intros x; try assumption.
elim x.
intros p p'; try assumption.
red in p'.
inversion p.
intros p p0 p'; simpl in |- *.
auto with algebra.
intros p p0 p'; try assumption.
red in p'.
simpl in p'.
inversion p'.
Qed.
Hint Resolve Zl2 Zl1 Zl3 nat_to_group_inverse: algebra.

Lemma nat_to_group_comp :
forall (r r' : G) (n : nat),
Equal r r' -> Equal (nat_to_group r n) (nat_to_group r' n).