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 set_invgK : involutive set_invg.
Definition group_set_baseGroupMixin : FinGroup.mixin_of (set_type gT) :=
FinGroup.BaseMixin set_mulgA set_mul1g set_invgK set_invgM.