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 triple_not_equal_zero :
forall a b c : Z,
~ (a = 0%Z /\ b = 0%Z /\ c = 0%Z) -> a <> 0%Z \/ b <> 0%Z \/ c <> 0%Z.