intros z1 z2 H; case (Zle_or_lt 0 z1); intros H1.
rewrite <- (Zabs_eq z1); auto.
apply Zle_trans with (Zabs z1); auto with zarith.
Qed.

(* Specifications: *)
Theorem Zlt_Zabs_Zpred :
forall z1 z2 : Z,
(Zabs z1 < z2)%Z -> z1 <> Zpred z2 -> (Zabs (Zsucc z1) < z2)%Z.