So I've been trying for a wile to write an article on 3 aplication of some theorem for a small journal. But after finding my second example I realized that I didn't need the theorem to prove it. Now, the two proof are linked by another theorem which I used in bouth for some constructions, but I use it just so I could generalize them from a particular case which I proved using other method. Now the question is do this two proofs still count as an aplication the second theorem?