proposition: Lemma nat_to_group_unit : forall n : nat, Equal (nat_to_group (monoid_unit G) n) (monoid_unit G).
proof: Proof. 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.
imports: Z_group