Loogle!

Result

Found 27 declarations mentioning List.Vector.map.

• List.Vector.map 📋 Mathlib.Data.Vector.Defs
  {α : Type u_1} {β : Type u_2} {n : ℕ} (f : α → β) : List.Vector α n → List.Vector β n
• List.Vector.map_nil 📋 Mathlib.Data.Vector.Defs
  {α : Type u_1} {β : Type u_2} (f : α → β) : List.Vector.map f List.Vector.nil = List.Vector.nil
• List.Vector.map_cons 📋 Mathlib.Data.Vector.Defs
  {α : Type u_1} {β : Type u_2} {n : ℕ} (f : α → β) (a : α) (v : List.Vector α n) : List.Vector.map f (a ::ᵥ v) = f a ::ᵥ List.Vector.map f v
• List.Vector.map_id 📋 Mathlib.Data.Vector.Basic
  {α : Type u_1} {n : ℕ} (v : List.Vector α n) : List.Vector.map id v = v
• List.Vector.get_map 📋 Mathlib.Data.Vector.Basic
  {α : Type u_1} {n : ℕ} {β : Type u_6} (v : List.Vector α n) (f : α → β) (i : Fin n) : (List.Vector.map f v).get i = f (v.get i)
• List.Vector.toList_map 📋 Mathlib.Data.Vector.Basic
  {α : Type u_1} {n : ℕ} {β : Type u_6} (v : List.Vector α n) (f : α → β) : (List.Vector.map f v).toList = List.map f v.toList
• List.Vector.head_map 📋 Mathlib.Data.Vector.Basic
  {α : Type u_1} {n : ℕ} {β : Type u_6} (v : List.Vector α (n + 1)) (f : α → β) : (List.Vector.map f v).head = f v.head
• List.Vector.traverse_eq_map_id 📋 Mathlib.Data.Vector.Basic
  {n : ℕ} {α β : Type u_6} (f : α → β) (x : List.Vector α n) : List.Vector.traverse (pure ∘ f) x = pure (List.Vector.map f x)
• List.Vector.map.eq_1 📋 Mathlib.Data.Vector.Basic
  {α : Type u_1} {β : Type u_2} {n : ℕ} (f : α → β) (l : List α) (h : l.length = n) : List.Vector.map f ⟨l, h⟩ = ⟨List.map f l, ⋯⟩
• List.Vector.getElem_map 📋 Mathlib.Data.Vector.Basic
  {α : Type u_1} {n : ℕ} {β : Type u_6} (v : List.Vector α n) (f : α → β) {i : ℕ} (hi : i < n) : (List.Vector.map f v)[i] = f v[i]
• List.Vector.tail_map 📋 Mathlib.Data.Vector.Basic
  {α : Type u_1} {n : ℕ} {β : Type u_6} (v : List.Vector α (n + 1)) (f : α → β) : (List.Vector.map f v).tail = List.Vector.map f v.tail
• List.Vector.map_snoc 📋 Mathlib.Data.Vector.Snoc
  {α : Type u_1} {β : Type u_2} {n : ℕ} {x : α} (xs : List.Vector α n) {f : α → β} : List.Vector.map f (xs.snoc x) = (List.Vector.map f xs).snoc (f x)
• List.Vector.map_map 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {n : ℕ} (xs : List.Vector α n) (f₁ : β → γ) (f₂ : α → β) : List.Vector.map f₁ (List.Vector.map f₂ xs) = List.Vector.map (fun x => f₁ (f₂ x)) xs
• List.Vector.map_eq_mapAccumr 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {n : ℕ} {xs : List.Vector α n} {f : α → β} : List.Vector.map f xs = (List.Vector.mapAccumr (fun x x_1 => ((), f x)) xs ()).2
• List.Vector.map_map₂ 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ζ : Type u_4} {n : ℕ} (xs : List.Vector α n) (ys : List.Vector β n) (f₁ : γ → ζ) (f₂ : α → β → γ) : List.Vector.map f₁ (List.Vector.map₂ f₂ xs ys) = List.Vector.map₂ (fun x y => f₁ (f₂ x y)) xs ys
• List.Vector.map₂_map_left 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ζ : Type u_4} {n : ℕ} (xs : List.Vector α n) (ys : List.Vector β n) (f₁ : γ → β → ζ) (f₂ : α → γ) : List.Vector.map₂ f₁ (List.Vector.map f₂ xs) ys = List.Vector.map₂ (fun x y => f₁ (f₂ x) y) xs ys
• List.Vector.map₂_map_right 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {ζ : Type u_4} {n : ℕ} (xs : List.Vector α n) (ys : List.Vector β n) (f₁ : α → γ → ζ) (f₂ : β → γ) : List.Vector.map₂ f₁ xs (List.Vector.map f₂ ys) = List.Vector.map₂ (fun x y => f₁ x (f₂ y)) xs ys
• List.Vector.mapAccumr_map 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {σ₁ : Type u_6} {n : ℕ} (xs : List.Vector α n) (f₁ : β → σ₁ → σ₁ × γ) {s : σ₁} (f₂ : α → β) : List.Vector.mapAccumr f₁ (List.Vector.map f₂ xs) s = List.Vector.mapAccumr (fun x s => f₁ (f₂ x) s) xs s
• List.Vector.mapAccumr_eq_map_of_constant_state 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {σ : Type u_5} {n : ℕ} {xs : List.Vector α n} (f : α → σ → σ × β) (s : σ) (h : ∀ (a : α), (f a s).1 = s) : List.Vector.mapAccumr f xs s = (s, List.Vector.map (fun x => (f x s).2) xs)
• List.Vector.mapAccumr_eq_map_of_unused_state 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {σ : Type u_5} {n : ℕ} {xs : List.Vector α n} (f : α → σ → σ × β) (s : σ) (h : ∀ (a : α) (s s' : σ), (f a s).2 = (f a s').2) : (List.Vector.mapAccumr f xs s).2 = List.Vector.map (fun x => (f x s).2) xs
• List.Vector.map_pmap 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {n : ℕ} (xs : List.Vector α n) {p : α → Prop} (f₁ : β → γ) (f₂ : (a : α) → p a → β) (H : ∀ x ∈ xs.toList, p x) : List.Vector.map f₁ (List.Vector.pmap f₂ xs H) = List.Vector.pmap (fun x hx => f₁ (f₂ x hx)) xs H
• List.Vector.map_mapAccumr 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {σ₂ : Type u_7} {n : ℕ} (xs : List.Vector α n) (f₂ : α → σ₂ → σ₂ × β) {s : σ₂} (f₁ : β → γ) : List.Vector.map f₁ (List.Vector.mapAccumr f₂ xs s).2 = (List.Vector.mapAccumr (fun x s => let r := f₂ x s; (r.1, f₁ r.2)) xs s).2
• List.Vector.mapAccumr_eq_map 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {σ : Type u_5} {n : ℕ} {xs : List.Vector α n} {f : α → σ → σ × β} {s₀ : σ} (S : Set σ) (h₀ : s₀ ∈ S) (closure : ∀ (a : α), ∀ s ∈ S, (f a s).1 ∈ S) (out : ∀ (a : α) (s s' : σ), s ∈ S → s' ∈ S → (f a s).2 = (f a s').2) : (List.Vector.mapAccumr f xs s₀).2 = List.Vector.map (fun x => (f x s₀).2) xs
• List.Vector.pmap_map 📋 Mathlib.Data.Vector.MapLemmas
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} {n : ℕ} (xs : List.Vector α n) {p : β → Prop} (f₁ : (b : β) → p b → γ) (f₂ : α → β) (H : ∀ x ∈ (List.Vector.map f₂ xs).toList, p x) : List.Vector.pmap f₁ (List.Vector.map f₂ xs) H = List.Vector.pmap (fun x hx => f₁ (f₂ x) hx) xs ⋯
• List.Vector.not_mem_map_zero 📋 Mathlib.Data.Vector.Mem
  {α : Type u_1} {β : Type u_2} (b : β) (v : List.Vector α 0) (f : α → β) : b ∉ (List.Vector.map f v).toList
• List.Vector.mem_map_iff 📋 Mathlib.Data.Vector.Mem
  {α : Type u_1} {β : Type u_2} {n : ℕ} (b : β) (v : List.Vector α n) (f : α → β) : b ∈ (List.Vector.map f v).toList ↔ ∃ a ∈ v.toList, f a = b
• List.Vector.mem_map_succ_iff 📋 Mathlib.Data.Vector.Mem
  {α : Type u_1} {β : Type u_2} {n : ℕ} (b : β) (v : List.Vector α (n + 1)) (f : α → β) : b ∈ (List.Vector.map f v).toList ↔ f v.head = b ∨ ∃ a ∈ v.tail.toList, f a = b

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