Proofs Section 2.1 (Theorem 1, Lemmas)

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Fair upfront warning: This is not a particularly readable proof section. There's a bunch of dense notation, logical leaps due to illusion of transparency since I've spent months getting fluent with these concepts, and a relative lack of editing since it's long. If you really want to read this, I'd suggest PM-ing me to get a link to MIRIxDiscord, where I'd be able to guide you through it and answer questions. This post will be recapping the notions and building up an arsenal of lemmas, the [next one](https://www.alignmentforum.org/posts/8tLPYYQJM8SwL2xn9/proofs-section-2-2-isomorphism-to-expectations) will show the isomorphism theorem, translation theorems, and behavior of mixing, and the [last one](https://www.alignmentforum.org/posts/9ekP8FojvLa8Pr6P7/proofs-section-2-3-updates-decision-theory) is about updates and the decision-theory results. It's advised to have them open in different tabs and go between them as needed. .mjx-chtml {display: inline-block; line-height: 0; text-inde...

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• [1] https://www.alignmentforum.org/posts/xQYF3LR64NYn8vkoy/proofs-section-2-1-theorem-1-lemmas