Loogle!

Result

Found 10 declarations mentioning DiscreteQuotient.map.

• DiscreteQuotient.map 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {A : DiscreteQuotient X} {B : DiscreteQuotient Y} (f : C(X, Y)) (cond : DiscreteQuotient.LEComap f A B) : Quotient A.toSetoid → Quotient B.toSetoid
• DiscreteQuotient.map_id 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} [TopologicalSpace X] {A : DiscreteQuotient X} : DiscreteQuotient.map (ContinuousMap.id X) ⋯ = id
• DiscreteQuotient.map_continuous 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {f : C(X, Y)} {A : DiscreteQuotient X} {B : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) : Continuous (DiscreteQuotient.map f cond)
• DiscreteQuotient.map_proj 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {f : C(X, Y)} {A : DiscreteQuotient X} {B : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) (x : X) : DiscreteQuotient.map f cond (A.proj x) = B.proj (f x)
• DiscreteQuotient.map_comp_proj 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {f : C(X, Y)} {A : DiscreteQuotient X} {B : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) : DiscreteQuotient.map f cond ∘ A.proj = B.proj ∘ ⇑f
• DiscreteQuotient.map_ofLE 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {f : C(X, Y)} {A A' : DiscreteQuotient X} {B : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) (h : A' ≤ A) (c : Quotient A'.toSetoid) : DiscreteQuotient.map f cond (DiscreteQuotient.ofLE h c) = DiscreteQuotient.map f ⋯ c
• DiscreteQuotient.ofLE_map 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {f : C(X, Y)} {A : DiscreteQuotient X} {B B' : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) (h : B ≤ B') (a : Quotient A.toSetoid) : DiscreteQuotient.ofLE h (DiscreteQuotient.map f cond a) = DiscreteQuotient.map f ⋯ a
• DiscreteQuotient.map_comp 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} {Z : Type u_4} [TopologicalSpace X] [TopologicalSpace Y] [TopologicalSpace Z] {f : C(X, Y)} {A : DiscreteQuotient X} {B : DiscreteQuotient Y} {g : C(Y, Z)} {C : DiscreteQuotient Z} (h1 : DiscreteQuotient.LEComap g B C) (h2 : DiscreteQuotient.LEComap f A B) : DiscreteQuotient.map (g.comp f) ⋯ = DiscreteQuotient.map g h1 ∘ DiscreteQuotient.map f h2
• DiscreteQuotient.map_comp_ofLE 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {f : C(X, Y)} {A A' : DiscreteQuotient X} {B : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) (h : A' ≤ A) : DiscreteQuotient.map f cond ∘ DiscreteQuotient.ofLE h = DiscreteQuotient.map f ⋯
• DiscreteQuotient.ofLE_comp_map 📋 Mathlib.Topology.DiscreteQuotient
  {X : Type u_2} {Y : Type u_3} [TopologicalSpace X] [TopologicalSpace Y] {f : C(X, Y)} {A : DiscreteQuotient X} {B B' : DiscreteQuotient Y} (cond : DiscreteQuotient.LEComap f A B) (h : B ≤ B') : DiscreteQuotient.ofLE h ∘ DiscreteQuotient.map f cond = DiscreteQuotient.map f ⋯

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