(* OZ *)
reflexivity.
(* pos n *)
simple induction n.
reflexivity.
intros; rewrite tech_add_pos_succZ; rewrite H; reflexivity.
(* neg n *)
simple induction n.
reflexivity.
intros; rewrite tech_add_neg_predZ; rewrite H; reflexivity.
Qed.

(*****************)
Lemma add_IZ_succZ : forall x : Z, addZ x IZ = succZ x.
intros.