Is using the phrase "... is left as an exercise for the reader" considered good style in academic papers/theses? Possible arguments:

Pro


For brevity for trivial deductions


Contra


Looks like the writer could not be bothered to write an extensive explanation
Definition of what is trivial to which reader and what not
I believe it's only appropriate in the type of writing where you are in a position to give the reader excercises. That is, in course books or other learning material. There, I think it's fine, assuming you've already given enough information for them to be able to perform such an excercise.

In papers or theses, you're actually trying to convince the reader that you're right - the reader is in the position of power, not you, as you want something from them (to accept your ideas) and not vice versa. Therefore, I'd never write such a phrase in a paper or thesis.

It's of course a viable requirement to leave out some parts of the work, either because of space constraints or because they're trivial, long but straightforward, would derail the course of the text, or something similar. If possible, such parts can be delegated to an appendix, or left out entirely. But I would accompany this with different phrasing, something like this:


  The formula (7) can be obtained from (6) using straightforward application of [insert appropriate math branch here]
  
  A detailed proof of statement (4) unfortunately exceeds the scope of this paper.
  
  The derivation of (3) from (1) is too long to present here, but it can be worked out using a symbolic computation system such as Mathematica.
  
  Equation (7) follows from a straightforward application of this-or-that theorem to equation (5); we refer the reader to existing literature on the topic for details of this.