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 mediant_1 :
forall m n m' n' : Z, (m' * n < m * n')%Z -> ((m + m') * n < m * (n + n'))%Z.