intros.
apply Zgt_trans with (m := (n + p)%Z).
rewrite Zplus_comm.
rewrite Zplus_comm with (n := n).
apply Zplus_gt_compat_l.
assumption.
apply Zplus_gt_compat_l.
assumption.
Qed.

Lemma Zmult_neg_pos : forall x y : Z, (x < 0)%Z -> (0 < y)%Z -> (x * y < 0)%Z.