Citation of a paper with a proof you would like to improve 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?
 A: Since this has been reopened, I'm going to repeat what I said in the meta thread before this question gets closed again:

stick the simplified proof on the nLab and cite that

This is a completely serious suggestion.  You have an improved version of the proof (whether it is globally improved or just locally improved[1]).  It's not "original research" so an "Established Journal" might be reluctant to publish it[2].  But hordes of other mathematicians will be interested in reading it so it should be put somewhere that they can find it.  This seems a perfect fit for the nLab.
If you have it written in reasonably standard LaTeX, I can even help you get it into the right formatting.
[1] A global improvement is one that anyone reading the original proof would be interested in, a local improvement is one that anyone reading your result that depends on it would be interested in.
[2] Insert standard rant about journals here.
A: The first question is whether your are bringing new ideas to the party. If so, then you add your new proof and trust that the referees do not get to picky about space constraints.
So you are in Case 4.
If there are no new ideas, but the proof can be significantly simplified in your situation
things are a little greyer. I would still say that you are in Case 4.
If the problem is that the original paper is a dog's breakfast, then I feel you just have
to hold your nose and cite it; you're in Case 1. (If you want to correct other people's work, someone must have homework lying around waiting to be marked...) In this case I think there is an argument that by reproving the original result you are making a kind of weak claim to it. Other authors might cite you when they should really cite the original.
In the case where you are offering more than improved exposition, it is mainly the space constraints that apply. I do not see any ethical issue then.
[In reference to some of the comments. Of course improving exposition is very valuable. But I
cannot think of any reasonable journal that would accept an article consisting of an improved exposition of an accepted result, unless it introduced new ideas. I am not defending
this situation, but it is a fact.]
A: 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.  
