intro n; elim n; auto with arith.
Qed.

(* Specifications: *)
Lemma succ_predZ : forall x : Z, succZ (predZ x) = x.
intro x; elim x; auto with arith.
Lemma succ_pred_pred_succZ : forall x : Z, succZ (predZ x) = predZ (succZ x).
intro x; try assumption.