I am writing a paper in mathematics that uses some technical results from a classic paper in the field, but not exactly in the way these results were stated at the time. Basically, I found that interesting, slightly more general versions of the statements are also true.
I can't say that these new more general versions are entirely obvious, a few hours of staring at the original statements passed before I even began to consider generalizing them, and then I had to work through the proofs themselves to make sure that the original proof basically goes through verbatim in this new setting. Or in some cases the proof of some equivalence actually breaks down, but one of the implication still holds, and that's enough for my purposes.
These new versions of existing lemmas and theorems are not the core contribution of my work, and I don't think they are interesting in their own right, but I do use them to derive some (at least seemingly) novel theorems. And here is my dilemma: If I present the proofs, I am essentially copying multiple pages of proofs written by my predecessors, which doesn't seem perfectly ethical to me. If I don't, I feel like I am doing the reader a disservice: I am basically asking them to believe me when I say "If you find a copy of this book, and change all instances of the word macguffin to weak macguffin on pages 438-442, you will find that the statements and proofs remain correct".
EDIT: I asked some colleagues and found out that the original versions of the statement are not really common knowledge, since they are more akin to lemmas than theorems. With that in mind, I guess a reader that sees a statement or its proof for the first time would not care too much if it's not that different from something already published elsewhere (and of course, I will be explicitly mentioning the source).