(* OZ *)
reflexivity.
(* pos n *)
trivial.
(* neg n *)
simple destruct n.
(* neg O *)
simpl in |- *; symmetry  in |- *; exact (succ_predZ y).
(* neg (S n0) *)
intros; symmetry  in |- *; rewrite addZ_eq5.
apply succ_predZ.
Qed.

(***************)
Lemma pred_addZ_l : forall x y : Z, addZ (predZ x) y = predZ (addZ x y).
intros; elim x.