intros G g x H'; try assumption.
elim H'.
intros x0 H'0; try assumption.
elim H'0; intros H'1 H'2; try exact H'2; clear H'0.
exists x0; try assumption.
Qed.

(* Specifications: *)
Lemma sgroup_powers_rev :
forall (G : GROUP) (g : G) (n : ZZ),
in_part (group_power G g n) (sgroup_powers g).