Documentation Verification Report

AddSub

πŸ“ Source: Mathlib/Data/Multiset/AddSub.lean

Statistics

MetricCount
Definitionsadd, erase, instAdd, instSub, sub
5
Theoremserase, add, add_assoc, add_comm, add_cons, add_le_add_iff_left, add_le_add_iff_right, add_le_add_left, add_le_add_right, add_left_inj, add_right_inj, add_singleton_eq_iff, add_sub_assoc, add_sub_cancel, add_sub_cancel_right, add_zero, card_add, card_erase_add_one, card_erase_eq_ite, card_erase_le, card_erase_lt_of_mem, card_erase_of_mem, card_sub, coe_add, coe_erase, coe_sub, cons_add, cons_erase, cons_sub_of_le, countP_add, countP_sub, count_add, count_erase_of_ne, count_erase_self, count_sub, eq_sub_of_add_eq, erase_add_left_neg, erase_add_left_pos, erase_add_right_neg, erase_add_right_pos, erase_comm, erase_cons_head, erase_cons_tail, erase_cons_tail_of_mem, erase_le, erase_le_erase, erase_le_iff_le_cons, erase_lt, erase_of_notMem, erase_singleton, erase_subset, erase_zero, instRightCommutativeErase, le_add_left, le_add_right, le_add_sub, le_cons_erase, le_iff_exists_add, le_of_add_le_add_left, le_of_add_le_add_right, le_sub_add, mem_add, mem_erase_of_ne, mem_of_mem_erase, mem_sub, mem_sub_of_nodup, nodup_singleton, not_nodup_pair, rel_add_left, rel_add_right, singleton_add, sub_add_cancel, sub_add_eq_sub_sub, sub_cons, sub_le_iff_le_add, sub_le_iff_le_add', sub_le_self, sub_le_sub_right, sub_singleton, sub_zero, subset_add_left, subset_add_right, zero_add, zero_sub
84
Total89

Multiset

Definitions

NameCategoryTheorems
add πŸ“–CompOpβ€”
erase πŸ“–CompOp
68 mathmath: erase_lt, hasFDerivAt_multiset_prod, noncommProd_erase_mul, fderiv_multiset_prod, Polynomial.Splits.eval_derivative, Polynomial.Splits.eval_root_derivative, HasFDerivWithinAt.multiset_prod, hasStrictFDerivAt_multiset_prod, Polynomial.eval_derivative_of_splits, map_erase, prod_map_erase, card_erase_add_one, card_erase_eq_ite, sum_erase, mem_erase_of_ne, Nodup.erase_eq_filter, mul_noncommProd_erase, sum_map_erase, erase_le_erase, instRightCommutativeErase, cons_inter_of_pos, erase_add_right_pos, HasFDerivAt.multiset_prod, card_erase_le, le_cons_erase, Sym.erase_mk, erase_add_left_pos, erase_cons_head, erase_add_left_neg, sub_cons, fderivWithin_multiset_prod, map_erase_of_mem, erase_singleton, Nodup.erase, card_erase_of_mem, erase_add_right_neg, Polynomial.aeval_derivative_of_splits, Polynomial.derivative_prod, erase_cons_tail, Sym.coe_erase, cons_erase, erase_attach_map, Nodup.mem_erase_iff, Polynomial.aeval_root_derivative_of_splits, sub_singleton, erase_zero, count_erase_of_ne, erase_le_iff_le_cons, prod_erase, HasStrictFDerivAt.multiset_prod, Polynomial.evalβ‚‚_derivative_of_splits, Relation.cutExpand_iff, count_erase_self, erase_subset, erase_of_notMem, erase_cons_tail_of_mem, erase_comm, Finset.erase_val, coe_erase, card_erase_lt_of_mem, sub_eq_fold_erase, Nodup.notMem_erase, erase_le, add_singleton_eq_iff, erase_attach_map_val, Polynomial.eval_multiset_prod_X_sub_C_derivative, Finpartition.avoid_parts_val, map_eq_cons
instAdd πŸ“–CompOp
161 mathmath: add_zero, product_cons, foldr_add, toFinsupp_add, revzip_powersetAux, equivDFinsupp_symm_apply, add_inter_distrib, Associates.factors_mul, coe_add, singleton_add, lcm_add, join_add, filter_cons, Icc_eq, fold_add, Finset.disjUnion_val, Relation.cutExpand_add_left, Equiv.Perm.Disjoint.cycleType, Finsupp.toMultiset_toFinsupp, sub_le_iff_le_add', toFinsupp_sum_eq, disjoint_add_left, instCanonicallyOrderedAdd, sum_add, card_add, equivDFinsupp_apply, bind_add, add_le_add_iff_right, add_right_inj, add_eq_union_iff_disjoint, disjoint_list_sum_left, instExistsAddOfLE, nsmul_cons, antidiagonal_cons, add_comm, dedup_add, MvPolynomial.degreesLE_add, toFinsupp_union, toFinset_add, UniqueFactorizationMonoid.normalizedFactors_mul, filter_add_filter, union_add_inter, mem_antidiagonal, Disjoint.ndunion_eq, toFinsupp_inter, inf_add, powersetCard_cons, sub_add_eq_sub_sub, toFinsupp_apply, add_sigma, le_add_sub, Sym.coe_fill, Relation.cutExpand_single_add, add_le_add_iff_left, add_assoc, add_sub_cancel, add_cons, mem_add, Associates.prod_add, sub_add_cancel, instAddLeftMono, uIcc_eq, le_add_left, cons_add, rel_add_left, erase_add_right_pos, Relation.cutExpand_fibration, Relation.cutExpand_le_invImage_lex, filter_add_not, erase_add_left_pos, SimpleGraph.Walk.coe_support_append, replicate_add, zero_add, sub_le_iff_le_add, Finsupp.toMultiset_add, toFinsupp_singleton, Nodup.add_iff, toFinsupp_symm_apply, erase_add_left_neg, add_sub_assoc, Equiv.Perm.OnCycleFactors.cycleType_kerParam_apply_apply, Finsupp.coe_orderIsoMultiset_symm, ndunion_le_add, sym2_cons, add_bind, Ico_add_Ico_eq_Ico, cons_product, Disjoint.dedup_add, erase_add_right_neg, filterMap_add, toFinsupp_zero, gcd_add, MvPolynomial.degrees_mul_le, toFinsupp_toMultiset, rel_add_right, join_cons, Polynomial.roots_mul, Rel.add, count_add, Nat.factorization_eq_primeFactorsList_multiset, revzip_powersetAux', cons_sigma, MvPolynomial.degrees_mul_eq, product_add, toFinsupp_eq_iff, subset_add_left, powerset_cons, prod_add, union_le_add, add_le_add_right, add_product, range_add, filter_add, subset_add_right, filterMap_cons, add_union_distrib, Associates.FactorSet.coe_add, bind_cons, Relation.cutExpand_iff, Relation.cutExpand_add_right, sections_add, instOrderedSub, sub_add_inter, Equiv.Perm.Disjoint.cycleType_mul, le_sub_add, Polynomial.aroots_mul, countP_add, Equiv.Perm.parts_partition, le_add_right, add_le_add_left, map_disjSum, add_sub_cancel_right, Subset.dedup_add_right, union_add_distrib, add_singleton_eq_iff, UniqueFactorizationMonoid.factors_mul, disjoint_add_right, add_left_inj, map_add, Subset.dedup_add_left, le_iff_exists_add, cons_bind, Sym.coe_append, Nat.Partition.coeff_genFun, add_eq_union_left_of_le, add_eq_union_right_of_le, disjoint_list_sum_right, Associates.FactorSet.sup_add_inf_eq_add, foldl_add, toFinsupp_support, toFinsupp_strictMono, instAddLeftReflectLE, sup_add, SimpleGraph.Walk.coe_support_append', inter_add_distrib, union_def, Relation.cutExpand_add_single, nodup_add, SimpleGraph.Walk.coe_support, Finsupp.toMultiset_eq_iff, sigma_add
instSub πŸ“–CompOp
38 mathmath: Ico_sub_Ico_right, sub_le_self, revzip_powersetAux_lemma, Ico_sub_Ico_left, Equiv.Perm.cycleType_mul_inv_mem_cycleFactorsFinset_eq_sub, inter_add_sub_of_add_eq_add, Finset.sdiff_val, sub_le_iff_le_add', mem_sub_of_nodup, antidiagonal_eq_map_powerset, countP_sub, sub_add_eq_sub_sub, le_add_sub, add_sub_cancel, sub_add_cancel, sub_le_sub_right, eq_sub_of_add_eq, sub_le_iff_le_add, coe_sub, sub_cons, count_sub, add_sub_assoc, cons_sub_of_le, zero_sub, sub_singleton, filter_sub, mem_sub, instOrderedSub, sub_add_inter, le_sub_add, sub_inter, sub_eq_fold_erase, add_sub_cancel_right, sub_filter_eq_filter_not, card_sub, SimpleGraph.Walk.coe_support_append', union_def, sub_zero
sub πŸ“–CompOpβ€”

Theorems

NameKindAssumesProvesValidatesDepends On
add_assoc πŸ“–mathematicalβ€”Multiset
instAdd
β€”β€”
add_comm πŸ“–mathematicalβ€”Multiset
instAdd
β€”β€”
add_cons πŸ“–mathematicalβ€”Multiset
instAdd
cons
β€”add_comm
cons_add
add_le_add_iff_left πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
β€”β€”
add_le_add_iff_right πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
β€”β€”
add_le_add_left πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAddβ€”add_le_add_iff_left
add_le_add_right πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAddβ€”add_le_add_iff_right
add_left_inj πŸ“–mathematicalβ€”Multiset
instAdd
β€”count_add
add_right_inj πŸ“–mathematicalβ€”Multiset
instAdd
β€”count_add
add_singleton_eq_iff πŸ“–mathematicalβ€”Multiset
instAdd
instSingleton
instMembership
erase
β€”add_comm
singleton_add
mem_cons_self
erase_cons_head
cons_erase
add_sub_assoc πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSub
instAdd
β€”ext'
count_sub
count_add
count_le_of_le
add_sub_cancel πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
instSub
β€”ext'
count_add
count_sub
count_le_of_le
add_sub_cancel_right πŸ“–mathematicalβ€”Multiset
instSub
instAdd
β€”ext'
count_sub
count_add
add_zero πŸ“–mathematicalβ€”Multiset
instAdd
instZero
β€”β€”
card_add πŸ“–mathematicalβ€”card
Multiset
instAdd
β€”β€”
card_erase_add_one πŸ“–mathematicalMultiset
instMembership
card
erase
β€”List.length_erase_add_one
card_erase_eq_ite πŸ“–mathematicalβ€”card
erase
Multiset
instMembership
decidableMem
β€”card_erase_of_mem
erase_of_notMem
card_erase_le πŸ“–mathematicalβ€”card
erase
β€”card_le_card
erase_le
card_erase_lt_of_mem πŸ“–mathematicalMultiset
instMembership
card
erase
β€”card_lt_card
erase_lt
card_erase_of_mem πŸ“–mathematicalMultiset
instMembership
card
erase
β€”β€”
card_sub πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
card
instSub
β€”card_add
sub_add_cancel
coe_add πŸ“–mathematicalβ€”Multiset
instAdd
ofList
β€”β€”
coe_erase πŸ“–mathematicalβ€”erase
ofList
β€”β€”
coe_sub πŸ“–mathematicalβ€”Multiset
instSub
ofList
β€”β€”
cons_add πŸ“–mathematicalβ€”Multiset
instAdd
cons
β€”singleton_add
add_assoc
cons_erase πŸ“–mathematicalMultiset
instMembership
cons
erase
β€”β€”
cons_sub_of_le πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSub
cons
β€”singleton_add
add_sub_assoc
countP_add πŸ“–mathematicalβ€”countP
Multiset
instAdd
β€”β€”
countP_sub πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
countP
instSub
β€”List.countP_diff
count_add πŸ“–mathematicalβ€”count
Multiset
instAdd
β€”countP_add
count_erase_of_ne πŸ“–mathematicalβ€”count
erase
β€”coe_count
count_erase_self πŸ“–mathematicalβ€”count
erase
β€”coe_count
count_sub πŸ“–mathematicalβ€”count
Multiset
instSub
β€”coe_count
List.count_diff
eq_sub_of_add_eq πŸ“–mathematicalMultiset
instAdd
instSubβ€”add_sub_cancel_right
erase_add_left_neg πŸ“–mathematicalMultiset
instMembership
erase
instAdd
β€”add_comm
erase_add_right_neg
erase_add_left_pos πŸ“–mathematicalMultiset
instMembership
erase
instAdd
β€”β€”
erase_add_right_neg πŸ“–mathematicalMultiset
instMembership
erase
instAdd
β€”β€”
erase_add_right_pos πŸ“–mathematicalMultiset
instMembership
erase
instAdd
β€”add_comm
erase_add_left_pos
erase_comm πŸ“–mathematicalβ€”eraseβ€”β€”
erase_cons_head πŸ“–mathematicalβ€”erase
cons
β€”β€”
erase_cons_tail πŸ“–mathematicalβ€”erase
cons
β€”not_beq_of_ne
erase_cons_tail_of_mem πŸ“–mathematicalMultiset
instMembership
erase
cons
β€”eq_or_ne
erase_cons_head
cons_erase
erase_cons_tail
erase_le πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
erase
β€”β€”
erase_le_erase πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
eraseβ€”leInductionOn
erase_le_iff_le_cons πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
erase
cons
β€”le_trans
le_cons_erase
cons_le_cons
cons_le_cons_iff
cons_erase
erase_le
le_cons_of_notMem
erase_lt πŸ“–mathematicalβ€”Multiset
Preorder.toLT
PartialOrder.toPreorder
instPartialOrder
erase
instMembership
β€”not_imp_comm
erase_of_notMem
ne_of_lt
cons_erase
lt_cons_self
erase_of_notMem πŸ“–mathematicalMultiset
instMembership
eraseβ€”β€”
erase_singleton πŸ“–mathematicalβ€”erase
Multiset
instSingleton
instZero
β€”erase_cons_head
erase_subset πŸ“–mathematicalβ€”Multiset
instHasSubset
erase
β€”subset_of_le
erase_le
erase_zero πŸ“–mathematicalβ€”erase
Multiset
instZero
β€”β€”
instRightCommutativeErase πŸ“–mathematicalβ€”RightCommutative
Multiset
erase
β€”erase_comm
le_add_left πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
β€”zero_add
add_le_add_right
zero_le
le_add_right πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
β€”add_zero
add_le_add_left
zero_le
le_add_sub πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
instSub
β€”sub_le_iff_le_add'
le_rfl
le_cons_erase πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
cons
erase
β€”le_of_eq
cons_erase
erase_of_notMem
le_cons_self
le_iff_exists_add πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
β€”leInductionOn
le_add_right
le_of_add_le_add_left πŸ“–β€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
β€”β€”add_le_add_iff_left
le_of_add_le_add_right πŸ“–β€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
β€”β€”add_le_add_iff_right
le_sub_add πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
instSub
β€”sub_le_iff_le_add
le_rfl
mem_add πŸ“–mathematicalβ€”Multiset
instMembership
instAdd
β€”β€”
mem_erase_of_ne πŸ“–mathematicalβ€”Multiset
instMembership
erase
β€”β€”
mem_of_mem_erase πŸ“–β€”Multiset
instMembership
erase
β€”β€”mem_of_subset
erase_subset
mem_sub πŸ“–mathematicalβ€”Multiset
instMembership
instSub
count
β€”count_pos
count_sub
mem_sub_of_nodup πŸ“–mathematicalNodupMultiset
instMembership
instSub
β€”mem_of_le
sub_le_self
count_eq_zero
count_sub
le_trans
nodup_iff_count_le_one
count_pos
mem_add
le_sub_add
nodup_singleton πŸ“–mathematicalβ€”Nodup
Multiset
instSingleton
β€”List.nodup_singleton
not_nodup_pair πŸ“–mathematicalβ€”Nodup
cons
Multiset
instZero
β€”List.not_nodup_pair
rel_add_left πŸ“–mathematicalβ€”Rel
Multiset
instAdd
β€”induction_on
zero_add
cons_add
rel_add_right πŸ“–mathematicalβ€”Rel
Multiset
instAdd
β€”rel_flip
rel_add_left
singleton_add πŸ“–mathematicalβ€”Multiset
instAdd
instSingleton
cons
β€”β€”
sub_add_cancel πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instAdd
instSub
β€”ext'
count_add
count_sub
count_le_of_le
sub_add_eq_sub_sub πŸ“–mathematicalβ€”Multiset
instSub
instAdd
β€”ext'
count_sub
count_add
sub_cons πŸ“–mathematicalβ€”Multiset
instSub
cons
erase
β€”β€”
sub_le_iff_le_add πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSub
instAdd
β€”induction_on
sub_zero
add_zero
sub_cons
add_cons
sub_le_iff_le_add' πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSub
instAdd
β€”sub_le_iff_le_add
add_comm
sub_le_self πŸ“–mathematicalβ€”Multiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSub
β€”sub_le_iff_le_add
le_add_right
sub_le_sub_right πŸ“–mathematicalMultiset
Preorder.toLE
PartialOrder.toPreorder
instPartialOrder
instSubβ€”sub_le_iff_le_add'
LE.le.trans
le_add_sub
sub_singleton πŸ“–mathematicalβ€”Multiset
instSub
instSingleton
erase
β€”ext'
count_sub
count_singleton
count_erase_of_ne
count.congr_simp
count_erase_self
sub_zero πŸ“–mathematicalβ€”Multiset
instSub
instZero
β€”β€”
subset_add_left πŸ“–mathematicalβ€”Multiset
instHasSubset
instAdd
β€”subset_of_le
le_add_right
subset_add_right πŸ“–mathematicalβ€”Multiset
instHasSubset
instAdd
β€”subset_of_le
le_add_left
zero_add πŸ“–mathematicalβ€”Multiset
instAdd
instZero
β€”β€”
zero_sub πŸ“–mathematicalβ€”Multiset
instSub
instZero
β€”induction_on
sub_cons
erase_of_notMem

Multiset.Nodup

Theorems

NameKindAssumesProvesValidatesDepends On
erase πŸ“–mathematicalMultiset.NodupMultiset.eraseβ€”Multiset.nodup_of_le
Multiset.erase_le

Multiset.Rel

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalMultiset.RelMultiset
Multiset.instAdd
β€”Multiset.zero_add
Multiset.cons_add

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