Support lift Comp
OracleComp.support_liftComp
Plain-language statement
Support is preserved by liftComp: lifting a computation to a larger oracle spec does not change which outputs are reachable. This is the support analogue of evalDist_liftComp.
Exact Lean statement
@[simp] lemma support_liftComp (mx : OracleComp spec α) :
support (liftComp mx superSpec) = support mxFormal artifact
Lean source
@[simp] lemma support_liftComp (mx : OracleComp spec α) : support (liftComp mx superSpec) = support mx := by simp only [liftComp] induction mx using OracleComp.inductionOn with | pure x => simp | query_bind t oa ih => simp only [simulateQ_query_bind, support_bind, OracleQuery.input_query, monadLift_self, ih] have hs : support (liftM (OracleSpec.query t) : OracleComp superSpec (spec.Range t)) = Set.univ := by change support ((liftM : OracleQuery superSpec _ → OracleComp superSpec _) ((monadLift : OracleQuery spec _ → OracleQuery superSpec _) (OracleSpec.query t))) = _ rw [support_liftM, show (monadLift (OracleSpec.query t) : OracleQuery superSpec _) = ⟨h.onQuery t, h.onResponse t⟩ from by convert h.liftM_eq_lift (OracleSpec.query t) using 1 <;> rfl] exact (LawfulSubSpec.onResponse_bijective (h := h) t).surjective.range_eq rw [hs]; simp- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/Coercions/SubSpec.lean:344-359
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