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_resp_Zle :
forall a x y : Z, (0 < a)%Z -> (a * y <= a * x)%Z -> (y <= x)%Z.