Section Mixin.
Variables (T : Type) (one : T) (mul : T -> T -> T) (inv : T -> T).
Hypothesis mulA : associative mul.
Hypothesis mul1 : left_id one mul.
Hypothesis mulV : left_inverse one inv mul.
Notation "1" := one.
Infix "*" := mul.
Notation "x ^-1" := (inv x).

Lemma mk_invgK : involutive inv.