Loogle!

Result

Found 19 declarations mentioning UniformSpace.Completion.map.

• UniformSpace.Completion.map 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] (f : α → β) : UniformSpace.Completion α → UniformSpace.Completion β
• UniformSpace.Completion.map_id 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] : UniformSpace.Completion.map id = id
• UniformSpace.Completion.uniformContinuous_map 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] {f : α → β} : UniformContinuous (UniformSpace.Completion.map f)
• UniformSpace.Completion.map_coe 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] {f : α → β} (hf : UniformContinuous f) (a : α) : UniformSpace.Completion.map f ↑a = ↑(f a)
• UniformSpace.Completion.continuous_map 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] {f : α → β} : Continuous (UniformSpace.Completion.map f)
• UniformSpace.Completion.map_unique 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] {f : α → β} {g : UniformSpace.Completion α → UniformSpace.Completion β} (hg : UniformContinuous g) (h : ∀ (a : α), ↑(f a) = g ↑a) : UniformSpace.Completion.map f = g
• UniformSpace.Completion.map_comp 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] {γ : Type u_3} [UniformSpace γ] {g : β → γ} {f : α → β} (hg : UniformContinuous g) (hf : UniformContinuous f) : UniformSpace.Completion.map g ∘ UniformSpace.Completion.map f = UniformSpace.Completion.map (g ∘ f)
• UniformSpace.Completion.extension_map 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] {γ : Type u_3} [UniformSpace γ] [CompleteSpace γ] [T0Space γ] {f : β → γ} {g : α → β} (hf : UniformContinuous f) (hg : UniformContinuous g) : UniformSpace.Completion.extension f ∘ UniformSpace.Completion.map g = UniformSpace.Completion.extension (f ∘ g)
• UniformSpace.Completion.instSMul.eq_1 📋 Mathlib.Topology.Algebra.UniformMulAction
  (M : Type v) (X : Type x) [UniformSpace X] [SMul M X] : UniformSpace.Completion.instSMul M X = { smul := fun c => UniformSpace.Completion.map fun x => c • x }
• UniformSpace.Completion.instVAdd.eq_1 📋 Mathlib.Topology.Algebra.UniformMulAction
  (M : Type v) (X : Type x) [UniformSpace X] [VAdd M X] : UniformSpace.Completion.instVAdd M X = { vadd := fun c => UniformSpace.Completion.map fun x => c +ᵥ x }
• UniformSpace.Completion.smul_def 📋 Mathlib.Topology.Algebra.UniformMulAction
  (M : Type v) (X : Type x) [UniformSpace X] [SMul M X] (c : M) (x : UniformSpace.Completion X) : c • x = UniformSpace.Completion.map (fun x => c • x) x
• UniformSpace.Completion.vadd_def 📋 Mathlib.Topology.Algebra.UniformMulAction
  (M : Type v) (X : Type x) [UniformSpace X] [VAdd M X] (c : M) (x : UniformSpace.Completion X) : c +ᵥ x = UniformSpace.Completion.map (fun x => c +ᵥ x) x
• Isometry.completion_map 📋 Mathlib.Topology.MetricSpace.Completion
  {α : Type u} {β : Type v} [PseudoMetricSpace α] [PseudoMetricSpace β] {f : α → β} (h : Isometry f) : Isometry (UniformSpace.Completion.map f)
• LipschitzWith.completion_map 📋 Mathlib.Topology.MetricSpace.Completion
  {α : Type u} {β : Type v} [PseudoMetricSpace α] [PseudoMetricSpace β] {f : α → β} {K : NNReal} (h : LipschitzWith K f) : LipschitzWith K (UniformSpace.Completion.map f)
• UniformSpace.Completion.map_smul_eq_mul_coe 📋 Mathlib.Topology.Algebra.UniformRing
  (A : Type u_2) [Ring A] [UniformSpace A] [IsUniformAddGroup A] [IsTopologicalRing A] (R : Type u_3) [CommSemiring R] [Algebra R A] [UniformContinuousConstSMul R A] (r : R) : (UniformSpace.Completion.map fun x => r • x) = fun x => ↑((algebraMap R A) r) * x
• NormedAddGroupHom.completion_coe' 📋 Mathlib.Analysis.Normed.Group.HomCompletion
  {G : Type u_1} [SeminormedAddCommGroup G] {H : Type u_2} [SeminormedAddCommGroup H] (f : NormedAddGroupHom G H) (g : G) : UniformSpace.Completion.map ⇑f ↑g = ↑(f g)
• NormedAddGroupHom.completion_coe_to_fun 📋 Mathlib.Analysis.Normed.Group.HomCompletion
  {G : Type u_1} [SeminormedAddCommGroup G] {H : Type u_2} [SeminormedAddCommGroup H] (f : NormedAddGroupHom G H) : ⇑f.completion = UniformSpace.Completion.map ⇑f
• NormedAddGroupHom.completion_def 📋 Mathlib.Analysis.Normed.Group.HomCompletion
  {G : Type u_1} [SeminormedAddCommGroup G] {H : Type u_2} [SeminormedAddCommGroup H] (f : NormedAddGroupHom G H) (x : UniformSpace.Completion G) : f.completion x = UniformSpace.Completion.map (⇑f) x
• UniformSpaceCat.completionFunctor_map 📋 Mathlib.Topology.Category.UniformSpace
  {X✝ Y✝ : UniformSpaceCat} (f : X✝ ⟶ Y✝) : UniformSpaceCat.completionFunctor.map f = UniformSpaceCat.ofHom ⟨UniformSpace.Completion.map ⇑f.hom', ⋯⟩

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