Documentation Verification Report

Summable

๐Ÿ“ Source: Mathlib/RingTheory/HahnSeries/Summable.lean

Statistics

MetricCount
DefinitionsSummableFamily, coeff, const, embDomain, hsum, instAdd, instAddCommGroup, instAddCommMonoid, instFunLike, instInhabited, instModule, instNeg, instSMul, instSMul_1, instSub, instZero, lsum, mul, ofFinsupp, powers, single, smul, smulFamily, toFun, instDivInvMonoid, instField, toOrderTopSubOnePos, Summable
28
TheoremsEquiv_toFun, add_apply, co_support_zero, coe_add, coe_injective, coe_mk, coe_neg, coe_ofFinsupp, coe_powers, coe_smul', coe_sub, coe_zero, coeff_apply, coeff_def, coeff_hsum, coeff_hsum_eq_sum, coeff_hsum_eq_sum_of_subset, coeff_hsum_mul, coeff_smul, coeff_support, const_toFun, embDomain_apply, embDomain_image, embDomain_notin_range, embDomain_succ_smul_powers, ext, ext_iff, finite_co_support, finite_co_support', finite_co_support_prod_mul, finite_co_support_prod_smul, hasFiniteSupport_smul, hsum_add, hsum_embDomain, hsum_equiv, hsum_leadingCoeff_of_le, hsum_mul, hsum_ofFinsupp, hsum_orderTop_of_le, hsum_single, hsum_smul, hsum_smulFamily, hsum_smul_module, hsum_sub, hsum_unique, hsum_zero, isPWO_iUnion_support, isPWO_iUnion_support', isPWO_iUnion_support_powers, isPWO_iUnion_support_prod_mul, isPWO_iUnion_support_prod_smul, le_hsum_support_mem, lsum_apply, mul_eq_smul, mul_toFun, neg_apply, one_sub_self_mul_hsum_powers, pow_finite_co_support, powers_of_not_orderTop_pos, powers_of_orderTop_pos, powers_toFun, powers_zero, single_toFun, smulFamily_toFun, smul_apply, smul_apply', smul_eq, smul_hsum, smul_support_finite, smul_support_subset_prod, smul_toFun, sub_apply, sum_vAddAntidiagonal_eq, support_hsum_subset, support_pow_subset_closure, zero_apply, inv_def, inv_single, isUnit_iff, isUnit_of_isUnit_leadingCoeff_AddUnitOrder, isUnit_of_orderTop_pos, one_minus_single_neg_mul, single_div_single, single_zero_ofScientific, unit_aux, val_inv_toOrderTopSubOnePos_coe, val_toOrderTopSubOnePos_coe
87
Total115

HahnSeries

Definitions

NameCategoryTheorems
SummableFamily ๐Ÿ“–CompData
60 mathmath: SummableFamily.powerSeriesFamily_add, SummableFamily.zero_apply, SummableFamily.embDomain_apply, SummableFamily.coe_neg, SummableFamily.mul_toFun, SummableFamily.coeff_hsum_eq_sum_of_subset, SummableFamily.ext_iff, SummableFamily.binomialFamily_orderTop_pos, SummableFamily.coe_add, SummableFamily.add_apply, SummableFamily.support_hsum_subset, SummableFamily.embDomain_notin_range, SummableFamily.binomialFamily_apply_of_orderTop_nonpos, SummableFamily.lsum_apply, SummableFamily.coeff_hsum_mul, SummableFamily.sub_apply, SummableFamily.hsum_smul_module, SummableFamily.smul_apply', SummableFamily.Equiv_toFun, SummableFamily.smul_apply, SummableFamily.coe_powers, SummableFamily.isPWO_iUnion_support, SummableFamily.coe_smul', SummableFamily.single_toFun, SummableFamily.embDomain_succ_smul_powers, SummableFamily.smul_support_subset_prod, SummableFamily.hsum_add, SummableFamily.smul_toFun, SummableFamily.smul_support_finite, SummableFamily.coe_injective, SummableFamily.const_toFun, SummableFamily.coeff_support, SummableFamily.smul_eq, SummableFamily.hasFiniteSupport_smul, SummableFamily.coe_mk, SummableFamily.coeff_smul, SummableFamily.coe_sub, SummableFamily.smulFamily_toFun, SummableFamily.binomialFamily_apply, SummableFamily.neg_apply, SummableFamily.coeff_hsum, SummableFamily.coe_zero, SummableFamily.sum_vAddAntidiagonal_eq, SummableFamily.powerSeriesFamily_of_orderTop_pos, SummableFamily.powers_toFun, SummableFamily.hsum_smul, SummableFamily.hsum_smulFamily, SummableFamily.coeff_apply, SummableFamily.hsum_unique, SummableFamily.embDomain_image, SummableFamily.powers_of_orderTop_pos, SummableFamily.hsum_sub, SummableFamily.coeff_hsum_eq_sum, SummableFamily.hsum_leadingCoeff_of_le, SummableFamily.coeff_def, SummableFamily.powerSeriesFamily_smul, cardSupp_hsum_le, SummableFamily.finite_co_support, SummableFamily.hsum_zero, SummableFamily.coe_ofFinsupp
instDivInvMonoid ๐Ÿ“–CompOp
6 mathmath: cardSupp_div_le, RatFunc.algebraMap_apply_div, single_div_single, inv_def, RatFunc.single_zpow, inv_single
instField ๐Ÿ“–CompOp
17 mathmath: mem_cardSuppLTSubfield, RatFunc.coe_X, RatFunc.coe_coe, LaurentSeries.inducing_coe, LaurentSeries.continuous_coe, cardSuppLTSubfield_carrier, LaurentSeries.exists_ratFunc_val_lt, RatFunc.valuation_eq_LaurentSeries_valuation, RatFunc.algebraMap_apply_div, LaurentSeries.continuous_coe', LaurentSeries.LaurentSeries_coe, LaurentSeries.valuation_coe_ratFunc, LaurentSeries.coe_range_dense, LaurentSeries.comparePkg_eq_extension, LaurentSeries.valuation_def, RatFunc.single_inv, cardSupp_inv_le
toOrderTopSubOnePos ๐Ÿ“–CompOp
4 mathmath: binomial_power, coeff_toOrderTopSubOnePos_pow, val_toOrderTopSubOnePos_coe, val_inv_toOrderTopSubOnePos_coe

Theorems

NameKindAssumesProvesValidatesDepends On
inv_def ๐Ÿ“–mathematicalโ€”HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
DivInvMonoid.toInv
instDivInvMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
instMul
AddCommGroup.toAddCommMonoid
DFunLike.coe
ZeroHom
instZero
ZeroHom.funLike
single
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
order
NegZeroClass.toZero
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
leadingCoeff
SummableFamily.hsum
SummableFamily.powers
instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
DivisionRing.toRing
Field.toDivisionRing
instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
โ€”โ€”
inv_single ๐Ÿ“–mathematicalโ€”HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
DivInvMonoid.toInv
instDivInvMonoid
DFunLike.coe
ZeroHom
instZero
ZeroHom.funLike
single
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
DivisionCommMonoid.toDivisionMonoid
CommGroupWithZero.toDivisionCommMonoid
Semifield.toCommGroupWithZero
Field.toSemifield
โ€”eq_or_ne
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
map_zero
ZeroHom.zeroHomClass
order_zero
neg_zero
leadingCoeff_zero
inv_zero
SummableFamily.powers.congr_simp
MulZeroClass.mul_zero
sub_zero
MulZeroClass.zero_mul
order_single
leadingCoeff_of_single
single_mul_single
neg_add_cancel
inv_mul_cancelโ‚€
sub_self
SummableFamily.powers_zero
SummableFamily.hsum_single
mul_one
isUnit_iff ๐Ÿ“–mathematicalโ€”IsUnit
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
AddCommGroup.toAddCommMonoid
IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
PartialOrder.toPreorder
CommSemiring.toSemiring
CommRing.toCommSemiring
leadingCoeff
โ€”IsOrderedAddMonoid.toIsOrderedCancelAddMonoid
IsUnit.of_mul_eq_one
instIsDedekindFiniteMonoid
coeff_mul_order_add_order
coeff_one
order_mul
IsDomain.to_noZeroDivisors
left_ne_zero_of_mul_eq_one
instNontrivialOfNonempty
Zero.instNonempty
IsDomain.toNontrivial
right_ne_zero_of_mul_eq_one
order_one
SummableFamily.one_sub_self_mul_hsum_powers
unit_aux
neg_add_cancel
isUnit_of_mul_isUnit_right
sub_sub_cancel
isUnit_of_isUnit_leadingCoeff_AddUnitOrder ๐Ÿ“–mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
CommSemiring.toSemiring
CommRing.toCommSemiring
leadingCoeff
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
IsAddUnit
AddCommMonoid.toAddMonoid
order
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
IsUnit
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
โ€”SummableFamily.one_sub_self_mul_hsum_powers
unit_aux
AddUnits.neg_add
isUnit_of_mul_isUnit_right
instIsDedekindFiniteMonoid
IsUnit.of_mul_eq_one
sub_sub_cancel
isUnit_of_orderTop_pos ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
IsUnit
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
โ€”subsingleton_or_nontrivial
isUnit_of_subsingleton
instSubsingleton
isUnit_of_isUnit_leadingCoeff_AddUnitOrder
orderTop_self_sub_one_pos_iff
isUnit_one
WithTop.coe_eq_zero
order_eq_orderTop_of_ne_zero
WithTop.top_ne_zero
orderTop_eq_top
isAddUnit_zero
one_minus_single_neg_mul ๐Ÿ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
leadingCoeff
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
HahnSeries
instAdd
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
DFunLike.coe
ZeroHom
instZero
ZeroHom.funLike
single
order
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
instOne
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
instMul
DFunLike.coe
ZeroHom
instZero
ZeroHom.funLike
single
instNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
โ€”mul_add
Distrib.leftDistribClass
single_mul_single
sub_add_eq_sub_sub_swap
sub_eq_neg_self
sub_eq_zero_of_eq
single_zero_one
single_div_single ๐Ÿ“–mathematicalโ€”HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
DivInvMonoid.toDiv
instDivInvMonoid
DFunLike.coe
ZeroHom
instZero
ZeroHom.funLike
single
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
DivisionRing.toDivInvMonoid
Field.toDivisionRing
โ€”div_eq_mul_inv
sub_eq_add_neg
inv_single
single_mul_single
single_zero_ofScientific ๐Ÿ“–mathematicalโ€”DFunLike.coe
ZeroHom
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Field.toCommRing
instZero
ZeroHom.funLike
single
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NNRatCast.toOfScientific
DivisionRing.toNNRatCast
Field.toDivisionRing
instNNRatCast
โ€”Rat.cast_ofScientific
single_zero_ratCast
unit_aux ๐Ÿ“–mathematicalDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
leadingCoeff
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
order
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
WithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
instMul
DFunLike.coe
ZeroHom
instZero
ZeroHom.funLike
single
โ€”eq_of_sub_eq_zero
single_mul_single
single_zero_one
sub_self
orderTop_zero
IsUnit.isRegular
IsUnit.of_mul_eq_one
instIsDedekindFiniteMonoid
order_single_mul_of_isRegular
pos_of_lt_add_right
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
add_assoc
add_comm
zero_add
order_lt_order_of_eq_add_single
sub_add_cancel
one_minus_single_neg_mul
orderTop_neg
zero_lt_orderTop_of_order
val_inv_toOrderTopSubOnePos_coe ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Units.val
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
Units
Units.instInv
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
orderTopSubOnePos
toOrderTopSubOnePos
Units.inv
IsUnit.unit
isUnit_of_orderTop_pos
โ€”โ€”
val_toOrderTopSubOnePos_coe ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Units.val
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
Units
Subgroup
Units.instGroup
SetLike.instMembership
Subgroup.instSetLike
orderTopSubOnePos
toOrderTopSubOnePos
โ€”โ€”

HahnSeries.SummableFamily

Definitions

NameCategoryTheorems
coeff ๐Ÿ“–CompOp
6 mathmath: PowerSeries.coeff_heval, coeff_support, coeff_apply, support_powerSeriesFamily_subset, coeff_hsum_eq_sum, coeff_def
const ๐Ÿ“–CompOp
2 mathmath: const_toFun, smul_eq
embDomain ๐Ÿ“–CompOp
5 mathmath: embDomain_apply, embDomain_notin_range, embDomain_succ_smul_powers, hsum_embDomain, embDomain_image
hsum ๐Ÿ“–CompOp
31 mathmath: hsum_orderTop_of_le, coeff_hsum_eq_sum_of_subset, support_hsum_subset, lsum_apply, coeff_hsum_mul, hsum_smul_module, hsum_powerSeriesFamily_mul, PowerSeries.heval_apply, smul_hsum, hsum_add, powerSeriesFamily_hsum_zero, hsum_embDomain, hsum_ofFinsupp, orderTop_hsum_binomialFamily_pos, HahnSeries.binomial_power, coeff_smul, hsum_single, one_sub_self_mul_hsum_powers, coeff_hsum, HahnSeries.inv_def, hsum_smul, hsum_mul, hsum_smulFamily, hsum_unique, hsum_equiv, HahnSeries.cardSupp_hsum_powers_le, hsum_sub, coeff_hsum_eq_sum, hsum_leadingCoeff_of_le, HahnSeries.cardSupp_hsum_le, hsum_zero
instAdd ๐Ÿ“–CompOp
4 mathmath: powerSeriesFamily_add, coe_add, add_apply, hsum_add
instAddCommGroup ๐Ÿ“–CompOpโ€”
instAddCommMonoid ๐Ÿ“–CompOp
1 mathmath: lsum_apply
instFunLike ๐Ÿ“–CompOp
50 mathmath: zero_apply, embDomain_apply, coe_neg, mul_toFun, coeff_hsum_eq_sum_of_subset, ext_iff, binomialFamily_orderTop_pos, coe_add, add_apply, support_hsum_subset, embDomain_notin_range, binomialFamily_apply_of_orderTop_nonpos, coeff_hsum_mul, sub_apply, smul_apply', Equiv_toFun, smul_apply, coe_powers, isPWO_iUnion_support, coe_smul', single_toFun, smul_support_subset_prod, smul_toFun, smul_support_finite, coe_injective, const_toFun, coeff_support, hasFiniteSupport_smul, coe_mk, coeff_smul, coe_sub, smulFamily_toFun, binomialFamily_apply, neg_apply, coeff_hsum, coe_zero, sum_vAddAntidiagonal_eq, powerSeriesFamily_of_orderTop_pos, powers_toFun, hsum_smulFamily, coeff_apply, hsum_unique, embDomain_image, powers_of_orderTop_pos, coeff_hsum_eq_sum, hsum_leadingCoeff_of_le, coeff_def, HahnSeries.cardSupp_hsum_le, finite_co_support, coe_ofFinsupp
instInhabited ๐Ÿ“–CompOpโ€”
instModule ๐Ÿ“–CompOp
1 mathmath: lsum_apply
instNeg ๐Ÿ“–CompOp
2 mathmath: coe_neg, neg_apply
instSMul ๐Ÿ“–CompOp
2 mathmath: smul_apply', coe_smul'
instSMul_1 ๐Ÿ“–CompOp
6 mathmath: hsum_smul_module, smul_apply, embDomain_succ_smul_powers, smul_eq, hsum_smul, powerSeriesFamily_smul
instSub ๐Ÿ“–CompOp
4 mathmath: sub_apply, embDomain_succ_smul_powers, coe_sub, hsum_sub
instZero ๐Ÿ“–CompOp
3 mathmath: zero_apply, coe_zero, hsum_zero
lsum ๐Ÿ“–CompOp
1 mathmath: lsum_apply
mul ๐Ÿ“–CompOp
6 mathmath: mul_toFun, coeff_hsum_mul, hsum_powerSeriesFamily_mul, hsum_mul, support_powerSeriesFamily_subset, mul_eq_smul
ofFinsupp ๐Ÿ“–CompOp
3 mathmath: embDomain_succ_smul_powers, hsum_ofFinsupp, coe_ofFinsupp
powers ๐Ÿ“–CompOp
9 mathmath: powers_zero, powers_of_not_orderTop_pos, coe_powers, embDomain_succ_smul_powers, one_sub_self_mul_hsum_powers, HahnSeries.inv_def, powers_toFun, powers_of_orderTop_pos, HahnSeries.cardSupp_hsum_powers_le
single ๐Ÿ“–CompOp
4 mathmath: powers_zero, powers_of_not_orderTop_pos, single_toFun, hsum_single
smul ๐Ÿ“–CompOp
5 mathmath: smul_hsum, smul_toFun, smul_eq, coeff_smul, mul_eq_smul
smulFamily ๐Ÿ“–CompOp
2 mathmath: smulFamily_toFun, hsum_smulFamily
toFun ๐Ÿ“–CompOp
4 mathmath: isPWO_iUnion_support', smul_support_subset_prod, sum_vAddAntidiagonal_eq, finite_co_support'

Theorems

NameKindAssumesProvesValidatesDepends On
Equiv_toFun ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
Equiv
Equiv
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
โ€”โ€”
add_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instAdd
HahnSeries.instAdd
โ€”โ€”
co_support_zero ๐Ÿ“–mathematicalโ€”Set
Set.instHasSubset
setOf
HahnSeries.coeff
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HahnSeries
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
HahnSeries.instSemiring
HahnSeries.instZero
Set.instSingletonSet
โ€”zero_pow
coe_add ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instAdd
Pi.instAdd
HahnSeries.instAdd
โ€”โ€”
coe_injective ๐Ÿ“–mathematicalโ€”HahnSeries.SummableFamily
DFunLike.coe
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
โ€”DFunLike.coe_injective
coe_mk ๐Ÿ“–mathematicalSet.IsPWO
PartialOrder.toPreorder
Set.iUnion
HahnSeries.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set.Finite
setOf
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
โ€”โ€”
coe_neg ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
AddCommGroup.toAddCommMonoid
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instNeg
Pi.instNeg
HahnSeries.instNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
โ€”โ€”
coe_ofFinsupp ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
ofFinsupp
Finsupp
HahnSeries.instZero
Finsupp.instFunLike
โ€”โ€”
coe_powers ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
HahnSeries.SummableFamily
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
powers
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
HahnSeries.instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
โ€”โ€”
coe_smul' ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instSMul
Function.hasSMul
HahnSeries.instSMul
โ€”โ€”
coe_sub ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
AddCommGroup.toAddCommMonoid
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instSub
Pi.instSub
HahnSeries.instSub
AddCommGroup.toAddGroup
โ€”โ€”
coe_zero ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instZero
Pi.instZero
HahnSeries.instZero
โ€”โ€”
coeff_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
Finsupp
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finsupp.instFunLike
coeff
HahnSeries.coeff
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”โ€”
coeff_def ๐Ÿ“–mathematicalโ€”DFunLike.coe
Finsupp
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Finsupp.instFunLike
coeff
HahnSeries.coeff
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”โ€”
coeff_hsum ๐Ÿ“–mathematicalโ€”HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
finsum
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”โ€”
coeff_hsum_eq_sum ๐Ÿ“–mathematicalโ€”HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
Finset.sum
Finsupp.support
coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”finite_co_support
finsum_eq_sum
coeff_hsum_eq_sum_of_subset ๐Ÿ“–mathematicalSet
Set.instHasSubset
setOf
HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
SetLike.coe
Finset
Finset.instSetLike
HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
Finset.sum
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”finite_co_support
finsum_eq_sum
Finset.sum_subset
Set.Finite.toFinset_subset
coeff_hsum_mul ๐Ÿ“–mathematicalโ€”HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
hsum
mul
Finset.sum
Finset.addAntidiagonal
Set.iUnion
HahnSeries.support
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
isPWO_iUnion_support
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
โ€”isPWO_iUnion_support
Finset.sum_congr
coeff_smul
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
coeff_smul ๐Ÿ“–mathematicalโ€”HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
smul
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
MulActionWithZero.toSMulWithZero
Semiring.toMonoidWithZero
Module.toMulActionWithZero
Finset.sum
Finset.VAddAntidiagonal
Set.iUnion
HahnSeries.support
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
isPWO_iUnion_support
SMulZeroClass.toSMul
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Module.toDistribMulAction
โ€”isPWO_iUnion_support
coeff_hsum
HahnSeries.isPWO_support
Equiv.symm_apply_apply
Finset.sum_congr
Finset.VAddAntidiagonal.congr_simp
coeff_hsum_eq_sum
isPWO_iUnion_support'
HahnSeries.isPWO_support'
sum_vAddAntidiagonal_eq
Finset.smul_sum
Finset.sum_smul
sum_finsum_comm
hasFiniteSupport_smul
finsum_eq_sum
Finset.sum_product_right'
Finset.sum_subset
Set.Finite.prod
finite_co_support'
smul_support_subset_prod
finite_co_support
Set.Finite.coe_toFinset
coeff_support ๐Ÿ“–mathematicalโ€”Finsupp.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
coeff
Set.Finite.toFinset
Function.support
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
finite_co_support
โ€”โ€”
const_toFun ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
const
โ€”โ€”
embDomain_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
embDomain
Set
Set.instMembership
Set.range
Function.Embedding
Function.instFunLikeEmbedding
HahnSeries.instZero
โ€”โ€”
embDomain_image ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
embDomain
Function.Embedding
Function.instFunLikeEmbedding
โ€”embDomain_apply
Set.mem_range_self
Function.Embedding.injective
embDomain_notin_range ๐Ÿ“–mathematicalSet
Set.instMembership
Set.range
DFunLike.coe
Function.Embedding
Function.instFunLikeEmbedding
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
embDomain
HahnSeries.instZero
โ€”embDomain_apply
embDomain_succ_smul_powers ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
embDomain
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
HahnSeries.SummableFamily
instSMul_1
MulZeroClass.toSMulWithZero
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddCommMonoid.toAddMonoid
AddAction.toAddSemigroupAction
AddMonoid.toAddAction
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
PartialOrder.toPreorder
powers
Nat.succ_injective
instSub
Ring.toAddCommGroup
CommRing.toRing
ofFinsupp
Finsupp.single
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
HahnSeries.instZero
HahnSeries.instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
โ€”ext
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
Nat.succ_injective
embDomain_notin_range
Nat.range_succ
coe_powers
pow_zero
Finsupp.single_eq_same
sub_self
IsRightCancelAdd.addRightStrictMono_of_addRightMono
instIsRightCancelAddOfAddRightReflectLE
contravariant_swap_add_of_contravariant_add
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
instIsLeftCancelAddOfAddLeftReflectLE
IsOrderedCancelAddMonoid.toAddLeftReflectLE
Nat.instIsOrderedCancelAddMonoid
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
Nat.instIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
Nat.instCanonicallyOrderedAdd
Nat.instZeroLEOneClass
Classical.choose_eq
powers_of_orderTop_pos
pow_succ'
Finsupp.single_eq_of_ne
sub_zero
ext ๐Ÿ“–โ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
โ€”โ€”DFunLike.ext
ext_iff ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
โ€”ext
finite_co_support ๐Ÿ“–mathematicalโ€”Function.HasFiniteSupport
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”finite_co_support'
finite_co_support' ๐Ÿ“–mathematicalโ€”Set.Finite
setOf
HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
toFun
โ€”โ€”
finite_co_support_prod_mul ๐Ÿ“–mathematicalโ€”Finite
Set.Elem
setOf
HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
โ€”finite_co_support_prod_smul
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
finite_co_support_prod_smul ๐Ÿ“–mathematicalโ€”Finite
Set.Elem
setOf
HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
โ€”Set.Finite.subset
isPWO_iUnion_support
Set.Finite.biUnion'
Finset.finite_toSet
hasFiniteSupport_smul
HahnSeries.isPWO_support
Finset.exists_ne_zero_of_sum_ne_zero
Set.iUnion_congr_Prop
left_ne_zero_of_smul
right_ne_zero_of_smul
Finset.mem_vaddAntidiagonal
hasFiniteSupport_smul ๐Ÿ“–mathematicalโ€”Function.HasFiniteSupport
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SMulZeroClass.toSMul
SMulWithZero.toSMulZeroClass
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”Set.Finite.subset
Set.Finite.prod
finite_co_support'
Set.toFinite
Finite.of_fintype
smul_support_subset_prod
hsum_add ๐Ÿ“–mathematicalโ€”hsum
HahnSeries.SummableFamily
instAdd
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.instAdd
โ€”HahnSeries.ext
finsum_add_distrib
finite_co_support
hsum_embDomain ๐Ÿ“–mathematicalโ€”hsum
embDomain
โ€”HahnSeries.ext
dite_apply
finsum_emb_domain
hsum_equiv ๐Ÿ“–mathematicalโ€”hsum
Equiv
โ€”HahnSeries.ext
finsum_eq_of_bijective
Equiv.bijective
hsum_leadingCoeff_of_le ๐Ÿ“–mathematicalWithTop.some
HahnSeries.orderTop
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
Preorder.toLE
PartialOrder.toPreorder
HahnSeries.coeff
HahnSeries.leadingCoeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”hsum_orderTop_of_le
HahnSeries.isWF_support
HahnSeries.orderTop.eq_1
HahnSeries.orderTop_ne_top
HahnSeries.leadingCoeff_of_ne_zero
HahnSeries.support_nonempty_iff
HahnSeries.untop_orderTop_of_ne_zero
finsum_eq_single
hsum_mul ๐Ÿ“–mathematicalโ€”hsum
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
mul
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.instMul
โ€”smul_eq_mul
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
mul_eq_smul
smul_hsum
hsum_ofFinsupp ๐Ÿ“–mathematicalโ€”hsum
ofFinsupp
Finsupp.sum
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.instZero
HahnSeries.instAddCommMonoid
โ€”HahnSeries.ext
Finset.sum_congr
map_sum
AddMonoidHom.instAddMonoidHomClass
finsum_eq_sum_of_support_subset
Mathlib.Tactic.Contrapose.contraposeโ‚ƒ
hsum_orderTop_of_le ๐Ÿ“–mathematicalWithTop.some
HahnSeries.orderTop
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
Preorder.toLE
PartialOrder.toPreorder
HahnSeries.coeff
HahnSeries.orderTop
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
WithTop.some
โ€”HahnSeries.orderTop_eq_of_le
ne_of_eq_of_ne
coeff_hsum
finsum_eq_single
HahnSeries.coeff_orderTop_ne
le_hsum_support_mem
hsum_single ๐Ÿ“–mathematicalโ€”hsum
single
โ€”HahnSeries.ext
coeff_hsum
finsum_eq_single
Pi.single_eq_of_ne
single_toFun
Pi.single_eq_same
hsum_smul ๐Ÿ“–mathematicalโ€”hsum
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HahnSeries
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
HahnSeries.SummableFamily
instSMul_1
MulZeroClass.toSMulWithZero
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddCommMonoid.toAddMonoid
AddAction.toAddSemigroupAction
AddMonoid.toAddAction
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
PartialOrder.toPreorder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
HahnSeries.instMul
โ€”instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
hsum_smul_module
HahnSeries.of_symm_smul_of_eq_mul
hsum_smulFamily ๐Ÿ“–mathematicalโ€”HahnSeries.coeff
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
smulFamily
finsum
SMulZeroClass.toSMul
SMulWithZero.toSMulZeroClass
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”โ€”
hsum_smul_module ๐Ÿ“–mathematicalโ€”hsum
HahnSeries
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HahnSeries.SummableFamily
instSMul_1
NonUnitalNonAssocSemiring.toAddCommMonoid
MulActionWithZero.toSMulWithZero
Semiring.toMonoidWithZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Module.toMulActionWithZero
DFunLike.coe
Equiv
HahnModule
SMulZeroClass.toSMul
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Module.toDistribMulAction
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
HahnModule.of
HahnModule.instSMul
โ€”Finite.of_fintype
smul_eq
hsum_equiv
smul_hsum
hsum_unique
const_toFun
hsum_sub ๐Ÿ“–mathematicalโ€”hsum
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
HahnSeries.SummableFamily
instSub
Ring.toAddCommGroup
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
โ€”instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
lsum_apply
map_sub
DistribMulActionSemiHomClass.toAddMonoidHomClass
SemilinearMapClass.distribMulActionSemiHomClass
LinearMap.semilinearMapClass
hsum_unique ๐Ÿ“–mathematicalโ€”hsum
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
Unique.instInhabited
โ€”HahnSeries.ext
finsum_unique
hsum_zero ๐Ÿ“–mathematicalโ€”hsum
HahnSeries.SummableFamily
instZero
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.instZero
โ€”HahnSeries.ext
finsum_zero
isPWO_iUnion_support ๐Ÿ“–mathematicalโ€”Set.IsPWO
PartialOrder.toPreorder
Set.iUnion
HahnSeries.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”isPWO_iUnion_support'
isPWO_iUnion_support' ๐Ÿ“–mathematicalโ€”Set.IsPWO
PartialOrder.toPreorder
Set.iUnion
HahnSeries.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
toFun
โ€”โ€”
isPWO_iUnion_support_powers ๐Ÿ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.order
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Set.IsPWO
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
Set.iUnion
HahnSeries.support
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HahnSeries
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
HahnSeries.instSemiring
โ€”Set.IsPWO.mono
Set.IsPWO.addSubmonoid_closure
le_trans
HahnSeries.order_le_of_coeff_ne_zero
Function.mem_support
HahnSeries.isPWO_support'
Set.iUnion_subset
support_pow_subset_closure
isPWO_iUnion_support_prod_mul ๐Ÿ“–mathematicalSet.IsPWO
PartialOrder.toPreorder
Set.iUnion
HahnSeries.support
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Set.IsPWO
PartialOrder.toPreorder
Set.iUnion
HahnSeries.support
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
โ€”isPWO_iUnion_support_prod_smul
isPWO_iUnion_support_prod_smul ๐Ÿ“–mathematicalSet.IsPWO
PartialOrder.toPreorder
Set.iUnion
HahnSeries.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Set.IsPWO
PartialOrder.toPreorder
Set.iUnion
HahnSeries.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
โ€”Set.IsPWO.mono
Set.IsPWO.vadd
IsOrderedCancelVAdd.toIsOrderedVAdd
Set.Subset.trans
HahnSeries.isPWO_support
Mathlib.Tactic.Contrapose.contraposeโ‚
HahnSeries.mem_support
HahnModule.coeff_smul
Finset.sum_empty
Finset.support_vaddAntidiagonal_subset_vadd
Set.iUnion_mono
Set.vadd_subset_vadd
Set.subset_iUnion_of_subset
le_hsum_support_mem ๐Ÿ“–mathematicalPreorder.toLE
PartialOrder.toPreorder
Set
Set.instMembership
HahnSeries.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
Preorder.toLE
PartialOrder.toPreorder
โ€”Finset.exists_ne_zero_of_sum_ne_zero
coeff_hsum_eq_sum
HahnSeries.mem_support
lsum_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
LinearMap
HahnSeries
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HahnSeries.instSemiring
RingHom.id
HahnSeries.instNonAssocSemiring
HahnSeries.SummableFamily
NonUnitalNonAssocSemiring.toAddCommMonoid
instAddCommMonoid
HahnSeries.instAddCommMonoid
instModule
AddMonoid.toAddAction
AddCommMonoid.toAddMonoid
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
PartialOrder.toPreorder
Semiring.toModule
LinearMap.instFunLike
lsum
hsum
โ€”instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
mul_eq_smul ๐Ÿ“–mathematicalโ€”mul
smul
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
MulZeroClass.toSMulWithZero
NonUnitalNonAssocSemiring.toMulZeroClass
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddCommMonoid.toAddMonoid
AddAction.toAddSemigroupAction
AddMonoid.toAddAction
instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
PartialOrder.toPreorder
โ€”โ€”
mul_toFun ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
mul
HahnSeries.instMul
โ€”โ€”
neg_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
AddCommGroup.toAddCommMonoid
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instNeg
HahnSeries.instNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
โ€”โ€”
one_sub_self_mul_hsum_powers ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
NonUnitalNonAssocSemiring.toAddCommMonoid
HahnSeries.instMul
HahnSeries.instSub
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
CommRing.toRing
HahnSeries.instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
hsum
powers
โ€”instIsOrderedCancelVAddOfIsOrderedAddCancelMonoid
hsum_smul
sub_smul
one_smul
hsum_sub
Nat.succ_injective
hsum_embDomain
embDomain_succ_smul_powers
hsum_ofFinsupp
Finsupp.sum_single_index
sub_sub_cancel
pow_finite_co_support ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
Set.Finite
setOf
HahnSeries.coeff
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
โ€”isPWO_iUnion_support_powers
HahnSeries.zero_le_orderTop_iff
le_of_lt
Set.Finite.subset
Set.finite_singleton
co_support_zero
Set.WellFoundedOn.induction
Set.IsPWO.isWF
HahnSeries.isPWO_support
Set.Finite.union
Set.Finite.image
Set.Finite.biUnion
Finset.finite_toSet
Finset.mem_addAntidiagonal
Finset.mem_coe
lt_add_of_pos_left
IsRightCancelAdd.addRightStrictMono_of_addRightMono
instIsRightCancelAddOfAddRightReflectLE
contravariant_swap_add_of_contravariant_add
IsLeftCancelAdd.addLeftReflectLE_of_addLeftReflectLT
instIsLeftCancelAddOfAddLeftReflectLE
IsOrderedCancelAddMonoid.toAddLeftReflectLE
contravariant_lt_of_covariant_le
IsOrderedAddMonoid.toAddLeftMono
IsOrderedCancelAddMonoid.toIsOrderedAddMonoid
covariant_swap_add_of_covariant_add
lt_of_lt_of_le
HahnSeries.zero_lt_orderTop_iff
HahnSeries.order_le_of_coeff_ne_zero
Function.mem_support
Set.mem_union_right
Set.mem_singleton
HahnSeries.support_mul_subset
Set.mem_union_left
Set.mem_iUnion
add_comm
Set.finite_empty
powers_of_not_orderTop_pos ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
powers
single
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
โ€”ext
HahnSeries.ext
eq_or_ne
pow_zero
HahnSeries.coeff_one
Pi.single_eq_same
zero_pow
Pi.single_eq_of_ne
powers_of_orderTop_pos ๐Ÿ“–mathematicalWithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
WithTop.zero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.orderTop
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
DFunLike.coe
HahnSeries.SummableFamily
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
powers
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
HahnSeries.instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
โ€”โ€”
powers_toFun ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
NonUnitalNonAssocSemiring.toAddCommMonoid
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
powers
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
HahnSeries.instSemiring
CommSemiring.toSemiring
CommRing.toCommSemiring
WithTop
Preorder.toLT
WithTop.instPreorder
PartialOrder.toPreorder
WithTop.zero
HahnSeries.orderTop
WithTop.decidableLT
LinearOrder.toDecidableLT
HahnSeries.instZero
โ€”โ€”
powers_zero ๐Ÿ“–mathematicalโ€”powers
HahnSeries
SemilatticeInf.toPartialOrder
Lattice.toSemilatticeInf
DistribLattice.toLattice
instDistribLatticeOfLinearOrder
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonUnitalNonAssocCommRing.toNonUnitalNonAssocRing
NonUnitalCommRing.toNonUnitalNonAssocCommRing
CommRing.toNonUnitalCommRing
HahnSeries.instZero
single
NonUnitalNonAssocSemiring.toAddCommMonoid
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.instOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
CommRing.toRing
โ€”ext
HahnSeries.ext
powers_of_orderTop_pos
HahnSeries.orderTop_zero
eq_or_ne
pow_zero
HahnSeries.coeff_one
Pi.single_eq_same
zero_pow
Pi.single_eq_of_ne
single_toFun ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
single
Pi.single
HahnSeries.instZero
โ€”โ€”
smulFamily_toFun ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
smulFamily
HahnSeries.instSMul
SMulWithZero.toSMulZeroClass
โ€”โ€”
smul_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instSMul_1
Equiv
HahnModule
SMulZeroClass.toSMul
SMulWithZero.toSMulZeroClass
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
HahnModule.of
HahnModule.instSMul
โ€”โ€”
smul_apply' ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instSMul
HahnSeries.instSMul
โ€”โ€”
smul_eq ๐Ÿ“–mathematicalโ€”HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.SummableFamily
instSMul_1
Equiv
Equiv.punitProd
smul
const
Finite.of_fintype
PUnit.fintype
โ€”โ€”
smul_hsum ๐Ÿ“–mathematicalโ€”hsum
smul
NonUnitalNonAssocSemiring.toAddCommMonoid
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
MulActionWithZero.toSMulWithZero
Semiring.toMonoidWithZero
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
Module.toMulActionWithZero
DFunLike.coe
Equiv
HahnModule
SMulZeroClass.toSMul
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
MonoidWithZero.toMonoid
Module.toDistribMulAction
HahnSeries
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
HahnModule.of
HahnModule.instSMul
โ€”HahnSeries.ext
isPWO_iUnion_support
coeff_smul
HahnSeries.isPWO_support
HahnModule.coeff_smul
Equiv.symm_apply_apply
Finset.sum_of_injOn
Finset.exists_ne_zero_of_sum_ne_zero
coeff_hsum_eq_sum
finite_co_support
finsum_zero
smul_eq_zero_of_left
Set.image_id'
smul_zero
smul_support_finite ๐Ÿ“–mathematicalโ€”Function.HasFiniteSupport
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SMulZeroClass.toSMul
SMulWithZero.toSMulZeroClass
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”hasFiniteSupport_smul
smul_support_subset_prod ๐Ÿ“–mathematicalโ€”Set
Set.instHasSubset
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SMulZeroClass.toSMul
SMulWithZero.toSMulZeroClass
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
SetLike.coe
Finset
Finset.instSetLike
Set.Finite.toFinset
SProd.sprod
Set.instSProd
setOf
toFun
Set.Finite.prod
finite_co_support'
โ€”Set.Finite.prod
finite_co_support'
Set.Finite.coe_toFinset
left_ne_zero_of_smul
right_ne_zero_of_smul
smul_toFun ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
smul
Equiv
HahnModule
SMulZeroClass.toSMul
SMulWithZero.toSMulZeroClass
EquivLike.toFunLike
Equiv.instEquivLike
Equiv.symm
HahnModule.of
HahnModule.instSMul
โ€”โ€”
sub_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
AddCommGroup.toAddCommMonoid
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instSub
HahnSeries.instSub
AddCommGroup.toAddGroup
โ€”โ€”
sum_vAddAntidiagonal_eq ๐Ÿ“–mathematicalโ€”Finset.sum
Finset.VAddAntidiagonal
Function.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
HahnSeries.coeff
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
HahnSeries.isPWO_support'
SMulZeroClass.toSMul
SMulWithZero.toSMulZeroClass
Set.iUnion
HahnSeries.support
toFun
isPWO_iUnion_support'
โ€”Finset.sum_subset
HahnSeries.isPWO_support'
isPWO_iUnion_support'
smul_eq_zero_of_left
smul_zero
support_hsum_subset ๐Ÿ“–mathematicalโ€”Set
Set.instHasSubset
HahnSeries.support
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
hsum
Set.iUnion
DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
instFunLike
โ€”finite_co_support
Finset.exists_ne_zero_of_sum_ne_zero
finsum_eq_sum
coeff_hsum
HahnSeries.mem_support
Set.mem_iUnion
support_pow_subset_closure ๐Ÿ“–mathematicalโ€”Set
Set.instHasSubset
HahnSeries.support
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
HahnSeries
Monoid.toPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
HahnSeries.instSemiring
SetLike.coe
AddSubmonoid
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
AddSubmonoid.instSetLike
AddSubmonoid.closure
โ€”pow_zero
HahnSeries.coeff_one
AddSubmonoid.zero_mem
HahnSeries.support_mul_subset
SetLike.mem_coe
AddSubmonoid.add_mem
AddSubmonoid.subset_closure
zero_apply ๐Ÿ“–mathematicalโ€”DFunLike.coe
HahnSeries.SummableFamily
HahnSeries
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
instFunLike
instZero
HahnSeries.instZero
โ€”โ€”

(root)

Definitions

NameCategoryTheorems
Summable ๐Ÿ“–MathDef
381 mathmath: NNReal.summable_and_Lr_rpow_le_Lp_mul_Lq_tsum, ZLattice.summable_norm_zpow, ArithmeticFunction.vonMangoldt.summable_residueClass_non_primes_div, NNReal.summable_coe, NNReal.summable_and_inner_le_Lp_mul_Lq_tsum, summable_sigma_of_nonneg, SummationFilter.summable_symmetricIco_of_summable_symmetricIcc, summable_of_isEquivalent_nat, Summable.abs, ZLattice.summable_norm_sub_inv_pow, summable_of_isEquivalent, NormedSpace.expSeries_summable_of_mem_ball, summable_riemannZetaSummand, Asymptotics.IsTheta.summable_iff_nat, Real.summable_ofDigitsTerm, summable_nat_add_iff, Summable.const_smul, Summable.map_iff_of_leftInverse, Summable.mapL, Real.summable_log_one_add_of_summable, Summable.ofStar, summable_matrix_transpose, summable_congr, MeasureTheory.Integrable.summable_of_dirac, Real.summable_one_div_nat_add_rpow, ENNReal.summable_toNNReal_of_tsum_ne_top, summable_star_iff, FormalMultilinearSeries.changeOriginSeries_summable_auxโ‚ƒ, Real.summable_one_div_int_pow, summable_norm_mul_geometric_of_norm_lt_one, MvPowerSeries.WithPiTopology.summable_of_tendsto_order_atTop_nhds_top, Summable.of_nnnorm_bounded, NNReal.summable_sigma, summable_mul_prod_iff_summable_mul_sigma_antidiagonal, Set.Finite.summable, summable_congr_atTop, ContinuousMap.summable_of_locally_summable_norm, summable_norm_mul_geometric_of_norm_lt_one', NNReal.not_summable_iff_tendsto_nat_atTop, Summable.matrix_blockDiagonal, Finset.summable, summable_condensed_iff_of_eventually_nonneg, summable_sum_mul_range_of_summable_norm', Summable.summable_compl_iff, Real.summable_nat_rpow_inv, Summable.comp_nat_add, NNReal.summable_geometric, HasSummableGeomSeries.summable_geometric_of_norm_lt_one, Summable.sigma, Summable.matrix_blockDiag, EisensteinSeries.summable_left_one_div_linear_sub_one_div_linear, Finset.summable_compl_iff, Summable.update, IsEquivalent.summable_iff_nat, EisensteinSeries.e2Summand_summable, Summable.mul_of_nonarchimedean, summable_finset_prod_of_summable_norm, NormedSpace.expSeries_summable, Summable.mul_right, MeasureTheory.integrable_sum_measure_iff, Complex.summable_conj, summable_mul_of_bigO_atTop, Summable.of_norm, Real.not_summable_indicator_one_div_natCast, Real.summable_abs_int_rpow, summable_mul_of_summable_norm, Summable.subtype, summable_eisSummand, Memโ„“p.summable_of_one, EisensteinSeries.summable_inv_of_isBigO_rpow_inv, not_summable_of_antitone_of_neg, Summable.neg, LiouvilleNumber.summable, lp.summable_mul, NormedSpace.norm_expSeries_summable, LSeries.summable_real_of_abscissaOfAbsConv_lt, summable_unop, summable_const_div_iff, SummableLocallyUniformlyOn.summable, memโ„“p_gen_iff, EisensteinSeries.summable_of_isBigO_rpow_norm, summable_matrix_diagonal, summable_schlomilch_iff_of_nonneg, RCLike.summable_ofReal, EisensteinSeries.summable_norm_eisSummand, summable_int_iff_summable_nat_and_neg_add_zero, ContinuousLinearMap.summable, Summable_cotTerm, summable_jacobiThetaโ‚‚_term_fderiv_iff, summable_sum_mul_antidiagonal_of_summable_mul, Asymptotics.IsBigO.comp_summable_norm, EisensteinSeries.linear_right_summable, EisensteinSeries.summable_linear_left_mul_linear_left, NormedSpace.norm_expSeries_summable_of_mem_ball', Summable.matrix_diagonal, NNReal.summable_nat_add, PowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top, summable_of_ratio_test_tendsto_lt_one, Function.Surjective.summable_iff_of_hasSum_iff, summable_norm_sum_mul_range_of_summable_norm, Equiv.summable_iff_of_support, Summable.add, LiouvilleNumber.remainder_summable, Orthonormal.inner_products_summable, ENNReal.summable, Summable.matrix_blockDiagonal', Nat.Partition.summable_genFun_term, NNReal.summable_mul_rpow_of_Lp_Lq, Summable.of_finite, Summable.of_nat_of_neg, Summable.of_nnnorm, Asymptotics.IsBigO.comp_summable, summable_iff_vanishing_norm, ArithmeticFunction.vonMangoldt.not_summable_residueClass_prime_div, summable_matrix_conjTranspose, NormedSpace.expSeries_summable', NormedSpace.norm_expSeries_summable_of_mem_ball, summable_prod_mul_pow, RCLike.summable_conj, Nat.Primes.not_summable_one_div, Summable.trans_sub, Summable.sub, summable_int_iff_summable_nat_and_neg, Summable.alternating, summable_div_const_iff, Real.summable_nat_pow_inv, ZLattice.summable_norm_rpow, FormalMultilinearSeries.not_summable_norm_of_radius_lt_nnnorm, PiCountable.dist_summable, Real.summable_exp_neg_nat, MvPowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zero, Summable.summable_log_norm_one_add, PeriodPair.summable_weierstrassPSummand, DirichletCharacter.summable_neg_log_one_sub_mul_prime_cpow, summable_matrix_blockDiagonal', EisensteinSeries.linear_left_summable, summable_powerSeries_of_norm_lt_one, summable_mul_of_summable_norm', summable_choose_mul_geometric_of_norm_lt_one, Complex.summable_ofReal, Real.Lp_add_le_tsum_of_nonneg, Summable.of_nonneg_of_le, summable_pnat_iff_summable_succ, Asymptotics.IsTheta.summable_iff, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_geometric, Summable.congr_cofinite, summable_pow_div_add, NormedSpace.expSeries_div_summable, summable_descFactorial_mul_geometric_of_norm_lt_one, Summable.matrix_blockDiag', OrthogonalFamily.summable_of_lp, Summable.matrix_diag, NNReal.summable_nat_add_iff, Real.summable_and_inner_le_Lp_mul_Lq_tsum_of_nonneg, Summable.star, Summable.sigma_factor, EisensteinSeries.summable_one_div_norm_rpow, Summable.clog_one_sub, summable_dirichletSummand, Real.summable_Lp_add_of_nonneg, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_geometric, HurwitzKernelBounds.summable_f_nat, NNReal.summable_comp_injective, Summable.prod, summable_of_ratio_norm_eventually_le, MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_weightedOrder_atTop_nhds_top, summable_powerSeries_of_norm_lt, not_summable_indicator_mod_of_antitone_of_neg, NNReal.summable_of_sum_range_le, HasSum.summable, Real.summable_one_div_nat_rpow, ZLattice.summable_norm_pow_inv, Summable.unop, summable_of_summable_hasFDerivAt, summable_of_hasFiniteSupport, NormedSpace.norm_expSeries_summable', summable_abs_iff, NormedSpace.norm_expSeries_div_summable_of_mem_ball, Pi.summable, Real.summable_exp_nat_mul_of_ge, summable_one_div_pow_of_le, Summable.const_div, Quaternion.summable_coe, summable_iff_not_tendsto_nat_atTop_of_nonneg, summable_norm_pow_mul_geometric_div_one_sub, NNReal.summable_Lp_add, summable_iff_of_summable_sub, lp.summable_inner, Summable.summable_of_eq_zero_or_self, summable_iff_vanishing, Summable.mul_left, NormedSpace.expSeries_div_summable_of_mem_ball, ENNReal.tsum_coe_ne_top_iff_summable_coe, summable_finset_prod_of_summable_nonneg, EisensteinSeries.summable_linear_sub_mul_linear_add, summable_mul_left_iff, FormalMultilinearSeries.changeOriginSeries_summable_auxโ‚, summable_sum, Summable.mul_of_nonneg, ModularForm.summable_logDeriv_one_sub_eta_q, summable_const_iff, ContinuousMap.summable_apply, Function.Injective.summable_iff, Summable.comp_injective, ZLattice.summable_norm_sub_rpow, summable_geometric_of_abs_lt_one, Topology.IsInducing.summable_iff_tsum_comp_mem_range, Real.summable_pow_div_factorial, ENNReal.tsum_coe_ne_top_iff_summable, Equiv.summable_iff, summable_condensed_iff_of_nonneg, Asymptotics.IsEquivalent.summable_iff, Real.not_summable_one_div_natCast, Summable.toNNReal, summable_of_summable_hasDerivAt_of_isPreconnected, Summable.of_abs, NNReal.summable_one_div_rpow, Summable.compl_add, summable_subtype_and_compl, Summable.matrix_transpose, Summable.mul_tendsto_const, FormalMultilinearSeries.changeOriginSeries_summable_auxโ‚‚, Summable.matrix_conjTranspose, IsEquivalent.summable_iff, Real.summable_pow_mul_exp_neg_nat_mul, MvPowerSeries.WithPiTopology.summable_prod_of_tendsto_order_atTop_nhds_top, Summable.prod_symm, EisensteinSeries.summable_e2Summand_symmetricIcc, MvPowerSeries.WithPiTopology.summable_iff_summable_coeff, Nat.Partition.summable_genFun_term', Real.summable_and_Lr_rpow_le_Lp_mul_Lq_tsum_of_nonneg, NNReal.indicator_summable, ENNReal.tsum_coe_eq_top_iff_not_summable_coe, ENNReal.summable_toReal, summable_of_ne_finset_zero, Summable.of_norm_bounded, summable_indicator_mod_iff_summable, summable_geometric_iff_norm_lt_one, summable_zero, summable_pow_mul_geometric_of_norm_lt_one, summable_of_absolute_convergence_real, NNReal.summable_rpow_inv, summable_of_sum_le, summable_iff_cauchySeq_finset, Complex.summable_one_div_nat_cpow, EulerProduct.summable_and_hasSum_smoothNumbers_prod_primesBelow_tsum, Summable.of_add_one_of_neg_add_one, summable_iff_tsum_vanishing, summable_prod_eisSummand, Nat.Primes.summable_rpow, summable_bot, Summable.smul_const, Real.not_summable_natCast_inv, SummableLocallyUniformly.summable, FormalMultilinearSeries.summable_nnnorm_mul_pow, Set.Finite.summable_compl_iff, HilbertBasis.summable_inner_mul_inner, summable_iff_cauchySeq_finset_and_tsum_mem, ZLattice.summable_norm_sub_zpow, summable_subtype_iff_indicator, NNReal.summable_mk, Summable.norm, summable_norm_iff, Summable.congr, Summable.of_norm_bounded_eventually, ContinuousLinearEquiv.summable, Metric.exists_subseq_summable_dist_of_cauchySeq, Complex.summable_log_one_add_of_summable, NonarchimedeanAddGroup.summable_iff_tendsto_cofinite_zero, not_summable_iff_tendsto_nat_atTop_of_nonneg, Summable.mono_filter, not_summable_of_ratio_norm_eventually_ge, SummableUniformlyOn.summable, summable_of_isBigO, summable_of_sum_range_le, Summable.even_add_odd, summable_sum_mul_antidiagonal_of_summable_norm', NNReal.summable_of_le, NNReal.summable_schlomilch_iff, summable_cotTerm, summable_norm_geometric_of_norm_lt_one, summable_geometric_two', Summable.sigma', Memโ„“p.summable, summable_op, summable_empty, NNReal.summable_iff_not_tendsto_nat_atTop, Summable.map, NormedSpace.norm_expSeries_div_summable, summable_pow_mul_jacobiThetaโ‚‚_term_bound, summable_bernoulli_fourier, not_summable_one_div_on_primes, EisensteinSeries.summable_e2Summand_symmetricIco, NNReal.summable_mul_of_Lp_Lq, summable_geometric_two, Summable.add_compl, FormalMultilinearSeries.radius_eq_top_iff_summable_norm, Real.summable_one_div_nat_pow, EisensteinSeries.summable_right_one_div_linear_sub_one_div_linear_succ, EisensteinSeries.summable_linear_right_add_one_mul_linear_right, summable_geometric_of_norm_lt_one, FormalMultilinearSeries.summable_norm_mul_pow, Summable.congr_atTop, summable_of_isBigO', summable_indicator_mod_iff_summable_indicator_mod, summable_star_iff', Summable.of_nat_of_neg_add_one, summable_of_summable_hasDerivAt, summable_norm_sum_mul_antidiagonal_of_summable_norm, summable_norm_pow_mul_geometric_of_norm_lt_one, NNReal.summable_condensed_iff, summable_iff_summable_compl_and_tsum_mem, summable_neg_iff, Real.summable_Lr_of_Lp_Lq_of_nonneg, summable_geometric_of_lt_one, summable_mul_right_iff, Summable.of_neg, SummableUniformly.summable, EulerProduct.summable_and_hasSum_factoredNumbers_prod_filter_prime_tsum, MeasureTheory.integrable_count_iff, PeriodPair.summable_weierstrassPExceptSummand, Summable.map_iff_of_equiv, FormalMultilinearSeries.summable, summable_of_isBigO_nat', Summable.indicator, FormalMultilinearSeries.summable_norm_apply, summable_of_sum_range_norm_le, NormedSpace.expSeries_summable_of_mem_ball', ProbabilityTheory.integrable_poissonMeasure_iff, PowerSeries.WithPiTopology.summable_of_tendsto_order_atTop_nhds_top, Summable.nat_add_neg_add_one, Summable.div_const, Summable.int_rec, summable_sum_mul_range_of_summable_mul, tsum_def, ModularForm.summable_eta_q, summable_extend_zero, NNReal.Lp_add_le_tsum, summable_pow_mul_cexp, summable_congr_cofinite, Summable.sum, Summable.mul_norm, summable_mul_of_bigO_atTop', OrthogonalFamily.summable_iff_norm_sq_summable, summable_partition, summable_jacobiThetaโ‚‚'_term_iff, summable_of_isBigO_nat, summable_of_summable_hasFDerivAt_of_isPreconnected, MeasureTheory.Integrable.summable_integral, MeasureTheory.summable_measure_toReal, Real.summable_nat_rpow, Summable.nsmul, Real.summable_exp_nat_mul_iff, Asymptotics.IsEquivalent.summable_iff_nat, not_summable_of_ratio_test_tendsto_gt_one, PowerSeries.WithPiTopology.summable_pow_of_constantCoeff_eq_zero, summable_prod_of_nonneg, Summable.of_subsingleton_cod, Summable.nat_add_neg, Summable.prod_factor, Real.summable_one_div_int_add_rpow, summable_iff_nat_tsum_vanishing, summable_matrix_blockDiagonal, Real.summable_mul_of_Lp_Lq_of_nonneg, PowerSeries.WithPiTopology.summable_iff_summable_coeff, summable_geometric_two_encode, MeasureTheory.hasFiniteIntegral_count_iff, summable_jacobiThetaโ‚‚_term_iff, MeasureTheory.integrable_sum_dirac_iff, HurwitzKernelBounds.summable_f_int, MvPowerSeries.WithPiTopology.summable_of_tendsto_weightedOrder_atTop_nhds_top, NNReal.summable_rpow, Cardinal.summable_cantor_function, lp.tsum_mul_le_mul_norm, summable_of_finite_support, FormalMultilinearSeries.comp_summable_nnreal, summable_indicator_mod_iff, Summable.of_norm_bounded_eventually_nat, Summable.op, summable_pnat_iff_summable_nat, NonarchimedeanAddGroup.summable_of_tendsto_cofinite_zero

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