Documentation Verification Report

Basic

πŸ“ Source: Mathlib/Algebra/BigOperators/Group/Finset/Basic.lean

Statistics

MetricCount
Definitions0
Theoremsadd_sum_erase, card_biUnion, card_biUnion_le, card_disjiUnion, card_eq_sum_card_fiberwise, card_eq_sum_card_image, card_eq_sum_ones, card_nsmul_add_sum, eq_of_card_le_one_of_prod_eq, eq_of_card_le_one_of_sum_eq, eq_one_of_prod_eq_one, eq_prod_range_div, eq_prod_range_div', eq_sum_range_sub, eq_sum_range_sub', eq_zero_of_sum_eq_zero, eventually_constant_prod, eventually_constant_sum, exists_ne_one_of_prod_ne_one, exists_ne_zero_of_sum_ne_zero, mem_sum, mul_prod_erase, nsmul_eq_sum_const, pow_card_mul_prod, pow_eq_prod_const, prod_attach, prod_biUnion, prod_biUnion_of_pairwise_eq_one, prod_bij_ne_one, prod_cancels_of_partition_cancels, prod_coe_sort, prod_comp, prod_comp_equiv, prod_compl_mul_prod, prod_congr, prod_congr_of_eq_on_inter, prod_congr_set, prod_cons, prod_cons', prod_const, prod_diag, prod_disjSum, prod_disjUnion, prod_disjiUnion, prod_dvd_prod_of_dvd, prod_eq_fold, prod_eq_ite, prod_eq_mul, prod_eq_mul_of_mem, prod_eq_one, prod_eq_one_iff, prod_eq_pow_card, prod_eq_prod_extend, prod_eq_single, prod_eq_single_of_mem, prod_erase, prod_erase_eq_div, prod_erase_lt_of_one_lt, prod_erase_mul, prod_extend_by_one, prod_fiberwise, prod_fiberwise', prod_fiberwise_eq_prod_filter, prod_fiberwise_eq_prod_filter', prod_fiberwise_of_maps_to, prod_fiberwise_of_maps_to', prod_filter, prod_filter_mul_prod_filter_not, prod_filter_ne_one, prod_filter_not_mul_prod_filter, prod_filter_of_ne, prod_filter_of_pairwise_eq_one, prod_filter_xor, prod_finset_coe, prod_flip, prod_image, prod_image', prod_image_of_disjoint, prod_image_of_pairwise_eq_one, prod_insert, prod_insert', prod_insert_div, prod_insert_of_eq_one_if_notMem, prod_insert_one, prod_involution, prod_ite_mem_eq, prod_list_count, prod_list_count_of_subset, prod_list_map_count, prod_map_equiv, prod_mul_distrib, prod_mul_eq_prod_mul_of_exists, prod_mul_pow_card, prod_mul_prod_comm, prod_mul_prod_compl, prod_multiset_count, prod_multiset_count_of_subset, prod_multiset_map_count, prod_ninvolution, prod_of_injOn, prod_pair, prod_partition, prod_pow_eq_pow_sum, prod_range_add, prod_range_add_div_prod_range, prod_range_div, prod_range_div', prod_range_induction, prod_range_one, prod_range_succ, prod_range_succ', prod_range_succ_comm, prod_sdiff, prod_sdiff_div_prod_sdiff, prod_sdiff_eq_div, prod_sdiff_eq_prod_sdiff_iff, prod_sdiff_ne_prod_sdiff_iff, prod_set_coe, prod_singleton, prod_singleton', prod_subset, prod_subset_one_on_sdiff, prod_subtype, prod_subtype_eq_prod_filter, prod_subtype_map_embedding, prod_subtype_of_mem, prod_sumElim, prod_sum_eq_prod_toLeft_mul_prod_toRight, prod_union, prod_union_eq_left, prod_union_eq_right, prod_union_inter, prod_unique_nonempty, sum_add_card_nsmul, sum_add_distrib, sum_add_eq_sum_add_of_exists, sum_add_sum_comm, sum_add_sum_compl, sum_attach, sum_biUnion, sum_biUnion_of_pairwise_eq_zero, sum_bij_ne_zero, sum_cancels_of_partition_cancels, sum_card_fiberwise_eq_card_filter, sum_coe_sort, sum_comp, sum_comp_equiv, sum_compl_add_sum, sum_congr, sum_congr_of_eq_on_inter, sum_congr_set, sum_cons, sum_cons', sum_const, sum_const_nat, sum_diag, sum_disjSum, sum_disjUnion, sum_disjiUnion, sum_eq_add, sum_eq_add_of_mem, sum_eq_card_nsmul, sum_eq_fold, sum_eq_ite, sum_eq_single, sum_eq_single_of_mem, sum_eq_sum_extend, sum_eq_zero, sum_eq_zero_iff, sum_erase, sum_erase_add, sum_erase_eq_sub, sum_erase_lt_of_pos, sum_extend_by_zero, sum_fiberwise, sum_fiberwise', sum_fiberwise_eq_sum_filter, sum_fiberwise_eq_sum_filter', sum_fiberwise_of_maps_to, sum_fiberwise_of_maps_to', sum_filter, sum_filter_add_sum_filter_not, sum_filter_ne_zero, sum_filter_not_add_sum_filter, sum_filter_of_ne, sum_filter_of_pairwise_eq_zero, sum_filter_xor, sum_finset_coe, sum_flip, sum_image, sum_image', sum_image_of_disjoint, sum_image_of_pairwise_eq_zero, sum_insert, sum_insert', sum_insert_of_eq_zero_if_notMem, sum_insert_sub, sum_insert_zero, sum_involution, sum_ite_mem_eq, sum_list_count, sum_list_count_of_subset, sum_list_map_count, sum_map_equiv, sum_multiset_count, sum_multiset_count_of_subset, sum_multiset_map_count, sum_ninvolution, sum_nsmul_assoc, sum_of_injOn, sum_pair, sum_partition, sum_range_add, sum_range_add_sub_sum_range, sum_range_induction, sum_range_one, sum_range_sub, sum_range_sub', sum_range_succ, sum_range_succ', sum_range_succ_comm, sum_range_tsub, sum_sdiff, sum_sdiff_eq_sub, sum_sdiff_eq_sum_sdiff_iff, sum_sdiff_ne_sum_sdiff_iff, sum_sdiff_sub_sum_sdiff, sum_set_coe, sum_singleton, sum_singleton', sum_subset, sum_subset_zero_on_sdiff, sum_subtype, sum_subtype_eq_sum_filter, sum_subtype_map_embedding, sum_subtype_of_mem, sum_sumElim, sum_sum_eq_sum_toLeft_add_sum_toRight, sum_tsub_distrib, sum_union, sum_union_eq_left, sum_union_eq_right, sum_union_inter, sum_unique_nonempty, prod_Prop, prod_fiberwise, prod_fiberwise', prod_of_injective, prod_subset, prod_subsingleton, prod_subtype_mul_prod_subtype, prod_unique, sum_Prop, sum_fiberwise, sum_fiberwise', sum_of_injective, sum_subset, sum_subsingleton, sum_subtype_add_sum_subtype, sum_unique, sum_iff, sum_univ_iff, prod_mul_prod, sum_add_sum, prod_iff, prod_univ_iff, prod_toFinset, sum_toFinset, sum_toFinset_count_eq_length, exists_smul_of_dvd_count, mem_sum, prod_map_prod, prod_sum, sum_count_eq_card, sum_map_sum, sum_sum, toFinset_sum_count_eq, toFinset_sum_count_nsmul_eq, nat_abs_sum_le
279
Total279

Finset

Theorems

NameKindAssumesProvesValidatesDepends On
add_sum_erase πŸ“–mathematicalFinset
instMembership
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
erase
β€”sum_insert
notMem_erase
insert_erase
card_biUnion πŸ“–mathematicalSet.PairwiseDisjoint
Finset
partialOrder
instOrderBot
SetLike.coe
instSetLike
card
biUnion
sum
Nat.instAddCommMonoid
β€”sum_congr
sum_const
mul_one
sum_biUnion
card_biUnion_le πŸ“–mathematicalβ€”card
biUnion
sum
Nat.instAddCommMonoid
β€”induction_on
biUnion_insert
card_union_le
card_disjiUnion πŸ“–mathematicalSet.PairwiseDisjoint
Finset
partialOrder
instOrderBot
SetLike.coe
instSetLike
card
disjiUnion
sum
Nat.instAddCommMonoid
β€”Multiset.card_bind
card_eq_sum_card_fiberwise πŸ“–mathematicalSet.MapsTo
SetLike.coe
Finset
instSetLike
card
sum
Nat.instAddCommMonoid
filter
β€”card_eq_sum_ones
sum_congr
sum_fiberwise_of_maps_to
card_eq_sum_card_image πŸ“–mathematicalβ€”card
sum
Nat.instAddCommMonoid
image
filter
β€”card_eq_sum_card_fiberwise
mem_image_of_mem
card_eq_sum_ones πŸ“–mathematicalβ€”card
sum
Nat.instAddCommMonoid
β€”sum_const
mul_one
card_nsmul_add_sum πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddMonoid.toNatSMul
card
sum
β€”sum_add_distrib
sum_const
eq_of_card_le_one_of_prod_eq πŸ“–β€”card
prod
Finset
instMembership
β€”β€”card_ne_zero_of_mem
le_antisymm
card_eq_one
eq_of_card_le_one_of_sum_eq πŸ“–β€”card
sum
Finset
instMembership
β€”β€”card_ne_zero_of_mem
le_antisymm
card_eq_one
eq_one_of_prod_eq_one πŸ“–β€”prod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset
instMembership
β€”β€”prod_singleton
prod_subset
singleton_subset_iff
notMem_singleton
eq_prod_range_div πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
prod
CommGroup.toCommMonoid
range
DivInvMonoid.toDiv
β€”prod_range_div
mul_div_cancel
eq_prod_range_div' πŸ“–mathematicalβ€”prod
CommGroup.toCommMonoid
range
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”eq_prod_range_div
prod_div_distrib
prod_range_succ'
prod_congr
mul_comm
eq_sum_range_sub πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sum
AddCommGroup.toAddCommMonoid
range
SubNegMonoid.toSub
β€”sum_range_sub
add_sub_cancel
eq_sum_range_sub' πŸ“–mathematicalβ€”sum
AddCommGroup.toAddCommMonoid
range
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”eq_sum_range_sub
sum_sub_distrib
sum_range_succ'
sum_congr
one_ne_zero
add_comm
eq_zero_of_sum_eq_zero πŸ“–β€”sum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset
instMembership
β€”β€”sum_singleton
sum_subset
singleton_subset_iff
notMem_singleton
eventually_constant_prod πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
range
β€”prod_congr
add_zero
prod_range_succ
mul_one
eventually_constant_sum πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
range
β€”sum_congr
add_zero
add_assoc
sum_range_succ
exists_ne_one_of_prod_ne_one πŸ“–mathematicalβ€”Finset
instMembership
β€”Mathlib.Tactic.Contrapose.contraposeβ‚‚
Mathlib.Tactic.Push.not_and_eq
prod_eq_one
exists_ne_zero_of_sum_ne_zero πŸ“–mathematicalβ€”Finset
instMembership
β€”Mathlib.Tactic.Contrapose.contraposeβ‚‚
Mathlib.Tactic.Push.not_exists
Mathlib.Tactic.Push.not_and_eq
sum_eq_zero
mem_sum πŸ“–mathematicalβ€”Multiset
Multiset.instMembership
sum
AddCancelCommMonoid.toAddCommMonoid
Multiset.instAddCancelCommMonoid
Finset
instMembership
β€”Multiset.mem_sum
mul_prod_erase πŸ“–mathematicalFinset
instMembership
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
erase
β€”prod_insert
notMem_erase
insert_erase
nsmul_eq_sum_const πŸ“–mathematicalβ€”AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
sum
range
β€”sum_const
card_range
pow_card_mul_prod πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Monoid.toNatPow
card
prod
β€”prod_mul_distrib
prod_const
pow_eq_prod_const πŸ“–mathematicalβ€”Monoid.toNatPow
CommMonoid.toMonoid
prod
range
β€”prod_const
card_range
prod_attach πŸ“–mathematicalβ€”prod
Finset
instMembership
attach
β€”prod_image
Function.Injective.injOn
Subtype.coe_injective
attach_image_val
prod_biUnion πŸ“–mathematicalSet.PairwiseDisjoint
Finset
partialOrder
instOrderBot
SetLike.coe
instSetLike
prod
biUnion
β€”disjiUnion_eq_biUnion
prod_disjiUnion
prod_biUnion_of_pairwise_eq_one πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
instSetLike
prod
biUnion
β€”ext
prod_filter_ne_one
prod_biUnion
prod_congr
prod_bij_ne_one πŸ“–mathematicalFinset
instMembership
prodβ€”prod_filter_ne_one
prod_bij
mem_filter
prod_cancels_of_partition_cancels πŸ“–β€”prod
filter
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”β€”prod_partition
prod_eq_one
mem_image
prod_congr
filter.congr_simp
prod_coe_sort πŸ“–mathematicalβ€”prod
Finset
SetLike.instMembership
instSetLike
univ
Subtype.fintype
β€”prod_attach
prod_comp πŸ“–mathematicalβ€”prod
image
Monoid.toNatPow
CommMonoid.toMonoid
card
filter
β€”prod_congr
prod_fiberwise_of_maps_to'
mem_image_of_mem
prod_comp_equiv πŸ“–mathematicalβ€”prod
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
map
Equiv.toEmbedding
β€”prod_congr
prod_map
prod_compl_mul_prod πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Compl.compl
Finset
BooleanAlgebra.toCompl
booleanAlgebra
univ
β€”IsCompl.prod_mul_prod
IsCompl.symm
isCompl_compl
prod_congr πŸ“–mathematicalβ€”prodβ€”fold_congr
CommMagma.to_isCommutative
Semigroup.to_isAssociative
prod_congr_of_eq_on_inter πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”sdiff_union_inter
prod_union_eq_right
inter_comm
prod_congr
prod_congr_set πŸ“–mathematicalSet
Set.instMembership
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
univ
Set.Elem
Subtype.fintype
β€”prod_subset
subset_univ
prod_subtype
prod_congr
prod_cons πŸ“–mathematicalFinset
instMembership
prod
cons
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”fold_cons
CommMagma.to_isCommutative
Semigroup.to_isAssociative
prod_cons' πŸ“–mathematicalFinset
instMembership
prod
cons
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_cons
prod_const πŸ“–mathematicalβ€”prod
Monoid.toNatPow
CommMonoid.toMonoid
card
β€”Multiset.map_const
Multiset.prod_replicate
prod_diag πŸ“–mathematicalβ€”prod
diag
β€”prod_map
prod_congr
prod_disjSum πŸ“–mathematicalβ€”prod
disjSum
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”disjoint_map_inl_map_inr
map_inl_disjUnion_map_inr
prod_disjUnion
prod_map
prod_disjUnion πŸ“–mathematicalDisjoint
Finset
partialOrder
instOrderBot
prod
disjUnion
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”CommMagma.to_isCommutative
Semigroup.to_isAssociative
one_mul
fold_disjUnion
prod_disjiUnion πŸ“–mathematicalSet.PairwiseDisjoint
Finset
partialOrder
instOrderBot
SetLike.coe
instSetLike
prod
disjiUnion
β€”CommMagma.to_isCommutative
Semigroup.to_isAssociative
instLeftCommutativeOfCommutativeOfAssociative
prod_const_one
fold_disjiUnion
prod_dvd_prod_of_dvd πŸ“–mathematicalsemigroupDvd
Monoid.toSemigroup
CommMonoid.toMonoid
prodβ€”Multiset.prod_dvd_prod_of_dvd
prod_eq_fold πŸ“–mathematicalβ€”prod
fold
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
CommMagma.to_isCommutative
CommSemigroup.toCommMagma
CommMonoid.toCommSemigroup
Semigroup.to_isAssociative
Monoid.toSemigroup
MulOne.toOne
β€”β€”
prod_eq_ite πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Finset
instMembership
decidableMem
β€”prod_eq_single_of_mem
prod_congr
prod_const_one
prod_eq_mul πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
MulOne.toMul
β€”prod_eq_mul_of_mem
mul_one
prod_eq_single_of_mem
one_mul
trans
IsPreorder.toIsTrans
IsEquiv.toIsPreorder
eq_isEquiv
prod_congr
prod_const_one
prod_eq_mul_of_mem πŸ“–mathematicalFinset
instMembership
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
MulOne.toMul
β€”prod_subset
prod_pair
prod_eq_one πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”prod_congr
prod_const_one
prod_eq_one_iff πŸ“–mathematicalβ€”prod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”cons_induction
instIsEmptyFalse
prod_cons
prod_eq_pow_card πŸ“–mathematicalβ€”prod
Monoid.toNatPow
CommMonoid.toMonoid
card
β€”prod_congr
prod_const
prod_eq_prod_extend πŸ“–mathematicalβ€”prod
Finset
SetLike.instMembership
instSetLike
univ
Subtype.fintype
Function.extend
Pi.instOne
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”univ_eq_attach
prod_attach
Function.Injective.extend_apply
Subtype.val_injective
prod_eq_single πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”by_cases
prod_eq_single_of_mem
prod_congr
prod_const_one
prod_eq_single_of_mem πŸ“–mathematicalFinset
instMembership
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”prod_subset
mem_singleton
prod_singleton
prod_erase πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
erase
β€”sdiff_singleton_eq_erase
prod_subset
sdiff_subset
prod_erase_eq_div πŸ“–mathematicalFinset
instMembership
prod
CommGroup.toCommMonoid
erase
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”eq_div_iff_mul_eq'
prod_erase_mul
prod_erase_lt_of_one_lt πŸ“–mathematicalFinset
instMembership
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
erase
β€”insert_erase
prod_insert
notMem_erase
lt_mul_of_one_lt_left'
covariant_swap_mul_of_covariant_mul
prod_erase_mul πŸ“–mathematicalFinset
instMembership
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
erase
β€”mul_comm
mul_prod_erase
prod_extend_by_one πŸ“–mathematicalβ€”prod
Finset
instMembership
decidableMem
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_congr
prod_fiberwise πŸ“–mathematicalβ€”prod
univ
filter
β€”prod_fiberwise_of_maps_to
mem_univ
prod_fiberwise' πŸ“–mathematicalβ€”prod
univ
filter
β€”prod_fiberwise_of_maps_to'
mem_univ
prod_fiberwise_eq_prod_filter πŸ“–mathematicalβ€”prod
filter
Finset
instMembership
decidableMem
β€”prod_disjiUnion
disjiUnion_filter_eq
prod_fiberwise_eq_prod_filter' πŸ“–mathematicalβ€”prod
filter
Finset
instMembership
decidableMem
β€”prod_congr
mem_filter
prod_fiberwise_eq_prod_filter
prod_fiberwise_of_maps_to πŸ“–mathematicalFinset
instMembership
prod
filter
β€”prod_disjiUnion
disjiUnion_filter_eq_of_maps_to
prod_fiberwise_of_maps_to' πŸ“–mathematicalFinset
instMembership
prod
filter
β€”prod_congr
mem_filter
prod_fiberwise_of_maps_to
prod_filter πŸ“–mathematicalβ€”prod
filter
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_congr
mem_filter
prod_subset
filter_subset
prod_filter_mul_prod_filter_not πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
filter
β€”prod_union
disjoint_filter_filter_not
filter_union_filter_not_eq
prod_filter_ne_one πŸ“–mathematicalβ€”prod
filter
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_filter_of_ne
prod_filter_not_mul_prod_filter πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
filter
β€”mul_comm
prod_filter_mul_prod_filter_not
prod_filter_of_ne πŸ“–mathematicalβ€”prod
filter
β€”prod_subset
filter_subset
not_imp_comm
mem_filter
prod_filter_of_pairwise_eq_one πŸ“–mathematicalFinset
instMembership
Set.Pairwise
SetLike.coe
instSetLike
prod
filter
β€”mul_one
prod_eq_one
mul_prod_erase
mem_filter
prod_filter_xor πŸ“–mathematicalβ€”prod
filter
Xor'
instDecidableXor'
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_union
disjoint_filter_and_not_filter
filter_or
prod_finset_coe πŸ“–mathematicalβ€”prod
Set.Elem
SetLike.coe
Finset
instSetLike
univ
FinsetCoe.fintype
Set
Set.instMembership
β€”prod_coe_sort
prod_flip πŸ“–mathematicalβ€”prod
range
β€”prod_range_one
prod_range_succ'
prod_range_succ
prod_congr
prod_image πŸ“–mathematicalSet.InjOn
SetLike.coe
Finset
instSetLike
prod
image
β€”fold_image
CommMagma.to_isCommutative
Semigroup.to_isAssociative
prod_image' πŸ“–mathematicalprod
filter
imageβ€”prod_congr
mem_image
prod_fiberwise_of_maps_to
mem_image_of_mem
prod_image_of_disjoint πŸ“–mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Set.PairwiseDisjoint
SetLike.coe
Finset
instSetLike
prod
image
β€”prod_image_of_pairwise_eq_one
Set.Pairwise.imp
disjoint_self
Function.onFun.eq_1
prod_image_of_pairwise_eq_one πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
instSetLike
prod
image
β€”prod_image'
prod_filter_of_pairwise_eq_one
prod_insert πŸ“–mathematicalFinset
instMembership
prod
instInsert
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”fold_insert
CommMagma.to_isCommutative
Semigroup.to_isAssociative
prod_insert' πŸ“–mathematicalFinset
instMembership
prod
instInsert
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_insert
prod_insert_div πŸ“–mathematicalFinset
instMembership
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
prod
CommGroup.toCommMonoid
instInsert
β€”prod_insert
mul_div_cancel_left
prod_insert_of_eq_one_if_notMem πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Finset
instInsert
β€”β€”
prod_insert_one πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Finset
instInsert
β€”prod_insert_of_eq_one_if_notMem
prod_involution πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
Finset
instMembership
prodβ€”eq_empty_or_nonempty
sdiff_subset
ssubset_iff
prod_sdiff
one_mul
eq_or_ne
prod_congr
insert_eq_of_mem
prod_singleton
prod_ite_mem_eq πŸ“–mathematicalβ€”prod
univ
Finset
instMembership
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_filter
prod_list_count πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
prod
List.toFinset
Monoid.toNatPow
β€”prod_congr
prod_list_map_count
prod_list_count_of_subset πŸ“–mathematicalFinset
instHasSubset
List.toFinset
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
prod
Monoid.toNatPow
β€”prod_list_count
prod_subset
List.mem_toFinset
pow_zero
prod_list_map_count πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
prod
List.toFinset
Monoid.toNatPow
β€”prod_congr
pow_zero
prod_const_one
List.toFinset_cons
insert_eq_of_mem
insert_erase
prod_insert
notMem_erase
mul_assoc
pow_succ'
ne_of_mem_erase
List.mem_toFinset
pow_one
prod_map_equiv πŸ“–mathematicalβ€”prod
map
Equiv.toEmbedding
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
β€”prod_congr
prod_map
Equiv.symm_apply_apply
prod_mul_distrib πŸ“–mathematicalβ€”prod
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”CommMagma.to_isCommutative
Semigroup.to_isAssociative
one_mul
fold_op_distrib
prod_mul_eq_prod_mul_of_exists πŸ“–mathematicalFinset
instMembership
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”insert_erase
prod_insert
mul_assoc
mul_comm
prod_mul_pow_card πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Monoid.toNatPow
card
β€”prod_mul_distrib
prod_const
prod_mul_prod_comm πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
β€”prod_mul_distrib
mul_mul_mul_comm
prod_mul_prod_compl πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Compl.compl
Finset
BooleanAlgebra.toCompl
booleanAlgebra
univ
β€”IsCompl.prod_mul_prod
isCompl_compl
prod_multiset_count πŸ“–mathematicalβ€”Multiset.prod
prod
Multiset.toFinset
Monoid.toNatPow
CommMonoid.toMonoid
Multiset.count
β€”Multiset.map_id
prod_congr
prod_multiset_map_count
prod_multiset_count_of_subset πŸ“–mathematicalFinset
instHasSubset
Multiset.toFinset
Multiset.prod
prod
Monoid.toNatPow
CommMonoid.toMonoid
Multiset.count
β€”Quot.induction_on
prod_congr
Multiset.coe_count
prod_list_count_of_subset
prod_multiset_map_count πŸ“–mathematicalβ€”Multiset.prod
Multiset.map
prod
Multiset.toFinset
Monoid.toNatPow
CommMonoid.toMonoid
Multiset.count
β€”Quot.induction_on
prod_list_map_count
prod_congr
Multiset.coe_count
prod_ninvolution πŸ“–mathematicalMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
Finset
instMembership
prodβ€”prod_involution
prod_of_injOn πŸ“–mathematicalSet.InjOn
SetLike.coe
Finset
instSetLike
Set.MapsTo
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”prod_nbij
mem_image_of_mem
coe_image
prod_subset
image_subset_iff
prod_pair πŸ“–mathematicalβ€”prod
Finset
instInsert
instSingleton
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_insert
notMem_singleton
prod_singleton
prod_partition πŸ“–mathematicalβ€”prod
image
filter
β€”prod_image'
prod_pow_eq_pow_sum πŸ“–mathematicalβ€”prod
Monoid.toNatPow
CommMonoid.toMonoid
sum
Nat.instAddCommMonoid
β€”cons_induction
pow_zero
prod_cons
sum_cons
pow_add
prod_range_add πŸ“–mathematicalβ€”prod
range
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_congr
add_zero
mul_one
prod_range_succ
mul_assoc
prod_range_add_div_prod_range πŸ“–mathematicalβ€”DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
prod
CommGroup.toCommMonoid
range
β€”div_eq_of_eq_mul'
prod_range_add
prod_range_div πŸ“–mathematicalβ€”prod
CommGroup.toCommMonoid
range
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”prod_range_induction
div_self'
div_mul_div_cancel'
prod_range_div' πŸ“–mathematicalβ€”prod
CommGroup.toCommMonoid
range
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”prod_range_induction
div_self'
div_mul_div_cancel
prod_range_induction πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toMul
prod
range
β€”prod_range_zero
prod_range_succ
prod_range_one πŸ“–mathematicalβ€”prod
range
β€”range_one
prod_singleton
prod_range_succ πŸ“–mathematicalβ€”prod
range
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_range_succ_comm
mul_comm
prod_range_succ' πŸ“–mathematicalβ€”prod
range
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_range_succ
mul_right_comm
prod_range_succ_comm πŸ“–mathematicalβ€”prod
range
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”range_add_one
prod_insert
notMem_range_self
prod_sdiff πŸ“–mathematicalFinset
instHasSubset
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
instSDiff
β€”prod_union
sdiff_disjoint
sdiff_union_of_subset
prod_sdiff_div_prod_sdiff πŸ“–mathematicalβ€”DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
prod
CommGroup.toCommMonoid
Finset
instSDiff
β€”prod_sdiff
inf_le_right
prod_congr
sdiff_inter_self_right
inf_le_left
sdiff_inter_self_left
mul_div_mul_right_eq_div
prod_sdiff_eq_div πŸ“–mathematicalFinset
instHasSubset
prod
CommGroup.toCommMonoid
instSDiff
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”eq_div_iff_mul_eq'
prod_sdiff
prod_sdiff_eq_prod_sdiff_iff πŸ“–mathematicalβ€”prod
CancelCommMonoid.toCommMonoid
Finset
instSDiff
β€”eq_iff_eq_of_mul_eq_mul
prod_union
disjoint_sdiff_self_left
sdiff_union_self_eq_union
union_comm
prod_sdiff_ne_prod_sdiff_iff πŸ“–β€”β€”β€”β€”Iff.not
prod_sdiff_eq_prod_sdiff_iff
prod_set_coe πŸ“–mathematicalβ€”prod
Set.Elem
univ
Set
Set.instMembership
Set.toFinset
β€”prod_subtype
Set.mem_toFinset
prod_singleton πŸ“–mathematicalβ€”prod
Finset
instSingleton
β€”fold_singleton
CommMagma.to_isCommutative
Semigroup.to_isAssociative
mul_one
prod_singleton' πŸ“–mathematicalβ€”prod
Finset
instSingleton
β€”prod_singleton
prod_subset πŸ“–mathematicalFinset
instHasSubset
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”prod_subset_one_on_sdiff
prod_subset_one_on_sdiff πŸ“–mathematicalFinset
instHasSubset
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prodβ€”prod_sdiff
prod_eq_one
one_mul
prod_congr
prod_subtype πŸ“–mathematicalFinset
instMembership
prod
univ
β€”Set.ext
prod_coe_sort
prod_congr
Lean.Meta.FastSubsingleton.elim
Fintype.instFastSubsingleton
prod_subtype_eq_prod_filter πŸ“–mathematicalβ€”prod
subtype
filter
β€”prod_map
prod_congr
subtype_map
prod_subtype_map_embedding πŸ“–mathematicalβ€”prod
map
Function.Embedding.subtype
β€”prod_map
prod_congr
prod_subtype_of_mem πŸ“–mathematicalβ€”prod
subtype
β€”prod_subtype_eq_prod_filter
filter_true_of_mem
prod_sumElim πŸ“–mathematicalβ€”prod
disjSum
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_disjSum
prod_congr
prod_sum_eq_prod_toLeft_mul_prod_toRight πŸ“–mathematicalβ€”prod
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
toLeft
toRight
β€”toLeft_disjSum_toRight
prod_disjSum
toLeft_disjSum
toRight_disjSum
prod_union πŸ“–mathematicalDisjoint
Finset
partialOrder
instOrderBot
prod
instUnion
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”prod_union_inter
disjoint_iff_inter_eq_empty
mul_one
prod_union_eq_left πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Finset
instUnion
β€”prod_subset
subset_union_left
mem_union
prod_union_eq_right πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Finset
instUnion
β€”union_comm
prod_union_eq_left
prod_union_inter πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
prod
Finset
instUnion
instInter
β€”fold_union_inter
CommMagma.to_isCommutative
Semigroup.to_isAssociative
prod_unique_nonempty πŸ“–mathematicalNonemptyprod
Unique.instInhabited
β€”Nonempty.eq_singleton_default
prod_singleton
sum_add_card_nsmul πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
AddMonoid.toNatSMul
card
β€”sum_add_distrib
sum_const
sum_add_distrib πŸ“–mathematicalβ€”sum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
zero_add
fold_op_distrib
sum_add_eq_sum_add_of_exists πŸ“–mathematicalFinset
instMembership
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”insert_erase
sum_insert
mem_erase
add_assoc
add_comm
sum_add_sum_comm πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
β€”sum_add_distrib
add_add_add_comm
sum_add_sum_compl πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Compl.compl
Finset
BooleanAlgebra.toCompl
booleanAlgebra
univ
β€”IsCompl.sum_add_sum
isCompl_compl
sum_attach πŸ“–mathematicalβ€”sum
Finset
instMembership
attach
β€”sum_image
Function.Injective.injOn
Subtype.coe_injective
attach_image_val
sum_biUnion πŸ“–mathematicalSet.PairwiseDisjoint
Finset
partialOrder
instOrderBot
SetLike.coe
instSetLike
sum
biUnion
β€”disjiUnion_eq_biUnion
sum_disjiUnion
sum_biUnion_of_pairwise_eq_zero πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
instSetLike
sum
biUnion
β€”ext
sum_filter_ne_zero
sum_biUnion
mem_filter
sum_congr
sum_bij_ne_zero πŸ“–mathematicalFinset
instMembership
sumβ€”sum_filter_ne_zero
sum_bij
mem_filter
sum_cancels_of_partition_cancels πŸ“–β€”sum
filter
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”β€”sum_partition
sum_eq_zero
mem_image
sum_congr
filter.congr_simp
Quotient.eq
sum_card_fiberwise_eq_card_filter πŸ“–mathematicalβ€”sum
Nat.instAddCommMonoid
card
filter
Finset
instMembership
decidableMem
β€”sum_congr
card_eq_sum_ones
sum_fiberwise_eq_sum_filter
sum_coe_sort πŸ“–mathematicalβ€”sum
Finset
SetLike.instMembership
instSetLike
univ
Subtype.fintype
β€”sum_attach
sum_comp πŸ“–mathematicalβ€”sum
image
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
card
filter
β€”sum_congr
sum_const
sum_fiberwise_of_maps_to'
mem_image_of_mem
sum_comp_equiv πŸ“–mathematicalβ€”sum
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
map
Equiv.toEmbedding
β€”sum_congr
sum_map
sum_compl_add_sum πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Compl.compl
Finset
BooleanAlgebra.toCompl
booleanAlgebra
univ
β€”IsCompl.sum_add_sum
IsCompl.symm
isCompl_compl
sum_congr πŸ“–mathematicalβ€”sumβ€”fold_congr
AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
sum_congr_of_eq_on_inter πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”sdiff_union_inter
sum_union_eq_right
mem_sdiff
mem_inter
inter_comm
sum_congr
sum_congr_set πŸ“–mathematicalSet
Set.instMembership
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
univ
Set.Elem
Subtype.fintype
β€”sum_subset
subset_univ
mem_univ
Set.mem_toFinset
sum_subtype
sum_congr
sum_cons πŸ“–mathematicalFinset
instMembership
sum
cons
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”fold_cons
AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
sum_cons' πŸ“–mathematicalFinset
instMembership
sum
cons
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_cons
sum_const πŸ“–mathematicalβ€”sum
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
card
β€”Multiset.map_const
Multiset.sum_replicate
sum_const_nat πŸ“–mathematicalβ€”sum
Nat.instAddCommMonoid
card
β€”Nat.nsmul_eq_mul
sum_const
sum_congr
sum_diag πŸ“–mathematicalβ€”sum
diag
β€”sum_map
sum_congr
sum_disjSum πŸ“–mathematicalβ€”sum
disjSum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”disjoint_map_inl_map_inr
map_inl_disjUnion_map_inr
sum_disjUnion
sum_map
sum_disjUnion πŸ“–mathematicalDisjoint
Finset
partialOrder
instOrderBot
sum
disjUnion
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
zero_add
fold_disjUnion
sum_disjiUnion πŸ“–mathematicalSet.PairwiseDisjoint
Finset
partialOrder
instOrderBot
SetLike.coe
instSetLike
sum
disjiUnion
β€”AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
instLeftCommutativeOfCommutativeOfAssociative
sum_const_zero
fold_disjiUnion
sum_eq_add πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
AddZero.toAdd
β€”sum_eq_add_of_mem
add_zero
sum_eq_single_of_mem
zero_add
trans
IsPreorder.toIsTrans
IsEquiv.toIsPreorder
eq_isEquiv
sum_congr
sum_const_zero
sum_eq_add_of_mem πŸ“–mathematicalFinset
instMembership
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
AddZero.toAdd
β€”sum_subset
sum_pair
sum_eq_card_nsmul πŸ“–mathematicalβ€”sum
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
card
β€”sum_congr
sum_const
sum_eq_fold πŸ“–mathematicalβ€”sum
fold
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddCommMagma.to_isCommutative
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddSemigroup.to_isAssociative
AddMonoid.toAddSemigroup
AddZero.toZero
β€”β€”
sum_eq_ite πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Finset
instMembership
decidableMem
β€”sum_eq_single_of_mem
sum_congr
sum_const_zero
sum_eq_single πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”by_cases
sum_eq_single_of_mem
sum_congr
sum_const_zero
sum_eq_single_of_mem πŸ“–mathematicalFinset
instMembership
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”sum_subset
mem_singleton
sum_singleton
sum_eq_sum_extend πŸ“–mathematicalβ€”sum
Finset
SetLike.instMembership
instSetLike
univ
Subtype.fintype
Function.extend
Pi.instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”univ_eq_attach
sum_attach
Function.Injective.extend_apply
Subtype.val_injective
sum_eq_zero πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”sum_congr
sum_const_zero
sum_eq_zero_iff πŸ“–mathematicalβ€”sum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”cons_induction
notMem_empty
IsEmpty.forall_iff
instIsEmptyFalse
sum_cons
add_eq_zero
mem_cons
sum_erase πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
erase
β€”sdiff_singleton_eq_erase
sum_subset
sdiff_subset
sum_erase_add πŸ“–mathematicalFinset
instMembership
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
erase
β€”add_comm
add_sum_erase
sum_erase_eq_sub πŸ“–mathematicalFinset
instMembership
sum
AddCommGroup.toAddCommMonoid
erase
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”eq_sub_iff_add_eq
sum_erase_add
sum_erase_lt_of_pos πŸ“–mathematicalFinset
instMembership
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
erase
β€”insert_erase
sum_insert
notMem_erase
lt_add_of_pos_left
covariant_swap_add_of_covariant_add
sum_extend_by_zero πŸ“–mathematicalβ€”sum
Finset
instMembership
decidableMem
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_congr
sum_fiberwise πŸ“–mathematicalβ€”sum
univ
filter
β€”sum_fiberwise_of_maps_to
mem_univ
sum_fiberwise' πŸ“–mathematicalβ€”sum
univ
filter
β€”sum_fiberwise_of_maps_to'
mem_univ
sum_fiberwise_eq_sum_filter πŸ“–mathematicalβ€”sum
filter
Finset
instMembership
decidableMem
β€”disjoint_left
mem_filter
sum_disjiUnion
disjiUnion_filter_eq
sum_fiberwise_eq_sum_filter' πŸ“–mathematicalβ€”sum
filter
Finset
instMembership
decidableMem
β€”sum_congr
mem_filter
sum_fiberwise_eq_sum_filter
sum_fiberwise_of_maps_to πŸ“–mathematicalFinset
instMembership
sum
filter
β€”disjoint_left
mem_filter
sum_disjiUnion
disjiUnion_filter_eq_of_maps_to
sum_fiberwise_of_maps_to' πŸ“–mathematicalFinset
instMembership
sum
filter
β€”sum_congr
mem_filter
sum_fiberwise_of_maps_to
sum_filter πŸ“–mathematicalβ€”sum
filter
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_congr
mem_filter
sum_subset
filter_subset
sum_filter_add_sum_filter_not πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
filter
β€”sum_union
disjoint_filter_filter_not
filter_union_filter_not_eq
sum_filter_ne_zero πŸ“–mathematicalβ€”sum
filter
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_filter_of_ne
sum_filter_not_add_sum_filter πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
filter
β€”add_comm
sum_filter_add_sum_filter_not
sum_filter_of_ne πŸ“–mathematicalβ€”sum
filter
β€”sum_subset
filter_subset
not_imp_comm
mem_filter
sum_filter_of_pairwise_eq_zero πŸ“–mathematicalFinset
instMembership
Set.Pairwise
SetLike.coe
instSetLike
sum
filter
β€”mem_erase
mem_filter
add_zero
sum_eq_zero
add_sum_erase
sum_filter_xor πŸ“–mathematicalβ€”sum
filter
Xor'
instDecidableXor'
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_union
disjoint_filter_and_not_filter
filter_or
sum_finset_coe πŸ“–mathematicalβ€”sum
Set.Elem
SetLike.coe
Finset
instSetLike
univ
FinsetCoe.fintype
Set
Set.instMembership
β€”sum_coe_sort
sum_flip πŸ“–mathematicalβ€”sum
range
β€”sum_range_one
sum_range_succ'
sum_range_succ
sum_congr
sum_image πŸ“–mathematicalSet.InjOn
SetLike.coe
Finset
instSetLike
sum
image
β€”fold_image
AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
sum_image' πŸ“–mathematicalsum
filter
imageβ€”sum_congr
mem_image
sum_fiberwise_of_maps_to
mem_image_of_mem
sum_image_of_disjoint πŸ“–mathematicalBot.bot
OrderBot.toBot
Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set.PairwiseDisjoint
SetLike.coe
Finset
instSetLike
sum
image
β€”sum_image_of_pairwise_eq_zero
Set.Pairwise.imp
disjoint_self
Function.onFun.eq_1
sum_image_of_pairwise_eq_zero πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
instSetLike
sum
image
β€”sum_image'
sum_filter_of_pairwise_eq_zero
sum_insert πŸ“–mathematicalFinset
instMembership
sum
instInsert
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”fold_insert
AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
sum_insert' πŸ“–mathematicalFinset
instMembership
sum
instInsert
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_insert
sum_insert_of_eq_zero_if_notMem πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Finset
instInsert
β€”β€”
sum_insert_sub πŸ“–mathematicalFinset
instMembership
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sum
AddCommGroup.toAddCommMonoid
instInsert
β€”sum_insert
add_sub_cancel_left
sum_insert_zero πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Finset
instInsert
β€”sum_insert_of_eq_zero_if_notMem
sum_involution πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
Finset
instMembership
sumβ€”eq_empty_or_nonempty
insert_subset_iff
singleton_subset_iff
sdiff_subset
ssubset_iff
mem_sdiff
mem_insert
mem_singleton
sum_sdiff
zero_add
eq_or_ne
sum_congr
insert_eq_of_mem
sum_singleton
sum_ite_mem_eq πŸ“–mathematicalβ€”sum
univ
Finset
instMembership
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_filter
sum_list_count πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
sum
List.toFinset
AddMonoid.toNatSMul
β€”sum_congr
sum_list_map_count
sum_list_count_of_subset πŸ“–mathematicalFinset
instHasSubset
List.toFinset
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
sum
AddMonoid.toNatSMul
β€”sum_list_count
sum_subset
List.mem_toFinset
zero_nsmul
sum_list_map_count πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
sum
List.toFinset
AddMonoid.toNatSMul
β€”sum_congr
zero_nsmul
sum_const_zero
List.toFinset_cons
insert_eq_of_mem
insert_erase
sum_insert
notMem_erase
add_assoc
succ_nsmul'
ne_of_mem_erase
List.mem_toFinset
one_nsmul
sum_map_equiv πŸ“–mathematicalβ€”sum
map
Equiv.toEmbedding
DFunLike.coe
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
β€”sum_congr
sum_map
Equiv.symm_apply_apply
sum_multiset_count πŸ“–mathematicalβ€”Multiset.sum
sum
Multiset.toFinset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
Multiset.count
β€”Multiset.map_id
sum_congr
sum_multiset_map_count
sum_multiset_count_of_subset πŸ“–mathematicalFinset
instHasSubset
Multiset.toFinset
Multiset.sum
sum
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
Multiset.count
β€”Quot.induction_on
sum_congr
Multiset.coe_count
sum_list_count_of_subset
sum_multiset_map_count πŸ“–mathematicalβ€”Multiset.sum
Multiset.map
sum
Multiset.toFinset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
Multiset.count
β€”Quot.induction_on
sum_list_map_count
sum_congr
Multiset.coe_count
sum_ninvolution πŸ“–mathematicalAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
Finset
instMembership
sumβ€”sum_involution
sum_nsmul_assoc πŸ“–mathematicalβ€”sum
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
Nat.instAddCommMonoid
β€”cons_induction
zero_nsmul
sum_cons
add_nsmul
sum_of_injOn πŸ“–mathematicalSet.InjOn
SetLike.coe
Finset
instSetLike
Set.MapsTo
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”sum_nbij
mem_image_of_mem
coe_image
Set.surjOn_image
sum_subset
image_subset_iff
mem_image
Set.mem_image
SetLike.mem_coe
sum_pair πŸ“–mathematicalβ€”sum
Finset
instInsert
instSingleton
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_insert
notMem_singleton
sum_singleton
sum_partition πŸ“–mathematicalβ€”sum
image
filter
β€”sum_image'
sum_range_add πŸ“–mathematicalβ€”sum
range
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_congr
add_zero
sum_range_succ
add_assoc
sum_range_add_sub_sum_range πŸ“–mathematicalβ€”SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sum
AddCommGroup.toAddCommMonoid
range
β€”sub_eq_of_eq_add'
sum_range_add
sum_range_induction πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toAdd
sum
range
β€”sum_range_zero
sum_range_succ
sum_range_one πŸ“–mathematicalβ€”sum
range
β€”range_one
sum_singleton
sum_range_sub πŸ“–mathematicalβ€”sum
AddCommGroup.toAddCommMonoid
range
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sum_range_induction
sub_self
sub_add_sub_cancel'
sum_range_sub' πŸ“–mathematicalβ€”sum
AddCommGroup.toAddCommMonoid
range
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sum_range_induction
sub_self
sub_add_sub_cancel
sum_range_succ πŸ“–mathematicalβ€”sum
range
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_range_succ_comm
add_comm
sum_range_succ' πŸ“–mathematicalβ€”sum
range
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_range_succ
add_right_comm
sum_range_succ_comm πŸ“–mathematicalβ€”sum
range
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”range_add_one
sum_insert
notMem_range_self
sum_range_tsub πŸ“–mathematicalMonotone
Nat.instPreorder
PartialOrder.toPreorder
sum
range
β€”sum_range_induction
tsub_eq_of_eq_add
zero_add
tsub_add_eq_add_tsub
add_tsub_cancel_of_le
sum_sdiff πŸ“–mathematicalFinset
instHasSubset
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
instSDiff
β€”sum_union
sdiff_disjoint
sdiff_union_of_subset
sum_sdiff_eq_sub πŸ“–mathematicalFinset
instHasSubset
sum
AddCommGroup.toAddCommMonoid
instSDiff
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”eq_sub_iff_add_eq
sum_sdiff
sum_sdiff_eq_sum_sdiff_iff πŸ“–mathematicalβ€”sum
AddCancelCommMonoid.toAddCommMonoid
Finset
instSDiff
β€”eq_iff_eq_of_add_eq_add
sum_union
disjoint_sdiff_self_left
sdiff_union_self_eq_union
union_comm
sum_sdiff_ne_sum_sdiff_iff πŸ“–β€”β€”β€”β€”Iff.not
sum_sdiff_eq_sum_sdiff_iff
sum_sdiff_sub_sum_sdiff πŸ“–mathematicalβ€”SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sum
AddCommGroup.toAddCommMonoid
Finset
instSDiff
β€”sum_sdiff
inf_le_right
sum_congr
sdiff_inter_self_right
inf_le_left
sdiff_inter_self_left
add_sub_add_right_eq_sub
sum_set_coe πŸ“–mathematicalβ€”sum
Set.Elem
univ
Set
Set.instMembership
Set.toFinset
β€”sum_subtype
Set.mem_toFinset
sum_singleton πŸ“–mathematicalβ€”sum
Finset
instSingleton
β€”fold_singleton
AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
add_zero
sum_singleton' πŸ“–mathematicalβ€”sum
Finset
instSingleton
β€”sum_singleton
sum_subset πŸ“–mathematicalFinset
instHasSubset
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”sum_subset_zero_on_sdiff
mem_sdiff
sum_subset_zero_on_sdiff πŸ“–mathematicalFinset
instHasSubset
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sumβ€”sum_sdiff
sum_eq_zero
zero_add
sum_congr
sum_subtype πŸ“–mathematicalFinset
instMembership
sum
univ
β€”Set.ext
sum_coe_sort
sum_congr
Lean.Meta.FastSubsingleton.elim
Fintype.instFastSubsingleton
sum_subtype_eq_sum_filter πŸ“–mathematicalβ€”sum
subtype
filter
β€”sum_map
sum_congr
subtype_map
sum_subtype_map_embedding πŸ“–mathematicalβ€”sum
map
Function.Embedding.subtype
β€”sum_map
sum_congr
sum_subtype_of_mem πŸ“–mathematicalβ€”sum
subtype
β€”sum_subtype_eq_sum_filter
filter_true_of_mem
sum_sumElim πŸ“–mathematicalβ€”sum
disjSum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_disjSum
sum_congr
sum_sum_eq_sum_toLeft_add_sum_toRight πŸ“–mathematicalβ€”sum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
toLeft
toRight
β€”toLeft_disjSum_toRight
sum_disjSum
toLeft_disjSum
toRight_disjSum
sum_tsub_distrib πŸ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
sumβ€”Multiset.sum_map_tsub
sum_union πŸ“–mathematicalDisjoint
Finset
partialOrder
instOrderBot
sum
instUnion
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”sum_union_inter
disjoint_iff_inter_eq_empty
add_zero
sum_union_eq_left πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Finset
instUnion
β€”sum_subset
subset_union_left
mem_union
sum_union_eq_right πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Finset
instUnion
β€”union_comm
sum_union_eq_left
sum_union_inter πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
sum
Finset
instUnion
instInter
β€”fold_union_inter
AddCommMagma.to_isCommutative
AddSemigroup.to_isAssociative
sum_unique_nonempty πŸ“–mathematicalNonemptysum
Unique.instInhabited
β€”Nonempty.eq_singleton_default
sum_singleton

Fintype

Theorems

NameKindAssumesProvesValidatesDepends On
prod_Prop πŸ“–mathematicalβ€”Finset.prod
Finset.univ
Prop.fintype
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Finset.prod_congr
univ_Prop
Finset.prod_insert
Finset.prod_singleton
prod_fiberwise πŸ“–mathematicalβ€”Finset.prod
Finset.univ
Subtype.fintype
β€”Finset.prod_fiberwise
Finset.prod_subtype
prod_fiberwise' πŸ“–mathematicalβ€”Finset.prod
Finset.univ
Subtype.fintype
β€”Finset.prod_fiberwise'
Finset.prod_subtype
prod_of_injective πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod
Finset.univ
β€”Finset.prod_of_injOn
Function.Injective.injOn
Finset.coe_univ
Set.image_univ
prod_subset πŸ“–mathematicalFinset
Finset.instMembership
Finset.prod
Finset.univ
β€”Finset.prod_subset
Finset.subset_univ
not_imp_comm
prod_subsingleton πŸ“–mathematicalβ€”Finset.prod
Finset.univ
β€”prod_unique
prod_subtype_mul_prod_subtype πŸ“–mathematicalβ€”MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod
Finset.univ
Subtype.fintype
β€”Finset.prod_subtype
Set.toFinset_setOf
Finset.compl_filter
Finset.prod_mul_prod_compl
prod_unique πŸ“–mathematicalβ€”Finset.prod
Finset.univ
Unique.instInhabited
β€”Finset.univ_unique
Finset.prod_singleton
sum_Prop πŸ“–mathematicalβ€”Finset.sum
Finset.univ
Prop.fintype
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Finset.sum_congr
univ_Prop
Finset.sum_insert
Finset.mem_singleton
Finset.sum_singleton
sum_fiberwise πŸ“–mathematicalβ€”Finset.sum
Finset.univ
Subtype.fintype
β€”Finset.sum_fiberwise
Finset.sum_subtype
Finset.mem_filter
Finset.mem_univ
sum_fiberwise' πŸ“–mathematicalβ€”Finset.sum
Finset.univ
Subtype.fintype
β€”Finset.sum_fiberwise'
Finset.sum_subtype
Finset.mem_filter
Finset.mem_univ
sum_of_injective πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum
Finset.univ
β€”Finset.sum_of_injOn
Function.Injective.injOn
Finset.coe_univ
Set.mapsTo_univ_iff
Set.mem_univ
Finset.mem_univ
Set.image_univ
Set.mem_range
sum_subset πŸ“–mathematicalFinset
Finset.instMembership
Finset.sum
Finset.univ
β€”Finset.sum_subset
Finset.subset_univ
Finset.mem_univ
not_imp_comm
sum_subsingleton πŸ“–mathematicalβ€”Finset.sum
Finset.univ
β€”sum_unique
sum_subtype_add_sum_subtype πŸ“–mathematicalβ€”AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum
Finset.univ
Subtype.fintype
β€”Finset.sum_subtype
Set.toFinset_setOf
Finset.mem_filter
Finset.mem_univ
Finset.compl_filter
Finset.sum_add_sum_compl
sum_unique πŸ“–mathematicalβ€”Finset.sum
Finset.univ
Unique.instInhabited
β€”Finset.univ_unique
Finset.sum_singleton

IsAddUnit

Theorems

NameKindAssumesProvesValidatesDepends On
sum_iff πŸ“–mathematicalβ€”IsAddUnit
AddCommMonoid.toAddMonoid
Finset.sum
β€”Finset.cons_induction
sum_univ_iff πŸ“–mathematicalβ€”IsAddUnit
AddCommMonoid.toAddMonoid
Finset.sum
Finset.univ
β€”sum_iff
Finset.mem_univ

IsCompl

Theorems

NameKindAssumesProvesValidatesDepends On
prod_mul_prod πŸ“–mathematicalIsCompl
Finset
Finset.partialOrder
Finset.boundedOrder
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod
Finset.univ
β€”disjoint
Finset.prod_disjUnion
Finset.disjUnion_eq_union
Finset.sup_eq_union
sup_eq_top
sum_add_sum πŸ“–mathematicalIsCompl
Finset
Finset.partialOrder
Finset.boundedOrder
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum
Finset.univ
β€”disjoint
Finset.sum_disjUnion
Finset.disjUnion_eq_union
Finset.sup_eq_union
sup_eq_top

IsUnit

Theorems

NameKindAssumesProvesValidatesDepends On
prod_iff πŸ“–mathematicalβ€”IsUnit
CommMonoid.toMonoid
Finset.prod
β€”Finset.cons_induction
prod_univ_iff πŸ“–mathematicalβ€”IsUnit
CommMonoid.toMonoid
Finset.prod
Finset.univ
β€”β€”

List

Theorems

NameKindAssumesProvesValidatesDepends On
prod_toFinset πŸ“–mathematicalβ€”Finset.prod
toFinset
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toOne
β€”Finset.prod_congr
toFinset_cons
Finset.prod_insert
mem_toFinset
sum_toFinset πŸ“–mathematicalβ€”Finset.sum
toFinset
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toZero
β€”Finset.sum_congr
toFinset_cons
Finset.sum_insert
mem_toFinset
sum_toFinset_count_eq_length πŸ“–mathematicalβ€”Finset.sum
Nat.instAddCommMonoid
toFinset
β€”Finset.sum_congr
mul_one
sum_replicate
Finset.sum_list_map_count

Multiset

Theorems

NameKindAssumesProvesValidatesDepends On
exists_smul_of_dvd_count πŸ“–mathematicalcountMultiset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
β€”Finset.sum_congr
mul_nsmul'
mem_toFinset
Finset.sum_nsmul
toFinset_sum_count_nsmul_eq
mem_sum πŸ“–mathematicalβ€”Multiset
instMembership
Finset.sum
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
Finset
Finset.instMembership
β€”Finset.cons_induction
prod_map_prod πŸ“–mathematicalβ€”prod
map
Finset.prod
β€”Finset.induction
map_congr
map_const'
prod_replicate
one_pow
Finset.prod_insert
prod_map_mul
prod_sum πŸ“–mathematicalβ€”prod
Finset.sum
Multiset
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
Finset.prod
β€”Finset.cons_induction
sum_count_eq_card πŸ“–mathematicalFinset
Finset.instMembership
Finset.sum
Nat.instAddCommMonoid
count
card
β€”toFinset_sum_count_eq
Finset.sum_filter_ne_zero
Finset.ext
Finset.filter.congr_simp
sum_map_sum πŸ“–mathematicalβ€”sum
map
Finset.sum
β€”Finset.induction
map_congr
map_const'
sum_replicate
nsmul_zero
Finset.sum_insert
sum_map_add
sum_sum πŸ“–mathematicalβ€”sum
Finset.sum
Multiset
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
β€”Finset.cons_induction
toFinset_sum_count_eq πŸ“–mathematicalβ€”Finset.sum
Nat.instAddCommMonoid
toFinset
count
card
β€”Finset.sum_congr
mul_one
map_const'
sum_replicate
Finset.sum_multiset_map_count
toFinset_sum_count_nsmul_eq πŸ“–mathematicalβ€”Finset.sum
Multiset
AddCancelCommMonoid.toAddCommMonoid
instAddCancelCommMonoid
toFinset
AddMonoid.toNatSMul
AddCommMonoid.toAddMonoid
count
instSingleton
β€”Finset.sum_multiset_map_count
sum_map_singleton

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
nat_abs_sum_le πŸ“–mathematicalβ€”Finset.sum
Int.instAddCommMonoid
Nat.instAddCommMonoid
β€”Finset.cons_induction

---

← Back to Index