So I've been trying for a while to write an article on 3 applications 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 proofs are linked by another theorem which I used in both 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 these two proofs still count as an application the second theorem?