Get Putative Root With Hash batch To Single Proof
InductiveMerkleTree.getPutativeRootWithHash_batchToSingleProof
Plain-language statement
Root preservation. The single-index opening extracted from a batch opening at any selected leaf recomputes exactly the batch opening's putative root. Consequently a batch opening that verifies against a root yields, at every selected leaf, a single-index opening that verifies against the same root.
Exact Lean statement
theorem getPutativeRootWithHash_batchToSingleProof (hashFn : α → α → α)
{s : Skeleton} {sel : LeafData Bool s}
(v : SelectedValues α sel) (p : BatchProof α sel)
(idx : SkeletonLeafIndex s) (hidx : sel.get idx = true) :
getPutativeRootWithHash idx (selectedValueAt v idx hidx)
(batchToSingleProof hashFn v p idx hidx) hashFn
= getPutativeBatchRootWithHash hashFn v pFormal artifact
Lean source
theorem getPutativeRootWithHash_batchToSingleProof (hashFn : α → α → α) {s : Skeleton} {sel : LeafData Bool s} (v : SelectedValues α sel) (p : BatchProof α sel) (idx : SkeletonLeafIndex s) (hidx : sel.get idx = true) : getPutativeRootWithHash idx (selectedValueAt v idx hidx) (batchToSingleProof hashFn v p idx hidx) hashFn = getPutativeBatchRootWithHash hashFn v p := by induction p with | leaf => cases idx with | ofLeaf => rfl | internalBoth pl pr ihl ihr => cases idx with | ofLeft idxL => exact congrArg₂ hashFn (ihl v.1 idxL (by simpa using hidx)) rfl | ofRight idxR => exact congrArg₂ hashFn rfl (ihr v.2 idxR (by simpa using hidx)) | pruneRight hr rightRoot pl ih => cases idx with | ofLeft idxL => exact congrArg₂ hashFn (ih v.1 idxL (by simpa using hidx)) rfl | ofRight idxR => exact absurd (LeafData.anySelected_of_get idxR (by simpa using hidx)) (by simp [hr]) | pruneLeft hl leftRoot pr ih => cases idx with | ofRight idxR => exact congrArg₂ hashFn rfl (ih v.2 idxR (by simpa using hidx)) | ofLeft idxL => exact absurd (LeafData.anySelected_of_get idxL (by simpa using hidx)) (by simp [hl])- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/MerkleTree/Inductive/Batch/ToSingle.lean:98-126
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