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Project-declaredLean 4.31.0 · null

Verify Matches Equivalent is complete

Cedar.Thm.verifyMatchesEquivalent_is_complete

Plain-language statement

The verifyMatchesEquivalent analysis is complete: if the assertions verifyMatchesEquivalent p₁ p₂ εnv are satisfiable for the policies p₁ and p₂ and the strongly well-formed symbolic environment εnv, then there exists a strongly well-formed concrete environment env ∈ᵢ εnv such that the policies will have different matching behavior (one matche...

Exact Lean statement

theorem verifyMatchesEquivalent_is_complete {p₁ p₂ : Policy} {εnv : SymEnv} {asserts : Asserts} :
  εnv.StronglyWellFormedForPolicy p₁ →
  εnv.StronglyWellFormedForPolicy p₂ →
  verifyMatchesEquivalent p₁ p₂ εnv = .ok asserts →
  εnv ⊧ asserts →
  ∃ env,
    env ∈ᵢ εnv ∧
    env.StronglyWellFormedForPolicy p₁ ∧
    env.StronglyWellFormedForPolicy p₂ ∧
    Env.EnumCompleteFor env εnv ∧
    (evaluate p₁.toExpr env.request env.entities = .ok true) ≠
    (evaluate p₂.toExpr env.request env.entities = .ok true)

Formal artifact

Lean source

Canonical source
Full Lean sourceLean 4
theorem verifyMatchesEquivalent_is_complete {p₁ p₂ : Policy} {εnv : SymEnv} {asserts : Asserts} :  εnv.StronglyWellFormedForPolicy p₁   εnv.StronglyWellFormedForPolicy p₂   verifyMatchesEquivalent p₁ p₂ εnv = .ok asserts   εnv ⊧ asserts    env,    env ᵢ εnv     env.StronglyWellFormedForPolicy p₁     env.StronglyWellFormedForPolicy p₂     Env.EnumCompleteFor env εnv     (evaluate p₁.toExpr env.request env.entities = .ok true)     (evaluate p₂.toExpr env.request env.entities = .ok true):= by  intro h₁ h₂ h₃ h₄  have env, h₅, h₆, h₇, h₈, h₉ := verifyEvaluatePair_is_complete verifyMatchesEquivalent_wbepq h₁ h₂ h₃ h₄  exists env  simp only [beq_eq_false_iff_ne, ne_eq] at h₉  apply And.intro h₅  apply And.intro h₆  apply And.intro h₇  apply And.intro h₈  cases hev₁ : evaluate p₁.toExpr env.request env.entities == .ok (.prim (.bool true))  · simp only [hev₁, Bool.false_eq, beq_eq_false_iff_ne, ne_eq, Decidable.not_not] at h₉    simp only [beq_eq_false_iff_ne, ne_eq] at hev₁    simp [*]  · simp only [hev₁, Bool.true_eq, beq_iff_eq] at h₉    simp only [beq_iff_eq] at hev₁    simp [*]
Project
Cedar Specification
License
Apache-2.0
Commit
3f093947b8ae
Source
cedar-lean/Cedar/Thm/Verification.lean:308-335

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