lincoln3 has this toy called the "Connecticut Do-Nothing Machine" which consists of a squarish wooden block with two grooves in it, one vertical and one horizontal, and a crank which is attached to two slidey pieces, one in each groove, such that you can turn the crank around and around forever. I had a dream in which I had this toy in the big bedroom I had in the old house by the lake my family lived in before my parents split up, and I cranked it around and around, and it played the most overwhelmingly beautiful version of Pachelbel's Canon, (which, if you know me well, you probably already know is one of a handful of songs (also including Jesu, Joy of Man's Desiring) that have a strange effect on me because I heard them so often and so early in my life since my mom played them on the old record player constantly...) but then in the middle of it, I heard a loud, sharp crack like a gunshot, and woke up.But later I fell back asleep and woke up with ways to generalize induction hypotheses swimming in my head. One of them worked, even, so Lemma B4 goes through now! I'm so excited. I think I've finally found my way down to the bottom of this chain of results, and all I have to do is climb back up and revise things a little so that everything is okay at every interface.