Proof of `Conditioning with a quantitative moment lower bound` (1st statement)
groundedproofs/Lax263307Proofs/HeavyConditioning.lean · lax-263307
What this proof establishes
Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.
Description
The expected entropy drop exceeds 2/p. Choices below the probability floor contribute at most 1/(2p), using the parent entropy bound. If every remaining choice dropped by at most 1/p, the total drop would be at most 3/(2p), a contradiction. Conditional moment identities identify the selected entropy with that of the enlarged conditioning set.