[refrigerator]

Ahh I did a bit of googling but couldn't find anything nice — sorry! Most of the time, the complex stuff is broken down into smaller "lemmas" with their own manageable proofs, and then the proof of the whole theorem will be something like "Follows from Lemma 2.1, Lemma 2.2, and a basic application of Theorem 1.4"

This is the theorem I was talking about: https://i.imgur.com/1xEH51Z.png (taken from https://taimur.me/posts/thinking-at-the-right-level-of-abstr... which touches on a similar topic to your post)