I will not be providing the proof in prose in this post, as it is not suitable for even impolite human company, but it sure does compile and comes out the other side with a machine-certified proof of what sure looks to be an even stronger correctly-expressed statement than the one I was originally aiming for.
It seems plausible to me that the the thing the AI proved turns out not to be the thing that you intended to prove. In my experience, this is absolutely the sort of thing that can happen, even when the proof is relatively simple and comprehensible.
What a bottleneck is, is a way to reduce the amorphous difficulty of a problem to something specific; that to solve the problem you have to figure out how to overcome this particular obstacle, or that by the laws of the universe a solution must take this particular shape. It’s not a luxury you always have, with hard problems, but it sure does help.