Section for "main results" and use of "conclusion" in a math article I am planning to submit an article to a mathematically-oriented journal (namely: Archive for Rational Mechanics and Analysis).

I have quite a lot of results so I wrote a section "Main Results". 

Question 1 In this section, the results are given as theorems, and each proof is given in another section. However, there is one simple theorem whose proof is only a few lines long. Can I provide the proof in the "Main Results" section, or is it not customary to include any proofs there?

Question 2 I am used to adding conclusions to my articles, but all the articles I read in this journal do not have any. Should I do the same and not add any conclusion (note that nothing is mentionned about this in the guidelines)?
Can I provide the proof in the "Main Results" section, or is it not
  customary to include any proofs there?


It is fine to include a proof of a few lines in a section titled Main Results, if you feel that that helps your narrative, if it adds some insight that is useful at this point in the paper, or if the proof is extremely elegant or interesting. It is also fine not to do so. Good writing cannot be summarized in a few rules, one needs to always think about what makes sense for the particular context one is thinking about.


  Should I do the same and not add any conclusion?


Pure math papers almost never have a Conclusion section. If the reader reads the introduction, the results and the proofs and still doesn't know what conclusions are to be drawn from the work, it is a bad paper and no final section will save it. For this reason, many if not most math papers simply end after the end of the last proof. Others will have a final section titled something like "Additional remarks", "Final remarks" or "Open problems". This section will usually be short and forward-looking, addressing possible extensions of the work, or containing some half-baked thoughts about aspects of the work or related questions that the authors still don't understand well.

Conclusion

I don't have any. :-)