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Result

Found 114 declarations mentioning IsUniformInducing.

• IsUniformInducing 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] (f : α → β) : Prop
• IsUniformEmbedding.isUniformInducing 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformEmbedding f) : IsUniformInducing f
• IsUniformEmbedding.toIsUniformInducing 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] {f : α → β} (self : IsUniformEmbedding f) : IsUniformInducing f
• IsUniformEmbedding.mk 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] {f : α → β} (toIsUniformInducing : IsUniformInducing f) (injective : Function.Injective f) : IsUniformEmbedding f
• isUniformEmbedding_iff 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] (f : α → β) : IsUniformEmbedding f ↔ IsUniformInducing f ∧ Function.Injective f
• IsUniformInducing.comap_uniformity 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] {f : α → β} (self : IsUniformInducing f) : Filter.comap (fun x => (f x.1, f x.2)) (uniformity β) = uniformity α
• IsUniformInducing.mk 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] {f : α → β} (comap_uniformity : Filter.comap (fun x => (f x.1, f x.2)) (uniformity β) = uniformity α) : IsUniformInducing f
• isUniformInducing_iff 📋 Mathlib.Topology.UniformSpace.Defs
  {α : Type ua} {β : Type ub} [UniformSpace α] [UniformSpace β] (f : α → β) : IsUniformInducing f ↔ Filter.comap (fun x => (f x.1, f x.2)) (uniformity β) = uniformity α
• IsUniformInducing.id 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} [UniformSpace α] : IsUniformInducing id
• SeparationQuotient.isUniformInducing_mk 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} [UniformSpace α] : IsUniformInducing SeparationQuotient.mk
• IsUniformInducing.uniformContinuous 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : UniformContinuous f
• IsUniformInducing.comap_uniformSpace 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} : IsUniformInducing f → UniformSpace.comap f inst✝ = inst✝¹
• IsUniformInducing.injective 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] [T0Space α] {f : α → β} (h : IsUniformInducing f) : Function.Injective f
• isUniformInducing_iff_uniformSpace 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} : IsUniformInducing f ↔ UniformSpace.comap f inst✝ = inst✝¹
• IsUniformInducing.completeSpace 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : IsComplete (Set.range f) → CompleteSpace α
• IsUniformInducing.isComplete_range 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} [CompleteSpace α] (hf : IsUniformInducing f) : IsComplete (Set.range f)
• IsUniformInducing.isInducing 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (h : IsUniformInducing f) : Topology.IsInducing f
• completeSpace_iff_isComplete_range 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : CompleteSpace α ↔ IsComplete (Set.range f)
• IsUniformInducing.completeSpace_congr 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) (hsurj : Function.Surjective f) : CompleteSpace α ↔ CompleteSpace β
• IsUniformInducing.isUniformEmbedding 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] [T0Space α] {f : α → β} (hf : IsUniformInducing f) : IsUniformEmbedding f
• isUniformEmbedding_iff_isUniformInducing 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] [T0Space α] {f : α → β} : IsUniformEmbedding f ↔ IsUniformInducing f
• isComplete_of_complete_image 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {m : α → β} {s : Set α} (hm : IsUniformInducing m) : IsComplete (m '' s) → IsComplete s
• totallyBounded_preimage 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} {s : Set β} (hf : IsUniformInducing f) (hs : TotallyBounded s) : TotallyBounded (f ⁻¹' s)
• Filter.totallyBounded_comap 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} {F : Filter β} (hf : IsUniformInducing f) (hF : F.TotallyBounded) : (Filter.comap f F).TotallyBounded
• isComplete_image_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {m : α → β} {s : Set α} (hm : IsUniformInducing m) : IsComplete (m '' s) ↔ IsComplete s
• totallyBounded_image_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} {s : Set α} (hf : IsUniformInducing f) : TotallyBounded (f '' s) ↔ TotallyBounded s
• Filter.totallyBounded_map_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} {F : Filter α} (hf : IsUniformInducing f) : (Filter.map f F).TotallyBounded ↔ F.TotallyBounded
• IsUniformInducing.cauchy_map_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) {F : Filter α} : Cauchy (Filter.map f F) ↔ Cauchy F
• IsUniformInducing.isComplete_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} {s : Set α} (hf : IsUniformInducing f) : IsComplete (f '' s) ↔ IsComplete s
• IsUniformInducing.isDenseInducing 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (h : IsUniformInducing f) (hd : DenseRange f) : IsDenseInducing f
• IsUniformInducing.comp 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {g : β → γ} (hg : IsUniformInducing g) {f : α → β} (hf : IsUniformInducing f) : IsUniformInducing (g ∘ f)
• IsUniformInducing.isUniformInducing_comp_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {g : β → γ} (hg : IsUniformInducing g) {f : α → β} : IsUniformInducing (g ∘ f) ↔ IsUniformInducing f
• IsUniformInducing.of_comp_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {g : β → γ} (hg : IsUniformInducing g) {f : α → β} : IsUniformInducing (g ∘ f) ↔ IsUniformInducing f
• IsUniformInducing.uniformContinuous_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {f : α → β} {g : β → γ} (hg : IsUniformInducing g) : UniformContinuous f ↔ UniformContinuous (g ∘ f)
• IsUniformInducing.uniformContinuousOn_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {f : α → β} {g : β → γ} {S : Set α} (hg : IsUniformInducing g) : UniformContinuousOn f S ↔ UniformContinuousOn (g ∘ f) S
• isUniformInducing_val 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} [UniformSpace α] (s : Set α) : IsUniformInducing Subtype.val
• IsUniformInducing.of_comp 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {f : α → β} {g : β → γ} (hf : UniformContinuous f) (hg : UniformContinuous g) (hgf : IsUniformInducing (g ∘ f)) : IsUniformInducing f
• IsUniformInducing.rangeFactorization 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : IsUniformInducing (Set.rangeFactorization f)
• isUniformInducing_rangeFactorization_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} : IsUniformInducing (Set.rangeFactorization f) ↔ IsUniformInducing f
• completeSpace_extension 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {m : β → α} (hm : IsUniformInducing m) (dense : DenseRange m) (h : ∀ (f : Filter β), Cauchy f → ∃ x, Filter.map m f ≤ nhds x) : CompleteSpace α
• IsUniformInducing.basis_uniformity 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) {ι : Sort u_1} {p : ι → Prop} {s : ι → Set (β × β)} (H : (uniformity β).HasBasis p s) : (uniformity α).HasBasis p fun i => Prod.map f f ⁻¹' s i
• uniformly_extend_exists 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {e : β → α} (h_e : IsUniformInducing e) (h_dense : DenseRange e) {f : β → γ} (h_f : UniformContinuous f) [CompleteSpace γ] (a : α) : ∃ c, Filter.Tendsto f (Filter.comap e (nhds a)) (nhds c)
• isUniformInducing_iff' 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} : IsUniformInducing f ↔ UniformContinuous f ∧ Filter.comap (Prod.map f f) (uniformity β) ≤ uniformity α
• IsUniformInducing.prod 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {α' : Type u_1} {β' : Type u_2} [UniformSpace α'] [UniformSpace β'] {e₁ : α → α'} {e₂ : β → β'} (h₁ : IsUniformInducing e₁) (h₂ : IsUniformInducing e₂) : IsUniformInducing fun p => (e₁ p.1, e₂ p.2)
• IsDenseInducing.isUniformInducing_extend 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {γ : Type u_3} [UniformSpace γ] [CompleteSpace β] [CompleteSpace γ] {i : α → β} {f : α → γ} (hid : IsDenseInducing i) (hi : IsUniformInducing i) (h : IsUniformInducing f) : IsUniformInducing (hid.extend f)
• uniformContinuous_uniformly_extend 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {e : β → α} (h_e : IsUniformInducing e) (h_dense : DenseRange e) {f : β → γ} (h_f : UniformContinuous f) [CompleteSpace γ] : UniformContinuous (⋯.extend f)
• uniformly_extend_of_ind 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {e : β → α} (h_e : IsUniformInducing e) (h_dense : DenseRange e) {f : β → γ} (h_f : UniformContinuous f) [T0Space γ] (b : β) : ⋯.extend f (e b) = f b
• uniformly_extend_unique 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {e : β → α} (h_e : IsUniformInducing e) (h_dense : DenseRange e) {f : β → γ} [T0Space γ] {g : α → γ} (hg : ∀ (b : β), g (e b) = f b) (hc : Continuous g) : ⋯.extend f = g
• uniformly_extend_spec 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [UniformSpace α] [UniformSpace β] [UniformSpace γ] {e : β → α} (h_e : IsUniformInducing e) (h_dense : DenseRange e) {f : β → γ} (h_f : UniformContinuous f) [CompleteSpace γ] (a : α) : Filter.Tendsto f (Filter.comap e (nhds a)) (nhds (⋯.extend f a))
• closure_image_mem_nhds_of_isUniformInducing 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {s : Set (α × α)} {e : α → β} (b : β) (he₁ : IsUniformInducing e) (he₂ : IsDenseInducing e) (hs : s ∈ uniformity α) : ∃ a, closure (e '' {a' | (a, a') ∈ s}) ∈ nhds b
• IsUniformInducing.mk' 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {f : α → β} (h : ∀ (s : Set (α × α)), s ∈ uniformity α ↔ ∃ t ∈ uniformity β, ∀ (x y : α), (f x, f y) ∈ t → (x, y) ∈ s) : IsUniformInducing f
• Filter.HasBasis.isUniformInducing_iff 📋 Mathlib.Topology.UniformSpace.UniformEmbedding
  {α : Type u} {β : Type v} [UniformSpace α] [UniformSpace β] {ι : Sort u_1} {ι' : Sort u_2} {p : ι → Prop} {p' : ι' → Prop} {s : ι → Set (α × α)} {s' : ι' → Set (β × β)} (h : (uniformity α).HasBasis p s) (h' : (uniformity β).HasBasis p' s') {f : α → β} : IsUniformInducing f ↔ (∀ (i : ι'), p' i → ∃ j, p j ∧ ∀ (x y : α), (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧ ∀ (j : ι), p j → ∃ i, p' i ∧ ∀ (x y : α), (f x, f y) ∈ s' i → (x, y) ∈ s j
• Equiv.toUniformEquivOfIsUniformInducing 📋 Mathlib.Topology.UniformSpace.Equiv
  {α : Type u} {β : Type u_1} [UniformSpace α] [UniformSpace β] (f : α ≃ β) (hf : IsUniformInducing ⇑f) : α ≃ᵤ β
• UniformEquiv.isUniformInducing 📋 Mathlib.Topology.UniformSpace.Equiv
  {α : Type u} {β : Type u_1} [UniformSpace α] [UniformSpace β] (h : α ≃ᵤ β) : IsUniformInducing ⇑h
• UniformFun.postcomp_isUniformInducing 📋 Mathlib.Topology.UniformSpace.UniformConvergenceTopology
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [UniformSpace β] [UniformSpace γ] {f : γ → β} (hf : IsUniformInducing f) : IsUniformInducing (⇑UniformFun.ofFun ∘ (fun x => f ∘ x) ∘ ⇑UniformFun.toFun)
• UniformOnFun.postcomp_isUniformInducing 📋 Mathlib.Topology.UniformSpace.UniformConvergenceTopology
  {α : Type u_1} {β : Type u_2} {γ : Type u_3} [UniformSpace β] {𝔖 : Set (Set α)} [UniformSpace γ] {f : γ → β} (hf : IsUniformInducing f) : IsUniformInducing (⇑(UniformOnFun.ofFun 𝔖) ∘ (fun x => f ∘ x) ∘ ⇑(UniformOnFun.toFun 𝔖))
• UniformOnFun.isUniformInducing_pi_restrict 📋 Mathlib.Topology.UniformSpace.UniformConvergenceTopology
  {α : Type u_1} {β : Type u_2} [UniformSpace β] {𝔖 : Set (Set α)} : IsUniformInducing fun f s => UniformFun.ofFun ((↑s).domRestrict ((UniformOnFun.toFun 𝔖) f))
• IsUniformInducing.equicontinuous_iff 📋 Mathlib.Topology.UniformSpace.Equicontinuity
  {ι : Type u_1} {X : Type u_3} {α : Type u_6} {β : Type u_8} [tX : TopologicalSpace X] [uα : UniformSpace α] [uβ : UniformSpace β] {F : ι → X → α} {u : α → β} (hu : IsUniformInducing u) : Equicontinuous F ↔ Equicontinuous ((fun x => u ∘ x) ∘ F)
• IsUniformInducing.uniformEquicontinuous_iff 📋 Mathlib.Topology.UniformSpace.Equicontinuity
  {ι : Type u_1} {α : Type u_6} {β : Type u_8} {γ : Type u_10} [uα : UniformSpace α] [uβ : UniformSpace β] [uγ : UniformSpace γ] {F : ι → β → α} {u : α → γ} (hu : IsUniformInducing u) : UniformEquicontinuous F ↔ UniformEquicontinuous ((fun x => u ∘ x) ∘ F)
• IsUniformInducing.equicontinuousAt_iff 📋 Mathlib.Topology.UniformSpace.Equicontinuity
  {ι : Type u_1} {X : Type u_3} {α : Type u_6} {β : Type u_8} [tX : TopologicalSpace X] [uα : UniformSpace α] [uβ : UniformSpace β] {F : ι → X → α} {x₀ : X} {u : α → β} (hu : IsUniformInducing u) : EquicontinuousAt F x₀ ↔ EquicontinuousAt ((fun x => u ∘ x) ∘ F) x₀
• IsUniformInducing.equicontinuousOn_iff 📋 Mathlib.Topology.UniformSpace.Equicontinuity
  {ι : Type u_1} {X : Type u_3} {α : Type u_6} {β : Type u_8} [tX : TopologicalSpace X] [uα : UniformSpace α] [uβ : UniformSpace β] {F : ι → X → α} {S : Set X} {u : α → β} (hu : IsUniformInducing u) : EquicontinuousOn F S ↔ EquicontinuousOn ((fun x => u ∘ x) ∘ F) S
• IsUniformInducing.uniformEquicontinuousOn_iff 📋 Mathlib.Topology.UniformSpace.Equicontinuity
  {ι : Type u_1} {α : Type u_6} {β : Type u_8} {γ : Type u_10} [uα : UniformSpace α] [uβ : UniformSpace β] [uγ : UniformSpace γ] {F : ι → β → α} {S : Set β} {u : α → γ} (hu : IsUniformInducing u) : UniformEquicontinuousOn F S ↔ UniformEquicontinuousOn ((fun x => u ∘ x) ∘ F) S
• IsUniformInducing.equicontinuousWithinAt_iff 📋 Mathlib.Topology.UniformSpace.Equicontinuity
  {ι : Type u_1} {X : Type u_3} {α : Type u_6} {β : Type u_8} [tX : TopologicalSpace X] [uα : UniformSpace α] [uβ : UniformSpace β] {F : ι → X → α} {S : Set X} {x₀ : X} {u : α → β} (hu : IsUniformInducing u) : EquicontinuousWithinAt F S x₀ ↔ EquicontinuousWithinAt ((fun x => u ∘ x) ∘ F) S x₀
• AddMonoidHom.isUniformInducing_of_isInducing 📋 Mathlib.Topology.Algebra.IsUniformGroup.Defs
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [AddGroup α] [IsUniformAddGroup α] {Hom : Type u_3} [UniformSpace β] [AddGroup β] [IsUniformAddGroup β] [FunLike Hom α β] [AddMonoidHomClass Hom α β] {f : Hom} (h : Topology.IsInducing ⇑f) : IsUniformInducing ⇑f
• MonoidHom.isUniformInducing_of_isInducing 📋 Mathlib.Topology.Algebra.IsUniformGroup.Defs
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [Group α] [IsUniformGroup α] {Hom : Type u_3} [UniformSpace β] [Group β] [IsUniformGroup β] [FunLike Hom α β] [MonoidHomClass Hom α β] {f : Hom} (h : Topology.IsInducing ⇑f) : IsUniformInducing ⇑f
• IsUniformInducing.isUniformAddGroup 📋 Mathlib.Topology.Algebra.IsUniformGroup.Constructions
  {G : Type u_1} {H : Type u_2} {hom : Type u_3} [AddGroup G] [AddGroup H] [UniformSpace G] [UniformSpace H] [IsUniformAddGroup H] [FunLike hom G H] [AddMonoidHomClass hom G H] (f : hom) (hf : IsUniformInducing ⇑f) : IsUniformAddGroup G
• IsUniformInducing.isUniformGroup 📋 Mathlib.Topology.Algebra.IsUniformGroup.Constructions
  {G : Type u_1} {H : Type u_2} {hom : Type u_3} [Group G] [Group H] [UniformSpace G] [UniformSpace H] [IsUniformGroup H] [FunLike hom G H] [MonoidHomClass hom G H] (f : hom) (hf : IsUniformInducing ⇑f) : IsUniformGroup G
• EMetric.isUniformInducing_iff 📋 Mathlib.Topology.EMetricSpace.Basic
  {γ : Type u} {β : Type v} [PseudoEMetricSpace γ] [PseudoEMetricSpace β] {f : γ → β} : IsUniformInducing f ↔ UniformContinuous f ∧ ∀ δ > 0, ∃ ε > 0, ∀ {a b : γ}, edist (f a) (f b) < ε → edist a b < δ
• EMetric.controlled_of_isUniformInducing 📋 Mathlib.Topology.EMetricSpace.Basic
  {γ : Type u} {β : Type v} [PseudoEMetricSpace γ] [PseudoEMetricSpace β] {f : γ → β} (h : IsUniformInducing f) : (∀ ε > 0, ∃ δ > 0, ∀ {a b : γ}, edist a b < δ → edist (f a) (f b) < ε) ∧ ∀ δ > 0, ∃ ε > 0, ∀ {a b : γ}, edist (f a) (f b) < ε → edist a b < δ
• Metric.isUniformInducing_iff 📋 Mathlib.Topology.MetricSpace.Pseudo.Basic
  {α : Type u} {β : Type v} [PseudoMetricSpace α] [PseudoMetricSpace β] {f : α → β} : IsUniformInducing f ↔ UniformContinuous f ∧ ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, dist (f a) (f b) < ε → dist a b < δ
• Metric.controlled_of_isUniformInducing 📋 Mathlib.Topology.MetricSpace.Pseudo.Basic
  {α : Type u} {β : Type v} [PseudoMetricSpace α] [PseudoMetricSpace β] {f : α → β} (h : IsUniformInducing f) : (∀ ε > 0, ∃ δ > 0, ∀ {a b : α}, dist a b < δ → dist (f a) (f b) < ε) ∧ ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, dist (f a) (f b) < ε → dist a b < δ
• IsUniformInducing.comapPseudoMetricSpace 📋 Mathlib.Topology.MetricSpace.Pseudo.Constructions
  {α : Type u_3} {β : Type u_4} [UniformSpace α] [m : PseudoMetricSpace β] (f : α → β) (h : IsUniformInducing f) : PseudoMetricSpace α
• AntilipschitzWith.isUniformInducing 📋 Mathlib.Topology.MetricSpace.Antilipschitz
  {α : Type u_1} {β : Type u_2} [PseudoEMetricSpace α] [PseudoEMetricSpace β] {K : NNReal} {f : α → β} (hf : AntilipschitzWith K f) (hfc : UniformContinuous f) : IsUniformInducing f
• Isometry.isUniformInducing 📋 Mathlib.Topology.MetricSpace.Isometry
  {α : Type u} {β : Type v} [PseudoEMetricSpace α] [PseudoEMetricSpace β] {f : α → β} (hf : Isometry f) : IsUniformInducing f
• AbstractCompletion.isUniformInducing 📋 Mathlib.Topology.UniformSpace.AbstractCompletion
  {α : Type u} [UniformSpace α] (self : AbstractCompletion.{v, u} α) : IsUniformInducing self.coe
• AbstractCompletion.mk 📋 Mathlib.Topology.UniformSpace.AbstractCompletion
  {α : Type u} [UniformSpace α] (space : Type v) (coe : α → space) (uniformStruct : UniformSpace space) (complete : CompleteSpace space) (separation : T0Space space) (isUniformInducing : IsUniformInducing coe) (dense : DenseRange coe) : AbstractCompletion.{v, u} α
• AbstractCompletion.isUniformInducing_extend 📋 Mathlib.Topology.UniformSpace.AbstractCompletion
  {α : Type uα} [UniformSpace α] (pkg : AbstractCompletion.{vα, uα} α) {β : Type uβ} [UniformSpace β] {f : α → β} [CompleteSpace β] (h : IsUniformInducing f) : IsUniformInducing (pkg.extend f)
• CauchyFilter.isUniformInducing_pureCauchy 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u} [UniformSpace α] : IsUniformInducing CauchyFilter.pureCauchy
• UniformSpace.Completion.isUniformInducing_coe 📋 Mathlib.Topology.UniformSpace.Completion
  (α : Type u_1) [UniformSpace α] : IsUniformInducing UniformSpace.Completion.coe'
• UniformSpace.Completion.isUniformInducing_extension 📋 Mathlib.Topology.UniformSpace.Completion
  {α : Type u_1} [UniformSpace α] {β : Type u_2} [UniformSpace β] {f : α → β} [CompleteSpace β] (h : IsUniformInducing f) : IsUniformInducing (UniformSpace.Completion.extension f)
• IsUniformInducing.uniformContinuousConstSMul 📋 Mathlib.Topology.Algebra.UniformMulAction
  {M : Type v} {X : Type x} {Y : Type y} [UniformSpace X] [UniformSpace Y] [SMul M X] [SMul M Y] [UniformContinuousConstSMul M Y] {f : X → Y} (hf : IsUniformInducing f) (hsmul : ∀ (c : M) (x : X), f (c • x) = c • f x) : UniformContinuousConstSMul M X
• IsUniformInducing.uniformContinuousConstVAdd 📋 Mathlib.Topology.Algebra.UniformMulAction
  {M : Type v} {X : Type x} {Y : Type y} [UniformSpace X] [UniformSpace Y] [VAdd M X] [VAdd M Y] [UniformContinuousConstVAdd M Y] {f : X → Y} (hf : IsUniformInducing f) (hvadd : ∀ (c : M) (x : X), f (c +ᵥ x) = c +ᵥ f x) : UniformContinuousConstVAdd M X
• Dilation.isUniformInducing 📋 Mathlib.Topology.MetricSpace.Dilation
  {α : Type u_1} {β : Type u_2} {F : Type u_4} [PseudoEMetricSpace α] [PseudoEMetricSpace β] [FunLike F α β] [DilationClass F α β] (f : F) : IsUniformInducing ⇑f
• SeparationQuotient.outCLM_isUniformInducing 📋 Mathlib.Topology.Algebra.SeparationQuotient.Section
  (K : Type u_1) (E : Type u_2) [DivisionRing K] [AddCommGroup E] [Module K E] [UniformSpace E] [IsUniformAddGroup E] [ContinuousConstSMul K E] : IsUniformInducing ⇑(SeparationQuotient.outCLM K E)
• UniformConvergenceCLM.isUniformInducing_coeFn 📋 Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM
  {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} [NormedField 𝕜₁] [NormedField 𝕜₂] (σ : 𝕜₁ →+* 𝕜₂) {E : Type u_3} (F : Type u_4) [AddCommGroup E] [Module 𝕜₁ E] [TopologicalSpace E] [AddCommGroup F] [Module 𝕜₂ F] [UniformSpace F] [IsUniformAddGroup F] (𝔖 : Set (Set E)) : IsUniformInducing (⇑(UniformOnFun.ofFun 𝔖) ∘ DFunLike.coe)
• UniformConvergenceCLM.isUniformInducing_postcomp 📋 Mathlib.Topology.Algebra.Module.Spaces.UniformConvergenceCLM
  {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} [NormedField 𝕜₁] [NormedField 𝕜₂] (σ : 𝕜₁ →+* 𝕜₂) {E : Type u_3} {F : Type u_4} {G : Type u_5} [AddCommGroup E] [Module 𝕜₁ E] [TopologicalSpace E] [AddCommGroup F] [Module 𝕜₂ F] [AddCommGroup G] [UniformSpace G] [IsUniformAddGroup G] {𝕜₃ : Type u_6} [NormedField 𝕜₃] [Module 𝕜₃ G] {τ : 𝕜₂ →+* 𝕜₃} {ρ : 𝕜₁ →+* 𝕜₃} [RingHomCompTriple σ τ ρ] [UniformSpace F] [IsUniformAddGroup F] (g : F →SL[τ] G) (hg : IsUniformInducing ⇑g) (𝔖 : Set (Set E)) : IsUniformInducing g.comp
• ContinuousLinearMap.isUniformInducing_postcomp 📋 Mathlib.Topology.Algebra.Module.Spaces.ContinuousLinearMap
  {𝕜₁ : Type u_1} {𝕜₂ : Type u_2} {𝕜₃ : Type u_3} [NormedField 𝕜₁] [NormedField 𝕜₂] [NormedField 𝕜₃] {σ : 𝕜₁ →+* 𝕜₂} {τ : 𝕜₂ →+* 𝕜₃} {ρ : 𝕜₁ →+* 𝕜₃} [RingHomCompTriple σ τ ρ] {E : Type u_4} {F : Type u_5} {G : Type u_6} [AddCommGroup E] [Module 𝕜₁ E] [AddCommGroup F] [Module 𝕜₂ F] [AddCommGroup G] [Module 𝕜₃ G] [TopologicalSpace E] [UniformSpace F] [IsUniformAddGroup F] [UniformSpace G] [IsUniformAddGroup G] (f : F →SL[τ] G) (hf : IsUniformInducing ⇑f) : IsUniformInducing f.comp
• ContinuousMap.isUniformInducing_comp 📋 Mathlib.Topology.UniformSpace.CompactConvergence
  {α : Type u₁} {β : Type u₂} [TopologicalSpace α] [UniformSpace β] {δ : Type u_2} [UniformSpace δ] (g : C(β, δ)) (hg : IsUniformInducing ⇑g) : IsUniformInducing g.comp
• ContinuousMultilinearMap.isUniformInducing_postcomp 📋 Mathlib.Topology.Algebra.Module.Multilinear.Topology
  {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} {F : Type u_4} [NormedField 𝕜] [(i : ι) → TopologicalSpace (E i)] [(i : ι) → AddCommGroup (E i)] [(i : ι) → Module 𝕜 (E i)] [AddCommGroup F] [Module 𝕜 F] [UniformSpace F] [IsUniformAddGroup F] {G : Type u_5} [AddCommGroup G] [UniformSpace G] [IsUniformAddGroup G] [Module 𝕜 G] (g : F →L[𝕜] G) (hg : IsUniformInducing ⇑g) : IsUniformInducing g.compContinuousMultilinearMap
• ContinuousMultilinearMap.isUniformInducing_toUniformOnFun 📋 Mathlib.Topology.Algebra.Module.Multilinear.Topology
  {𝕜 : Type u_1} {ι : Type u_2} {E : ι → Type u_3} {F : Type u_4} [NormedField 𝕜] [(i : ι) → TopologicalSpace (E i)] [(i : ι) → AddCommGroup (E i)] [(i : ι) → Module 𝕜 (E i)] [AddCommGroup F] [Module 𝕜 F] [UniformSpace F] [IsUniformAddGroup F] : IsUniformInducing ContinuousMultilinearMap.toUniformOnFun
• IsDenseInducing.extendRingHom 📋 Mathlib.Topology.Algebra.UniformRing
  {α : Type u_1} [UniformSpace α] [Semiring α] {β : Type u_2} [UniformSpace β] [Semiring β] [IsTopologicalSemiring β] {γ : Type u_3} [UniformSpace γ] [Semiring γ] [IsTopologicalSemiring γ] [T2Space γ] [CompleteSpace γ] {i : α →+* β} {f : α →+* γ} (ue : IsUniformInducing ⇑i) (dr : DenseRange ⇑i) (hf : UniformContinuous ⇑f) : β →+* γ
• ContinuousLinearMap.extend_unique 📋 Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Extend
  {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_3} {F : Type u_4} {Eₗ : Type u_5} [AddCommGroup E] [UniformSpace E] [IsUniformAddGroup E] [AddCommGroup F] [UniformSpace F] [IsUniformAddGroup F] [T0Space F] [AddCommMonoid Eₗ] [UniformSpace Eₗ] [ContinuousAdd Eₗ] [Semiring 𝕜] [Semiring 𝕜₂] [Module 𝕜 E] [Module 𝕜₂ F] [Module 𝕜 Eₗ] [ContinuousConstSMul 𝕜 Eₗ] [ContinuousConstSMul 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} (f : E →SL[σ₁₂] F) [CompleteSpace F] {e : E →L[𝕜] Eₗ} (h_dense : DenseRange ⇑e) (h_e : IsUniformInducing ⇑e) (g : Eₗ →SL[σ₁₂] F) (H : g ∘SL e = f) : f.extend e = g
• ContinuousLinearMap.extend_zero 📋 Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Extend
  {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_3} {F : Type u_4} {Eₗ : Type u_5} [AddCommGroup E] [UniformSpace E] [IsUniformAddGroup E] [AddCommGroup F] [UniformSpace F] [IsUniformAddGroup F] [T0Space F] [AddCommMonoid Eₗ] [UniformSpace Eₗ] [ContinuousAdd Eₗ] [Semiring 𝕜] [Semiring 𝕜₂] [Module 𝕜 E] [Module 𝕜₂ F] [Module 𝕜 Eₗ] [ContinuousConstSMul 𝕜 Eₗ] [ContinuousConstSMul 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} [CompleteSpace F] {e : E →L[𝕜] Eₗ} (h_dense : DenseRange ⇑e) (h_e : IsUniformInducing ⇑e) : ContinuousLinearMap.extend 0 e = 0
• ContinuousLinearMap.extend_eq 📋 Mathlib.Topology.Algebra.Module.ContinuousLinearMap.Extend
  {𝕜 : Type u_1} {𝕜₂ : Type u_2} {E : Type u_3} {F : Type u_4} {Eₗ : Type u_5} [AddCommGroup E] [UniformSpace E] [IsUniformAddGroup E] [AddCommGroup F] [UniformSpace F] [IsUniformAddGroup F] [T0Space F] [AddCommMonoid Eₗ] [UniformSpace Eₗ] [ContinuousAdd Eₗ] [Semiring 𝕜] [Semiring 𝕜₂] [Module 𝕜 E] [Module 𝕜₂ F] [Module 𝕜 Eₗ] [ContinuousConstSMul 𝕜 Eₗ] [ContinuousConstSMul 𝕜₂ F] {σ₁₂ : 𝕜 →+* 𝕜₂} (f : E →SL[σ₁₂] F) [CompleteSpace F] {e : E →L[𝕜] Eₗ} (h_dense : DenseRange ⇑e) (h_e : IsUniformInducing ⇑e) (x : E) : (f.extend e) (e x) = f x
• MeasureTheory.Lp.simpleFunc.isUniformInducing 📋 Mathlib.MeasureTheory.Function.SimpleFuncDenseLp
  {α : Type u_1} {E : Type u_4} [MeasurableSpace α] [NormedAddCommGroup E] {p : ENNReal} {μ : MeasureTheory.Measure α} [Fact (1 ≤ p)] : IsUniformInducing Subtype.val
• ContinuousMap.isUniformInducing_equivBoundedOfCompact 📋 Mathlib.Topology.ContinuousMap.Compact
  (α : Type u_1) (β : Type u_2) [TopologicalSpace α] [CompactSpace α] [PseudoMetricSpace β] : IsUniformInducing ⇑(ContinuousMap.equivBoundedOfCompact α β)
• WithLp.isUniformInducing_toLp 📋 Mathlib.Analysis.Normed.Lp.ProdLp
  (p : ENNReal) (α : Type u_2) (β : Type u_3) [hp : Fact (1 ≤ p)] [PseudoEMetricSpace α] [PseudoEMetricSpace β] : IsUniformInducing (WithLp.toLp p)
• PiLp.isUniformInducing_toLp 📋 Mathlib.Analysis.Normed.Lp.PiLp
  (p : ENNReal) {ι : Type u_2} (β : ι → Type u_4) [hp : Fact (1 ≤ p)] [Finite ι] [(i : ι) → PseudoEMetricSpace (β i)] : IsUniformInducing (WithLp.toLp p)
• IsUniformInducing.completableTopField 📋 Mathlib.Topology.Algebra.UniformField
  {α : Type u_3} {β : Type u_4} [Field β] [b : UniformSpace β] [CompletableTopField β] [Field α] [UniformSpace α] [T0Space α] {f : α →+* β} (hf : IsUniformInducing ⇑f) : CompletableTopField α
• IsDedekindDomain.HeightOneSpectrum.adicCompletion.isUniformInducing_toCompletion 📋 Mathlib.RingTheory.DedekindDomain.AdicValuation
  {R : Type u_1} [CommRing R] [IsDedekindDomain R] (K : Type u_2) [Field K] [Algebra R K] [IsFractionRing R K] (v : IsDedekindDomain.HeightOneSpectrum R) : IsUniformInducing IsDedekindDomain.HeightOneSpectrum.adicCompletion.toCompletion
• MvPolynomial.toMvPowerSeries_isUniformInducing 📋 Mathlib.RingTheory.MvPowerSeries.Evaluation
  {σ : Type u_1} {R : Type u_2} [CommRing R] [UniformSpace R] : IsUniformInducing MvPolynomial.toMvPowerSeries
• ContinuousAlternatingMap.isUniformInducing_postcomp 📋 Mathlib.Topology.Algebra.Module.Alternating.Topology
  {𝕜 : Type u_1} {E : Type u_2} {F : Type u_3} {ι : Type u_4} [NormedField 𝕜] [AddCommGroup E] [Module 𝕜 E] [TopologicalSpace E] [AddCommGroup F] [Module 𝕜 F] [UniformSpace F] [IsUniformAddGroup F] {G : Type u_5} [AddCommGroup G] [UniformSpace G] [IsUniformAddGroup G] [Module 𝕜 G] (g : F →L[𝕜] G) (hg : IsUniformInducing ⇑g) : IsUniformInducing g.compContinuousAlternatingMap
• UniformSpace.hausdorff.isUniformInducing_closure 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} [UniformSpace α] : IsUniformInducing closure
• TopologicalSpace.Closeds.isUniformInducing_closure 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} [UniformSpace α] : IsUniformInducing TopologicalSpace.Closeds.closure
• IsUniformInducing.image_hausdorff 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : IsUniformInducing fun x => f '' x
• IsUniformInducing.compacts_map 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : IsUniformInducing (TopologicalSpace.Compacts.map f ⋯)
• IsUniformInducing.nonemptyCompacts_map 📋 Mathlib.Topology.UniformSpace.Closeds
  {α : Type u_1} {β : Type u_2} [UniformSpace α] [UniformSpace β] {f : α → β} (hf : IsUniformInducing f) : IsUniformInducing (TopologicalSpace.NonemptyCompacts.map f ⋯)
• ODE.FunSpace.isUniformInducing_toContinuousMap 📋 Mathlib.Analysis.ODE.PicardLindelof
  {E : Type u_1} [NormedAddCommGroup E] {tmin tmax : ℝ} {t₀ : ↑(Set.Icc tmin tmax)} {x₀ : E} {r L : NNReal} : IsUniformInducing fun α => ODE.FunSpace.toContinuousMap α
• Padic.isUniformInducing_cast_withVal 📋 Mathlib.NumberTheory.Padics.WithVal
  {p : ℕ} [Fact (Nat.Prime p)] : IsUniformInducing ⇑((Rat.castHom ℚ_[p]).comp (WithVal.equiv (Rat.padicValuation p)).toRingHom)
• LaurentSeries.inducing_coe 📋 Mathlib.RingTheory.LaurentSeries
  {K : Type u_2} [Field K] : IsUniformInducing ⇑(algebraMap (RatFunc K) (LaurentSeries K))
• Equicontinuous.isUniformInducing_uniformFun_iff_pi 📋 Mathlib.Topology.UniformSpace.Ascoli
  {ι : Type u_1} {X : Type u_2} {α : Type u_3} [TopologicalSpace X] [UniformSpace α] {F : ι → X → α} [UniformSpace ι] [CompactSpace X] (F_eqcont : Equicontinuous F) : IsUniformInducing (⇑UniformFun.ofFun ∘ F) ↔ IsUniformInducing F
• EquicontinuousOn.isUniformInducing_uniformOnFun_iff_pi 📋 Mathlib.Topology.UniformSpace.Ascoli
  {ι : Type u_1} {X : Type u_2} {α : Type u_3} [TopologicalSpace X] [UniformSpace α] {F : ι → X → α} [UniformSpace ι] {𝔖 : Set (Set X)} (𝔖_covers : ⋃₀ 𝔖 = Set.univ) (𝔖_compact : ∀ K ∈ 𝔖, IsCompact K) (F_eqcont : ∀ K ∈ 𝔖, EquicontinuousOn F K) : IsUniformInducing (⇑(UniformOnFun.ofFun 𝔖) ∘ F) ↔ IsUniformInducing F
• EquicontinuousOn.isUniformInducing_uniformOnFun_iff_pi' 📋 Mathlib.Topology.UniformSpace.Ascoli
  {ι : Type u_1} {X : Type u_2} {α : Type u_3} [TopologicalSpace X] [UniformSpace α] {F : ι → X → α} [UniformSpace ι] {𝔖 : Set (Set X)} (𝔖_compact : ∀ K ∈ 𝔖, IsCompact K) (F_eqcont : ∀ K ∈ 𝔖, EquicontinuousOn F K) : IsUniformInducing (⇑(UniformOnFun.ofFun 𝔖) ∘ F) ↔ IsUniformInducing ((⋃₀ 𝔖).domRestrict ∘ F)
• IsUniformInducing.isUltraUniformity 📋 Mathlib.Topology.UniformSpace.Ultra.Completion
  {X : Type u_1} {Y : Type u_2} [UniformSpace X] [UniformSpace Y] [IsUltraUniformity Y] {f : X → Y} (hf : IsUniformInducing f) : IsUltraUniformity X

About

Loogle searches Lean and Mathlib definitions and theorems.

You can use Loogle from within the Lean4 VSCode language extension using the Loogle command from the command palette. 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.

5. You can filter for definitions vs theorems: Using ⊢ (_ : Type _) finds all definitions which provide data while ⊢ (_ : Prop) finds all theorems (and definitions of proofs).

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. Please review the Lean FRO Terms of Use and Privacy Policy.

This is Loogle revision 9f11169 serving mathlib revision ce5dd8c