topology.uniform_space.uniform_embedding

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

195fcd60

(last sync)

refactor(topology/uniform_space/basic): review API (#18516)

API about uniform embeddings

Add mk_iff to uniform_inducing and uniform_embedding.
Move lemmas about uniform_inducing up.
Add uniform_inducing.comap_uniform_space, uniform_inducing_iff', and filter.has_basis.uniform_inducing_iff.
Add uniform_embedding_iff', filter.has_basis.uniform_embedding_iff', and filter.has_basis.uniform_embedding_iff.
Drop uniform_embedding_def and uniform_embedding_def'.
Add uniform_embedding_iff_uniform_inducing.

Other changes

Add rescale_to_shell_semi_normed_zpow and rescale_to_shell_zpow.
Generalize continuous_linear_map.antilipschitz_of_uniform_embedding to continuous_linear_map.antilipschitz_of_embedding, add an even more general version linear_map.antilipschitz_of_comap_nhds_le.
Use fully_applied := ff to generate equiv.prod_congr_apply.
Use edist := λ _ _, 0 in metric_space instances for empty and punit.
Add inducing.injective, inducing.embedding, and embedding_iff_inducing
Allow Sort*s in filter.has_basis.uniform_continuous_iff and filter.has_basis.uniform_continuous_on_iff.
Rename
- metric.of_t0_pseudo_metric_space to metric_space.of_t0_pseudo_metric_space;
- emetric.of_t0_pseudo_emetric_space to emetric_space.of_t0_pseudo_emetric_space;
- metric.metric_space.to_emetric_space to metric_space.to_emetric_space;
- uniform_embedding_iff' to emetric.uniform_embedding_iff'

Diff

@@ -16,7 +16,7 @@ import topology.dense_embedding
 Extension of uniform continuous functions.
 -/
 
-open filter topological_space set classical
+open filter topological_space set function classical
 open_locale classical uniformity topology filter
 
 section
@@ -24,12 +24,33 @@ variables {α : Type*} {β : Type*} {γ : Type*}
           [uniform_space α] [uniform_space β] [uniform_space γ]
 universes u v
 
+/-!
+### Uniform inducing maps
+-/
+
 /-- A map `f : α → β` between uniform spaces is called *uniform inducing* if the uniformity filter
 on `α` is the pullback of the uniformity filter on `β` under `prod.map f f`. If `α` is a separated
 space, then this implies that `f` is injective, hence it is a `uniform_embedding`. -/
+@[mk_iff]
 structure uniform_inducing (f : α → β) : Prop :=
 (comap_uniformity : comap (λx:α×α, (f x.1, f x.2)) (𝓤 β) = 𝓤 α)
 
+protected lemma uniform_inducing.comap_uniform_space {f : α → β} (hf : uniform_inducing f) :
+  ‹uniform_space β›.comap f = ‹uniform_space α› :=
+uniform_space_eq hf.1
+
+lemma uniform_inducing_iff' {f : α → β} :
+  uniform_inducing f ↔ uniform_continuous f ∧ comap (prod.map f f) (𝓤 β) ≤ 𝓤 α :=
+by rw [uniform_inducing_iff, uniform_continuous, tendsto_iff_comap, le_antisymm_iff, and_comm]; refl
+
+protected lemma filter.has_basis.uniform_inducing_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+  (h : (𝓤 α).has_basis p s) (h' : (𝓤 β).has_basis p' s') {f : α → β} :
+  uniform_inducing f ↔
+    (∀ i, p' i → ∃ j, p j ∧ ∀ x y, (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧
+      (∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j) :=
+by simp [uniform_inducing_iff', h.uniform_continuous_iff h', (h'.comap _).le_basis_iff h,
+  subset_def]
+
 lemma uniform_inducing.mk' {f : α → β} (h : ∀ s, s ∈ 𝓤 α ↔
     ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s) : uniform_inducing f :=
 ⟨by simp [eq_comm, filter.ext_iff, subset_def, h]⟩
@@ -39,9 +60,7 @@ lemma uniform_inducing_id : uniform_inducing (@id α) :=
 
 lemma uniform_inducing.comp {g : β → γ} (hg : uniform_inducing g)
   {f : α → β} (hf : uniform_inducing f) : uniform_inducing (g ∘ f) :=
-⟨ by rw [show (λ (x : α × α), ((g ∘ f) x.1, (g ∘ f) x.2)) =
-         (λ y : β × β, (g y.1, g y.2)) ∘ (λ x : α × α, (f x.1, f x.2)), by ext ; simp,
-        ← filter.comap_comap, hg.1, hf.1]⟩
+⟨by rw [← hf.1, ← hg.1, comap_comap]⟩
 
 lemma uniform_inducing.basis_uniformity {f : α → β} (hf : uniform_inducing f)
   {ι : Sort*} {p : ι → Prop} {s : ι → set (β × β)} (H : (𝓤 β).has_basis p s) :
@@ -61,11 +80,60 @@ begin
   exact comap_mono hg.le_comap
 end
 
+lemma uniform_inducing.uniform_continuous {f : α → β}
+  (hf : uniform_inducing f) : uniform_continuous f :=
+(uniform_inducing_iff'.1 hf).1
+
+lemma uniform_inducing.uniform_continuous_iff {f : α → β} {g : β → γ} (hg : uniform_inducing g) :
+  uniform_continuous f ↔ uniform_continuous (g ∘ f) :=
+by { dsimp only [uniform_continuous, tendsto],
+  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, filter.map_map] }
+
+protected lemma uniform_inducing.inducing {f : α → β} (h : uniform_inducing f) : inducing f :=
+begin
+  unfreezingI { obtain rfl := h.comap_uniform_space },
+  letI := uniform_space.comap f _,
+  exact ⟨rfl⟩
+end
+
+lemma uniform_inducing.prod {α' : Type*} {β' : Type*} [uniform_space α'] [uniform_space β']
+  {e₁ : α → α'} {e₂ : β → β'} (h₁ : uniform_inducing e₁) (h₂ : uniform_inducing e₂) :
+  uniform_inducing (λp:α×β, (e₁ p.1, e₂ p.2)) :=
+⟨by simp [(∘), uniformity_prod, h₁.comap_uniformity.symm, h₂.comap_uniformity.symm,
+           comap_inf, comap_comap]⟩
+
+lemma uniform_inducing.dense_inducing {f : α → β} (h : uniform_inducing f) (hd : dense_range f) :
+  dense_inducing f :=
+{ dense   := hd,
+  induced := h.inducing.induced }
+
+protected lemma uniform_inducing.injective [t0_space α] {f : α → β} (h : uniform_inducing f) :
+  injective f :=
+h.inducing.injective
+
 /-- A map `f : α → β` between uniform spaces is a *uniform embedding* if it is uniform inducing and
 injective. If `α` is a separated space, then the latter assumption follows from the former. -/
+@[mk_iff]
 structure uniform_embedding (f : α → β) extends uniform_inducing f : Prop :=
 (inj : function.injective f)
 
+theorem uniform_embedding_iff' {f : α → β} :
+  uniform_embedding f ↔ injective f ∧ uniform_continuous f ∧ comap (prod.map f f) (𝓤 β) ≤ 𝓤 α :=
+by rw [uniform_embedding_iff, and_comm, uniform_inducing_iff']
+
+theorem filter.has_basis.uniform_embedding_iff' {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+  (h : (𝓤 α).has_basis p s) (h' : (𝓤 β).has_basis p' s') {f : α → β} :
+  uniform_embedding f ↔ injective f ∧
+    (∀ i, p' i → ∃ j, p j ∧ ∀ x y, (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧
+      (∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j) :=
+by rw [uniform_embedding_iff, and_comm, h.uniform_inducing_iff h']
+
+theorem filter.has_basis.uniform_embedding_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+  (h : (𝓤 α).has_basis p s) (h' : (𝓤 β).has_basis p' s') {f : α → β} :
+  uniform_embedding f ↔ injective f ∧ uniform_continuous f ∧
+      (∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j) :=
+by simp only [h.uniform_embedding_iff' h', h.uniform_continuous_iff h', exists_prop]
+
 lemma uniform_embedding_subtype_val {p : α → Prop} :
   uniform_embedding (subtype.val : subtype p → α) :=
 { comap_uniformity := rfl,
@@ -86,79 +154,38 @@ lemma uniform_embedding.comp {g : β → γ} (hg : uniform_embedding g)
 { inj := hg.inj.comp hf.inj,
   ..hg.to_uniform_inducing.comp hf.to_uniform_inducing }
 
-theorem uniform_embedding_def {f : α → β} :
-  uniform_embedding f ↔ function.injective f ∧ ∀ s, s ∈ 𝓤 α ↔
-    ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s :=
-begin
-  split,
-  { rintro ⟨⟨h⟩, h'⟩,
-    rw [eq_comm, filter.ext_iff] at h,
-    simp [*, subset_def] },
-  { rintro ⟨h, h'⟩,
-    refine uniform_embedding.mk ⟨_⟩ h,
-    rw [eq_comm, filter.ext_iff],
-    simp [*, subset_def] }
-end
-
-theorem uniform_embedding_def' {f : α → β} :
-  uniform_embedding f ↔ function.injective f ∧ uniform_continuous f ∧
-    ∀ s, s ∈ 𝓤 α →
-      ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s :=
-by simp only [uniform_embedding_def, uniform_continuous_def]; exact
-⟨λ ⟨I, H⟩, ⟨I, λ s su, (H _).2 ⟨s, su, λ x y, id⟩, λ s, (H s).1⟩,
- λ ⟨I, H₁, H₂⟩, ⟨I, λ s, ⟨H₂ s,
-   λ ⟨t, tu, h⟩, mem_of_superset (H₁ t tu) (λ ⟨a, b⟩, h a b)⟩⟩⟩
-
 lemma equiv.uniform_embedding {α β : Type*} [uniform_space α] [uniform_space β] (f : α ≃ β)
   (h₁ : uniform_continuous f) (h₂ : uniform_continuous f.symm) : uniform_embedding f :=
-{ comap_uniformity :=
-  begin
-    refine le_antisymm _ _,
-    { change comap (f.prod_congr f) _ ≤ _,
-      rw ← map_equiv_symm (f.prod_congr f),
-      exact h₂ },
-    { rw ← map_le_iff_le_comap,
-      exact h₁ }
-  end,
-  inj := f.injective }
+uniform_embedding_iff'.2 ⟨f.injective, h₁, by rwa [← equiv.prod_congr_apply, ← map_equiv_symm]⟩
 
 theorem uniform_embedding_inl : uniform_embedding (sum.inl : α → α ⊕ β) :=
 begin
-  apply uniform_embedding_def.2 ⟨sum.inl_injective, λ s, ⟨_, _⟩⟩,
-  { assume hs,
-    refine ⟨(λ p : α × α, (sum.inl p.1, sum.inl p.2)) '' s ∪
-      (λ p : β × β, (sum.inr p.1, sum.inr p.2)) '' univ, _, _⟩,
-    { exact union_mem_uniformity_sum hs univ_mem },
-    { simp } },
-  { rintros ⟨t, ht, h't⟩,
-    simp only [sum.uniformity, mem_sup, mem_map] at ht,
-    apply filter.mem_of_superset ht.1,
-    rintros ⟨x, y⟩ hx,
-    exact h't _ _ hx }
+  refine ⟨⟨_⟩, sum.inl_injective⟩,
+  rw [sum.uniformity, comap_sup, comap_map, comap_eq_bot_iff_compl_range.2 _, sup_bot_eq],
+  { refine mem_map.2 (univ_mem' _),
+    simp },
+  { exact sum.inl_injective.prod_map sum.inl_injective }
 end
 
 theorem uniform_embedding_inr : uniform_embedding (sum.inr : β → α ⊕ β) :=
 begin
-  apply uniform_embedding_def.2 ⟨sum.inr_injective, λ s, ⟨_, _⟩⟩,
-  { assume hs,
-    refine ⟨(λ p : α × α, (sum.inl p.1, sum.inl p.2)) '' univ ∪
-      (λ p : β × β, (sum.inr p.1, sum.inr p.2)) '' s, _, _⟩,
-    { exact union_mem_uniformity_sum univ_mem hs },
-    { simp } },
-  { rintros ⟨t, ht, h't⟩,
-    simp only [sum.uniformity, mem_sup, mem_map] at ht,
-    apply filter.mem_of_superset ht.2,
-    rintros ⟨x, y⟩ hx,
-    exact h't _ _ hx }
+  refine ⟨⟨_⟩, sum.inr_injective⟩,
+  rw [sum.uniformity, comap_sup, comap_eq_bot_iff_compl_range.2 _, comap_map, bot_sup_eq],
+  { exact sum.inr_injective.prod_map sum.inr_injective },
+  { refine mem_map.2 (univ_mem' _),
+    simp },
 end
 
 /-- If the domain of a `uniform_inducing` map `f` is a `separated_space`, then `f` is injective,
 hence it is a `uniform_embedding`. -/
-protected theorem uniform_inducing.uniform_embedding [separated_space α] {f : α → β}
+protected theorem uniform_inducing.uniform_embedding [t0_space α] {f : α → β}
   (hf : uniform_inducing f) :
   uniform_embedding f :=
-⟨hf, λ x y h, eq_of_uniformity_basis (hf.basis_uniformity (𝓤 β).basis_sets) $
-  λ s hs, mem_preimage.2 $ mem_uniformity_of_eq hs h⟩
+⟨hf, hf.injective⟩
+
+theorem uniform_embedding_iff_uniform_inducing [t0_space α] {f : α → β} :
+  uniform_embedding f ↔ uniform_inducing f :=
+⟨uniform_embedding.to_uniform_inducing, uniform_inducing.uniform_embedding⟩
 
 /-- If a map `f : α → β` sends any two distinct points to point that are **not** related by a fixed
 `s ∈ 𝓤 β`, then `f` is uniform inducing with respect to the discrete uniformity on `α`:
@@ -186,35 +213,7 @@ begin
   exact uniform_inducing.uniform_embedding ⟨comap_uniformity_of_spaced_out hs hf⟩
 end
 
-lemma uniform_inducing.uniform_continuous {f : α → β}
-  (hf : uniform_inducing f) : uniform_continuous f :=
-by simp [uniform_continuous, hf.comap_uniformity.symm, tendsto_comap]
-
-lemma uniform_inducing.uniform_continuous_iff {f : α → β} {g : β → γ} (hg : uniform_inducing g) :
-  uniform_continuous f ↔ uniform_continuous (g ∘ f) :=
-by { dsimp only [uniform_continuous, tendsto],
-  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, filter.map_map] }
-
-lemma uniform_inducing.inducing {f : α → β} (h : uniform_inducing f) : inducing f :=
-begin
-  refine ⟨eq_of_nhds_eq_nhds $ assume a, _ ⟩,
-  rw [nhds_induced, nhds_eq_uniformity, nhds_eq_uniformity, ← h.comap_uniformity,
-    comap_lift'_eq, comap_lift'_eq2],
-  exacts [rfl, monotone_preimage]
-end
-
-lemma uniform_inducing.prod {α' : Type*} {β' : Type*} [uniform_space α'] [uniform_space β']
-  {e₁ : α → α'} {e₂ : β → β'} (h₁ : uniform_inducing e₁) (h₂ : uniform_inducing e₂) :
-  uniform_inducing (λp:α×β, (e₁ p.1, e₂ p.2)) :=
-⟨by simp [(∘), uniformity_prod, h₁.comap_uniformity.symm, h₂.comap_uniformity.symm,
-           comap_inf, comap_comap]⟩
-
-lemma uniform_inducing.dense_inducing {f : α → β} (h : uniform_inducing f) (hd : dense_range f) :
-  dense_inducing f :=
-{ dense   := hd,
-  induced := h.inducing.induced }
-
-lemma uniform_embedding.embedding {f : α → β} (h : uniform_embedding f) : embedding f :=
+protected lemma uniform_embedding.embedding {f : α → β} (h : uniform_embedding f) : embedding f :=
 { induced := h.to_uniform_inducing.inducing.induced,
   inj := h.inj }
 
@@ -237,7 +236,7 @@ end
 lemma closure_image_mem_nhds_of_uniform_inducing
   {s : set (α×α)} {e : α → β} (b : β)
   (he₁ : uniform_inducing e) (he₂ : dense_inducing e) (hs : s ∈ 𝓤 α) :
-  ∃a, closure (e '' {a' | (a, a') ∈ s}) ∈ 𝓝 b :=
+  ∃ a, closure (e '' {a' | (a, a') ∈ s}) ∈ 𝓝 b :=
 have s ∈ comap (λp:α×α, (e p.1, e p.2)) (𝓤 β),
   from he₁.comap_uniformity.symm ▸ hs,
 let ⟨t₁, ht₁u, ht₁⟩ := this in

2705404e

(first ported)

Changes in mathlib3port

mathlib3

mathlib3port

195fcd60

bump to nightly-2024-04-25-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

ad7a2212

Diff

@@ -54,7 +54,7 @@ protected theorem UniformInducing.comap_uniformSpace {f : α → β} (hf : Unifo
 #print uniformInducing_iff' /-
 theorem uniformInducing_iff' {f : α → β} :
     UniformInducing f ↔ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
-  rw [uniformInducing_iff, UniformContinuous, tendsto_iff_comap, le_antisymm_iff, and_comm'] <;> rfl
+  rw [uniformInducing_iff, UniformContinuous, tendsto_iff_comap, le_antisymm_iff, and_comm] <;> rfl
 #align uniform_inducing_iff' uniformInducing_iff'
 -/
 
@@ -177,7 +177,7 @@ structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop wher
 #print uniformEmbedding_iff' /-
 theorem uniformEmbedding_iff' {f : α → β} :
     UniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
-  rw [uniformEmbedding_iff, and_comm', uniformInducing_iff']
+  rw [uniformEmbedding_iff, and_comm, uniformInducing_iff']
 #align uniform_embedding_iff' uniformEmbedding_iff'
 -/
 
@@ -188,7 +188,7 @@ theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : 
       Injective f ∧
         (∀ i, p' i → ∃ j, p j ∧ ∀ x y, (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧
           ∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j :=
-  by rw [uniformEmbedding_iff, and_comm', h.uniform_inducing_iff h']
+  by rw [uniformEmbedding_iff, and_comm, h.uniform_inducing_iff h']
 #align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'
 -/

195fcd60

bump to nightly-2024-03-21-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

b0154c5c

Diff

@@ -330,7 +330,7 @@ theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopolo
   rcases DiscreteTopology.eq_bot α with rfl; letI : UniformSpace α := ⊥
   exact
     { (uniformEmbedding_of_spaced_out hs hf).Embedding with
-      closed_range := isClosed_range_of_spaced_out hs hf }
+      isClosed_range := isClosed_range_of_spaced_out hs hf }
 #align closed_embedding_of_spaced_out closedEmbedding_of_spaced_out
 -/

195fcd60

bump to nightly-2024-03-17-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

22f01ce4

Diff

@@ -302,7 +302,7 @@ theorem uniformEmbedding_of_spaced_out {α} {f : α → β} {s : Set (β × β)}
     (hf : Pairwise fun x y => (f x, f y) ∉ s) : @UniformEmbedding α β ⊥ ‹_› f :=
   by
   letI : UniformSpace α := ⊥; haveI := discreteTopology_bot α
-  haveI : SeparatedSpace α := separated_iff_t2.2 inferInstance
+  haveI : T0Space α := R1Space.t2Space_iff_t0Space.2 inferInstance
   exact UniformInducing.uniformEmbedding ⟨comap_uniformity_of_spaced_out hs hf⟩
 #align uniform_embedding_of_spaced_out uniformEmbedding_of_spaced_out
 -/
@@ -324,10 +324,9 @@ theorem UniformEmbedding.denseEmbedding {f : α → β} (h : UniformEmbedding f)
 -/
 
 #print closedEmbedding_of_spaced_out /-
-theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopology α]
-    [SeparatedSpace β] {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
-    (hf : Pairwise fun x y => (f x, f y) ∉ s) : ClosedEmbedding f :=
-  by
+theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopology α] [T0Space β]
+    {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β) (hf : Pairwise fun x y => (f x, f y) ∉ s) :
+    ClosedEmbedding f := by
   rcases DiscreteTopology.eq_bot α with rfl; letI : UniformSpace α := ⊥
   exact
     { (uniformEmbedding_of_spaced_out hs hf).Embedding with
@@ -394,10 +393,10 @@ theorem isComplete_of_complete_image {m : α → β} {s : Set α} (hm : UniformI
     (hs : IsComplete (m '' s)) : IsComplete s :=
   by
   intro f hf hfs
-  rw [le_principal_iff] at hfs 
+  rw [le_principal_iff] at hfs
   obtain ⟨_, ⟨x, hx, rfl⟩, hyf⟩ : ∃ y ∈ m '' s, map m f ≤ 𝓝 y
   exact hs (f.map m) (hf.map hm.uniform_continuous) (le_principal_iff.2 (image_mem_map hfs))
-  rw [map_le_iff_le_comap, ← nhds_induced, ← hm.inducing.induced] at hyf 
+  rw [map_le_iff_le_comap, ← nhds_induced, ← hm.inducing.induced] at hyf
   exact ⟨x, hx, hyf⟩
 #align is_complete_of_complete_image isComplete_of_complete_image
 -/
@@ -417,14 +416,14 @@ theorem isComplete_image_iff {m : α → β} {s : Set α} (hm : UniformInducing
   refine' ⟨isComplete_of_complete_image hm, fun c => _⟩
   haveI : CompleteSpace s := c.complete_space_coe
   set m' : s → β := m ∘ coe
-  suffices IsComplete (range m') by rwa [range_comp, Subtype.range_coe] at this 
+  suffices IsComplete (range m') by rwa [range_comp, Subtype.range_coe] at this
   have hm' : UniformInducing m' := hm.comp uniform_embedding_subtype_coe.to_uniform_inducing
   intro f hf hfm
-  rw [Filter.le_principal_iff] at hfm 
+  rw [Filter.le_principal_iff] at hfm
   have cf' : Cauchy (comap m' f) :=
     hf.comap' hm'.comap_uniformity.le (ne_bot.comap_of_range_mem hf.1 hfm)
   rcases CompleteSpace.complete cf' with ⟨x, hx⟩
-  rw [hm'.inducing.nhds_eq_comap, comap_le_comap_iff hfm] at hx 
+  rw [hm'.inducing.nhds_eq_comap, comap_le_comap_iff hfm] at hx
   use m' x, mem_range_self _, hx
 #align is_complete_image_iff isComplete_image_iff
 -/
@@ -532,7 +531,7 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
 theorem totallyBounded_preimage {f : α → β} {s : Set β} (hf : UniformEmbedding f)
     (hs : TotallyBounded s) : TotallyBounded (f ⁻¹' s) := fun t ht =>
   by
-  rw [← hf.comap_uniformity] at ht 
+  rw [← hf.comap_uniformity] at ht
   rcases mem_comap.2 ht with ⟨t', ht', ts⟩
   rcases totallyBounded_iff_subset.1 (totallyBounded_subset (image_preimage_subset f s) hs) _
       ht' with
@@ -616,10 +615,10 @@ theorem uniform_extend_subtype [CompleteSpace γ] {p : α → Prop} {e : α →
       (hc :
         tendsto (f ∘ Subtype.val) (comap (DenseEmbedding.subtypeEmb p e) (𝓝 ⟨b, this⟩)) (𝓝 c))⟩ :=
     uniformly_extend_exists ue'.to_uniformInducing de'.dense hf _
-  rw [nhds_subtype_eq_comap] at hc 
-  simp [comap_comap] at hc 
-  change tendsto (f ∘ @Subtype.val α p) (comap (e ∘ @Subtype.val α p) (𝓝 b)) (𝓝 c) at hc 
-  rw [← comap_comap, tendsto_comap'_iff] at hc 
+  rw [nhds_subtype_eq_comap] at hc
+  simp [comap_comap] at hc
+  change tendsto (f ∘ @Subtype.val α p) (comap (e ∘ @Subtype.val α p) (𝓝 b)) (𝓝 c) at hc
+  rw [← comap_comap, tendsto_comap'_iff] at hc
   exact ⟨c, hc⟩
   exact
     ⟨_, hb, fun x => by
@@ -660,12 +659,12 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
   have : preimage (fun p : β × β => (f p.1, f p.2)) s ∈ 𝓤 β := h_f hs
   have :
     preimage (fun p : β × β => (f p.1, f p.2)) s ∈ comap (fun x : β × β => (e x.1, e x.2)) (𝓤 α) :=
-    by rwa [h_e.comap_uniformity.symm] at this 
+    by rwa [h_e.comap_uniformity.symm] at this
   let ⟨t, ht, ts⟩ := this
   show preimage (fun p : α × α => (ψ p.1, ψ p.2)) d ∈ 𝓤 α from
     (𝓤 α).sets_of_superset (interior_mem_uniformity ht) fun ⟨x₁, x₂⟩ hx_t =>
       have : 𝓝 (x₁, x₂) ≤ 𝓟 (interior t) := isOpen_iff_nhds.mp isOpen_interior (x₁, x₂) hx_t
-      have : interior t ∈ 𝓝 x₁ ×ᶠ 𝓝 x₂ := by rwa [nhds_prod_eq, le_principal_iff] at this 
+      have : interior t ∈ 𝓝 x₁ ×ᶠ 𝓝 x₂ := by rwa [nhds_prod_eq, le_principal_iff] at this
       let ⟨m₁, hm₁, m₂, hm₂, (hm : m₁ ×ˢ m₂ ⊆ interior t)⟩ := mem_prod_iff.mp this
       let ⟨a, ha₁, _, ha₂⟩ := h_pnt hm₁
       let ⟨b, hb₁, hb₂, _⟩ := h_pnt hm₂
@@ -687,7 +686,7 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
 #align uniform_continuous_uniformly_extend uniformContinuous_uniformly_extend
 -/
 
-variable [SeparatedSpace γ]
+variable [T0Space γ]
 
 #print uniformly_extend_of_ind /-
 theorem uniformly_extend_of_ind (b : β) : ψ (e b) = f b :=

195fcd60

bump to nightly-2024-01-30-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/65a1391a0106c9204fe45bc73a039f056558cb83

708b9b61

Diff

@@ -625,7 +625,7 @@ theorem uniform_extend_subtype [CompleteSpace γ] {p : α → Prop} {e : α →
     ⟨_, hb, fun x => by
       change e x ∈ closure (e '' s) → x ∈ range Subtype.val
       rw [← closure_induced, mem_closure_iff_clusterPt, ClusterPt, ne_bot_iff, nhds_induced, ←
-        de.to_dense_inducing.nhds_eq_comap, ← mem_closure_iff_nhds_neBot, hs.closure_eq]
+        de.to_dense_inducing.nhds_eq_comap, ← mem_closure_iff_nhds_ne_bot, hs.closure_eq]
       exact fun hxs => ⟨⟨x, hp x hxs⟩, rfl⟩⟩
 #align uniform_extend_subtype uniform_extend_subtype
 -/

195fcd60

bump to nightly-2023-09-24-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce64cd319bb6b3e82f31c2d38e79080d377be451

5655435f

Diff

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
 -/
-import Mathbin.Topology.UniformSpace.Cauchy
-import Mathbin.Topology.UniformSpace.Separation
-import Mathbin.Topology.DenseEmbedding
+import Topology.UniformSpace.Cauchy
+import Topology.UniformSpace.Separation
+import Topology.DenseEmbedding
 
 #align_import topology.uniform_space.uniform_embedding from "leanprover-community/mathlib"@"195fcd60ff2bfe392543bceb0ec2adcdb472db4c"

195fcd60

bump to nightly-2023-08-23-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

f612b9e0

Diff

@@ -47,7 +47,7 @@ structure UniformInducing (f : α → β) : Prop where
 #print UniformInducing.comap_uniformSpace /-
 protected theorem UniformInducing.comap_uniformSpace {f : α → β} (hf : UniformInducing f) :
     ‹UniformSpace β›.comap f = ‹UniformSpace α› :=
-  uniformSpace_eq hf.1
+  UniformSpace.ext hf.1
 #align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
 -/

195fcd60

bump to nightly-2023-07-20-09

mathlib commit https://github.com/leanprover-community/mathlib/commit/8ea5598db6caeddde6cb734aa179cc2408dbd345

9c56d0dd

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.uniform_space.uniform_embedding
-! leanprover-community/mathlib commit 195fcd60ff2bfe392543bceb0ec2adcdb472db4c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.UniformSpace.Cauchy
 import Mathbin.Topology.UniformSpace.Separation
 import Mathbin.Topology.DenseEmbedding
 
+#align_import topology.uniform_space.uniform_embedding from "leanprover-community/mathlib"@"195fcd60ff2bfe392543bceb0ec2adcdb472db4c"
+
 /-!
 # Uniform embeddings of uniform spaces.

195fcd60

bump to nightly-2023-06-13-21

mathlib commit https://github.com/leanprover-community/mathlib/commit/9fb8964792b4237dac6200193a0d533f1b3f7423

829520ac

Diff

@@ -54,11 +54,14 @@ protected theorem UniformInducing.comap_uniformSpace {f : α → β} (hf : Unifo
 #align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
 -/
 
+#print uniformInducing_iff' /-
 theorem uniformInducing_iff' {f : α → β} :
     UniformInducing f ↔ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
   rw [uniformInducing_iff, UniformContinuous, tendsto_iff_comap, le_antisymm_iff, and_comm'] <;> rfl
 #align uniform_inducing_iff' uniformInducing_iff'
+-/
 
+#print Filter.HasBasis.uniformInducing_iff /-
 protected theorem Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformInducing f ↔
@@ -67,11 +70,14 @@ protected theorem Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop}
   by
   simp [uniformInducing_iff', h.uniform_continuous_iff h', (h'.comap _).le_basis_iffₓ h, subset_def]
 #align filter.has_basis.uniform_inducing_iff Filter.HasBasis.uniformInducing_iff
+-/
 
+#print UniformInducing.mk' /-
 theorem UniformInducing.mk' {f : α → β}
     (h : ∀ s, s ∈ 𝓤 α ↔ ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s) : UniformInducing f :=
   ⟨by simp [eq_comm, Filter.ext_iff, subset_def, h]⟩
 #align uniform_inducing.mk' UniformInducing.mk'
+-/
 
 #print uniformInducing_id /-
 theorem uniformInducing_id : UniformInducing (@id α) :=
@@ -86,11 +92,13 @@ theorem UniformInducing.comp {g : β → γ} (hg : UniformInducing g) {f : α 
 #align uniform_inducing.comp UniformInducing.comp
 -/
 
+#print UniformInducing.basis_uniformity /-
 theorem UniformInducing.basis_uniformity {f : α → β} (hf : UniformInducing f) {ι : Sort _}
     {p : ι → Prop} {s : ι → Set (β × β)} (H : (𝓤 β).HasBasis p s) :
     (𝓤 α).HasBasis p fun i => Prod.map f f ⁻¹' s i :=
   hf.1 ▸ H.comap _
 #align uniform_inducing.basis_uniformity UniformInducing.basis_uniformity
+-/
 
 #print UniformInducing.cauchy_map_iff /-
 theorem UniformInducing.cauchy_map_iff {f : α → β} (hf : UniformInducing f) {F : Filter α} :
@@ -135,6 +143,7 @@ protected theorem UniformInducing.inducing {f : α → β} (h : UniformInducing
 #align uniform_inducing.inducing UniformInducing.inducing
 -/
 
+#print UniformInducing.prod /-
 theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
     {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformInducing e₁) (h₂ : UniformInducing e₂) :
     UniformInducing fun p : α × β => (e₁ p.1, e₂ p.2) :=
@@ -142,6 +151,7 @@ theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [U
     simp [(· ∘ ·), uniformity_prod, h₁.comap_uniformity.symm, h₂.comap_uniformity.symm, comap_inf,
       comap_comap]⟩
 #align uniform_inducing.prod UniformInducing.prod
+-/
 
 #print UniformInducing.denseInducing /-
 theorem UniformInducing.denseInducing {f : α → β} (h : UniformInducing f) (hd : DenseRange f) :
@@ -167,11 +177,14 @@ structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop wher
 #align uniform_embedding UniformEmbedding
 -/
 
+#print uniformEmbedding_iff' /-
 theorem uniformEmbedding_iff' {f : α → β} :
     UniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
   rw [uniformEmbedding_iff, and_comm', uniformInducing_iff']
 #align uniform_embedding_iff' uniformEmbedding_iff'
+-/
 
+#print Filter.HasBasis.uniformEmbedding_iff' /-
 theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformEmbedding f ↔
@@ -180,7 +193,9 @@ theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : 
           ∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j :=
   by rw [uniformEmbedding_iff, and_comm', h.uniform_inducing_iff h']
 #align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'
+-/
 
+#print Filter.HasBasis.uniformEmbedding_iff /-
 theorem Filter.HasBasis.uniformEmbedding_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformEmbedding f ↔
@@ -188,6 +203,7 @@ theorem Filter.HasBasis.uniformEmbedding_iff {ι ι'} {p : ι → Prop} {p' : ι
         UniformContinuous f ∧ ∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j :=
   by simp only [h.uniform_embedding_iff' h', h.uniform_continuous_iff h', exists_prop]
 #align filter.has_basis.uniform_embedding_iff Filter.HasBasis.uniformEmbedding_iff
+-/
 
 #print uniformEmbedding_subtype_val /-
 theorem uniformEmbedding_subtype_val {p : α → Prop} :
@@ -220,10 +236,12 @@ theorem UniformEmbedding.comp {g : β → γ} (hg : UniformEmbedding g) {f : α
 #align uniform_embedding.comp UniformEmbedding.comp
 -/
 
+#print Equiv.uniformEmbedding /-
 theorem Equiv.uniformEmbedding {α β : Type _} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
     (h₁ : UniformContinuous f) (h₂ : UniformContinuous f.symm) : UniformEmbedding f :=
   uniformEmbedding_iff'.2 ⟨f.Injective, h₁, by rwa [← Equiv.prodCongr_apply, ← map_equiv_symm]⟩
 #align equiv.uniform_embedding Equiv.uniformEmbedding
+-/
 
 #print uniformEmbedding_inl /-
 theorem uniformEmbedding_inl : UniformEmbedding (Sum.inl : α → Sum α β) :=
@@ -263,6 +281,7 @@ theorem uniformEmbedding_iff_uniformInducing [T0Space α] {f : α → β} :
 #align uniform_embedding_iff_uniform_inducing uniformEmbedding_iff_uniformInducing
 -/
 
+#print comap_uniformity_of_spaced_out /-
 /-- If a map `f : α → β` sends any two distinct points to point that are **not** related by a fixed
 `s ∈ 𝓤 β`, then `f` is uniform inducing with respect to the discrete uniformity on `α`:
 the preimage of `𝓤 β` under `prod.map f f` is the principal filter generated by the diagonal in
@@ -277,7 +296,9 @@ theorem comap_uniformity_of_spaced_out {α} {f : α → β} {s : Set (β × β)}
     _ ≤ 𝓟 idRel := principal_mono.2 _
   rintro ⟨x, y⟩; simpa [not_imp_not] using @hf x y
 #align comap_uniformity_of_spaced_out comap_uniformity_of_spaced_out
+-/
 
+#print uniformEmbedding_of_spaced_out /-
 /-- If a map `f : α → β` sends any two distinct points to point that are **not** related by a fixed
 `s ∈ 𝓤 β`, then `f` is a uniform embedding with respect to the discrete uniformity on `α`. -/
 theorem uniformEmbedding_of_spaced_out {α} {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
@@ -287,6 +308,7 @@ theorem uniformEmbedding_of_spaced_out {α} {f : α → β} {s : Set (β × β)}
   haveI : SeparatedSpace α := separated_iff_t2.2 inferInstance
   exact UniformInducing.uniformEmbedding ⟨comap_uniformity_of_spaced_out hs hf⟩
 #align uniform_embedding_of_spaced_out uniformEmbedding_of_spaced_out
+-/
 
 #print UniformEmbedding.embedding /-
 protected theorem UniformEmbedding.embedding {f : α → β} (h : UniformEmbedding f) : Embedding f :=
@@ -304,6 +326,7 @@ theorem UniformEmbedding.denseEmbedding {f : α → β} (h : UniformEmbedding f)
 #align uniform_embedding.dense_embedding UniformEmbedding.denseEmbedding
 -/
 
+#print closedEmbedding_of_spaced_out /-
 theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopology α]
     [SeparatedSpace β] {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
     (hf : Pairwise fun x y => (f x, f y) ∉ s) : ClosedEmbedding f :=
@@ -313,6 +336,7 @@ theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopolo
     { (uniformEmbedding_of_spaced_out hs hf).Embedding with
       closed_range := isClosed_range_of_spaced_out hs hf }
 #align closed_embedding_of_spaced_out closedEmbedding_of_spaced_out
+-/
 
 #print closure_image_mem_nhds_of_uniformInducing /-
 theorem closure_image_mem_nhds_of_uniformInducing {s : Set (α × α)} {e : α → β} (b : β)
@@ -360,11 +384,13 @@ theorem uniformEmbedding_subtypeEmb (p : α → Prop) {e : α → β} (ue : Unif
 #align uniform_embedding_subtype_emb uniformEmbedding_subtypeEmb
 -/
 
+#print UniformEmbedding.prod /-
 theorem UniformEmbedding.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
     {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformEmbedding e₁) (h₂ : UniformEmbedding e₂) :
     UniformEmbedding fun p : α × β => (e₁ p.1, e₂ p.2) :=
   { h₁.to_uniformInducing.Prod h₂.to_uniformInducing with inj := h₁.inj.Prod_map h₂.inj }
 #align uniform_embedding.prod UniformEmbedding.prod
+-/
 
 #print isComplete_of_complete_image /-
 theorem isComplete_of_complete_image {m : α → β} {s : Set α} (hm : UniformInducing m)
@@ -453,6 +479,7 @@ instance ULift.completeSpace [h : CompleteSpace α] : CompleteSpace (ULift α) :
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print completeSpace_extension /-
 theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense : DenseRange m)
     (h : ∀ f : Filter β, Cauchy f → ∃ x : α, map m f ≤ 𝓝 x) : CompleteSpace α :=
   ⟨fun f : Filter α => fun hf : Cauchy f =>
@@ -502,6 +529,7 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
         f ≤ g := by assumption
         _ ≤ 𝓝 x := le_nhds_of_cauchy_adhp ‹Cauchy g› this⟩⟩
 #align complete_space_extension completeSpace_extension
+-/
 
 #print totallyBounded_preimage /-
 theorem totallyBounded_preimage {f : α → β} {s : Set β} (hf : UniformEmbedding f)
@@ -532,11 +560,13 @@ instance CompleteSpace.sum [CompleteSpace α] [CompleteSpace β] : CompleteSpace
 
 end
 
+#print uniformEmbedding_comap /-
 theorem uniformEmbedding_comap {α : Type _} {β : Type _} {f : α → β} [u : UniformSpace β]
     (hf : Function.Injective f) : @UniformEmbedding α β (UniformSpace.comap f u) u f :=
   @UniformEmbedding.mk _ _ (UniformSpace.comap f u) _ _
     (@UniformInducing.mk _ _ (UniformSpace.comap f u) _ _ rfl) hf
 #align uniform_embedding_comap uniformEmbedding_comap
+-/
 
 #print Embedding.comapUniformSpace /-
 /-- Pull back a uniform space structure by an embedding, adjusting the new uniform structure to
@@ -547,11 +577,13 @@ def Embedding.comapUniformSpace {α β} [TopologicalSpace α] [u : UniformSpace
 #align embedding.comap_uniform_space Embedding.comapUniformSpace
 -/
 
+#print Embedding.to_uniformEmbedding /-
 theorem Embedding.to_uniformEmbedding {α β} [TopologicalSpace α] [u : UniformSpace β] (f : α → β)
     (h : Embedding f) : @UniformEmbedding α β (h.comap_uniformSpace f) u f :=
   { comap_uniformity := rfl
     inj := h.inj }
 #align embedding.to_uniform_embedding Embedding.to_uniformEmbedding
+-/
 
 section UniformExtension
 
@@ -559,7 +591,6 @@ variable {α : Type _} {β : Type _} {γ : Type _} [UniformSpace α] [UniformSpa
   {e : β → α} (h_e : UniformInducing e) (h_dense : DenseRange e) {f : β → γ}
   (h_f : UniformContinuous f)
 
--- mathport name: exprψ
 local notation "ψ" => (h_e.DenseInducing h_dense).extend f
 
 #print uniformly_extend_exists /-
@@ -573,6 +604,7 @@ theorem uniformly_extend_exists [CompleteSpace γ] (a : α) : ∃ c, Tendsto f (
 #align uniformly_extend_exists uniformly_extend_exists
 -/
 
+#print uniform_extend_subtype /-
 theorem uniform_extend_subtype [CompleteSpace γ] {p : α → Prop} {e : α → β} {f : α → γ} {b : β}
     {s : Set α} (hf : UniformContinuous fun x : Subtype p => f x.val) (he : UniformEmbedding e)
     (hd : ∀ x : β, x ∈ closure (range e)) (hb : closure (e '' s) ∈ 𝓝 b) (hs : IsClosed s)
@@ -599,8 +631,7 @@ theorem uniform_extend_subtype [CompleteSpace γ] {p : α → Prop} {e : α →
         de.to_dense_inducing.nhds_eq_comap, ← mem_closure_iff_nhds_neBot, hs.closure_eq]
       exact fun hxs => ⟨⟨x, hp x hxs⟩, rfl⟩⟩
 #align uniform_extend_subtype uniform_extend_subtype
-
-include h_f
+-/
 
 #print uniformly_extend_spec /-
 theorem uniformly_extend_spec [CompleteSpace γ] (a : α) : Tendsto f (comap e (𝓝 a)) (𝓝 (ψ a)) := by
@@ -614,6 +645,7 @@ theorem uniformly_extend_spec [CompleteSpace γ] (a : α) : Tendsto f (comap e (
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print uniformContinuous_uniformly_extend /-
 theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformContinuous ψ :=
   fun d hd =>
   let ⟨s, hs, hs_comp⟩ :=
@@ -656,8 +688,7 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
       have : (a, b) ∈ s := @this (a, b) ⟨ha₁, hb₁⟩
       hs_comp <| show (ψ x₁, ψ x₂) ∈ compRel s (compRel s s) from ⟨a, ha₂, ⟨b, this, hb₂⟩⟩
 #align uniform_continuous_uniformly_extend uniformContinuous_uniformly_extend
-
-omit h_f
+-/
 
 variable [SeparatedSpace γ]
 
@@ -667,9 +698,11 @@ theorem uniformly_extend_of_ind (b : β) : ψ (e b) = f b :=
 #align uniformly_extend_of_ind uniformly_extend_of_ind
 -/
 
+#print uniformly_extend_unique /-
 theorem uniformly_extend_unique {g : α → γ} (hg : ∀ b, g (e b) = f b) (hc : Continuous g) : ψ = g :=
   DenseInducing.extend_unique _ hg hc
 #align uniformly_extend_unique uniformly_extend_unique
+-/
 
 end UniformExtension

195fcd60

bump to nightly-2023-06-09-07

mathlib commit https://github.com/leanprover-community/mathlib/commit/7e5137f579de09a059a5ce98f364a04e221aabf0

16afdc39

Diff

@@ -275,7 +275,6 @@ theorem comap_uniformity_of_spaced_out {α} {f : α → β} {s : Set (β × β)}
     comap (Prod.map f f) (𝓤 β) ≤ comap (Prod.map f f) (𝓟 s) := comap_mono (le_principal_iff.2 hs)
     _ = 𝓟 (Prod.map f f ⁻¹' s) := comap_principal
     _ ≤ 𝓟 idRel := principal_mono.2 _
-    
   rintro ⟨x, y⟩; simpa [not_imp_not] using @hf x y
 #align comap_uniformity_of_spaced_out comap_uniformity_of_spaced_out
 
@@ -501,8 +500,7 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
     ⟨x,
       calc
         f ≤ g := by assumption
-        _ ≤ 𝓝 x := le_nhds_of_cauchy_adhp ‹Cauchy g› this
-        ⟩⟩
+        _ ≤ 𝓝 x := le_nhds_of_cauchy_adhp ‹Cauchy g› this⟩⟩
 #align complete_space_extension completeSpace_extension
 
 #print totallyBounded_preimage /-
@@ -647,7 +645,6 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
           _ ⊆ preimage (fun p : β × β => (e p.1, e p.2)) (interior t) := preimage_mono hm
           _ ⊆ preimage (fun p : β × β => (e p.1, e p.2)) t := (preimage_mono interior_subset)
           _ ⊆ preimage (fun p : β × β => (f p.1, f p.2)) s := ts
-          
       have : (f '' (e ⁻¹' m₁)) ×ˢ (f '' (e ⁻¹' m₂)) ⊆ s :=
         calc
           (f '' (e ⁻¹' m₁)) ×ˢ (f '' (e ⁻¹' m₂)) =
@@ -656,7 +653,6 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
           _ ⊆ (fun p : β × β => (f p.1, f p.2)) '' ((fun p : β × β => (f p.1, f p.2)) ⁻¹' s) :=
             (monotone_image this)
           _ ⊆ s := image_preimage_subset _ _
-          
       have : (a, b) ∈ s := @this (a, b) ⟨ha₁, hb₁⟩
       hs_comp <| show (ψ x₁, ψ x₂) ∈ compRel s (compRel s s) from ⟨a, ha₂, ⟨b, this, hb₂⟩⟩
 #align uniform_continuous_uniformly_extend uniformContinuous_uniformly_extend

195fcd60

bump to nightly-2023-06-04-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/5f25c089cb34db4db112556f23c50d12da81b297

3fb4268b

Diff

@@ -318,35 +318,34 @@ theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopolo
 #print closure_image_mem_nhds_of_uniformInducing /-
 theorem closure_image_mem_nhds_of_uniformInducing {s : Set (α × α)} {e : α → β} (b : β)
     (he₁ : UniformInducing e) (he₂ : DenseInducing e) (hs : s ∈ 𝓤 α) :
-    ∃ a, closure (e '' { a' | (a, a') ∈ s }) ∈ 𝓝 b :=
+    ∃ a, closure (e '' {a' | (a, a') ∈ s}) ∈ 𝓝 b :=
   have : s ∈ comap (fun p : α × α => (e p.1, e p.2)) (𝓤 β) := he₁.comap_uniformity.symm ▸ hs
   let ⟨t₁, ht₁u, ht₁⟩ := this
   have ht₁ : ∀ p : α × α, (e p.1, e p.2) ∈ t₁ → p ∈ s := ht₁
   let ⟨t₂, ht₂u, ht₂s, ht₂c⟩ := comp_symm_of_uniformity ht₁u
   let ⟨t, htu, hts, htc⟩ := comp_symm_of_uniformity ht₂u
-  have : preimage e { b' | (b, b') ∈ t₂ } ∈ comap e (𝓝 b) :=
+  have : preimage e {b' | (b, b') ∈ t₂} ∈ comap e (𝓝 b) :=
     preimage_mem_comap <| mem_nhds_left b ht₂u
   let ⟨a, (ha : (b, e a) ∈ t₂)⟩ := (he₂.comap_nhds_neBot _).nonempty_of_mem this
   have :
     ∀ (b') (s' : Set (β × β)),
-      (b, b') ∈ t →
-        s' ∈ 𝓤 β → ({ y : β | (b', y) ∈ s' } ∩ e '' { a' : α | (a, a') ∈ s }).Nonempty :=
+      (b, b') ∈ t → s' ∈ 𝓤 β → ({y : β | (b', y) ∈ s'} ∩ e '' {a' : α | (a, a') ∈ s}).Nonempty :=
     fun b' s' hb' hs' =>
-    have : preimage e { b'' | (b', b'') ∈ s' ∩ t } ∈ comap e (𝓝 b') :=
+    have : preimage e {b'' | (b', b'') ∈ s' ∩ t} ∈ comap e (𝓝 b') :=
       preimage_mem_comap <| mem_nhds_left b' <| inter_mem hs' htu
     let ⟨a₂, ha₂s', ha₂t⟩ := (he₂.comap_nhds_neBot _).nonempty_of_mem this
     have : (e a, e a₂) ∈ t₁ :=
       ht₂c <| prod_mk_mem_compRel (ht₂s ha) <| htc <| prod_mk_mem_compRel hb' ha₂t
-    have : e a₂ ∈ { b'' : β | (b', b'') ∈ s' } ∩ e '' { a' | (a, a') ∈ s } :=
+    have : e a₂ ∈ {b'' : β | (b', b'') ∈ s'} ∩ e '' {a' | (a, a') ∈ s} :=
       ⟨ha₂s', mem_image_of_mem _ <| ht₁ (a, a₂) this⟩
     ⟨_, this⟩
-  have : ∀ b', (b, b') ∈ t → NeBot (𝓝 b' ⊓ 𝓟 (e '' { a' | (a, a') ∈ s })) :=
+  have : ∀ b', (b, b') ∈ t → NeBot (𝓝 b' ⊓ 𝓟 (e '' {a' | (a, a') ∈ s})) :=
     by
     intro b' hb'
     rw [nhds_eq_uniformity, lift'_inf_principal_eq, lift'_ne_bot_iff]
     exact fun s => this b' s hb'
     exact monotone_preimage.inter monotone_const
-  have : ∀ b', (b, b') ∈ t → b' ∈ closure (e '' { a' | (a, a') ∈ s }) := fun b' hb' => by
+  have : ∀ b', (b, b') ∈ t → b' ∈ closure (e '' {a' | (a, a') ∈ s}) := fun b' hb' => by
     rw [closure_eq_cluster_pts] <;> exact this b' hb'
   ⟨a, (𝓝 b).sets_of_superset (mem_nhds_left b htu) this⟩
 #align closure_image_mem_nhds_of_uniform_inducing closure_image_mem_nhds_of_uniformInducing
@@ -458,7 +457,7 @@ instance ULift.completeSpace [h : CompleteSpace α] : CompleteSpace (ULift α) :
 theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense : DenseRange m)
     (h : ∀ f : Filter β, Cauchy f → ∃ x : α, map m f ≤ 𝓝 x) : CompleteSpace α :=
   ⟨fun f : Filter α => fun hf : Cauchy f =>
-    let p : Set (α × α) → Set α → Set α := fun s t => { y : α | ∃ x : α, x ∈ t ∧ (x, y) ∈ s }
+    let p : Set (α × α) → Set α → Set α := fun s t => {y : α | ∃ x : α, x ∈ t ∧ (x, y) ∈ s}
     let g := (𝓤 α).lift fun s => f.lift' (p s)
     have mp₀ : Monotone p := fun a b h t s ⟨x, xs, xa⟩ => ⟨x, xs, h xa⟩
     have mp₁ : ∀ {s}, Monotone (p s) := fun s a b h x ⟨y, ya, yxs⟩ => ⟨y, h ya, yxs⟩
@@ -475,11 +474,11 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
         let ⟨t'', ht'', ht'_sub⟩ := (mem_lift'_sets mp₁).mp ht_mem
         let ⟨x, (hx : x ∈ t'')⟩ := hf.left.nonempty_of_mem ht''
         have h₀ : NeBot (𝓝[range m] x) := Dense.nhdsWithin_neBot x
-        have h₁ : { y | (x, y) ∈ t' } ∈ 𝓝[range m] x :=
+        have h₁ : {y | (x, y) ∈ t'} ∈ 𝓝[range m] x :=
           @mem_inf_of_left α (𝓝 x) (𝓟 (range m)) _ <| mem_nhds_left x ht'
         have h₂ : range m ∈ 𝓝[range m] x :=
           @mem_inf_of_right α (𝓝 x) (𝓟 (range m)) _ <| Subset.refl _
-        have : { y | (x, y) ∈ t' } ∩ range m ∈ 𝓝[range m] x := @inter_mem α (𝓝[range m] x) _ _ h₁ h₂
+        have : {y | (x, y) ∈ t'} ∩ range m ∈ 𝓝[range m] x := @inter_mem α (𝓝[range m] x) _ _ h₁ h₂
         let ⟨y, xyt', b, b_eq⟩ := h₀.nonempty_of_mem this
         ⟨b, b_eq.symm ▸ ht'_sub ⟨x, hx, xyt'⟩⟩
     have : Cauchy g :=
@@ -584,8 +583,7 @@ theorem uniform_extend_subtype [CompleteSpace γ] {p : α → Prop} {e : α →
   have de : DenseEmbedding e := he.DenseEmbedding hd
   have de' : DenseEmbedding (DenseEmbedding.subtypeEmb p e) := de.subtype p
   have ue' : UniformEmbedding (DenseEmbedding.subtypeEmb p e) := uniformEmbedding_subtypeEmb _ he de
-  have : b ∈ closure (e '' { x | p x }) :=
-    (closure_mono <| monotone_image <| hp) (mem_of_mem_nhds hb)
+  have : b ∈ closure (e '' {x | p x}) := (closure_mono <| monotone_image <| hp) (mem_of_mem_nhds hb)
   let
     ⟨c,
       (hc :
@@ -627,8 +625,7 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
     fun a m hm =>
     have nb : NeBot (map f (comap e (𝓝 a))) :=
       ((h_e.DenseInducing h_dense).comap_nhds_neBot _).map _
-    have :
-      f '' preimage e m ∩ ({ c | (c, ψ a) ∈ s } ∩ { c | (ψ a, c) ∈ s }) ∈ map f (comap e (𝓝 a)) :=
+    have : f '' preimage e m ∩ ({c | (c, ψ a) ∈ s} ∩ {c | (ψ a, c) ∈ s}) ∈ map f (comap e (𝓝 a)) :=
       inter_mem (image_mem_map <| preimage_mem_comap <| hm)
         (uniformly_extend_spec h_e h_dense h_f _
           (inter_mem (mem_nhds_right _ hs) (mem_nhds_left _ hs)))

195fcd60

bump to nightly-2023-06-01-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/cca40788df1b8755d5baf17ab2f27dacc2e17acb

b9c87c70

Diff

@@ -373,10 +373,10 @@ theorem isComplete_of_complete_image {m : α → β} {s : Set α} (hm : UniformI
     (hs : IsComplete (m '' s)) : IsComplete s :=
   by
   intro f hf hfs
-  rw [le_principal_iff] at hfs
+  rw [le_principal_iff] at hfs 
   obtain ⟨_, ⟨x, hx, rfl⟩, hyf⟩ : ∃ y ∈ m '' s, map m f ≤ 𝓝 y
   exact hs (f.map m) (hf.map hm.uniform_continuous) (le_principal_iff.2 (image_mem_map hfs))
-  rw [map_le_iff_le_comap, ← nhds_induced, ← hm.inducing.induced] at hyf
+  rw [map_le_iff_le_comap, ← nhds_induced, ← hm.inducing.induced] at hyf 
   exact ⟨x, hx, hyf⟩
 #align is_complete_of_complete_image isComplete_of_complete_image
 -/
@@ -396,14 +396,14 @@ theorem isComplete_image_iff {m : α → β} {s : Set α} (hm : UniformInducing
   refine' ⟨isComplete_of_complete_image hm, fun c => _⟩
   haveI : CompleteSpace s := c.complete_space_coe
   set m' : s → β := m ∘ coe
-  suffices IsComplete (range m') by rwa [range_comp, Subtype.range_coe] at this
+  suffices IsComplete (range m') by rwa [range_comp, Subtype.range_coe] at this 
   have hm' : UniformInducing m' := hm.comp uniform_embedding_subtype_coe.to_uniform_inducing
   intro f hf hfm
-  rw [Filter.le_principal_iff] at hfm
+  rw [Filter.le_principal_iff] at hfm 
   have cf' : Cauchy (comap m' f) :=
     hf.comap' hm'.comap_uniformity.le (ne_bot.comap_of_range_mem hf.1 hfm)
   rcases CompleteSpace.complete cf' with ⟨x, hx⟩
-  rw [hm'.inducing.nhds_eq_comap, comap_le_comap_iff hfm] at hx
+  rw [hm'.inducing.nhds_eq_comap, comap_le_comap_iff hfm] at hx 
   use m' x, mem_range_self _, hx
 #align is_complete_image_iff isComplete_image_iff
 -/
@@ -510,13 +510,13 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
 theorem totallyBounded_preimage {f : α → β} {s : Set β} (hf : UniformEmbedding f)
     (hs : TotallyBounded s) : TotallyBounded (f ⁻¹' s) := fun t ht =>
   by
-  rw [← hf.comap_uniformity] at ht
+  rw [← hf.comap_uniformity] at ht 
   rcases mem_comap.2 ht with ⟨t', ht', ts⟩
   rcases totallyBounded_iff_subset.1 (totallyBounded_subset (image_preimage_subset f s) hs) _
       ht' with
     ⟨c, cs, hfc, hct⟩
   refine' ⟨f ⁻¹' c, hfc.preimage (hf.inj.inj_on _), fun x h => _⟩
-  have := hct (mem_image_of_mem f h); simp at this⊢
+  have := hct (mem_image_of_mem f h); simp at this ⊢
   rcases this with ⟨z, zc, zt⟩
   rcases cs zc with ⟨y, yc, rfl⟩
   exact ⟨y, zc, ts zt⟩
@@ -591,10 +591,10 @@ theorem uniform_extend_subtype [CompleteSpace γ] {p : α → Prop} {e : α →
       (hc :
         tendsto (f ∘ Subtype.val) (comap (DenseEmbedding.subtypeEmb p e) (𝓝 ⟨b, this⟩)) (𝓝 c))⟩ :=
     uniformly_extend_exists ue'.to_uniformInducing de'.dense hf _
-  rw [nhds_subtype_eq_comap] at hc
-  simp [comap_comap] at hc
-  change tendsto (f ∘ @Subtype.val α p) (comap (e ∘ @Subtype.val α p) (𝓝 b)) (𝓝 c) at hc
-  rw [← comap_comap, tendsto_comap'_iff] at hc
+  rw [nhds_subtype_eq_comap] at hc 
+  simp [comap_comap] at hc 
+  change tendsto (f ∘ @Subtype.val α p) (comap (e ∘ @Subtype.val α p) (𝓝 b)) (𝓝 c) at hc 
+  rw [← comap_comap, tendsto_comap'_iff] at hc 
   exact ⟨c, hc⟩
   exact
     ⟨_, hb, fun x => by
@@ -636,12 +636,12 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
   have : preimage (fun p : β × β => (f p.1, f p.2)) s ∈ 𝓤 β := h_f hs
   have :
     preimage (fun p : β × β => (f p.1, f p.2)) s ∈ comap (fun x : β × β => (e x.1, e x.2)) (𝓤 α) :=
-    by rwa [h_e.comap_uniformity.symm] at this
+    by rwa [h_e.comap_uniformity.symm] at this 
   let ⟨t, ht, ts⟩ := this
   show preimage (fun p : α × α => (ψ p.1, ψ p.2)) d ∈ 𝓤 α from
     (𝓤 α).sets_of_superset (interior_mem_uniformity ht) fun ⟨x₁, x₂⟩ hx_t =>
       have : 𝓝 (x₁, x₂) ≤ 𝓟 (interior t) := isOpen_iff_nhds.mp isOpen_interior (x₁, x₂) hx_t
-      have : interior t ∈ 𝓝 x₁ ×ᶠ 𝓝 x₂ := by rwa [nhds_prod_eq, le_principal_iff] at this
+      have : interior t ∈ 𝓝 x₁ ×ᶠ 𝓝 x₂ := by rwa [nhds_prod_eq, le_principal_iff] at this 
       let ⟨m₁, hm₁, m₂, hm₂, (hm : m₁ ×ˢ m₂ ⊆ interior t)⟩ := mem_prod_iff.mp this
       let ⟨a, ha₁, _, ha₂⟩ := h_pnt hm₁
       let ⟨b, hb₁, hb₂, _⟩ := h_pnt hm₂

195fcd60

bump to nightly-2023-05-28-18

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

8d353152

Diff

@@ -24,7 +24,7 @@ Extension of uniform continuous functions.
 
 open Filter TopologicalSpace Set Function Classical
 
-open Classical uniformity Topology Filter
+open scoped Classical uniformity Topology Filter
 
 section

195fcd60

bump to nightly-2023-05-28-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

ba5d8b97

Diff

@@ -54,20 +54,11 @@ protected theorem UniformInducing.comap_uniformSpace {f : α → β} (hf : Unifo
 #align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
 -/
 
-/- warning: uniform_inducing_iff' -> uniformInducing_iff' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toHasLe.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instPartialOrderFilter.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align uniform_inducing_iff' uniformInducing_iff'ₓ'. -/
 theorem uniformInducing_iff' {f : α → β} :
     UniformInducing f ↔ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
   rw [uniformInducing_iff, UniformContinuous, tendsto_iff_comap, le_antisymm_iff, and_comm'] <;> rfl
 #align uniform_inducing_iff' uniformInducing_iff'
 
-/- warning: filter.has_basis.uniform_inducing_iff -> Filter.HasBasis.uniformInducing_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align filter.has_basis.uniform_inducing_iff Filter.HasBasis.uniformInducing_iffₓ'. -/
 protected theorem Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformInducing f ↔
@@ -77,12 +68,6 @@ protected theorem Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop}
   simp [uniformInducing_iff', h.uniform_continuous_iff h', (h'.comap _).le_basis_iffₓ h, subset_def]
 #align filter.has_basis.uniform_inducing_iff Filter.HasBasis.uniformInducing_iff
 
-/- warning: uniform_inducing.mk' -> UniformInducing.mk' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) (Exists.{succ u2} (Set.{u2} (Prod.{u2, u2} β β)) (fun (t : Set.{u2} (Prod.{u2, u2} β β)) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) => forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) t) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s))))) -> (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f)
-but is expected to have type
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 theorem UniformInducing.mk' {f : α → β}
     (h : ∀ s, s ∈ 𝓤 α ↔ ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s) : UniformInducing f :=
   ⟨by simp [eq_comm, Filter.ext_iff, subset_def, h]⟩
@@ -101,12 +86,6 @@ theorem UniformInducing.comp {g : β → γ} (hg : UniformInducing g) {f : α 
 #align uniform_inducing.comp UniformInducing.comp
 -/
 
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 theorem UniformInducing.basis_uniformity {f : α → β} (hf : UniformInducing f) {ι : Sort _}
     {p : ι → Prop} {s : ι → Set (β × β)} (H : (𝓤 β).HasBasis p s) :
     (𝓤 α).HasBasis p fun i => Prod.map f f ⁻¹' s i :=
@@ -156,12 +135,6 @@ protected theorem UniformInducing.inducing {f : α → β} (h : UniformInducing
 #align uniform_inducing.inducing UniformInducing.inducing
 -/
 
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 theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
     {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformInducing e₁) (h₂ : UniformInducing e₂) :
     UniformInducing fun p : α × β => (e₁ p.1, e₂ p.2) :=
@@ -194,20 +167,11 @@ structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop wher
 #align uniform_embedding UniformEmbedding
 -/
 
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 theorem uniformEmbedding_iff' {f : α → β} :
     UniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
   rw [uniformEmbedding_iff, and_comm', uniformInducing_iff']
 #align uniform_embedding_iff' uniformEmbedding_iff'
 
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-<too large>
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 theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformEmbedding f ↔
@@ -217,9 +181,6 @@ theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : 
   by rw [uniformEmbedding_iff, and_comm', h.uniform_inducing_iff h']
 #align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'
 
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 theorem Filter.HasBasis.uniformEmbedding_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformEmbedding f ↔
@@ -259,12 +220,6 @@ theorem UniformEmbedding.comp {g : β → γ} (hg : UniformEmbedding g) {f : α
 #align uniform_embedding.comp UniformEmbedding.comp
 -/
 
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 theorem Equiv.uniformEmbedding {α β : Type _} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
     (h₁ : UniformContinuous f) (h₂ : UniformContinuous f.symm) : UniformEmbedding f :=
   uniformEmbedding_iff'.2 ⟨f.Injective, h₁, by rwa [← Equiv.prodCongr_apply, ← map_equiv_symm]⟩
@@ -308,12 +263,6 @@ theorem uniformEmbedding_iff_uniformInducing [T0Space α] {f : α → β} :
 #align uniform_embedding_iff_uniform_inducing uniformEmbedding_iff_uniformInducing
 -/
 
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 /-- If a map `f : α → β` sends any two distinct points to point that are **not** related by a fixed
 `s ∈ 𝓤 β`, then `f` is uniform inducing with respect to the discrete uniformity on `α`:
 the preimage of `𝓤 β` under `prod.map f f` is the principal filter generated by the diagonal in
@@ -330,12 +279,6 @@ theorem comap_uniformity_of_spaced_out {α} {f : α → β} {s : Set (β × β)}
   rintro ⟨x, y⟩; simpa [not_imp_not] using @hf x y
 #align comap_uniformity_of_spaced_out comap_uniformity_of_spaced_out
 
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 /-- If a map `f : α → β` sends any two distinct points to point that are **not** related by a fixed
 `s ∈ 𝓤 β`, then `f` is a uniform embedding with respect to the discrete uniformity on `α`. -/
 theorem uniformEmbedding_of_spaced_out {α} {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
@@ -362,12 +305,6 @@ theorem UniformEmbedding.denseEmbedding {f : α → β} (h : UniformEmbedding f)
 #align uniform_embedding.dense_embedding UniformEmbedding.denseEmbedding
 -/
 
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-Case conversion may be inaccurate. Consider using '#align closed_embedding_of_spaced_out closedEmbedding_of_spaced_outₓ'. -/
 theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopology α]
     [SeparatedSpace β] {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
     (hf : Pairwise fun x y => (f x, f y) ∉ s) : ClosedEmbedding f :=
@@ -425,12 +362,6 @@ theorem uniformEmbedding_subtypeEmb (p : α → Prop) {e : α → β} (ue : Unif
 #align uniform_embedding_subtype_emb uniformEmbedding_subtypeEmb
 -/
 
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-Case conversion may be inaccurate. Consider using '#align uniform_embedding.prod UniformEmbedding.prodₓ'. -/
 theorem UniformEmbedding.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
     {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformEmbedding e₁) (h₂ : UniformEmbedding e₂) :
     UniformEmbedding fun p : α × β => (e₁ p.1, e₂ p.2) :=
@@ -521,12 +452,6 @@ instance ULift.completeSpace [h : CompleteSpace α] : CompleteSpace (ULift α) :
 #align ulift.complete_space ULift.completeSpace
 -/
 
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-Case conversion may be inaccurate. Consider using '#align complete_space_extension completeSpace_extensionₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -610,12 +535,6 @@ instance CompleteSpace.sum [CompleteSpace α] [CompleteSpace β] : CompleteSpace
 
 end
 
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-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align uniform_embedding_comap uniformEmbedding_comapₓ'. -/
 theorem uniformEmbedding_comap {α : Type _} {β : Type _} {f : α → β} [u : UniformSpace β]
     (hf : Function.Injective f) : @UniformEmbedding α β (UniformSpace.comap f u) u f :=
   @UniformEmbedding.mk _ _ (UniformSpace.comap f u) _ _
@@ -631,12 +550,6 @@ def Embedding.comapUniformSpace {α β} [TopologicalSpace α] [u : UniformSpace
 #align embedding.comap_uniform_space Embedding.comapUniformSpace
 -/
 
-/- warning: embedding.to_uniform_embedding -> Embedding.to_uniformEmbedding is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align embedding.to_uniform_embedding Embedding.to_uniformEmbeddingₓ'. -/
 theorem Embedding.to_uniformEmbedding {α β} [TopologicalSpace α] [u : UniformSpace β] (f : α → β)
     (h : Embedding f) : @UniformEmbedding α β (h.comap_uniformSpace f) u f :=
   { comap_uniformity := rfl
@@ -663,12 +576,6 @@ theorem uniformly_extend_exists [CompleteSpace γ] (a : α) : ∃ c, Tendsto f (
 #align uniformly_extend_exists uniformly_extend_exists
 -/
 
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-Case conversion may be inaccurate. Consider using '#align uniform_extend_subtype uniform_extend_subtypeₓ'. -/
 theorem uniform_extend_subtype [CompleteSpace γ] {p : α → Prop} {e : α → β} {f : α → γ} {b : β}
     {s : Set α} (hf : UniformContinuous fun x : Subtype p => f x.val) (he : UniformEmbedding e)
     (hd : ∀ x : β, x ∈ closure (range e)) (hb : closure (e '' s) ∈ 𝓝 b) (hs : IsClosed s)
@@ -706,12 +613,6 @@ theorem uniformly_extend_spec [CompleteSpace γ] (a : α) : Tendsto f (comap e (
 #align uniformly_extend_spec uniformly_extend_spec
 -/
 
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-Case conversion may be inaccurate. Consider using '#align uniform_continuous_uniformly_extend uniformContinuous_uniformly_extendₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -773,12 +674,6 @@ theorem uniformly_extend_of_ind (b : β) : ψ (e b) = f b :=
 #align uniformly_extend_of_ind uniformly_extend_of_ind
 -/
 
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-Case conversion may be inaccurate. Consider using '#align uniformly_extend_unique uniformly_extend_uniqueₓ'. -/
 theorem uniformly_extend_unique {g : α → γ} (hg : ∀ b, g (e b) = f b) (hc : Continuous g) : ψ = g :=
   DenseInducing.extend_unique _ hg hc
 #align uniformly_extend_unique uniformly_extend_unique

195fcd60

bump to nightly-2023-05-28-04

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6797a637

Diff

@@ -247,10 +247,7 @@ theorem uniformEmbedding_subtype_val {p : α → Prop} : UniformEmbedding (coe :
 #print uniformEmbedding_set_inclusion /-
 theorem uniformEmbedding_set_inclusion {s t : Set α} (hst : s ⊆ t) :
     UniformEmbedding (inclusion hst) :=
-  { comap_uniformity :=
-      by
-      erw [uniformity_subtype, uniformity_subtype, comap_comap]
-      congr
+  { comap_uniformity := by erw [uniformity_subtype, uniformity_subtype, comap_comap]; congr
     inj := inclusion_injective hst }
 #align uniform_embedding_set_inclusion uniformEmbedding_set_inclusion
 -/

195fcd60

bump to nightly-2023-05-28-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/917c3c072e487b3cccdbfeff17e75b40e45f66cb

6c6011cf

Diff

@@ -66,10 +66,7 @@ theorem uniformInducing_iff' {f : α → β} :
 #align uniform_inducing_iff' uniformInducing_iff'
 
 /- warning: filter.has_basis.uniform_inducing_iff -> Filter.HasBasis.uniformInducing_iff is a dubious translation:
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-  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {ι : Sort.{u2}} {ι' : Sort.{u1}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u3} (Prod.{u3, u3} α α))} {s' : ι' -> (Set.{u4} (Prod.{u4, u4} β β))}, (Filter.HasBasis.{u3, u2} (Prod.{u3, u3} α α) ι (uniformity.{u3} α _inst_1) p s) -> (Filter.HasBasis.{u4, u1} (Prod.{u4, u4} β β) ι' (uniformity.{u4} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformInducing.{u3, u4} α β _inst_1 _inst_2 f) (And (forall (i : ι'), (p' i) -> (Exists.{u2} ι (fun (j : ι) => And (p j) (forall (x : α) (y : α), (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)) -> (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)))))) (forall (j : ι), (p j) -> (Exists.{u1} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)) -> (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.uniform_inducing_iff Filter.HasBasis.uniformInducing_iffₓ'. -/
 protected theorem Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
@@ -209,10 +206,7 @@ theorem uniformEmbedding_iff' {f : α → β} :
 #align uniform_embedding_iff' uniformEmbedding_iff'
 
 /- warning: filter.has_basis.uniform_embedding_iff' -> Filter.HasBasis.uniformEmbedding_iff' is a dubious translation:
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {ι : Sort.{u3}} {ι' : Sort.{u4}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u1} (Prod.{u1, u1} α α))} {s' : ι' -> (Set.{u2} (Prod.{u2, u2} β β))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) ι (uniformity.{u1} α _inst_1) p s) -> (Filter.HasBasis.{u2, u4} (Prod.{u2, u2} β β) ι' (uniformity.{u2} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (forall (i : ι'), (p' i) -> (Exists.{u3} ι (fun (j : ι) => And (p j) (forall (x : α) (y : α), (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j)) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)))))) (forall (j : ι), (p j) -> (Exists.{u4} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j)))))))))
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {ι : Sort.{u2}} {ι' : Sort.{u1}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u3} (Prod.{u3, u3} α α))} {s' : ι' -> (Set.{u4} (Prod.{u4, u4} β β))}, (Filter.HasBasis.{u3, u2} (Prod.{u3, u3} α α) ι (uniformity.{u3} α _inst_1) p s) -> (Filter.HasBasis.{u4, u1} (Prod.{u4, u4} β β) ι' (uniformity.{u4} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u3, u4} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u3, succ u4} α β f) (And (forall (i : ι'), (p' i) -> (Exists.{u2} ι (fun (j : ι) => And (p j) (forall (x : α) (y : α), (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)) -> (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)))))) (forall (j : ι), (p j) -> (Exists.{u1} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)) -> (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'ₓ'. -/
 theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
@@ -224,10 +218,7 @@ theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : 
 #align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'
 
 /- warning: filter.has_basis.uniform_embedding_iff -> Filter.HasBasis.uniformEmbedding_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {ι : Sort.{u3}} {ι' : Sort.{u4}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u1} (Prod.{u1, u1} α α))} {s' : ι' -> (Set.{u2} (Prod.{u2, u2} β β))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) ι (uniformity.{u1} α _inst_1) p s) -> (Filter.HasBasis.{u2, u4} (Prod.{u2, u2} β β) ι' (uniformity.{u2} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (forall (j : ι), (p j) -> (Exists.{u4} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j)))))))))
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {ι : Sort.{u2}} {ι' : Sort.{u1}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u3} (Prod.{u3, u3} α α))} {s' : ι' -> (Set.{u4} (Prod.{u4, u4} β β))}, (Filter.HasBasis.{u3, u2} (Prod.{u3, u3} α α) ι (uniformity.{u3} α _inst_1) p s) -> (Filter.HasBasis.{u4, u1} (Prod.{u4, u4} β β) ι' (uniformity.{u4} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u3, u4} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u3, succ u4} α β f) (And (UniformContinuous.{u3, u4} α β _inst_1 _inst_2 f) (forall (j : ι), (p j) -> (Exists.{u1} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)) -> (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.uniform_embedding_iff Filter.HasBasis.uniformEmbedding_iffₓ'. -/
 theorem Filter.HasBasis.uniformEmbedding_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :

195fcd60

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -275,7 +275,7 @@ theorem UniformEmbedding.comp {g : β → γ} (hg : UniformEmbedding g) {f : α
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_4 : UniformSpace.{u1} α] [_inst_5 : UniformSpace.{u2} β] (f : Equiv.{succ u1, succ u2} α β), (UniformContinuous.{u1, u2} α β _inst_4 _inst_5 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) f)) -> (UniformContinuous.{u2, u1} β α _inst_5 _inst_4 (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} β α) (fun (_x : Equiv.{succ u2, succ u1} β α) => β -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} β α) (Equiv.symm.{succ u1, succ u2} α β f))) -> (UniformEmbedding.{u1, u2} α β _inst_4 _inst_5 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) f))
 but is expected to have type
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+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_4 : UniformSpace.{u2} α] [_inst_5 : UniformSpace.{u1} β] (f : Equiv.{succ u2, succ u1} α β), (UniformContinuous.{u2, u1} α β _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) f)) -> (UniformContinuous.{u1, u2} β α _inst_5 _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : β) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} β α) (Equiv.symm.{succ u2, succ u1} α β f))) -> (UniformEmbedding.{u2, u1} α β _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.812 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) f))
 Case conversion may be inaccurate. Consider using '#align equiv.uniform_embedding Equiv.uniformEmbeddingₓ'. -/
 theorem Equiv.uniformEmbedding {α β : Type _} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
     (h₁ : UniformContinuous f) (h₂ : UniformContinuous f.symm) : UniformEmbedding f :=

195fcd60

bump to nightly-2023-05-16-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/0b9eaaa7686280fad8cce467f5c3c57ee6ce77f8

9cb92e8c

Diff

@@ -56,7 +56,7 @@ protected theorem UniformInducing.comap_uniformSpace {f : α → β} (hf : Unifo
 
 /- warning: uniform_inducing_iff' -> uniformInducing_iff' is a dubious translation:
 lean 3 declaration is
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+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toHasLe.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instPartialOrderFilter.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align uniform_inducing_iff' uniformInducing_iff'ₓ'. -/
@@ -199,7 +199,7 @@ structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop wher
 
 /- warning: uniform_embedding_iff' -> uniformEmbedding_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toHasLe.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instPartialOrderFilter.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1))))
 Case conversion may be inaccurate. Consider using '#align uniform_embedding_iff' uniformEmbedding_iff'ₓ'. -/
@@ -535,7 +535,7 @@ instance ULift.completeSpace [h : CompleteSpace α] : CompleteSpace (ULift α) :
 
 /- warning: complete_space_extension -> completeSpace_extension is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {m : β -> α}, (UniformInducing.{u2, u1} β α _inst_2 _inst_1 m) -> (DenseRange.{u1, u2} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) β m) -> (forall (f : Filter.{u2} β), (Cauchy.{u2} β _inst_2 f) -> (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.map.{u2, u1} β α m f) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))) -> (CompleteSpace.{u1} α _inst_1)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {m : β -> α}, (UniformInducing.{u2, u1} β α _inst_2 _inst_1 m) -> (DenseRange.{u1, u2} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) β m) -> (forall (f : Filter.{u2} β), (Cauchy.{u2} β _inst_2 f) -> (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) (Filter.map.{u2, u1} β α m f) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))) -> (CompleteSpace.{u1} α _inst_1)
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {m : β -> α}, (UniformInducing.{u2, u1} β α _inst_2 _inst_1 m) -> (DenseRange.{u1, u2} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) β m) -> (forall (f : Filter.{u2} β), (Cauchy.{u2} β _inst_2 f) -> (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Filter.map.{u2, u1} β α m f) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))) -> (CompleteSpace.{u1} α _inst_1)
 Case conversion may be inaccurate. Consider using '#align complete_space_extension completeSpace_extensionₓ'. -/

195fcd60

bump to nightly-2023-05-14-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/e3fb84046afd187b710170887195d50bada934ee

d31da313

Diff

@@ -550,10 +550,10 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
     have mp₀ : Monotone p := fun a b h t s ⟨x, xs, xa⟩ => ⟨x, xs, h xa⟩
     have mp₁ : ∀ {s}, Monotone (p s) := fun s a b h x ⟨y, ya, yxs⟩ => ⟨y, h ya, yxs⟩
     have : f ≤ g :=
-      le_infᵢ fun s =>
-        le_infᵢ fun hs =>
-          le_infᵢ fun t =>
-            le_infᵢ fun ht =>
+      le_iInf fun s =>
+        le_iInf fun hs =>
+          le_iInf fun t =>
+            le_iInf fun ht =>
               le_principal_iff.mpr <| mem_of_superset ht fun x hx => ⟨x, hx, refl_mem_uniformity hs⟩
     have : NeBot g := hf.left.mono this
     have : NeBot (comap m g) :=

195fcd60

bump to nightly-2023-03-11-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

a8ee822f

Diff

@@ -275,7 +275,7 @@ theorem UniformEmbedding.comp {g : β → γ} (hg : UniformEmbedding g) {f : α
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_4 : UniformSpace.{u1} α] [_inst_5 : UniformSpace.{u2} β] (f : Equiv.{succ u1, succ u2} α β), (UniformContinuous.{u1, u2} α β _inst_4 _inst_5 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) f)) -> (UniformContinuous.{u2, u1} β α _inst_5 _inst_4 (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} β α) (fun (_x : Equiv.{succ u2, succ u1} β α) => β -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} β α) (Equiv.symm.{succ u1, succ u2} α β f))) -> (UniformEmbedding.{u1, u2} α β _inst_4 _inst_5 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) f))
 but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_4 : UniformSpace.{u2} α] [_inst_5 : UniformSpace.{u1} β] (f : Equiv.{succ u2, succ u1} α β), (UniformContinuous.{u2, u1} α β _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) f)) -> (UniformContinuous.{u1, u2} β α _inst_5 _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : β) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} β α) (Equiv.symm.{succ u2, succ u1} α β f))) -> (UniformEmbedding.{u2, u1} α β _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.805 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) f))
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_4 : UniformSpace.{u2} α] [_inst_5 : UniformSpace.{u1} β] (f : Equiv.{succ u2, succ u1} α β), (UniformContinuous.{u2, u1} α β _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) f)) -> (UniformContinuous.{u1, u2} β α _inst_5 _inst_4 (FunLike.coe.{max (succ u2) (succ u1), succ u1, succ u2} (Equiv.{succ u1, succ u2} β α) β (fun (_x : β) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : β) => α) _x) (Equiv.instFunLikeEquiv.{succ u1, succ u2} β α) (Equiv.symm.{succ u2, succ u1} α β f))) -> (UniformEmbedding.{u2, u1} α β _inst_4 _inst_5 (FunLike.coe.{max (succ u2) (succ u1), succ u2, succ u1} (Equiv.{succ u2, succ u1} α β) α (fun (_x : α) => (fun (x._@.Mathlib.Logic.Equiv.Defs._hyg.808 : α) => β) _x) (Equiv.instFunLikeEquiv.{succ u2, succ u1} α β) f))
 Case conversion may be inaccurate. Consider using '#align equiv.uniform_embedding Equiv.uniformEmbeddingₓ'. -/
 theorem Equiv.uniformEmbedding {α β : Type _} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
     (h₁ : UniformContinuous f) (h₂ : UniformContinuous f.symm) : UniformEmbedding f :=

195fcd60

bump to nightly-2023-03-02-23

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

ec1a9cbb

Diff

@@ -47,16 +47,30 @@ structure UniformInducing (f : α → β) : Prop where
 #align uniform_inducing UniformInducing
 -/
 
+#print UniformInducing.comap_uniformSpace /-
 protected theorem UniformInducing.comap_uniformSpace {f : α → β} (hf : UniformInducing f) :
     ‹UniformSpace β›.comap f = ‹UniformSpace α› :=
   uniformSpace_eq hf.1
 #align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
+-/
 
+/- warning: uniform_inducing_iff' -> uniformInducing_iff' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instPartialOrderFilter.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align uniform_inducing_iff' uniformInducing_iff'ₓ'. -/
 theorem uniformInducing_iff' {f : α → β} :
     UniformInducing f ↔ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
   rw [uniformInducing_iff, UniformContinuous, tendsto_iff_comap, le_antisymm_iff, and_comm'] <;> rfl
 #align uniform_inducing_iff' uniformInducing_iff'
 
+/- warning: filter.has_basis.uniform_inducing_iff -> Filter.HasBasis.uniformInducing_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {ι : Sort.{u3}} {ι' : Sort.{u4}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u1} (Prod.{u1, u1} α α))} {s' : ι' -> (Set.{u2} (Prod.{u2, u2} β β))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) ι (uniformity.{u1} α _inst_1) p s) -> (Filter.HasBasis.{u2, u4} (Prod.{u2, u2} β β) ι' (uniformity.{u2} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) (And (forall (i : ι'), (p' i) -> (Exists.{u3} ι (fun (j : ι) => And (p j) (forall (x : α) (y : α), (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j)) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)))))) (forall (j : ι), (p j) -> (Exists.{u4} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j))))))))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {ι : Sort.{u2}} {ι' : Sort.{u1}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u3} (Prod.{u3, u3} α α))} {s' : ι' -> (Set.{u4} (Prod.{u4, u4} β β))}, (Filter.HasBasis.{u3, u2} (Prod.{u3, u3} α α) ι (uniformity.{u3} α _inst_1) p s) -> (Filter.HasBasis.{u4, u1} (Prod.{u4, u4} β β) ι' (uniformity.{u4} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformInducing.{u3, u4} α β _inst_1 _inst_2 f) (And (forall (i : ι'), (p' i) -> (Exists.{u2} ι (fun (j : ι) => And (p j) (forall (x : α) (y : α), (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)) -> (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)))))) (forall (j : ι), (p j) -> (Exists.{u1} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)) -> (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j))))))))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.uniform_inducing_iff Filter.HasBasis.uniformInducing_iffₓ'. -/
 protected theorem Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformInducing f ↔
@@ -167,10 +181,12 @@ theorem UniformInducing.denseInducing {f : α → β} (h : UniformInducing f) (h
 #align uniform_inducing.dense_inducing UniformInducing.denseInducing
 -/
 
+#print UniformInducing.injective /-
 protected theorem UniformInducing.injective [T0Space α] {f : α → β} (h : UniformInducing f) :
     Injective f :=
   h.Inducing.Injective
 #align uniform_inducing.injective UniformInducing.injective
+-/
 
 #print UniformEmbedding /-
 /-- A map `f : α → β` between uniform spaces is a *uniform embedding* if it is uniform inducing and
@@ -181,11 +197,23 @@ structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop wher
 #align uniform_embedding UniformEmbedding
 -/
 
+/- warning: uniform_embedding_iff' -> uniformEmbedding_iff' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instPartialOrderFilter.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (Prod.map.{u1, u2, u1, u2} α β α β f f) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1))))
+Case conversion may be inaccurate. Consider using '#align uniform_embedding_iff' uniformEmbedding_iff'ₓ'. -/
 theorem uniformEmbedding_iff' {f : α → β} :
     UniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
   rw [uniformEmbedding_iff, and_comm', uniformInducing_iff']
 #align uniform_embedding_iff' uniformEmbedding_iff'
 
+/- warning: filter.has_basis.uniform_embedding_iff' -> Filter.HasBasis.uniformEmbedding_iff' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {ι : Sort.{u3}} {ι' : Sort.{u4}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u1} (Prod.{u1, u1} α α))} {s' : ι' -> (Set.{u2} (Prod.{u2, u2} β β))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) ι (uniformity.{u1} α _inst_1) p s) -> (Filter.HasBasis.{u2, u4} (Prod.{u2, u2} β β) ι' (uniformity.{u2} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (forall (i : ι'), (p' i) -> (Exists.{u3} ι (fun (j : ι) => And (p j) (forall (x : α) (y : α), (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j)) -> (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)))))) (forall (j : ι), (p j) -> (Exists.{u4} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j)))))))))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {ι : Sort.{u2}} {ι' : Sort.{u1}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u3} (Prod.{u3, u3} α α))} {s' : ι' -> (Set.{u4} (Prod.{u4, u4} β β))}, (Filter.HasBasis.{u3, u2} (Prod.{u3, u3} α α) ι (uniformity.{u3} α _inst_1) p s) -> (Filter.HasBasis.{u4, u1} (Prod.{u4, u4} β β) ι' (uniformity.{u4} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u3, u4} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u3, succ u4} α β f) (And (forall (i : ι'), (p' i) -> (Exists.{u2} ι (fun (j : ι) => And (p j) (forall (x : α) (y : α), (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)) -> (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)))))) (forall (j : ι), (p j) -> (Exists.{u1} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)) -> (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)))))))))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'ₓ'. -/
 theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformEmbedding f ↔
@@ -195,6 +223,12 @@ theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : 
   by rw [uniformEmbedding_iff, and_comm', h.uniform_inducing_iff h']
 #align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'
 
+/- warning: filter.has_basis.uniform_embedding_iff -> Filter.HasBasis.uniformEmbedding_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {ι : Sort.{u3}} {ι' : Sort.{u4}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u1} (Prod.{u1, u1} α α))} {s' : ι' -> (Set.{u2} (Prod.{u2, u2} β β))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) ι (uniformity.{u1} α _inst_1) p s) -> (Filter.HasBasis.{u2, u4} (Prod.{u2, u2} β β) ι' (uniformity.{u2} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (forall (j : ι), (p j) -> (Exists.{u4} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) (s' i)) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (s j)))))))))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {ι : Sort.{u2}} {ι' : Sort.{u1}} {p : ι -> Prop} {p' : ι' -> Prop} {s : ι -> (Set.{u3} (Prod.{u3, u3} α α))} {s' : ι' -> (Set.{u4} (Prod.{u4, u4} β β))}, (Filter.HasBasis.{u3, u2} (Prod.{u3, u3} α α) ι (uniformity.{u3} α _inst_1) p s) -> (Filter.HasBasis.{u4, u1} (Prod.{u4, u4} β β) ι' (uniformity.{u4} β _inst_2) p' s') -> (forall {f : α -> β}, Iff (UniformEmbedding.{u3, u4} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u3, succ u4} α β f) (And (UniformContinuous.{u3, u4} α β _inst_1 _inst_2 f) (forall (j : ι), (p j) -> (Exists.{u1} ι' (fun (i : ι') => And (p' i) (forall (x : α) (y : α), (Membership.mem.{u4, u4} (Prod.{u4, u4} β β) (Set.{u4} (Prod.{u4, u4} β β)) (Set.instMembershipSet.{u4} (Prod.{u4, u4} β β)) (Prod.mk.{u4, u4} β β (f x) (f y)) (s' i)) -> (Membership.mem.{u3, u3} (Prod.{u3, u3} α α) (Set.{u3} (Prod.{u3, u3} α α)) (Set.instMembershipSet.{u3} (Prod.{u3, u3} α α)) (Prod.mk.{u3, u3} α α x y) (s j)))))))))
+Case conversion may be inaccurate. Consider using '#align filter.has_basis.uniform_embedding_iff Filter.HasBasis.uniformEmbedding_iffₓ'. -/
 theorem Filter.HasBasis.uniformEmbedding_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
     (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
     UniformEmbedding f ↔
@@ -279,10 +313,12 @@ protected theorem UniformInducing.uniformEmbedding [T0Space α] {f : α → β}
 #align uniform_inducing.uniform_embedding UniformInducing.uniformEmbedding
 -/
 
+#print uniformEmbedding_iff_uniformInducing /-
 theorem uniformEmbedding_iff_uniformInducing [T0Space α] {f : α → β} :
     UniformEmbedding f ↔ UniformInducing f :=
   ⟨UniformEmbedding.to_uniformInducing, UniformInducing.uniformEmbedding⟩
 #align uniform_embedding_iff_uniform_inducing uniformEmbedding_iff_uniformInducing
+-/
 
 /- warning: comap_uniformity_of_spaced_out -> comap_uniformity_of_spaced_out is a dubious translation:
 lean 3 declaration is

195fcd60

bump to nightly-2023-03-02-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/195fcd60ff2bfe392543bceb0ec2adcdb472db4c

db7421c3

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
 
 ! This file was ported from Lean 3 source module topology.uniform_space.uniform_embedding
-! leanprover-community/mathlib commit 0a0ec35061ed9960bf0e7ffb0335f44447b58977
+! leanprover-community/mathlib commit 195fcd60ff2bfe392543bceb0ec2adcdb472db4c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -22,7 +22,7 @@ Extension of uniform continuous functions.
 -/
 
 
-open Filter TopologicalSpace Set Classical
+open Filter TopologicalSpace Set Function Classical
 
 open Classical uniformity Topology Filter
 
@@ -32,15 +32,40 @@ variable {α : Type _} {β : Type _} {γ : Type _} [UniformSpace α] [UniformSpa
 
 universe u v
 
+/-!
+### Uniform inducing maps
+-/
+
+
 #print UniformInducing /-
 /-- A map `f : α → β` between uniform spaces is called *uniform inducing* if the uniformity filter
 on `α` is the pullback of the uniformity filter on `β` under `prod.map f f`. If `α` is a separated
 space, then this implies that `f` is injective, hence it is a `uniform_embedding`. -/
+@[mk_iff]
 structure UniformInducing (f : α → β) : Prop where
   comap_uniformity : comap (fun x : α × α => (f x.1, f x.2)) (𝓤 β) = 𝓤 α
 #align uniform_inducing UniformInducing
 -/
 
+protected theorem UniformInducing.comap_uniformSpace {f : α → β} (hf : UniformInducing f) :
+    ‹UniformSpace β›.comap f = ‹UniformSpace α› :=
+  uniformSpace_eq hf.1
+#align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
+
+theorem uniformInducing_iff' {f : α → β} :
+    UniformInducing f ↔ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
+  rw [uniformInducing_iff, UniformContinuous, tendsto_iff_comap, le_antisymm_iff, and_comm'] <;> rfl
+#align uniform_inducing_iff' uniformInducing_iff'
+
+protected theorem Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+    (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
+    UniformInducing f ↔
+      (∀ i, p' i → ∃ j, p j ∧ ∀ x y, (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧
+        ∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j :=
+  by
+  simp [uniformInducing_iff', h.uniform_continuous_iff h', (h'.comap _).le_basis_iffₓ h, subset_def]
+#align filter.has_basis.uniform_inducing_iff Filter.HasBasis.uniformInducing_iff
+
 /- warning: uniform_inducing.mk' -> UniformInducing.mk' is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) (Exists.{succ u2} (Set.{u2} (Prod.{u2, u2} β β)) (fun (t : Set.{u2} (Prod.{u2, u2} β β)) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) => forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) t) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s))))) -> (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f)
@@ -61,12 +86,7 @@ theorem uniformInducing_id : UniformInducing (@id α) :=
 #print UniformInducing.comp /-
 theorem UniformInducing.comp {g : β → γ} (hg : UniformInducing g) {f : α → β}
     (hf : UniformInducing f) : UniformInducing (g ∘ f) :=
-  ⟨by
-    rw [show
-        (fun x : α × α => ((g ∘ f) x.1, (g ∘ f) x.2)) =
-          (fun y : β × β => (g y.1, g y.2)) ∘ fun x : α × α => (f x.1, f x.2)
-        by ext <;> simp,
-      ← Filter.comap_comap, hg.1, hf.1]⟩
+  ⟨by rw [← hf.1, ← hg.1, comap_comap]⟩
 #align uniform_inducing.comp UniformInducing.comp
 -/
 
@@ -100,14 +120,89 @@ theorem uniformInducing_of_compose {f : α → β} {g : β → γ} (hf : Uniform
 #align uniform_inducing_of_compose uniformInducing_of_compose
 -/
 
+#print UniformInducing.uniformContinuous /-
+theorem UniformInducing.uniformContinuous {f : α → β} (hf : UniformInducing f) :
+    UniformContinuous f :=
+  (uniformInducing_iff'.1 hf).1
+#align uniform_inducing.uniform_continuous UniformInducing.uniformContinuous
+-/
+
+#print UniformInducing.uniformContinuous_iff /-
+theorem UniformInducing.uniformContinuous_iff {f : α → β} {g : β → γ} (hg : UniformInducing g) :
+    UniformContinuous f ↔ UniformContinuous (g ∘ f) :=
+  by
+  dsimp only [UniformContinuous, tendsto]
+  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map]
+#align uniform_inducing.uniform_continuous_iff UniformInducing.uniformContinuous_iff
+-/
+
+#print UniformInducing.inducing /-
+protected theorem UniformInducing.inducing {f : α → β} (h : UniformInducing f) : Inducing f :=
+  by
+  obtain rfl := h.comap_uniform_space
+  letI := UniformSpace.comap f _
+  exact ⟨rfl⟩
+#align uniform_inducing.inducing UniformInducing.inducing
+-/
+
+/- warning: uniform_inducing.prod -> UniformInducing.prod is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {α' : Type.{u3}} {β' : Type.{u4}} [_inst_4 : UniformSpace.{u3} α'] [_inst_5 : UniformSpace.{u4} β'] {e₁ : α -> α'} {e₂ : β -> β'}, (UniformInducing.{u1, u3} α α' _inst_1 _inst_4 e₁) -> (UniformInducing.{u2, u4} β β' _inst_2 _inst_5 e₂) -> (UniformInducing.{max u1 u2, max u3 u4} (Prod.{u1, u2} α β) (Prod.{u3, u4} α' β') (Prod.uniformSpace.{u1, u2} α β _inst_1 _inst_2) (Prod.uniformSpace.{u3, u4} α' β' _inst_4 _inst_5) (fun (p : Prod.{u1, u2} α β) => Prod.mk.{u3, u4} α' β' (e₁ (Prod.fst.{u1, u2} α β p)) (e₂ (Prod.snd.{u1, u2} α β p))))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {α' : Type.{u2}} {β' : Type.{u1}} [_inst_4 : UniformSpace.{u2} α'] [_inst_5 : UniformSpace.{u1} β'] {e₁ : α -> α'} {e₂ : β -> β'}, (UniformInducing.{u3, u2} α α' _inst_1 _inst_4 e₁) -> (UniformInducing.{u4, u1} β β' _inst_2 _inst_5 e₂) -> (UniformInducing.{max u3 u4, max u1 u2} (Prod.{u3, u4} α β) (Prod.{u2, u1} α' β') (instUniformSpaceProd.{u3, u4} α β _inst_1 _inst_2) (instUniformSpaceProd.{u2, u1} α' β' _inst_4 _inst_5) (fun (p : Prod.{u3, u4} α β) => Prod.mk.{u2, u1} α' β' (e₁ (Prod.fst.{u3, u4} α β p)) (e₂ (Prod.snd.{u3, u4} α β p))))
+Case conversion may be inaccurate. Consider using '#align uniform_inducing.prod UniformInducing.prodₓ'. -/
+theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
+    {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformInducing e₁) (h₂ : UniformInducing e₂) :
+    UniformInducing fun p : α × β => (e₁ p.1, e₂ p.2) :=
+  ⟨by
+    simp [(· ∘ ·), uniformity_prod, h₁.comap_uniformity.symm, h₂.comap_uniformity.symm, comap_inf,
+      comap_comap]⟩
+#align uniform_inducing.prod UniformInducing.prod
+
+#print UniformInducing.denseInducing /-
+theorem UniformInducing.denseInducing {f : α → β} (h : UniformInducing f) (hd : DenseRange f) :
+    DenseInducing f :=
+  { dense := hd
+    induced := h.Inducing.induced }
+#align uniform_inducing.dense_inducing UniformInducing.denseInducing
+-/
+
+protected theorem UniformInducing.injective [T0Space α] {f : α → β} (h : UniformInducing f) :
+    Injective f :=
+  h.Inducing.Injective
+#align uniform_inducing.injective UniformInducing.injective
+
 #print UniformEmbedding /-
 /-- A map `f : α → β` between uniform spaces is a *uniform embedding* if it is uniform inducing and
 injective. If `α` is a separated space, then the latter assumption follows from the former. -/
+@[mk_iff]
 structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop where
   inj : Function.Injective f
 #align uniform_embedding UniformEmbedding
 -/
 
+theorem uniformEmbedding_iff' {f : α → β} :
+    UniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
+  rw [uniformEmbedding_iff, and_comm', uniformInducing_iff']
+#align uniform_embedding_iff' uniformEmbedding_iff'
+
+theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+    (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
+    UniformEmbedding f ↔
+      Injective f ∧
+        (∀ i, p' i → ∃ j, p j ∧ ∀ x y, (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧
+          ∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j :=
+  by rw [uniformEmbedding_iff, and_comm', h.uniform_inducing_iff h']
+#align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'
+
+theorem Filter.HasBasis.uniformEmbedding_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+    (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
+    UniformEmbedding f ↔
+      Injective f ∧
+        UniformContinuous f ∧ ∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j :=
+  by simp only [h.uniform_embedding_iff' h', h.uniform_continuous_iff h', exists_prop]
+#align filter.has_basis.uniform_embedding_iff Filter.HasBasis.uniformEmbedding_iff
+
 #print uniformEmbedding_subtype_val /-
 theorem uniformEmbedding_subtype_val {p : α → Prop} :
     UniformEmbedding (Subtype.val : Subtype p → α) :=
@@ -142,44 +237,6 @@ theorem UniformEmbedding.comp {g : β → γ} (hg : UniformEmbedding g) {f : α
 #align uniform_embedding.comp UniformEmbedding.comp
 -/
 
-/- warning: uniform_embedding_def -> uniformEmbedding_def is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) (Exists.{succ u2} (Set.{u2} (Prod.{u2, u2} β β)) (fun (t : Set.{u2} (Prod.{u2, u2} β β)) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) => forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) t) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s))))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) (Exists.{succ u2} (Set.{u2} (Prod.{u2, u2} β β)) (fun (t : Set.{u2} (Prod.{u2, u2} β β)) => And (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) (forall (x : α) (y : α), (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) t) -> (Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s))))))
-Case conversion may be inaccurate. Consider using '#align uniform_embedding_def uniformEmbedding_defₓ'. -/
-theorem uniformEmbedding_def {f : α → β} :
-    UniformEmbedding f ↔
-      Function.Injective f ∧ ∀ s, s ∈ 𝓤 α ↔ ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s :=
-  by
-  constructor
-  · rintro ⟨⟨h⟩, h'⟩
-    rw [eq_comm, Filter.ext_iff] at h
-    simp [*, subset_def]
-  · rintro ⟨h, h'⟩
-    refine' UniformEmbedding.mk ⟨_⟩ h
-    rw [eq_comm, Filter.ext_iff]
-    simp [*, subset_def]
-#align uniform_embedding_def uniformEmbedding_def
-
-/- warning: uniform_embedding_def' -> uniformEmbedding_def' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u2} (Set.{u2} (Prod.{u2, u2} β β)) (fun (t : Set.{u2} (Prod.{u2, u2} β β)) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (Filter.hasMem.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) => forall (x : α) (y : α), (Membership.Mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.hasMem.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) t) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s)))))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f) (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u2} (Set.{u2} (Prod.{u2, u2} β β)) (fun (t : Set.{u2} (Prod.{u2, u2} β β)) => And (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} β β)) (Filter.{u2} (Prod.{u2, u2} β β)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} β β)) t (uniformity.{u2} β _inst_2)) (forall (x : α) (y : α), (Membership.mem.{u2, u2} (Prod.{u2, u2} β β) (Set.{u2} (Prod.{u2, u2} β β)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} β β)) (Prod.mk.{u2, u2} β β (f x) (f y)) t) -> (Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s)))))))
-Case conversion may be inaccurate. Consider using '#align uniform_embedding_def' uniformEmbedding_def'ₓ'. -/
-theorem uniformEmbedding_def' {f : α → β} :
-    UniformEmbedding f ↔
-      Function.Injective f ∧
-        UniformContinuous f ∧ ∀ s, s ∈ 𝓤 α → ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s :=
-  by
-  simp only [uniformEmbedding_def, uniformContinuous_def] <;>
-    exact
-      ⟨fun ⟨I, H⟩ => ⟨I, fun s su => (H _).2 ⟨s, su, fun x y => id⟩, fun s => (H s).1⟩,
-        fun ⟨I, H₁, H₂⟩ =>
-        ⟨I, fun s => ⟨H₂ s, fun ⟨t, tu, h⟩ => mem_of_superset (H₁ t tu) fun ⟨a, b⟩ => h a b⟩⟩⟩
-#align uniform_embedding_def' uniformEmbedding_def'
-
 /- warning: equiv.uniform_embedding -> Equiv.uniformEmbedding is a dubious translation:
 lean 3 declaration is
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_4 : UniformSpace.{u1} α] [_inst_5 : UniformSpace.{u2} β] (f : Equiv.{succ u1, succ u2} α β), (UniformContinuous.{u1, u2} α β _inst_4 _inst_5 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) f)) -> (UniformContinuous.{u2, u1} β α _inst_5 _inst_4 (coeFn.{max 1 (max (succ u2) (succ u1)) (succ u1) (succ u2), max (succ u2) (succ u1)} (Equiv.{succ u2, succ u1} β α) (fun (_x : Equiv.{succ u2, succ u1} β α) => β -> α) (Equiv.hasCoeToFun.{succ u2, succ u1} β α) (Equiv.symm.{succ u1, succ u2} α β f))) -> (UniformEmbedding.{u1, u2} α β _inst_4 _inst_5 (coeFn.{max 1 (max (succ u1) (succ u2)) (succ u2) (succ u1), max (succ u1) (succ u2)} (Equiv.{succ u1, succ u2} α β) (fun (_x : Equiv.{succ u1, succ u2} α β) => α -> β) (Equiv.hasCoeToFun.{succ u1, succ u2} α β) f))
@@ -188,68 +245,44 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align equiv.uniform_embedding Equiv.uniformEmbeddingₓ'. -/
 theorem Equiv.uniformEmbedding {α β : Type _} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
     (h₁ : UniformContinuous f) (h₂ : UniformContinuous f.symm) : UniformEmbedding f :=
-  { comap_uniformity := by
-      refine' le_antisymm _ _
-      · change comap (f.prod_congr f) _ ≤ _
-        rw [← map_equiv_symm (f.prod_congr f)]
-        exact h₂
-      · rw [← map_le_iff_le_comap]
-        exact h₁
-    inj := f.Injective }
+  uniformEmbedding_iff'.2 ⟨f.Injective, h₁, by rwa [← Equiv.prodCongr_apply, ← map_equiv_symm]⟩
 #align equiv.uniform_embedding Equiv.uniformEmbedding
 
 #print uniformEmbedding_inl /-
 theorem uniformEmbedding_inl : UniformEmbedding (Sum.inl : α → Sum α β) :=
   by
-  apply uniformEmbedding_def.2 ⟨Sum.inl_injective, fun s => ⟨_, _⟩⟩
-  · intro hs
-    refine'
-      ⟨(fun p : α × α => (Sum.inl p.1, Sum.inl p.2)) '' s ∪
-          (fun p : β × β => (Sum.inr p.1, Sum.inr p.2)) '' univ,
-        _, _⟩
-    · exact union_mem_uniformity_sum hs univ_mem
-    · simp
-  · rintro ⟨t, ht, h't⟩
-    simp only [Sum.uniformity, mem_sup, mem_map] at ht
-    apply Filter.mem_of_superset ht.1
-    rintro ⟨x, y⟩ hx
-    exact h't _ _ hx
+  refine' ⟨⟨_⟩, Sum.inl_injective⟩
+  rw [Sum.uniformity, comap_sup, comap_map, comap_eq_bot_iff_compl_range.2 _, sup_bot_eq]
+  · refine' mem_map.2 (univ_mem' _)
+    simp
+  · exact sum.inl_injective.prod_map Sum.inl_injective
 #align uniform_embedding_inl uniformEmbedding_inl
 -/
 
 #print uniformEmbedding_inr /-
 theorem uniformEmbedding_inr : UniformEmbedding (Sum.inr : β → Sum α β) :=
   by
-  apply uniformEmbedding_def.2 ⟨Sum.inr_injective, fun s => ⟨_, _⟩⟩
-  · intro hs
-    refine'
-      ⟨(fun p : α × α => (Sum.inl p.1, Sum.inl p.2)) '' univ ∪
-          (fun p : β × β => (Sum.inr p.1, Sum.inr p.2)) '' s,
-        _, _⟩
-    · exact union_mem_uniformity_sum univ_mem hs
-    · simp
-  · rintro ⟨t, ht, h't⟩
-    simp only [Sum.uniformity, mem_sup, mem_map] at ht
-    apply Filter.mem_of_superset ht.2
-    rintro ⟨x, y⟩ hx
-    exact h't _ _ hx
+  refine' ⟨⟨_⟩, Sum.inr_injective⟩
+  rw [Sum.uniformity, comap_sup, comap_eq_bot_iff_compl_range.2 _, comap_map, bot_sup_eq]
+  · exact sum.inr_injective.prod_map Sum.inr_injective
+  · refine' mem_map.2 (univ_mem' _)
+    simp
 #align uniform_embedding_inr uniformEmbedding_inr
 -/
 
-/- warning: uniform_inducing.uniform_embedding -> UniformInducing.uniformEmbedding is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] [_inst_4 : SeparatedSpace.{u1} α _inst_1] {f : α -> β}, (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) -> (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] [_inst_4 : T0Space.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)] {f : α -> β}, (UniformInducing.{u1, u2} α β _inst_1 _inst_2 f) -> (UniformEmbedding.{u1, u2} α β _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align uniform_inducing.uniform_embedding UniformInducing.uniformEmbeddingₓ'. -/
+#print UniformInducing.uniformEmbedding /-
 /-- If the domain of a `uniform_inducing` map `f` is a `separated_space`, then `f` is injective,
 hence it is a `uniform_embedding`. -/
-protected theorem UniformInducing.uniformEmbedding [SeparatedSpace α] {f : α → β}
+protected theorem UniformInducing.uniformEmbedding [T0Space α] {f : α → β}
     (hf : UniformInducing f) : UniformEmbedding f :=
-  ⟨hf, fun x y h =>
-    eq_of_uniformity_basis (hf.basis_uniformity (𝓤 β).basis_sets) fun s hs =>
-      mem_preimage.2 <| mem_uniformity_of_eq hs h⟩
+  ⟨hf, hf.Injective⟩
 #align uniform_inducing.uniform_embedding UniformInducing.uniformEmbedding
+-/
+
+theorem uniformEmbedding_iff_uniformInducing [T0Space α] {f : α → β} :
+    UniformEmbedding f ↔ UniformInducing f :=
+  ⟨UniformEmbedding.to_uniformInducing, UniformInducing.uniformEmbedding⟩
+#align uniform_embedding_iff_uniform_inducing uniformEmbedding_iff_uniformInducing
 
 /- warning: comap_uniformity_of_spaced_out -> comap_uniformity_of_spaced_out is a dubious translation:
 lean 3 declaration is
@@ -289,55 +322,8 @@ theorem uniformEmbedding_of_spaced_out {α} {f : α → β} {s : Set (β × β)}
   exact UniformInducing.uniformEmbedding ⟨comap_uniformity_of_spaced_out hs hf⟩
 #align uniform_embedding_of_spaced_out uniformEmbedding_of_spaced_out
 
-#print UniformInducing.uniformContinuous /-
-theorem UniformInducing.uniformContinuous {f : α → β} (hf : UniformInducing f) :
-    UniformContinuous f := by simp [UniformContinuous, hf.comap_uniformity.symm, tendsto_comap]
-#align uniform_inducing.uniform_continuous UniformInducing.uniformContinuous
--/
-
-#print UniformInducing.uniformContinuous_iff /-
-theorem UniformInducing.uniformContinuous_iff {f : α → β} {g : β → γ} (hg : UniformInducing g) :
-    UniformContinuous f ↔ UniformContinuous (g ∘ f) :=
-  by
-  dsimp only [UniformContinuous, tendsto]
-  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map]
-#align uniform_inducing.uniform_continuous_iff UniformInducing.uniformContinuous_iff
--/
-
-#print UniformInducing.inducing /-
-theorem UniformInducing.inducing {f : α → β} (h : UniformInducing f) : Inducing f :=
-  by
-  refine' ⟨eq_of_nhds_eq_nhds fun a => _⟩
-  rw [nhds_induced, nhds_eq_uniformity, nhds_eq_uniformity, ← h.comap_uniformity, comap_lift'_eq,
-    comap_lift'_eq2]
-  exacts[rfl, monotone_preimage]
-#align uniform_inducing.inducing UniformInducing.inducing
--/
-
-/- warning: uniform_inducing.prod -> UniformInducing.prod is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {α' : Type.{u3}} {β' : Type.{u4}} [_inst_4 : UniformSpace.{u3} α'] [_inst_5 : UniformSpace.{u4} β'] {e₁ : α -> α'} {e₂ : β -> β'}, (UniformInducing.{u1, u3} α α' _inst_1 _inst_4 e₁) -> (UniformInducing.{u2, u4} β β' _inst_2 _inst_5 e₂) -> (UniformInducing.{max u1 u2, max u3 u4} (Prod.{u1, u2} α β) (Prod.{u3, u4} α' β') (Prod.uniformSpace.{u1, u2} α β _inst_1 _inst_2) (Prod.uniformSpace.{u3, u4} α' β' _inst_4 _inst_5) (fun (p : Prod.{u1, u2} α β) => Prod.mk.{u3, u4} α' β' (e₁ (Prod.fst.{u1, u2} α β p)) (e₂ (Prod.snd.{u1, u2} α β p))))
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u4}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u4} β] {α' : Type.{u2}} {β' : Type.{u1}} [_inst_4 : UniformSpace.{u2} α'] [_inst_5 : UniformSpace.{u1} β'] {e₁ : α -> α'} {e₂ : β -> β'}, (UniformInducing.{u3, u2} α α' _inst_1 _inst_4 e₁) -> (UniformInducing.{u4, u1} β β' _inst_2 _inst_5 e₂) -> (UniformInducing.{max u3 u4, max u1 u2} (Prod.{u3, u4} α β) (Prod.{u2, u1} α' β') (instUniformSpaceProd.{u3, u4} α β _inst_1 _inst_2) (instUniformSpaceProd.{u2, u1} α' β' _inst_4 _inst_5) (fun (p : Prod.{u3, u4} α β) => Prod.mk.{u2, u1} α' β' (e₁ (Prod.fst.{u3, u4} α β p)) (e₂ (Prod.snd.{u3, u4} α β p))))
-Case conversion may be inaccurate. Consider using '#align uniform_inducing.prod UniformInducing.prodₓ'. -/
-theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
-    {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformInducing e₁) (h₂ : UniformInducing e₂) :
-    UniformInducing fun p : α × β => (e₁ p.1, e₂ p.2) :=
-  ⟨by
-    simp [(· ∘ ·), uniformity_prod, h₁.comap_uniformity.symm, h₂.comap_uniformity.symm, comap_inf,
-      comap_comap]⟩
-#align uniform_inducing.prod UniformInducing.prod
-
-#print UniformInducing.denseInducing /-
-theorem UniformInducing.denseInducing {f : α → β} (h : UniformInducing f) (hd : DenseRange f) :
-    DenseInducing f :=
-  { dense := hd
-    induced := h.Inducing.induced }
-#align uniform_inducing.dense_inducing UniformInducing.denseInducing
--/
-
 #print UniformEmbedding.embedding /-
-theorem UniformEmbedding.embedding {f : α → β} (h : UniformEmbedding f) : Embedding f :=
+protected theorem UniformEmbedding.embedding {f : α → β} (h : UniformEmbedding f) : Embedding f :=
   { induced := h.to_uniformInducing.Inducing.induced
     inj := h.inj }
 #align uniform_embedding.embedding UniformEmbedding.embedding
@@ -628,7 +614,7 @@ but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [u : UniformSpace.{u1} β] (f : α -> β) (h : Embedding.{u2, u1} α β _inst_1 (UniformSpace.toTopologicalSpace.{u1} β u) f), UniformEmbedding.{u2, u1} α β (Embedding.comapUniformSpace.{u2, u1} α β _inst_1 u f h) u f
 Case conversion may be inaccurate. Consider using '#align embedding.to_uniform_embedding Embedding.to_uniformEmbeddingₓ'. -/
 theorem Embedding.to_uniformEmbedding {α β} [TopologicalSpace α] [u : UniformSpace β] (f : α → β)
-    (h : Embedding f) : @UniformEmbedding α β (h.comapUniformSpace f) u f :=
+    (h : Embedding f) : @UniformEmbedding α β (h.comap_uniformSpace f) u f :=
   { comap_uniformity := rfl
     inj := h.inj }
 #align embedding.to_uniform_embedding Embedding.to_uniformEmbedding

0a0ec350

bump to nightly-2023-03-01-20

mathlib commit https://github.com/leanprover-community/mathlib/commit/4c586d291f189eecb9d00581aeb3dd998ac34442

20cadee0

Diff

@@ -737,7 +737,7 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
       have : (e ⁻¹' m₁) ×ˢ (e ⁻¹' m₂) ⊆ (fun p : β × β => (f p.1, f p.2)) ⁻¹' s :=
         calc
           _ ⊆ preimage (fun p : β × β => (e p.1, e p.2)) (interior t) := preimage_mono hm
-          _ ⊆ preimage (fun p : β × β => (e p.1, e p.2)) t := preimage_mono interior_subset
+          _ ⊆ preimage (fun p : β × β => (e p.1, e p.2)) t := (preimage_mono interior_subset)
           _ ⊆ preimage (fun p : β × β => (f p.1, f p.2)) s := ts
           
       have : (f '' (e ⁻¹' m₁)) ×ˢ (f '' (e ⁻¹' m₂)) ⊆ s :=
@@ -746,7 +746,7 @@ theorem uniformContinuous_uniformly_extend [cγ : CompleteSpace γ] : UniformCon
               (fun p : β × β => (f p.1, f p.2)) '' (e ⁻¹' m₁) ×ˢ (e ⁻¹' m₂) :=
             prod_image_image_eq
           _ ⊆ (fun p : β × β => (f p.1, f p.2)) '' ((fun p : β × β => (f p.1, f p.2)) ⁻¹' s) :=
-            monotone_image this
+            (monotone_image this)
           _ ⊆ s := image_preimage_subset _ _
           
       have : (a, b) ∈ s := @this (a, b) ⟨ha₁, hb₁⟩

0a0ec350

bump to nightly-2023-02-21-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/bd9851ca476957ea4549eb19b40e7b5ade9428cc

1107b979

Changes in mathlib4

mathlib3

mathlib4

195fcd60

chore: adapt to multiple goal linter 3 (#12372)

A PR analogous to #12338 and #12361: reformatting proofs following the multiple goals linter of #12339.

d29b3780

Diff

@@ -286,7 +286,7 @@ theorem isComplete_of_complete_image {m : α → β} {s : Set α} (hm : UniformI
   intro f hf hfs
   rw [le_principal_iff] at hfs
   obtain ⟨_, ⟨x, hx, rfl⟩, hyf⟩ : ∃ y ∈ m '' s, map m f ≤ 𝓝 y
-  exact hs (f.map m) (hf.map hm.uniformContinuous) (le_principal_iff.2 (image_mem_map hfs))
+  · exact hs (f.map m) (hf.map hm.uniformContinuous) (le_principal_iff.2 (image_mem_map hfs))
   rw [map_le_iff_le_comap, ← nhds_induced, ← hm.inducing.induced] at hyf
   exact ⟨x, hx, hyf⟩
 #align is_complete_of_complete_image isComplete_of_complete_image

195fcd60

chore: rename open_range to isOpen_range, closed_range to isClosed_range (#11438)

All these lemmas refer to the range of some function being open/range (i.e. isOpen or isClosed).

75784e0d

Diff

@@ -249,7 +249,7 @@ theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopolo
   rcases @DiscreteTopology.eq_bot α _ _ with rfl; let _ : UniformSpace α := ⊥
   exact
     { (uniformEmbedding_of_spaced_out hs hf).embedding with
-      closed_range := isClosed_range_of_spaced_out hs hf }
+      isClosed_range := isClosed_range_of_spaced_out hs hf }
 #align closed_embedding_of_spaced_out closedEmbedding_of_spaced_out
 
 theorem closure_image_mem_nhds_of_uniformInducing {s : Set (α × α)} {e : α → β} (b : β)

195fcd60

refactor(UniformSpace): drop separationRel (#10644)

We had duplicated API between topological spaces and uniform spaces. In this PR I mostly deduplicate it with some exceptions:

SeparationQuotient.lift' and SeparationQuotient.map are leftovers from the old version that are designed to work with uniform spaces;
probably, some theorems/instances still assume UniformSpace when TopologicalSpace would work.

Outside of UniformSpace/Separation, I mostly changed SeparatedSpace to T0Space and separationRel to Inseparable. I also rewrote a few proofs that were broken by the API change.

Fixes #2031

38155ec4

Diff

@@ -124,6 +124,9 @@ theorem UniformInducing.denseInducing {f : α → β} (h : UniformInducing f) (h
     induced := h.inducing.induced }
 #align uniform_inducing.dense_inducing UniformInducing.denseInducing
 
+theorem SeparationQuotient.uniformInducing_mk : UniformInducing (mk : α → SeparationQuotient α) :=
+  ⟨comap_mk_uniformity⟩
+
 protected theorem UniformInducing.injective [T0Space α] {f : α → β} (h : UniformInducing f) :
     Injective f :=
   h.inducing.injective
@@ -241,7 +244,7 @@ theorem UniformEmbedding.denseEmbedding {f : α → β} (h : UniformEmbedding f)
 #align uniform_embedding.dense_embedding UniformEmbedding.denseEmbedding
 
 theorem closedEmbedding_of_spaced_out {α} [TopologicalSpace α] [DiscreteTopology α]
-    [SeparatedSpace β] {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
+    [T0Space β] {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
     (hf : Pairwise fun x y => (f x, f y) ∉ s) : ClosedEmbedding f := by
   rcases @DiscreteTopology.eq_bot α _ _ with rfl; let _ : UniformSpace α := ⊥
   exact
@@ -320,6 +323,16 @@ theorem UniformInducing.isComplete_range [CompleteSpace α] {f : α → β} (hf
   (completeSpace_iff_isComplete_range hf).1 ‹_›
 #align uniform_inducing.is_complete_range UniformInducing.isComplete_range
 
+theorem SeparationQuotient.completeSpace_iff :
+    CompleteSpace (SeparationQuotient α) ↔ CompleteSpace α := by
+  rw [completeSpace_iff_isComplete_univ, ← range_mk,
+    ← completeSpace_iff_isComplete_range uniformInducing_mk]
+
+instance SeparationQuotient.instCompleteSpace [CompleteSpace α] :
+    CompleteSpace (SeparationQuotient α) :=
+  completeSpace_iff.2 ‹_›
+#align uniform_space.complete_space_separation SeparationQuotient.instCompleteSpace
+
 theorem completeSpace_congr {e : α ≃ β} (he : UniformEmbedding e) :
     CompleteSpace α ↔ CompleteSpace β := by
   rw [completeSpace_iff_isComplete_range he.toUniformInducing, e.range_eq_univ,
@@ -496,7 +509,7 @@ theorem uniformContinuous_uniformly_extend [CompleteSpace γ] : UniformContinuou
       exact hs_comp ⟨f a, ha₂, ⟨f b, this, hb₂⟩⟩
 #align uniform_continuous_uniformly_extend uniformContinuous_uniformly_extend
 
-variable [SeparatedSpace γ]
+variable [T0Space γ]
 
 theorem uniformly_extend_of_ind (b : β) : ψ (e b) = f b :=
   DenseInducing.extend_eq_at _ h_f.continuous.continuousAt

195fcd60

chore: tidy various files (#10311)

890dba74

Diff

@@ -105,7 +105,7 @@ theorem UniformInducing.uniformContinuousOn_iff {f : α → β} {g : β → γ}
     (hg : UniformInducing g) :
     UniformContinuousOn f S ↔ UniformContinuousOn (g ∘ f) S := by
   dsimp only [UniformContinuousOn, Tendsto]
-  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map]; rfl
+  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map, comp_def, comp_def]
 
 theorem UniformInducing.inducing {f : α → β} (h : UniformInducing f) : Inducing f := by
   obtain rfl := h.comap_uniformSpace

195fcd60

feat: iff version of UniformInducing.comap_uniformSpace (#10153)

Preliminaries for #6844

c68625d2

Diff

@@ -38,9 +38,12 @@ structure UniformInducing (f : α → β) : Prop where
 #align uniform_inducing UniformInducing
 #align uniform_inducing_iff uniformInducing_iff
 
-protected lemma UniformInducing.comap_uniformSpace {f : α → β} (hf : UniformInducing f) :
-    ‹UniformSpace β›.comap f = ‹UniformSpace α› :=
-  UniformSpace.ext hf.1
+lemma uniformInducing_iff_uniformSpace {f : α → β} :
+    UniformInducing f ↔ ‹UniformSpace β›.comap f = ‹UniformSpace α› := by
+  rw [uniformInducing_iff, UniformSpace.ext_iff, Filter.ext_iff]
+  rfl
+
+protected alias ⟨UniformInducing.comap_uniformSpace, _⟩ := uniformInducing_iff_uniformSpace
 #align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
 
 lemma uniformInducing_iff' {f : α → β} :

195fcd60

refactor: decapitalize names in @[mk_iff] (#9378)

@[mk_iff] class MyPred now generates myPred_iff, not MyPred_iff
add Lean.Name.decapitalize
fix indentation and a few typos in the docs/comments.

Partially addresses issue #9129

5192777c

Diff

@@ -30,7 +30,7 @@ variable {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpa
 /-- A map `f : α → β` between uniform spaces is called *uniform inducing* if the uniformity filter
 on `α` is the pullback of the uniformity filter on `β` under `Prod.map f f`. If `α` is a separated
 space, then this implies that `f` is injective, hence it is a `UniformEmbedding`. -/
-@[mk_iff uniformInducing_iff]
+@[mk_iff]
 structure UniformInducing (f : α → β) : Prop where
   /-- The uniformity filter on the domain is the pullback of the uniformity filter on the codomain
   under `Prod.map f f`. -/
@@ -131,7 +131,7 @@ protected theorem UniformInducing.injective [T0Space α] {f : α → β} (h : Un
 
 /-- A map `f : α → β` between uniform spaces is a *uniform embedding* if it is uniform inducing and
 injective. If `α` is a separated space, then the latter assumption follows from the former. -/
-@[mk_iff uniformEmbedding_iff]
+@[mk_iff]
 structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop where
   /-- A uniform embedding is injective. -/
   inj : Function.Injective f

195fcd60

feat: misc lemmas on uniform spaces (#9305)

521f71ff

Diff

@@ -98,6 +98,12 @@ theorem UniformInducing.uniformContinuous_iff {f : α → β} {g : β → γ} (h
   rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map]; rfl
 #align uniform_inducing.uniform_continuous_iff UniformInducing.uniformContinuous_iff
 
+theorem UniformInducing.uniformContinuousOn_iff {f : α → β} {g : β → γ} {S : Set α}
+    (hg : UniformInducing g) :
+    UniformContinuousOn f S ↔ UniformContinuousOn (g ∘ f) S := by
+  dsimp only [UniformContinuousOn, Tendsto]
+  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map]; rfl
+
 theorem UniformInducing.inducing {f : α → β} (h : UniformInducing f) : Inducing f := by
   obtain rfl := h.comap_uniformSpace
   exact inducing_induced f

195fcd60

chore: fix some cases in names (#7469)

And fix some names in comments where this revealed issues

be0d066c

Diff

@@ -201,7 +201,7 @@ theorem uniformEmbedding_iff_uniformInducing [T0Space α] {f : α → β} :
 
 /-- If a map `f : α → β` sends any two distinct points to point that are **not** related by a fixed
 `s ∈ 𝓤 β`, then `f` is uniform inducing with respect to the discrete uniformity on `α`:
-the preimage of `𝓤 β` under `prod.map f f` is the principal filter generated by the diagonal in
+the preimage of `𝓤 β` under `Prod.map f f` is the principal filter generated by the diagonal in
 `α × α`. -/
 theorem comap_uniformity_of_spaced_out {α} {f : α → β} {s : Set (β × β)} (hs : s ∈ 𝓤 β)
     (hf : Pairwise fun x y => (f x, f y) ∉ s) : comap (Prod.map f f) (𝓤 β) = 𝓟 idRel := by

195fcd60

chore: more predictable ext lemmas for TopologicalSpace and UniformSpace (#6705)

db373a75

Diff

@@ -40,7 +40,7 @@ structure UniformInducing (f : α → β) : Prop where
 
 protected lemma UniformInducing.comap_uniformSpace {f : α → β} (hf : UniformInducing f) :
     ‹UniformSpace β›.comap f = ‹UniformSpace α› :=
-  uniformSpace_eq hf.1
+  UniformSpace.ext hf.1
 #align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
 
 lemma uniformInducing_iff' {f : α → β} :

195fcd60

chore: banish Type _ and Sort _ (#6499)

We remove all possible occurences of Type _ and Sort _ in favor of Type* and Sort*.

This has nice performance benefits.

32de3f67

Diff

@@ -70,7 +70,7 @@ theorem UniformInducing.comp {g : β → γ} (hg : UniformInducing g) {f : α 
   ⟨by rw [← hf.1, ← hg.1, comap_comap]; rfl⟩
 #align uniform_inducing.comp UniformInducing.comp
 
-theorem UniformInducing.basis_uniformity {f : α → β} (hf : UniformInducing f) {ι : Sort _}
+theorem UniformInducing.basis_uniformity {f : α → β} (hf : UniformInducing f) {ι : Sort*}
     {p : ι → Prop} {s : ι → Set (β × β)} (H : (𝓤 β).HasBasis p s) :
     (𝓤 α).HasBasis p fun i => Prod.map f f ⁻¹' s i :=
   hf.1 ▸ H.comap _
@@ -103,7 +103,7 @@ theorem UniformInducing.inducing {f : α → β} (h : UniformInducing f) : Induc
   exact inducing_induced f
 #align uniform_inducing.inducing UniformInducing.inducing
 
-theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
+theorem UniformInducing.prod {α' : Type*} {β' : Type*} [UniformSpace α'] [UniformSpace β']
     {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformInducing e₁) (h₂ : UniformInducing e₂) :
     UniformInducing fun p : α × β => (e₁ p.1, e₂ p.2) :=
   ⟨by simp [(· ∘ ·), uniformity_prod, ← h₁.1, ← h₂.1, comap_inf, comap_comap]⟩
@@ -170,7 +170,7 @@ theorem UniformEmbedding.comp {g : β → γ} (hg : UniformEmbedding g) {f : α
   { hg.toUniformInducing.comp hf.toUniformInducing with inj := hg.inj.comp hf.inj }
 #align uniform_embedding.comp UniformEmbedding.comp
 
-theorem Equiv.uniformEmbedding {α β : Type _} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
+theorem Equiv.uniformEmbedding {α β : Type*} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
     (h₁ : UniformContinuous f) (h₂ : UniformContinuous f.symm) : UniformEmbedding f :=
   uniformEmbedding_iff'.2 ⟨f.injective, h₁, by rwa [← Equiv.prodCongr_apply, ← map_equiv_symm]⟩
 #align equiv.uniform_embedding Equiv.uniformEmbedding
@@ -263,7 +263,7 @@ theorem uniformEmbedding_subtypeEmb (p : α → Prop) {e : α → β} (ue : Unif
     inj := (de.subtype p).inj }
 #align uniform_embedding_subtype_emb uniformEmbedding_subtypeEmb
 
-theorem UniformEmbedding.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
+theorem UniformEmbedding.prod {α' : Type*} {β' : Type*} [UniformSpace α'] [UniformSpace β']
     {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformEmbedding e₁) (h₂ : UniformEmbedding e₂) :
     UniformEmbedding fun p : α × β => (e₁ p.1, e₂ p.2) :=
   { h₁.toUniformInducing.prod h₂.toUniformInducing with inj := h₁.inj.Prod_map h₂.inj }
@@ -401,7 +401,7 @@ instance CompleteSpace.sum [CompleteSpace α] [CompleteSpace β] : CompleteSpace
 
 end
 
-theorem uniformEmbedding_comap {α : Type _} {β : Type _} {f : α → β} [u : UniformSpace β]
+theorem uniformEmbedding_comap {α : Type*} {β : Type*} {f : α → β} [u : UniformSpace β]
     (hf : Function.Injective f) : @UniformEmbedding α β (UniformSpace.comap f u) u f :=
   @UniformEmbedding.mk _ _ (UniformSpace.comap f u) _ _
     (@UniformInducing.mk _ _ (UniformSpace.comap f u) _ _ rfl) hf
@@ -423,7 +423,7 @@ theorem Embedding.to_uniformEmbedding {α β} [TopologicalSpace α] [u : Uniform
 
 section UniformExtension
 
-variable {α : Type _} {β : Type _} {γ : Type _} [UniformSpace α] [UniformSpace β] [UniformSpace γ]
+variable {α : Type*} {β : Type*} {γ : Type*} [UniformSpace α] [UniformSpace β] [UniformSpace γ]
   {e : β → α} (h_e : UniformInducing e) (h_dense : DenseRange e) {f : β → γ}
   (h_f : UniformContinuous f)

195fcd60

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

89aa3a3b

Diff

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.uniform_space.uniform_embedding
-! leanprover-community/mathlib commit 195fcd60ff2bfe392543bceb0ec2adcdb472db4c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.UniformSpace.Cauchy
 import Mathlib.Topology.UniformSpace.Separation
 import Mathlib.Topology.DenseEmbedding
 
+#align_import topology.uniform_space.uniform_embedding from "leanprover-community/mathlib"@"195fcd60ff2bfe392543bceb0ec2adcdb472db4c"
+
 /-!
 # Uniform embeddings of uniform spaces.

195fcd60

chore: clean up spacing around at and goals (#5387)

Changes are of the form

some_tactic at h⊢ -> some_tactic at h ⊢
some_tactic at h -> some_tactic at h

2a870323

Diff

@@ -390,7 +390,7 @@ theorem totallyBounded_preimage {f : α → β} {s : Set β} (hf : UniformEmbedd
   rcases totallyBounded_iff_subset.1 (totallyBounded_subset (image_preimage_subset f s) hs) _ ht'
     with ⟨c, cs, hfc, hct⟩
   refine' ⟨f ⁻¹' c, hfc.preimage (hf.inj.injOn _), fun x h => _⟩
-  have := hct (mem_image_of_mem f h); simp at this⊢
+  have := hct (mem_image_of_mem f h); simp at this ⊢
   rcases this with ⟨z, zc, zt⟩
   rcases cs zc with ⟨y, -, rfl⟩
   exact ⟨y, zc, ts zt⟩

195fcd60

refactor: use the typeclass SProd to implement overloaded notation · ×ˢ · (#4200)

Currently, the following notations are changed from · ×ˢ · because Lean 4 can't deal with ambiguous notations. | Definition | Notation | | :

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: Kyle Miller <kmill31415@gmail.com> Co-authored-by: Chris Hughes <chrishughes24@gmail.com>

6c01dc6e

Diff

@@ -367,8 +367,8 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
         have hg₁ : p (preimage Prod.swap s₁) t ∈ g :=
           mem_lift (symm_le_uniformity hs₁) <| @mem_lift' α α f _ t ht
         have hg₂ : p s₂ t ∈ g := mem_lift hs₂ <| @mem_lift' α α f _ t ht
-        have hg : p (Prod.swap ⁻¹' s₁) t ×ˢ p s₂ t ∈ g ×ᶠ g := @prod_mem_prod α α _ _ g g hg₁ hg₂
-        (g ×ᶠ g).sets_of_superset hg fun ⟨a, b⟩ ⟨⟨c₁, c₁t, hc₁⟩, ⟨c₂, c₂t, hc₂⟩⟩ =>
+        have hg : p (Prod.swap ⁻¹' s₁) t ×ˢ p s₂ t ∈ g ×ˢ g := @prod_mem_prod α α _ _ g g hg₁ hg₂
+        (g ×ˢ g).sets_of_superset hg fun ⟨a, b⟩ ⟨⟨c₁, c₁t, hc₁⟩, ⟨c₂, c₂t, hc₂⟩⟩ =>
           have : (c₁, c₂) ∈ t ×ˢ t := ⟨c₁t, c₂t⟩
           comp_s₁ <| prod_mk_mem_compRel hc₁ <| comp_s₂ <| prod_mk_mem_compRel (prod_t this) hc₂⟩
     have : Cauchy (Filter.comap m g) := ‹Cauchy g›.comap' (le_of_eq hm.comap_uniformity) ‹_›

195fcd60

chore: Rename to sSup/iSup (#3938)

As discussed on Zulip

Renames

supₛ → sSup
infₛ → sInf
supᵢ → iSup
infᵢ → iInf
bsupₛ → bsSup
binfₛ → bsInf
bsupᵢ → biSup
binfᵢ → biInf
csupₛ → csSup
cinfₛ → csInf
csupᵢ → ciSup
cinfᵢ → ciInf
unionₛ → sUnion
interₛ → sInter
unionᵢ → iUnion
interᵢ → iInter
bunionₛ → bsUnion
binterₛ → bsInter
bunionᵢ → biUnion
binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

d1eb6264

Diff

@@ -343,7 +343,7 @@ theorem completeSpace_extension {m : β → α} (hm : UniformInducing m) (dense
     let g := (𝓤 α).lift fun s => f.lift' (p s)
     have mp₀ : Monotone p := fun a b h t s ⟨x, xs, xa⟩ => ⟨x, xs, h xa⟩
     have mp₁ : ∀ {s}, Monotone (p s) := fun h x ⟨y, ya, yxs⟩ => ⟨y, h ya, yxs⟩
-    have : f ≤ g := le_infᵢ₂ fun s hs => le_infᵢ₂ fun t ht =>
+    have : f ≤ g := le_iInf₂ fun s hs => le_iInf₂ fun t ht =>
       le_principal_iff.mpr <| mem_of_superset ht fun x hx => ⟨x, hx, refl_mem_uniformity hs⟩
     have : NeBot g := hf.left.mono this
     have : NeBot (comap m g) :=

195fcd60

refactor: review API of UniformEmbedding (#2584)

Forward-port leanprover-community/mathlib#18516

28d1ea57

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Sébastien Gouëzel, Patrick Massot
 
 ! This file was ported from Lean 3 source module topology.uniform_space.uniform_embedding
-! leanprover-community/mathlib commit 2705404e701abc6b3127da906f40bae062a169c9
+! leanprover-community/mathlib commit 195fcd60ff2bfe392543bceb0ec2adcdb472db4c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -26,26 +26,44 @@ section
 universe u v w
 variable {α : Type u} {β : Type v} {γ : Type w} [UniformSpace α] [UniformSpace β] [UniformSpace γ]
 
+/-!
+### Uniform inducing maps
+-/
+
 /-- A map `f : α → β` between uniform spaces is called *uniform inducing* if the uniformity filter
 on `α` is the pullback of the uniformity filter on `β` under `Prod.map f f`. If `α` is a separated
 space, then this implies that `f` is injective, hence it is a `UniformEmbedding`. -/
+@[mk_iff uniformInducing_iff]
 structure UniformInducing (f : α → β) : Prop where
   /-- The uniformity filter on the domain is the pullback of the uniformity filter on the codomain
   under `Prod.map f f`. -/
   comap_uniformity : comap (fun x : α × α => (f x.1, f x.2)) (𝓤 β) = 𝓤 α
 #align uniform_inducing UniformInducing
+#align uniform_inducing_iff uniformInducing_iff
+
+protected lemma UniformInducing.comap_uniformSpace {f : α → β} (hf : UniformInducing f) :
+    ‹UniformSpace β›.comap f = ‹UniformSpace α› :=
+  uniformSpace_eq hf.1
+#align uniform_inducing.comap_uniform_space UniformInducing.comap_uniformSpace
+
+lemma uniformInducing_iff' {f : α → β} :
+    UniformInducing f ↔ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
+  rw [uniformInducing_iff, UniformContinuous, tendsto_iff_comap, le_antisymm_iff, and_comm]; rfl
+#align uniform_inducing_iff' uniformInducing_iff'
+
+protected lemma Filter.HasBasis.uniformInducing_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+    (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
+    UniformInducing f ↔
+      (∀ i, p' i → ∃ j, p j ∧ ∀ x y, (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧
+        (∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j) := by
+  simp [uniformInducing_iff', h.uniformContinuous_iff h', (h'.comap _).le_basis_iff h, subset_def]
+#align filter.has_basis.uniform_inducing_iff Filter.HasBasis.uniformInducing_iff
 
 theorem UniformInducing.mk' {f : α → β}
     (h : ∀ s, s ∈ 𝓤 α ↔ ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s) : UniformInducing f :=
   ⟨by simp [eq_comm, Filter.ext_iff, subset_def, h]⟩
 #align uniform_inducing.mk' UniformInducing.mk'
 
-theorem UniformInducing.inducing {f : α → β} (h : UniformInducing f) : Inducing f :=
-  inducing_iff_nhds.2 fun a => by
-    simp only [nhds_eq_comap_uniformity, ← h.comap_uniformity, comap_comap]
-    rfl
-#align uniform_inducing.inducing UniformInducing.inducing
-
 theorem uniformInducing_id : UniformInducing (@id α) :=
   ⟨by rw [← Prod.map_def, Prod.map_id, comap_id]⟩
 #align uniform_inducing_id uniformInducing_id
@@ -73,12 +91,69 @@ theorem uniformInducing_of_compose {f : α → β} {g : β → γ} (hf : Uniform
   exact comap_mono hg.le_comap
 #align uniform_inducing_of_compose uniformInducing_of_compose
 
+theorem UniformInducing.uniformContinuous {f : α → β} (hf : UniformInducing f) :
+    UniformContinuous f := (uniformInducing_iff'.1 hf).1
+#align uniform_inducing.uniform_continuous UniformInducing.uniformContinuous
+
+theorem UniformInducing.uniformContinuous_iff {f : α → β} {g : β → γ} (hg : UniformInducing g) :
+    UniformContinuous f ↔ UniformContinuous (g ∘ f) := by
+  dsimp only [UniformContinuous, Tendsto]
+  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map]; rfl
+#align uniform_inducing.uniform_continuous_iff UniformInducing.uniformContinuous_iff
+
+theorem UniformInducing.inducing {f : α → β} (h : UniformInducing f) : Inducing f := by
+  obtain rfl := h.comap_uniformSpace
+  exact inducing_induced f
+#align uniform_inducing.inducing UniformInducing.inducing
+
+theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
+    {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformInducing e₁) (h₂ : UniformInducing e₂) :
+    UniformInducing fun p : α × β => (e₁ p.1, e₂ p.2) :=
+  ⟨by simp [(· ∘ ·), uniformity_prod, ← h₁.1, ← h₂.1, comap_inf, comap_comap]⟩
+#align uniform_inducing.prod UniformInducing.prod
+
+theorem UniformInducing.denseInducing {f : α → β} (h : UniformInducing f) (hd : DenseRange f) :
+    DenseInducing f :=
+  { dense := hd
+    induced := h.inducing.induced }
+#align uniform_inducing.dense_inducing UniformInducing.denseInducing
+
+protected theorem UniformInducing.injective [T0Space α] {f : α → β} (h : UniformInducing f) :
+    Injective f :=
+  h.inducing.injective
+
+/-!
+### Uniform embeddings
+-/
+
 /-- A map `f : α → β` between uniform spaces is a *uniform embedding* if it is uniform inducing and
 injective. If `α` is a separated space, then the latter assumption follows from the former. -/
+@[mk_iff uniformEmbedding_iff]
 structure UniformEmbedding (f : α → β) extends UniformInducing f : Prop where
   /-- A uniform embedding is injective. -/
   inj : Function.Injective f
 #align uniform_embedding UniformEmbedding
+#align uniform_embedding_iff uniformEmbedding_iff
+
+theorem uniformEmbedding_iff' {f : α → β} :
+    UniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧ comap (Prod.map f f) (𝓤 β) ≤ 𝓤 α := by
+  rw [uniformEmbedding_iff, and_comm, uniformInducing_iff']
+#align uniform_embedding_iff' uniformEmbedding_iff'
+
+theorem Filter.HasBasis.uniformEmbedding_iff' {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+    (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
+    UniformEmbedding f ↔ Injective f ∧
+      (∀ i, p' i → ∃ j, p j ∧ ∀ x y, (x, y) ∈ s j → (f x, f y) ∈ s' i) ∧
+        (∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j) := by
+  rw [uniformEmbedding_iff, and_comm, h.uniformInducing_iff h']
+#align filter.has_basis.uniform_embedding_iff' Filter.HasBasis.uniformEmbedding_iff'
+
+theorem Filter.HasBasis.uniformEmbedding_iff {ι ι'} {p : ι → Prop} {p' : ι' → Prop} {s s'}
+    (h : (𝓤 α).HasBasis p s) (h' : (𝓤 β).HasBasis p' s') {f : α → β} :
+    UniformEmbedding f ↔ Injective f ∧ UniformContinuous f ∧
+      (∀ j, p j → ∃ i, p' i ∧ ∀ x y, (f x, f y) ∈ s' i → (x, y) ∈ s j) := by
+  simp only [h.uniformEmbedding_iff' h', h.uniformContinuous_iff h']
+#align filter.has_basis.uniform_embedding_iff Filter.HasBasis.uniformEmbedding_iff
 
 theorem uniformEmbedding_subtype_val {p : α → Prop} :
     UniformEmbedding (Subtype.val : Subtype p → α) :=
@@ -98,46 +173,21 @@ theorem UniformEmbedding.comp {g : β → γ} (hg : UniformEmbedding g) {f : α
   { hg.toUniformInducing.comp hf.toUniformInducing with inj := hg.inj.comp hf.inj }
 #align uniform_embedding.comp UniformEmbedding.comp
 
-theorem uniformEmbedding_def {f : α → β} :
-    UniformEmbedding f ↔
-      Function.Injective f ∧ ∀ s, s ∈ 𝓤 α ↔ ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s := by
-  constructor
-  · rintro ⟨⟨h⟩, h'⟩
-    rw [eq_comm, Filter.ext_iff] at h
-    simp [*, subset_def]
-  · rintro ⟨h, h'⟩
-    refine' UniformEmbedding.mk ⟨_⟩ h
-    rw [eq_comm, Filter.ext_iff]
-    simp [*, subset_def]
-#align uniform_embedding_def uniformEmbedding_def
-
-theorem uniformEmbedding_def' {f : α → β} :
-    UniformEmbedding f ↔
-      Function.Injective f ∧
-        UniformContinuous f ∧ ∀ s, s ∈ 𝓤 α → ∃ t ∈ 𝓤 β, ∀ x y : α, (f x, f y) ∈ t → (x, y) ∈ s := by
-  simp only [uniformEmbedding_def, uniformContinuous_def]
-  exact ⟨fun ⟨I, H⟩ => ⟨I, fun s su => (H _).2 ⟨s, su, fun x y => id⟩, fun s => (H s).1⟩,
-    fun ⟨I, H₁, H₂⟩ => ⟨I, fun s =>
-      ⟨H₂ s, fun ⟨t, tu, h⟩ => mem_of_superset (H₁ t tu) fun ⟨a, b⟩ => h a b⟩⟩⟩
-#align uniform_embedding_def' uniformEmbedding_def'
-
 theorem Equiv.uniformEmbedding {α β : Type _} [UniformSpace α] [UniformSpace β] (f : α ≃ β)
     (h₁ : UniformContinuous f) (h₂ : UniformContinuous f.symm) : UniformEmbedding f :=
-  { toUniformInducing := uniformInducing_of_compose h₁ h₂ <| by
-      rw [f.symm_comp_self]; exact uniformInducing_id
-    inj := f.injective }
+  uniformEmbedding_iff'.2 ⟨f.injective, h₁, by rwa [← Equiv.prodCongr_apply, ← map_equiv_symm]⟩
 #align equiv.uniform_embedding Equiv.uniformEmbedding
 
 theorem uniformEmbedding_inl : UniformEmbedding (Sum.inl : α → α ⊕ β) :=
-  uniformEmbedding_def'.2 ⟨Sum.inl_injective, uniformContinuous_inl, fun s hs =>
+  uniformEmbedding_iff'.2 ⟨Sum.inl_injective, uniformContinuous_inl, fun s hs =>
     ⟨Prod.map Sum.inl Sum.inl '' s ∪ range (Prod.map Sum.inr Sum.inr),
-      union_mem_sup (image_mem_map hs) range_mem_map, fun x y h => by simpa using h⟩⟩
+      union_mem_sup (image_mem_map hs) range_mem_map, fun x h => by simpa using h⟩⟩
 #align uniform_embedding_inl uniformEmbedding_inl
 
 theorem uniformEmbedding_inr : UniformEmbedding (Sum.inr : β → α ⊕ β) :=
-  uniformEmbedding_def'.2 ⟨Sum.inr_injective, uniformContinuous_inr, fun s hs =>
+  uniformEmbedding_iff'.2 ⟨Sum.inr_injective, uniformContinuous_inr, fun s hs =>
     ⟨range (Prod.map Sum.inl Sum.inl) ∪ Prod.map Sum.inr Sum.inr '' s,
-      union_mem_sup range_mem_map (image_mem_map hs), fun x y h => by simpa using h⟩⟩
+      union_mem_sup range_mem_map (image_mem_map hs), fun x h => by simpa using h⟩⟩
 #align uniform_embedding_inr uniformEmbedding_inr
 
 /-- If the domain of a `UniformInducing` map `f` is a T₀ space, then `f` is injective,
@@ -147,6 +197,11 @@ protected theorem UniformInducing.uniformEmbedding [T0Space α] {f : α → β}
   ⟨hf, hf.inducing.injective⟩
 #align uniform_inducing.uniform_embedding UniformInducing.uniformEmbedding
 
+theorem uniformEmbedding_iff_uniformInducing [T0Space α] {f : α → β} :
+    UniformEmbedding f ↔ UniformInducing f :=
+  ⟨UniformEmbedding.toUniformInducing, UniformInducing.uniformEmbedding⟩
+#align uniform_embedding_iff_uniform_inducing uniformEmbedding_iff_uniformInducing
+
 /-- If a map `f : α → β` sends any two distinct points to point that are **not** related by a fixed
 `s ∈ 𝓤 β`, then `f` is uniform inducing with respect to the discrete uniformity on `α`:
 the preimage of `𝓤 β` under `prod.map f f` is the principal filter generated by the diagonal in
@@ -169,29 +224,7 @@ theorem uniformEmbedding_of_spaced_out {α} {f : α → β} {s : Set (β × β)}
   exact UniformInducing.uniformEmbedding ⟨comap_uniformity_of_spaced_out hs hf⟩
 #align uniform_embedding_of_spaced_out uniformEmbedding_of_spaced_out
 
-theorem UniformInducing.uniformContinuous {f : α → β} (hf : UniformInducing f) :
-    UniformContinuous f := by simp [UniformContinuous, hf.comap_uniformity.symm, tendsto_comap]
-#align uniform_inducing.uniform_continuous UniformInducing.uniformContinuous
-
-theorem UniformInducing.uniformContinuous_iff {f : α → β} {g : β → γ} (hg : UniformInducing g) :
-    UniformContinuous f ↔ UniformContinuous (g ∘ f) := by
-  dsimp only [UniformContinuous, Tendsto]
-  rw [← hg.comap_uniformity, ← map_le_iff_le_comap, Filter.map_map]; rfl
-#align uniform_inducing.uniform_continuous_iff UniformInducing.uniformContinuous_iff
-
-theorem UniformInducing.prod {α' : Type _} {β' : Type _} [UniformSpace α'] [UniformSpace β']
-    {e₁ : α → α'} {e₂ : β → β'} (h₁ : UniformInducing e₁) (h₂ : UniformInducing e₂) :
-    UniformInducing fun p : α × β => (e₁ p.1, e₂ p.2) :=
-  ⟨by simp [(· ∘ ·), uniformity_prod, ← h₁.1, ← h₂.1, comap_inf, comap_comap]⟩
-#align uniform_inducing.prod UniformInducing.prod
-
-theorem UniformInducing.denseInducing {f : α → β} (h : UniformInducing f) (hd : DenseRange f) :
-    DenseInducing f :=
-  { dense := hd
-    induced := h.inducing.induced }
-#align uniform_inducing.dense_inducing UniformInducing.denseInducing
-
-theorem UniformEmbedding.embedding {f : α → β} (h : UniformEmbedding f) : Embedding f :=
+protected theorem UniformEmbedding.embedding {f : α → β} (h : UniformEmbedding f) : Embedding f :=
   { toInducing := h.toUniformInducing.inducing
     inj := h.inj }
 #align uniform_embedding.embedding UniformEmbedding.embedding

2705404e

feat: port Topology.UniformSpace.UniformEmbedding (#2038)

3af293c6

`topology.uniform_space.uniform_embedding` ⟷ `Mathlib.Topology.UniformSpace.UniformEmbedding`

Changes since the initial port

Changes in mathlib3

API about uniform embeddings

Other changes

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 310

topology.uniform_space.uniform_embedding ⟷ Mathlib.Topology.UniformSpace.UniformEmbedding

Changes since the initial port

Changes in mathlib3

API about uniform embeddings

Other changes

Changes in mathlib3port

Changes in mathlib4

Renames

Dependencies 8 + 310

`topology.uniform_space.uniform_embedding` ⟷ `Mathlib.Topology.UniformSpace.UniformEmbedding`