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.

(* Omega can't solve this *)
Lemma Zmult_pos_pos : forall x y : Z, (0 < x)%Z -> (0 < y)%Z -> (0 < x * y)%Z.