>>> One can now check that the next statement is true with a certain amount of essentially mechanical, though perhaps laborious, checking. I, the author, could do it, but it would use up a large amount of space and perhaps not accomplish much, since it'd be best for you to go ahead and do the computation to clarify for yourself what's going on here. I promise that no new ideas are involved, though of course you might need to think a little in order to find just the right combination of good ideas to apply.
I hate that. When I program my computer, I specify all the steps to accomplish something. If it's too verbose, then I abstract it in a function.
I even add comments to make sure that a human reader easily and completely understands what I do.
I do that because I want the computer and the human reader to be productive in their understanding of what I do. And because I want the human reader to see that it's either elegant or just mechanical.
I'm not that pretentious to say "hey, I've hidden a few details because if you are as smart as I am, then you'll understand easily".
I had this when learning maths. As a student I was sometimes lost because I always thought maths were hard. Should I have had all the details, I'd seen it was indeed much easier than I thought and wouldn't have been intimidated. Now, I'm older, and I know all of that and I'm much better at mathematics. But what a waste of time.
And the space argument, come one. Just put all the stuff in annexes and it'll be fine.