intros p; elim p; simpl in |- *; auto;
try (red in |- *; intros; discriminate; fail).
Qed.
Hint Resolve Zle_Zabs: zarith.

Theorem Zlt_mult_simpl_l :
forall a b c : Z, (0 < c)%Z -> (c * a < c * b)%Z -> (a < b)%Z.