Append coordinate Wise Special Sound
Verifier.append_coordinateWiseSpecialSound
Plain-language statement
Coordinate-wise special soundness is preserved by binary verifier append. The deterministic first-verifier output identifies the input statement of each suffix tree consumed by the second verifier's extractor.
Exact Lean statement
theorem append_coordinateWiseSpecialSound
(V₁ : Verifier oSpec Stmt₁ Stmt₂ pSpec₁)
(V₂ : Verifier oSpec Stmt₂ Stmt₃ pSpec₂)
(D₁ : CWSSStructure pSpec₁) (D₂ : CWSSStructure pSpec₂)
(verify₁ : Stmt₁ → pSpec₁.FullTranscript → Stmt₂)
(hV₁ : ∀ stmt tr, V₁.verify stmt tr = pure (verify₁ stmt tr))
(h₁ : V₁.coordinateWiseSpecialSound init impl D₁ rel₁ rel₂)
(h₂ : V₂.coordinateWiseSpecialSound init impl D₂ rel₂ rel₃) :
(V₁.append V₂).coordinateWiseSpecialSound init impl
(CWSSStructure.append D₁ D₂) rel₁ rel₃Formal artifact
Lean source
theorem append_coordinateWiseSpecialSound (V₁ : Verifier oSpec Stmt₁ Stmt₂ pSpec₁) (V₂ : Verifier oSpec Stmt₂ Stmt₃ pSpec₂) (D₁ : CWSSStructure pSpec₁) (D₂ : CWSSStructure pSpec₂) (verify₁ : Stmt₁ → pSpec₁.FullTranscript → Stmt₂) (hV₁ : ∀ stmt tr, V₁.verify stmt tr = pure (verify₁ stmt tr)) (h₁ : V₁.coordinateWiseSpecialSound init impl D₁ rel₁ rel₂) (h₂ : V₂.coordinateWiseSpecialSound init impl D₂ rel₂ rel₃) : (V₁.append V₂).coordinateWiseSpecialSound init impl (CWSSStructure.append D₁ D₂) rel₁ rel₃ := by change (V₁.append V₂).treeSpecialSound init impl (CWSSStructure.toShape (CWSSStructure.append D₁ D₂)) rel₁ rel₃ rw [CWSSStructure.toShape_append] exact append_treeSpecialSound init impl V₁ V₂ (CWSSStructure.toShape D₁) (CWSSStructure.toShape D₂) verify₁ hV₁ h₁ h₂- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/OracleReduction/Security/CoordinateWiseSpecialSoundness/Composition.lean:414-428
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