(* OZ *)
reflexivity.
(* pos n *)
simple destruct n.
simpl in |- *; rewrite pred_succZ; trivial.
intros; rewrite addZ_eq3; rewrite pred_succZ; trivial.
trivial.
Qed.

(**********************)
Lemma tech_add_pos_succZ :
forall (x : nat) (y : Z), addZ (pos (S x)) y = succZ (addZ (pos x) y).