Log Has Collision of chain In Log of ne
InductiveMerkleTree.logHasCollision_of_chainInLog_of_ne
Plain-language statement
Log-level binding (Collision Lemma at the log level). Log-formalized analog of getPutativeRootWithHash_binding_collision: two distinct openings (x, proof₁) ≠ (y, proof₂) of the same root at the same index, both witnessed by hash chains ChainInLog in the same log, force log to contain a hash collision (two log entries with equal responses b...
Exact Lean statement
theorem logHasCollision_of_chainInLog_of_ne
{s : Skeleton} (idx : SkeletonLeafIndex s)
(log : (spec α).QueryLog) (root x y : α)
(proof₁ proof₂ : List.Vector α idx.depth)
(hne : (x, proof₁) ≠ (y, proof₂))
(hc₁ : ChainInLog log x root idx proof₁)
(hc₂ : ChainInLog log y root idx proof₂) :
LogHasCollision logFormal artifact
Lean source
theorem logHasCollision_of_chainInLog_of_ne {s : Skeleton} (idx : SkeletonLeafIndex s) (log : (spec α).QueryLog) (root x y : α) (proof₁ proof₂ : List.Vector α idx.depth) (hne : (x, proof₁) ≠ (y, proof₂)) (hc₁ : ChainInLog log x root idx proof₁) (hc₂ : ChainInLog log y root idx proof₂) : LogHasCollision log := by induction idx generalizing root x y with | ofLeaf => exact absurd (Prod.ext (hc₁.trans hc₂.symm) (List.Vector.ext (fun i => i.elim0))) hne | @ofLeft sl sr idxLeft ih => obtain ⟨a₁, h₁_mem, hc₁⟩ := hc₁ obtain ⟨a₂, h₂_mem, hc₂⟩ := hc₂ by_cases hpair : (a₁, proof₁.head) = (a₂, proof₂.head) · obtain ⟨rfl, hhead⟩ := Prod.mk.inj hpair refine ih _ _ _ _ _ (fun heq => hne ?_) hc₁ hc₂ obtain ⟨rfl, htail⟩ := Prod.mk.inj heq exact Prod.ext rfl (((List.Vector.eq_cons_iff _ _ _).mpr ⟨hhead, htail⟩).trans proof₂.cons_head_tail) · exact LogHasCollision.of_mem (fun h => hpair (congrArg Sigma.fst h)) h₁_mem h₂_mem (heq_of_eq rfl) | @ofRight sl sr idxRight ih => obtain ⟨a₁, h₁_mem, hc₁⟩ := hc₁ obtain ⟨a₂, h₂_mem, hc₂⟩ := hc₂ by_cases hpair : (proof₁.head, a₁) = (proof₂.head, a₂) · obtain ⟨hhead, rfl⟩ := Prod.mk.inj hpair refine ih _ _ _ _ _ (fun heq => hne ?_) hc₁ hc₂ obtain ⟨rfl, htail⟩ := Prod.mk.inj heq exact Prod.ext rfl (((List.Vector.eq_cons_iff _ _ _).mpr ⟨hhead, htail⟩).trans proof₂.cons_head_tail) · exact LogHasCollision.of_mem (fun h => hpair (congrArg Sigma.fst h)) h₁_mem h₂_mem (heq_of_eq rfl)- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/CryptoFoundations/MerkleTree/Inductive/Extractability.lean:393-425
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