apply
Trans with (group_power G g (sgroup_law ZZ (monoid_unit ZZ) (ring_unit ZZ)));
auto with algebra.
Qed.
Hint Resolve group_power_1: algebra.

Lemma group_power_inv :
forall (g : G) (n : ZZ),
Equal (group_power G g (group_inverse ZZ n))
(group_power G (group_inverse G g) n).