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[Merged by Bors] - feat(Algebra/Group/TypeTags): Add toMul_eq_one and toAdd_eq_zero #14097

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[Merged by Bors] - feat(Algebra/Group/TypeTags): Add toMul_eq_one and toAdd_eq_zero #14097

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10 changes: 10 additions & 0 deletions Mathlib/Algebra/Group/TypeTags.lean
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Original file line number Diff line number Diff line change
Expand Up @@ -249,6 +249,11 @@ theorem ofMul_eq_zero {A : Type*} [One A] {x : A} : Additive.ofMul x = 0 ↔ x =
theorem toMul_zero [One α] : toMul (0 : Additive α) = 1 := rfl
#align to_mul_zero toMul_zero

@[simp]
lemma toMul_eq_one {α : Type*} [One α] {x : Additive α} :
Additive.toMul x = 1 ↔ x = 0 :=
Iff.rfl

instance [Zero α] : One (Multiplicative α) :=
⟨Multiplicative.ofAdd 0⟩

Expand All @@ -267,6 +272,11 @@ theorem toAdd_one [Zero α] : toAdd (1 : Multiplicative α) = 0 :=
rfl
#align to_add_one toAdd_one

@[simp]
lemma toAdd_eq_zero {α : Type*} [Zero α] {x : Multiplicative α} :
Multiplicative.toAdd x = 0 ↔ x = 1 :=
Iff.rfl

instance Additive.addZeroClass [MulOneClass α] : AddZeroClass (Additive α) where
zero := 0
add := (· + ·)
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