Loogle!

Result

Found 8 declarations mentioning Quot.map.

• Quot.map 📋 Mathlib.Data.Quot
  {α : Sort u_1} {β : Sort u_2} {ra : α → α → Prop} {rb : β → β → Prop} (f : α → β) (h : ∀ ⦃a b : α⦄, ra a b → rb (f a) (f b)) : Quot ra → Quot rb
• Quot.map.eq_1 📋 Mathlib.Logic.Equiv.Defs
  {α : Sort u_1} {β : Sort u_2} {ra : α → α → Prop} {rb : β → β → Prop} (f : α → β) (h : ∀ ⦃a b : α⦄, ra a b → rb (f a) (f b)) : Quot.map f h = Quot.lift (fun x => Quot.mk rb (f x)) ⋯
• FreeAddGroup.instNeg.eq_1 📋 Mathlib.GroupTheory.FreeGroup.Basic
  {α : Type u} : FreeAddGroup.instNeg = { neg := Quot.map FreeAddGroup.negRev ⋯ }
• FreeGroup.instInv.eq_1 📋 Mathlib.GroupTheory.FreeGroup.Basic
  {α : Type u} : FreeGroup.instInv = { inv := Quot.map FreeGroup.invRev ⋯ }
• FreeAddGroup.quot_map_mk 📋 Mathlib.GroupTheory.FreeGroup.Basic
  {α : Type u} {L : List (α × Bool)} (β : Type v) (f : List (α × Bool) → List (β × Bool)) (H : Relator.LiftFun FreeAddGroup.Red.Step FreeAddGroup.Red.Step f f) : Quot.map f H (FreeAddGroup.mk L) = FreeAddGroup.mk (f L)
• FreeGroup.quot_map_mk 📋 Mathlib.GroupTheory.FreeGroup.Basic
  {α : Type u} {L : List (α × Bool)} (β : Type v) (f : List (α × Bool) → List (β × Bool)) (H : Relator.LiftFun FreeGroup.Red.Step FreeGroup.Red.Step f f) : Quot.map f H (FreeGroup.mk L) = FreeGroup.mk (f L)
• FreeAddGroup.map.eq_1 📋 Mathlib.GroupTheory.FreeGroup.Basic
  {α : Type u} {β : Type v} (f : α → β) : FreeAddGroup.map f = AddMonoidHom.mk' (Quot.map (List.map fun x => (f x.1, x.2)) ⋯) ⋯
• FreeGroup.map.eq_1 📋 Mathlib.GroupTheory.FreeGroup.Basic
  {α : Type u} {β : Type v} (f : α → β) : FreeGroup.map f = MonoidHom.mk' (Quot.map (List.map fun x => (f x.1, x.2)) ⋯) ⋯

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