Monad Lift lift M Option T
OracleComp.monadLift_liftM_OptionT
Plain-language statement
Coherence: lifting an OracleComp to a superspec and then into OptionT via the standard MonadLift equals lifting directly through the transitive MonadLiftT chain (which goes through the simulateQ-based OptionT MonadLift instance).
Exact Lean statement
@[simp]
lemma monadLift_liftM_OptionT [MonadLift (OracleQuery spec) (OracleQuery superSpec)]
(mx : OracleComp spec α) :
(monadLift (liftM mx : OracleComp superSpec α) : OptionT (OracleComp superSpec) α) =
(liftM mx : OptionT (OracleComp superSpec) α)Formal artifact
Lean source
@[simp]lemma monadLift_liftM_OptionT [MonadLift (OracleQuery spec) (OracleQuery superSpec)] (mx : OracleComp spec α) : (monadLift (liftM mx : OracleComp superSpec α) : OptionT (OracleComp superSpec) α) = (liftM mx : OptionT (OracleComp superSpec) α) := by apply OptionT.ext simp only [OptionT.run_monadLift, monadLift_eq_self] conv_rhs => dsimp only [liftM, MonadLiftT.monadLift, MonadLift.monadLift] simp only [OptionT.run_mk, OptionT.lift] rw [simulateQ_bind] simp only [simulateQ_pure, ← map_eq_pure_bind] rfl- Project
- VCVio
- License
- Apache-2.0
- Commit
- 2ceb2d825ee3
- Source
- VCVio/OracleComp/Coercions/SubSpec.lean:480-491
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