case (Z_gt_le_dec (ring_unit ZZ) 0).
intros z; try assumption.
simpl in |- *.
auto with *.
intros z; try assumption.
case (Z_le_lt_eq_dec (ring_unit ZZ) 0 z).
intros z0; try assumption.
absurd (ring_unit ZZ < 0)%Z; auto with *.
intros H'; try assumption.
inversion H'.
Qed.
Hint Resolve Zl5: algebra.

(* Specifications: *)
Lemma nat_to_group_com4 :
forall n m : nat,
Equal (sgroup_law G (nat_to_group m) (group_inverse G (nat_to_group n)))
(sgroup_law G (group_inverse G (nat_to_group n)) (nat_to_group m)).