How do you structure proofs that are longer than say half a page?
I have already encountered a variety of styles (in my short math life), some of which I list below and I just hoped to hear some wise words or your ideas on the topic, for example in which situation to use which (lecture, tutorial, research paper, thesis, book, etc.)
- Write the proof down in running text, proof auxiliary claims that are need within the proof where they are needed.
Write the proof down in running text; where auxiliary claims are needed refer to them and
2.1 make lemmata before the theorem that contain the auxiliary claims
2.2 make lemmata after the theorem that contain the auxiliary claims
Give a list of steps, the last one being the conclusion using the prior steps.
3.1 Proof step 1 before writing down step 2 etc.
3.2 First write all steps down, then proof them in the same order
3.3 First write all steps down, then write down the conclusion including running text proof, then prove the remaining steps