Section PreGroupIdentities.
Variable T : baseFinGroupType.
Implicit Types x y z : T.
Local Notation mulgT := (@mulg T).

Lemma mulgA : associative mulgT.  Proof. by case: T => ? []. Qed.
Lemma mul1g : left_id 1 mulgT.  Proof. by case: T => ? []. Qed.
Lemma invgK : @involutive T invg.   Proof. by case: T => ? []. Qed.
Lemma invMg x y : (x * y)^-1 = y^-1 * x^-1. Proof. by case: T x y => ? []. Qed.