intro n; elim n; auto with arith.
simpl in |- *.
intro y.
rewrite succ_predZ; auto with arith.
intros; symmetry  in |- *; rewrite addZ_eq5.
apply succ_predZ.
Qed.

Lemma pred_addZ_l : forall x y : Z, addZ (predZ x) y = predZ (addZ x y).
intros; elim x.