Documentation Verification Report

Group

πŸ“ Source: Mathlib/Topology/Algebra/InfiniteSum/Group.lean

Statistics

MetricCount
Definitions0
TheoremshasProd_compl_iff, hasProd_iff_compl, hasSum_compl_iff, hasSum_iff_compl, multipliable_compl_iff, summable_compl_iff, congr_cofiniteβ‚€, div, hasProd_compl_iff, hasProd_iff_compl, inv, update, hasSum_compl_iff, hasSum_iff_compl, neg, sub, update, comp_injective, congr_atTop, congr_cofinite, congr_cofiniteβ‚€, countable_mulSupport, div, finite_mulSupport_of_discreteTopology, inv, mulIndicator, multipliable_compl_iff, multipliable_of_eq_one_or_self, of_inv, prod_mul_tprod_compl, prod_mul_tprod_subtype_compl, subtype, tendsto_cofinite_one, tprod_div, tprod_eq_mul_tprod_ite, tprod_subtype_mul_tprod_subtype_compl, tprod_vanishing, trans_div, tsum_congr_cofiniteβ‚€, update, vanishing, multipliable_compl_iff, summable_compl_iff, comp_injective, congr_atTop, congr_cofinite, countable_support, finite_support_of_discreteTopology, indicator, neg, of_neg, sub, subtype, sum_add_tsum_compl, sum_add_tsum_subtype_compl, summable_compl_iff, summable_of_eq_zero_or_self, tendsto_cofinite_zero, trans_sub, tsum_eq_add_tsum_ite, tsum_sub, tsum_subtype_add_tsum_subtype_compl, tsum_vanishing, update, vanishing, cauchySeq_finset_iff_prod_vanishing, cauchySeq_finset_iff_sum_vanishing, cauchySeq_finset_iff_tprod_vanishing, cauchySeq_finset_iff_tsum_vanishing, hasProd_ite_div_hasProd, hasSum_ite_sub_hasSum, multipliable_congr_atTop, multipliable_congr_cofinite, multipliable_const_iff, multipliable_iff_cauchySeq_finset, multipliable_iff_of_multipliable_div, multipliable_iff_tprod_vanishing, multipliable_iff_vanishing, multipliable_inv_iff, multipliable_subtype_and_compl, summable_congr_atTop, summable_congr_cofinite, summable_const_iff, summable_iff_cauchySeq_finset, summable_iff_of_summable_sub, summable_iff_tsum_vanishing, summable_iff_vanishing, summable_neg_iff, summable_subtype_and_compl, tendsto_tprod_compl_atTop_one, tendsto_tsum_compl_atTop_zero, tprod_const, tprod_inv, tsum_const, tsum_neg
95
Total95

Finset

Theorems

NameKindAssumesProvesValidatesDepends On
hasProd_compl_iff πŸ“–mathematicalβ€”HasProd
Finset
instMembership
CommGroup.toCommMonoid
SummationFilter.unconditional
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
prod
β€”HasProd.hasProd_compl_iff
hasProd
SummationFilter.instLeAtTopUnconditional
mul_comm
hasProd_iff_compl πŸ“–mathematicalβ€”HasProd
CommGroup.toCommMonoid
SummationFilter.unconditional
Finset
instMembership
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
prod
β€”HasProd.hasProd_iff_compl
hasProd
SummationFilter.instLeAtTopUnconditional
hasSum_compl_iff πŸ“–mathematicalβ€”HasSum
Finset
instMembership
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sum
β€”HasSum.hasSum_compl_iff
hasSum
SummationFilter.instLeAtTopUnconditional
add_comm
hasSum_iff_compl πŸ“–mathematicalβ€”HasSum
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Finset
instMembership
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sum
β€”HasSum.hasSum_iff_compl
hasSum
SummationFilter.instLeAtTopUnconditional
multipliable_compl_iff πŸ“–mathematicalβ€”Multipliable
Finset
instMembership
CommGroup.toCommMonoid
SummationFilter.unconditional
β€”Multipliable.multipliable_compl_iff
multipliable
summable_compl_iff πŸ“–mathematicalβ€”Summable
Finset
instMembership
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
β€”Summable.summable_compl_iff
summable

HasProd

Theorems

NameKindAssumesProvesValidatesDepends On
congr_cofiniteβ‚€ πŸ“–mathematicalHasProd
CommMonoidWithZero.toCommMonoid
CommGroupWithZero.toCommMonoidWithZero
SummationFilter.unconditional
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
Finset.prod
β€”Filter.Tendsto.congr'
Filter.mp_mem
Filter.eventually_ge_atTop
Filter.univ_mem'
Finset.union_sdiff_of_subset
Finset.prod_union
Finset.disjoint_sdiff
Finset.prod_congr
Finset.mem_sdiff
mul_div_assoc
div_mul_eq_mul_div
div_self
Finset.prod_ne_zero_iff
GroupWithZero.toNontrivial
GroupWithZero.noZeroDivisors
one_mul
mul_comm
Filter.Tendsto.mul_const
div πŸ“–mathematicalHasProd
CommGroup.toCommMonoid
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”div_eq_mul_inv
mul
IsTopologicalGroup.toContinuousMul
inv
hasProd_compl_iff πŸ“–mathematicalHasProd
Set.Elem
CommGroup.toCommMonoid
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
β€”mul_compl
IsTopologicalGroup.toContinuousMul
hasProd_subtype_iff_mulIndicator
Set.mulIndicator_compl
div_eq_mul_inv
mul_inv_cancel_comm
div
hasProd_iff_compl πŸ“–mathematicalHasProd
Set.Elem
CommGroup.toCommMonoid
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”hasProd_compl_iff
mul_div_cancel
inv πŸ“–mathematicalHasProd
CommGroup.toCommMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”map
MonoidHom.instMonoidHomClass
ContinuousInv.continuous_inv
IsTopologicalGroup.toContinuousInv
update πŸ“–mathematicalHasProd
CommGroup.toCommMonoid
Function.update
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
DivInvMonoid.toDiv
β€”Function.update_self
div_mul_cancel
Function.update_of_ne
one_mul
mul
IsTopologicalGroup.toContinuousMul
hasProd_ite_eq

HasSum

Theorems

NameKindAssumesProvesValidatesDepends On
hasSum_compl_iff πŸ“–mathematicalHasSum
Set.Elem
AddCommGroup.toAddCommMonoid
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”add_compl
IsTopologicalAddGroup.toContinuousAdd
hasSum_subtype_iff_indicator
Set.indicator_compl'
sub_eq_add_neg
add_neg_cancel_comm
sub
hasSum_iff_compl πŸ“–mathematicalHasSum
Set.Elem
AddCommGroup.toAddCommMonoid
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”hasSum_compl_iff
add_sub_cancel
neg πŸ“–mathematicalHasSum
AddCommGroup.toAddCommMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”map
AddMonoidHom.instAddMonoidHomClass
ContinuousNeg.continuous_neg
IsTopologicalAddGroup.toContinuousNeg
sub πŸ“–mathematicalHasSum
AddCommGroup.toAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”sub_eq_add_neg
add
IsTopologicalAddGroup.toContinuousAdd
neg
update πŸ“–mathematicalHasSum
AddCommGroup.toAddCommMonoid
Function.update
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
SubNegMonoid.toSub
β€”Function.update_self
sub_add_cancel
Function.update_of_ne
zero_add
add
IsTopologicalAddGroup.toContinuousAdd
hasSum_ite_eq

Multipliable

Theorems

NameKindAssumesProvesValidatesDepends On
comp_injective πŸ“–β€”Multipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
β€”β€”Set.mulIndicator_range_comp
Function.Injective.multipliable_iff
Set.mulIndicator_of_notMem
mulIndicator
congr_atTop πŸ“–β€”Multipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
Filter.EventuallyEq
Filter.atTop
Nat.instPreorder
β€”β€”congr_cofinite
Nat.cofinite_eq_atTop
congr_cofinite πŸ“–β€”Multipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
β€”β€”Set.Finite.multipliable_compl_iff
congr
compl_compl
congr_cofiniteβ‚€ πŸ“–β€”Multipliable
CommMonoidWithZero.toCommMonoid
CommGroupWithZero.toCommMonoidWithZero
SummationFilter.unconditional
β€”β€”HasProd.multipliable
HasProd.congr_cofiniteβ‚€
countable_mulSupport πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
Set.Countable
Function.mulSupport
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”ker_nhds
Filter.Tendsto.countable_compl_preimage_ker
FirstCountableTopology.nhds_generated_countable
tendsto_cofinite_one
div πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”HasProd.multipliable
HasProd.div
hasProd
finite_mulSupport_of_discreteTopology πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
Set.Finite
Function.mulSupport
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”tendsto_cofinite_one
IsTopologicalGroup.toContinuousMul
topologicalGroup_of_discreteTopology
IsTopologicalGroup.toContinuousInv
discreteTopology_iff_singleton_mem_nhds
inv πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”HasProd.multipliable
HasProd.inv
hasProd
mulIndicator πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set.mulIndicator
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”multipliable_of_eq_one_or_self
Set.mulIndicator_eq_one_or_self
multipliable_compl_iff πŸ“–mathematicalMultipliable
Set.Elem
CommGroup.toCommMonoid
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
β€”HasProd.multipliable
HasProd.hasProd_compl_iff
hasProd
HasProd.hasProd_iff_compl
multipliable_of_eq_one_or_self πŸ“–β€”Multipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”β€”multipliable_iff_vanishing
Finset.prod_congr
Finset.mem_filter
Finset.prod_subset
Finset.filter_subset
Finset.disjoint_of_subset_left
of_inv πŸ“–β€”Multipliable
CommGroup.toCommMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”β€”inv_inv
inv
prod_mul_tprod_compl πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
Finset.prod
tprod
Set.Elem
Compl.compl
Set
Set.instCompl
SetLike.coe
Finset
Finset.instSetLike
Set.instMembership
β€”HasProd.tprod_eq
SummationFilter.instNeBotUnconditional
HasProd.mul_compl
IsTopologicalGroup.toContinuousMul
Finset.hasProd
SummationFilter.instLeAtTopUnconditional
hasProd
Finset.multipliable_compl_iff
prod_mul_tprod_subtype_compl πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
Finset.prod
tprod
Finset
Finset.instMembership
β€”tprod_subtype_mul_tprod_subtype_compl
Finset.tprod_subtype'
LeftCancelSemigroup.toIsLeftCancelMul
subtype πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set.Elem
Set
Set.instMembership
β€”comp_injective
Subtype.coe_injective
tendsto_cofinite_one πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
Filter.Tendsto
Filter.cofinite
nhds
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Filter.mem_map
vanishing
Filter.Eventually.mono
Finset.eventually_cofinite_notMem
Finset.prod_singleton
Finset.disjoint_singleton_left
tprod_div πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
tprod
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”HasProd.tprod_eq
HasProd.div
hasProd
tprod_eq_mul_tprod_ite πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
tprod
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”HasProd.tprod_eq
SummationFilter.instNeBotUnconditional
hasProd_ite_div_hasProd
SummationFilter.instLeAtTopUnconditional
hasProd
mul_div_cancel
tprod_subtype_mul_tprod_subtype_compl πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
tprod
Set.Elem
Set
Set.instMembership
Compl.compl
Set.instCompl
β€”HasProd.unique
SummationFilter.instNeBotUnconditional
HasProd.mul_compl
IsTopologicalGroup.toContinuousMul
IsUniformGroup.to_topologicalGroup
hasProd
subtype
tprod_vanishing πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
Set
Filter
Filter.instMembership
nhds
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
Set.instMembership
tprod
Set.Elem
β€”isUniformGroup_of_commGroup
cauchySeq_finset_iff_tprod_vanishing
Filter.Tendsto.cauchySeq
hasProd
trans_div πŸ“–β€”Multipliable
CommGroup.toCommMonoid
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”β€”div_mul_cancel
mul
IsTopologicalGroup.toContinuousMul
tsum_congr_cofiniteβ‚€ πŸ“–mathematicalMultipliable
CommMonoidWithZero.toCommMonoid
CommGroupWithZero.toCommMonoidWithZero
SummationFilter.unconditional
tprod
MulZeroClass.toMul
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
GroupWithZero.toMonoidWithZero
CommGroupWithZero.toGroupWithZero
DivInvMonoid.toDiv
GroupWithZero.toDivInvMonoid
Finset.prod
β€”HasProd.tprod_eq
SummationFilter.instNeBotUnconditional
HasProd.congr_cofiniteβ‚€
hasProd
update πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
Function.updateβ€”HasProd.multipliable
HasProd.update
hasProd
vanishing πŸ“–mathematicalMultipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
Set
Filter
Filter.instMembership
nhds
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
Set.instMembership
Finset.prod
β€”isUniformGroup_of_commGroup
cauchySeq_finset_iff_prod_vanishing
Filter.Tendsto.cauchySeq
hasProd

Set.Finite

Theorems

NameKindAssumesProvesValidatesDepends On
multipliable_compl_iff πŸ“–mathematicalβ€”Multipliable
Set.Elem
Compl.compl
Set
Set.instCompl
CommGroup.toCommMonoid
Set.instMembership
SummationFilter.unconditional
β€”Multipliable.multipliable_compl_iff
multipliable
summable_compl_iff πŸ“–mathematicalβ€”Summable
Set.Elem
Compl.compl
Set
Set.instCompl
AddCommGroup.toAddCommMonoid
Set.instMembership
SummationFilter.unconditional
β€”Summable.summable_compl_iff
summable

Summable

Theorems

NameKindAssumesProvesValidatesDepends On
comp_injective πŸ“–β€”Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
β€”β€”Set.indicator_range_comp
Function.Injective.summable_iff
Set.indicator_of_notMem
indicator
congr_atTop πŸ“–β€”Summable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Filter.EventuallyEq
Filter.atTop
Nat.instPreorder
β€”β€”congr_cofinite
Nat.cofinite_eq_atTop
congr_cofinite πŸ“–β€”Summable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
β€”β€”Set.Finite.summable_compl_iff
congr
compl_compl
countable_support πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Set.Countable
Function.support
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”ker_nhds
Filter.Tendsto.countable_compl_preimage_ker
FirstCountableTopology.nhds_generated_countable
tendsto_cofinite_zero
finite_support_of_discreteTopology πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Set.Finite
Function.support
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”tendsto_cofinite_zero
IsTopologicalAddGroup.toContinuousAdd
topologicalAddGroup_of_discreteTopology
IsTopologicalAddGroup.toContinuousNeg
discreteTopology_iff_singleton_mem_nhds
indicator πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set.indicator
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”summable_of_eq_zero_or_self
Set.indicator_eq_zero_or_self
neg πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”HasSum.summable
HasSum.neg
hasSum
of_neg πŸ“–β€”Summable
AddCommGroup.toAddCommMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”β€”neg_neg
neg
sub πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”HasSum.summable
HasSum.sub
hasSum
subtype πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set.Elem
Set
Set.instMembership
β€”comp_injective
Subtype.coe_injective
sum_add_tsum_compl πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
Finset.sum
tsum
Set.Elem
Compl.compl
Set
Set.instCompl
SetLike.coe
Finset
Finset.instSetLike
Set.instMembership
β€”HasSum.tsum_eq
SummationFilter.instNeBotUnconditional
HasSum.add_compl
IsTopologicalAddGroup.toContinuousAdd
Finset.hasSum
SummationFilter.instLeAtTopUnconditional
hasSum
Finset.summable_compl_iff
sum_add_tsum_subtype_compl πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
Finset.sum
tsum
Finset
Finset.instMembership
β€”tsum_subtype_add_tsum_subtype_compl
Finset.tsum_subtype'
AddLeftCancelSemigroup.toIsLeftCancelAdd
summable_compl_iff πŸ“–mathematicalSummable
Set.Elem
AddCommGroup.toAddCommMonoid
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
β€”HasSum.summable
HasSum.hasSum_compl_iff
hasSum
HasSum.hasSum_iff_compl
summable_of_eq_zero_or_self πŸ“–β€”Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”β€”summable_iff_vanishing
Finset.sum_congr
Finset.mem_filter
Finset.sum_subset
Finset.filter_subset
Finset.disjoint_of_subset_left
tendsto_cofinite_zero πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Filter.Tendsto
Filter.cofinite
nhds
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Filter.mem_map
vanishing
Filter.Eventually.mono
Finset.eventually_cofinite_notMem
Finset.sum_singleton
Finset.disjoint_singleton_left
trans_sub πŸ“–β€”Summable
AddCommGroup.toAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”β€”sub_add_cancel
add
IsTopologicalAddGroup.toContinuousAdd
tsum_eq_add_tsum_ite πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
tsum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”HasSum.tsum_eq
SummationFilter.instNeBotUnconditional
hasSum_ite_sub_hasSum
SummationFilter.instLeAtTopUnconditional
hasSum
add_sub_cancel
tsum_sub πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
tsum
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”HasSum.tsum_eq
HasSum.sub
hasSum
tsum_subtype_add_tsum_subtype_compl πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
tsum
Set.Elem
Set
Set.instMembership
Compl.compl
Set.instCompl
β€”HasSum.unique
SummationFilter.instNeBotUnconditional
HasSum.add_compl
IsTopologicalAddGroup.toContinuousAdd
IsUniformAddGroup.to_topologicalAddGroup
hasSum
subtype
tsum_vanishing πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Set
Filter
Filter.instMembership
nhds
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Set.instMembership
tsum
Set.Elem
β€”isUniformAddGroup_of_addCommGroup
cauchySeq_finset_iff_tsum_vanishing
Filter.Tendsto.cauchySeq
hasSum
update πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
Function.updateβ€”HasSum.summable
HasSum.update
hasSum
vanishing πŸ“–mathematicalSummable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Set
Filter
Filter.instMembership
nhds
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Set.instMembership
Finset.sum
β€”isUniformAddGroup_of_addCommGroup
cauchySeq_finset_iff_sum_vanishing
Filter.Tendsto.cauchySeq
hasSum

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
cauchySeq_finset_iff_prod_vanishing πŸ“–mathematicalβ€”CauchySeq
Finset
PartialOrder.toPreorder
Finset.partialOrder
Finset.prod
CommGroup.toCommMonoid
Set
Set.instMembership
β€”Finset.isDirected_le
Filter.prod_atTop_atTop_eq
uniformity_eq_comap_nhds_one
IsUniformGroup.isRightUniformGroup
Filter.tendsto_atTop'
SemilatticeSup.instIsDirectedOrder
Finset.prod_union
Disjoint.symm
mul_div_cancel_left
le_sup_left
le_sup_of_le_left
le_sup_right
exists_nhds_split_inv
IsUniformGroup.to_topologicalGroup
Finset.prod_sdiff
mul_div_mul_right_eq_div
Finset.sdiff_disjoint
cauchySeq_finset_iff_sum_vanishing πŸ“–mathematicalβ€”CauchySeq
Finset
PartialOrder.toPreorder
Finset.partialOrder
Finset.sum
AddCommGroup.toAddCommMonoid
Set
Set.instMembership
β€”cauchy_map_iff
Filter.atTop_neBot
Finset.isDirected_le
Filter.prod_atTop_atTop_eq
uniformity_eq_comap_nhds_zero
IsUniformAddGroup.isRightUniformAddGroup
Filter.tendsto_comap_iff
Filter.tendsto_atTop'
SemilatticeSup.instIsDirectedOrder
Finset.sum_union
Disjoint.symm
add_sub_cancel_left
le_sup_left
le_sup_of_le_left
le_sup_right
exists_nhds_half_neg
IsUniformAddGroup.to_topologicalAddGroup
Finset.sum_sdiff
add_sub_add_right_eq_sub
Finset.sdiff_disjoint
cauchySeq_finset_iff_tprod_vanishing πŸ“–mathematicalβ€”CauchySeq
Finset
PartialOrder.toPreorder
Finset.partialOrder
Finset.prod
CommGroup.toCommMonoid
Set
Set.instMembership
tprod
Set.Elem
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
β€”exists_mem_nhds_isClosed_subset
IsTopologicalGroup.regularSpace
IsUniformGroup.to_topologicalGroup
IsClosed.mem_of_tendsto
SummationFilter.instNeBotFinsetFilterOfNeBot
SummationFilter.instNeBotUnconditional
Multipliable.hasProd
Filter.Eventually.of_forall
Finset.prod_subtype_map_embedding
Subtype.prop
mem_of_mem_nhds
tprod_eq_one_of_not_multipliable
Finset.tprod_subtype
cauchySeq_finset_iff_tsum_vanishing πŸ“–mathematicalβ€”CauchySeq
Finset
PartialOrder.toPreorder
Finset.partialOrder
Finset.sum
AddCommGroup.toAddCommMonoid
Set
Set.instMembership
tsum
Set.Elem
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
β€”cauchySeq_finset_iff_sum_vanishing
Set.disjoint_left
Finset.disjoint_left
exists_mem_nhds_isClosed_subset
IsTopologicalAddGroup.regularSpace
IsUniformAddGroup.to_topologicalAddGroup
IsClosed.mem_of_tendsto
SummationFilter.instNeBotFinsetFilterOfNeBot
SummationFilter.instNeBotUnconditional
Summable.hasSum
Filter.Eventually.of_forall
Finset.sum_subtype_map_embedding
Finset.mem_map
Subtype.prop
mem_of_mem_nhds
tsum_eq_zero_of_not_summable
Finset.tsum_subtype
hasProd_ite_div_hasProd πŸ“–mathematicalHasProd
CommGroup.toCommMonoid
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”Function.update_apply
div_mul_eq_mul_div
one_mul
HasProd.update
hasSum_ite_sub_hasSum πŸ“–mathematicalHasSum
AddCommGroup.toAddCommMonoid
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”Function.update_apply
sub_add_eq_add_sub
zero_add
HasSum.update
multipliable_congr_atTop πŸ“–mathematicalFilter.EventuallyEq
Filter.atTop
Nat.instPreorder
Multipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
β€”multipliable_congr_cofinite
Nat.cofinite_eq_atTop
multipliable_congr_cofinite πŸ“–mathematicalβ€”Multipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
β€”Multipliable.congr_cofinite
Filter.Eventually.mono
multipliable_const_iff πŸ“–mathematicalβ€”Multipliable
CommGroup.toCommMonoid
SummationFilter.unconditional
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”compl_singleton_mem_nhds
T2Space.t1Space
Set.preimage_const_of_mem
Set.compl_univ
Filter.cofinite_neBot
Multipliable.tendsto_cofinite_one
not_finite
multipliable_one
multipliable_iff_cauchySeq_finset πŸ“–mathematicalβ€”Multipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
CauchySeq
Finset
PartialOrder.toPreorder
Finset.partialOrder
Finset.prod
β€”cauchy_map_iff_exists_tendsto
SummationFilter.instNeBotFinsetFilterOfNeBot
SummationFilter.instNeBotUnconditional
multipliable_iff_of_multipliable_div πŸ“–β€”Multipliable
CommGroup.toCommMonoid
DivInvMonoid.toDiv
Group.toDivInvMonoid
CommGroup.toGroup
β€”β€”Multipliable.trans_div
inv_div
Multipliable.inv
multipliable_iff_tprod_vanishing πŸ“–mathematicalβ€”Multipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set
Set.instMembership
tprod
Set.Elem
β€”multipliable_iff_cauchySeq_finset
cauchySeq_finset_iff_tprod_vanishing
multipliable_iff_vanishing πŸ“–mathematicalβ€”Multipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set
Set.instMembership
Finset.prod
β€”multipliable_iff_cauchySeq_finset
cauchySeq_finset_iff_prod_vanishing
multipliable_inv_iff πŸ“–mathematicalβ€”Multipliable
CommGroup.toCommMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Multipliable.of_inv
Multipliable.inv
multipliable_subtype_and_compl πŸ“–mathematicalβ€”Multipliable
Set.Elem
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
β€”Multipliable.mul_compl
IsTopologicalGroup.toContinuousMul
IsUniformGroup.to_topologicalGroup
Multipliable.subtype
summable_congr_atTop πŸ“–mathematicalFilter.EventuallyEq
Filter.atTop
Nat.instPreorder
Summable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
β€”summable_congr_cofinite
Nat.cofinite_eq_atTop
summable_congr_cofinite πŸ“–mathematicalβ€”Summable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
β€”Summable.congr_cofinite
Filter.Eventually.mono
summable_const_iff πŸ“–mathematicalβ€”Summable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”compl_singleton_mem_nhds
T2Space.t1Space
Set.finite_univ_iff
Filter.mem_map
Set.preimage_const_of_mem
Set.mem_singleton_iff
Set.compl_univ
Filter.empty_notMem
Filter.cofinite_neBot
Summable.tendsto_cofinite_zero
not_finite
summable_zero
summable_iff_cauchySeq_finset πŸ“–mathematicalβ€”Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
CauchySeq
Finset
PartialOrder.toPreorder
Finset.partialOrder
Finset.sum
β€”cauchy_map_iff_exists_tendsto
SummationFilter.instNeBotFinsetFilterOfNeBot
SummationFilter.instNeBotUnconditional
summable_iff_of_summable_sub πŸ“–β€”Summable
AddCommGroup.toAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
β€”β€”Summable.trans_sub
neg_sub
Summable.neg
summable_iff_tsum_vanishing πŸ“–mathematicalβ€”Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set
Set.instMembership
tsum
Set.Elem
β€”summable_iff_cauchySeq_finset
cauchySeq_finset_iff_tsum_vanishing
summable_iff_vanishing πŸ“–mathematicalβ€”Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
Set
Set.instMembership
Finset.sum
β€”summable_iff_cauchySeq_finset
cauchySeq_finset_iff_sum_vanishing
summable_neg_iff πŸ“–mathematicalβ€”Summable
AddCommGroup.toAddCommMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Summable.of_neg
Summable.neg
summable_subtype_and_compl πŸ“–mathematicalβ€”Summable
Set.Elem
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
β€”Summable.add_compl
IsTopologicalAddGroup.toContinuousAdd
IsUniformAddGroup.to_topologicalAddGroup
Summable.subtype
tendsto_tprod_compl_atTop_one πŸ“–mathematicalβ€”Filter.Tendsto
Finset
tprod
Finset.instMembership
CommGroup.toCommMonoid
SummationFilter.unconditional
Filter.atTop
PartialOrder.toPreorder
Finset.partialOrder
nhds
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Multipliable.tprod_vanishing
Filter.mem_map
Filter.mem_atTop_sets
Finset.isDirected_le
Set.disjoint_left
Filter.Tendsto.congr
tprod_eq_one_of_not_multipliable
Finset.multipliable_compl_iff
tendsto_const_nhds
tendsto_tsum_compl_atTop_zero πŸ“–mathematicalβ€”Filter.Tendsto
Finset
tsum
Finset.instMembership
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Filter.atTop
PartialOrder.toPreorder
Finset.partialOrder
nhds
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Summable.tsum_vanishing
Filter.mem_map
Filter.mem_atTop_sets
Finset.isDirected_le
Set.disjoint_left
Filter.Tendsto.congr
tsum_eq_zero_of_not_summable
Finset.summable_compl_iff
tendsto_const_nhds
tprod_const πŸ“–mathematicalβ€”tprod
CommGroup.toCommMonoid
SummationFilter.unconditional
Monoid.toNatPow
DivInvMonoid.toMonoid
Group.toDivInvMonoid
CommGroup.toGroup
Nat.card
β€”finite_or_infinite
tprod_eq_prod
SummationFilter.instLeAtTopUnconditional
Finset.mem_univ
Finset.prod_const
Nat.card_eq_fintype_card
Nat.card_eq_zero_of_infinite
pow_zero
eq_or_ne
tprod_one
tprod_eq_one_of_not_multipliable
tprod_inv πŸ“–mathematicalβ€”tprod
CommGroup.toCommMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
β€”Topology.IsClosedEmbedding.map_tprod
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
Homeomorph.isClosedEmbedding
IsTopologicalGroup.toContinuousInv
tsum_const πŸ“–mathematicalβ€”tsum
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
Nat.card
β€”finite_or_infinite
tsum_eq_sum
SummationFilter.instLeAtTopUnconditional
Finset.mem_univ
Finset.sum_const
Nat.card_eq_fintype_card
Nat.card_eq_zero_of_infinite
zero_nsmul
eq_or_ne
tsum_zero
tsum_eq_zero_of_not_summable
summable_const_iff
tsum_neg πŸ“–mathematicalβ€”tsum
AddCommGroup.toAddCommMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
β€”Topology.IsClosedEmbedding.map_tsum
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
Homeomorph.isClosedEmbedding
IsTopologicalAddGroup.toContinuousNeg

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