Verifier coordinate Wise Special Sound
SendWitness.verifier_coordinateWiseSpecialSound
Project documentation
Coordinate-wise special soundness of SendWitness. The verifier has no challenge rounds, so CWSS collapses (via the no-challenge bridge coordinateWiseSpecialSound_of_isEmpty_challengeIdx) to a transcript-level extraction obligation. The extractor is e := fun _ tr => tr 0: the witness is the (single) prover message. Since the verifier is pure wi...
Exact Lean statement
theorem verifier_coordinateWiseSpecialSound (D : CWSSStructure (pSpec Witness)) :
(verifier oSpec Statement Witness).coordinateWiseSpecialSound init impl D relIn
(toRelOut relIn)Formal artifact
Lean source
theorem verifier_coordinateWiseSpecialSound (D : CWSSStructure (pSpec Witness)) : (verifier oSpec Statement Witness).coordinateWiseSpecialSound init impl D relIn (toRelOut relIn) := by refine Verifier.coordinateWiseSpecialSound_of_isEmpty_challengeIdx init impl D (verifier oSpec Statement Witness) relIn (toRelOut relIn) (fun _ tr => tr 0) ?_ intro stmtIn tr hAcc have hmem : (⟨stmtIn, tr 0⟩ : Statement × Witness) ∈ (toRelOut relIn).language := Verifier.mem_of_pure_accepting init impl (verifier oSpec Statement Witness) stmtIn tr (toRelOut relIn).language ⟨stmtIn, tr 0⟩ rfl 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:109-119
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