Loogle!

Result

Found 3608 definitions mentioning List and Nat. Of these, 39 match your pattern(s).

• List.set 📋 Init.Prelude
  {α : Type u_1} : List α → ℕ → α → List α
• List.replicate 📋 Init.Data.List.Basic
  {α : Type u} (n : ℕ) (a : α) : List α
• List.replicateTR 📋 Init.Data.List.Basic
  {α : Type u} (n : ℕ) (a : α) : List α
• List.leftpad 📋 Init.Data.List.Basic
  {α : Type u} (n : ℕ) (a : α) (l : List α) : List α
• List.leftpadTR 📋 Init.Data.List.Basic
  {α : Type u} (n : ℕ) (a : α) (l : List α) : List α
• List.rightpad 📋 Init.Data.List.Basic
  {α : Type u} (n : ℕ) (a : α) (l : List α) : List α
• List.replicateTR.loop 📋 Init.Data.List.Basic
  {α : Type u} (a : α) : ℕ → List α → List α
• List.replicate_eq_replicateTR 📋 Init.Data.List.Basic
  : @List.replicate = @List.replicateTR
• List.leftpad_eq_leftpadTR 📋 Init.Data.List.Basic
  : @List.leftpad = @List.leftpadTR
• List.range' 📋 Init.Data.List.Basic
  (start len : ℕ) (step : ℕ := 1) : List ℕ
• List.range'TR 📋 Init.Data.List.Basic
  (s n : ℕ) (step : ℕ := 1) : List ℕ
• List.range'TR.go 📋 Init.Data.List.Basic
  (step : ℕ := 1) : ℕ → ℕ → List ℕ → List ℕ
• List.range'_eq_range'TR 📋 Init.Data.List.Basic
  : @List.range' = @List.range'TR
• List.setTR 📋 Init.Data.List.Impl
  {α : Type u_1} (l : List α) (n : ℕ) (a : α) : List α
• List.set_eq_setTR 📋 Init.Data.List.Impl
  : @List.set = @List.setTR
• List.setTR.go 📋 Init.Data.List.Impl
  {α : Type u_1} (l : List α) (a : α) : List α → ℕ → Array α → List α
• List.insertIdx 📋 Batteries.Data.List.Basic
  {α : Type u_1} (n : ℕ) (a : α) : List α → List α
• List.insertIdxTR 📋 Batteries.Data.List.Basic
  {α : Type u_1} (n : ℕ) (a : α) (l : List α) : List α
• List.insertNth 📋 Batteries.Data.List.Basic
  {α : Type u_1} (n : ℕ) (a : α) : List α → List α
• List.takeD 📋 Batteries.Data.List.Basic
  {α : Type u_1} : ℕ → List α → α → List α
• List.takeDTR 📋 Batteries.Data.List.Basic
  {α : Type u_1} (n : ℕ) (l : List α) (dflt : α) : List α
• List.toChunks 📋 Batteries.Data.List.Basic
  {α : Type u_1} : ℕ → List α → List (List α)
• List.insertIdxTR.go 📋 Batteries.Data.List.Basic
  {α : Type u_1} (a : α) : ℕ → List α → Array α → List α
• List.takeDTR.go 📋 Batteries.Data.List.Basic
  {α : Type u_1} (dflt : α) : ℕ → List α → Array α → List α
• List.insertIdx_eq_insertIdxTR 📋 Batteries.Data.List.Basic
  : @List.insertIdx = @List.insertIdxTR
• List.takeD_eq_takeDTR 📋 Batteries.Data.List.Basic
  : @List.takeD = @List.takeDTR
• List.toChunks.go 📋 Batteries.Data.List.Basic
  {α : Type u_1} (n : ℕ) : List α → Array α → Array (List α) → List (List α)
• List.iterate 📋 Mathlib.Data.List.Defs
  {α : Type u_1} (f : α → α) (a : α) (n : ℕ) : List α
• List.iterateTR 📋 Mathlib.Data.List.Defs
  {α : Type u_1} (f : α → α) (a : α) (n : ℕ) : List α
• List.iterateTR.loop 📋 Mathlib.Data.List.Defs
  {α : Type u_1} (f : α → α) (a : α) (n : ℕ) (l : List α) : List α
• List.iterate_eq_iterateTR 📋 Mathlib.Data.List.Defs
  : @List.iterate = @List.iterateTR
• List.sublistsLen 📋 Mathlib.Data.List.Sublists
  {α : Type u} (n : ℕ) (l : List α) : List (List α)
• List.splitWrtComposition 📋 Mathlib.Combinatorics.Enumerative.Composition
  {n : ℕ} {α : Type u_1} (l : List α) (c : Composition n) : List (List α)
• Nat.digits 📋 Mathlib.Data.Nat.Digits
  : ℕ → ℕ → List ℕ
• Nat.digitsAux 📋 Mathlib.Data.Nat.Digits
  (b : ℕ) (h : 2 ≤ b) : ℕ → List ℕ
• Matrix.Pivot.listTransvecCol 📋 Mathlib.LinearAlgebra.Matrix.Transvection
  {𝕜 : Type u_3} [Field 𝕜] {r : ℕ} (M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜) : List (Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜)
• Matrix.Pivot.listTransvecRow 📋 Mathlib.LinearAlgebra.Matrix.Transvection
  {𝕜 : Type u_3} [Field 𝕜] {r : ℕ} (M : Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜) : List (Matrix (Fin r ⊕ Unit) (Fin r ⊕ Unit) 𝕜)
• List.Ico 📋 Mathlib.Data.List.Intervals
  (n m : ℕ) : List ℕ
• CoxeterSystem.alternatingWord 📋 Mathlib.GroupTheory.Coxeter.Basic
  {B : Type u_1} (i i' : B) (m : ℕ) : List 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, _ * _, _ ^ _, |- _ < _ → _
woould 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 4e1aab0 serving mathlib revision 2d53f5f