Lax Lean Archive

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Proof of `A small conditioning set gives low edge cost`

groundedproofs/Lax263307Proofs/ConditioningExistence.lean · lax-263307

What this proof establishes

thm✓Lax263307.ConditioningExistence

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 conditioning process reaches the required edge-cost threshold within the available number of vertices.

Proof strategy

Assume that every admissible small conditioning set exceeds the threshold. Starting at the empty set, repeatedly apply the strict entropy-decrease statement. After rr steps the entropy would be strictly less than zero, contradicting the entropy bounds. The resulting set inherits the checked cost bounds and mass equation.

Attribution

Bonnet–Chang, proof of Lemma 12.