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_plus_r_dep :
forall x y m n : Z, (m + x)%Z = (n + y)%Z -> x = y -> m = n.