Documentation Verification Report

Multiset

📁 Source: Mathlib/Algebra/Order/Group/Multiset.lean

Statistics

MetricCount
DefinitionscardHom, countAddMonoidHom, countPAddMonoidHom, instAddCancelCommMonoid, mapAddMonoidHom, replicateAddMonoidHom
6
Theoremsle_nsmul_iff_le, addHom_ext, addHom_ext_iff, cardHom_apply, card_nsmul, coe_countAddMonoidHom, coe_countPAddMonoidHom, coe_mapAddMonoidHom, countP_nsmul, count_nsmul, dedup_nsmul, filter_nsmul, instAddLeftMono, instAddLeftReflectLE, instExistsAddOfLE, instOrderedSub, le_smul_dedup, mapAddMonoidHom_apply, map_nsmul, mem_nsmul, mem_nsmul_of_ne_zero, mem_of_mem_nsmul, nsmul_cons, nsmul_replicate, nsmul_singleton, replicateAddMonoidHom_apply
26
Total32

Multiset

Definitions

NameCategoryTheorems
cardHom 📖CompOp
1 mathmath: cardHom_apply
countAddMonoidHom 📖CompOp
1 mathmath: coe_countAddMonoidHom
countPAddMonoidHom 📖CompOp
1 mathmath: coe_countPAddMonoidHom
instAddCancelCommMonoid 📖CompOp
132 mathmath: Polynomial.rightInverse_ofMultiset_roots, Finsupp.sum_toMultiset, DFinsupp.toMultiset_sup, Polynomial.roots_expand, MvPolynomial.degrees_monomial, disjoint_finset_sum_left, Finsupp.toMultiset_strictMono, equivDFinsupp_symm_apply, toDFinsupp_support, filter_nsmul, Polynomial.roots_monomial, Finsupp.prod_toMultiset, mapAddMonoidHom_apply, Finsupp.toMultiset_zero, Polynomial.roots_C_mul_X_pow, prod_sum, instIsAddTorsionFree, Icc_eq, Finset.mem_sum, coe_sumAddMonoidHom, Finsupp.toMultiset_toFinsupp, MvPolynomial.totalDegree_eq, instIsOrderedCancelAddMonoid, toDFinsupp_apply, MvPolynomial.degrees_def, Finsupp.card_toMultiset, Sym.coe_equivNatSum_symm_apply, addHom_ext_iff, UniqueFactorizationMonoid.factors_pow, Associates.pow_factors, equivDFinsupp_apply, DFinsupp.toMultiset_single, Sym.coe_equivNatSumOfFintype_symm_apply, Finsupp.toMultiset_apply, Polynomial.roots_X_pow_char_pow_sub_C_pow, MvPolynomial.degreesLE_nsmul, nsmul_cons, finset_sum_eq_sup_iff_disjoint, toFinset_nsmul, count_sum, dedup_nsmul, Polynomial.roots_pow, Polynomial.roots_expand_map_frobenius, cardHom_apply, card_nsmul, sum_nsmul, DFinsupp.toMultiset_le_toMultiset, MvPolynomial.degrees_pow_le, exists_smul_of_dvd_count, Finsupp.mem_toMultiset, coe_countPAddMonoidHom, toDFinsupp_replicate, disjoint_finset_sum_right, sum_sum, uIcc_eq, Finsupp.count_toMultiset, disjoint_sum_left, MvPolynomial.degrees_indicator, DFinsupp.toMultiset_toDFinsupp, prod_nsmul, Polynomial.roots_X_pow_char_sub_C_pow, count_sum', Finsupp.toMultiset_add, Polynomial.roots_ofMultiset, mem_nsmul, Polynomial.roots_expand_pow_map_iterateFrobenius_le, toFinsupp_symm_apply, DFinsupp.toMultiset_inf, replicateAddMonoidHom_apply, count_nsmul, Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply, card_sum, PrimeMultiset.coe_coePNatMonoidHom, nsmul_replicate, MvPolynomial.degrees_prod_le, Polynomial.ofMultiset_apply, Polynomial.roots_expand_pow_map_iterateFrobenius, DFinsupp.toMultiset_injective, toFinsupp_toMultiset, toFinset_card_eq_one_iff, Polynomial.aroots_C_mul_X_pow, Finsupp.toFinset_toMultiset, Nodup.le_nsmul_iff_le, toFinsupp_eq_iff, Finsupp.multiset_sum_sum, Finsupp.toMultiset_sum, toDFinsupp_injective, Polynomial.aroots_monomial, Finset.sum_multiset_singleton, Polynomial.aroots_X_pow, PrimeMultiset.coe_coeNatMonoidHom, toDFinsupp_le_toDFinsupp, toDFinsupp_toMultiset, sum_map_singleton, toDFinsupp_singleton, Finsupp.multiset_map_sum, mem_nsmul_of_ne_zero, UniqueFactorizationMonoid.normalizedFactors_pow, nsmul_singleton, Polynomial.roots_X_pow_char_sub_C, coe_countAddMonoidHom, MvPolynomial.degrees_monomial_eq, mem_sum, Polynomial.roots_expand_pow, toDFinsupp_inter, Finsupp.toMultiset_single, toDFinsupp_lt_toDFinsupp, toDFinsupp_union, card_finsuppSum, Polynomial.roots_X_pow, Finsupp.toMultiset_sup, DFinsupp.toMultiset_inj, Equiv.Perm.Disjoint.cycleType_noncommProd, le_smul_dedup, DFinsupp.toMultiset_lt_toMultiset, toFinset_sum_count_nsmul_eq, Polynomial.ofMultiset_injective, Finsupp.toMultiset_sum_single, map_nsmul, Finsupp.toMultiset_map, disjoint_sum_right, Finsupp.toMultiset_inf, Polynomial.roots_expand_map_frobenius_le, Finsupp.coe_orderIsoMultiset, UniqueFactorizationMonoid.normalizedFactors_multiset_prod, countP_nsmul, toDFinsupp_inj, Polynomial.roots_X_pow_char_pow_sub_C, Finsupp.toMultiset_eq_iff, coe_mapAddMonoidHom, Polynomial.aroots_pow, toFinset_eq_singleton_iff
mapAddMonoidHom 📖CompOp
2 mathmath: mapAddMonoidHom_apply, coe_mapAddMonoidHom
replicateAddMonoidHom 📖CompOp
1 mathmath: replicateAddMonoidHom_apply

Theorems

NameKindAssumesProvesValidatesDepends On
addHom_ext 📖DFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
AddMonoidHom.instFunLike
instSingleton
AddMonoidHom.ext
induction_on
map_zero
AddMonoidHomClass.toZeroHomClass
AddMonoidHom.instAddMonoidHomClass
map_add
AddMonoidHomClass.toAddHomClass
addHom_ext_iff 📖mathematicalDFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
AddMonoidHom.instFunLike
instSingleton
addHom_ext
cardHom_apply 📖mathematicalDFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
Nat.instAddMonoid
AddMonoidHom.instFunLike
cardHom
card
card_nsmul 📖mathematicalcard
Multiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
AddMonoidHom.map_nsmul
coe_countAddMonoidHom 📖mathematicalDFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
Nat.instAddMonoid
AddMonoidHom.instFunLike
countAddMonoidHom
count
coe_countPAddMonoidHom 📖mathematicalDFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
Nat.instAddMonoid
AddMonoidHom.instFunLike
countPAddMonoidHom
countP
coe_mapAddMonoidHom 📖mathematicalDFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
AddMonoidHom.instFunLike
mapAddMonoidHom
map
countP_nsmul 📖mathematicalcountP
Multiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
countP_congr
zero_nsmul
succ_nsmul
countP_add
count_nsmul 📖mathematicalcount
Multiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
count.congr_simp
zero_nsmul
count_eq_zero_of_notMem
succ_nsmul
count_add
dedup_nsmul 📖mathematicaldedup
Multiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
ext'
count_eq_one_of_mem
count_eq_zero_of_notMem
filter_nsmul 📖mathematicalfilter
Multiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
induction_on
filter.congr_simp
nsmul_zero
nsmul_cons
filter_add
filter_cons
nsmul_add
mem_singleton
mem_of_mem_nsmul
instAddLeftMono 📖mathematicalAddLeftMono
Multiset
instAdd
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
add_le_add_left
instAddLeftReflectLE 📖mathematicalAddLeftReflectLE
Multiset
instAdd
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
le_of_add_le_add_left
instExistsAddOfLE 📖mathematicalExistsAddOfLE
Multiset
instAdd
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
leInductionOn
instOrderedSub 📖mathematicalOrderedSub
Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
instSub
sub_le_iff_le_add
le_smul_dedup 📖mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
dedup
le_iff_count
count_nsmul
le_imp_le_of_le_of_le
le_refl
mul_le_mul_right
Nat.instMulLeftMono
one_le_count_iff_mem
mem_dedup
fold.congr_simp
map_cons
fold_cons_left
mul_one
cons_erase
count_eq_zero
mapAddMonoidHom_apply 📖mathematicalDFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
AddMonoidHom.instFunLike
mapAddMonoidHom
map
map_nsmul 📖mathematicalmap
Multiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
AddMonoidHom.map_nsmul
mem_nsmul 📖mathematicalMultiset
instMembership
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
zero_nsmul
mem_of_mem_nsmul
succ_nsmul
mem_add
mem_nsmul_of_ne_zero 📖mathematicalMultiset
instMembership
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
mem_of_mem_nsmul 📖Multiset
instMembership
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
zero_nsmul
notMem_zero
mem_add
succ_nsmul
nsmul_cons 📖mathematicalMultiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
cons
instAdd
instSingleton
singleton_add
nsmul_add
nsmul_replicate 📖mathematicalMultiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
replicate
AddMonoidHom.map_nsmul
nsmul_singleton 📖mathematicalMultiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
instSingleton
replicate
replicate_one
nsmul_replicate
mul_one
replicateAddMonoidHom_apply 📖mathematicalDFunLike.coe
AddMonoidHom
Multiset
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
Nat.instAddMonoid
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
AddMonoidHom.instFunLike
replicateAddMonoidHom
replicate

Multiset.Nodup

Theorems

NameKindAssumesProvesValidatesDepends On
le_nsmul_iff_le 📖mathematicalMultiset.NodupMultiset
Preorder.toLE
PartialOrder.toPreorder
Multiset.instPartialOrder
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
Multiset.instAddCancelCommMonoid
le_dedup_iff_le
Multiset.dedup_nsmul
Multiset.dedup_idem

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