simple induction n; simpl in |- *; auto with algebra.
intros n0 H'; try assumption.
apply Trans with (sgroup_law G (monoid_unit G) (monoid_unit G));
auto with algebra.
Qed.
Hint Resolve nat_to_group_unit: algebra.

Lemma Z_to_group_nat_unit :
forall n : Z, Equal (Z_to_group_nat_fun (monoid_unit G) n) (monoid_unit G).