Documentation Verification Report

Order

📁 Source: Mathlib/Topology/Algebra/InfiniteSum/Order.lean

Statistics

MetricCount
DefinitionsevalTsum
1
Theoremsof_summable_const, abs, le_one, one_le, nonneg, nonpos, abs, abs_tprod, le_tprod, le_tprod', one_lt_tprod, prod_le_tprod, tprod_eq_one_iff, tprod_le_of_prod_le, tprod_le_of_prod_range_le, tprod_le_tprod, tprod_le_tprod_of_inj, tprod_lt_tprod, tprod_mono, tprod_ne_one_iff, tprod_strict_mono, tprod_subtype_le, of_summable_const, abs, le_tsum, le_tsum', of_abs, sum_le_tsum, tendsto_atTop_of_pos, tsum_eq_zero_iff, tsum_le_of_sum_le, tsum_le_of_sum_range_le, tsum_le_tsum, tsum_le_tsum_of_inj, tsum_lt_tsum, tsum_mono, tsum_ne_zero_iff, tsum_pos, tsum_strict_mono, tsum_subtype_le, hasProd_le, hasProd_le_inj, hasProd_le_of_prod_le, hasProd_lt, hasProd_mono, hasProd_of_isGLB_of_le_one, hasProd_of_isLUB, hasProd_of_isLUB_of_one_le, hasProd_one_iff, hasProd_one_iff_of_one_le, hasProd_strict_mono, hasSum_le, hasSum_le_inj, hasSum_le_of_sum_le, hasSum_lt, hasSum_mono, hasSum_of_isGLB_of_nonpos, hasSum_of_isLUB, hasSum_of_isLUB_of_nonneg, hasSum_strict_mono, hasSum_zero_iff, hasSum_zero_iff_of_nonneg, isLUB_hasProd, isLUB_hasProd', isLUB_hasSum, isLUB_hasSum', le_hasProd, le_hasProd', le_hasProd_of_le_prod, le_hasSum, le_hasSum', le_hasSum_of_le_sum, lt_hasProd, lt_hasSum, multipliable_mabs_iff, one_le_tprod, prod_le_hasProd, sum_le_hasSum, summable_abs_iff, tprod_le_of_prod_le', tprod_le_one, tsum_le_of_sum_le', tsum_nonneg, tsum_nonpos
84
Total85

Finite

Theorems

NameKindAssumesProvesValidatesDepends On
of_summable_const 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Summable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
FiniteFinset.sum_const
sum_le_hasSum
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
LT.lt.le
Summable.hasSum
Archimedean.arch
nsmul_le_nsmul_iff_left
IsLeftCancelAdd.addLeftStrictMono_of_addLeftMono
AddLeftCancelSemigroup.toIsLeftCancelAdd
IsOrderedAddMonoid.toAddLeftMono
LE.le.trans
of_fintype

HasProd

Theorems

NameKindAssumesProvesValidatesDepends On
abs 📖mathematicalHasProd
CommRing.toCommMonoid
SummationFilter.unconditional
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
Finset.prod_congr
Filter.Tendsto.abs
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
le_one 📖Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
hasProd_le
hasProd_one
one_le 📖Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
hasProd_le
hasProd_one

HasSum

Theorems

NameKindAssumesProvesValidatesDepends On
nonneg 📖Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
hasSum_le
hasSum_zero
nonpos 📖Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
hasSum_le
hasSum_zero

Mathlib.Meta.Positivity

Definitions

NameCategoryTheorems
evalTsum 📖CompOp

Multipliable

Theorems

NameKindAssumesProvesValidatesDepends On
abs 📖mathematicalMultipliable
CommRing.toCommMonoid
SummationFilter.unconditional
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
HasProd.abs
abs_tprod 📖mathematicalMultipliable
CommRing.toCommMonoid
SummationFilter.unconditional
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
tprod
HasProd.tprod_eq
OrderClosedTopology.to_t2Space
OrderTopology.to_orderClosedTopology
SummationFilter.instNeBotUnconditional
HasProd.abs
hasProd
le_tprod 📖mathematicalMultipliable
Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprodle_hasProd
hasProd
le_tprod' 📖mathematicalMultipliable
SummationFilter.unconditional
Preorder.toLE
PartialOrder.toPreorder
tprod
le_tprod
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
one_le
one_lt_tprod 📖mathematicalMultipliable
CommGroup.toCommMonoid
Preorder.toLE
PartialOrder.toPreorder
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
Preorder.toLT
tprodtprod_one
tprod_lt_tprod
multipliable_one
prod_le_tprod 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Multipliable
Finset.prod
tprod
prod_le_hasProd
hasProd
tprod_eq_one_iff 📖mathematicalMultipliable
SummationFilter.unconditional
tprod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
hasProd_one_iff
hasProd_iff
OrderClosedTopology.to_t2Space
SummationFilter.instNeBotUnconditional
tprod_le_of_prod_le 📖mathematicalMultipliable
Preorder.toLE
PartialOrder.toPreorder
Finset.prod
tprodhasProd_le_of_prod_le
instClosedIicTopology
hasProd
tprod_le_of_prod_range_le 📖mathematicalMultipliable
SummationFilter.unconditional
Preorder.toLE
Finset.prod
Finset.range
tprodle_of_tendsto'
Filter.atTop_neBot
instIsDirectedOrder
IsStrictOrderedRing.toIsOrderedRing
Nat.instIsStrictOrderedRing
instArchimedeanNat
HasProd.tendsto_prod_nat
hasProd
tprod_le_tprod 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Multipliable
tprodhasProd_le
hasProd
tprod_le_tprod_of_inj 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Multipliable
SummationFilter.unconditional
tprodhasProd
tprod_lt_tprod 📖mathematicalPi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
Multipliable
CommGroup.toCommMonoid
tprodhasProd_lt
hasProd
tprod_mono 📖mathematicalMultipliable
Pi.hasLe
Preorder.toLE
PartialOrder.toPreorder
tprodtprod_le_tprod
tprod_ne_one_iff 📖Multipliable
SummationFilter.unconditional
tprod_eq_one_iff
tprod_strict_mono 📖mathematicalMultipliable
CommGroup.toCommMonoid
Preorder.toLT
Pi.preorder
PartialOrder.toPreorder
tprodPi.lt_def
tprod_lt_tprod
tprod_subtype_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
Multipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
tprod
Set.Elem
Set
Set.instMembership
Subtype.coe_injective
Subtype.range_coe_subtype
subtype

Set.Finite

Theorems

NameKindAssumesProvesValidatesDepends On
of_summable_const 📖mathematicalPreorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Summable
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Set.Finite
Set.univ
Set.finite_univ_iff
Finite.of_summable_const

Summable

Theorems

NameKindAssumesProvesValidatesDepends On
abs 📖mathematicalSummable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommGroup.toAddGroup
summable_abs_iff
le_tsum 📖mathematicalSummable
Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsumle_hasSum
hasSum
le_tsum' 📖mathematicalSummable
SummationFilter.unconditional
Preorder.toLE
PartialOrder.toPreorder
tsum
le_tsum
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
zero_le
of_abs 📖Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommGroup.toAddGroup
SummationFilter.unconditional
summable_abs_iff
sum_le_tsum 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Summable
Finset.sum
tsum
sum_le_hasSum
hasSum
tendsto_atTop_of_pos 📖mathematicalSummable
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
Pi.instInv
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
SummationFilter.unconditional
Preorder.toLT
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Filter.Tendsto
Filter.atTop
Nat.instPreorder
Filter.Tendsto.inv_tendsto_nhdsGT_zero
inv_inv
tendsto_nhdsWithin_of_tendsto_nhds_of_eventually_within
tendsto_atTop_zero
LinearOrderedAddCommGroup.toIsTopologicalAddGroup
IsOrderedRing.toIsOrderedAddMonoid
IsStrictOrderedRing.toIsOrderedRing
Filter.Eventually.of_forall
inv_pos
PosMulReflectLE.toPosMulReflectLT
PosMulStrictMono.toPosMulReflectLE
IsStrictOrderedRing.toPosMulStrictMono
tsum_eq_zero_iff 📖mathematicalSummable
SummationFilter.unconditional
tsum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hasSum_zero_iff
hasSum_iff
OrderClosedTopology.to_t2Space
SummationFilter.instNeBotUnconditional
tsum_le_of_sum_le 📖mathematicalSummable
Preorder.toLE
PartialOrder.toPreorder
Finset.sum
tsumhasSum_le_of_sum_le
instClosedIicTopology
hasSum
tsum_le_of_sum_range_le 📖mathematicalSummable
SummationFilter.unconditional
Preorder.toLE
Finset.sum
Finset.range
tsumle_of_tendsto'
Filter.atTop_neBot
instIsDirectedOrder
IsStrictOrderedRing.toIsOrderedRing
Nat.instIsStrictOrderedRing
instArchimedeanNat
HasSum.tendsto_sum_nat
hasSum
tsum_le_tsum 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
Summable
tsumhasSum_le
hasSum
tsum_le_tsum_of_inj 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Summable
SummationFilter.unconditional
tsumhasSum
tsum_lt_tsum 📖mathematicalPi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
Summable
AddCommGroup.toAddCommMonoid
tsumhasSum_lt
hasSum
tsum_mono 📖mathematicalSummable
Pi.hasLe
Preorder.toLE
PartialOrder.toPreorder
tsumtsum_le_tsum
tsum_ne_zero_iff 📖Summable
SummationFilter.unconditional
tsum_eq_zero_iff
tsum_pos 📖mathematicalSummable
AddCommGroup.toAddCommMonoid
Preorder.toLE
PartialOrder.toPreorder
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Preorder.toLT
tsumtsum_zero
tsum_lt_tsum
summable_zero
tsum_strict_mono 📖mathematicalSummable
AddCommGroup.toAddCommMonoid
Preorder.toLT
Pi.preorder
PartialOrder.toPreorder
tsumPi.lt_def
tsum_lt_tsum
tsum_subtype_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
tsum
Set.Elem
Set
Set.instMembership
Subtype.coe_injective
Subtype.range_coe_subtype
le_refl
subtype

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
hasProd_le 📖Preorder.toLE
PartialOrder.toPreorder
HasProd
le_of_tendsto_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
Finset.prod_le_prod'
IsOrderedMonoid.toMulLeftMono
hasProd_le_inj 📖Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
SummationFilter.unconditional
hasProd_le
em
Function.Injective.extend_apply
Function.extend_apply'
hasProd_extend_one
SummationFilter.instNeBotUnconditional
hasProd_le_of_prod_le 📖HasProd
Preorder.toLE
Finset.prod
le_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
hasProd_lt 📖Pi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
HasProd
CommGroup.toCommMonoid
update_le_update_iff
Eq.le
hasProd_le
HasProd.update
one_div
mul_inv_cancel_left
mul_lt_mul_of_lt_of_le
IsOrderedMonoid.toMulLeftMono
IsRightCancelMul.mulRightStrictMono_of_mulRightMono
RightCancelSemigroup.toIsRightCancelMul
covariant_swap_mul_of_covariant_mul
hasProd_mono 📖HasProd
Pi.hasLe
Preorder.toLE
PartialOrder.toPreorder
hasProd_le
hasProd_of_isGLB_of_le_one 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
IsGLB
Set.range
Finset
Finset.prod
HasProd
SummationFilter.unconditional
tendsto_atTop_isGLB
LinearOrder.infConvergenceClass
Finset.prod_anti_set_of_le_one
IsOrderedMonoid.toMulLeftMono
hasProd_of_isLUB 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.range
Finset
Finset.prod
HasProd
SummationFilter.unconditional
tendsto_atTop_isLUB
LinearOrder.supConvergenceClass
Finset.prod_mono_set'
hasProd_of_isLUB_of_one_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
IsLUB
Set.range
Finset
Finset.prod
HasProd
SummationFilter.unconditional
tendsto_atTop_isLUB
LinearOrder.supConvergenceClass
Finset.prod_mono_set_of_one_le'
IsOrderedMonoid.toMulLeftMono
hasProd_one_iff 📖mathematicalHasProd
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
SummationFilter.unconditional
hasProd_one_iff_of_one_le
SummationFilter.instLeAtTopUnconditional
SummationFilter.instNeBotUnconditional
one_le
hasProd_one_iff_of_one_le 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
Pi.instOne
LE.le.antisymm'
le_hasProd
hasProd_one
hasProd_strict_mono 📖HasProd
CommGroup.toCommMonoid
SummationFilter.unconditional
Preorder.toLT
Pi.preorder
PartialOrder.toPreorder
Pi.lt_def
hasProd_lt
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
hasSum_le 📖Preorder.toLE
PartialOrder.toPreorder
HasSum
le_of_tendsto_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
Finset.sum_le_sum
IsOrderedAddMonoid.toAddLeftMono
hasSum_le_inj 📖Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
SummationFilter.unconditional
hasSum_le
em
Function.Injective.extend_apply
Function.extend_apply'
hasSum_extend_zero
SummationFilter.instNeBotUnconditional
hasSum_le_of_sum_le 📖HasSum
Preorder.toLE
Finset.sum
le_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
hasSum_lt 📖Pi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
HasSum
AddCommGroup.toAddCommMonoid
update_le_update_iff
Eq.le
hasSum_le
HasSum.update
zero_sub
add_neg_cancel_left
add_lt_add_of_lt_of_le
IsOrderedAddMonoid.toAddLeftMono
IsRightCancelAdd.addRightStrictMono_of_addRightMono
AddRightCancelSemigroup.toIsRightCancelAdd
covariant_swap_add_of_covariant_add
hasSum_mono 📖HasSum
Pi.hasLe
Preorder.toLE
PartialOrder.toPreorder
hasSum_le
hasSum_of_isGLB_of_nonpos 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
IsGLB
Set.range
Finset
Finset.sum
HasSum
SummationFilter.unconditional
tendsto_atTop_isGLB
LinearOrder.infConvergenceClass
Finset.sum_anti_set_of_nonpos
IsOrderedAddMonoid.toAddLeftMono
hasSum_of_isLUB 📖mathematicalIsLUB
Preorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.range
Finset
Finset.sum
HasSum
SummationFilter.unconditional
tendsto_atTop_isLUB
LinearOrder.supConvergenceClass
Finset.sum_mono_set
hasSum_of_isLUB_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
IsLUB
Set.range
Finset
Finset.sum
HasSum
SummationFilter.unconditional
tendsto_atTop_isLUB
LinearOrder.supConvergenceClass
Finset.sum_mono_set_of_nonneg
IsOrderedAddMonoid.toAddLeftMono
hasSum_strict_mono 📖HasSum
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Preorder.toLT
Pi.preorder
PartialOrder.toPreorder
Pi.lt_def
hasSum_lt
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
hasSum_zero_iff 📖mathematicalHasSum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SummationFilter.unconditional
hasSum_zero_iff_of_nonneg
SummationFilter.instLeAtTopUnconditional
SummationFilter.instNeBotUnconditional
zero_le
hasSum_zero_iff_of_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
Pi.instZero
LE.le.antisymm'
le_hasSum
hasSum_zero
isLUB_hasProd 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
SummationFilter.unconditional
IsLUB
Set.range
Finset
Finset.prod
isLUB_of_tendsto_atTop
Finset.isDirected_le
Finset.prod_mono_set_of_one_le'
IsOrderedMonoid.toMulLeftMono
isLUB_hasProd' 📖mathematicalHasProd
SummationFilter.unconditional
IsLUB
Preorder.toLE
PartialOrder.toPreorder
Set.range
Finset
Finset.prod
isLUB_of_tendsto_atTop
Finset.isDirected_le
Finset.prod_mono_set'
isLUB_hasSum 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
SummationFilter.unconditional
IsLUB
Set.range
Finset
Finset.sum
isLUB_of_tendsto_atTop
Finset.isDirected_le
Finset.sum_mono_set_of_nonneg
IsOrderedAddMonoid.toAddLeftMono
isLUB_hasSum' 📖mathematicalHasSum
SummationFilter.unconditional
IsLUB
Preorder.toLE
PartialOrder.toPreorder
Set.range
Finset
Finset.sum
isLUB_of_tendsto_atTop
Finset.isDirected_le
Finset.sum_mono_set
le_hasProd 📖HasProd
Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod_singleton
prod_le_hasProd
le_hasProd' 📖mathematicalHasProd
SummationFilter.unconditional
Preorder.toLE
PartialOrder.toPreorder
le_hasProd
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
one_le
le_hasProd_of_le_prod 📖HasProd
Preorder.toLE
Finset.prod
ge_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
le_hasSum 📖HasSum
Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum_singleton
sum_le_hasSum
Finset.mem_singleton
le_hasSum' 📖mathematicalHasSum
SummationFilter.unconditional
Preorder.toLE
PartialOrder.toPreorder
le_hasSum
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
zero_le
le_hasSum_of_le_sum 📖HasSum
Preorder.toLE
Finset.sum
ge_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
lt_hasProd 📖HasProd
Preorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Preorder.toLT
lt_mul_of_one_lt_left'
Finset.prod_pair
prod_le_hasProd
Finset.mem_insert_of_mem
Finset.mem_singleton
lt_hasSum 📖HasSum
Preorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Preorder.toLT
lt_add_of_pos_left
Finset.sum_pair
sum_le_hasSum
Finset.mem_insert_of_mem
Finset.mem_singleton
multipliable_mabs_iff 📖mathematicalMultipliable
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
mabs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
CommGroup.toGroup
SummationFilter.unconditional
mabs_of_one_le
IsOrderedMonoid.toMulLeftMono
mabs_of_lt_one
not_le
multipliable_subtype_and_compl
IsUniformGroup.to_topologicalGroup
one_le_tprod 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprodHasProd.one_le
Multipliable.hasProd
tprod_bot
one_le_finprod'
tprod_eq_one_of_not_multipliable
le_refl
prod_le_hasProd 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
Finset.prodge_of_tendsto
instClosedIciTopology
SummationFilter.instNeBotFinsetFilterOfNeBot
Filter.Eventually.filter_mono
SummationFilter.LeAtTop.le_atTop
Filter.eventually_atTop
Finset.isDirected_le
Finset.prod_le_prod_of_subset_of_one_le'
IsOrderedMonoid.toMulLeftMono
sum_le_hasSum 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
Finset.sumge_of_tendsto
instClosedIciTopology
SummationFilter.instNeBotFinsetFilterOfNeBot
Filter.Eventually.filter_mono
SummationFilter.LeAtTop.le_atTop
Filter.eventually_atTop
Finset.isDirected_le
Finset.sum_le_sum_of_subset_of_nonneg
IsOrderedAddMonoid.toAddLeftMono
summable_abs_iff 📖mathematicalSummable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommGroup.toAddGroup
SummationFilter.unconditional
abs_of_nonneg
IsOrderedAddMonoid.toAddLeftMono
abs_of_neg
not_le
summable_subtype_and_compl
summable_neg_iff
IsUniformAddGroup.to_topologicalAddGroup
tprod_le_of_prod_le' 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod
tprodMultipliable.tprod_le_of_prod_le
tprod_eq_one_of_not_multipliable
tprod_bot
finprod_eq_prod
finprod_of_infinite_mulSupport
tprod_le_one 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprodHasProd.le_one
Multipliable.hasProd
tprod_bot
finprod_induction
le_rfl
mul_le_one'
IsOrderedMonoid.toMulLeftMono
tprod_eq_one_of_not_multipliable
le_refl
tsum_le_of_sum_le' 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum
tsumSummable.tsum_le_of_sum_le
tsum_eq_zero_of_not_summable
tsum_bot
finsum_eq_sum
finsum_of_infinite_support
tsum_nonneg 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsumHasSum.nonneg
Summable.hasSum
tsum_bot
finsum_nonneg
tsum_eq_zero_of_not_summable
le_refl
tsum_nonpos 📖mathematicalPreorder.toLE
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsumHasSum.nonpos
Summable.hasSum
tsum_bot
finsum_induction
le_rfl
add_nonpos
IsOrderedAddMonoid.toAddLeftMono
tsum_eq_zero_of_not_summable
le_refl

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