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Proof of `The finite randomized PCP-to-clique transfer` (1st statement)

groundedproofs/Lax253009Proofs/RandomizedReduction.lean · lax-253009

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.

Read the Lean proof on GitHub

Description

The explicit gap forces every complete sampled instance to be accepted. On a sound instance, acceptance forces the clique number into the bad event already bounded by the sampling theorem.