Project-declaredLean 4.32.0 · mathlib@81a5d257

Simulate Q run preserves Inv

OracleComp.simulateQ_run_preservesInv

program verification separation logic cryptography preserves inv

Plain-language statement

If impl preserves Inv, then simulating any oracle computation with simulateQ impl preserves Inv on the final state (support-wise).

Exact Lean statement

theorem simulateQ_run_preservesInv
    {ι : Type} {spec : OracleSpec ι} {σ α : Type}
    (impl : QueryImpl spec (StateT σ ProbComp)) (Inv : σ → Prop)
    (himpl : QueryImpl.PreservesInv impl Inv) :
    ∀ oa : OracleComp spec α,
    ∀ σ0, Inv σ0 →
      ∀ z ∈ support ((simulateQ impl oa).run σ0), Inv z.2

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem simulateQ_run_preservesInv    {ι : Type} {spec : OracleSpec ι} {σ α : Type}    (impl : QueryImpl spec (StateT σ ProbComp)) (Inv : σ → Prop)    (himpl : QueryImpl.PreservesInv impl Inv) :    ∀ oa : OracleComp spec α,    ∀ σ0, Inv σ0 →      ∀ z ∈ support ((simulateQ impl oa).run σ0), Inv z.2 := by  intro oa  induction oa using OracleComp.inductionOn with  | pure a =>      intro σ0 hσ0 z hz      simp_all  | query_bind t oa ih =>      intro σ0 hσ0 z hz      have hz' :          z ∈ support            (((simulateQ impl                  (OracleSpec.query t : OracleComp spec (spec.Range t))).run σ0) >>=              fun us => (simulateQ impl (oa us.1)).run us.2) := by        simpa [simulateQ_bind, OracleComp.liftM_def] using hz      rcases (mem_support_bind_iff _ _ _).1 hz' with ⟨us, hus, hzcont⟩      have hus' : us ∈ support ((impl t).run σ0) := by        simpa [simulateQ_spec_query] using hus      exact ih us.1 us.2 (himpl t σ0 hσ0 us hus') z hzcont

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/OracleComp/SimSemantics/StateT/PreservesInv.lean:79-102

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