Project-declaredLean 4.32.0 · mathlib@81a5d257

With Programming empty run' eq

OracleComp.ProgramLogic.Relational.withProgramming_empty_run'_eq

program verification separation logic cryptography programming oracle

Plain-language statement

run' projection corollary of withProgramming_empty_run_proj_eq.

Exact Lean statement

theorem withProgramming_empty_run'_eq
    {ι : Type} [DecidableEq ι] {spec : OracleSpec ι} (so : QueryImpl spec ProbComp)
    (oa : OracleComp spec α) (cache : spec.QueryCache) (bad : Bool) :
    (simulateQ (so.withProgramming ProgrammingPolicy.empty) oa).run' (cache, bad) =
      (simulateQ so.withCaching oa).run' cache

Formal artifact

Lean source

Canonical source

Full Lean sourceLean 4

theorem withProgramming_empty_run'_eq    {ι : Type} [DecidableEq ι] {spec : OracleSpec ι} (so : QueryImpl spec ProbComp)    (oa : OracleComp spec α) (cache : spec.QueryCache) (bad : Bool) :    (simulateQ (so.withProgramming ProgrammingPolicy.empty) oa).run' (cache, bad) =      (simulateQ so.withCaching oa).run' cache := by  rw [StateT.run', StateT.run']  have hmap := congrArg (fun p => Prod.fst <$> p)    (withProgramming_empty_run_proj_eq so oa cache bad)  change (fun a => id a.1) <$>      (simulateQ (so.withProgramming ProgrammingPolicy.empty) oa).run (cache, bad) =    Prod.fst <$> (simulateQ so.withCaching oa).run cache  simpa only [Functor.map_map, Function.comp_def, Prod.map] using hmap

Project: VCVio
License: Apache-2.0
Commit: 2ceb2d825ee3
Source: VCVio/OracleComp/QueryTracking/ProgrammingOracle.lean:267-278

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