intros n m.
unfold Zpred in |- *; unfold Zsucc in |- *; ring.
Qed.

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