Where to break paragraphs in a proof? I have some rules of thumb about writing research papers that I can actually articulate. For example, leave all definitions as late as possible (but not later!), so the reader won't fear "Do I need to understand this definition for this theorem?" nor wonder "Did I understand that theorem, insofar as it didn't seem to use the previous definition?"
One I don't have, though, is where to include paragraph breaks in proofs. If I follow the usual maxim that each paragraph should be about a single idea, then interpreted variously, this leads to sentence-long or page-long paragraphs.
More specifically, do you think of "It remains only to show some big thing" as an announcement with which to begin a new paragraph, or as a capstone with which to end the previous one?

Do you have a maxim describing where to put paragraph breaks in proofs, that doesn't lead to ones that are too short or too long?

 A: I'm not sure what type of answer to give here, except don't be tasteless, and do what looks right. The obvious thing to do, if an idea is spanning multiple paragraphs, is to make it a separate proposition and cite it from within the larger argument. I've found how-to-write-readable-computer-code type guides rather useful in this regard.
The harder problem appears to be when to group separate ideas into a larger paragraph, for which it seems difficult to consistently defend any universal prescriptivist stance. Here's an example (yes, I understand that it is a bit of a low-blow to bring up something you wrote a long time ago): it has often confounded me why the proof of Lemma 7 on page 18 of your honeycomb paper spans three paragraphs. On the other hand, I was really glad that Lemma 8 was broken into various pieces, otherwise it would have taken me much longer to parse.
Maybe the golden rule should apply: would I want to read this in someone else's paper? Personally, I find it much more psychologically satisfying to see "only one more thing remains" at the end of a paragraph rather than at the beginning of the next one.
A: While writing, I usually read aloud the text: I like that what I write be not very different from what I would say. Since paragraphs are separated by pauses, which are usually quite obvious when talking, a bad paragraph break or a missing one tends to make itself quite obvious in this way.
This does not constitute a rule, of course, for paragraph breaking, but is a useful way to probe them. 
Good paragraph breaking is like pornography, in a way.
Regarding your specific example: without context, I don't think we can decide if a «It remains only to show some big thing» is better at the end of a paragraph or at the beginning. If you have a paragraph whose point is to explain why to obtain the desired result A it is enough to prove B, then it may well end with a «It remains only to show that B holds.» On the other hand, if that point was done earlier in the argument, and since then time has been spent on doing some other menial task, it would be nice to start the paragraph that begins the remaining task with an announcement that «It remains only to show that B holds» if only to be nice to the reader who might have by now forgotten the big lines of our reasoning.
A: Here is a useful quote from Zinsser's "On writing well", a timeless guide to all such matters:

Keep your paragraphs short. Writing is visual—it catches the eye
  before it has a chance to catch the brain. Short paragraphs put air
  around what you write and make it look inviting, whereas a long chunk
  of type can discourage a reader from even starting to read.
But don't go berserk. A succession of tiny paragraphs is as annoying
  as a paragraph that's too long. I'm thinking of all those midget
  paragraphs—verbless wonders—written by modern journalists trying to
  make their articles quick 'n' easy. Actually they make the reader's
  job harder by chopping up a natural train of thought.

