intros z1 z2 H; apply Zsucc_le_reg.
repeat rewrite <- Zsucc_pred; auto.
Qed.
Hint Resolve Zle_Zpred_Zpred: zarith.

Theorem Zle_ZERO_Zabs : forall z : Z, (0 <= Zabs z)%Z.
intros z; case z; simpl in |- *; auto with zarith.