Oracle Verifier coordinate Wise Special Sound
SendSingleWitness.oracleVerifier_coordinateWiseSpecialSound
Project documentation
Coordinate-wise special soundness of SendSingleWitness. The oracle verifier has no challenge rounds, so CWSS collapses (via the oracle no-challenge bridge coordinateWiseSpecialSound_of_isEmpty_challengeIdx) to a transcript-level extraction obligation on the combined statement Statement × (∀ i, OStatement i). The extractor is `e := fun _ tr => tr...
Exact Lean statement
theorem oracleVerifier_coordinateWiseSpecialSound (D : CWSSStructure (oraclePSpec Witness)) :
(oracleVerifier oSpec Statement OStatement Witness).coordinateWiseSpecialSound init impl D
oRelIn (toORelOut oRelIn)Formal artifact
Lean source
theorem oracleVerifier_coordinateWiseSpecialSound (D : CWSSStructure (oraclePSpec Witness)) : (oracleVerifier oSpec Statement OStatement Witness).coordinateWiseSpecialSound init impl D oRelIn (toORelOut oRelIn) := by refine OracleVerifier.coordinateWiseSpecialSound_of_isEmpty_challengeIdx init impl D (oracleVerifier oSpec Statement OStatement Witness) oRelIn (toORelOut oRelIn) (fun _ tr => tr 0) ?_ rintro ⟨stmt, oStmt⟩ tr hAcc have hmem := Verifier.mem_of_pure_accepting init impl (oracleVerifier oSpec Statement OStatement Witness).toVerifier ⟨stmt, oStmt⟩ tr (toORelOut oRelIn).language _ (oracleVerifier_toVerifier_run (oSpec := oSpec)) hAcc obtain ⟨_, hu⟩ := (Set.mem_language_iff _ _).1 hmem exact hu- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/ProofSystem/Component/SendWitness.lean:366-377
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