I am writing an academic paper for submission to a journal. One of my co-authors wrote the following:



> 
> **Theorem** Statement of the theorem
> 
> 
> **Proof of theorem** We first show the following result
> 
> 
> **Lemma** Statement of lemma used to prove the theorem
> 
> 
> 


However, I think that it is more natural to present things in the following way:



> 
> **Theorem** Statement of the theorem
> 
> 
> We first show the following result which is used to prove the theorem:
> 
> 
> **Lemma** Statement of lemma used to prove the theorem
> 
> 
> **Proof of theorem** blah blah
> 
> 
> 


I understand that this is a subjective question so I am happy to mark this as community wiki if most people feel that it belongs there.



What are good ways to present proofs of theorems requiring auxiliary lemmas?
The guiding principle should be: think of your readers. Nesting results inside the proofs of other results can make things confusing. I am looking right now at a paper that has three instances of that, and one of them is truly egregious: the bracket diagram is like this: $((((()))(())))$.


Maybe one nested lemma is ok, but if I could avoid it I would just put the lemma before, and say something like: "The following lemma will be used in the proof of Theorem 1." If you really want to state the theorem before the lemma, then your second option is better.


OK, I'll stop grinding this axe now.


