Chapter 12

After chapter 11 which had some long difficult predicate logic proofs, chapter 12 is such a break. This chapter is on identities or "x=y" type statements.

So when I approached the proofs, my brain was still in "the more difficult proof" mode. It was somewhere about the third proof I realized that the proofs were very easy! My brain was making them more complicated than necessary! The first time I did one proof, I finished in 40+ steps. Then I decided to go back and redo the proof to see how streamlined I could get it. It decreased to 18 steps. Then I realized I could streamline it even more and I realized the proof had extraneous information that I did not need to use at all! Following is the ultra-streamlined proof.