intros; elim n.
(* O *)
reflexivity.
(* S y *)
intros y H; rewrite (tech_mult_negZ y (neg m)); rewrite H;
unfold oppZ in |- *.
rewrite (tech_add_pos_posZ (y * m + (y + m)) m).
elim (technical_lemma y m); reflexivity.
Qed.

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