I just have a Master in Physics, but here is my take: The thing is that mathematic proofs work on different levels of "zoom", ranging from just stating "it fol

I just have a Master in Physics, but here is my take: The thing is that mathematic proofs work on different levels of "zoom", ranging from just stating "it follows trivially" to formal proofs. And this is a normal process, that's how Mathematicians boil down long proofs to simple lines of reasoning. I think what happens here I that the author of the original proof is arguing on a high "it's obvious" level and seems to be unwilling to go into detail.