unfold group_power in |- *.
simpl in |- *.
intros g n; try assumption.
apply
Trans
with (sgroup_law G (Z_to_group_fun g n) (Z_to_group_fun g (ring_unit Zr)));
auto with algebra.
Qed.
Hint Resolve group_power_S: algebra.

Lemma group_power_0 :
forall g : G, Equal (group_power G g (monoid_unit ZZ)) (monoid_unit G).