Suppose that paper A has a lemma called Lemma A, along with its proof.
I want to use this lemma in another paper B. However, in the scope of my paper, I have to change it slightly, but without losing the general idea.
For instance, the original lemma might read as follows:
Lemma A: The intersection of two straight lines in the plane is either empty, a single point, or a straight line.
Suppose I need the following variant in paper B:
Lemma B: The intersection of two planes in 3-space is either empty, a single line, or a plane.
Also, the proofs for both lemmas are very similar. Therefore, I have two questions:
- Can I use the same methodology and same terminology with similar words to prove my own lemmas?
- If I can, is citing paper A in my lemma confusing? If I cannot, can I just specify the lemma in paper A and say that this lemma and proof can also be used etc.?