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
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
Reuse this declaration
Bring the exact result into your workflow
The import identifies the source module. Your project still needs the pinned package dependency shown on this page.
What this badge means
This completion status comes from the project or community source. It has not yet been represented here as an independent rebuild and axiom audit.
Continue in this project
Related declarations
Find? ext
Cedar.Data.Map.find?_ext
Plain-language statement
Two well-formed maps are equal if they have the same find? for every key.
Source project: Cedar Specification
Person-level attribution pending.
Find? notmem keys
Cedar.Data.Map.find?_notmem_keys
Plain-language statement
Inverse of find?_mem_toList, except that this requires wf
Source project: Cedar Specification
Person-level attribution pending.
Find? some iff in values
Cedar.Data.Map.find?_some_iff_in_values
Plain-language statement
The mp direction of this does not need the wf precondition and, in fact, is available separately as find?_some_implies_in_values above
Source project: Cedar Specification
Person-level attribution pending.