Documentation Verification Report

Parity

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

Statistics

MetricCount
DefinitionsinstDecidablePredOdd
1
Theoremseven, add_odd, add_one, mul_left, mul_right, neg_one_pow, neg_one_zpow, neg_pow, neg_zpow, odd_add, of_isUnit_two, one_add, pow_of_ne_zero, sub_odd, trans_dvd, two_dvd, iterate_bit0, iterate_bit1, iterate_eq_id, iterate_eq_self, iterate_even, iterate_odd, iterate_two_mul, iterate_two_mul_add_one, zero, sub_odd, of_mul_left, of_mul_right, sub_even, sub_odd, div_two_mul_two_add_one_of_odd, even_add', even_div, even_or_odd, even_or_odd', even_sub', even_xor_odd, even_xor_odd', mod_two_add_add_odd_mod_two, mod_two_add_succ_mod_two, ne_of_odd_add, not_even_bit1, not_even_iff_odd, not_even_two_mul_add_one, not_odd_iff, not_odd_iff_even, not_odd_zero, odd_add, odd_add', odd_add_one, odd_iff, odd_mul, odd_pow_iff, odd_sub, odd_sub', one_add_div_two_mul_two_of_odd, succ_mod_two_add_mod_two, two_dvd_mul_add_one, two_dvd_mul_sub_one, two_mul_div_two_add_one_of_odd, add_even, add_odd, add_one, exists_bit1, map, mul, natCast, neg, neg_one_pow, neg_pow, not_two_dvd_nat, of_isUnit_two, one_add, pow, pow_add_pow_eq_zero, sub_even, sub_odd, tsub_odd, even_add_one, even_add_two, even_iff_exists_two_mul, even_iff_two_dvd, even_neg_two, even_sub_one, even_sub_two, even_two, even_two_mul, isUnit_two_iff_forall_even, natCast_eq_one_of_odd_of_two_eq_zero, natCast_eq_zero_of_even_of_two_eq_zero, natCast_eq_zero_or_one_of_two_eq_zero, neg_one_pow_congr, neg_one_pow_eq_ite, neg_one_pow_eq_neg_one_iff_odd, neg_one_pow_eq_one_iff_even, neg_one_zpow_eq_ite, odd_add_one, odd_add_one_self, odd_add_one_self', odd_add_self_one', odd_add_two, odd_iff_exists_bit1, odd_neg, odd_neg_one, odd_one, odd_sub_one, odd_sub_two, odd_two_mul_add_one, range_two_mul, range_two_mul_add_one
110
Total111

Dvd.dvd

Theorems

NameKindAssumesProvesValidatesDepends On
even 📖semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Semiring.toNonUnitalSemiring
Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Even.trans_dvd

Even

Theorems

NameKindAssumesProvesValidatesDepends On
add_odd 📖Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Odd
mul_add
Distrib.leftDistribClass
Nat.instAtLeastTwoHAddOfNat
two_mul
add_assoc
add_one 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Odd
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
add_odd
odd_one
mul_left 📖Evenmul_add
mul_right 📖Evenadd_mul
neg_one_pow 📖mathematicalEvenMonoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
neg_pow
one_pow
neg_one_zpow 📖mathematicalEvenDivInvMonoid.toZPow
DivisionMonoid.toDivInvMonoid
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
neg_zpow
one_zpow
neg_pow 📖mathematicalEvenMonoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
Nat.instAtLeastTwoHAddOfNat
pow_mul
neg_sq
neg_zpow 📖mathematicalEvenDivInvMonoid.toZPow
DivisionMonoid.toDivInvMonoid
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
zpow_mul
zpow_two
neg_mul_neg
odd_add 📖Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Odd
add_odd
add_comm
of_isUnit_two 📖mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
Nat.instAtLeastTwoHAddOfNat
Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Nat.instAtLeastTwoHAddOfNat
mul_add
Distrib.leftDistribClass
two_mul
Units.inv_mul_cancel_left
one_add 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Odd
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
odd_add
odd_one
pow_of_ne_zero 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
pow_succ
mul_left
Distrib.leftDistribClass
sub_odd 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
Odd
Ring.toSemiring
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
sub_eq_add_neg
add_odd
Odd.neg
trans_dvd 📖Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Semiring.toNonUnitalSemiring
Nat.instAtLeastTwoHAddOfNat
even_iff_two_dvd
Dvd.dvd.trans
two_dvd
two_dvd 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Semiring.toNonUnitalSemiring
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
even_iff_two_dvd

Function.Involutive

Theorems

NameKindAssumesProvesValidatesDepends On
iterate_bit0 📖mathematicalFunction.InvolutiveNat.iterateiterate_two_mul
iterate_bit1 📖mathematicalFunction.InvolutiveNat.iterateiterate_two_mul_add_one
iterate_eq_id 📖mathematicalFunction.InvolutiveNat.iterate
Even
Nat.not_odd_iff_even
iterate_odd
iterate_even
iterate_eq_self 📖mathematicalFunction.InvolutiveNat.iterate
Odd
Nat.instSemiring
Nat.not_even_iff_odd
iterate_even
iterate_odd
iterate_even 📖mathematicalFunction.Involutive
Even
Nat.iterateNat.instAtLeastTwoHAddOfNat
two_mul
iterate_two_mul
iterate_odd 📖mathematicalFunction.Involutive
Odd
Nat.instSemiring
Nat.iterateFunction.iterate_add
iterate_two_mul
Function.iterate_one
iterate_two_mul 📖mathematicalFunction.InvolutiveNat.iterateFunction.iterate_mul
Function.involutive_iff_iter_2_eq_id
Function.iterate_id
iterate_two_mul_add_one 📖mathematicalFunction.InvolutiveNat.iterateFunction.iterate_succ
iterate_two_mul

IsSquare

Theorems

NameKindAssumesProvesValidatesDepends On
zero 📖mathematicalIsSquare
MulZeroClass.toMul
MulZeroClass.toZero
MulZeroClass.mul_zero

Nat

Definitions

NameCategoryTheorems
instDecidablePredOdd 📖CompOp
8 mathmath: Finset.even_sum_iff_even_card_odd, SimpleGraph.odd_card_odd_degree_vertices_ne, Equiv.Perm.sign_of_cycleType_eq_replicate, AlternatingGroup.card_of_cycleType_singleton, SimpleGraph.even_card_odd_degree_vertices, Finset.odd_sum_iff_odd_card_odd, schnirelmannDensity_setOf_Odd, SimpleGraph.Walk.IsEulerian.card_odd_degree

Theorems

NameKindAssumesProvesValidatesDepends On
div_two_mul_two_add_one_of_odd 📖Odd
instSemiring
even_add' 📖mathematicalEven
Odd
instSemiring
even_div 📖mathematicalEveninstAtLeastTwoHAddOfNat
even_iff_two_dvd
mul_comm
even_or_odd 📖mathematicalEven
Odd
instSemiring
Xor'.or
even_xor_odd
even_or_odd' 📖instAtLeastTwoHAddOfNat
even_or_odd
even_sub' 📖mathematicalEven
Odd
instSemiring
even_xor_odd 📖mathematicalXor'
Even
Odd
instSemiring
even_xor_odd' 📖mathematicalXor'even_or_odd
mod_two_add_add_odd_mod_two 📖Odd
instSemiring
mod_two_add_succ_mod_two 📖
ne_of_odd_add 📖Odd
instSemiring
not_even_bit1 📖mathematicalEvenDistrib.rightDistribClass
instAtLeastTwoHAddOfNat
not_even_iff_odd 📖mathematicalEven
Odd
instSemiring
not_even_two_mul_add_one 📖mathematicalEven
not_odd_iff 📖mathematicalOdd
instSemiring
not_odd_iff_even 📖mathematicalOdd
instSemiring
Even
not_odd_zero 📖mathematicalOdd
instSemiring
odd_add 📖mathematicalOdd
instSemiring
Even
odd_add' 📖mathematicalOdd
instSemiring
Even
odd_add_one 📖mathematicalOdd
instSemiring
odd_iff 📖mathematicalOdd
instSemiring
odd_mul 📖mathematicalOdd
instSemiring
odd_pow_iff 📖mathematicalOdd
instSemiring
Monoid.toNatPow
instMonoid
odd_sub 📖mathematicalOdd
instSemiring
Even
odd_sub' 📖mathematicalOdd
instSemiring
Even
one_add_div_two_mul_two_of_odd 📖Odd
instSemiring
succ_mod_two_add_mod_two 📖
two_dvd_mul_add_one 📖instAtLeastTwoHAddOfNat
even_iff_two_dvd
even_mul_succ_self
two_dvd_mul_sub_one 📖MulZeroClass.mul_zero
mul_comm
two_dvd_mul_add_one
two_mul_div_two_add_one_of_odd 📖Odd
instSemiring

Nat.Even

Theorems

NameKindAssumesProvesValidatesDepends On
sub_odd 📖Even
Odd
Nat.instSemiring

Nat.Odd

Theorems

NameKindAssumesProvesValidatesDepends On
of_mul_left 📖Odd
Nat.instSemiring
Nat.odd_mul
of_mul_right 📖Odd
Nat.instSemiring
Nat.odd_mul
sub_even 📖Odd
Nat.instSemiring
Even
sub_odd 📖mathematicalOdd
Nat.instSemiring
Even

Odd

Theorems

NameKindAssumesProvesValidatesDepends On
add_even 📖Odd
Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Even.add_odd
add_comm
add_odd 📖mathematicalOddEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Nat.instAtLeastTwoHAddOfNat
two_mul
AddSemigroup.to_isAssociative
AddCommMagma.to_isCommutative
add_one 📖mathematicalOddEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
add_odd
odd_one
exists_bit1 📖mathematicalOddDistrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
AddMonoidWithOne.toOne
Nat.instAtLeastTwoHAddOfNat
odd_iff_exists_bit1
map 📖mathematicalOddDFunLike.coetwo_mul
map_add
AddMonoidHomClass.toAddHomClass
RingHomClass.toAddMonoidHomClass
map_one
MonoidHomClass.toOneHomClass
MonoidWithZeroHomClass.toMonoidHomClass
RingHomClass.toMonoidWithZeroHomClass
mul 📖mathematicalOddDistrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Nat.instAtLeastTwoHAddOfNat
mul_add
Distrib.leftDistribClass
add_mul
Distrib.rightDistribClass
mul_one
add_assoc
one_mul
mul_assoc
Nat.cast_two
Nat.cast_comm
natCast 📖mathematicalOdd
Nat.instSemiring
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
map
RingHom.instRingHomClass
neg 📖mathematicalOdd
Ring.toSemiring
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
mul_neg
mul_add
Distrib.leftDistribClass
neg_add
add_assoc
Nat.instAtLeastTwoHAddOfNat
two_mul
neg_add_cancel_right
neg_one_pow 📖mathematicalOdd
Nat.instSemiring
Monoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
neg_pow
one_pow
neg_pow 📖mathematicalOdd
Nat.instSemiring
Monoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
pow_add
pow_mul
neg_sq
pow_one
mul_neg
not_two_dvd_nat 📖Odd
Nat.instSemiring
of_isUnit_two 📖mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
Ring.toSemiring
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Nat.instAtLeastTwoHAddOfNat
OddNat.instAtLeastTwoHAddOfNat
sub_add_cancel
Even.add_one
Even.of_isUnit_two
one_add 📖mathematicalOddEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
add_odd
odd_one
pow 📖mathematicalOddMonoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
pow_zero
pow_succ
mul
pow_add_pow_eq_zero 📖mathematicalOdd
Nat.instSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
MulZeroClass.toZero
NonUnitalNonAssocSemiring.toMulZeroClass
Monoid.toNatPow
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
MulZeroClass.mul_zero
zero_add
pow_one
add_right_cancel
IsCancelAdd.toIsRightCancelAdd
sq
mul_add
Distrib.leftDistribClass
add_mul
Distrib.rightDistribClass
add_comm
MulZeroClass.zero_mul
pow_add
add_right_comm
sub_even 📖mathematicalOdd
Ring.toSemiring
Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
sub_eq_add_neg
add_even
Even.neg
sub_odd 📖mathematicalOdd
Ring.toSemiring
Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
sub_eq_add_neg
add_odd
neg
tsub_odd 📖mathematicalOdd
Nat.instSemiring
EvenNat.Odd.sub_odd

(root)

Theorems

NameKindAssumesProvesValidatesDepends On
even_add_one 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Odd
Ring.toSemiring
eq_sub_iff_add_eq
Even.sub_odd
odd_one
Odd.add_one
even_add_two 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
eq_sub_iff_add_eq
Even.sub
even_two
Even.add
even_iff_exists_two_mul 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
nsmul_eq_mul
even_iff_two_dvd 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
semigroupDvd
SemigroupWithZero.toSemigroup
NonUnitalSemiring.toSemigroupWithZero
Semiring.toNonUnitalSemiring
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
two_mul
even_neg_two 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
even_sub_one 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Odd
Ring.toSemiring
sub_add_cancel
Even.add_odd
odd_one
Odd.sub_odd
even_sub_two 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
sub_add_cancel
Even.add
even_two
Even.sub
even_two 📖mathematicalEven
AddSemigroup.toAdd
AddMonoid.toAddSemigroup
AddMonoidWithOne.toAddMonoid
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
one_add_one_eq_two
even_two_mul 📖mathematicalEven
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
two_mul
isUnit_two_iff_forall_even 📖mathematicalIsUnit
MonoidWithZero.toMonoid
Semiring.toMonoidWithZero
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
Nat.instAtLeastTwoHAddOfNat
Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Nat.instAtLeastTwoHAddOfNat
Even.of_isUnit_two
two_mul
Commute.eq
Commute.ofNat_right
natCast_eq_one_of_odd_of_two_eq_zero 📖mathematicalOdd
Nat.instSemiring
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
Nat.instAtLeastTwoHAddOfNat
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddMonoidWithOne.toOneNat.instAtLeastTwoHAddOfNat
natCast_eq_zero_of_even_of_two_eq_zero 📖Even
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
Nat.instAtLeastTwoHAddOfNat
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
Nat.instAtLeastTwoHAddOfNat
natCast_eq_zero_or_one_of_two_eq_zero 📖mathematicalinstOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
Nat.instAtLeastTwoHAddOfNat
AddZero.toZero
AddZeroClass.toAddZero
AddMonoid.toAddZeroClass
AddMonoidWithOne.toAddMonoid
AddMonoidWithOne.toOneNat.instAtLeastTwoHAddOfNat
Nat.even_or_odd
natCast_eq_zero_of_even_of_two_eq_zero
natCast_eq_one_of_odd_of_two_eq_zero
neg_one_pow_congr 📖mathematicalEvenMonoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
neg_one_pow_eq_ite
neg_one_pow_eq_ite 📖mathematicalMonoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
Even
Nat.instDecidablePredEven
Nat.even_or_odd
Even.neg_one_pow
Odd.neg_one_pow
neg_one_pow_eq_neg_one_iff_odd 📖mathematicalMonoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
Odd
Nat.instSemiring
neg_one_pow_eq_ite
neg_one_pow_eq_one_iff_even 📖mathematicalMonoid.toNatPow
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
MulOne.toOne
Even
neg_one_pow_eq_ite
neg_one_zpow_eq_ite 📖mathematicalDivInvMonoid.toZPow
DivisionMonoid.toDivInvMonoid
InvolutiveNeg.toNeg
HasDistribNeg.toInvolutiveNeg
MulOne.toMul
MulOneClass.toMulOne
Monoid.toMulOneClass
DivInvMonoid.toMonoid
InvOneClass.toOne
DivInvOneMonoid.toInvOneClass
DivisionMonoid.toDivInvOneMonoid
Even
Int.instDecidablePredEven
zpow_natCast
neg_one_pow_eq_ite
zpow_neg
inv_neg
inv_one
odd_add_one 📖mathematicalOdd
Ring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Even
eq_sub_iff_add_eq
Odd.sub_odd
odd_one
Even.add_one
odd_add_one_self 📖mathematicalOdd
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
add_comm
odd_add_one_self' 📖mathematicalOdd
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
add_comm
odd_add_self_one' 📖mathematicalOdd
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
odd_add_two 📖mathematicalOdd
Ring.toSemiring
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
one_add_one_eq_two
add_assoc
odd_add_one
even_add_one
odd_iff_exists_bit1 📖mathematicalOdd
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
AddMonoidWithOne.toOne
Nat.instAtLeastTwoHAddOfNat
two_mul
odd_neg 📖mathematicalOdd
Ring.toSemiring
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
Odd.neg
neg_neg
odd_neg_one 📖mathematicalOdd
Ring.toSemiring
NegZeroClass.toNeg
SubNegZeroMonoid.toNegZeroClass
SubtractionMonoid.toSubNegZeroMonoid
SubtractionCommMonoid.toSubtractionMonoid
AddCommGroup.toDivisionAddCommMonoid
Ring.toAddCommGroup
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Ring.toAddGroupWithOne
odd_one 📖mathematicalOdd
AddMonoidWithOne.toOne
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Semiring.toNonAssocSemiring
zero_add
MulZeroClass.mul_zero
odd_sub_one 📖mathematicalOdd
Ring.toSemiring
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
AddMonoidWithOne.toOne
AddGroupWithOne.toAddMonoidWithOne
Even
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonUnitalNonAssocRing.toNonUnitalNonAssocSemiring
NonAssocRing.toNonUnitalNonAssocRing
Ring.toNonAssocRing
sub_add_cancel
Odd.add_odd
odd_one
Even.sub_odd
odd_sub_two 📖mathematicalOdd
Ring.toSemiring
SubNegMonoid.toSub
AddGroup.toSubNegMonoid
AddGroupWithOne.toAddGroup
Ring.toAddGroupWithOne
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddGroupWithOne.toAddMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
Nat.instAtLeastTwoHAddOfNat
odd_add_two
add_comm_sub
sub_self
add_zero
odd_two_mul_add_one 📖mathematicalOdd
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
AddMonoidWithOne.toOne
Nat.instAtLeastTwoHAddOfNat
range_two_mul 📖mathematicalSet.range
Distrib.toMul
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
setOf
Even
Distrib.toAdd
Set.ext
Nat.instAtLeastTwoHAddOfNat
two_mul
range_two_mul_add_one 📖mathematicalSet.range
Distrib.toAdd
NonUnitalNonAssocSemiring.toDistrib
NonAssocSemiring.toNonUnitalNonAssocSemiring
Semiring.toNonAssocSemiring
Distrib.toMul
instOfNatAtLeastTwo
AddMonoidWithOne.toNatCast
AddCommMonoidWithOne.toAddMonoidWithOne
NonAssocSemiring.toAddCommMonoidWithOne
Nat.instAtLeastTwoHAddOfNat
AddMonoidWithOne.toOne
setOf
Odd
Set.ext
Nat.instAtLeastTwoHAddOfNat

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