Proof of `Sampling finite choices with a fixed supply of fair bits` (2nd statement)
groundedproofs/Lax253009Proofs/FreshBitSampling.lean · lax-253009
What this proof establishes
no assumptions
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
Every tuple of residues has at least floor(B/r)^N preimages. Apply this lower bound to the complement event, then Bernoulli's inequality bounds the mass lost in incomplete residue blocks by Nr/B.