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[Merged by Bors] - feat: isUnit_iff_eq_one #9706

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[Merged by Bors] - feat: isUnit_iff_eq_one #9706

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9e698bd
feat: isUnit_iff_eq_one
Ruben-VandeVelde Jan 12, 2024
68d3a31
chore: move units_eq_one earlier
Ruben-VandeVelde Jan 13, 2024
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4 changes: 0 additions & 4 deletions Mathlib/Algebra/Associated.lean
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Expand Up @@ -706,10 +706,6 @@ section UniqueUnits

variable [Monoid α] [Unique αˣ]

theorem units_eq_one (u : αˣ) : u = 1 :=
Subsingleton.elim u 1
#align units_eq_one units_eq_one

theorem associated_iff_eq {x y : α} : x ~ᵤ y ↔ x = y := by
constructor
· rintro ⟨c, rfl⟩
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7 changes: 7 additions & 0 deletions Mathlib/Algebra/Group/Units.lean
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Expand Up @@ -702,6 +702,13 @@ lemma IsUnit.exists_left_inv [Monoid M] {a : M} (h : IsUnit a) : ∃ b, b * a =
#align is_unit.pow IsUnit.pow
#align is_add_unit.nsmul IsAddUnit.nsmul

theorem units_eq_one [Unique Mˣ] (u : Mˣ) : u = 1 :=
Subsingleton.elim u 1
#align units_eq_one units_eq_one

@[to_additive] lemma isUnit_iff_eq_one [Unique Mˣ] {x : M} : IsUnit x ↔ x = 1 :=
⟨fun ⟨u, hu⟩ ↦ by rw [← hu, Subsingleton.elim u 1, Units.val_one], fun h ↦ h ▸ isUnit_one⟩

end Monoid

@[to_additive]
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