Is it acceptable to include footnotes in mathematical proofs?
Like almost anything else in writing, style should follow function. In other words, if you think that a footnote makes it easier for your reader to follow a text (for example, because it explains an aside that is too long for a parenthetical remark), then it is appropriate to use one. There is no general guideline whether footnotes are acceptable or not. It all depends on what you want to say and how you want to say it -- choose whatever means you think are appropriate to tell the story of the proof.