Loogle!

Result

Found 25 declarations mentioning Stream'.map.

• Stream'.map 📋 Mathlib.Data.Stream.Defs
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' α) : Stream' β
• Stream'.map_id 📋 Mathlib.Data.Stream.Init
  {α : Type u} (s : Stream' α) : Stream'.map id s = s
• Stream'.nats_eq 📋 Mathlib.Data.Stream.Init
  : Stream'.nats = Stream'.cons 0 (Stream'.map Nat.succ Stream'.nats)
• Stream'.head_map 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' α) : (Stream'.map f s).head = f s.head
• Stream'.map_const 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (a : α) : Stream'.map f (Stream'.const a) = Stream'.const (f a)
• Stream'.map_iterate 📋 Mathlib.Data.Stream.Init
  {α : Type u} (f : α → α) (a : α) : Stream'.iterate f (f a) = Stream'.map f (Stream'.iterate f a)
• Stream'.map.eq_1 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' α) (n : ℕ) : Stream'.map f s n = f (s.get n)
• Stream'.get_map 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (n : ℕ) (s : Stream' α) : (Stream'.map f s).get n = f (s.get n)
• Stream'.map_eq_apply 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' α) : Stream'.map f s = Stream'.pure f ⊛ s
• Stream'.map_tail 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' α) : Stream'.map f s.tail = (Stream'.map f s).tail
• Stream'.tail_map 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' α) : (Stream'.map f s).tail = Stream'.map f s.tail
• Stream'.corec_def 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (g : α → α) (a : α) : Stream'.corec f g a = Stream'.map f (Stream'.iterate g a)
• Stream'.drop_map 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (n : ℕ) (s : Stream' α) : Stream'.drop n (Stream'.map f s) = Stream'.map f (Stream'.drop n s)
• Stream'.map_take 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (n : ℕ) (a : Stream' α) (f : α → β) : List.map f (Stream'.take n a) = Stream'.take n (Stream'.map f a)
• Stream'.map_cons 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (a : α) (s : Stream' α) : Stream'.map f (Stream'.cons a s) = Stream'.cons (f a) (Stream'.map f s)
• Stream'.map_eq 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' α) : Stream'.map f s = Stream'.cons (f s.head) (Stream'.map f s.tail)
• Stream'.mem_map 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) {a : α} {s : Stream' α} : a ∈ s → f a ∈ Stream'.map f s
• Stream'.map_append_stream 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} (f : α → β) (l : List α) (s : Stream' α) : Stream'.map f (l ++ₛ s) = List.map f l ++ₛ Stream'.map f s
• Stream'.map_map 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} {δ : Type w} (g : β → δ) (f : α → β) (s : Stream' α) : Stream'.map g (Stream'.map f s) = Stream'.map (g ∘ f) s
• Stream'.inits_eq 📋 Mathlib.Data.Stream.Init
  {α : Type u} (s : Stream' α) : s.inits = Stream'.cons [s.head] (Stream'.map (List.cons s.head) s.tail.inits)
• Stream'.exists_of_mem_map 📋 Mathlib.Data.Stream.Init
  {α : Type u} {β : Type v} {f : α → β} {b : β} {s : Stream' α} : b ∈ Stream'.map f s → ∃ a ∈ s, f a = b
• Computation.map.eq_1 📋 Mathlib.Data.Seq.Computation
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' (Option α)) (al : ∀ ⦃n : ℕ⦄ ⦃a : α⦄, s n = some a → s (n + 1) = some a) : Computation.map f ⟨s, al⟩ = ⟨Stream'.map (fun o => Option.casesOn o none (some ∘ f)) s, ⋯⟩
• Stream'.Seq.ofStream.eq_1 📋 Mathlib.Data.Seq.Seq
  {α : Type u} (s : Stream' α) : ↑s = ⟨Stream'.map some s, ⋯⟩
• Stream'.Seq.map.eq_1 📋 Mathlib.Algebra.ContinuedFractions.Computation.Translations
  {α : Type u} {β : Type v} (f : α → β) (s : Stream' (Option α)) (al : s.IsSeq) : Stream'.Seq.map f ⟨s, al⟩ = ⟨Stream'.map (Option.map f) s, ⋯⟩
• GenContFract.IntFractPair.coe_stream'_rat_eq 📋 Mathlib.Algebra.ContinuedFractions.Computation.TerminatesIffRat
  {K : Type u_1} [Field K] [LinearOrder K] [IsStrictOrderedRing K] [FloorRing K] {v : K} {q : ℚ} (v_eq_q : v = ↑q) : Stream'.map (Option.map (GenContFract.IntFractPair.mapFr Rat.cast)) (GenContFract.IntFractPair.stream q) = GenContFract.IntFractPair.stream v

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 19971e9 serving mathlib revision bce1d65