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 card_mem_repr A : #|A| > 0 -> repr A \in A.