Loogle!

Result

Found 66 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.map.eq_1 📋 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.map f x = { Property := fun b => ∃ a, f ↑a = b, operation := (fun a => ⟨f ↑a, ⋯⟩) <$> x.operation }
• Std.Iterators.PostconditionT.operation_map 📋 Init.Data.Iterators.PostconditionMonad
  {m : Type w → Type w'} [Functor m] {α β : Type w} {x : Std.Iterators.PostconditionT m α} {f : α → β} : (Std.Iterators.PostconditionT.map f x).operation = (fun a => ⟨f ↑a, ⋯⟩) <$> x.operation
• Std.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.Iterators.Types.Map.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  (α : Type w) {β γ : Type w} (m : Type w → Type w') (n : Type w → Type w'') (lift : ⦃α : Type w⦄ → m α → n α) [Functor n] (f : β → Std.Iterators.PostconditionT n γ) : Std.Iterators.Types.Map α m n lift f = Std.Iterators.Types.FilterMap α m n lift fun b => Std.Iterators.PostconditionT.map some (f b)
• Std.IterM.InternalCombinators.map.eq_1 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad n] (lift : ⦃α : Type w⦄ → m α → n α) [Std.Iterator α m β] (f : β → Std.Iterators.PostconditionT n γ) (it : Std.IterM m β) : Std.IterM.InternalCombinators.map lift f it = Std.IterM.mk { inner := it } n γ
• Std.Iterators.Types.Map.instIterator.eq_1 📋 Init.Data.Iterators.Lemmas.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 = inferInstanceAs (Std.Iterator (Std.Iterators.Types.FilterMap α m n lift fun b => Std.Iterators.PostconditionT.map some (f b)) n γ)
• Std.IterM.filterWithPostcondition.eq_1 📋 Init.Data.Iterators.Lemmas.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.filterWithPostcondition f it = Std.IterM.filterMapWithPostcondition (fun b => Std.Iterators.PostconditionT.map (fun x => if x.down = true then some b else none) (f b)) it
• Std.IterM.filterM.eq_1 📋 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] [Monad n] [MonadAttach n] [MonadLiftT m n] (f : β → n (ULift.{w, 0} Bool)) (it : Std.IterM m β) : Std.IterM.filterM f it = Std.IterM.filterMapWithPostcondition (fun b => Std.Iterators.PostconditionT.map (fun x => if x.down = true then some b else none) (Std.Iterators.PostconditionT.attachLift (f b))) it
• 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.filterWithPostcondition.eq_1 📋 Init.Data.Iterators.Lemmas.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.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.filterM.eq_1 📋 Init.Data.Iterators.Lemmas.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.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⦄

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using (by default) Ctrl-K Ctrl-S. 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.

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.

This is Loogle revision 36960b0 serving mathlib revision 9a4cf1d