My power-seeking theorems seem a bit like Vingean reflection. In Vingean reflection, you reason about an agent which is significantly smarter than you: if I'm playing chess against an opponent who plays the optimal policy for the chess objective function, then I predict that I'll lose the game. I predict that I'll lose, even though I can't predict my opponent's (optimal) moves - otherwise I'd probably be that good myself.

My power-seeking theorems show that most objectives have optimal policies which e.g. avoid shutdown and survive into the far future, even without saying what particular actions these policies take to get there. I may not even be able to compute a single optimal policy for a single non-trivial objective, but I can still reason about the statistical tendencies of optimal policies.