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 Zlt_mult_cancel_l :
forall x y z : Z, (0 < x)%Z -> (x * y < x * z)%Z -> (y < z)%Z.