intros n m p H H1;
apply Z.lt_gt; apply Zmult_lt_neg_compat_l_rev with p; auto with zarith.
Qed.
(* For replace *)

Theorem eq_Zlt_trans_l : forall x y z, (x = z) -> (x < y) -> (z < y).
intros x y z H; rewrite H; auto.