Proof of `Exact rational search for a conditioning set` (3rd statement)
groundedproofs/Lax263307Proofs/RationalConditioning.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 exact rational search terminates with a set satisfying the costs and mass conditions of Lemma 12.
Proof strategy
The entropy argument guarantees a suitable set, and completeness places it in the candidate list. Clearing positive denominators proves the equivalence of the rational test and the edge-cost bound. The first successful candidate inherits the conditioning invariants.
Attribution
Bonnet–Chang, the deterministic enumeration in the proof of Lemma 12.