(* OZ *)
reflexivity.
(* pos n *)
simple induction n.
(* pos O *)
reflexivity.
(* pos (S y) *)
intros y H; rewrite (tech_mult_posZ y OZ); rewrite H; reflexivity.
(* neg n *)
simple induction n.
(* neg O *)
reflexivity.
(* neg (S y) *)
intros y H; rewrite (tech_mult_negZ y OZ); rewrite H; reflexivity.
Qed.

(* Specifications: *)
(************)
Lemma mult_IZ : forall x : Z, multZ x IZ = x.
simple destruct x.