intros; elim n.
(* O *)
reflexivity.
(* S n0 *)
intros; rewrite (tech_add_pos_succZ n0 (pos m)); rewrite H; reflexivity.
Qed.

(*********************)
Lemma tech_add_neg_negZ :
forall n m : nat, addZ (neg n) (neg m) = neg (S (n + m)).