proposition: Lemma intro_unit x y : y * x = 1 /\ x * y = 1 -> x \is a unit.
proof: Proof. by case=> yx1 xy1; apply/existsP; exists y; rewrite /is_inv xy1 yx1 !eqxx. Qed.
imports: HB(structures) mathcomp(ssreflect ssrfun ssrbool eqtype ssrnat seq choice) mathcomp(fintype finset fingroup morphism perm action) mathcomp(ssralg countalg)