Hint Resolve commute1 : core.
Arguments invg_inj {T} [x1 x2].
Prenex Implicits commute invgK.
Section GroupIdentities.
Variable T : finGroupType.
Implicit Types x y z : T.
Local Notation mulgT := (@mulg T).

Lemma commgEl x y : [~ x, y] = x^-1 * x ^ y. Proof. by []. Qed.