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?
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1$\begingroup$ Without more detail (and maybe even with more detail), this seems like not a research question, and at best opinion-based. $\endgroup$– LSpiceCommented Jul 17, 2020 at 19:24
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It's really hard to answer this question when you phrase things so vaguely. I take your question to mean:
- There is a theorem, let's call it Theorem A.
- You thought you had three new results that are applications of Theorem A.
- You realized you could prove those results via a generalization of Theorem B instead.
If that's right, then from a mathematical-writing perspective, how about: "Three applications of (a generalization of) Theorem B"
I have certainly seen text like this in plenty of papers. Alternatively, you could ditch the language about "Applications of" and just focus your paper on the three examples, no matter how you prove whatever you are trying to prove about them.
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$\begingroup$ The results are not proven using a generalized form of Theorem B. I use Theorem B to get to them by generalizing some smaller results. But the parts where I use Theorem B don't constitute very much of the proof. So I don't know if I could really call this results an aplication of the theorem, if I only use it just at the end of the proofs. $\endgroup$ Commented Jul 17, 2020 at 20:07
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$\begingroup$ @fisurafilozofica, rather than clarifying vagueness with further vagueness, why not just put your paper on the arXiv if it isn't already and point us to it? $\endgroup$– LSpiceCommented Jul 17, 2020 at 22:07
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$\begingroup$ If you use the theorem in the proof, I think you can call it an "application." I have done this in a lot of my papers (which are all on arxiv). One of my co-authors prefers the word "example," reserving "application" for when it's a big deal. But my other 7 co-authors seem fine with "application" even for small results. $\endgroup$ Commented Jul 17, 2020 at 22:55