Imagine that you are in the following situation: You write up a proof which eventually gets published. There you need a result which is not so well-known but it is contained in another paper P; therefore you just cite it. You read P and come to the conclusion: It's awful. You need plenty of time to insert the details or even correct it. It may also happen that the proof is somewhat too complicated because in your situation it is much easier. Maybe you have found a shorter proof, but based on the ideas in P. Now what do you do? Several options come into my mind:


* Just cite the paper without any further explanation.
* Cite the paper but give a short hint how to simplify the arguments.
* Cite the paper but give a more elaborate explanation of the arguments.
* Write up the details of the proof of the desired result in your situation and remark somewhere that it was inspired by the paper P.


For each option there are pros and cons. For example, you don't want to blow up your proof with material which does not seem be so important. Also, you don't want to bore your readers. This favors the first options. On the other hand, you might want to be sure that the readers understand the argument and don't have to read P. This favors the last options. What do you think, which option is your favorite and why? Also, are there other appropriate options?



Citation of a paper with a proof you would like to improve
Improving existing proofs is an important and undervalued part of mathematics. We don't just want to know *whether* something is true; we want to know *why* it's true. So I think that if you have a better proof of something, you should find a way to share it with the world.


Here are a couple of thoughts about the practicalities, to add to Andrew's suggestion about the nLab. 


First, you could put the simplified proof into an appendix to your paper. I quite like appendices, as both a reader and a writer. Used well, they help to keep the main part of the paper flowing, while providing crucial details to those who want them. 


Second, it's entirely possible that the author of [Awful 2009] will referee your paper. So whatever you write, you need to keep them sweet. I think this also favours the appendix option. 


