simple induction n; simpl in |- *; auto with algebra.
intros p; try assumption.
apply Trans with (nat_to_group (monoid_unit G) (nat_of_P (pos_abs (ax3 p))));
auto with algebra.
intros p; try assumption.
apply
Trans
with
(group_inverse G
(nat_to_group (monoid_unit G) (nat_of_P (pos_abs (ax3 p)))));
auto with algebra.
apply Trans with (group_inverse G (monoid_unit G)); auto with algebra.
Qed.
Hint Resolve Z_to_group_nat_unit: algebra.

Lemma group_power_plus :
forall (g : G) (n m : ZZ),
Equal (group_power G g (sgroup_law ZZ n m))
(sgroup_law G (group_power G g n) (group_power G g m)).