Documentation Verification Report

Basic

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

Statistics

MetricCount
Definitions0
TheoremshasProd_iff, hasProd_iff_of_mulSupport, hasSum_iff, hasSum_iff_of_support, multipliable_iff, multipliable_iff_of_mulSupport, summable_iff, summable_iff_of_support, tprod_eq, tprod_eq_tprod_of_mulSupport, tsum_eq, tsum_eq_tsum_of_support, multipliable, summable, tprod_subtype, tprod_subtype', tsum_subtype, tsum_subtype', hasProd_range_iff, hasSum_range_iff, multipliable_iff, summable_iff, tprod_eq, tsum_eq, map_tprod, map_tsum, multipliable_iff_of_hasProd_iff, summable_iff_of_hasSum_iff, tprod_eq_tprod_of_hasProd_iff_hasProd, tsum_eq_tsum_of_hasSum_iff_hasSum, compl_mul, congr_fun, hasProd_of_prod_eq, map, mul, mul_compl, mul_disjoint, mul_isCompl, of_subsingleton_cod, update', add, add_compl, add_disjoint, add_isCompl, compl_add, congr_fun, hasSum_of_sum_eq, map, of_subsingleton_cod, update', compl_add, map, map_iff_of_equiv, map_iff_of_leftInverse, map_tprod, mul, mul_compl, of_finite, of_subsingleton_cod, tprod_eq_mul_tprod_ite', tprod_finsetProd, tprod_finset_bUnion_disjoint, tprod_mul, tprod_mul_tprod_compl, tprod_union_disjoint, multipliable, summable, add, add_compl, compl_add, map, map_iff_of_equiv, map_iff_of_leftInverse, map_tsum, of_finite, of_subsingleton_cod, tsum_add, tsum_add_tsum_compl, tsum_eq_add_tsum_ite', tsum_finsetSum, tsum_finset_bUnion_disjoint, tsum_union_disjoint, map_tprod, map_tsum, hasProd_iff, hasSum_iff, multipliable_iff_tprod_comp_mem_range, summable_iff_tsum_comp_mem_range, eq_add_of_hasSum_ite, eq_mul_of_hasProd_ite, hasProd_empty, hasProd_extend_one, hasProd_iff_hasProd, hasProd_iff_hasProd_of_ne_one_bij, hasProd_ite_eq, hasProd_one, hasProd_prod, hasProd_prod_disjoint, hasProd_single, hasProd_singleton, hasProd_subtype_iff_mulIndicator, hasProd_subtype_mulSupport, hasProd_unique, hasProd_zero_of_exists_eq_zero, hasSum_empty, hasSum_extend_zero, hasSum_iff_hasSum, hasSum_iff_hasSum_of_ne_zero_bij, hasSum_ite_eq, hasSum_single, hasSum_singleton, hasSum_subtype_iff_indicator, hasSum_subtype_support, hasSum_sum, hasSum_sum_disjoint, hasSum_unique, hasSum_zero, multipliable_congr, multipliable_empty, multipliable_extend_one, multipliable_of_exists_eq_zero, multipliable_of_finite_mulSupport, multipliable_one, multipliable_prod, multipliable_subtype_iff_mulIndicator, prod_eq_tprod_mulIndicator, sum_eq_tsum_indicator, summable_congr, summable_empty, summable_extend_zero, summable_of_finite_support, summable_subtype_iff_indicator, summable_sum, summable_zero, tprod_bool, tprod_comp_neg, tprod_congr, tprod_congr_set_coe, tprod_congr_subtype, tprod_congrβ‚‚, tprod_dite_left, tprod_dite_right, tprod_empty, tprod_eq_finprod, tprod_eq_mulSingle, tprod_eq_prod, tprod_eq_prod', tprod_eq_tprod_diff_singleton, tprod_eq_tprod_of_hasProd_iff_hasProd, tprod_eq_tprod_of_ne_one_bij, tprod_extend_one, tprod_fintype, tprod_image, tprod_ite_eq, tprod_of_exists_eq_zero, tprod_one, tprod_range, tprod_setElem_eq_tprod_setElem_diff, tprod_singleton, tprod_subtype, tprod_subtype_eq_of_mulSupport_subset, tprod_subtype_mulSupport, tprod_tprod_eq_mulSingle, tprod_univ, tsum_bool, tsum_comp_neg, tsum_congr, tsum_congr_set_coe, tsum_congr_subtype, tsum_congrβ‚‚, tsum_dite_left, tsum_dite_right, tsum_empty, tsum_eq_finsum, tsum_eq_single, tsum_eq_sum, tsum_eq_sum', tsum_eq_tsum_diff_singleton, tsum_eq_tsum_of_hasSum_iff_hasSum, tsum_eq_tsum_of_ne_zero_bij, tsum_extend_zero, tsum_fintype, tsum_image, tsum_ite_eq, tsum_range, tsum_setElem_eq_tsum_setElem_diff, tsum_singleton, tsum_subtype, tsum_subtype_eq_of_support_subset, tsum_subtype_support, tsum_tsum_eq_single, tsum_univ, tsum_zero
193
Total193

Equiv

Theorems

NameKindAssumesProvesValidatesDepends On
hasProd_iff πŸ“–mathematicalβ€”HasProd
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
SummationFilter.unconditional
β€”Function.Injective.hasProd_iff
injective
EquivLike.range_eq_univ
instIsEmptyFalse
hasProd_iff_of_mulSupport πŸ“–mathematicalSet
Set.instMembership
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
DFunLike.coe
Equiv
Set.Elem
EquivLike.toFunLike
instEquivLike
HasProd
SummationFilter.unconditional
β€”hasProd_subtype_mulSupport
hasProd_iff
hasSum_iff πŸ“–mathematicalβ€”HasSum
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
SummationFilter.unconditional
β€”Function.Injective.hasSum_iff
injective
EquivLike.range_eq_univ
Set.mem_univ
IsEmpty.forall_iff
instIsEmptyFalse
hasSum_iff_of_support πŸ“–mathematicalSet
Set.instMembership
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DFunLike.coe
Equiv
Set.Elem
EquivLike.toFunLike
instEquivLike
HasSum
SummationFilter.unconditional
β€”hasSum_subtype_support
hasSum_iff
multipliable_iff πŸ“–mathematicalβ€”Multipliable
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
SummationFilter.unconditional
β€”hasProd_iff
multipliable_iff_of_mulSupport πŸ“–mathematicalSet
Set.instMembership
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
DFunLike.coe
Equiv
Set.Elem
EquivLike.toFunLike
instEquivLike
Multipliable
SummationFilter.unconditional
β€”hasProd_iff_of_mulSupport
summable_iff πŸ“–mathematicalβ€”Summable
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
SummationFilter.unconditional
β€”hasSum_iff
summable_iff_of_support πŸ“–mathematicalSet
Set.instMembership
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DFunLike.coe
Equiv
Set.Elem
EquivLike.toFunLike
instEquivLike
Summable
SummationFilter.unconditional
β€”hasSum_iff_of_support
tprod_eq πŸ“–mathematicalβ€”tprod
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
SummationFilter.unconditional
β€”Function.Injective.tprod_eq
injective
EquivLike.range_eq_univ
tprod_eq_tprod_of_mulSupport πŸ“–mathematicalSet
Set.instMembership
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
DFunLike.coe
Equiv
Set.Elem
EquivLike.toFunLike
instEquivLike
tprod
SummationFilter.unconditional
β€”tprod_eq_tprod_of_ne_one_bij
Subtype.val_injective
injective
EquivLike.range_comp
Subtype.range_coe_subtype
tsum_eq πŸ“–mathematicalβ€”tsum
DFunLike.coe
Equiv
EquivLike.toFunLike
instEquivLike
SummationFilter.unconditional
β€”Function.Injective.tsum_eq
injective
EquivLike.range_eq_univ
Set.subset_univ
tsum_eq_tsum_of_support πŸ“–mathematicalSet
Set.instMembership
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DFunLike.coe
Equiv
Set.Elem
EquivLike.toFunLike
instEquivLike
tsum
SummationFilter.unconditional
β€”tsum_eq_tsum_of_ne_zero_bij
Subtype.val_injective
injective
EquivLike.range_comp
Subtype.range_coe_subtype
Function.mem_support
Function.support_subset_iff

Finset

Theorems

NameKindAssumesProvesValidatesDepends On
multipliable πŸ“–mathematicalβ€”Multipliable
Set.Elem
SetLike.coe
Finset
instSetLike
Set
Set.instMembership
SummationFilter.unconditional
β€”HasProd.multipliable
hasProd
SummationFilter.instLeAtTopUnconditional
summable πŸ“–mathematicalβ€”Summable
Set.Elem
SetLike.coe
Finset
instSetLike
Set
Set.instMembership
SummationFilter.unconditional
β€”HasSum.summable
hasSum
SummationFilter.instLeAtTopUnconditional
tprod_subtype πŸ“–mathematicalβ€”tprod
Finset
instMembership
SummationFilter.unconditional
prod
β€”prod_attach
tprod_fintype
SummationFilter.instLeAtTopUnconditional
tprod_subtype' πŸ“–mathematicalβ€”tprod
Set.Elem
SetLike.coe
Finset
instSetLike
Set
Set.instMembership
SummationFilter.unconditional
prod
β€”tprod_fintype
SummationFilter.instLeAtTopUnconditional
prod_attach
tsum_subtype πŸ“–mathematicalβ€”tsum
Finset
instMembership
SummationFilter.unconditional
sum
β€”sum_attach
tsum_fintype
SummationFilter.instLeAtTopUnconditional
tsum_subtype' πŸ“–mathematicalβ€”tsum
Set.Elem
SetLike.coe
Finset
instSetLike
Set
Set.instMembership
SummationFilter.unconditional
sum
β€”tsum_fintype
SummationFilter.instLeAtTopUnconditional
sum_attach

Function.Injective

Theorems

NameKindAssumesProvesValidatesDepends On
hasProd_range_iff πŸ“–mathematicalβ€”HasProd
Set.Elem
Set.range
Set
Set.instMembership
SummationFilter.unconditional
β€”Equiv.hasProd_iff
hasSum_range_iff πŸ“–mathematicalβ€”HasSum
Set.Elem
Set.range
Set
Set.instMembership
SummationFilter.unconditional
β€”Equiv.hasSum_iff
multipliable_iff πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Multipliable
SummationFilter.unconditional
β€”hasProd_iff
summable_iff πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Summable
SummationFilter.unconditional
β€”hasSum_iff
tprod_eq πŸ“–mathematicalSet
Set.instHasSubset
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Set.range
tprod
SummationFilter.unconditional
β€”Function.mulSupport_comp_eq_preimage
Set.image_preimage_eq_iff
Set.Finite.preimage
injOn
CanLift.prf
Function.instCanLiftForallEmbeddingCoeInjective
tprod_eq_prod'
Eq.ge
Set.Finite.coe_toFinset
SummationFilter.instLeAtTopUnconditional
Finset.prod_congr
Finset.coe_injective
Finset.coe_map
Set.Finite.toFinset.congr_simp
Set.finite_image_iff
tprod_def
SummationFilter.support_eq_univ
Set.inter_univ
SummationFilter.instHasSupportOfLeAtTop
hasProd_iff
Function.mulSupport_subset_iff'
tsum_eq πŸ“–mathematicalSet
Set.instHasSubset
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set.range
tsum
SummationFilter.unconditional
β€”Function.support_comp_eq_preimage
Set.image_preimage_eq_iff
Set.Finite.preimage
injOn
CanLift.prf
Function.instCanLiftForallEmbeddingCoeInjective
tsum_eq_sum'
Eq.ge
Set.Finite.coe_toFinset
SummationFilter.instLeAtTopUnconditional
Finset.sum_congr
Finset.sum_map
Finset.coe_injective
Finset.coe_map
Set.Finite.toFinset.congr_simp
Set.finite_image_iff
tsum_def
SummationFilter.support_eq_univ
Set.inter_univ
SummationFilter.instHasSupportOfLeAtTop
hasSum_iff
Function.support_subset_iff'

Function.LeftInverse

Theorems

NameKindAssumesProvesValidatesDepends On
map_tprod πŸ“–mathematicalContinuous
DFunLike.coe
tprodβ€”Topology.IsClosedEmbedding.map_tprod
isClosedEmbedding
map_tsum πŸ“–mathematicalContinuous
DFunLike.coe
tsumβ€”Topology.IsClosedEmbedding.map_tsum
isClosedEmbedding

Function.Surjective

Theorems

NameKindAssumesProvesValidatesDepends On
multipliable_iff_of_hasProd_iff πŸ“–mathematicalHasProd
SummationFilter.unconditional
Multipliableβ€”exists
summable_iff_of_hasSum_iff πŸ“–mathematicalHasSum
SummationFilter.unconditional
Summableβ€”exists
tprod_eq_tprod_of_hasProd_iff_hasProd πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
SummationFilter.unconditional
tprodβ€”by_cases
HasProd.tprod_eq
SummationFilter.instNeBotUnconditional
Multipliable.hasProd
multipliable_iff_of_hasProd_iff
tprod_def
tsum_eq_tsum_of_hasSum_iff_hasSum πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
SummationFilter.unconditional
tsumβ€”by_cases
HasSum.tsum_eq
SummationFilter.instNeBotUnconditional
Summable.hasSum
summable_iff_of_hasSum_iff
tsum_def

HasProd

Theorems

NameKindAssumesProvesValidatesDepends On
compl_mul πŸ“–mathematicalHasProd
Set.Elem
Compl.compl
Set
Set.instCompl
Set.instMembership
SummationFilter.unconditional
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”mul_isCompl
IsCompl.symm
isCompl_compl
congr_fun πŸ“–β€”HasProdβ€”β€”β€”
hasProd_of_prod_eq πŸ“–β€”Finset
Finset.instHasSubset
Finset.prod
HasProd
SummationFilter.unconditional
β€”β€”le_trans
Filter.map_atTop_finset_prod_le_of_prod_eq
map πŸ“–β€”HasProd
Continuous
DFunLike.coe
β€”β€”map_prod
Filter.Tendsto.comp
Continuous.tendsto
mul πŸ“–mathematicalHasProdMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Finset.prod_mul_distrib
Filter.Tendsto.mul
mul_compl πŸ“–mathematicalHasProd
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”mul_isCompl
isCompl_compl
mul_disjoint πŸ“–mathematicalDisjoint
Set
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
HasProd
Set.Elem
Set.instMembership
SummationFilter.unconditional
Set.instUnion
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”hasProd_subtype_iff_mulIndicator
Set.mulIndicator_union_of_disjoint
mul
mul_isCompl πŸ“–mathematicalIsCompl
Set
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.instBoundedOrder
HasProd
Set.Elem
Set.instMembership
SummationFilter.unconditional
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”IsCompl.compl_eq
Set.mulIndicator_self_mul_compl_apply
mul
hasProd_subtype_iff_mulIndicator
of_subsingleton_cod πŸ“–mathematicalβ€”HasProd
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForall
hasProd_one
update' πŸ“–mathematicalHasProd
Function.update
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Function.update_apply
mul_comm
mul
hasProd_ite_eq
unique

HasSum

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalHasSumAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Finset.sum_add_distrib
Filter.Tendsto.add
add_compl πŸ“–mathematicalHasSum
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”add_isCompl
isCompl_compl
add_disjoint πŸ“–mathematicalDisjoint
Set
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
HasSum
Set.Elem
Set.instMembership
SummationFilter.unconditional
Set.instUnion
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”hasSum_subtype_iff_indicator
Set.indicator_union_of_disjoint
add
add_isCompl πŸ“–mathematicalIsCompl
Set
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
Set.instBoundedOrder
HasSum
Set.Elem
Set.instMembership
SummationFilter.unconditional
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”IsCompl.compl_eq
Set.indicator_self_add_compl_apply
add
hasSum_subtype_iff_indicator
compl_add πŸ“–mathematicalHasSum
Set.Elem
Compl.compl
Set
Set.instCompl
Set.instMembership
SummationFilter.unconditional
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”add_isCompl
IsCompl.symm
isCompl_compl
congr_fun πŸ“–β€”HasSumβ€”β€”β€”
hasSum_of_sum_eq πŸ“–β€”Finset
Finset.instHasSubset
Finset.sum
HasSum
SummationFilter.unconditional
β€”β€”le_trans
Filter.map_atTop_finset_sum_le_of_sum_eq
map πŸ“–β€”HasSum
Continuous
DFunLike.coe
β€”β€”map_sum
Filter.Tendsto.comp
Continuous.tendsto
of_subsingleton_cod πŸ“–mathematicalβ€”HasSum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForall
hasSum_zero
update' πŸ“–mathematicalHasSum
Function.update
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Function.update_apply
add_comm
add
hasSum_ite_eq
unique

Multipliable

Theorems

NameKindAssumesProvesValidatesDepends On
compl_add πŸ“–β€”Multipliable
Set.Elem
Compl.compl
Set
Set.instCompl
Set.instMembership
SummationFilter.unconditional
β€”β€”HasProd.multipliable
HasProd.compl_mul
hasProd
map πŸ“–β€”Multipliable
Continuous
DFunLike.coe
β€”β€”HasProd.multipliable
HasProd.map
hasProd
map_iff_of_equiv πŸ“–mathematicalContinuous
DFunLike.coe
EquivLike.toFunLike
EquivLike.inv
Multipliableβ€”map_iff_of_leftInverse
MulEquivClass.instMonoidHomClass
MulEquiv.instMulEquivClass
EquivLike.left_inv
map_iff_of_leftInverse πŸ“–mathematicalContinuous
DFunLike.coe
Multipliableβ€”map
Function.comp_assoc
map_tprod πŸ“–mathematicalMultipliable
Continuous
DFunLike.coe
tprodβ€”HasProd.tprod_eq
HasProd.map
hasProd
mul πŸ“–mathematicalMultipliableMulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”HasProd.multipliable
HasProd.mul
hasProd
mul_compl πŸ“–β€”Multipliable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
β€”β€”HasProd.multipliable
HasProd.mul_compl
hasProd
of_finite πŸ“–mathematicalβ€”Multipliableβ€”multipliable_of_finite_mulSupport
Set.Finite.subset
Set.finite_univ
Set.subset_univ
of_subsingleton_cod πŸ“–mathematicalβ€”Multipliableβ€”HasProd.multipliable
HasProd.of_subsingleton_cod
tprod_eq_mul_tprod_ite' πŸ“–mathematicalMultipliable
Function.update
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
MulOne.toMul
β€”tprod_congr
Function.update_apply
mul_one
Function.update_of_ne
one_mul
tprod_mul
hasProd_single
tprod_eq_mulSingle
tprod_finsetProd πŸ“–mathematicalMultipliabletprod
Finset.prod
β€”HasProd.tprod_eq
hasProd_prod
hasProd
tprod_finset_bUnion_disjoint πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
Finset.instSetLike
Function.onFun
Set
Disjoint
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Multipliable
Set.Elem
Set.instMembership
SummationFilter.unconditional
tprod
Set.iUnion
Finset.instMembership
Finset.prod
β€”HasProd.tprod_eq
SummationFilter.instNeBotUnconditional
hasProd_prod_disjoint
hasProd
tprod_mul πŸ“–mathematicalMultipliabletprod
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”HasProd.tprod_eq
HasProd.mul
hasProd
tprod_mul_tprod_compl πŸ“–mathematicalMultipliable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
β€”HasProd.tprod_eq
SummationFilter.instNeBotUnconditional
HasProd.mul_compl
hasProd
tprod_union_disjoint πŸ“–mathematicalDisjoint
Set
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Multipliable
Set.Elem
Set.instMembership
SummationFilter.unconditional
tprod
Set.instUnion
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”HasProd.tprod_eq
SummationFilter.instNeBotUnconditional
HasProd.mul_disjoint
hasProd

Set.Finite

Theorems

NameKindAssumesProvesValidatesDepends On
multipliable πŸ“–mathematicalβ€”Multipliable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
β€”Finset.multipliable
coe_toFinset
summable πŸ“–mathematicalβ€”Summable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
β€”Finset.summable
coe_toFinset

Summable

Theorems

NameKindAssumesProvesValidatesDepends On
add πŸ“–mathematicalSummableAddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”HasSum.summable
HasSum.add
hasSum
add_compl πŸ“–β€”Summable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
β€”β€”HasSum.summable
HasSum.add_compl
hasSum
compl_add πŸ“–β€”Summable
Set.Elem
Compl.compl
Set
Set.instCompl
Set.instMembership
SummationFilter.unconditional
β€”β€”HasSum.summable
HasSum.compl_add
hasSum
map πŸ“–β€”Summable
Continuous
DFunLike.coe
β€”β€”HasSum.summable
HasSum.map
hasSum
map_iff_of_equiv πŸ“–mathematicalContinuous
DFunLike.coe
EquivLike.toFunLike
EquivLike.inv
Summableβ€”map_iff_of_leftInverse
AddEquivClass.instAddMonoidHomClass
AddEquiv.instAddEquivClass
EquivLike.left_inv
map_iff_of_leftInverse πŸ“–mathematicalContinuous
DFunLike.coe
Summableβ€”map
Function.comp_assoc
map_tsum πŸ“–mathematicalSummable
Continuous
DFunLike.coe
tsumβ€”HasSum.tsum_eq
HasSum.map
hasSum
of_finite πŸ“–mathematicalβ€”Summableβ€”summable_of_finite_support
Set.Finite.subset
Set.finite_univ
Set.subset_univ
of_subsingleton_cod πŸ“–mathematicalβ€”Summableβ€”HasSum.summable
HasSum.of_subsingleton_cod
tsum_add πŸ“–mathematicalSummabletsum
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”HasSum.tsum_eq
HasSum.add
hasSum
tsum_add_tsum_compl πŸ“–mathematicalSummable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Compl.compl
Set.instCompl
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
β€”HasSum.tsum_eq
SummationFilter.instNeBotUnconditional
HasSum.add_compl
hasSum
tsum_eq_add_tsum_ite' πŸ“–mathematicalSummable
Function.update
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
AddZero.toAdd
β€”tsum_congr
Function.update_apply
add_zero
Function.update_of_ne
zero_add
tsum_add
hasSum_single
tsum_eq_single
tsum_finsetSum πŸ“–mathematicalSummabletsum
Finset.sum
β€”HasSum.tsum_eq
hasSum_sum
hasSum
tsum_finset_bUnion_disjoint πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
Finset.instSetLike
Function.onFun
Set
Disjoint
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Summable
Set.Elem
Set.instMembership
SummationFilter.unconditional
tsum
Set.iUnion
Finset.instMembership
Finset.sum
β€”HasSum.tsum_eq
SummationFilter.instNeBotUnconditional
hasSum_sum_disjoint
hasSum
tsum_union_disjoint πŸ“–mathematicalDisjoint
Set
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
Summable
Set.Elem
Set.instMembership
SummationFilter.unconditional
tsum
Set.instUnion
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”HasSum.tsum_eq
SummationFilter.instNeBotUnconditional
HasSum.add_disjoint
hasSum

Topology.IsClosedEmbedding

Theorems

NameKindAssumesProvesValidatesDepends On
map_tprod πŸ“–mathematicalTopology.IsClosedEmbedding
DFunLike.coe
tprodβ€”Multipliable.map_tprod
continuous
tprod_eq_one_of_not_multipliable
Mathlib.Tactic.Contrapose.contraposeβ‚„
Finset.prod_congr
IsClosed.mem_of_tendsto
SummationFilter.instNeBotFinsetFilterOfNeBot
isClosed_range
Filter.Eventually.of_forall
tendsto_nhds_iff
map_prod
map_one
MonoidHomClass.toOneHomClass
tprod_bot
MonoidHom.map_finprod_of_injective
Topology.IsEmbedding.injective
toIsEmbedding
map_tsum πŸ“–mathematicalTopology.IsClosedEmbedding
DFunLike.coe
tsumβ€”Summable.map_tsum
continuous
tsum_eq_zero_of_not_summable
Mathlib.Tactic.Contrapose.contraposeβ‚„
Finset.sum_congr
IsClosed.mem_of_tendsto
SummationFilter.instNeBotFinsetFilterOfNeBot
isClosed_range
Filter.Eventually.of_forall
map_sum
Set.mem_range
tendsto_nhds_iff
map_zero
AddMonoidHomClass.toZeroHomClass
tsum_bot
AddMonoidHom.map_finsum_of_injective
Topology.IsEmbedding.injective
toIsEmbedding

Topology.IsInducing

Theorems

NameKindAssumesProvesValidatesDepends On
hasProd_iff πŸ“–mathematicalTopology.IsInducing
DFunLike.coe
HasProdβ€”Finset.prod_congr
tendsto_nhds_iff
hasSum_iff πŸ“–mathematicalTopology.IsInducing
DFunLike.coe
HasSumβ€”Finset.sum_congr
map_sum
tendsto_nhds_iff
multipliable_iff_tprod_comp_mem_range πŸ“–mathematicalTopology.IsInducing
DFunLike.coe
Multipliable
Set
Set.instMembership
Set.range
tprod
β€”Multipliable.map
continuous
Multipliable.map_tprod
tprod_bot
finprod_eq_prod
map_one
MonoidHomClass.toOneHomClass
finprod_of_infinite_mulSupport
Multipliable.hasProd
hasProd_iff
summable_iff_tsum_comp_mem_range πŸ“–mathematicalTopology.IsInducing
DFunLike.coe
Summable
Set
Set.instMembership
Set.range
tsum
β€”Summable.map
continuous
Summable.map_tsum
tsum_bot
finsum_eq_sum
map_sum
Set.mem_range
map_zero
AddMonoidHomClass.toZeroHomClass
finsum_of_infinite_support
Summable.hasSum
hasSum_iff

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
eq_add_of_hasSum_ite πŸ“–mathematicalHasSum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddZero.toAddβ€”add_zero
HasSum.update'
Function.update_apply
eq_mul_of_hasProd_ite πŸ“–mathematicalHasProd
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
MulOne.toMulβ€”mul_one
HasProd.update'
Function.update_apply
hasProd_empty πŸ“–mathematicalβ€”HasProd
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForallOfFastIsEmpty
hasProd_one
hasProd_extend_one πŸ“–mathematicalβ€”HasProd
Function.extend
Pi.instOne
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
SummationFilter.unconditional
β€”Function.Injective.hasProd_iff
Function.extend_apply'
Function.extend_comp
hasProd_iff_hasProd πŸ“–mathematicalFinset
Finset.instHasSubset
Finset.prod
HasProd
SummationFilter.unconditional
β€”HasProd.hasProd_of_prod_eq
hasProd_iff_hasProd_of_ne_one_bij πŸ“–mathematicalSet.Elem
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Set
Set.instHasSubset
Set.range
Set.instMembership
HasProd
SummationFilter.unconditional
β€”Equiv.hasProd_iff_of_mulSupport
Subtype.coe_prop
hasProd_ite_eq πŸ“–mathematicalβ€”HasProd
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”hasProd_single
hasProd_one πŸ“–mathematicalβ€”HasProd
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Finset.prod_congr
Finset.prod_const_one
hasProd_prod πŸ“–mathematicalHasProdFinset.prodβ€”Finset.induction_on
Finset.prod_insert
HasProd.mul
hasProd_prod_disjoint πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
Finset.instSetLike
Function.onFun
Set
Disjoint
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
HasProd
Set.Elem
Set.instMembership
SummationFilter.unconditional
Set.iUnion
Finset.instMembership
Finset.prod
β€”Finset.mulIndicator_biUnion
hasProd_prod
hasProd_single πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProdβ€”hasProd_prod_of_ne_finset_one
Finset.prod_singleton
hasProd_singleton πŸ“–mathematicalβ€”HasProd
Set.Elem
Set
Set.instSingletonSet
Set.restrict
SummationFilter.unconditional
β€”hasProd_unique
SummationFilter.instLeAtTopUnconditional
hasProd_subtype_iff_mulIndicator πŸ“–mathematicalβ€”HasProd
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.mulIndicator
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Set.mulIndicator_range_comp
Subtype.range_coe
hasProd_subtype_iff_of_mulSupport_subset
Set.mulSupport_mulIndicator_subset
hasProd_subtype_mulSupport πŸ“–mathematicalβ€”HasProd
Set.Elem
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Set
Set.instMembership
SummationFilter.unconditional
β€”hasProd_subtype_iff_of_mulSupport_subset
Set.Subset.refl
hasProd_unique πŸ“–mathematicalβ€”HasProd
Unique.instInhabited
β€”hasProd_single
Unique.uniq
hasProd_zero_of_exists_eq_zero πŸ“–mathematicalMulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
HasProd
CommMonoidWithZero.toCommMonoid
β€”Filter.Tendsto.congr'
tendsto_const_nhds
Filter.mp_mem
Filter.Eventually.filter_mono
SummationFilter.LeAtTop.le_atTop
Filter.eventually_ge_atTop
Filter.univ_mem'
Finset.prod_eq_zero
Finset.singleton_subset_iff
hasSum_empty πŸ“–mathematicalβ€”HasSum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForallOfFastIsEmpty
hasSum_zero
hasSum_extend_zero πŸ“–mathematicalβ€”HasSum
Function.extend
Pi.instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SummationFilter.unconditional
β€”Function.Injective.hasSum_iff
Function.extend_apply'
Function.extend_comp
hasSum_iff_hasSum πŸ“–mathematicalFinset
Finset.instHasSubset
Finset.sum
HasSum
SummationFilter.unconditional
β€”HasSum.hasSum_of_sum_eq
hasSum_iff_hasSum_of_ne_zero_bij πŸ“–mathematicalSet.Elem
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set
Set.instHasSubset
Set.range
Set.instMembership
HasSum
SummationFilter.unconditional
β€”Equiv.hasSum_iff_of_support
Subtype.coe_prop
hasSum_ite_eq πŸ“–mathematicalβ€”HasSum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”hasSum_single
hasSum_single πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSumβ€”hasSum_sum_of_ne_finset_zero
Finset.mem_singleton
Finset.sum_singleton
hasSum_singleton πŸ“–mathematicalβ€”HasSum
Set.Elem
Set
Set.instSingletonSet
Set.restrict
SummationFilter.unconditional
β€”hasSum_unique
SummationFilter.instLeAtTopUnconditional
hasSum_subtype_iff_indicator πŸ“–mathematicalβ€”HasSum
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.indicator
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Set.indicator_range_comp
Subtype.range_coe
hasSum_subtype_iff_of_support_subset
Set.support_indicator_subset
hasSum_subtype_support πŸ“–mathematicalβ€”HasSum
Set.Elem
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set
Set.instMembership
SummationFilter.unconditional
β€”hasSum_subtype_iff_of_support_subset
Set.Subset.refl
hasSum_sum πŸ“–mathematicalHasSumFinset.sumβ€”Finset.induction_on
hasSum_zero
forall_true_iff
Finset.mem_insert
Finset.sum_insert
HasSum.add
hasSum_sum_disjoint πŸ“–mathematicalSet.Pairwise
SetLike.coe
Finset
Finset.instSetLike
Function.onFun
Set
Disjoint
ConditionallyCompletePartialOrderSup.toPartialOrder
ConditionallyCompletePartialOrder.toConditionallyCompletePartialOrderSup
ConditionallyCompleteLattice.toConditionallyCompletePartialOrder
CompleteLattice.toConditionallyCompleteLattice
CompleteBooleanAlgebra.toCompleteLattice
CompleteAtomicBooleanAlgebra.toCompleteBooleanAlgebra
Set.instCompleteAtomicBooleanAlgebra
HeytingAlgebra.toOrderBot
Order.Frame.toHeytingAlgebra
CompleteDistribLattice.toFrame
CompleteBooleanAlgebra.toCompleteDistribLattice
HasSum
Set.Elem
Set.instMembership
SummationFilter.unconditional
Set.iUnion
Finset.instMembership
Finset.sum
β€”hasSum_subtype_iff_indicator
Finset.indicator_biUnion
hasSum_sum
hasSum_unique πŸ“–mathematicalβ€”HasSum
Unique.instInhabited
β€”hasSum_single
Unique.uniq
hasSum_zero πŸ“–mathematicalβ€”HasSum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Finset.sum_congr
Finset.sum_const_zero
tendsto_const_nhds
multipliable_congr πŸ“–mathematicalβ€”Multipliableβ€”β€”
multipliable_empty πŸ“–mathematicalβ€”Multipliableβ€”HasProd.multipliable
hasProd_empty
multipliable_extend_one πŸ“–mathematicalβ€”Multipliable
Function.extend
Pi.instOne
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
SummationFilter.unconditional
β€”hasProd_extend_one
multipliable_of_exists_eq_zero πŸ“–mathematicalMulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
Multipliable
CommMonoidWithZero.toCommMonoid
β€”hasProd_zero_of_exists_eq_zero
multipliable_of_finite_mulSupport πŸ“–mathematicalβ€”Multipliableβ€”multipliable_of_ne_finset_one
multipliable_one πŸ“–mathematicalβ€”Multipliable
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”HasProd.multipliable
hasProd_one
multipliable_prod πŸ“–mathematicalMultipliableFinset.prodβ€”HasProd.multipliable
hasProd_prod
Multipliable.hasProd
multipliable_subtype_iff_mulIndicator πŸ“–mathematicalβ€”Multipliable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.mulIndicator
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”hasProd_subtype_iff_mulIndicator
prod_eq_tprod_mulIndicator πŸ“–mathematicalβ€”Finset.prod
tprod
Set.mulIndicator
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
SetLike.coe
Finset
Finset.instSetLike
β€”tprod_eq_prod'
Set.mulSupport_mulIndicator_subset
Finset.prod_mulIndicator_subset
Finset.Subset.rfl
sum_eq_tsum_indicator πŸ“–mathematicalβ€”Finset.sum
tsum
Set.indicator
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SetLike.coe
Finset
Finset.instSetLike
β€”tsum_eq_sum'
Set.support_indicator_subset
Finset.sum_indicator_subset
Finset.Subset.rfl
summable_congr πŸ“–mathematicalβ€”Summableβ€”β€”
summable_empty πŸ“–mathematicalβ€”Summableβ€”HasSum.summable
hasSum_empty
summable_extend_zero πŸ“–mathematicalβ€”Summable
Function.extend
Pi.instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SummationFilter.unconditional
β€”hasSum_extend_zero
summable_of_finite_support πŸ“–mathematicalβ€”Summableβ€”summable_of_ne_finset_zero
Set.Finite.mem_toFinset
Function.mem_support
summable_subtype_iff_indicator πŸ“–mathematicalβ€”Summable
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.indicator
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”hasSum_subtype_iff_indicator
summable_sum πŸ“–mathematicalSummableFinset.sumβ€”HasSum.summable
hasSum_sum
Summable.hasSum
summable_zero πŸ“–mathematicalβ€”Summable
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”HasSum.summable
hasSum_zero
tprod_bool πŸ“–mathematicalβ€”tprod
SummationFilter.unconditional
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”tprod_fintype
SummationFilter.instLeAtTopUnconditional
Fintype.prod_bool
mul_comm
tprod_comp_neg πŸ“–mathematicalβ€”tprod
InvolutiveNeg.toNeg
SummationFilter.unconditional
β€”Equiv.tprod_eq
tprod_congr πŸ“–mathematicalβ€”tprodβ€”β€”
tprod_congr_set_coe πŸ“–mathematicalβ€”tprod
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
β€”β€”
tprod_congr_subtype πŸ“–mathematicalβ€”tprod
SummationFilter.unconditional
β€”tprod_congr_set_coe
Set.ext
tprod_congrβ‚‚ πŸ“–mathematicalβ€”tprodβ€”tprod_congr
tprod_dite_left πŸ“–mathematicalβ€”tprod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”tprod_one
tprod_dite_right πŸ“–mathematicalβ€”tprod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”tprod_one
tprod_empty πŸ“–mathematicalβ€”tprod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForallOfFastIsEmpty
tprod_one
tprod_eq_finprod πŸ“–mathematicalβ€”tprod
finprod
β€”tprod_def
multipliable_of_finite_mulSupport
SummationFilter.instHasSupportOfLeAtTop
SummationFilter.support_eq_univ
Set.inter_univ
Set.mulIndicator_univ
tprod_eq_mulSingle πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprodβ€”tprod_eq_prod
Finset.prod_singleton
tprod_eq_prod πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
Finset.prod
β€”tprod_eq_prod'
Function.mulSupport_subset_iff'
tprod_eq_prod' πŸ“–mathematicalSet
Set.instHasSubset
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
SetLike.coe
Finset
Finset.instSetLike
tprod
Finset.prod
β€”tprod_eq_finprod
Set.Finite.subset
Finset.finite_toSet
finprod_eq_prod_of_mulSupport_subset
tprod_eq_tprod_diff_singleton πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.instSDiff
Set.instSingletonSet
β€”tprod_setElem_eq_tprod_setElem_diff
tprod_eq_tprod_of_hasProd_iff_hasProd πŸ“–mathematicalHasProd
SummationFilter.unconditional
tprodβ€”Function.Surjective.tprod_eq_tprod_of_hasProd_iff_hasProd
tprod_eq_tprod_of_ne_one_bij πŸ“–mathematicalSet.Elem
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Set
Set.instHasSubset
Set.range
Set.instMembership
tprod
SummationFilter.unconditional
β€”tprod_subtype_mulSupport
Function.Injective.tprod_eq
tprod_extend_one πŸ“–mathematicalβ€”tprod
Function.extend
Pi.instOne
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
SummationFilter.unconditional
β€”Function.mulSupport_subset_iff'
Function.extend_apply'
Function.Injective.tprod_eq
Function.Injective.extend_apply
tprod_fintype πŸ“–mathematicalβ€”tprod
Finset.prod
Finset.univ
β€”tprod_eq_prod
instIsEmptyFalse
tprod_image πŸ“–mathematicalSet.InjOntprod
Set.Elem
Set.image
Set
Set.instMembership
SummationFilter.unconditional
β€”Equiv.tprod_eq
tprod_ite_eq πŸ“–mathematicalβ€”tprod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”tprod_eq_mulSingle
tprod_of_exists_eq_zero πŸ“–mathematicalMulZeroClass.toZero
MulZeroOneClass.toMulZeroClass
MonoidWithZero.toMulZeroOneClass
CommMonoidWithZero.toMonoidWithZero
tprod
CommMonoidWithZero.toCommMonoid
β€”HasProd.tprod_eq
hasProd_zero_of_exists_eq_zero
tprod_one πŸ“–mathematicalβ€”tprod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”tprod_def
multipliable_one
Function.mulSupport_fun_one
Set.empty_inter
Set.mulIndicator_one
finprod_one
eq_true_intro
hasProd_one
tprod_range πŸ“–mathematicalβ€”tprod
Set.Elem
Set.range
Set
Set.instMembership
SummationFilter.unconditional
β€”Set.image_univ
tprod_image
Function.Injective.injOn
tprod_univ
tprod_setElem_eq_tprod_setElem_diff πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.instSDiff
β€”Function.Injective.tprod_eq
Set.diff_subset
Set.inclusion_injective
Function.mulSupport_subset_iff'
Set.range_inclusion
tprod_singleton πŸ“–mathematicalβ€”tprod
Set.Elem
Set
Set.instSingletonSet
Set.instMembership
SummationFilter.unconditional
β€”tprod_fintype
SummationFilter.instLeAtTopUnconditional
Finset.prod_congr
Finset.univ_unique
Finset.prod_singleton
tprod_subtype πŸ“–mathematicalβ€”tprod
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.mulIndicator
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
β€”tprod_subtype_eq_of_mulSupport_subset
Set.mulSupport_mulIndicator_subset
tprod_congr
Set.mulIndicator_of_mem
tprod_subtype_eq_of_mulSupport_subset πŸ“–mathematicalSet
Set.instHasSubset
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
Set.Elem
Set.instMembership
SummationFilter.unconditional
β€”Function.Injective.tprod_eq
Subtype.val_injective
Subtype.range_coe_subtype
tprod_subtype_mulSupport πŸ“–mathematicalβ€”tprod
Set.Elem
Function.mulSupport
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Set
Set.instMembership
SummationFilter.unconditional
β€”tprod_subtype_eq_of_mulSupport_subset
Set.Subset.rfl
tprod_tprod_eq_mulSingle πŸ“–mathematicalMulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
SummationFilter.unconditional
β€”tprod_congr
tprod_eq_mulSingle
SummationFilter.instLeAtTopUnconditional
tprod_univ πŸ“–mathematicalβ€”tprod
Set.Elem
Set.univ
Set
Set.instMembership
SummationFilter.unconditional
β€”tprod_subtype_eq_of_mulSupport_subset
Set.subset_univ
tsum_bool πŸ“–mathematicalβ€”tsum
SummationFilter.unconditional
AddZero.toAdd
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”tsum_fintype
SummationFilter.instLeAtTopUnconditional
Fintype.sum_bool
add_comm
tsum_comp_neg πŸ“–mathematicalβ€”tsum
InvolutiveNeg.toNeg
SummationFilter.unconditional
β€”Equiv.tsum_eq
tsum_congr πŸ“–mathematicalβ€”tsumβ€”β€”
tsum_congr_set_coe πŸ“–mathematicalβ€”tsum
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
β€”β€”
tsum_congr_subtype πŸ“–mathematicalβ€”tsum
SummationFilter.unconditional
β€”tsum_congr_set_coe
Set.ext
tsum_congrβ‚‚ πŸ“–mathematicalβ€”tsumβ€”tsum_congr
tsum_dite_left πŸ“–mathematicalβ€”tsum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”tsum_zero
tsum_dite_right πŸ“–mathematicalβ€”tsum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”tsum_zero
tsum_empty πŸ“–mathematicalβ€”tsum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”Lean.Meta.FastSubsingleton.elim
Lean.Meta.instFastSubsingletonForallOfFastIsEmpty
tsum_zero
tsum_eq_finsum πŸ“–mathematicalβ€”tsum
finsum
β€”tsum_def
summable_of_finite_support
SummationFilter.instHasSupportOfLeAtTop
SummationFilter.support_eq_univ
Set.inter_univ
Set.indicator_univ
tsum_eq_single πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsumβ€”tsum_eq_sum
Finset.mem_singleton
Finset.sum_singleton
tsum_eq_sum πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
Finset.sum
β€”tsum_eq_sum'
Function.support_subset_iff'
tsum_eq_sum' πŸ“–mathematicalSet
Set.instHasSubset
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SetLike.coe
Finset
Finset.instSetLike
tsum
Finset.sum
β€”tsum_eq_finsum
Set.Finite.subset
Finset.finite_toSet
finsum_eq_sum_of_support_subset
tsum_eq_tsum_diff_singleton πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.instSDiff
Set.instSingletonSet
β€”tsum_setElem_eq_tsum_setElem_diff
tsum_eq_tsum_of_hasSum_iff_hasSum πŸ“–mathematicalHasSum
SummationFilter.unconditional
tsumβ€”Function.Surjective.tsum_eq_tsum_of_hasSum_iff_hasSum
tsum_eq_tsum_of_ne_zero_bij πŸ“–mathematicalSet.Elem
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set
Set.instHasSubset
Set.range
Set.instMembership
tsum
SummationFilter.unconditional
β€”tsum_subtype_support
Function.Injective.tsum_eq
tsum_extend_zero πŸ“–mathematicalβ€”tsum
Function.extend
Pi.instZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SummationFilter.unconditional
β€”Function.support_subset_iff'
Function.extend_apply'
Function.Injective.tsum_eq
Function.Injective.extend_apply
tsum_fintype πŸ“–mathematicalβ€”tsum
Finset.sum
Finset.univ
β€”tsum_eq_sum
Finset.mem_univ
IsEmpty.forall_iff
instIsEmptyFalse
tsum_image πŸ“–mathematicalSet.InjOntsum
Set.Elem
Set.image
Set
Set.instMembership
SummationFilter.unconditional
β€”Equiv.tsum_eq
tsum_ite_eq πŸ“–mathematicalβ€”tsum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”tsum_eq_single
tsum_range πŸ“–mathematicalβ€”tsum
Set.Elem
Set.range
Set
Set.instMembership
SummationFilter.unconditional
β€”Set.image_univ
tsum_image
Function.Injective.injOn
tsum_univ
tsum_setElem_eq_tsum_setElem_diff πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.instSDiff
β€”Function.Injective.tsum_eq
Set.diff_subset
Set.inclusion_injective
Function.support_subset_iff'
Set.range_inclusion
Set.mem_diff
Subtype.coe_prop
tsum_singleton πŸ“–mathematicalβ€”tsum
Set.Elem
Set
Set.instSingletonSet
Set.instMembership
SummationFilter.unconditional
β€”tsum_fintype
SummationFilter.instLeAtTopUnconditional
Finset.sum_congr
Finset.univ_unique
Finset.sum_singleton
tsum_subtype πŸ“–mathematicalβ€”tsum
Set.Elem
Set
Set.instMembership
SummationFilter.unconditional
Set.indicator
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”tsum_subtype_eq_of_support_subset
Set.support_indicator_subset
tsum_congr
Set.indicator_of_mem
Subtype.coe_prop
tsum_subtype_eq_of_support_subset πŸ“–mathematicalSet
Set.instHasSubset
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
Set.Elem
Set.instMembership
SummationFilter.unconditional
β€”Function.Injective.tsum_eq
Subtype.val_injective
Subtype.range_coe_subtype
Function.support_subset_iff
tsum_subtype_support πŸ“–mathematicalβ€”tsum
Set.Elem
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set
Set.instMembership
SummationFilter.unconditional
β€”tsum_subtype_eq_of_support_subset
Set.Subset.rfl
tsum_tsum_eq_single πŸ“–mathematicalAddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
SummationFilter.unconditional
β€”tsum_congr
tsum_eq_single
SummationFilter.instLeAtTopUnconditional
tsum_univ πŸ“–mathematicalβ€”tsum
Set.Elem
Set.univ
Set
Set.instMembership
SummationFilter.unconditional
β€”tsum_subtype_eq_of_support_subset
Set.subset_univ
tsum_zero πŸ“–mathematicalβ€”tsum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
β€”tsum_def
summable_zero
Function.support_fun_zero
Set.empty_inter
Set.indicator_zero
finsum_zero
eq_true_intro
hasSum_zero

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