Loogle!

Result

Found 12 declarations mentioning Path.map.

• Path.map 📋 Mathlib.Topology.Path
  {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [TopologicalSpace Y] {x y : X} (γ : Path x y) {f : X → Y} (h : Continuous f) : Path (f x) (f y)
• Path.map_id 📋 Mathlib.Topology.Path
  {X : Type u_1} [TopologicalSpace X] {x y : X} (γ : Path x y) : γ.map ⋯ = γ
• Path.map_symm 📋 Mathlib.Topology.Path
  {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [TopologicalSpace Y] {x y : X} (γ : Path x y) {f : X → Y} (h : Continuous f) : (γ.map h).symm = γ.symm.map h
• Path.map_trans 📋 Mathlib.Topology.Path
  {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [TopologicalSpace Y] {x y z : X} (γ : Path x y) (γ' : Path y z) {f : X → Y} (h : Continuous f) : (γ.trans γ').map h = (γ.map h).trans (γ'.map h)
• Path.map_coe 📋 Mathlib.Topology.Path
  {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [TopologicalSpace Y] {x y : X} (γ : Path x y) {f : X → Y} (h : Continuous f) : ⇑(γ.map h) = f ∘ ⇑γ
• Path.map_map 📋 Mathlib.Topology.Path
  {X : Type u_1} {Y : Type u_2} [TopologicalSpace X] [TopologicalSpace Y] {x y : X} (γ : Path x y) {Z : Type u_4} [TopologicalSpace Z] {f : X → Y} (hf : Continuous f) {g : Y → Z} (hg : Continuous g) : (γ.map hf).map hg = γ.map ⋯
• Path.add.eq_1 📋 Mathlib.Topology.Path
  {X : Type u_1} [TopologicalSpace X] [Add X] [ContinuousAdd X] {a₁ b₁ a₂ b₂ : X} (γ₁ : Path a₁ b₁) (γ₂ : Path a₂ b₂) : γ₁.add γ₂ = (γ₁.prod γ₂).map ⋯
• Path.mul.eq_1 📋 Mathlib.Topology.Path
  {X : Type u_1} [TopologicalSpace X] [Mul X] [ContinuousMul X] {a₁ b₁ a₂ b₂ : X} (γ₁ : Path a₁ b₁) (γ₂ : Path a₂ b₂) : γ₁.mul γ₂ = (γ₁.prod γ₂).map ⋯
• Path.Homotopic.map 📋 Mathlib.Topology.Homotopy.Path
  {X : Type u} {Y : Type v} [TopologicalSpace X] [TopologicalSpace Y] {x₀ x₁ : X} {p q : Path x₀ x₁} (h : p.Homotopic q) (f : C(X, Y)) : (p.map ⋯).Homotopic (q.map ⋯)
• Path.Homotopy.map 📋 Mathlib.Topology.Homotopy.Path
  {X : Type u} {Y : Type v} [TopologicalSpace X] [TopologicalSpace Y] {x₀ x₁ : X} {p q : Path x₀ x₁} (F : p.Homotopy q) (f : C(X, Y)) : (p.map ⋯).Homotopy (q.map ⋯)
• Path.Homotopic.map_lift 📋 Mathlib.Topology.Homotopy.Path
  {X : Type u} {Y : Type v} [TopologicalSpace X] [TopologicalSpace Y] {x₀ x₁ : X} (P₀ : Path x₀ x₁) (f : C(X, Y)) : ⟦P₀.map ⋯⟧ = Path.Homotopic.Quotient.mapFn ⟦P₀⟧ f
• Path.Homotopy.map_apply 📋 Mathlib.Topology.Homotopy.Path
  {X : Type u} {Y : Type v} [TopologicalSpace X] [TopologicalSpace Y] {x₀ x₁ : X} {p q : Path x₀ x₁} (F : p.Homotopy q) (f : C(X, Y)) (a✝ : ↑unitInterval × ↑unitInterval) : (F.map f) a✝ = (⇑f ∘ ⇑F) a✝

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