intros x y; case x; case y; unfold Zlt in |- *; simpl in |- *; auto.
Qed.
Hint Resolve Zlt_mult_ZERO: zarith.

Theorem Zlt_Zminus_ZERO :
forall z1 z2 : Z, (z2 < z1)%Z -> (0 < z1 - z2)%Z.