reflexivity.
simple induction n.
simpl in |- *; apply succ_pred_pred_succZ.
intros.
do 2 rewrite (tech_add_pos_succZ n0).
rewrite H; apply succ_pred_pred_succZ.
simple induction n.
reflexivity.
intros.
do 2 rewrite (tech_add_neg_predZ n0).
elim H; reflexivity.
Qed.

Lemma add_OZ : forall x : Z, addZ x OZ = x.
simple induction x.