Loogle!

Result

Found 25 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.Iterators.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.Iterators.Iterator α m β] (f : β → Std.Iterators.PostconditionT n (ULift.{w, 0} Bool)) (it : Std.IterM m β) : Std.IterM n β
• Std.Iterators.IterM.filterM 📋 Init.Data.Iterators.Combinators.Monadic.FilterMap
  {α β : Type w} {m : Type w → Type w'} {n : Type w → Type w''} [Std.Iterators.Iterator α m β] [Monad n] [MonadLiftT m n] (f : β → n (ULift.{w, 0} Bool)) (it : Std.IterM m β) : Std.IterM n β
• Std.Iterators.Iter.filterWithPostcondition 📋 Init.Data.Iterators.Combinators.FilterMap
  {α β : Type w} [Std.Iterators.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.Iterators.Iter.filterM 📋 Init.Data.Iterators.Combinators.FilterMap
  {α β : Type w} [Std.Iterators.Iterator α Id β] {m : Type w → Type w'} [Monad m] (f : β → m (ULift.{w, 0} Bool)) (it : Std.Iter β) : Std.IterM m β
• Std.Iterators.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.Map α m n lift f = Std.Iterators.FilterMap α m n lift fun b => Std.Iterators.PostconditionT.map some (f b)
• Std.Iterators.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.Iterators.Iterator α m β] (f : β → Std.Iterators.PostconditionT n γ) (it : Std.IterM m β) : Std.Iterators.IterM.InternalCombinators.map lift f it = Std.Iterators.toIterM { inner := it } n γ
• Std.Iterators.instIteratorMap.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.Iterators.Iterator α m β] {lift : ⦃α : Type w⦄ → m α → n α} {f : β → Std.Iterators.PostconditionT n γ} : Std.Iterators.instIteratorMap = inferInstanceAs (Std.Iterators.Iterator (Std.Iterators.FilterMap α m n lift fun b => Std.Iterators.PostconditionT.map some (f b)) n γ)
• Std.Iterators.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.Iterators.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.Iterators.IterM.mapWithPostcondition f it).step = do let __do_lift ← liftM it.step match __do_lift with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let out' ← (f out).operation pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.IterM.mapWithPostcondition f it') ↑out' ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.mapWithPostcondition f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.IterM.step_map 📋 Init.Data.Iterators.Lemmas.Combinators.Monadic.FilterMap
  {α β β' : Type w} {m : Type w → Type w'} [Std.Iterators.Iterator α m β] {it : Std.IterM m β} [Monad m] [LawfulMonad m] {f : β → β'} : (Std.Iterators.IterM.map f it).step = do let __do_lift ← it.step match __do_lift with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => let out' := f out; pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.IterM.map f it') out' ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.map f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.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.Iterators.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.Iterators.IterM.filterWithPostcondition f it).step = do let __do_lift ← liftM it.step match __do_lift with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let __do_lift ← (f out).operation match __do_lift with | ⟨{ down := false }, h'⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.filterWithPostcondition f it') ⋯) | ⟨{ down := true }, h'⟩ => pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.IterM.filterWithPostcondition f it') out ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.filterWithPostcondition f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.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.Iterators.Iterator α m β] {it : Std.IterM m β} {f : β → n (ULift.{w, 0} Bool)} [Monad n] [LawfulMonad n] [MonadLiftT m n] : (Std.Iterators.IterM.filterM f it).step = do let __do_lift ← liftM it.step match __do_lift with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let __do_lift ← f out match __do_lift with | { down := false } => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.filterM f it') ⋯) | { down := true } => pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.IterM.filterM f it') out ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.IterM.filterM f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.Iter.filterWithPostcondition_eq_toIter_filterMapWithPostcondition_toIterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterators.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.Iterators.Iter.filterWithPostcondition f it = Std.Iterators.IterM.filterWithPostcondition f it.toIterM
• Std.Iterators.Iter.filterM_eq_toIter_filterM_toIterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} [Monad m] {f : β → m (ULift.{w, 0} Bool)} : Std.Iterators.Iter.filterM f it = Std.Iterators.IterM.filterM f it.toIterM
• Std.Iterators.Iter.step_mapWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} {m : Type w → Type w'} {n : Type w → Type w''} {f : β → Std.Iterators.PostconditionT n γ} [Monad n] [LawfulMonad n] [MonadLiftT m n] : (Std.Iterators.Iter.mapWithPostcondition f it).step = match it.step with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let out' ← (f out).operation pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.Iter.mapWithPostcondition f it') ↑out' ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.mapWithPostcondition f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.Iter.step_map 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β γ : Type w} [Std.Iterators.Iterator α Id β] {it : Std.Iter β} {f : β → γ} : (Std.Iterators.Iter.map f it).step = match it.step with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => Std.Iterators.PlausibleIterStep.yield (Std.Iterators.Iter.map f it') (f out) ⋯ | ⟨Std.Iterators.IterStep.skip it', h⟩ => Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.map f it') ⋯ | ⟨Std.Iterators.IterStep.done, h⟩ => Std.Iterators.PlausibleIterStep.done ⋯
• Std.Iterators.Iter.step_filterWithPostcondition 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterators.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.Iterators.Iter.filterWithPostcondition f it).step = match it.step with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let __do_lift ← (f out).operation match __do_lift with | ⟨{ down := false }, h'⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.filterWithPostcondition f it') ⋯) | ⟨{ down := true }, h'⟩ => pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.Iter.filterWithPostcondition f it') out ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.filterWithPostcondition f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.Iter.step_filterM 📋 Init.Data.Iterators.Lemmas.Combinators.FilterMap
  {α β : Type w} [Std.Iterators.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] [LawfulMonad n] [MonadLiftT m n] : (Std.Iterators.Iter.filterM f it).step = match it.step with | ⟨Std.Iterators.IterStep.yield it' out, h⟩ => do let __do_lift ← f out match __do_lift with | { down := false } => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.filterM f it') ⋯) | { down := true } => pure (Std.Iterators.PlausibleIterStep.yield (Std.Iterators.Iter.filterM f it') out ⋯) | ⟨Std.Iterators.IterStep.skip it', h⟩ => pure (Std.Iterators.PlausibleIterStep.skip (Std.Iterators.Iter.filterM f it') ⋯) | ⟨Std.Iterators.IterStep.done, h⟩ => pure (Std.Iterators.PlausibleIterStep.done ⋯)
• Std.Iterators.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.Iterators.Iterator α₁ m β] [Std.Iterators.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.Iterators.IterM.filterWithPostcondition f ita).Equiv (Std.Iterators.IterM.filterWithPostcondition f itb)
• Std.Iterators.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] [LawfulMonad n] [Std.Iterators.Iterator α₁ m β] [Std.Iterators.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.Iterators.IterM.filterM f ita).Equiv (Std.Iterators.IterM.filterM f itb)

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 ff04530 serving mathlib revision 8623f65