simpl in |- *; auto with zarith.
repeat rewrite Zabs_eq; auto with zarith.
intros p; rewrite Zabs_eq_opp; auto with zarith.
2: unfold Zsucc in |- *; replace 0%Z with (-1 + 1)%Z; auto with zarith.
2: case p; simpl in |- *; intros; red in |- *; simpl in |- *; intros;
red in |- *; intros; discriminate.
replace (- Zsucc (Zneg p))%Z with (Zpos p - 1)%Z.
replace (Zsucc (Zabs (Zneg p))) with (Zpos p + 1)%Z;
auto with zarith.
unfold Zsucc in |- *; rewrite Zopp_plus_distr.
auto with zarith.
Qed.
Hint Resolve Zabs_Zs: zarith.

Theorem Zle_Zpred : forall x y : Z, (x < y)%Z -> (x <= Zpred y)%Z.
intros x y H; apply Zlt_succ_le.