Pondering the Ugly Underbelly, and Whether Images are Real

I tell my computer science students that we go through proofs not to show WHAT is true, but WHY it's true. During an interesting consultation with a graduate student who wanted to know whether I proved the Cook-Levin Theorem when I taught that result in the Foundations of Computing class, I said that I had, indeed, and that every teacher should. As is the human predilection, I became ever more fully convinced that I was right as I expounded on it. The textbook in use is Michael Sipser 3rd Edition [Sipser]. In Section 7.4, we see Cook-Levin as Theorem 7.37: SAT is NP-Complete.