Loogle!

Result

Found 8 declarations mentioning Quotient.map.

• Quotient.map 📋 Mathlib.Data.Quot
  {α : Sort u_1} {β : Sort u_2} {sa : Setoid α} {sb : Setoid β} (f : α → β) (h : ∀ ⦃a b : α⦄, a ≈ b → f a ≈ f b) : Quotient sa → Quotient sb
• Quotient.map_mk 📋 Mathlib.Data.Quot
  {α : Sort u_1} {β : Sort u_2} {sa : Setoid α} {sb : Setoid β} (f : α → β) (h : ∀ ⦃a b : α⦄, a ≈ b → f a ≈ f b) (x : α) : Quotient.map f h ⟦x⟧ = ⟦f x⟧
• SMulCon.instSMulQuotient.eq_1 📋 Mathlib.Algebra.Module.Congruence.Defs
  {S : Type u_2} (M : Type u_3) [SMul S M] (c : SMulCon S M) : SMulCon.instSMulQuotient M c = { smul := fun s => Quotient.map (fun x => s • x) ⋯ }
• VAddCon.instVAddQuotient.eq_1 📋 Mathlib.Algebra.Module.Congruence.Defs
  {S : Type u_2} (M : Type u_3) [VAdd S M] (c : VAddCon S M) : VAddCon.instVAddQuotient M c = { vadd := fun s => Quotient.map (fun x => s +ᵥ x) ⋯ }
• Quotient.map.congr_simp 📋 Mathlib.Data.Fintype.Quotient
  {α : Sort u_1} {β : Sort u_2} {sa : Setoid α} {sb : Setoid β} (f f✝ : α → β) (e_f : f = f✝) (h : ∀ ⦃a b : α⦄, a ≈ b → f a ≈ f b) (a✝ a✝¹ : Quotient sa) : a✝ = a✝¹ → Quotient.map f h a✝ = Quotient.map f✝ ⋯ a✝¹
• CategoryTheory.ThinSkeleton.map_obj 📋 Mathlib.CategoryTheory.Skeletal
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (F : CategoryTheory.Functor C D) (a✝ : Quotient (CategoryTheory.isIsomorphicSetoid C)) : (CategoryTheory.ThinSkeleton.map F).obj a✝ = Quotient.map F.obj ⋯ a✝
• CategoryTheory.ThinSkeleton.map_map 📋 Mathlib.CategoryTheory.Skeletal
  {C : Type u₁} [CategoryTheory.Category.{v₁, u₁} C] {D : Type u₂} [CategoryTheory.Category.{v₂, u₂} D] (F : CategoryTheory.Functor C D) {X Y : CategoryTheory.ThinSkeleton C} (a✝ : X ⟶ Y) : (CategoryTheory.ThinSkeleton.map F).map a✝ = Quotient.recOnSubsingleton₂ (motive := fun x x_1 => (x ⟶ x_1) → (Quotient.map F.obj ⋯ x ⟶ Quotient.map F.obj ⋯ x_1)) X Y (fun x x_1 k => CategoryTheory.homOfLE ⋯) a✝
• Path.Homotopic.pi.eq_1 📋 Mathlib.Topology.Homotopy.Product
  {ι : Type u_1} {X : ι → Type u_2} [(i : ι) → TopologicalSpace (X i)] {as bs : (i : ι) → X i} (γ : (i : ι) → Path.Homotopic.Quotient (as i) (bs i)) : Path.Homotopic.pi γ = Quotient.map Path.pi ⋯ (Quotient.choice γ)

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 edaf32c