iff, Associates.factors_mul, Associates.prod_top, Multiset.zero_ndunion, Equiv.Perm.card_of_cycleType_mul_eq, Multiset.coe_add, Multiset.coe_subsingletonEquiv, Multiset.antidiagonal_coe', Multiset.filter_nsmul, UniqueFactorizationMonoid.disjoint_normalizedFactors, Multiset.Nat.antidiagonalTuple_one, Multiset.map_surjective_of_surjective, Multiset.singleton_add, Multiset.prod_map_sum, Polynomial.roots_monomial, Multiset.card_filter_le_iff, Multiset.Nat.antidiagonalTuple_zero_right, Polynomial.zero_notMem_multiset_map_X_sub_C, Multiset.range_add_eq_union, Multiset.prod_join, Finsupp.prod_toMultiset, Multiset.lcm_add, Multiset.mapAddMonoidHom_apply, Finsupp.toMultiset_zero, Finset.val_lt_iff, Polynomial.irreducible_iff_roots_eq_zero_of_degree_le_three, Multiset.fold_union_inter, Multiset.sup_zero, Multiset.Ico_filter_lt_of_le_left, Multiset.powersetCard_zero_right, Multiset.fmap_def, Multiset.singleton_join, Relation.cutExpand_double_left, Polynomial.roots_C_mul_X_pow, Multiset.count_attach, Multiset.prod_sum, Multiset.card_Ico, Multiset.canLiftFinset, Multiset.isWellFounded_ssubset, Multiset.Ico_subset_Ico_iff, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero', Multiset.antidiagonal_map_snd, Multiset.instIsAddTorsionFree, Multiset.Ico_eq_zero, Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub, Multiset.join_add, Multiset.filter_cons, Multiset.ndunion_eq_union, Finset.singleton_val, Multiset.product_singleton, Multiset.sigma_singleton, Multiset.filter_singleton, Multiset.mem_powerset, Multiset.Icc_eq, Multiset.powersetCard_one, Multiset.powersetCard_card_add, Polynomial.map_sub_roots_sprod_eq_prod_map_eval, Multiset.mem_coe, Polynomial.aroots_X, Multiset.mem_union, Multiset.card_eq_three, Multiset.map_singleton, Multiset.fold_add, Finset.mem_mk, Multiset.mem_sigma, Multiset.lt_iff_cons_le, Multiset.coe_eq_zero, IsUltrametricDist.exists_norm_multiset_prod_le, Finset.disjUnion_val, Multiset.cons_subset, Finset.mem_sum, Finset.ordConnected_range_val, Relation.cutExpand_add_left, Multiset.coe_sumAddMonoidHom, Multiset.map_eq_zero, prime_factors_irreducible, Polynomial.roots_eq_zero_iff_isRoot_eq_bot, Multiset.toFinset_eq_empty, Multiset.isAtom_singleton, Equiv.Perm.Disjoint.cycleType, Prime.exists_mem_multiset_map_dvd, Multiset.filter_subset, Finset.sdiff_val, Multiset.keys_zero, Polynomial.roots_degree_eq_one, Multiset.sum_smul_sum, Finsupp.toMultiset_toFinsupp, Multiset.mem_pi, Multiset.sub_le_iff_le_add', Multiset.bind_filterMap, UniqueFactorizationMonoid.factors_eq_singleton_of_irreducible, Multiset.mem_powersetCardAux, Multiset.inr_mem_disjSum, Multiset.coe_mem, MvPolynomial.totalDegree_eq, Multiset.instIsOrderedCancelAddMonoid, Multiset.Ioc_eq_zero, Multiset.bind_zero, Polynomial.roots_zero, Multiset.toFinsupp_sum_eq, Multiset.disjoint_add_left, Multiset.toDFinsupp_apply, Cubic.mem_roots_iff, Finset.map_val_val_powersetCard, Multiset.range_disjoint_map_add, Multiset.mem_sub_of_nodup, Multiset.disjoint_singleton, UniqueFactorizationMonoid.normalizedFactors_zero, Multiset.id_traverse, Multiset.Nat.antidiagonal_zero, Multiset.attach_map_val', mem_rootsOfUnity_iff_mem_nthRoots, MvPolynomial.degrees_def, Multiset.replicate_left_injective, Relation.cutExpand_double, Multiset.le_ndinsert_self, Multiset.le_dedup, Fin.cycleType_cycleIcc_of_ge, Multiset.Icc_eq_zero_iff, Multiset.mem_powersetCard, MultilinearMap.dfinsuppFamily_apply_support', Multiset.recOn_0, Multiset.lcm_singleton, Polynomial.roots_eq_zero_of_irreducible_of_natDegree_ne_one, Finsupp.card_toMultiset, Multiset.subset_ndunion_left, Sym.coe_equivNatSum_symm_apply, Multiset.instCanonicallyOrderedAdd, Multiset.addHom_ext_iff, UniqueFactorizationMonoid.factors_pow, Multiset.left_notMem_Ioo, Multiset.sum_add, Finset.mk_cons, Multiset.map_comp_cons, Multiset.disjSum_strictMono_left, UniqueFactorizationMonoid.exists_mem_factors, Associates.pow_factors, Finset.map_sym_eq_piAntidiag, Multiset.card_add, Equiv.Perm.cycleType_swap_mul_swap_of_nodup, Multiset.sup_singleton, Associates.prod_le_prod_iff_le, Multiset.eq_zero_iff_forall_notMem, Multiset.mem_map, IsSepClosed.roots_eq_zero_iff, Multiset.sup_powerset_len, Cycle.mem_lists_iff_coe_eq, Prime.exists_mem_multiset_dvd, Multiset.bind_filter, Multiset.equivDFinsupp_apply, Multiset.singleton_inj, Multiset.Ico_filter_le_of_right_le, DFinsupp.toMultiset_single, Multiset.Nat.mem_antidiagonalTuple, Multiset.Nodup.inter, Multiset.bind_add, Multiset.bell_zero, Multiset.add_le_add_iff_right, Multiset.Nat.mem_antidiagonal, Finset.map_comp_coe_apply, Sym.coe_equivNatSumOfFintype_symm_apply, Finsupp.toMultiset_apply, Multiset.add_right_inj, Multiset.add_eq_union_iff_disjoint, Cycle.nil_toMultiset, Multiset.disjoint_list_sum_left, Polynomial.roots_X_pow_char_pow_sub_C_pow, Sym.attach_mk, Multiset.prod_X_sub_C_dvd_iff_le_roots, MvPolynomial.degreesLE_nsmul, Multiset.antidiagonal_eq_map_powerset, Polynomial.nthRoots_two_one, Mathlib.Meta.Multiset.range_zero', Multiset.instExistsAddOfLE, Multiset.disjoint_union_left, Multiset.nsmul_cons, AlternatingGroup.card_of_cycleType_singleton, Multiset.filter_union, Multiset.setOf_mem_sym2, Multiset.map_zero, Acc.cutExpand, normalizedFactorsEquivOfQuotEquiv_symm, Multiset.bind_singleton, Multiset.antidiagonal_cons, Multiset.add_comm, Multiset.finset_sum_eq_sup_iff_disjoint, Associates.count_some, Associates.count_zero, Multiset.toFinset_nsmul, Multiset.mem_ndinsert, Multiset.count_sum, Ideal.IsPrime.multiset_prod_map_le, Sym.mem_mk, Multiset.powerset_zero, Multiset.dedup_add, MvPolynomial.degreesLE_add, Multiset.keys_singleton, Multiset.toFinsupp_union, MvPolynomial.degrees_C, Equiv.Perm.card_of_cycleType_eq_zero_iff, Multiset.toFinset_add, Multiset.dedup_nsmul, IsNonarchimedean.multiset_image_add_of_nonempty, UniqueFactorizationMonoid.normalizedFactors_mul, Polynomial.mem_roots_map_of_injective, Multiset.mem_sup_map_support_iff, Finmap.mem_def, Finset.mem_univ_val, Multiset.filter_add_filter, Multiset.count_singleton_self, Multiset.right_notMem_Ico, Multiset.comp_traverse, Associates.factors_zero, Polynomial.roots_pow, UniqueFactorizationMonoid.normalizedFactors_one, Multiset.revzip_powersetAux_perm_aux', Multiset.nodup_bind, Multiset.attach_map_val, UniqueFactorizationMonoid.normalizedFactors_pos, Multiset.inf_zero, Multiset.prod_eq_zero_iff, Multiset.Nodup.powersetCard, Polynomial.roots_expand_map_frobenius, Multiset.card_Ioc, Finset.val_eq_zero, Multiset.le_dedup_self, Multiset.Ico_filter_le_left, Polynomial.roots_C_mul_X_sub_C_of_IsUnit, Multiset.cons_union_distrib, Multiset.le_union_right, Multiset.union_add_inter, Multiset.card_erase_eq_ite, Multiset.mem_antidiagonal, Multiset.ndinsert_zero, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero, Multiset.map_fst_le_of_subset_toEnumFinset, Multiset.toFinsupp_inter, Relation.cutExpand_singleton, Associates.factors_subsingleton, Multiset.mem_erase_of_ne, UniqueFactorizationMonoid.factors_pos, Multiset.mk_mem_sym2_iff, Multiset.powersetCard_coe, Multiset.inf_add, Finset.noncommProd_lemma, Multiset.powersetCard_cons, Associates.mem_factorSet_some, Multiset.prod_singleton, Multiset.instLawfulFunctor, Multiset.Nodup.inter_left, Multiset.powerset_coe, Multiset.dedup_zero, Multiset.sub_add_eq_sub_sub, Multiset.not_nodup_pair, Associates.factors_mk, Multiset.toFinsupp_apply, Multiset.mem_dedup, Relation.cutExpand_zero, Multiset.sym2_eq_zero_iff, Multiset.cardHom_apply, Polynomial.roots_C_mul_X_add_C, Multiset.card_nsmul, IsUltrametricDist.exists_norm_multiset_sum_le, Multiset.filter_eq_nil, Multiset.add_sigma, Multiset.le_add_sub, Multiset.nodup_cons, Multiset.prod_map_add, Sym.coe_fill, Multiset.sum_nsmul, Multiset.Nodup.inter_right, alternatingGroup.coe_kleinFour_of_card_eq_four, Relation.cutExpand_single_add, Multiset.add_le_add_iff_left, Multiset.gcd_singleton, alternatingGroup.mem_kleinFour_of_order_two_pow, Multiset.sum_pair, Multiset.card_uIcc, MvPolynomial.degrees_X, Multiset.singleton_bind, Multiset.add_assoc, Multiset.inl_mem_disjSum, DFinsupp.toMultiset_le_toMultiset, MvPolynomial.degrees_pow_le, Multiset.lcm_zero, Multiset.monotone_filter_right, Multiset.card_eq_four, Multiset.replicate_le_replicate, Multiset.exists_smul_of_dvd_count, Equiv.Perm.card_of_cycleType, Finsupp.mem_toMultiset, Polynomial.roots_X_sub_C, Multiset.add_cons, Nat.Partition.partition_zero_parts, Equiv.Perm.IsCycle.cycleType, Multiset.ndinter_le_left, Equiv.Perm.mem_cycleType_iff, Multiset.mem_add, Nat.Partition.partition_one_parts, Associates.prod_add, Multiset.nodup_powerset, Associates.factors_le, UniqueFactorizationMonoid.exists_mem_normalizedFactors, Multiset.mem_sym2_iff, Multiset.sections_zero, Multiset.sort_zero, Multiset.ssubset_singleton_iff, Multiset.mem_disjSum, Multiset.mem_range, Multiset.disjSum_zero, Multiset.left_notMem_Ioc, Multiset.wellFounded_isDershowitzMannaLT, Polynomial.map_roots_le, Multiset.product_zero, Polynomial.map_sub_sprod_roots_eq_prod_map_eval, UniqueFactorizationMonoid.normalizedFactors_of_isUnit, MvPolynomial.degrees_rename, Multiset.map_single_le_powerset, Multiset.coe_countPAddMonoidHom, Multiset.exists_max_image, Multiset.toDFinsupp_replicate, IsLocalization.OverPrime.mem_normalizedFactors_of_isPrime, Multiset.instRightCommutativeErase, Multiset.left_mem_Ico, Multiset.mem_ndunion, Multiset.mem_sections, Multiset.disjoint_finset_sum_right, Multiset.instAddLeftMono, Multiset.card_attach, Multiset.sum_sum, Multiset.uIcc_eq, Multiset.replicate_inter, Finsupp.count_toMultiset, Multiset.toEnumFinset_subset_iff, Multiset.le_add_left, Associates.factors_prime_pow, MvPolynomial.degrees_map_le, Polynomial.roots_X, Multiset.canLift, Multiset.cons_add, Finset.sum_pow_of_commute, Multiset.antidiagonal_coe, Multiset.range_subset, Multiset.count_ne_zero, Multiset.countP_attach, Multiset.disjSum_mono_right, Multiset.rel_add_left, Cubic.splits_iff_roots_eq_three, Multiset.bot_eq_zero, Ideal.IsPrime.multiset_prod_le, Relation.cutExpand_pair_left, Multiset.disjoint_sum_left, Multiset.le_ndinter, Relation.cutExpand_fibration, Finset.noncommSum_insert_of_notMem, Multiset.filterMap_zero, Multiset.card_singleton, MvPolynomial.degrees_indicator, Multiset.card_powersetCard, Multiset.sum_zero, DirectSum.addEquivProdDirectSum_symm_apply_support', Multiset.count_union, Associates.factors_mono, Multiset.le_inter_iff, Multiset.mem_map_of_injective, Multiset.antidiagonal_map_fst, Multiset.multinomial_zero, IsAlgClosed.roots_eq_zero_iff_natDegree_eq_zero, Associates.factors_eq_some_iff_ne_zero, Multiset.finite_toSet, Multiset.ndunion_le, Relation.cutExpand_le_invImage_lex, Multiset.subset_ndunion_right, MvPolynomial.degrees_sub_le, Multiset.fold_zero, Multiset.le_cons_erase, Multiset.nodup_sup_iff, Multiset.le_union_left, Multiset.filter_add_not, Multiset.count_pos, AlternatingGroup.card_of_cycleType, DFinsupp.toMultiset_toDFinsupp, SimpleGraph.Walk.coe_support_append, Multiset.right_mem_Icc, Multiset.Ico_inter_Ico, Multiset.filterMap_eq_bind, Multiset.sections_cons, Multiset.instWellFoundedLT, Multiset.Ioc_eq_zero_of_le, Multiset.iSup_mem_map_of_ne_zero, Multiset.attach_cons, Finset.noncommSum_insert_of_notMem', Multiset.prod_nsmul, Multiset.count_zero, Finset.val_injective, Finset.noncommSum_cons, Multiset.empty_toList, Polynomial.roots_X_pow_char_sub_C_pow, Multiset.disjoint_map_map, Associates.mem_factors'_iff_dvd, Multiset.count_sum', Algebra.IsAlgebraic.lift_cardinalMk_le_sigma_polynomial, MvPolynomial.degrees_sum_le, Multiset.map_hcongr, Multiset.empty_eq_zero, Multiset.mem_filterMap, Multiset.sum_singleton, Multiset.filter_le, MvPolynomial.degreesLE_zero, Multiset.foldl_zero, Multiset.replicate_add, Multiset.zero_add, Multiset.prod_map_product_eq_prod_prod, Multiset.filter_attach, Multiset.sub_le_iff_le_add, Finsupp.toMultiset_add, Polynomial.roots_ofMultiset, Multiset.mem_nsmul, Multiset.toFinsupp_singleton, Finset.subset_def, Multiset.Nodup.add_iff, Multiset.filter_inter, Polynomial.roots_expand_pow_map_iterateFrobenius_le, Multiset.sym2_zero, Multiset.mem_lists_iff, Multiset.toFinsupp_symm_apply, Multiset.singleton_eq_cons_iff, FreeCommRing.of_cons, Multiset.nodup_iff_le, Relation.cutExpand_singleton_singleton, UniqueFactorizationMonoid.exists_mem_normalizedFactors_of_dvd, DFinsupp.toMultiset_inf, Multiset.coe_sub, Polynomial.map_roots_le_of_injective, Multiset.replicateAddMonoidHom_apply, Cardinal.mk_multiset_of_infinite, Multiset.pairwise_disjoint_powersetCard, Multiset.sub_cons, Polynomial.Splits.dvd_iff_roots_le_roots, Multiset.count_dedup, Multiset.lcm_union, MvPolynomial.degrees_one, Polynomial.aroots_zero, Multiset.map_finset_sup, Multiset.mem_cons, Finset.map_comp_coe, Ideal.IsPrime.multiset_prod_mem_iff_exists_mem, Polynomial.mem_roots_sub_C, Multiset.count_nsmul, Multiset.count_sub, Multiset.mem_Ioi, Finmap.mem_lookup_iff, Multiset.card_antidiagonal, Equiv.Perm.IsThreeCycle.cycleType, Algebra.IsAlgebraic.cardinalMk_le_sigma_polynomial, Polynomial.mem_roots_iff_aeval_eq_zero, Finset.product_val, Multiset.inter_zero, UniqueFactorizationMonoid.mem_primeFactors, Multiset.disjoint_left, Multiset.count_injective, Multiset.Subset.refl, Multiset.instIsNonstrictStrictOrder, Multiset.card_product, Multiset.Ioo_self, Associates.mem_factorSet_top, Ideal.mem_normalizedFactors_iff, Multiset.mem_replicate, Multiset.card_zero, Polynomial.nthRoots_zero, Multiset.antidiagonal_zero, Multiset.Icc_eq_zero_of_lt, Multiset.map_mono, Finsupp.mem_support_multiset_sum, Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply, MvPolynomial.mem_degreesLE, Multiset.toFinset_zero, Multiset.mem_Ioc, Multiset.Ioo_eq_zero_iff, Finsupp.coe_orderIsoMultiset_symm, Multiset.card_sum, Multiset.count_inter, Multiset.Ico_eq_zero_of_le, Multiset.inter_le_ndinter, Multiset.ndunion_le_add, Multiset.filter_join, Associates.exists_mem_multiset_le_of_prime, Multiset.nodup_union, Multiset.sym2_cons, Multiset.dedup_le, alternatingGroup.coe_two_sylow_of_card_eq_four, PrimeMultiset.coe_coePNatMonoidHom, Multiset.mem_attach, Multiset.zero_subset, Multiset.zero_ndinter, Multiset.card_mono, Sym2.mem_toMultiset, Multiset.singleton_subset, Multiset.add_bind, Equiv.Perm.cycleType_eq_zero, Multiset.erase_singleton, Multiset.mem_sort, Multiset.mem_singleton, Multiset.nsmul_replicate, MvPolynomial.degrees_prod_le, Multiset.instLawfulSingleton, Polynomial.aroots_quadratic_eq_pair_iff_of_ne_zero, Multiset.coe_sections, Multiset.mem_sup, Multiset.Ico_add_Ico_eq_Ico, Multiset.pair_comm, IntermediateField.algHomAdjoinIntegralEquiv_symm_apply_gen, Multiset.notMem_range_self, Multiset.coe_eq_singleton, Polynomial.ofMultiset_apply, Multiset.disjoint_toFinset, Multiset.Nodup.powerset, Multiset.Ico_disjoint_Ico, PrimeMultiset.mem_ofNatMultiset, Multiset.Icc_self, Multiset.le_ndunion_left, Associates.factors_eq_top_iff_zero, Multiset.cons_product, Multiset.map_union, List.cycleType_formPerm, Multiset.lt_cons_self, Polynomial.roots_expand_pow_map_iterateFrobenius, Multiset.exists_min_image, Multiset.powersetCard_eq_empty, Finset.mk_zero, Multiset.filterMap_add, Multiset.powersetCardAux_perm, MvPolynomial.degrees_add_le, Multiset.map_le_map_iff, DFinsupp.toMultiset_injective, Multiset.toFinsupp_zero, Multiset.gcd_add, MvPolynomial.degrees_mul_le, Multiset.toFinsupp_toMultiset, Multiset.disjoint_cons_left, Finset.noncommProd_cons', SimpleGraph.ComponentCompl.infinite_iff_in_all_ranges, Multiset.toFinset_card_eq_one_iff, UniqueFactorizationMonoid.normalizedFactors_irreducible, Multiset.rel_add_right, Multiset.join_cons, Multiset.subset_iff, Multiset.toFinset_union, Multiset.zero_sub, Polynomial.roots_mul, Relation.cutExpand_pair_right, Polynomial.aroots_C_mul_X_pow, Multiset.powersetAux_eq_map_coe, Multiset.Ico_inter_Ico_of_le, Polynomial.mem_roots, Multiset.Nodup.attach, Multiset.Rel.add, Multiset.grade_eq, Multiset.count_finset_sup, Equiv.Perm.cycleType_one, Multiset.count_add, Multiset.disjoint_union_right, Multiset.inf_eq_inter, Nat.factorization_eq_primeFactorsList_multiset, Finset.disjoint_val, Multiset.inter_le_right, Ideal.mem_primesOver_iff_mem_normalizedFactors, Polynomial.mem_roots', Multiset.mem_Ioo, Multiset.cons_sigma, Multiset.subset_zero, emultiplicity_normalizedFactorsEquivSpanNormalizedFactors_symm_eq_emultiplicity, Polynomial.nthRoots_two_eq_zero_iff, Multiset.subset_cons, Multiset.map_traverse, Polynomial.resultant_eq_prod_roots_sub, Multiset.Ioo_eq_zero, Multiset.monotone_filter_left, Multiset.card_eq_two, Finsupp.toFinset_toMultiset, Polynomial.roots.le_of_dvd, Multiset.count_eq_of_nodup, ZMod.erdos_ginzburg_ziv_multiset, Finset.grade_multiset_eq, Multiset.mapEmbedding_apply, Multiset.Nodup.le_nsmul_iff_le, Multiset.disjoint_cons_right, MvPolynomial.degrees_mul_eq, Multiset.erase_attach_map, Multiset.product_add, Multiset.Nodup.mem_erase_iff, Multiset.replicate_subset_singleton, Multiset.subset_dedup', Multiset.toFinsupp_eq_iff, Polynomial.mem_roots_map, Multiset.mem_Iio, Sym.coe_injective, cycleType_finRotate, Multiset.subset_add_left, Multiset.powerset_cons, Multiset.sub_singleton, Polynomial.mem_normalizedFactors_iff, Multiset.prod_add, Multiset.cons_lt_cons_iff, Multiset.toList_eq_singleton_iff, Multiset.card_powerset, Multiset.naturality, Finsupp.multiset_sum_sum, Multiset.union_le_add, UniqueFactorizationMonoid.le_emultiplicity_iff_replicate_le_normalizedFactors, Multiset.zero_inter, Finsupp.toMultiset_sum, Multiset.rel_iff, Multiset.mem_toList, Multiset.zero_disjoint, Multiset.add_product, Multiset.inter_le_left, Multiset.finite_toSet_toFinset, Multiset.toDFinsupp_injective, Multiset.Nodup.ext, Multiset.mem_bind, Multiset.map_injective, Multiset.range_add, Multiset.disjoint_ndinsert_right, Sym.coe_nil, Multiset.ndinter_subset_left, Multiset.filter_add, Multiset.powersetAux'_nil, Polynomial.aroots_monomial, Finset.sum_multiset_singleton, Polynomial.aroots_X_pow, Multiset.erase_zero, Polynomial.roots_one, cycleType_finRotate_of_le, PrimeMultiset.coe_coeNatMonoidHom, Multiset.le_zero, MvPolynomial.degrees_zero, Multiset.subset_add_right, Multiset.filter_sub, Multiset.ndinter_eq_inter, Multiset.foldr_zero, Polynomial.roots_C_mul_X_sub_C, Multiset.erase_le_iff_le_cons, Multiset.inf_union, Multiset.powersetCard_map, Multiset.toDFinsupp_le_toDFinsupp, Multiset.toDFinsupp_toMultiset, Multiset.filterMap_cons, Multiset.sum_map_singleton, BoxIntegral.TaggedPrepartition.single_boxes_val, Multiset.map_strictMono, Polynomial.mem_aroots, Multiset.toDFinsupp_singleton, Polynomial.roots_quadratic_eq_pair_iff_of_ne_zero', Finset.union_val, Finsupp.multiset_map_sum, max_norm_root_eq_spectralValue, Multiset.toFinset_subset, PowerBasis.liftEquiv'_apply_coe, Multiset.coe_disjoint, Multiset.powersetAux'_cons, Multiset.powerset_aux'_perm, Multiset.mem_nsmul_of_ne_zero, Multiset.add_union_distrib, Equiv.Perm.cycleType_le_of_mem_cycleFactorsFinset, Multiset.zero_union, Multiset.countP_pos, Multiset.mem_Iic, UniqueFactorizationMonoid.normalizedFactors_pow, Multiset.union_comm, WCovBy.finset_val, Multiset.nsmul_singleton, Associates.FactorSet.coe_add, Multiset.subset_dedup, Equiv.Perm.isSwap_iff_cycleType, Multiset.mem_singleton_self, Multiset.ndinter_subset_right, Polynomial.roots_X_pow_char_sub_C, Multiset.bind_cons, Multiset.map_comp_coe, Multiset.pmap_zero, Sym.oneEquiv_apply, Multiset.card_Iic, Multiset.mem_sub, Multiset.coe_countAddMonoidHom, Relation.cutExpand_iff, Multiset.right_notMem_Ioo, Multiset.bind_def, UniqueFactorizationMonoid.mem_normalizedFactors_iff', Multiset.le_count_iff_replicate_le, UniqueFactorizationMonoid.dvd_iff_normalizedFactors_le_normalizedFactors, Relation.cutExpand_add_right, Multiset.sections_add, Multiset.ndinsert_le, Multiset.gcd_union, Multiset.mem_filter, Multiset.le_cons_self, MvPolynomial.degrees_monomial_eq, rootsOfUnityEquivNthRoots_apply, Multiset.instOrderedSub, Multiset.card_sections, Multiset.sub_add_inter, Multiset.toFinset_inter, Multiset.gcd_zero, Multiset.erase_subset, Multiset.card_eq_one, Finset.val_wcovBy_val, UniqueFactorizationMonoid.normalizedFactors_eq_zero_iff, Multiset.fold_singleton, Finset.noncommProd_insert_of_notMem', Multiset.range_le, Multiset.mem_sum, PrimeMultiset.coePNat_ofPrime, Multiset.le_replicate_iff, MvPolynomial.degrees_X', Polynomial.aroots_one, IsAlgClosed.roots_eq_zero_iff, Multiset.attach_zero, KummerDedekind.normalizedFactors_ideal_map_eq_normalizedFactors_min_poly_mk_map, Polynomial.roots_eq_zero_iff_eq_zero_or_isRoot_eq_bot, Multiset.disjoint_right, Equiv.Perm.Disjoint.cycleType_mul, Multiset.filter_false, Multiset.replicate_zero, Multiset.toFinset_ssubset, Multiset.sort_singleton, Multiset.le_sub_add, Multiset.card_join, Finset.empty_val, Multiset.count_singleton, Multiset.attach_bind_coe, Multiset.inf_singleton, MvPolynomial.mem_degrees, Polynomial.aroots_mul, Multiset.countP_add, Equiv.Perm.parts_partition, Polynomial.roots_expand_pow, Multiset.filter_eq_bind, Multiset.mem_join, Multiset.sub_inter, Multiset.le_add_right, NumberField.mem_multisetInfinitePlace, Multiset.exists_mem_of_ne_zero, Multiset.toDFinsupp_inter, Multiset.Ico_eq_zero_iff, IsNonarchimedean.multiset_image_add, Multiset.card_Icc, Multiset.mem_Icc, Multiset.map_swap_product, Multiset.powersetCard_le_powerset, Multiset.revzip_powersetAux_perm, Cardinal.mk_multiset_of_isEmpty, Multiset.sup_union, Sym.mem_coe, Multiset.esymm_pair_two, Multiset.sub_eq_fold_erase, Multiset.lt_singleton, Multiset.map_disjSum, Multiset.zero_sigma, PowerBasis.liftEquiv'_symm_apply_apply, Multiset.filter_zero, Multiset.Nodup.notMem_erase, Polynomial.exists_prod_multiset_X_sub_C_mul, Finsupp.toMultiset_single, Cycle.lists_nil, Finset.noncommSum_cons', Multiset.add_sub_cancel_right, Int.erdos_ginzburg_ziv_multiset, Multiset.union_add_distrib, Multiset.erase_le, Multiset.dedup_subset', Multiset.sum_join, Multiset.toDFinsupp_lt_toDFinsupp, Multiset.rel_zero_right, PNat.mem_factorMultiset, Multiset.mem_cons_self, Multiset.toDFinsupp_union, Multiset.coe_singleton, Multiset.count_eq_zero, UniqueFactorizationMonoid.factors_zero, Multiset.add_singleton_eq_iff, Multiset.right_mem_Ioc, Multiset.Nat.antidiagonalTuple_zero_succ, Multiset.card_pos_iff_exists_mem, sup_eq_prod_inf_factors, Multiset.covBy_cons, Finset.sup_toFinset, Multiset.range_zero, Multiset.instIsEmptyToTypeOfNat, Multiset.Icc_eq_zero, Multiset.zero_le, Ideal.multiset_prod_eq_bot, Multiset.powersetAux_perm, Finset.sum_pow, Multiset.card_finsuppSum, Multiset.powersetCard_coe', Multiset.union_zero, Multiset.ndinter_le_right, Polynomial.mem_nthRoots, UniqueFactorizationMonoid.factors_mul, Finset.inter_val, Polynomial.roots_X_pow, Multiset.singleton_le, Polynomial.roots_X_add_C, Finsupp.toMultiset_sup, Multiset.Nodup.le_dedup_iff_le, DFinsupp.toMultiset_inj, Multiset.left_mem_Icc, Equiv.Perm.Disjoint.cycleType_noncommProd, Multiset.gcd_ne_zero_iff, Multiset.sub_filter_eq_filter_not, Multiset.card_pair, PrimeMultiset.coeNat_injective, Multiset.disjoint_add_right, Multiset.le_smul_dedup, Multiset.add_left_inj, Multiset.toList_eq_nil, Multiset.prod_pair, Multiset.replicate_right_injective, Multiset.mem_Ici, Equiv.Perm.card_of_cycleType_singleton, Fin.cycleType_cycleIcc_of_lt, Multiset.mem_of_mem_toEnumFinset, DFinsupp.toMultiset_lt_toMultiset, Multiset.countP_zero, Multiset.map_add, FreeRing.coe_eq, Multiset.toFinset_sum_count_nsmul_eq, Multiset.insert_eq_cons, Multiset.zero_bind, AlternatingGroup.map_subtype_of_cycleType, Multiset.toList_singleton, Polynomial.ofMultiset_injective, Multiset.le_iff_exists_add, Multiset.lcm_ne_zero_iff, Multiset.Ioc_eq_zero_iff, Multiset.cons_bind, Multiset.replicate_mono, Multiset.replicate_le_coe, Sym.coe_append, Multiset.pure_def, Associates.factors_self, PrimeMultiset.coePNat_injective, Nat.Partition.coeff_genFun, Multiset.cons_inter_distrib, Multiset.bind_powerset_len, Equiv.Perm.closure_cycleType_eq_2_2_eq_alternatingGroup, Associates.prod_le, Multiset.esymm_pair_one, Multiset.nodup_singleton, Fin.cycleType_cycleRange, Multiset.cons_zero, Multiset.cons_le_cons_iff, UniqueFactorizationMonoid.factors_of_isUnit, Multiset.mem_powersetAux, Multiset.ndinter_eq_zero_iff_disjoint, Multiset.disjSum_strictMono_right, Multiset.powersetCardAux_nil, Polynomial.roots_C_mul_X_add_C_of_IsUnit, Multiset.card_bind, Multiset.card_Ioo, PrimeMultiset.coeNat_ofPrime, Multiset.dedup_singleton, Multiset.le_ndunion_right, rootsOfUnityEquivNthRoots_symm_apply, Multiset.Ioc_self, Multiset.replicate_one, Polynomial.zero_notMem_multiset_map_X_add_C, Multiset.foldr_singleton, Multiset.pi_zero, Multiset.dedup_subset, Associates.factors_one, Multiset.map_eq_singleton, Relation.instIsWellFoundedMultisetCutExpand, Multiset.self_mem_range_succ, Multiset.one_le_count_iff_mem, Multiset.inter_comm, Polynomial.aroots_C, Multiset.instLawfulMonad, Multiset.disjoint_list_sum_right, UniqueFactorizationMonoid.factors_eq_zero, Multiset.le_filter, Polynomial.roots_C, Finsupp.toMultiset_sum_single, Associates.FactorSet.sup_add_inf_eq_add, Multiset.foldl_add, Finset.val_le_iff_val_subset, PrimeMultiset.mem_ofNatList, Multiset.toFinsupp_support, Multiset.isAtom_iff, Multiset.mem_toFinset, UniqueFactorizationMonoid.zero_notMem_normalizedFactors, Multiset.map_nsmul, Multiset.toFinset_singleton, Multiset.lt_replicate_succ, Finsupp.toMultiset_map, Multiset.erase_attach_map_val, Multiset.empty_or_exists_mem, Finset.noncommProd_insert_of_notMem, Multiset.nodup_zero, UniqueFactorizationMonoid.radical_dvd_radical_iff_normalizedFactors_subset_normalizedFactors, Multiset.nodup_attach, Associates.mem_factors'_of_dvd, Multiset.disjoint_ndinsert_left, Multiset.disjoint_sum_right, Multiset.mem_ndinter, Multiset.toFinsupp_strictMono, Multiset.toList_zero, Multiset.zero_ssubset, Sym.val_replicate, Finsupp.toMultiset_inf, Multiset.inter_replicate, Multiset.filter_attach', AlternatingGroup.card_of_cycleType_mul_eq, Multiset.rel_zero_left, Associates.prod_coe, Multiset.Ico_self, Multiset.instAddLeftReflectLE, Relation.not_cutExpand_zero, Finset.val_le_iff, Multiset.Nat.antidiagonalTuple_zero_zero, NumberField.Ideal.primesOverSpanEquivMonicFactorsMod_symm_apply, Multiset.singleton_disjoint, Multiset.disjoint_iff_ne, Multiset.Nodup.product, Polynomial.roots_expand_map_frobenius_le, Multiset.powersetCardAux_zero, Multiset.mem_Ico, Finset.noncommSum_lemma, Finset.mem_val, Multiset.pairwise_zero, Finsupp.coe_orderIsoMultiset, Multiset.sup_add, Finset.mem_def, Multiset.mem_ndinsert_self, Multiset.map_join, SimpleGraph.Walk.coe_support_append', Polynomial.Monic.irreducible_iff_roots_eq_zero_of_degree_le_three, IsAlgClosed.dvd_iff_roots_le_roots, Associates.FactorSet.prod_eq_zero_iff, Multiset.inter_eq_zero_iff_disjoint, Multiset.mem_pmap, ADEInequality.classification, Multiset.monotone_sym2, Multiset.instIsEmptyToTypeEmptyCollection, Multiset.inter_add_distrib, Multiset.countP_nsmul, Multiset.pmap_eq_map_attach, Multiset.toDFinsupp_inj, Multiset.union_def, UniqueFactorizationMonoid.dvdNotUnit_iff_normalizedFactors_lt_normalizedFactors, Relation.cutExpand_add_single, Multiset.nodup_add, Multiset.sub_zero, Multiset.Ioo_eq_zero_of_le, SimpleGraph.Walk.coe_support, Multiset.card_strictMono, Multiset.powersetCardAux_cons, Finset.noncommProd_cons, Polynomial.roots_X_pow_char_pow_sub_C, Finsupp.toMultiset_eq_iff, Multiset.coe_join, Multiset.zero_disjSum, Mathlib.Meta.Multiset.insert_eq_cons, Multiset.mem_product, Multiset.filterMap_join, Polynomial.roots_def, Multiset.coe_mapAddMonoidHom, Polynomial.aroots_pow, Multiset.disjSum_mono_left, Multiset.map_eq_cons, Finset.val_covBy_val, Multiset.coe_nil, Multiset.coe_eq_zero_iff_isEmpty, Finset.val_eq_singleton_iff, Multiset.toFinset_eq_singleton_iff, UniqueFactorizationMonoid.exists_mem_factors_of_dvd, Multiset.sigma_add, Multiset.mem_inter, Polynomial.toSubring_one
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