Lean4
/-- The element of the group of units, corresponding to an element of a monoid which is a unit. As
opposed to `IsUnit.unit`, the inverse is computable and comes from the inversion on `α`. This is
useful to transfer properties of inversion in `Units α` to `α`. See also `toUnits`. -/
@[to_additive (attr := simps val) /--
The element of the additive group of additive units, corresponding to an element of
an additive monoid which is an additive unit. As opposed to `IsAddUnit.addUnit`, the negation is
computable and comes from the negation on `α`. This is useful to transfer properties of negation
in `AddUnits α` to `α`. See also `toAddUnits`. -/
]
def unit' (h : IsUnit a) : αˣ :=
⟨a, a⁻¹, h.mul_inv_cancel, h.inv_mul_cancel⟩
