Loogle!

Result

Found 4546 declarations mentioning List and Nat. Of these, 33 match your pattern(s).

• List.iota 📋 Init.Data.List.Basic
  : ℕ → List ℕ
• List.iotaTR 📋 Init.Data.List.Basic
  (n : ℕ) : List ℕ
• List.range 📋 Init.Data.List.Basic
  (n : ℕ) : List ℕ
• List.iotaTR.go 📋 Init.Data.List.Basic
  : ℕ → List ℕ → List ℕ
• List.range.loop 📋 Init.Data.List.Basic
  : ℕ → List ℕ → List ℕ
• List.iota_eq_iotaTR 📋 Init.Data.List.Basic
  : List.iota = List.iotaTR
• 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
• Lean.Data.AC.insert 📋 Init.Data.AC
  (x : ℕ) : List ℕ → List ℕ
• Lean.Data.AC.mergeIdem.loop 📋 Init.Data.AC
  : ℕ → List ℕ → List ℕ
• Plausible.Nat.shrink 📋 Plausible.Sampleable
  (n : ℕ) : List ℕ
• Nat.primeFactorsList 📋 Mathlib.Data.Nat.Factors
  : ℕ → List ℕ
• Nat.digitsAux0 📋 Mathlib.Data.Nat.Digits
  : ℕ → List ℕ
• Nat.digitsAux1 📋 Mathlib.Data.Nat.Digits
  (n : ℕ) : List ℕ
• Nat.digits 📋 Mathlib.Data.Nat.Digits
  : ℕ → ℕ → List ℕ
• Nat.digits.eq_1 📋 Mathlib.Data.Nat.Digits
  : Nat.digits 0 = Nat.digitsAux0
• Nat.digits.eq_2 📋 Mathlib.Data.Nat.Digits
  : Nat.digits 1 = Nat.digitsAux1
• Nat.digitsAux 📋 Mathlib.Data.Nat.Digits
  (b : ℕ) (h : 2 ≤ b) : ℕ → List ℕ
• Nat.digits.eq_3 📋 Mathlib.Data.Nat.Digits
  (b : ℕ) : b.succ.succ.digits = (b + 2).digitsAux ⋯
• Composition.blocks 📋 Mathlib.Combinatorics.Enumerative.Composition
  {n : ℕ} (self : Composition n) : List ℕ
• CompositionAsSet.blocks 📋 Mathlib.Combinatorics.Enumerative.Composition
  {n : ℕ} (c : CompositionAsSet n) : List ℕ
• Denumerable.lower 📋 Mathlib.Logic.Equiv.Multiset
  : List ℕ → ℕ → List ℕ
• Denumerable.raise 📋 Mathlib.Logic.Equiv.Multiset
  : List ℕ → ℕ → List ℕ
• Denumerable.lower' 📋 Mathlib.Logic.Equiv.Finset
  : List ℕ → ℕ → List ℕ
• Denumerable.raise' 📋 Mathlib.Logic.Equiv.Finset
  : List ℕ → ℕ → List ℕ
• SimplexCategoryGenRel.simplicialInsert 📋 Mathlib.AlgebraicTopology.SimplexCategory.GeneratorsRelations.NormalForms
  (a : ℕ) : List ℕ → List ℕ
• Nat.bitIndices 📋 Mathlib.Data.Nat.BitIndices
  (n : ℕ) : List ℕ
• PosNum.oneBits 📋 Mathlib.Data.Num.Bitwise
  : PosNum → ℕ → List ℕ
• List.Ico 📋 Mathlib.Data.List.Intervals
  (n m : ℕ) : List ℕ
• Nat.zeckendorf 📋 Mathlib.Data.Nat.Fib.Zeckendorf
  : ℕ → List ℕ
• DihedralGroup.reciprocalFactors 📋 Mathlib.GroupTheory.CommutingProbability
  (n : ℕ) : List ℕ

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 3008304