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
instIsLeftCancelAddOfAddLeftReflectLE
IsOrderedCancelAddMonoid.toAddLeftReflectLE
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
IsOrderedAddMonoid.toAddLeftMono
LE.le.trans
of_fintype

HasProd

Theorems

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

HasSum

Theorems

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

Mathlib.Meta.Positivity

Definitions

NameCategoryTheorems
evalTsum 📖CompOp

Multipliable

Theorems

NameKindAssumesProvesValidatesDepends On
abs 📖mathematicalMultipliable
CommRing.toCommMonoid
SummationFilter.unconditional
Multipliable
CommRing.toCommMonoid
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
SummationFilter.unconditional
HasProd.abs
abs_tprod 📖mathematicalMultipliable
CommRing.toCommMonoid
SummationFilter.unconditional
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
tprod
CommRing.toCommMonoid
SummationFilter.unconditional
HasProd.tprod_eq
OrderClosedTopology.to_t2Space
OrderTopology.to_orderClosedTopology
SummationFilter.instNeBotUnconditional
HasProd.abs
hasProd
le_tprod 📖mathematicalMultipliable
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Preorder.toLE
tprod
le_hasProd
hasProd
le_tprod' 📖mathematicalMultipliable
SummationFilter.unconditional
Preorder.toLE
PartialOrder.toPreorder
tprod
SummationFilter.unconditional
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
Preorder.toLT
PartialOrder.toPreorder
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroup.toDivisionCommMonoid
tprod
CommGroup.toCommMonoid
tprod_one
tprod_lt_tprod
multipliable_one
prod_le_tprod 📖mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Multipliable
Preorder.toLE
Finset.prod
tprod
prod_le_hasProd
hasProd
tprod_eq_one_iff 📖mathematicalMultipliable
SummationFilter.unconditional
tprod
SummationFilter.unconditional
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
Finset.prod
Preorder.toLE
tprod
hasProd_le_of_prod_le
instClosedIicTopology
hasProd
tprod_le_of_prod_range_le 📖mathematicalMultipliable
SummationFilter.unconditional
Preorder.toLE
Finset.prod
Finset.range
Preorder.toLE
tprod
SummationFilter.unconditional
le_of_tendsto'
Filter.atTop_neBot
instIsDirectedOrder
IsStrictOrderedRing.toIsOrderedRing
Nat.instIsStrictOrderedRing
instArchimedeanNat
HasProd.tendsto_prod_nat
hasProd
tprod_le_tprod 📖mathematicalPreorder.toLE
Multipliable
Preorder.toLE
tprod
hasProd_le
hasProd
tprod_le_tprod_of_inj 📖mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Multipliable
SummationFilter.unconditional
Preorder.toLE
tprod
SummationFilter.unconditional
hasProd
tprod_lt_tprod 📖mathematicalPi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
Multipliable
CommGroup.toCommMonoid
Preorder.toLT
PartialOrder.toPreorder
tprod
CommGroup.toCommMonoid
hasProd_lt
hasProd
tprod_mono 📖mathematicalMultipliable
Pi.hasLe
Preorder.toLE
Preorder.toLE
tprod
tprod_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
Preorder.toLT
PartialOrder.toPreorder
tprod
CommGroup.toCommMonoid
Pi.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
Preorder.toLE
PartialOrder.toPreorder
tprod
Set.Elem
CommGroup.toCommMonoid
UniformSpace.toTopologicalSpace
Set
Set.instMembership
SummationFilter.unconditional
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
Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommGroup.toAddGroup
SummationFilter.unconditional
summable_abs_iff
le_tsum 📖mathematicalSummable
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Preorder.toLE
tsum
le_hasSum
hasSum
le_tsum' 📖mathematicalSummable
SummationFilter.unconditional
Preorder.toLE
PartialOrder.toPreorder
tsum
SummationFilter.unconditional
le_tsum
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
zero_le
of_abs 📖mathematicalSummable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
abs
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddCommGroup.toAddGroup
SummationFilter.unconditional
Summable
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
SummationFilter.unconditional
summable_abs_iff
sum_le_tsum 📖mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Summable
Preorder.toLE
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
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
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
SummationFilter.unconditional
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
Finset.sum
Preorder.toLE
tsum
hasSum_le_of_sum_le
instClosedIicTopology
hasSum
tsum_le_of_sum_range_le 📖mathematicalSummable
SummationFilter.unconditional
Preorder.toLE
Finset.sum
Finset.range
Preorder.toLE
tsum
SummationFilter.unconditional
le_of_tendsto'
Filter.atTop_neBot
instIsDirectedOrder
IsStrictOrderedRing.toIsOrderedRing
Nat.instIsStrictOrderedRing
instArchimedeanNat
HasSum.tendsto_sum_nat
hasSum
tsum_le_tsum 📖mathematicalPreorder.toLE
Summable
Preorder.toLE
tsum
hasSum_le
hasSum
tsum_le_tsum_of_inj 📖mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Summable
SummationFilter.unconditional
Preorder.toLE
tsum
SummationFilter.unconditional
hasSum
tsum_lt_tsum 📖mathematicalPi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
Summable
AddCommGroup.toAddCommMonoid
Preorder.toLT
PartialOrder.toPreorder
tsum
AddCommGroup.toAddCommMonoid
hasSum_lt
hasSum
tsum_mono 📖mathematicalSummable
Pi.hasLe
Preorder.toLE
Preorder.toLE
tsum
tsum_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
Preorder.toLT
PartialOrder.toPreorder
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
tsum
AddCommGroup.toAddCommMonoid
tsum_zero
tsum_lt_tsum
summable_zero
tsum_strict_mono 📖mathematicalSummable
AddCommGroup.toAddCommMonoid
Preorder.toLT
Pi.preorder
PartialOrder.toPreorder
Preorder.toLT
PartialOrder.toPreorder
tsum
AddCommGroup.toAddCommMonoid
Pi.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
Preorder.toLE
PartialOrder.toPreorder
tsum
Set.Elem
AddCommGroup.toAddCommMonoid
UniformSpace.toTopologicalSpace
Set
Set.instMembership
SummationFilter.unconditional
Subtype.coe_injective
Subtype.range_coe_subtype
le_refl
subtype

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
hasProd_le 📖mathematicalPreorder.toLE
HasProd
Preorder.toLEle_of_tendsto_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
Finset.prod_le_prod'
IsOrderedMonoid.toMulLeftMono
hasProd_le_inj 📖mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
SummationFilter.unconditional
Preorder.toLEhasProd_le
em
Function.Injective.extend_apply
Function.extend_apply'
hasProd_extend_one
SummationFilter.instNeBotUnconditional
hasProd_le_of_prod_le 📖mathematicalHasProd
Preorder.toLE
Finset.prod
Preorder.toLEle_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
hasProd_lt 📖mathematicalPi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
HasProd
CommGroup.toCommMonoid
Preorder.toLT
PartialOrder.toPreorder
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
instIsRightCancelMulOfMulRightReflectLE
contravariant_swap_mul_of_contravariant_mul
IsLeftCancelMul.mulLeftReflectLE_of_mulLeftReflectLT
instIsLeftCancelMulOfMulLeftReflectLE
IsOrderedCancelMonoid.toMulLeftReflectLE
IsOrderedMonoid.toIsOrderedCancelMonoid
IsOrderedCancelMonoid.toMulLeftReflectLT
covariant_swap_mul_of_covariant_mul
hasProd_mono 📖mathematicalHasProd
Pi.hasLe
Preorder.toLE
Preorder.toLEhasProd_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
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Pi.instOne
LE.le.antisymm'
le_hasProd
hasProd_one
hasProd_strict_mono 📖mathematicalHasProd
CommGroup.toCommMonoid
SummationFilter.unconditional
Preorder.toLT
Pi.preorder
PartialOrder.toPreorder
Preorder.toLT
PartialOrder.toPreorder
Pi.lt_def
hasProd_lt
SummationFilter.instNeBotUnconditional
SummationFilter.instLeAtTopUnconditional
hasSum_le 📖mathematicalPreorder.toLE
HasSum
Preorder.toLEle_of_tendsto_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
Finset.sum_le_sum
IsOrderedAddMonoid.toAddLeftMono
hasSum_le_inj 📖mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
SummationFilter.unconditional
Preorder.toLEhasSum_le
em
Function.Injective.extend_apply
Function.extend_apply'
hasSum_extend_zero
SummationFilter.instNeBotUnconditional
hasSum_le_of_sum_le 📖mathematicalHasSum
Preorder.toLE
Finset.sum
Preorder.toLEle_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
hasSum_lt 📖mathematicalPi.hasLe
Preorder.toLE
PartialOrder.toPreorder
Preorder.toLT
HasSum
AddCommGroup.toAddCommMonoid
Preorder.toLT
PartialOrder.toPreorder
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
instIsRightCancelAddOfAddRightReflectLE
contravariant_swap_add_of_contravariant_add
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
instIsLeftCancelAddOfAddLeftReflectLE
IsOrderedCancelAddMonoid.toAddLeftReflectLE
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
IsOrderedCancelAddMonoid.toAddLeftReflectLT
covariant_swap_add_of_covariant_add
hasSum_mono 📖mathematicalHasSum
Pi.hasLe
Preorder.toLE
Preorder.toLEhasSum_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 📖mathematicalHasSum
AddCommGroup.toAddCommMonoid
SummationFilter.unconditional
Preorder.toLT
Pi.preorder
PartialOrder.toPreorder
Preorder.toLT
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
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Pi.instZero
LE.le.antisymm'
le_hasSum
hasSum_zero
isLUB_hasProd 📖mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
SummationFilter.unconditional
IsLUB
Preorder.toLE
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
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
SummationFilter.unconditional
IsLUB
Preorder.toLE
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 📖mathematicalHasProd
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Preorder.toLEFinset.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 📖mathematicalHasProd
Preorder.toLE
Finset.prod
Preorder.toLEge_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
le_hasSum 📖mathematicalHasSum
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Preorder.toLEFinset.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 📖mathematicalHasSum
Preorder.toLE
Finset.sum
Preorder.toLEge_of_tendsto'
SummationFilter.instNeBotFinsetFilterOfNeBot
lt_hasProd 📖mathematicalHasProd
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Preorder.toLT
Preorder.toLTlt_mul_of_one_lt_left'
Finset.prod_pair
prod_le_hasProd
Finset.mem_insert_of_mem
Finset.mem_singleton
lt_hasSum 📖mathematicalHasSum
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Preorder.toLT
Preorder.toLTlt_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
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Preorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
tprod
HasProd.one_le
Multipliable.hasProd
tprod_bot
one_le_finprod'
tprod_eq_one_of_not_multipliable
le_refl
prod_le_hasProd 📖mathematicalPreorder.toLE
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd
Preorder.toLE
Finset.prod
ge_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
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum
Preorder.toLE
Finset.sum
ge_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
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Finset.prod
Preorder.toLE
tprod
Multipliable.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
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
Preorder.toLE
tprod
MulOne.toOne
MulOneClass.toMulOne
Monoid.toMulOneClass
CommMonoid.toMonoid
HasProd.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
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finset.sum
Preorder.toLE
tsum
Summable.tsum_le_of_sum_le
tsum_eq_zero_of_not_summable
tsum_bot
finsum_eq_sum
finsum_of_infinite_support
tsum_nonneg 📖mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Preorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
tsum
HasSum.nonneg
Summable.hasSum
tsum_bot
finsum_nonneg
tsum_eq_zero_of_not_summable
le_refl
tsum_nonpos 📖mathematicalPreorder.toLE
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Preorder.toLE
tsum
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HasSum.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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