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 double_not_equal_zero :
forall c d : Z, ~ (c = 0%Z /\ d = 0%Z) -> c <> d \/ c <> 0%Z.