Loogle!

Result

Found 19 declarations whose name contains "NatLit".

• rawNatLit 📋 Init.Notation
  : Lean.ParserDescr
• Lean.Syntax.decodeNatLitVal? 📋 Init.Meta
  (s : String) : Option ℕ
• Lean.Syntax.isNatLit? 📋 Init.Meta
  (s : Lean.Syntax) : Option ℕ
• Lean.Syntax.mkNatLit 📋 Init.Meta
  (val : ℕ) (info : Lean.SourceInfo := Lean.SourceInfo.none) : Lean.NumLit
• Std.Tactic.BVDecide.LRAT.Internal.natLiteralToPosFinLiteral 📋 Std.Tactic.BVDecide.LRAT.Internal.Actions
  {n : ℕ} (x : Std.Sat.Literal ℕ) : Option (Std.Sat.Literal (Std.Tactic.BVDecide.LRAT.Internal.PosFin n))
• Lean.getPPNatLit 📋 Lean.PrettyPrinter.Delaborator.Options
  (o : Lean.Options) : Bool
• Lean.pp.natLit 📋 Lean.PrettyPrinter.Delaborator.Options
  : Lean.Option Bool
• Lean.mkNatLit 📋 Lean.Expr
  (n : ℕ) : Lean.Expr
• Lean.mkRawNatLit 📋 Lean.Expr
  (n : ℕ) : Lean.Expr
• Lean.Expr.isRawNatLit 📋 Lean.Expr
  : Lean.Expr → Bool
• Lean.Expr.rawNatLit? 📋 Lean.Expr
  : Lean.Expr → Option ℕ
• Lean.Meta.Simp.isOfNatNatLit 📋 Lean.Meta.Tactic.Simp.Main
  (e : Lean.Expr) : Bool
• Lean.Meta.Simp.foldRawNatLit 📋 Lean.Meta.Tactic.Simp.Main
  (e : Lean.Expr) : Lean.Meta.SimpM Lean.Expr
• Lean.Elab.Term.elabRawNatLit 📋 Lean.Elab.BuiltinTerm
  : Lean.Elab.Term.TermElab
• Lean.Expr.natLit! 📋 Batteries.Lean.Expr
  : Lean.Expr → ℕ
• Lean.Compiler.LCNF.Simp.ConstantFold.mkNatLit 📋 Lean.Compiler.LCNF.Simp.ConstantFold
  (n : ℕ) : Lean.Compiler.LCNF.Simp.ConstantFold.FolderM Lean.Compiler.LCNF.LetValue
• Lean.Compiler.LCNF.Simp.ConstantFold.getNatLit 📋 Lean.Compiler.LCNF.Simp.ConstantFold
  (fvarId : Lean.FVarId) : Lean.Compiler.LCNF.CompilerM (Option ℕ)
• Mathlib.Notation3.natLitMatcher 📋 Mathlib.Util.Notation3
  (n : ℕ) : Mathlib.Notation3.Matcher
• Mathlib.Meta.Positivity.evalLogNatLit 📋 Mathlib.Analysis.SpecialFunctions.Log.Basic
  : Mathlib.Meta.Positivity.PositivityExt

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