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chore: rename DivInvMonoid.Pow #19884

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chore: rename DivInvMonoid.Pow #19884

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9c15e5f
chore: rename `DivInvMonoid.Pow`
eric-wieser Dec 11, 2024
6c54764
Update Defs.lean
eric-wieser Dec 11, 2024
e3ac753
Update IntUnitsPower.lean
eric-wieser Dec 11, 2024
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6 changes: 3 additions & 3 deletions Mathlib/Algebra/Group/Defs.lean
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Expand Up @@ -858,13 +858,13 @@ class SubNegMonoid (G : Type u) extends AddMonoid G, Neg G, Sub G where

attribute [to_additive SubNegMonoid] DivInvMonoid

instance DivInvMonoid.Pow {M} [DivInvMonoid M] : Pow M ℤ :=
instance DivInvMonoid.toZPow {M} [DivInvMonoid M] : Pow M ℤ :=
⟨fun x n ↦ DivInvMonoid.zpow n x⟩

instance SubNegMonoid.SMulInt {M} [SubNegMonoid M] : SMul ℤ M :=
instance SubNegMonoid.toZSMul {M} [SubNegMonoid M] : SMul ℤ M :=
⟨SubNegMonoid.zsmul⟩

attribute [to_additive existing SubNegMonoid.SMulInt] DivInvMonoid.Pow
attribute [to_additive existing] DivInvMonoid.toZPow

/-- A group is called *cyclic* if it is generated by a single element. -/
class IsAddCyclic (G : Type u) [SMul ℤ G] : Prop where
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2 changes: 1 addition & 1 deletion Mathlib/Data/ZMod/IntUnitsPower.lean
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Expand Up @@ -60,7 +60,7 @@ instance Int.instUnitsPow : Pow ℤˣ R where
-- The above instances form no typeclass diamonds with the standard power operators
-- but we will need `reducible_and_instances` which currently fails https://github.com/leanprover-community/mathlib4/issues/10906
example : Int.instUnitsPow = Monoid.toNatPow := rfl
example : Int.instUnitsPow = DivInvMonoid.Pow := rfl
example : Int.instUnitsPow = DivInvMonoid.toZPow := rfl

@[simp] lemma ofMul_uzpow (u : ℤˣ) (r : R) : Additive.ofMul (u ^ r) = r • Additive.ofMul u := rfl

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