Loogle!

Result

Found 12 declarations mentioning Std.Iterators.HetT.map.

• Std.Iterators.HetT.map 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Functor m] {α : Type u} {β : Type v} (f : α → β) (x : Std.Iterators.HetT m α) : Std.Iterators.HetT m β
• Std.Iterators.HetT.map.eq_1 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Functor m] {α : Type u} {β : Type v} (f : α → β) (x : Std.Iterators.HetT m α) : Std.Iterators.HetT.map f x = x.pmap fun a x => f a
• Std.Iterators.HetT.property_map 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Functor m] {α : Type u} {β : Type v} {x : Std.Iterators.HetT m α} {f : α → β} {b : β} : (Std.Iterators.HetT.map f x).Property b ↔ ∃ a, f a = b ∧ x.Property a
• Std.Iterators.HetT.map_pure 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Monad m] [LawfulMonad m] {α : Type u} {β : Type v} {f : α → β} {a : α} : Std.Iterators.HetT.map f (Std.Iterators.HetT.pure a) = Std.Iterators.HetT.pure (f a)
• Std.Iterators.HetT.map_eq_pure_bind 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Monad m] [LawfulMonad m] {α : Type u} {β : Type v} {f : α → β} {x : Std.Iterators.HetT m α} : Std.Iterators.HetT.map f x = x.bind (Std.Iterators.HetT.pure ∘ f)
• Std.Iterators.HetT.comp_map 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Monad m] [LawfulMonad m] {α : Type u} {β : Type v} {γ : Type x} {f : α → β} {g : β → γ} {x : Std.Iterators.HetT m α} : Std.Iterators.HetT.map (g ∘ f) x = Std.Iterators.HetT.map g (Std.Iterators.HetT.map f x)
• Std.Iterators.HetT.map_pmap 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Monad m] [LawfulMonad m] {α : Type u} {β : Type v} {γ : Type x} {x : Std.Iterators.HetT m α} {f : (a : α) → x.Property a → β} {g : β → γ} : Std.Iterators.HetT.map g (x.pmap f) = x.pmap fun a ha => g (f a ha)
• Std.Iterators.HetT.pmap_map 📋 Std.Data.Iterators.Lemmas.Equivalence.HetT
  {m : Type w → Type w'} [Monad m] [LawfulMonad m] {α : Type u} {β : Type v} {γ : Type x} {x : Std.Iterators.HetT m α} {f : α → β} {g : (b : β) → (Std.Iterators.HetT.map f x).Property b → γ} : (Std.Iterators.HetT.map f x).pmap g = x.pmap fun a ha => g (f a) ⋯
• Std.Iterators.BundledIterM.step.eq_1 📋 Std.Data.Iterators.Lemmas.Equivalence.Basic
  {β : Type w} {m : Type w → Type w'} [Monad m] [LawfulMonad m] (it : Std.Iterators.BundledIterM m β) : it.step = Std.Iterators.HetT.map (Std.Iterators.IterStep.mapIterator Std.Iterators.BundledIterM.ofIterM) it.iterator.stepAsHetT
• Std.Iterators.BundledIterM.Equiv.coinduct 📋 Std.Data.Iterators.Lemmas.Equivalence.Basic
  (m : Type w → Type w') (β : Type w) [Monad m] [LawfulMonad m] (x : Std.Iterators.BundledIterM m β → Std.Iterators.BundledIterM m β → Prop) (y : ∀ (x_1 x_2 : Std.Iterators.BundledIterM m β), x x_1 x_2 → Std.Iterators.HetT.map (Std.Iterators.IterStep.mapIterator (Quot.mk x)) x_1.step = Std.Iterators.HetT.map (Std.Iterators.IterStep.mapIterator (Quot.mk x)) x_2.step) (x✝ x✝¹ : Std.Iterators.BundledIterM m β) : x x✝ x✝¹ → Std.Iterators.BundledIterM.Equiv m β x✝ x✝¹
• Std.Iterators.BundledIterM.Equiv.eq_1 📋 Std.Data.Iterators.Lemmas.Equivalence.Basic
  (m : Type w → Type w') (β : Type w) [Monad m] [LawfulMonad m] (ita itb : Std.Iterators.BundledIterM m β) : Std.Iterators.BundledIterM.Equiv m β ita itb = (Std.Iterators.HetT.map (Std.Iterators.IterStep.mapIterator (Quot.mk (Std.Iterators.BundledIterM.Equiv m β))) ita.step = Std.Iterators.HetT.map (Std.Iterators.IterStep.mapIterator (Quot.mk (Std.Iterators.BundledIterM.Equiv m β))) itb.step)
• Std.Iterators.BundledIterM.Equiv.eq_def 📋 Std.Data.Iterators.Lemmas.Equivalence.Basic
  (m : Type w → Type w') (β : Type w) [Monad m] [LawfulMonad m] (ita itb : Std.Iterators.BundledIterM m β) : Std.Iterators.BundledIterM.Equiv m β ita itb = (Std.Iterators.HetT.map (Std.Iterators.IterStep.mapIterator (Quot.mk (Std.Iterators.BundledIterM.Equiv m β))) ita.step = Std.Iterators.HetT.map (Std.Iterators.IterStep.mapIterator (Quot.mk (Std.Iterators.BundledIterM.Equiv m β))) itb.step)

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