Right Prefix leaf eq append
ProtocolSpec.ChallengeTree.rightPrefix_leaf_eq_append
Plain-language statement
At the right boundary (pre₂ is a full right transcript) the embedding is literally tr₁ ++ₜ.
Exact Lean statement
theorem rightPrefix_leaf_eq_append (tr₁ : FullTranscript pSpec₁)
(pre₂ : Transcript (Fin.last n) pSpec₂) :
rightPrefix tr₁ pre₂ = tr₁ ++ₜ pre₂Formal artifact
Lean source
theorem rightPrefix_leaf_eq_append (tr₁ : FullTranscript pSpec₁) (pre₂ : Transcript (Fin.last n) pSpec₂) : rightPrefix tr₁ pre₂ = tr₁ ++ₜ pre₂ := by funext j refine Fin.addCases (fun i => ?_) (fun i => ?_) j · simp only [FullTranscript.append, rightPrefix] rw [Fin.happend_left, dif_pos (by simp)]; rfl · simp only [FullTranscript.append, rightPrefix] rw [Fin.happend_right, dif_neg (by simp)] refine cast_eq_iff_heq.mpr (HEq.trans ?_ (cast_heq _ _).symm) congr 1 exact Fin.ext (by simp only [Fin.val_natAdd]; omega)- Project
- ArkLib
- License
- Apache-2.0
- Commit
- fad5cbf80877
- Source
- ArkLib/OracleReduction/Security/TranscriptTree/Composition.lean:775-786
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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.
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ArkLib.Lattices.Ajtai.gadgetDecompose_coeff
Plain-language statement
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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.