Oracle Verifier to Verifier run
SendClaim.oracleVerifier_toVerifier_run
Plain-language statement
The pure pass-through oracle verifier's underlying non-oracle verifier returns the statement together with the output oracle statements (input oracles at inl, the message at inr 0).
Exact Lean statement
theorem oracleVerifier_toVerifier_run {stmt : Statement} {oStmt : ∀ i, OStatement i}
{tr : (pSpec Message).FullTranscript} :
(oracleVerifier oSpec Statement OStatement Message).toVerifier.run ⟨stmt, oStmt⟩ tr =
pure ⟨stmt, Sum.rec oStmt (fun i => match i with | 0 => tr 0)⟩Formal artifact
Lean source
theorem oracleVerifier_toVerifier_run {stmt : Statement} {oStmt : ∀ i, OStatement i} {tr : (pSpec Message).FullTranscript} : (oracleVerifier oSpec Statement OStatement Message).toVerifier.run ⟨stmt, oStmt⟩ tr = pure ⟨stmt, Sum.rec oStmt (fun i => match i with | 0 => tr 0)⟩ := by simp only [Verifier.run, OracleVerifier.toVerifier, oracleVerifier] rw [show simulateQ (OracleInterface.simOracle2 oSpec oStmt tr.messages) (pure stmt : OptionT (OracleComp _) Statement) = (pure stmt : OptionT (OracleComp oSpec) Statement) from rfl, pure_bind] congr 1 congr 1 funext idx rcases idx with j | j · rfl · fin_cases j; rfl- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/ProofSystem/Component/SendClaim.lean:109-122
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Project documentation
This lemma proves the final algebraic step in the DG25 Theorem 3.1 proof. It shows that if R > e + 1, then e * (R / (R - 1)) < e + 1. The intuition is that the fraction R / (R - 1) is always greater than 1, but as R gets larger, it gets closer to 1. The hypothesis R > e + 1 provides a strong enough bound to ensure the product e * (fraction) do...
Source project: ArkLib
Person-level attribution pending.
Gadget Decompose coeff
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Plain-language statement
The k-th coefficient (k < deg φ) of a gadget-decomposition block is exactly the corresponding digit of the corresponding input coefficient.
Source project: ArkLib
Person-level attribution pending.
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ArkLib.Lattices.Ajtai.gadgetDecompose_lawful
Plain-language statement
The base-b gadget decomposition is a lawful gadget decomposition.
Source project: ArkLib
Person-level attribution pending.