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.PeriodicFunction.Periodic
prod
Pi.commMonoid
List.periodic_prod
prod_map_toList
periodic_sum 📖mathematicalFunction.PeriodicFunction.Periodic
sum
Pi.addCommMonoid
List.periodic_sum
mem_toList
sum_map_toList

Function

Definitions

NameCategoryTheorems
Antiperiodic 📖MathDef
31 mathmath: Antiperiodic.mul_const', Antiperiodic.const_mul, Complex.cos_antiperiodic, Antiperiodic.neg, Antiperiodic.int_odd_mul_antiperiodic, Antiperiodic.div_inv, Real.sin_antiperiodic, Complex.exp_antiperiodic, Antiperiodic.const_add, Antiperiodic.const_inv_smul₀, Antiperiodic.add_const, Antiperiodic.const_sub, Antiperiodic.const_inv_mul, Complex.sin_antiperiodic, Periodic.add_antiperiod, Antiperiodic.odd_zsmul_antiperiodic, Antiperiodic.const_smul₀, Antiperiodic.mul_const, Antiperiodic.const_smul, Real.cos_antiperiodic, Antiperiodic.sub_const, Antiperiodic.odd_nsmul_antiperiodic, Antiperiodic.smul, Antiperiodic.mul_const_inv, Periodic.sub_antiperiod, Real.Angle.sin_antiperiodic, Complex.exp_mul_I_antiperiodic, Real.Angle.cos_antiperiodic, Antiperiodic.const_inv_smul, Antiperiodic.nat_odd_mul_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.Periodic
AddSemigroup.toAdd
neg_neg
add_const 📖mathematicalFunction.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
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.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoid.toNSMul
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Monoid.toPow
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
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
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 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
Function.Antiperiodic
AddSemigroup.toAdd
add_assoc
const_inv_smul 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
Function.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
Function.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
Function.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
DivisionMonoid.toDivInvMonoid
neg_div_neg_eq
eq 📖mathematicalFunction.Antiperiodic
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
zero_add
even_nsmul_periodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
InvolutiveNeg.toNeg
Function.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoid.toNSMul
Function.Periodic.nsmul
periodic
mul_nsmul
even_zsmul_periodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
Function.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toZSMul
mul_comm
mul_zsmul
two_zsmul
two_nsmul
Function.Periodic.zsmul
periodic
funext 📖mathematicalFunction.AntiperiodicPi.instNeg
funext' 📖mathematicalFunction.Antiperiodic
InvolutiveNeg.toNeg
InvolutiveNeg.toNegneg_eq_iff_eq_neg
funext
int_even_mul_periodic 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
InvolutiveNeg.toNeg
Function.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
AddGroupWithOne.toIntCast
AddCommGroupWithOne.toAddGroupWithOne
NonAssocRing.toAddCommGroupWithOne
NegZeroClass.toZero
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
AddGroupWithOne.toIntCast
Units.val
Int.instMonoid
Int.negOnePow
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
NonUnitalNonAssocRing.toAddCommGroup
zsmul_eq_mul
zsmul_sub_eq
int_odd_mul_antiperiodic 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
InvolutiveNeg.toNeg
Function.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.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
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
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
NegZeroClass.toZero
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
Function.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
Function.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
InvolutiveNeg.toNeg
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.toNSMul
SubNegMonoid.toAddMonoid
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Monoid.toPow
Int.instMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
natCast_zsmul
zsmul_sub_eq
odd_nsmul_antiperiodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
InvolutiveNeg.toNeg
Function.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
InvolutiveNeg.toNeg
AddMonoid.toNSMul
add_nsmul
one_nsmul
add_assoc
even_nsmul_periodic
odd_zsmul_antiperiodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
Function.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
SubNegMonoid.toZSMul
add_zsmul
one_zsmul
add_assoc
even_zsmul_periodic
periodic 📖mathematicalFunction.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
InvolutiveNeg.toNeg
Function.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoid.toNSMul
two_nsmul
neg_neg
periodic_two_mul 📖mathematicalFunction.Antiperiodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
InvolutiveNeg.toNeg
Function.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
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
Function.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
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toSub
sub_eq_add_neg
add
neg
sub_const 📖mathematicalFunction.Antiperiodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
SubtractionCommMonoid.toAddCommMonoid
Function.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.toSub
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
sub_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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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
AddGroup.toSubNegMonoid
AddMonoid.toNSMul
SubNegMonoid.toAddMonoid
SubNegMonoid.toZSMul
SubtractionMonoid.toSubNegMonoid
Monoid.toPow
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
AddGroup.toSubNegMonoid
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
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
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.PeriodicFunction.Periodic
Pi.instAdd
add_antiperiod 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
Function.Antiperiodic
Function.Antiperiodic
AddSemigroup.toAdd
add_antiperiod_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
Function.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
Function.Antiperiodic.eq
add_antiperiod
add_const 📖mathematicalFunction.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
Function.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
add_right_comm
add_period 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
Function.Periodic
AddSemigroup.toAdd
comp 📖mathematicalFunction.PeriodicFunction.Periodic
comp_addHom 📖mathematicalFunction.Periodic
DFunLike.coe
AddHom
AddHom.funLike
Function.Periodic
DFunLike.coe
AddHom
AddHom.funLike
map_add
AddHom.addHomClass
const_add 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
Function.Periodic
AddSemigroup.toAdd
add_assoc
const_inv_smul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
Function.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
Function.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
Function.Periodic
AddCommMagma.toAdd
AddCommSemigroup.toAddCommMagma
AddCommMonoid.toAddCommSemigroup
AddCommGroup.toAddCommMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddCommGroup.toAddGroup
sub_eq
div 📖mathematicalFunction.PeriodicFunction.Periodic
Pi.instDiv
eq 📖mathematicalFunction.Periodic
AddZero.toAdd
AddZeroClass.toAddZero
AddZero.toZero
AddZeroClass.toAddZero
zero_add
funext 📖Function.Periodic
int_mul 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Function.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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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.PeriodicFunction.Periodic
Pi.instMul
nat_mul 📖mathematicalFunction.Periodic
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Function.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
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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
Function.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
Function.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
Function.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
AddGroup.toSubtractionMonoid
AddMonoid.toNSMul
neg
nsmul
not_injective 📖Function.Periodic
AddZero.toAdd
AddZeroClass.toAddZero
eq
nsmul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
Function.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoid.toNSMul
zero_nsmul
add_zero
add_nsmul
one_smul
nsmul_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoid.toNSMul
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.toNSMul
SubNegMonoid.toAddMonoid
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
sub_eq'
nsmul
smul 📖mathematicalFunction.PeriodicFunction.Periodic
Pi.instSMul
sub 📖mathematicalFunction.PeriodicFunction.Periodic
Pi.instSub
sub_antiperiod 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
Function.Antiperiodic
InvolutiveNeg.toNeg
Function.Antiperiodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
SubNegMonoid.toSub
sub_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
AddGroup.toSubNegMonoid
InvolutiveNeg.toNeg
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
Function.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.toSub
AddGroup.toSubNegMonoid
sub_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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
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
AddGroup.toSubNegMonoid
AddMonoid.toNSMul
SubNegMonoid.toAddMonoid
sub_eq_add_neg
neg_nsmul
sub_period 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
Function.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toSub
sub_eq_add_neg
add_assoc
neg
sub_zsmul_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
SubNegMonoid.toZSMul
sub_eq
zsmul
vadd 📖mathematicalFunction.PeriodicFunction.Periodic
HVAdd.hVAdd
instHVAdd
Pi.instVAdd
zsmul 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
Function.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toZSMul
natCast_zsmul
nsmul
negSucc_zsmul
neg
zsmul_eq 📖mathematicalFunction.Periodic
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
SubNegMonoid.toAddMonoid
AddGroup.toSubNegMonoid
SubNegMonoid.toZSMul
AddGroup.toSubNegMonoid
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.PeriodicFunction.Periodic
Pi.instMul
MulOne.toMul
MulOneClass.toMulOne
Pi.instOne
MulOne.toOne
Function.Periodic.mul
periodic_sum 📖mathematicalFunction.PeriodicFunction.Periodic
Pi.instAdd
AddZero.toAdd
AddZeroClass.toAddZero
Pi.instZero
AddZero.toZero
Function.Periodic.add

Multiset

Theorems

NameKindAssumesProvesValidatesDepends On
periodic_prod 📖mathematicalFunction.PeriodicFunction.Periodic
prod
Pi.commMonoid
List.periodic_prod
prod_toList
mem_toList
periodic_sum 📖mathematicalFunction.PeriodicFunction.Periodic
sum
Pi.addCommMonoid
List.periodic_sum
sum_toList
mem_toList

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