Loogle!

Result

Found 71 declarations mentioning Std.Iterators.PostconditionT.map.

• Std.Iterators.PostconditionT.map 📋 Init.Data.Iterators.PostconditionMonad
  {m : Type w → Type w'} [Functor m] {α β : Type w} (f : α → β) (x : Std.Iterators.PostconditionT m α) : Std.Iterators.PostconditionT m β
• Std.Iterators.PostconditionT.property_map 📋 Init.Data.Iterators.PostconditionMonad
  {m : Type w → Type w'} [Functor m] {α β : Type w} {x : Std.Iterators.PostconditionT m α} {f : α → β} {b : β} : (Std.Iterators.PostconditionT.map f x).Property b ↔ ∃ a, f a = b ∧ x.Property a
• Std.Iterators.PostconditionT.map_eq_pure_bind 📋 Init.Data.Iterators.PostconditionMonad
  {m : Type w → Type w'} [Monad m] [LawfulMonad m] {α β : Type w} {f : α → β} {x : Std.Iterators.PostconditionT m α} : Std.Iterators.PostconditionT.map f x = x.bind (pure ∘ f)
• Std.Iterators.PostconditionT.map_pure 📋 Init.Data.Iterators.PostconditionMonad
  {m : Type w → Type w'} [Monad m] [LawfulMonad m] {α β : Type w} {f : α → β} {a : α} : Std.Iterators.PostconditionT.map f (pure a) = pure (f a)
• Std.Iterators.PostconditionT.operation_map 📋 Init.Data.Iterators.PostconditionMonad
  {m : Type w → Type w'} [Functor m] {α β : Type w} {x : Std.Iterators.PostconditionT m α} {f : α → β} : (Std.Iterators.PostconditionT.map f x).operation = (fun a => ⟨f ↑a, ⋯⟩) <$> x.operation
• Std.Iterators.Types.Map.instIterator_eq_filterMapInstIterator 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [Std.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} : Std.Iterators.Types.Map.instIterator = Std.Iterators.Types.FilterMap.instIterator
• Std.IterM.filterWithPostcondition 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] [MonadLiftT m n] [Std.Iterator α m β] (f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)) (it : Std.IterM m β) : Std.IterM n β
• Std.IterM.filterM 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] [Monad n] [MonadAttach n] [MonadLiftT m n] (f : β → n (ULift.{w, 0} Bool)) (it : Std.IterM m β) : Std.IterM n β
• Std.Iter.filterWithPostcondition 📋 Init.Data.Iterators.Combinators.FilterMap
  {α β : Type w} [Std.Iterator α Id β] {m : Type w → Type w'} [Monad m] (f : β → Std.Iterators.PostconditionT m (ULift.{w, 0} Bool)) (it : Std.Iter β) : Std.IterM m β
• Std.Iter.filterM 📋 Init.Data.Iterators.Combinators.FilterMap
  {α β : Type w} [Std.Iterator α Id β] {m : Type w → Type w'} [Monad m] [MonadAttach m] (f : β → m (ULift.{w, 0} Bool)) (it : Std.Iter β) : Std.IterM m β
• Std.IterM.toArray_mapWithPostcondition_eq_toArray_filterMapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → Std.Iterators.PostconditionT n γ} {it : Std.IterM m β} : (Std.IterM.mapWithPostcondition f it).toArray = (Std.IterM.filterMapWithPostcondition (fun x => Std.Iterators.PostconditionT.map some (f x)) it).toArray
• Std.IterM.toListRev_mapWithPostcondition_eq_toListRev_filterMapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → Std.Iterators.PostconditionT n γ} {it : Std.IterM m β} : (Std.IterM.mapWithPostcondition f it).toListRev = (Std.IterM.filterMapWithPostcondition (fun x => Std.Iterators.PostconditionT.map some (f x)) it).toListRev
• Std.IterM.toList_mapWithPostcondition_eq_toList_filterMapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → Std.Iterators.PostconditionT n γ} {it : Std.IterM m β} : (Std.IterM.mapWithPostcondition f it).toList = (Std.IterM.filterMapWithPostcondition (fun x => Std.Iterators.PostconditionT.map some (f x)) it).toList
• Std.IterM.fold_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.IterM m β} : Std.IterM.fold g init (Std.IterM.filterWithPostcondition f it) = Std.IterM.foldM (fun d b => do let __do_lift ← (f b).run pure (if __do_lift.down = true then g d b else d)) init it
• Std.IterM.fold_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.IterM m β} : Std.IterM.fold g init (Std.IterM.filterM f it) = Std.IterM.foldM (fun d b => do let __do_lift ← f b pure (if __do_lift.down = true then g d b else d)) init it
• Std.IterM.foldM_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Monad n] [Monad o] [LawfulMonad m] [LawfulMonad n] [LawfulMonad o] [Std.IteratorLoop α m n] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m n] [Std.LawfulIteratorLoop α m o] [MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.IterM m β} : Std.IterM.foldM g init (Std.IterM.filterWithPostcondition f it) = Std.IterM.foldM (fun d b => do let __do_lift ← liftM (f b).run if __do_lift.down = true then g d b else pure d) init it
• Std.IterM.foldM_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Monad o] [LawfulMonad o] [Std.IteratorLoop α m n] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m n] [Std.LawfulIteratorLoop α m o] [MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.IterM m β} : Std.IterM.foldM g init (Std.IterM.filterM f it) = Std.IterM.foldM (fun d b => do let __do_lift ← liftM (f b) if __do_lift.down = true then g d b else pure d) init it
• Std.IterM.anyM_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [MonadLiftT m n] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] {it : Std.IterM m β} {f p : β → n (ULift.{w, 0} Bool)} : Std.IterM.anyM p (Std.IterM.filterM f it) = Std.IterM.anyM (fun x => do let __do_lift ← f x if __do_lift.down = true then p x else pure { down := false }) (Std.IterM.mapM pure it)
• Std.IterM.allM_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [MonadLiftT m n] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [LawfulMonadLiftT m n] {it : Std.IterM m β} {f p : β → n (ULift.{w, 0} Bool)} : Std.IterM.allM p (Std.IterM.filterM f it) = Std.IterM.allM (fun x => do let __do_lift ← f x if __do_lift.down = true then p x else pure { down := true }) (Std.IterM.mapM pure it)
• Std.IterM.forIn_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {m : Type u_1 → Type u_2} {n : Type u_1 → Type u_3} {o : Type u_1 → Type u_4} {α β γ : Type u_1} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [MonadLiftT m n] [LawfulMonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m o] {it : Std.IterM m β} {f : β → Std.Iterators.PostconditionT n (ULift.{u_1, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} : forIn (Std.IterM.filterWithPostcondition f it) init g = forIn it init fun out acc => do let __do_lift ← liftM (f out).run if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)
• Std.IterM.forIn_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {m : Type u_1 → Type u_2} {n : Type u_1 → Type u_3} {o : Type u_1 → Type u_4} {α β γ : Type u_1} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [MonadAttach n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m o] {it : Std.IterM m β} {f : β → n (ULift.{u_1, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} : forIn (Std.IterM.filterM f it) init g = forIn it init fun out acc => do let __do_lift ← liftM (f out) if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)
• Std.IterM.all_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [MonadLiftT m n] [Std.IteratorLoop α m m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [LawfulMonadLiftT m n] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → n (ULift.{w, 0} Bool)} {p : β → Bool} : Std.IterM.all p (Std.IterM.filterM f it) = Std.IterM.allM (fun x => do let __do_lift ← f x if __do_lift.down = true then pure { down := p x } else pure { down := true }) (Std.IterM.mapM pure it)
• Std.IterM.any_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [MonadLiftT m n] [Std.IteratorLoop α m m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [LawfulMonadLiftT m n] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → n (ULift.{w, 0} Bool)} {p : β → Bool} : Std.IterM.any p (Std.IterM.filterM f it) = Std.IterM.anyM (fun x => do let __do_lift ← f x if __do_lift.down = true then pure { down := p x } else pure { down := false }) (Std.IterM.mapM pure it)
• Std.IterM.step_mapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] {it : Std.IterM m β} {γ : Type w} {f : β → Std.Iterators.PostconditionT n γ} [Monad n] [LawfulMonad n] [MonadLiftT m n] : (Std.IterM.mapWithPostcondition f it).step = do let __do_lift ← liftM it.step match __do_lift.inflate with | ⟨Std.IterStep.yield it' out, h⟩ => do let out' ← (f out).operation pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.IterM.mapWithPostcondition f it') ↑out' ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.IterM.mapWithPostcondition f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.IterM.step_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] {it : Std.IterM m β} {γ : Type w} {f : β → n γ} [Monad n] [MonadAttach n] [LawfulMonad n] [MonadLiftT m n] : (Std.IterM.mapM f it).step = do let __do_lift ← liftM it.step match __do_lift.inflate with | ⟨Std.IterStep.yield it' out, h⟩ => do let out' ← MonadAttach.attach (f out) pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.IterM.mapM f it') ↑out' ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.IterM.mapM f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.IterM.step_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterator α m β] {it : Std.IterM m β} [Monad m] [LawfulMonad m] {f : β → β'} : (Std.IterM.map f it).step = do let __do_lift ← it.step match __do_lift.inflate with | ⟨Std.IterStep.yield it' out, h⟩ => let out' := f out; pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.IterM.map f it') out' ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.IterM.map f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.IterM.step_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] {it : Std.IterM m β} {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} [Monad n] [LawfulMonad n] [MonadLiftT m n] : (Std.IterM.filterWithPostcondition f it).step = do let __do_lift ← liftM it.step match __do_lift.inflate with | ⟨Std.IterStep.yield it' out, h⟩ => do let __do_lift ← (f out).operation match __do_lift with | ⟨{ down := false }, h'⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.IterM.filterWithPostcondition f it') ⋯)) | ⟨{ down := true }, h'⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.IterM.filterWithPostcondition f it') out ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.IterM.filterWithPostcondition f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.IterM.step_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterator α m β] {it : Std.IterM m β} {f : β → n (ULift.{w, 0} Bool)} [Monad n] [MonadAttach n] [LawfulMonad n] [MonadLiftT m n] : (Std.IterM.filterM f it).step = do let __do_lift ← liftM it.step match __do_lift.inflate with | ⟨Std.IterStep.yield it' out, h⟩ => do let __do_lift ← MonadAttach.attach (f out) match __do_lift with | ⟨{ down := false }, hf⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.IterM.filterM f it') ⋯)) | ⟨{ down := true }, hf⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.IterM.filterM f it') out ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.IterM.filterM f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.Iter.filterWithPostcondition_eq_toIter_filterMapWithPostcondition_toIterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} [Monad m] {f : β → Std.Iterators.PostconditionT m (ULift.{w, 0} Bool)} : Std.Iter.filterWithPostcondition f it = Std.IterM.filterWithPostcondition f it.toIterM
• Std.Iter.filterM_eq_toIter_filterM_toIterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} [Monad m] [MonadAttach m] {f : β → m (ULift.{w, 0} Bool)} : Std.Iter.filterM f it = Std.IterM.filterM f it.toIterM
• Std.Iter.fold_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β δ : Type w} {n : Type w → Type w''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [LawfulMonad n] [Std.IteratorLoop α Id n] [Std.LawfulIteratorLoop α Id n] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.Iter β} : Std.IterM.fold g init (Std.Iter.filterWithPostcondition f it) = Std.Iter.foldM (fun d b => do let __do_lift ← (f b).run pure (if __do_lift.down = true then g d b else d)) init it
• Std.Iter.fold_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β δ : Type w} {n : Type w → Type w''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Std.IteratorLoop α Id n] [Std.LawfulIteratorLoop α Id n] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.Iter β} : Std.IterM.fold g init (Std.Iter.filterM f it) = Std.Iter.foldM (fun d b => do let __do_lift ← f b pure (if __do_lift.down = true then g d b else d)) init it
• Std.Iter.foldM_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β δ : Type w} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [Monad o] [LawfulMonad n] [LawfulMonad o] [Std.IteratorLoop α Id n] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id n] [Std.LawfulIteratorLoop α Id o] [MonadLiftT n o] [LawfulMonadLiftT n o] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.Iter β} : Std.IterM.foldM g init (Std.Iter.filterWithPostcondition f it) = Std.Iter.foldM (fun d b => do let __do_lift ← liftM (f b).run if __do_lift.down = true then g d b else pure d) init it
• Std.Iter.foldM_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β δ : Type w} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Monad o] [LawfulMonad o] [Std.IteratorLoop α Id n] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id n] [Std.LawfulIteratorLoop α Id o] [MonadLiftT n o] [LawfulMonadLiftT n o] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.Iter β} : Std.IterM.foldM g init (Std.Iter.filterM f it) = Std.Iter.foldM (fun d b => do let __do_lift ← liftM (f b) if __do_lift.down = true then g d b else pure d) init it
• Std.Iter.forIn_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterator α Id β] {n : Type w → Type w''} {o : Type w → Type u_1} [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id o] {it : Std.Iter β} {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} : forIn (Std.Iter.filterWithPostcondition f it) init g = forIn it init fun out acc => do let __do_lift ← liftM (f out).run if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)
• Std.Iter.forIn_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterator α Id β] {n : Type w → Type w''} {o : Type w → Type u_1} [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [MonadAttach n] [WeaklyLawfulMonadAttach n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id o] {it : Std.Iter β} {f : β → n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} : forIn (Std.Iter.filterM f it) init g = forIn it init fun out acc => do let __do_lift ← liftM (f out) if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)
• Std.Iter.allM_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} {m : Type w → Type w'} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] {it : Std.Iter β} {f p : β → m (ULift.{w, 0} Bool)} : Std.IterM.allM p (Std.Iter.filterM f it) = Std.IterM.allM (fun x => do let __do_lift ← f x if __do_lift.down = true then p x else pure { down := true }) (Std.Iter.mapM pure it)
• Std.Iter.anyM_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} {m : Type w → Type w'} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] {it : Std.Iter β} {f p : β → m (ULift.{w, 0} Bool)} : Std.IterM.anyM p (Std.Iter.filterM f it) = Std.IterM.anyM (fun x => do let __do_lift ← f x if __do_lift.down = true then p x else pure { down := false }) (Std.Iter.mapM pure it)
• Std.Iter.all_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} {m : Type w → Type w'} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id m] [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.LawfulIteratorLoop α Id m] {it : Std.Iter β} {f : β → m (ULift.{w, 0} Bool)} {p : β → Bool} : Std.IterM.all p (Std.Iter.filterM f it) = Std.IterM.allM (fun x => do let __do_lift ← f x if __do_lift.down = true then pure { down := p x } else pure { down := true }) (Std.Iter.mapM pure it)
• Std.Iter.any_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} {m : Type w → Type w'} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id m] [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.LawfulIteratorLoop α Id m] {it : Std.Iter β} {f : β → m (ULift.{w, 0} Bool)} {p : β → Bool} : Std.IterM.any p (Std.Iter.filterM f it) = Std.IterM.anyM (fun x => do let __do_lift ← f x if __do_lift.down = true then pure { down := p x } else pure { down := false }) (Std.Iter.mapM pure it)
• Std.Iter.step_map 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterator α Id β] {it : Std.Iter β} {f : β → γ} : (Std.Iter.map f it).step = match it.step with | ⟨Std.IterStep.yield it' out, h⟩ => Std.PlausibleIterStep.yield (Std.Iter.map f it') (f out) ⋯ | ⟨Std.IterStep.skip it', h⟩ => Std.PlausibleIterStep.skip (Std.Iter.map f it') ⋯ | ⟨Std.IterStep.done, h⟩ => Std.PlausibleIterStep.done ⋯
• Std.Iter.step_mapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterator α Id β] {it : Std.Iter β} {n : Type w → Type w''} {f : β → Std.Iterators.PostconditionT n γ} [Monad n] [LawfulMonad n] : (Std.Iter.mapWithPostcondition f it).step = match it.step with | ⟨Std.IterStep.yield it' out, h⟩ => do let out' ← (f out).operation pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.Iter.mapWithPostcondition f it') ↑out' ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.Iter.mapWithPostcondition f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.Iter.step_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterator α Id β] {it : Std.Iter β} {n : Type w → Type w''} {f : β → n γ} [Monad n] [MonadAttach n] [LawfulMonad n] : (Std.Iter.mapM f it).step = match it.step with | ⟨Std.IterStep.yield it' out, h⟩ => do let out' ← MonadAttach.attach (f out) pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.Iter.mapM f it') ↑out' ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.Iter.mapM f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.Iter.step_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} {n : Type w → Type w''} {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} [Monad n] [LawfulMonad n] [MonadLiftT m n] : (Std.Iter.filterWithPostcondition f it).step = match it.step with | ⟨Std.IterStep.yield it' out, h⟩ => do let __do_lift ← (f out).operation match __do_lift with | ⟨{ down := false }, h'⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.Iter.filterWithPostcondition f it') ⋯)) | ⟨{ down := true }, h'⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.Iter.filterWithPostcondition f it') out ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.Iter.filterWithPostcondition f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.Iter.step_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} {n : Type w → Type w''} {f : β → n (ULift.{w, 0} Bool)} [Monad n] [MonadAttach n] [LawfulMonad n] [MonadLiftT m n] : (Std.Iter.filterM f it).step = match it.step with | ⟨Std.IterStep.yield it' out, h⟩ => do let __do_lift ← MonadAttach.attach (f out) match __do_lift with | ⟨{ down := false }, hf⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.Iter.filterM f it') ⋯)) | ⟨{ down := true }, hf⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.yield (Std.Iter.filterM f it') out ⋯)) | ⟨Std.IterStep.skip it', h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.skip (Std.Iter.filterM f it') ⋯)) | ⟨Std.IterStep.done, h⟩ => pure (Std.Shrink.deflate (Std.PlausibleIterStep.done ⋯))
• Std.IterM.Equiv.filterWithPostcondition 📋 Std.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α₁ α₂ β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Std.Iterator α₁ m β] [Std.Iterator α₂ m β] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {ita : Std.IterM m β} {itb : Std.IterM m β} (h : ita.Equiv itb) : (Std.IterM.filterWithPostcondition f ita).Equiv (Std.IterM.filterWithPostcondition f itb)
• Std.IterM.Equiv.filterM 📋 Std.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α₁ α₂ β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [Std.Iterator α₁ m β] [Std.Iterator α₂ m β] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → n (ULift.{w, 0} Bool)} {ita : Std.IterM m β} {itb : Std.IterM m β} (h : ita.Equiv itb) : (Std.IterM.filterM f ita).Equiv (Std.IterM.filterM f itb)
• Std.Do.Iter.fold_filterWithPostcondition 📋 Std.Do.Triple.SpecLemmas
  {ps : Std.Do.PostShape} {α β δ : Type w} {n : Type w → Type w''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [LawfulMonad n] [Std.Do.WPMonad n ps] [Std.IteratorLoop α Id n] [Std.LawfulIteratorLoop α Id n] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.Iter β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.Iter.foldM (fun d b => do let __do_lift ← (f b).run pure (if __do_lift.down = true then g d b else d)) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.fold g init (Std.Iter.filterWithPostcondition f it) ⦃Q⦄
• Std.Do.Spec.IterM.fold_filterWithPostcondition 📋 Std.Do.Triple.SpecLemmas
  {α β δ : Type w} {m : Type w → Type w'} {ps : Std.Do.PostShape} {n : Type w → Type w''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Std.Do.WPMonad n ps] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.IterM m β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.IterM.foldM (fun d b => do let __do_lift ← (f b).run pure (if __do_lift.down = true then g d b else d)) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.fold g init (Std.IterM.filterWithPostcondition f it) ⦃Q⦄
• Std.Do.Iter.fold_filterM 📋 Std.Do.Triple.SpecLemmas
  {ps : Std.Do.PostShape} {α β δ : Type w} {n : Type w → Type w''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Std.Do.WPMonad n ps] [Std.IteratorLoop α Id n] [Std.LawfulIteratorLoop α Id n] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.Iter β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.Iter.foldM (fun d b => do let __do_lift ← f b pure (if __do_lift.down = true then g d b else d)) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.fold g init (Std.Iter.filterM f it) ⦃Q⦄
• Std.Do.Spec.IterM.fold_filterM 📋 Std.Do.Triple.SpecLemmas
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {ps : Std.Do.PostShape} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Std.Do.WPMonad n ps] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.IterM m β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.IterM.foldM (fun d b => do let __do_lift ← f b pure (if __do_lift.down = true then g d b else d)) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.fold g init (Std.IterM.filterM f it) ⦃Q⦄
• Std.Do.Iter.foldM_filterWithPostcondition 📋 Std.Do.Triple.SpecLemmas
  {ps : Std.Do.PostShape} {α β δ : Type w} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [Monad o] [LawfulMonad n] [LawfulMonad o] [Std.Do.WPMonad o ps] [Std.IteratorLoop α Id n] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id n] [Std.LawfulIteratorLoop α Id o] [MonadLiftT n o] [LawfulMonadLiftT n o] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.Iter β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.Iter.foldM (fun d b => do let __do_lift ← liftM (f b).run if __do_lift.down = true then g d b else pure d) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.foldM g init (Std.Iter.filterWithPostcondition f it) ⦃Q⦄
• Std.Do.Iter.foldM_filterM 📋 Std.Do.Triple.SpecLemmas
  {ps : Std.Do.PostShape} {α β δ : Type w} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Monad o] [LawfulMonad o] [Std.Do.WPMonad o ps] [Std.IteratorLoop α Id n] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id n] [Std.LawfulIteratorLoop α Id o] [MonadLiftT n o] [LawfulMonadLiftT n o] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.Iter β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.Iter.foldM (fun d b => do let __do_lift ← liftM (f b) if __do_lift.down = true then g d b else pure d) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.foldM g init (Std.Iter.filterM f it) ⦃Q⦄
• Std.Do.Spec.IterM.foldM_filterWithPostcondition 📋 Std.Do.Triple.SpecLemmas
  {α β δ : Type w} {ps : Std.Do.PostShape} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Monad n] [Monad o] [LawfulMonad m] [LawfulMonad n] [LawfulMonad o] [Std.Do.WPMonad o ps] [Std.IteratorLoop α m n] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m n] [Std.LawfulIteratorLoop α m o] [MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.IterM m β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.IterM.foldM (fun d b => do let __do_lift ← liftM (f b).run if __do_lift.down = true then g d b else pure d) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.foldM g init (Std.IterM.filterWithPostcondition f it) ⦃Q⦄
• Std.Do.Spec.IterM.foldM_filterM 📋 Std.Do.Triple.SpecLemmas
  {α β δ : Type w} {ps : Std.Do.PostShape} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Monad o] [LawfulMonad o] [Std.Do.WPMonad o ps] [Std.IteratorLoop α m n] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m n] [Std.LawfulIteratorLoop α m o] [MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.IterM m β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.IterM.foldM (fun d b => do let __do_lift ← liftM (f b) if __do_lift.down = true then g d b else pure d) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.foldM g init (Std.IterM.filterM f it) ⦃Q⦄
• Std.Do.Spec.Iter.forIn_filterWithPostcondition 📋 Std.Do.Triple.SpecLemmas
  {α β γ : Type w} [Std.Iterator α Id β] {ps : Std.Do.PostShape} {n : Type w → Type u_1} {o : Type w → Type u_2} [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Do.WPMonad o ps] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id o] {it : Std.Iter β} {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond γ ps} (h : ⦃P⦄ forIn it init fun out acc => do let __do_lift ← liftM (f out).run if __do_lift.down = true then g out acc else pure (ForInStep.yield acc) ⦃Q⦄) : ⦃P⦄ forIn (Std.Iter.filterWithPostcondition f it) init g ⦃Q⦄
• Std.Do.Spec.IterM.forIn_filterWithPostcondition 📋 Std.Do.Triple.SpecLemmas
  {α : Type u₁} {n : Type u₁ → Type u_1} {o : Type u₁ → Type u_2} {γ : Type u₁} {m : Type u₁ → Type u_3} {β : Type u₁} {ps : Std.Do.PostShape} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Do.WPMonad o ps] [MonadLiftT m n] [LawfulMonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m o] {it : Std.IterM m β} {f : β → Std.Iterators.PostconditionT n (ULift.{u₁, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond γ ps} (h : ⦃P⦄ forIn it init fun out acc => do let __do_lift ← liftM (f out).run if __do_lift.down = true then g out acc else pure (ForInStep.yield acc) ⦃Q⦄) : ⦃P⦄ forIn (Std.IterM.filterWithPostcondition f it) init g ⦃Q⦄
• Std.Do.Spec.Iter.forIn_filterM 📋 Std.Do.Triple.SpecLemmas
  {α β γ : Type w} [Std.Iterator α Id β] {ps : Std.Do.PostShape} {n : Type w → Type u_1} {o : Type w → Type u_2} [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Do.WPMonad o ps] [MonadAttach n] [WeaklyLawfulMonadAttach n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id o] {it : Std.Iter β} {f : β → n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond γ ps} (h : ⦃P⦄ forIn it init fun out acc => do let __do_lift ← liftM (f out) if __do_lift.down = true then g out acc else pure (ForInStep.yield acc) ⦃Q⦄) : ⦃P⦄ forIn (Std.Iter.filterM f it) init g ⦃Q⦄
• Std.Do.Spec.IterM.forIn_filterM 📋 Std.Do.Triple.SpecLemmas
  {α : Type u₁} {n : Type u₁ → Type u_1} {o : Type u₁ → Type u_2} {γ : Type u₁} {m : Type u₁ → Type u_3} {β : Type u₁} {ps : Std.Do.PostShape} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Do.WPMonad o ps] [MonadAttach n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m o] {it : Std.IterM m β} {f : β → n (ULift.{u₁, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond γ ps} (h : ⦃P⦄ forIn it init fun out acc => do let __do_lift ← liftM (f out) if __do_lift.down = true then g out acc else pure (ForInStep.yield acc) ⦃Q⦄) : ⦃P⦄ forIn (Std.IterM.filterM f it) init g ⦃Q⦄
• Std.Internal.Do.Spec.Iter.fold_filterWithPostcondition 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {n : Type w → Type w'} {Pred EPred : Type w} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [LawfulMonad n] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad n Pred EPred] [Std.IteratorLoop α Id n] [Std.LawfulIteratorLoop α Id n] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.Iter β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.Iter.foldM (fun d b => do let __do_lift ← (f b).run pure (if __do_lift.down = true then g d b else d)) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.fold g init (Std.Iter.filterWithPostcondition f it)) Q eQ
• Std.Internal.Do.Spec.IterM.fold_filterWithPostcondition 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {Pred EPred : Type w} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad n Pred EPred] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.IterM m β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.IterM.foldM (fun d b => do let __do_lift ← (f b).run pure (if __do_lift.down = true then g d b else d)) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.fold g init (Std.IterM.filterWithPostcondition f it)) Q eQ
• Std.Internal.Do.Spec.Iter.fold_filterM 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {n : Type w → Type w'} {Pred EPred : Type w} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad n Pred EPred] [Std.IteratorLoop α Id n] [Std.LawfulIteratorLoop α Id n] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.Iter β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.Iter.foldM (fun d b => do let __do_lift ← f b pure (if __do_lift.down = true then g d b else d)) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.fold g init (Std.Iter.filterM f it)) Q eQ
• Std.Internal.Do.Spec.IterM.fold_filterM 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {Pred EPred : Type w} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad n Pred EPred] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → δ} {init : δ} {it : Std.IterM m β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.IterM.foldM (fun d b => do let __do_lift ← f b pure (if __do_lift.down = true then g d b else d)) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.fold g init (Std.IterM.filterM f it)) Q eQ
• Std.Internal.Do.Spec.Iter.foldM_filterWithPostcondition 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {n : Type w → Type w'} {o : Type w → Type w''} {Pred EPred : Type w} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [Monad o] [LawfulMonad n] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [Std.IteratorLoop α Id n] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id n] [Std.LawfulIteratorLoop α Id o] [MonadLiftT n o] [LawfulMonadLiftT n o] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.Iter β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.Iter.foldM (fun d b => do let __do_lift ← liftM (f b).run if __do_lift.down = true then g d b else pure d) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.foldM g init (Std.Iter.filterWithPostcondition f it)) Q eQ
• Std.Internal.Do.Spec.Iter.foldM_filterM 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {n : Type w → Type w'} {o : Type w → Type w''} {Pred EPred : Type w} [Std.Iterator α Id β] [Std.Iterators.Finite α Id] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Monad o] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [Std.IteratorLoop α Id n] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id n] [Std.LawfulIteratorLoop α Id o] [MonadLiftT n o] [LawfulMonadLiftT n o] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.Iter β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.Iter.foldM (fun d b => do let __do_lift ← liftM (f b) if __do_lift.down = true then g d b else pure d) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.foldM g init (Std.Iter.filterM f it)) Q eQ
• Std.Internal.Do.Spec.IterM.foldM_filterWithPostcondition 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} {Pred EPred : Type w} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Monad n] [Monad o] [LawfulMonad m] [LawfulMonad n] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [Std.IteratorLoop α m n] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m n] [Std.LawfulIteratorLoop α m o] [MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o] {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.IterM m β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.IterM.foldM (fun d b => do let __do_lift ← liftM (f b).run if __do_lift.down = true then g d b else pure d) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.foldM g init (Std.IterM.filterWithPostcondition f it)) Q eQ
• Std.Internal.Do.Spec.IterM.foldM_filterM 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} {Pred EPred : Type w} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [Monad o] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [Std.IteratorLoop α m n] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m n] [Std.LawfulIteratorLoop α m o] [MonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT m n] [LawfulMonadLiftT n o] {f : β → n (ULift.{w, 0} Bool)} {g : δ → β → o δ} {init : δ} {it : Std.IterM m β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.IterM.foldM (fun d b => do let __do_lift ← liftM (f b) if __do_lift.down = true then g d b else pure d) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.foldM g init (Std.IterM.filterM f it)) Q eQ
• Std.Internal.Do.Spec.Iter.forIn_filterWithPostcondition 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β γ : Type w} {n : Type w → Type w'} {o : Type w → Type w''} {Pred EPred : Type w} [Std.Iterator α Id β] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id o] {it : Std.Iter β} {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Pred} {Q : γ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (forIn it init fun out acc => do let __do_lift ← liftM (f out).run if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)) Q eQ) : Std.Internal.Do.Triple P (forIn (Std.Iter.filterWithPostcondition f it) init g) Q eQ
• Std.Internal.Do.Spec.IterM.forIn_filterWithPostcondition 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} {Pred EPred : Type w} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [MonadLiftT m n] [LawfulMonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m o] {it : Std.IterM m β} {f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Pred} {Q : γ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (forIn it init fun out acc => do let __do_lift ← liftM (f out).run if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)) Q eQ) : Std.Internal.Do.Triple P (forIn (Std.IterM.filterWithPostcondition f it) init g) Q eQ
• Std.Internal.Do.Spec.Iter.forIn_filterM 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β γ : Type w} {n : Type w → Type w'} {o : Type w → Type w''} {Pred EPred : Type w} [Std.Iterator α Id β] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [MonadAttach n] [WeaklyLawfulMonadAttach n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterators.Finite α Id] [Std.IteratorLoop α Id o] [Std.LawfulIteratorLoop α Id o] {it : Std.Iter β} {f : β → n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Pred} {Q : γ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (forIn it init fun out acc => do let __do_lift ← liftM (f out) if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)) Q eQ) : Std.Internal.Do.Triple P (forIn (Std.Iter.filterM f it) init g) Q eQ
• Std.Internal.Do.Spec.IterM.forIn_filterM 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {o : Type w → Type w'''} {Pred EPred : Type w} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Monad o] [LawfulMonad o] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad o Pred EPred] [MonadAttach n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [MonadLiftT n o] [LawfulMonadLiftT n o] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m o] [Std.LawfulIteratorLoop α m o] {it : Std.IterM m β} {f : β → n (ULift.{w, 0} Bool)} {init : γ} {g : β → γ → o (ForInStep γ)} {P : Pred} {Q : γ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (forIn it init fun out acc => do let __do_lift ← liftM (f out) if __do_lift.down = true then g out acc else pure (ForInStep.yield acc)) Q eQ) : Std.Internal.Do.Triple P (forIn (Std.IterM.filterM f it) init g) Q eQ

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using the Loogle command from the command palette. You can also try the #loogle command from LeanSearchClient, the CLI version, the Loogle VS Code extension, the lean.nvim integration or the Zulip bot.

Usage

Loogle finds definitions and lemmas in various ways:

1. By constant:
   🔍 Real.sin
   finds all lemmas whose statement somehow mentions the sine function.

2. By lemma name substring:
   🔍 "differ"
   finds all lemmas that have "differ" somewhere in their lemma name.

3. By subexpression:
   🔍 _ * (_ ^ _)
   finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

   The pattern can also be non-linear, as in
   🔍 Real.sqrt ?a * Real.sqrt ?a

   If the pattern has parameters, they are matched in any order. Both of these will find List.map:
   🔍 (?a -> ?b) -> List ?a -> List ?b
   🔍 List ?a -> (?a -> ?b) -> List ?b

4. By main conclusion:
   🔍 |- tsum _ = _ * tsum _
   finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

   As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example,
   🔍 |- _ < _ → tsum _ < tsum _
   will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search
🔍 Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _
would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

The #lucky button will directly send you to the documentation of the first hit.

Source code

You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is provided by the Lean FRO. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision a114d38 serving mathlib revision 5d1abc4