intros n x; elim x.
(* OZ *)
reflexivity.
(* pos n0 *)
intros n0; rewrite (tech_mult_neg_posZ n n0); intros.
absurd (neg (n * n0 + (n + n0)) = OZ). discriminate. exact H.
(* neg n0 *)
intros n0; rewrite (tech_mult_neg_negZ n n0); intros.
absurd (pos (n * n0 + (n + n0)) = OZ). discriminate. exact H.
Qed.

(*****************)
Theorem integrityZ : integrity Z multZ OZ.
unfold integrity in |- *; intros a b; elim a.