Hi


I have a proof for a Lemma which splits into an odd and even case.


The proof for the even case was already published by someone else in a different context and the proof for for the odd case is very similar (but not trivial) to the even case proof.


So how should I now proceed about the odd case proof?
Is it ok if I make it clear that the odd case proof closely follows the idea of the even case proof, published by someone else? 



Reusing Parts of a Proof
Mathematics often progresses by small changes in already extant work. In fact I like to work by writing and rewriting, trying to make things clear, in the first place to me. 


You need only say, for example, that the proof for the even case given by X can with some non trivial modifications also work for the odd case. 


That seems like progress! Then it is up to a referee. 


There are numerous, maybe all too many, examples of writers not mentioning where the ideas came from. 


