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 Zsimpl_mult_l :
forall n m p : Z, n <> 0%Z -> (n * m)%Z = (n * p)%Z -> m = p.