intros; elim n.
(* O *)
reflexivity.
(* S y *)
intros y H; rewrite (tech_mult_posZ y (pos m)); rewrite H.
rewrite (tech_add_pos_posZ (y * m + (y + m)) m).
elim (technical_lemma y m); reflexivity.
Qed.

(***********************)
Lemma tech_mult_neg_negZ :
forall n m : nat, multZ (neg n) (neg m) = pos (n * m + (n + m)).