Triple writer T iff forall support
OracleComp.ProgramLogic.StdDo.triple_writerT_iff_forall_support
Plain-language statement
Support characterization of Std.Do.Triple on WriterT ω (OracleComp spec). A triple ⦃P⦄ mx ⦃Q⦄ over the writer log holds iff every outcome (a, w) in the support of mx.run satisfies Q.1 a (s ++ w) for every starting log s satisfying P. The starting log s threads through the WP interpretation itself, not through mx: WriterT.run mx alway...
Exact Lean statement
theorem triple_writerT_iff_forall_support {ω α : Type}
[EmptyCollection ω] [Append ω] [LawfulAppend ω]
(mx : WriterT ω (OracleComp spec) α)
(P : Std.Do.Assertion (.arg ω .pure)) (Q : Std.Do.PostCond α (.arg ω .pure)) :
Std.Do.Triple mx P Q ↔
∀ s : ω, (P s).down →
∀ a w, (a, w) ∈ support mx.run → (Q.1 a (s ++ w)).downFormal artifact
Lean source
theorem triple_writerT_iff_forall_support {ω α : Type} [EmptyCollection ω] [Append ω] [LawfulAppend ω] (mx : WriterT ω (OracleComp spec) α) (P : Std.Do.Assertion (.arg ω .pure)) (Q : Std.Do.PostCond α (.arg ω .pure)) : Std.Do.Triple mx P Q ↔ ∀ s : ω, (P s).down → ∀ a w, (a, w) ∈ support mx.run → (Q.1 a (s ++ w)).down := by rw [Std.Do.Triple.iff] simp only [SPred.entails_1] refine forall_congr' (fun s => imp_congr_right (fun _hP => ?_)) change wpProp (spec := spec) mx.run (fun p => (Q.1 p.1 (s ++ p.2)).down) ↔ _ rw [wpProp_iff_forall_support, Prod.forall]- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/ProgramLogic/Unary/StdDoBridge.lean:121-133
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