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Let's say I was writing a proof that required a lot of leg work or "rough work" in order to arrive at the conclusion. I want to show the reader (say a professor) that rough work because it's important. The actual proof after the work is trivial but long. Is it legitimate for me to (after the work) say something like, "Choose $x = \dots $, and the result will follow."?

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  • $\begingroup$ I feel like this is extremely subjective and depends too much on the professor. In the case of writing an article, it’s fine, but a professor likely doesn’t view you as a professional mathematician and so wants to see all of the intermediate steps, even if they are trivial. $\endgroup$ – Clayton Oct 10 '17 at 18:39
  • $\begingroup$ There's a lot of missing context here. What is this proof for? A published paper, a homework exercise, ...? How trivial are the details you want to leave out? If the reader is "a professor", it might be best to ask that professor. $\endgroup$ – Robert Israel Oct 10 '17 at 18:46
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I would say it depends on how 'trivial' it is. Triviality can be subjective. You can say it, but you could also include just the general idea of the remaining steps. For instance, "choose x=... and the result will follow by simple algebraic manipulations". Not always necessary, of course, but it puts you in a 'safer' position, so to speak.

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  • $\begingroup$ I like the idea of sketching out the general techniques to complete, even though I have a qualm about whether the "trivial" final steps might interact critically with some aspect of the detail work. $\endgroup$ – Joffan Oct 10 '17 at 18:41
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In my view (and this is not shared by everyone!) the correct way to do this is to put into an appendix as much detail as you feel would let someone actually verify your assertion easily. Yes, this might make your paper/answer/whatever fifty times longer; but bytes are cheap.

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