unfold group_power in |- *.
simpl in |- *.
intros g; try assumption.
apply Trans with (Z_to_group_nat_fun g 0%Z); auto with algebra.
Qed.
Hint Resolve group_power_0: algebra.

Lemma group_power_1 : forall g : G, Equal (group_power G g (ring_unit ZZ)) g.
intros g; try assumption.