Loogle!

Result

Found 1551 declarations mentioning LT. Of these, 480 have a name containing "Std.". Of these, 18 match your pattern(s).

• Std.LawfulOrderLT 📋 Init.Data.Order.Classes
  (α : Type u) [LT α] [LE α] : Prop
• Std.PRange.LawfulUpwardEnumerableLT 📋 Init.Data.Range.Polymorphic.UpwardEnumerable
  (α : Type u) [Std.PRange.UpwardEnumerable α] [LT α] : Prop
• Std.Rxo.IsAlwaysFinite 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type u) [Std.PRange.UpwardEnumerable α] [LT α] : Prop
• Std.Rcc.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Rcc.HasRcoIntersection α] : Prop
• Std.Rci.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Rci.HasRcoIntersection α] : Prop
• Std.Rco.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Rco.HasRcoIntersection α] : Prop
• Std.Ric.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Ric.HasRcoIntersection α] : Prop
• Std.Rio.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Rio.HasRcoIntersection α] : Prop
• Std.Roc.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Roc.HasRcoIntersection α] : Prop
• Std.Roi.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Roi.HasRcoIntersection α] : Prop
• Std.Roo.LawfulRcoIntersection 📋 Init.Data.Range.Polymorphic.PRange
  (α : Type w) [LT α] [LE α] [Std.Roo.HasRcoIntersection α] : Prop
• Std.Rxo.LawfulHasSize 📋 Init.Data.Range.Polymorphic.Basic
  (α : Type u) [LT α] [Std.PRange.UpwardEnumerable α] [Std.Rxo.HasSize α] : Prop
• Std.LawfulLTOrd 📋 Batteries.Classes.Order
  (α : Type u_1) [LT α] [Ord α] : Prop
• Std.LawfulLTCmp 📋 Batteries.Classes.Order
  {α : Type u_1} [LT α] (cmp : α → α → Ordering) : Prop
• Std.LawfulOrd 📋 Batteries.Classes.Order
  (α : Type u_1) [LE α] [LT α] [Ord α] : Prop
• Std.LawfulCmp 📋 Batteries.Classes.Order
  {α : Type u_1} [LE α] [LT α] (cmp : α → α → Ordering) : Prop
• Std.LawfulBOrd 📋 Batteries.Classes.Order
  (α : Type u_1) [LE α] [LT α] [BEq α] [Ord α] : Prop
• Std.LawfulBCmp 📋 Batteries.Classes.Order
  {α : Type u_1} [LE α] [LT α] [BEq α] (cmp : α → α → Ordering) : Prop

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 6ff4759 serving mathlib revision abad10c