Loogle!

Result

Found 37 declarations mentioning Std.IterM.map.

• Std.IterM.map 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Std.Iterator α m β] [Monad m] (f : β → γ) (it : Std.IterM m β) : Std.IterM m γ
• Std.IterM.toArray_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} (it : Std.IterM m β) : (Std.IterM.map f it).toArray = (fun x => Array.map f x) <$> it.toArray
• Std.IterM.toListRev_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} (it : Std.IterM m β) : (Std.IterM.map f it).toListRev = (fun x => List.map f x) <$> it.toListRev
• Std.IterM.toList_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → β'} (it : Std.IterM m β) : (Std.IterM.map f it).toList = (fun x => List.map f x) <$> it.toList
• Std.IterM.count_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type u_1} {m : Type u_1 → Type u_2} [Std.Iterator α m β] [Monad m] [Std.IteratorLoop α m m] [Std.Iterators.Finite α m] [LawfulMonad m] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} : (Std.IterM.map f it).length = it.length
• Std.IterM.length_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterator α m β] [Monad m] [Std.IteratorLoop α m m] [Std.Iterators.Finite α m] [LawfulMonad m] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} : (Std.IterM.map f it).length = it.length
• Std.IterM.all_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.IteratorLoop α m m] [LawfulMonad m] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → Bool} : Std.IterM.all p (Std.IterM.map f it) = Std.IterM.all (fun x => p (f x)) it
• Std.IterM.any_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.IteratorLoop α m m] [LawfulMonad m] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → Bool} : Std.IterM.any p (Std.IterM.map f it) = Std.IterM.any (fun x => p (f x)) it
• Std.IterM.allM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.IteratorLoop α m m] [LawfulMonad m] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → m (ULift.{w, 0} Bool)} : Std.IterM.allM p (Std.IterM.map f it) = Std.IterM.allM (fun x => p (f x)) it
• Std.IterM.anyM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [Std.IteratorLoop α m m] [LawfulMonad m] [Std.LawfulIteratorLoop α m m] {it : Std.IterM m β} {f : β → β'} {p : β' → m (ULift.{w, 0} Bool)} : Std.IterM.anyM p (Std.IterM.map f it) = Std.IterM.anyM (fun x => p (f x)) it
• Std.IterM.fold_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Std.IteratorLoop α m m] [Std.LawfulIteratorLoop α m m] {f : β → γ} {g : δ → γ → δ} {init : δ} {it : Std.IterM m β} : Std.IterM.fold g init (Std.IterM.map f it) = Std.IterM.fold (fun d b => g d (f b)) init it
• Std.IterM.foldM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ 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] [Monad n] [LawfulMonad m] [LawfulMonad n] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] [MonadLiftT m n] [LawfulMonadLiftT m n] {f : β → γ} {g : δ → γ → n δ} {init : δ} {it : Std.IterM m β} : Std.IterM.foldM g init (Std.IterM.map f it) = Std.IterM.foldM (fun d b => g d (f b)) init it
• Std.IterM.toArray_map_eq_toArray_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {it : Std.IterM m β} : (Std.IterM.map f it).toArray = (Std.IterM.mapM (fun b => pure (f b)) it).toArray
• Std.IterM.toListRev_map_eq_toListRev_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {it : Std.IterM m β} : (Std.IterM.map f it).toListRev = (Std.IterM.mapM (fun b => pure (f b)) it).toListRev
• Std.IterM.toList_map_eq_toList_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {it : Std.IterM m β} : (Std.IterM.map f it).toList = (Std.IterM.mapM (fun b => pure (f b)) it).toList
• Std.IterM.toArray_map_eq_toArray_filterMapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {it : Std.IterM m β} : (Std.IterM.map f it).toArray = (Std.IterM.filterMapM (fun b => pure (some (f b))) it).toArray
• Std.IterM.toListRev_map_eq_toListRev_filterMapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {it : Std.IterM m β} : (Std.IterM.map f it).toListRev = (Std.IterM.filterMapM (fun b => pure (some (f b))) it).toListRev
• Std.IterM.toList_map_eq_toList_filterMapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ : Type w} {m : Type w → Type w'} [Monad m] [MonadAttach m] [LawfulMonad m] [WeaklyLawfulMonadAttach m] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {it : Std.IterM m β} : (Std.IterM.map f it).toList = (Std.IterM.filterMapM (fun b => pure (some (f b))) it).toList
• Std.IterM.forIn_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {m : Type u_1 → Type u_2} {n : Type u_1 → Type u_3} {α β β₂ γ : Type u_1} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] {it : Std.IterM m β} {f : β → β₂} {init : γ} {g : β₂ → γ → n (ForInStep γ)} : forIn (Std.IterM.map f it) init g = forIn it init fun out acc => g (f out) acc
• Std.IterM.toArray_filterMapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n (Option δ)} {it : Std.IterM m β} : (Std.IterM.filterMapM g (Std.IterM.map f it)).toArray = (Std.IterM.filterMapM (fun b => g (f b)) it).toArray
• Std.IterM.toListRev_filterMapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n (Option δ)} {it : Std.IterM m β} : (Std.IterM.filterMapM g (Std.IterM.map f it)).toListRev = (Std.IterM.filterMapM (fun b => g (f b)) it).toListRev
• Std.IterM.toList_filterMapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n (Option δ)} {it : Std.IterM m β} : (Std.IterM.filterMapM g (Std.IterM.map f it)).toList = (Std.IterM.filterMapM (fun b => g (f b)) it).toList
• Std.IterM.toArray_mapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n δ} {it : Std.IterM m β} : (Std.IterM.mapM g (Std.IterM.map f it)).toArray = (Std.IterM.mapM (fun b => g (f b)) it).toArray
• Std.IterM.toListRev_mapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n δ} {it : Std.IterM m β} : (Std.IterM.mapM g (Std.IterM.map f it)).toListRev = (Std.IterM.mapM (fun b => g (f b)) it).toListRev
• Std.IterM.toList_mapM_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → γ} {g : γ → n δ} {it : Std.IterM m β} : (Std.IterM.mapM g (Std.IterM.map f it)).toList = (Std.IterM.mapM (fun b => g (f b)) it).toList
• Std.IterM.toArray_map_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → n γ} {g : γ → δ} {it : Std.IterM m β} : (Std.IterM.map g (Std.IterM.mapM f it)).toArray = (Std.IterM.mapM (fun b => do let __do_lift ← f b pure (g __do_lift)) it).toArray
• Std.IterM.toListRev_map_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → n γ} {g : γ → δ} {it : Std.IterM m β} : (Std.IterM.map g (Std.IterM.mapM f it)).toListRev = (Std.IterM.mapM (fun b => do let __do_lift ← f b pure (g __do_lift)) it).toListRev
• Std.IterM.toList_map_mapM 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β γ δ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Monad m] [LawfulMonad m] [Monad n] [MonadAttach n] [LawfulMonad n] [WeaklyLawfulMonadAttach n] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] {f : β → n γ} {g : γ → δ} {it : Std.IterM m β} : (Std.IterM.map g (Std.IterM.mapM f it)).toList = (Std.IterM.mapM (fun b => do let __do_lift ← f b pure (g __do_lift)) it).toList
• 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.Iter.map_eq_toIter_map_toIterM 📋 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 = (Std.IterM.map f it.toIterM).toIter
• Std.IterM.Equiv.map 📋 Std.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α₁ α₂ β γ : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] [Std.Iterator α₁ m β] [Std.Iterator α₂ m β] {f : β → γ} {ita : Std.IterM m β} {itb : Std.IterM m β} (h : ita.Equiv itb) : (Std.IterM.map f ita).Equiv (Std.IterM.map f itb)
• Std.Do.Spec.IterM.fold_map 📋 Std.Do.Triple.SpecLemmas
  {α β γ δ : Type w} {m : Type w → Type w'} {ps : Std.Do.PostShape} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Std.Do.WPMonad m ps] [Std.IteratorLoop α m m] [Std.LawfulIteratorLoop α m m] {f : β → γ} {g : δ → γ → δ} {init : δ} {it : Std.IterM m β} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond δ ps} (h : ⦃P⦄ Std.IterM.fold (fun d b => g d (f b)) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.fold g init (Std.IterM.map f it) ⦃Q⦄
• Std.Do.Spec.IterM.foldM_map 📋 Std.Do.Triple.SpecLemmas
  {α β γ 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] [Monad n] [LawfulMonad m] [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 → γ} {g : δ → γ → n 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 => g d (f b)) init it ⦃Q⦄) : ⦃P⦄ Std.IterM.foldM g init (Std.IterM.map f it) ⦃Q⦄
• Std.Do.Spec.IterM.forIn_map 📋 Std.Do.Triple.SpecLemmas
  {α : Type u₁} {n : Type u₁ → Type u_1} {β₂ γ : Type u₁} {m : Type u₁ → Type u_2} {β : Type u₁} {ps : Std.Do.PostShape} [Monad m] [LawfulMonad m] [Monad n] [LawfulMonad n] [Std.Do.WPMonad n ps] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] {it : Std.IterM m β} {f : β → β₂} {init : γ} {g : β₂ → γ → n (ForInStep γ)} {P : Std.Do.Assertion ps} {Q : Std.Do.PostCond γ ps} (h : ⦃P⦄ forIn it init fun out acc => g (f out) acc ⦃Q⦄) : ⦃P⦄ forIn (Std.IterM.map f it) init g ⦃Q⦄
• Std.Internal.Do.Spec.IterM.fold_map 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β γ δ : Type w} {m : Type w → Type w'} {Pred EPred : Type w} [Std.Iterator α m β] [Std.Iterators.Finite α m] [Monad m] [LawfulMonad m] [Std.Internal.Do.Assertion Pred] [Std.Internal.Do.Assertion EPred] [Std.Internal.Do.WPMonad m Pred EPred] [Std.IteratorLoop α m m] [Std.LawfulIteratorLoop α m m] {f : β → γ} {g : δ → γ → δ} {init : δ} {it : Std.IterM m β} {P : Pred} {Q : δ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (Std.IterM.fold (fun d b => g d (f b)) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.fold g init (Std.IterM.map f it)) Q eQ
• Std.Internal.Do.Spec.IterM.foldM_map 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β γ 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] [Monad n] [LawfulMonad m] [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 → γ} {g : δ → γ → n 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 => g d (f b)) init it) Q eQ) : Std.Internal.Do.Triple P (Std.IterM.foldM g init (Std.IterM.map f it)) Q eQ
• Std.Internal.Do.Spec.IterM.forIn_map 📋 Std.Internal.Do.Triple.SpecLemmas
  {α β β₂ γ : Type w} {m : Type w → Type w'} {n : Type w → Type w''} {Pred EPred : Type w} [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] [MonadLiftT m n] [LawfulMonadLiftT m n] [Std.Iterator α m β] [Std.Iterators.Finite α m] [Std.IteratorLoop α m n] [Std.LawfulIteratorLoop α m n] {it : Std.IterM m β} {f : β → β₂} {init : γ} {g : β₂ → γ → n (ForInStep γ)} {P : Pred} {Q : γ → Pred} {eQ : EPred} (h : Std.Internal.Do.Triple P (forIn it init fun out acc => g (f out) acc) Q eQ) : Std.Internal.Do.Triple P (forIn (Std.IterM.map 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

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This is Loogle revision a114d38 serving mathlib revision 476fb97