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 Zopp_Zlt : forall x y : Z, (y < x)%Z -> (- x < - y)%Z.