simple induction n; simpl in |- *; auto with algebra.
Qed.
Hint Resolve nat_to_group_comp: algebra.

Lemma Z_to_group_nat_fun_comp :
forall (r r' : G) (n : Z),
Equal r r' -> Equal (Z_to_group_nat_fun r n) (Z_to_group_nat_fun r' n).