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