When you hit upon a proof like that, you know it. If you're struggling and need feedback, then your solution is probably more complicated than the elegant one in the book, and the question you're asking is, okay, my solution isn't great, but is it even a solution?
There's a reason these books declare some level of "mathematical maturity" as a prerequisite. By the time you get to certain content you have to either be comfortable checking a proof (maybe set it aside for a few days like you would any other writing) or have human help.
There's a reason these books declare some level of "mathematical maturity" as a prerequisite. By the time you get to certain content you have to either be comfortable checking a proof (maybe set it aside for a few days like you would any other writing) or have human help.