Documentation Verification Report

Periodic

📁 Source: Mathlib/Algebra/Ring/Periodic.lean

Statistics

MetricCount
DefinitionsAntiperiodic
1
Theoremsperiodic_prod, periodic_sum, add, add_const, add_int_mul_eq, add_nsmul_eq, add_zsmul_eq, const_add, const_inv_smul, const_smul, const_sub, div, eq, even_nsmul_periodic, even_zsmul_periodic, funext, funext', int_even_mul_periodic, int_mul_eq_of_eq_zero, int_mul_sub_eq, int_odd_mul_antiperiodic, mul, nat_even_mul_periodic, nat_mul_eq_of_eq_zero, nat_odd_mul_antiperiodic, neg, neg_eq, nsmul_sub_eq, odd_nsmul_antiperiodic, odd_zsmul_antiperiodic, periodic, periodic_two_mul, smul, sub, sub_const, sub_eq, sub_eq', sub_int_mul_eq, sub_nsmul_eq, sub_zsmul_eq, zsmul_sub_eq, periodic_iterate, add, add_antiperiod, add_antiperiod_eq, add_const, add_period, comp, comp_addHom, const_add, const_inv_smul, const_smul, const_sub, div, eq, funext, int_mul, int_mul_eq, int_mul_sub_eq, isPeriodicPt, lift_coe, map_vadd_multiples, map_vadd_zmultiples, mul, nat_mul, nat_mul_eq, nat_mul_sub_eq, neg, neg_eq, neg_nat_mul, neg_nsmul, not_injective, nsmul, nsmul_eq, nsmul_sub_eq, smul, sub, sub_antiperiod, sub_antiperiod_eq, sub_const, sub_eq, sub_eq', sub_int_mul_eq, sub_nat_mul_eq, sub_nsmul_eq, sub_period, sub_zsmul_eq, vadd, zsmul, zsmul_eq, zsmul_sub_eq, periodic_iterate_iff, periodic_with_period_zero, periodic_prod, periodic_sum, periodic_prod, periodic_sum
97
Total98

Finset

Theorems

NameKindAssumesProvesValidatesDepends On
periodic_prod 📖mathematicalFunction.Periodicprod
Pi.commMonoid
List.periodic_prod
prod_map_toList
periodic_sum 📖mathematicalFunction.Periodicsum
Pi.addCommMonoid
List.periodic_sum
mem_toList
sum_map_toList

Function

Definitions

NameCategoryTheorems
Antiperiodic 📖MathDef
9 mathmath: Complex.cos_antiperiodic, Real.sin_antiperiodic, Complex.exp_antiperiodic, Complex.sin_antiperiodic, Real.cos_antiperiodic, Real.Angle.sin_antiperiodic, Complex.exp_mul_I_antiperiodic, Real.Angle.cos_antiperiodic, Real.Angle.sign_antiperiodic

Theorems

NameKindAssumesProvesValidatesDepends On
periodic_iterate_iff 📖mathematicalPeriodic
Nat.iterate
IsPeriodicPt
Periodic.eq
iterate_add_apply
IsFixedPt.eq
periodic_with_period_zero 📖mathematicalPeriodic
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
add_zero

Function.Antiperiodic

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
InvolutiveNeg.toNeg
Function.Periodicneg_neg
add_const 📖Function.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
add_right_comm
add_int_mul_eq 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
Distrib.toMul
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Units.val
Int.instMonoid
Int.negOnePow
zsmul_eq_mul
add_zsmul_eq
add_nsmul_eq 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddMonoid.toNatSMul
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Monoid.toNatPow
Int.instMonoid
Nat.even_or_odd'
even_nsmul_periodic
Even.neg_pow
Distrib.rightDistribClass
Nat.instAtLeastTwoHAddOfNat
one_pow
one_smul
odd_nsmul_antiperiodic
pow_add
pow_one
mul_neg
mul_one
neg_zsmul
add_zsmul_eq 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Units.val
Int.instMonoid
Int.negOnePow
Int.even_or_odd'
even_zsmul_periodic
Int.negOnePow_two_mul
Units.val_one
one_zsmul
odd_zsmul_antiperiodic
Int.negOnePow_two_mul_add_one
Units.val_neg
neg_zsmul
const_add 📖Function.Antiperiodic
AddSemigroup.toAdd
add_assoc
const_inv_smul 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
DivInvMonoid.toMonoid
Group.toDivInvMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
inv_inv
const_smul
const_smul 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
DivInvMonoid.toMonoid
Group.toDivInvMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
smul_add
smul_inv_smul
const_sub 📖mathematicalFunction.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
InvolutiveNeg.toNeg
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sub_eq
div 📖mathematicalFunction.Antiperiodic
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
DivisionMonoid.toDivInvMonoid
Function.Periodic
Pi.instDiv
DivInvMonoid.toDiv
neg_div_neg_eq
eq 📖mathematicalFunction.Antiperiodic
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZerozero_add
even_nsmul_periodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
InvolutiveNeg.toNeg
Function.Periodic
AddMonoid.toNatSMul
Function.Periodic.nsmul
periodic
mul_nsmul
even_zsmul_periodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
Function.Periodic
SubNegMonoid.toZSMul
mul_comm
mul_zsmul
two_zsmul
two_nsmul
Function.Periodic.zsmul
periodic
funext 📖mathematicalFunction.AntiperiodicPi.instNeg
funext' 📖Function.Antiperiodic
InvolutiveNeg.toNeg
neg_eq_iff_eq_neg
funext
int_even_mul_periodic 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
InvolutiveNeg.toNeg
Function.Periodic
Distrib.toMul
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Function.Periodic.int_mul
Nat.instAtLeastTwoHAddOfNat
periodic_two_mul
int_mul_eq_of_eq_zero 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NegZeroClass.toZero
Distrib.toMul
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Int.cast_natCast
nat_mul_eq_of_eq_zero
Int.cast_negSucc
neg_mul
mul_neg
neg
int_mul_sub_eq 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Distrib.toMul
AddGroupWithOne.toIntCast
Units.val
Int.instMonoid
Int.negOnePow
zsmul_eq_mul
zsmul_sub_eq
int_odd_mul_antiperiodic 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
InvolutiveNeg.toNeg
Distrib.toMul
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
add_assoc
int_even_mul_periodic
mul 📖mathematicalFunction.Antiperiodic
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
Function.Periodic
Pi.instMul
mul_neg
neg_mul
neg_neg
nat_even_mul_periodic 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
InvolutiveNeg.toNeg
Function.Periodic
Distrib.toMul
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
instOfNatAtLeastTwo
Nat.instAtLeastTwoHAddOfNat
Function.Periodic.nat_mul
Nat.instAtLeastTwoHAddOfNat
periodic_two_mul
nat_mul_eq_of_eq_zero 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
NegZeroClass.toNeg
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
NegZeroClass.toZero
Distrib.toMul
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.cast_zero
MulZeroClass.zero_mul
Nat.cast_add
Nat.cast_one
add_mul
Distrib.rightDistribClass
one_mul
neg_zero
nat_odd_mul_antiperiodic 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
InvolutiveNeg.toNeg
Distrib.toMul
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
instOfNatAtLeastTwo
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
add_assoc
nat_even_mul_periodic
neg 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
sub_eq_add_neg
sub_eq
neg_eq 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
NegZeroClass.toZero
zero_add
neg
nsmul_sub_eq 📖mathematicalFunction.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Monoid.toNatPow
Int.instMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
natCast_zsmul
zsmul_sub_eq
odd_nsmul_antiperiodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
InvolutiveNeg.toNeg
AddMonoid.toNatSMuladd_nsmul
one_nsmul
add_assoc
even_nsmul_periodic
odd_zsmul_antiperiodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
SubNegMonoid.toZSMuladd_zsmul
one_zsmul
add_assoc
even_zsmul_periodic
periodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
InvolutiveNeg.toNeg
Function.Periodic
AddMonoid.toNatSMul
two_nsmul
neg_neg
periodic_two_mul 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
InvolutiveNeg.toNeg
Function.Periodic
Distrib.toMul
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
periodic
nsmul_eq_mul
smul 📖mathematicalFunction.Antiperiodic
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
Pi.instSMul
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
smul_neg
sub 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
Function.Periodic
SubNegMonoid.toSub
sub_eq_add_neg
add
neg
sub_const 📖mathematicalFunction.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
SubtractionCommMonoid.toAddCommMonoid
SubNegMonoid.toSub
SubtractionMonoid.toSubNegMonoid
SubtractionCommMonoid.toSubtractionMonoid
sub_eq_add_neg
add_const
sub_eq 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
SubNegMonoid.toSubsub_add_cancel
sub_eq' 📖mathematicalFunction.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
SubtractionCommMonoid.toAddCommMonoid
SubNegMonoid.toSub
SubtractionMonoid.toSubNegMonoid
SubtractionCommMonoid.toSubtractionMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
sub_eq_neg_add
sub_int_mul_eq 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Distrib.toMul
AddGroupWithOne.toIntCast
Units.val
Int.instMonoid
Int.negOnePow
zsmul_eq_mul
sub_zsmul_eq
sub_nsmul_eq 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubNegMonoid.toSub
AddMonoid.toNatSMul
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Monoid.toNatPow
Int.instMonoid
natCast_zsmul
sub_zsmul_eq
sub_zsmul_eq 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubNegMonoid.toSub
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Units.val
Int.instMonoid
Int.negOnePow
sub_eq_add_neg
neg_zsmul
Int.negOnePow_neg
add_zsmul_eq
zsmul_sub_eq 📖mathematicalFunction.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Units.val
Int.instMonoid
Int.negOnePow
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
sub_eq_add_neg
add_comm
add_zsmul_eq

Function.IsPeriodicPt

Theorems

NameKindAssumesProvesValidatesDepends On
periodic_iterate 📖mathematicalFunction.IsPeriodicPtFunction.Periodic
Nat.iterate
Function.periodic_iterate_iff

Function.Periodic

Theorems

NameKindAssumesProvesValidatesDepends On
add 📖mathematicalFunction.PeriodicPi.instAdd
add_antiperiod 📖Function.Periodic
AddSemigroup.toAdd
Function.Antiperiodic
add_antiperiod_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
Function.Antiperiodic
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
Function.Antiperiodic.eq
add_antiperiod
add_const 📖Function.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
add_right_comm
add_period 📖Function.Periodic
AddSemigroup.toAdd
comp 📖Function.Periodic
comp_addHom 📖Function.Periodic
DFunLike.coe
AddHom
AddHom.funLike
map_add
AddHom.addHomClass
const_add 📖Function.Periodic
AddSemigroup.toAdd
add_assoc
const_inv_smul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
DivInvMonoid.toMonoid
Group.toDivInvMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
inv_inv
const_smul
const_smul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SMulZeroClass.toSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
DistribSMul.toSMulZeroClass
DistribMulAction.toDistribSMul
DivInvMonoid.toMonoid
Group.toDivInvMonoid
InvOneClass.toInv
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Group.toDivisionMonoid
smul_add
smul_inv_smul
const_sub 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sub_eq
div 📖mathematicalFunction.PeriodicPi.instDiv
eq 📖mathematicalFunction.Periodic
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZerozero_add
funext 📖Function.Periodic
int_mul 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Distrib.toMul
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
zsmul_eq_mul
zsmul
int_mul_eq 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Distrib.toMul
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
eq
int_mul
int_mul_sub_eq 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Distrib.toMul
AddGroupWithOne.toIntCast
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
sub_eq'
int_mul
isPeriodicPt 📖mathematicalFunction.Periodic
Nat.iterate
Function.IsPeriodicPtFunction.periodic_iterate_iff
lift_coe 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
lift
AddSubgroup.zmultiples
map_vadd_multiples 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
HVAdd.hVAdd
AddSubmonoid
AddMonoid.toAddZeroClass
AddCommMonoid.toAddMonoid
SetLike.instMembership
AddSubmonoid.instSetLike
AddSubmonoid.multiples
instHVAdd
AddSubmonoid.vadd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
AddAction.toAddSemigroupAction
AddMonoid.toAddAction
add_comm
nsmul
map_vadd_zmultiples 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
HVAdd.hVAdd
AddSubgroup
AddCommGroup.toAddGroup
SetLike.instMembership
AddSubgroup.instSetLike
AddSubgroup.zmultiples
instHVAdd
AddSemigroupAction.toVAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
AddSubgroup.toAddGroup
AddAction.toAddSemigroupAction
AddAction.instAddAction
AddMonoid.toAddAction
add_comm
zsmul
mul 📖mathematicalFunction.PeriodicPi.instMul
nat_mul 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Distrib.toMul
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
nsmul_eq_mul
nsmul
nat_mul_eq 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Distrib.toMul
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
eq
nat_mul
nat_mul_sub_eq 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Distrib.toMul
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
sub_eq_neg_add
nat_mul
neg 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
sub_eq_add_neg
sub_eq
neg_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
NegZeroClass.toZero
eq
neg
neg_nat_mul 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
Distrib.toMul
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
neg
nat_mul
neg_nsmul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddMonoid.toNatSMul
neg
nsmul
not_injective 📖Function.Periodic
AddZero.toAdd
AddZeroClass.toAddZero
eq
nsmul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoid.toNatSMulzero_nsmul
add_zero
add_nsmul
one_smul
nsmul_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoid.toNatSMul
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
eq
nsmul
nsmul_sub_eq 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
SubtractionCommMonoid.toAddCommMonoid
SubNegMonoid.toSub
SubtractionMonoid.toSubNegMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddMonoid.toNatSMul
SubNegMonoid.toAddMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
sub_eq'
nsmul
smul 📖mathematicalFunction.PeriodicPi.instSMul
sub 📖mathematicalFunction.PeriodicPi.instSub
sub_antiperiod 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
Function.Antiperiodic
InvolutiveNeg.toNeg
SubNegMonoid.toSubsub_eq_add_neg
add_antiperiod
Function.Antiperiodic.neg
sub_antiperiod_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
Function.Antiperiodic
InvolutiveNeg.toNeg
SubNegMonoid.toSub
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
Function.Antiperiodic.eq
sub_antiperiod
sub_const 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
SubtractionCommMonoid.toAddCommMonoid
SubNegMonoid.toSub
SubtractionMonoid.toSubNegMonoid
SubtractionCommMonoid.toSubtractionMonoid
sub_eq_add_neg
add_const
sub_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toSubsub_add_cancel
sub_eq' 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
SubtractionCommMonoid.toAddCommMonoid
SubNegMonoid.toSub
SubtractionMonoid.toSubNegMonoid
SubtractionCommMonoid.toSubtractionMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
sub_eq_neg_add
sub_int_mul_eq 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Distrib.toMul
AddGroupWithOne.toIntCast
sub_eq
int_mul
sub_nat_mul_eq 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
Distrib.toMul
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
nsmul_eq_mul
sub_nsmul_eq
sub_nsmul_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toSub
AddMonoid.toNatSMul
sub_eq_add_neg
neg_nsmul
sub_period 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toSubsub_eq_add_neg
add_assoc
neg
sub_zsmul_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toSub
SubNegMonoid.toZSMul
sub_eq
zsmul
vadd 📖mathematicalFunction.PeriodicHVAdd.hVAdd
instHVAdd
Pi.instVAdd
zsmul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toZSMulnatCast_zsmul
nsmul
negSucc_zsmul
neg
zsmul_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toZSMul
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
eq
zsmul
zsmul_sub_eq 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
SubNegMonoid.toZSMul
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
sub_eq'
zsmul

List

Theorems

NameKindAssumesProvesValidatesDepends On
periodic_prod 📖mathematicalFunction.PeriodicPi.instMul
MulOne.toMul
MulOneClass.toMulOne
Pi.instOne
MulOne.toOne
Function.Periodic.mul
periodic_sum 📖mathematicalFunction.PeriodicPi.instAdd
AddZero.toAdd
AddZeroClass.toAddZero
Pi.instZero
AddZero.toZero
Function.Periodic.add

Multiset

Theorems

NameKindAssumesProvesValidatesDepends On
periodic_prod 📖mathematicalFunction.Periodicprod
Pi.commMonoid
List.periodic_prod
prod_toList
mem_toList
periodic_sum 📖mathematicalFunction.Periodicsum
Pi.addCommMonoid
List.periodic_sum
sum_toList
mem_toList

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