Submitting a companion paper with detailed proofs ? In papers there are often sketchy arguments in proofs that I find hard to understand. Filling in the gaps is laborious and time-consuming. According to the post www.mathoverflow.net/questions/40729/does-a-referee-have-to-check-carefully-the-proof, referees seem to be faced with this problem as well. 
Presently I'm preparing my first paper for submission to a journal. Of course I approve the usual conventions and write more or less sketchy proofs myself in order to keep the paper short (around 15 pages). On the other hand, I checked the proofs carefully. So I could support the publishing process by this idea: 

Submit two versions of the paper: 
  
  
*
  
*a short one, designated for publishing 
  
*a long one, assigned for the referee with proofs given in full detail 
  

Is this a good idea that simplifies the referee's life (and, maybe, helps getting the paper accepted) or is it, in contrast, maybe even a no-go ? 
I appreciate your opinions very, very much. Thanks in advance. 
N.b. I intentionally ask the question on MO (and not on academia.stackexchange.com) because I think checking proofs is particular to mathematics and doesn't occur this way in most other fields of science. 
 A: When I write a paper, I include "notes" with additional details etc. The package "version" then makes it very easy to produce pdf files with or without the notes. I find this very useful for myself. I submit the version without notes, and sometimes put the version with notes on my website or the arXiv (and occasionally alert the journal to its existence).
A: You should submit only one version of the paper. Think of the referee as a typical reader, not a judge providing a certificate of correctness. If the referee needs additional information, then other readers will need it too. 
Regarding putting a proof in an appendix: There are exceptional cases when this is necessary, but most often it is not, and it can even be annoying to the reader (or seen as a warning sign of a bogus paper!) when important arguments are removed from their context. 
Reading a math paper will always be time consuming, but I don't think there is a general convention that proofs should be sketchy. As an inexperienced writer, it is sometimes hard to know when something should be left out, and when leaving it out will be regarded as a gap. Feedback from teachers and supervisors on this matter can be contradictory and confusing. If you feel you still haven't got the knack for it, bear in mind that it is much easier for a referee to ask you to remove details than to figure out when they are missing. I would not endorse any general advice to write sketchy proofs in order to keep the paper short.
A: I don't think the editor will assign the referees a different version of the paper; after all, they are supposed to be judging whether the journal should publish the paper they are reviewing or not.  I think you could post an extended version on the arXiv and make sure the referees are aware of its existence.  Some of them may then give you useful feedback about whether they found the extended version helpful and may suggest moving some material into the main paper or vice versa.
Having said that, I think your chances of having the paper accepted are improved by submitting the best version you can up front.  If you're not sure whether your proofs are too short or too long, have someone (your advisor?) read the paper and give you comments before submitting.  This can only help your chances.
A: I don't understand why you "approve the usual conventions and write more or less sketchy proofs myself in order to keep the paper short", unless the journal you
want to submit to has a size limitation.
Indeed, it was a custom in the past to write a very short note with a sketch of
the proof (or without a proof at all), and publish it as a "research announcement". There were special journals for such short announcements
(Comptes rendus in France, similar thing in Russia, and many more).
I think the reason for this practice was to secure priority. Publication (and writing) of the full text could take a lot of time. Then usually several such short notes were followed by a large, long paper.
On my opinion, this practice is obsolete. Today you can post an arbitrarily long
paper on the arXiv to secure priority, and the only reason to publish "sketch proofs" in a journal could be the journal policy of length limitation.
On my opinion, the author should do everything to make his/her paper easier to read, is s/he really wants the paper to be read by the others.
A: I put the detailed version on the arXiv, and publish a short version. (Reviewers always like shorter proofs than I do, so I can never publish the long version.) I fix typos in arXiv versions, no matter how old, even if the corrections are too minor to submit an erratum to the published version.
A: In my community, sketchy proofs are only acceptable in a survey paper, and in such cases, references are given for more rigorous treatments. We also tend to put the ugly, technical proofs in an appendix. I don't know your community, but you might consider putting your "long" proofs in an appendix (at the very least for the referees, perhaps as an arXiv version), and let the referees suggest what to cut out.
A: Here is an illuminating quote from Terence Tao's journal submission guidelines; I could not have said it better:
"Give appropriate amounts of detail.  A paper should dwell at length on the most important, innovative, and crucial components of the paper, and be brief on the routine, expected, and standard components of the paper.  In particular, a paper should identify which of its components are the most interesting.  Note that this means interesting to experts in the field, and not just interesting to yourself; for instance, if you have just learnt how to prove a standard lemma which is well known to the experts and already in the literature, this does not mean that you should provide the standard proof of this standard lemma, unless this serves some greater purpose in the paper (e.g. by motivating a less standard lemma).  Conversely, some computations which you are very familiar with, but are not widely known in the field, should be expounded on detail, even if these details are “obvious” to you due to your extensive work in this area."
A: The referee gets to opine on the validity of the paper, and the editor on the readability and worthiness
of publishing in the journal.  At least, that's how it roughly goes.  You have to make the paper accessible by
expository skill, finding the right mix of detail to leave in or out. 
I recommend asking the editor if it is best to put stuff in for the referee and editor to cut, or to submit something more concise with a promise to expand on whatever needs clarification.  Even better than asking the editor is to ask colleagues who have submitted to that journal recently, or similar, and get their war stories and guidance.
