intros z1 z2 H; rewrite (Zsucc_pred z1); rewrite (Zsucc_pred z2);
auto with zarith.
Qed.

Theorem Zpred_Zopp_Zs : forall z : Z, Zpred (- z) = (- Zsucc z)%Z.
intros z; unfold Zpred, Zsucc in |- *; ring.