topology.dense_embedding ⟷ Mathlib.Topology.DenseEmbedding

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

@@ -258,7 +258,7 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
     dsimp [V₁, φ]
     rwa [di.extend_eq_of_tendsto hc]
   obtain ⟨V₂, V₂_in, V₂_op, hV₂⟩ : ∃ V₂ ∈ 𝓝 b, IsOpen V₂ ∧ ∀ x ∈ i ⁻¹' V₂, f x ∈ V' := by
-    simpa [and_assoc'] using
+    simpa [and_assoc] using
       ((nhds_basis_opens' b).comap i).tendsto_left_iffₓ.mp (mem_of_mem_nhds V₁_in : b ∈ V₁) V' V'_in
   suffices ∀ x ∈ V₁ ∩ V₂, φ x ∈ V' by filter_upwards [inter_mem V₁_in V₂_in] using this
   rintro x ⟨x_in₁, x_in₂⟩

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

@@ -81,7 +81,7 @@ protected theorem preconnectedSpace [PreconnectedSpace α] (di : DenseInducing i
 theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs : s ∈ 𝓝 a) :
     closure (i '' s) ∈ 𝓝 (i a) :=
   by
-  rw [di.nhds_eq_comap a, ((nhds_basis_opens _).comap _).mem_iff] at hs 
+  rw [di.nhds_eq_comap a, ((nhds_basis_opens _).comap _).mem_iff] at hs
   rcases hs with ⟨U, ⟨haU, hUo⟩, sub : i ⁻¹' U ⊆ s⟩
   refine' mem_of_superset (hUo.mem_nhds haU) _
   calc
@@ -106,9 +106,9 @@ theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dens
     {s : Set α} (hs : IsCompact s) : interior s = ∅ :=
   by
   refine' eq_empty_iff_forall_not_mem.2 fun x hx => _
-  rw [mem_interior_iff_mem_nhds] at hx 
+  rw [mem_interior_iff_mem_nhds] at hx
   have := di.closure_image_mem_nhds hx
-  rw [(hs.image di.continuous).IsClosed.closure_eq] at this 
+  rw [(hs.image di.continuous).IsClosed.closure_eq] at this
   rcases hd.inter_nhds_nonempty this with ⟨y, hyi, hys⟩
   exact hyi (image_subset_range _ _ hys)
 #align dense_inducing.interior_compact_eq_empty DenseInducing.interior_compact_eq_empty
@@ -147,9 +147,9 @@ theorem tendsto_comap_nhds_nhds {d : δ} {a : α} (di : DenseInducing i)
   by
   have lim1 : map g (comap g (𝓝 d)) ≤ 𝓝 d := map_comap_le
   replace lim1 : map h (map g (comap g (𝓝 d))) ≤ map h (𝓝 d) := map_mono lim1
-  rw [Filter.map_map, comm, ← Filter.map_map, map_le_iff_le_comap] at lim1 
+  rw [Filter.map_map, comm, ← Filter.map_map, map_le_iff_le_comap] at lim1
   have lim2 : comap i (map h (𝓝 d)) ≤ comap i (𝓝 (i a)) := comap_mono H
-  rw [← di.nhds_eq_comap] at lim2 
+  rw [← di.nhds_eq_comap] at lim2
   exact le_trans lim1 lim2
 #align dense_inducing.tendsto_comap_nhds_nhds DenseInducing.tendsto_comap_nhds_nhds
 -/
@@ -217,7 +217,7 @@ theorem extend_eq' [T2Space γ] {f : α → γ} (di : DenseInducing i)
   by
   rcases hf (i a) with ⟨b, hb⟩
   refine' di.extend_eq_at' b _
-  rwa [← di.to_inducing.nhds_eq_comap] at hb 
+  rwa [← di.to_inducing.nhds_eq_comap] at hb
 #align dense_inducing.extend_eq' DenseInducing.extend_eq'
 -/
 
@@ -355,7 +355,7 @@ protected theorem subtype (p : α → Prop) : DenseEmbedding (subtypeEmb p e) :=
   { dense :=
       dense_iff_closure_eq.2 <| by
         ext ⟨x, hx⟩
-        rw [image_eq_range] at hx 
+        rw [image_eq_range] at hx
         simpa [closure_subtype, ← range_comp, (· ∘ ·)]
     inj := (de.inj.comp Subtype.coe_injective).codRestrict _
     induced :=

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

@@ -3,8 +3,8 @@ Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
 -/
-import Mathbin.Topology.Separation
-import Mathbin.Topology.Bases
+import Topology.Separation
+import Topology.Bases
 
 #align_import topology.dense_embedding from "leanprover-community/mathlib"@"148aefbd371a25f1cff33c85f20c661ce3155def"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c0c52abb75074ed8b73a948341f50521fbf43b4c

@@ -6,7 +6,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
 import Mathbin.Topology.Separation
 import Mathbin.Topology.Bases
 
-#align_import topology.dense_embedding from "leanprover-community/mathlib"@"0ebfdb71919ac6ca5d7fbc61a082fa2519556818"
+#align_import topology.dense_embedding from "leanprover-community/mathlib"@"148aefbd371a25f1cff33c85f20c661ce3155def"
 
 /-!
 # Dense embeddings
@@ -17,8 +17,8 @@ import Mathbin.Topology.Bases
 This file defines three properties of functions:
 
 * `dense_range f`      means `f` has dense image;
-* `dense_inducing i`   means `i` is also `inducing`;
-* `dense_embedding e`  means `e` is also an `embedding`.
+* `dense_inducing i`   means `i` is also `inducing`, namely it induces the topology on its codomain;
+* `dense_embedding e`  means `e` is further an `embedding`, namely it is injective and `inducing`.
 
 The main theorem `continuous_extend` gives a criterion for a function
 `f : X → Z` to a T₃ space Z to extend along a dense embedding

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.dense_embedding
-! leanprover-community/mathlib commit 0ebfdb71919ac6ca5d7fbc61a082fa2519556818
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Separation
 import Mathbin.Topology.Bases
 
+#align_import topology.dense_embedding from "leanprover-community/mathlib"@"0ebfdb71919ac6ca5d7fbc61a082fa2519556818"
+
 /-!
 # Dense embeddings
 

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

@@ -55,13 +55,17 @@ variable [TopologicalSpace α] [TopologicalSpace β]
 
 variable {i : α → β} (di : DenseInducing i)
 
+#print DenseInducing.nhds_eq_comap /-
 theorem nhds_eq_comap (di : DenseInducing i) : ∀ a : α, 𝓝 a = comap i (𝓝 <| i a) :=
   di.to_inducing.nhds_eq_comap
 #align dense_inducing.nhds_eq_comap DenseInducing.nhds_eq_comap
+-/
 
+#print DenseInducing.continuous /-
 protected theorem continuous (di : DenseInducing i) : Continuous i :=
   di.to_inducing.Continuous
 #align dense_inducing.continuous DenseInducing.continuous
+-/
 
 #print DenseInducing.closure_range /-
 theorem closure_range : closure (range i) = univ :=
@@ -69,11 +73,14 @@ theorem closure_range : closure (range i) = univ :=
 #align dense_inducing.closure_range DenseInducing.closure_range
 -/
 
+#print DenseInducing.preconnectedSpace /-
 protected theorem preconnectedSpace [PreconnectedSpace α] (di : DenseInducing i) :
     PreconnectedSpace β :=
   di.dense.PreconnectedSpace di.Continuous
 #align dense_inducing.preconnected_space DenseInducing.preconnectedSpace
+-/
 
+#print DenseInducing.closure_image_mem_nhds /-
 theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs : s ∈ 𝓝 a) :
     closure (i '' s) ∈ 𝓝 (i a) :=
   by
@@ -84,14 +91,18 @@ theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs
     U ⊆ closure (i '' (i ⁻¹' U)) := di.dense.subset_closure_image_preimage_of_is_open hUo
     _ ⊆ closure (i '' s) := closure_mono (image_subset i sub)
 #align dense_inducing.closure_image_mem_nhds DenseInducing.closure_image_mem_nhds
+-/
 
+#print DenseInducing.dense_image /-
 theorem dense_image (di : DenseInducing i) {s : Set α} : Dense (i '' s) ↔ Dense s :=
   by
   refine' ⟨fun H x => _, di.dense.dense_image di.continuous⟩
   rw [di.to_inducing.closure_eq_preimage_closure_image, H.closure_eq, preimage_univ]
   trivial
 #align dense_inducing.dense_image DenseInducing.dense_image
+-/
 
+#print DenseInducing.interior_compact_eq_empty /-
 /-- If `i : α → β` is a dense embedding with dense complement of the range, then any compact set in
 `α` has empty interior. -/
 theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dense (range iᶜ))
@@ -104,7 +115,9 @@ theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dens
   rcases hd.inter_nhds_nonempty this with ⟨y, hyi, hys⟩
   exact hyi (image_subset_range _ _ hys)
 #align dense_inducing.interior_compact_eq_empty DenseInducing.interior_compact_eq_empty
+-/
 
+#print DenseInducing.prod /-
 /-- The product of two dense inducings is a dense inducing -/
 protected theorem prod [TopologicalSpace γ] [TopologicalSpace δ] {e₁ : α → β} {e₂ : γ → δ}
     (de₁ : DenseInducing e₁) (de₂ : DenseInducing e₂) :
@@ -112,16 +125,20 @@ protected theorem prod [TopologicalSpace γ] [TopologicalSpace δ] {e₁ : α 
   { induced := (de₁.to_inducing.prod_mk de₂.to_inducing).induced
     dense := de₁.dense.Prod_map de₂.dense }
 #align dense_inducing.prod DenseInducing.prod
+-/
 
 open TopologicalSpace
 
+#print DenseInducing.separableSpace /-
 /-- If the domain of a `dense_inducing` map is a separable space, then so is the codomain. -/
 protected theorem separableSpace [SeparableSpace α] : SeparableSpace β :=
   di.dense.SeparableSpace di.Continuous
 #align dense_inducing.separable_space DenseInducing.separableSpace
+-/
 
 variable [TopologicalSpace δ] {f : γ → α} {g : γ → δ} {h : δ → β}
 
+#print DenseInducing.tendsto_comap_nhds_nhds /-
 /-- ```
  γ -f→ α
 g↓     ↓e
@@ -138,16 +155,21 @@ theorem tendsto_comap_nhds_nhds {d : δ} {a : α} (di : DenseInducing i)
   rw [← di.nhds_eq_comap] at lim2 
   exact le_trans lim1 lim2
 #align dense_inducing.tendsto_comap_nhds_nhds DenseInducing.tendsto_comap_nhds_nhds
+-/
 
+#print DenseInducing.nhdsWithin_neBot /-
 protected theorem nhdsWithin_neBot (di : DenseInducing i) (b : β) : NeBot (𝓝[range i] b) :=
   di.dense.nhdsWithin_neBot b
 #align dense_inducing.nhds_within_ne_bot DenseInducing.nhdsWithin_neBot
+-/
 
+#print DenseInducing.comap_nhds_neBot /-
 theorem comap_nhds_neBot (di : DenseInducing i) (b : β) : NeBot (comap i (𝓝 b)) :=
   comap_neBot fun s hs =>
     let ⟨_, ⟨ha, a, rfl⟩⟩ := mem_closure_iff_nhds.1 (di.dense b) s hs
     ⟨a, ha⟩
 #align dense_inducing.comap_nhds_ne_bot DenseInducing.comap_nhds_neBot
+-/
 
 variable [TopologicalSpace γ]
 
@@ -161,26 +183,35 @@ def extend (di : DenseInducing i) (f : α → γ) (b : β) : γ :=
 #align dense_inducing.extend DenseInducing.extend
 -/
 
+#print DenseInducing.extend_eq_of_tendsto /-
 theorem extend_eq_of_tendsto [T2Space γ] {b : β} {c : γ} {f : α → γ}
     (hf : Tendsto f (comap i (𝓝 b)) (𝓝 c)) : di.extend f b = c :=
   haveI := di.comap_nhds_ne_bot
   hf.lim_eq
 #align dense_inducing.extend_eq_of_tendsto DenseInducing.extend_eq_of_tendsto
+-/
 
+#print DenseInducing.extend_eq_at /-
 theorem extend_eq_at [T2Space γ] {f : α → γ} {a : α} (hf : ContinuousAt f a) :
     di.extend f (i a) = f a :=
   extend_eq_of_tendsto _ <| di.nhds_eq_comap a ▸ hf
 #align dense_inducing.extend_eq_at DenseInducing.extend_eq_at
+-/
 
+#print DenseInducing.extend_eq_at' /-
 theorem extend_eq_at' [T2Space γ] {f : α → γ} {a : α} (c : γ) (hf : Tendsto f (𝓝 a) (𝓝 c)) :
     di.extend f (i a) = f a :=
   di.extend_eq_at (continuousAt_of_tendsto_nhds hf)
 #align dense_inducing.extend_eq_at' DenseInducing.extend_eq_at'
+-/
 
+#print DenseInducing.extend_eq /-
 theorem extend_eq [T2Space γ] {f : α → γ} (hf : Continuous f) (a : α) : di.extend f (i a) = f a :=
   di.extend_eq_at hf.ContinuousAt
 #align dense_inducing.extend_eq DenseInducing.extend_eq
+-/
 
+#print DenseInducing.extend_eq' /-
 /-- Variation of `extend_eq` where we ask that `f` has a limit along `comap i (𝓝 b)` for each
 `b : β`. This is a strictly stronger assumption than continuity of `f`, but in a lot of cases
 you'd have to prove it anyway to use `continuous_extend`, so this avoids doing the work twice. -/
@@ -191,7 +222,9 @@ theorem extend_eq' [T2Space γ] {f : α → γ} (di : DenseInducing i)
   refine' di.extend_eq_at' b _
   rwa [← di.to_inducing.nhds_eq_comap] at hb 
 #align dense_inducing.extend_eq' DenseInducing.extend_eq'
+-/
 
+#print DenseInducing.extend_unique_at /-
 theorem extend_unique_at [T2Space γ] {b : β} {f : α → γ} {g : β → γ} (di : DenseInducing i)
     (hf : ∀ᶠ x in comap i (𝓝 b), g (i x) = f x) (hg : ContinuousAt g b) : di.extend f b = g b :=
   by
@@ -203,12 +236,16 @@ theorem extend_unique_at [T2Space γ] {b : β} {f : α → γ} {g : β → γ} (
   rintro _ hxs x rfl
   exact hxs
 #align dense_inducing.extend_unique_at DenseInducing.extend_unique_at
+-/
 
+#print DenseInducing.extend_unique /-
 theorem extend_unique [T2Space γ] {f : α → γ} {g : β → γ} (di : DenseInducing i)
     (hf : ∀ x, g (i x) = f x) (hg : Continuous g) : di.extend f = g :=
   funext fun b => extend_unique_at di (eventually_of_forall hf) hg.ContinuousAt
 #align dense_inducing.extend_unique DenseInducing.extend_unique
+-/
 
+#print DenseInducing.continuousAt_extend /-
 theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInducing i)
     (hf : ∀ᶠ x in 𝓝 b, ∃ c, Tendsto f (comap i <| 𝓝 x) (𝓝 c)) : ContinuousAt (di.extend f) b :=
   by
@@ -233,12 +270,16 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
   use V₂
   tauto
 #align dense_inducing.continuous_at_extend DenseInducing.continuousAt_extend
+-/
 
+#print DenseInducing.continuous_extend /-
 theorem continuous_extend [T3Space γ] {f : α → γ} (di : DenseInducing i)
     (hf : ∀ b, ∃ c, Tendsto f (comap i (𝓝 b)) (𝓝 c)) : Continuous (di.extend f) :=
   continuous_iff_continuousAt.mpr fun b => di.continuousAt_extend <| univ_mem' hf
 #align dense_inducing.continuous_extend DenseInducing.continuous_extend
+-/
 
+#print DenseInducing.mk' /-
 theorem mk' (i : α → β) (c : Continuous i) (dense : ∀ x, x ∈ closure (range i))
     (H : ∀ (a : α), ∀ s ∈ 𝓝 a, ∃ t ∈ 𝓝 (i a), ∀ b, i b ∈ t → b ∈ s) : DenseInducing i :=
   { induced :=
@@ -246,6 +287,7 @@ theorem mk' (i : α → β) (c : Continuous i) (dense : ∀ x, x ∈ closure (ra
         le_antisymm (tendsto_iff_comap.1 <| c.Tendsto _) (by simpa [Filter.le_def] using H a)
     dense }
 #align dense_inducing.mk' DenseInducing.mk'
+-/
 
 end DenseInducing
 
@@ -257,11 +299,13 @@ structure DenseEmbedding [TopologicalSpace α] [TopologicalSpace β] (e : α →
 #align dense_embedding DenseEmbedding
 -/
 
+#print DenseEmbedding.mk' /-
 theorem DenseEmbedding.mk' [TopologicalSpace α] [TopologicalSpace β] (e : α → β) (c : Continuous e)
     (dense : DenseRange e) (inj : Function.Injective e)
     (H : ∀ (a : α), ∀ s ∈ 𝓝 a, ∃ t ∈ 𝓝 (e a), ∀ b, e b ∈ t → b ∈ s) : DenseEmbedding e :=
   { DenseInducing.mk' e c Dense H with inj }
 #align dense_embedding.mk' DenseEmbedding.mk'
+-/
 
 namespace DenseEmbedding
 
@@ -277,22 +321,28 @@ theorem inj_iff {x y} : e x = e y ↔ x = y :=
 #align dense_embedding.inj_iff DenseEmbedding.inj_iff
 -/
 
+#print DenseEmbedding.to_embedding /-
 theorem to_embedding : Embedding e :=
   { induced := de.induced
     inj := de.inj }
 #align dense_embedding.to_embedding DenseEmbedding.to_embedding
+-/
 
+#print DenseEmbedding.separableSpace /-
 /-- If the domain of a `dense_embedding` is a separable space, then so is its codomain. -/
 protected theorem separableSpace [SeparableSpace α] : SeparableSpace β :=
   de.to_denseInducing.SeparableSpace
 #align dense_embedding.separable_space DenseEmbedding.separableSpace
+-/
 
+#print DenseEmbedding.prod /-
 /-- The product of two dense embeddings is a dense embedding. -/
 protected theorem prod {e₁ : α → β} {e₂ : γ → δ} (de₁ : DenseEmbedding e₁)
     (de₂ : DenseEmbedding e₂) : DenseEmbedding fun p : α × γ => (e₁ p.1, e₂ p.2) :=
   { DenseInducing.prod de₁.to_denseInducing de₂.to_denseInducing with
     inj := fun ⟨x₁, x₂⟩ ⟨y₁, y₂⟩ => by simp <;> exact fun h₁ h₂ => ⟨de₁.inj h₁, de₂.inj h₂⟩ }
 #align dense_embedding.prod DenseEmbedding.prod
+-/
 
 #print DenseEmbedding.subtypeEmb /-
 /-- The dense embedding of a subtype inside its closure. -/
@@ -303,6 +353,7 @@ def subtypeEmb {α : Type _} (p : α → Prop) (e : α → β) (x : { x // p x }
 #align dense_embedding.subtype_emb DenseEmbedding.subtypeEmb
 -/
 
+#print DenseEmbedding.subtype /-
 protected theorem subtype (p : α → Prop) : DenseEmbedding (subtypeEmb p e) :=
   { dense :=
       dense_iff_closure_eq.2 <| by
@@ -315,10 +366,13 @@ protected theorem subtype (p : α → Prop) : DenseEmbedding (subtypeEmb p e) :=
         simp [subtype_emb, nhds_subtype_eq_comap, de.to_inducing.nhds_eq_comap, comap_comap,
           (· ∘ ·)] }
 #align dense_embedding.subtype DenseEmbedding.subtype
+-/
 
+#print DenseEmbedding.dense_image /-
 theorem dense_image {s : Set α} : Dense (e '' s) ↔ Dense s :=
   de.to_denseInducing.dense_image
 #align dense_embedding.dense_image DenseEmbedding.dense_image
+-/
 
 end DenseEmbedding
 
@@ -347,12 +401,15 @@ theorem isClosed_property [TopologicalSpace β] {e : α → β} {p : β → Prop
 #align is_closed_property isClosed_property
 -/
 
+#print isClosed_property2 /-
 theorem isClosed_property2 [TopologicalSpace β] {e : α → β} {p : β → β → Prop} (he : DenseRange e)
     (hp : IsClosed {q : β × β | p q.1 q.2}) (h : ∀ a₁ a₂, p (e a₁) (e a₂)) : ∀ b₁ b₂, p b₁ b₂ :=
   have : ∀ q : β × β, p q.1 q.2 := isClosed_property (he.Prod_map he) hp fun _ => h _ _
   fun b₁ b₂ => this ⟨b₁, b₂⟩
 #align is_closed_property2 isClosed_property2
+-/
 
+#print isClosed_property3 /-
 theorem isClosed_property3 [TopologicalSpace β] {e : α → β} {p : β → β → β → Prop}
     (he : DenseRange e) (hp : IsClosed {q : β × β × β | p q.1 q.2.1 q.2.2})
     (h : ∀ a₁ a₂ a₃, p (e a₁) (e a₂) (e a₃)) : ∀ b₁ b₂ b₃, p b₁ b₂ b₃ :=
@@ -360,6 +417,7 @@ theorem isClosed_property3 [TopologicalSpace β] {e : α → β} {p : β → β
     isClosed_property (he.Prod_map <| he.Prod_map he) hp fun _ => h _ _ _
   fun b₁ b₂ b₃ => this ⟨b₁, b₂, b₃⟩
 #align is_closed_property3 isClosed_property3
+-/
 
 #print DenseRange.induction_on /-
 @[elab_as_elim]
@@ -369,19 +427,23 @@ theorem DenseRange.induction_on [TopologicalSpace β] {e : α → β} (he : Dens
 #align dense_range.induction_on DenseRange.induction_on
 -/
 
+#print DenseRange.induction_on₂ /-
 @[elab_as_elim]
 theorem DenseRange.induction_on₂ [TopologicalSpace β] {e : α → β} {p : β → β → Prop}
     (he : DenseRange e) (hp : IsClosed {q : β × β | p q.1 q.2}) (h : ∀ a₁ a₂, p (e a₁) (e a₂))
     (b₁ b₂ : β) : p b₁ b₂ :=
   isClosed_property2 he hp h _ _
 #align dense_range.induction_on₂ DenseRange.induction_on₂
+-/
 
+#print DenseRange.induction_on₃ /-
 @[elab_as_elim]
 theorem DenseRange.induction_on₃ [TopologicalSpace β] {e : α → β} {p : β → β → β → Prop}
     (he : DenseRange e) (hp : IsClosed {q : β × β × β | p q.1 q.2.1 q.2.2})
     (h : ∀ a₁ a₂ a₃, p (e a₁) (e a₂) (e a₃)) (b₁ b₂ b₃ : β) : p b₁ b₂ b₃ :=
   isClosed_property3 he hp h _ _ _
 #align dense_range.induction_on₃ DenseRange.induction_on₃
+-/
 
 section
 
@@ -389,14 +451,17 @@ variable [TopologicalSpace β] [TopologicalSpace γ] [T2Space γ]
 
 variable {f : α → β}
 
+#print DenseRange.equalizer /-
 /-- Two continuous functions to a t2-space that agree on the dense range of a function are equal. -/
 theorem DenseRange.equalizer (hfd : DenseRange f) {g h : β → γ} (hg : Continuous g)
     (hh : Continuous h) (H : g ∘ f = h ∘ f) : g = h :=
   funext fun y => hfd.inductionOn y (isClosed_eq hg hh) <| congr_fun H
 #align dense_range.equalizer DenseRange.equalizer
+-/
 
 end
 
+#print Filter.HasBasis.hasBasis_of_denseInducing /-
 -- Bourbaki GT III §3 no.4 Proposition 7 (generalised to any dense-inducing map to a T₃ space)
 theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [TopologicalSpace β]
     [T3Space β] {ι : Type _} {s : ι → Set α} {p : ι → Prop} {x : α} (h : (𝓝 x).HasBasis p s)
@@ -419,4 +484,5 @@ theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [Topolog
     replace h := (h (s i)).mpr ⟨i, hi, subset.rfl⟩
     exact hf.closure_image_mem_nhds h
 #align filter.has_basis.has_basis_of_dense_inducing Filter.HasBasis.hasBasis_of_denseInducing
+-/
 

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

@@ -83,7 +83,6 @@ theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs
   calc
     U ⊆ closure (i '' (i ⁻¹' U)) := di.dense.subset_closure_image_preimage_of_is_open hUo
     _ ⊆ closure (i '' s) := closure_mono (image_subset i sub)
-    
 #align dense_inducing.closure_image_mem_nhds DenseInducing.closure_image_mem_nhds
 
 theorem dense_image (di : DenseInducing i) {s : Set α} : Dense (i '' s) ↔ Dense s :=
@@ -344,7 +343,6 @@ theorem isClosed_property [TopologicalSpace β] {e : α → β} {p : β → Prop
       univ = closure (range e) := he.closure_range.symm
       _ ⊆ closure {b | p b} := (closure_mono <| range_subset_iff.mpr h)
       _ = _ := hp.closure_eq
-      
   fun b => this trivial
 #align is_closed_property isClosed_property
 -/

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

@@ -218,7 +218,7 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
   suffices ∀ V' ∈ 𝓝 (φ b), IsClosed V' → φ ⁻¹' V' ∈ 𝓝 b by
     simpa [ContinuousAt, (closed_nhds_basis _).tendsto_right_iff]
   intro V' V'_in V'_closed
-  set V₁ := { x | tendsto f (comap i <| 𝓝 x) (𝓝 <| φ x) }
+  set V₁ := {x | tendsto f (comap i <| 𝓝 x) (𝓝 <| φ x)}
   have V₁_in : V₁ ∈ 𝓝 b := by
     filter_upwards [hf]
     rintro x ⟨c, hc⟩
@@ -227,7 +227,7 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
   obtain ⟨V₂, V₂_in, V₂_op, hV₂⟩ : ∃ V₂ ∈ 𝓝 b, IsOpen V₂ ∧ ∀ x ∈ i ⁻¹' V₂, f x ∈ V' := by
     simpa [and_assoc'] using
       ((nhds_basis_opens' b).comap i).tendsto_left_iffₓ.mp (mem_of_mem_nhds V₁_in : b ∈ V₁) V' V'_in
-  suffices ∀ x ∈ V₁ ∩ V₂, φ x ∈ V' by filter_upwards [inter_mem V₁_in V₂_in]using this
+  suffices ∀ x ∈ V₁ ∩ V₂, φ x ∈ V' by filter_upwards [inter_mem V₁_in V₂_in] using this
   rintro x ⟨x_in₁, x_in₂⟩
   have hV₂x : V₂ ∈ 𝓝 x := IsOpen.mem_nhds V₂_op x_in₂
   apply V'_closed.mem_of_tendsto x_in₁
@@ -299,7 +299,7 @@ protected theorem prod {e₁ : α → β} {e₂ : γ → δ} (de₁ : DenseEmbed
 /-- The dense embedding of a subtype inside its closure. -/
 @[simps]
 def subtypeEmb {α : Type _} (p : α → Prop) (e : α → β) (x : { x // p x }) :
-    { x // x ∈ closure (e '' { x | p x }) } :=
+    { x // x ∈ closure (e '' {x | p x}) } :=
   ⟨e x, subset_closure <| mem_image_of_mem e x.Prop⟩
 #align dense_embedding.subtype_emb DenseEmbedding.subtypeEmb
 -/
@@ -338,11 +338,11 @@ theorem Dense.denseEmbedding_val [TopologicalSpace α] {s : Set α} (hs : Dense
 
 #print isClosed_property /-
 theorem isClosed_property [TopologicalSpace β] {e : α → β} {p : β → Prop} (he : DenseRange e)
-    (hp : IsClosed { x | p x }) (h : ∀ a, p (e a)) : ∀ b, p b :=
-  have : univ ⊆ { b | p b } :=
+    (hp : IsClosed {x | p x}) (h : ∀ a, p (e a)) : ∀ b, p b :=
+  have : univ ⊆ {b | p b} :=
     calc
       univ = closure (range e) := he.closure_range.symm
-      _ ⊆ closure { b | p b } := (closure_mono <| range_subset_iff.mpr h)
+      _ ⊆ closure {b | p b} := (closure_mono <| range_subset_iff.mpr h)
       _ = _ := hp.closure_eq
       
   fun b => this trivial
@@ -350,13 +350,13 @@ theorem isClosed_property [TopologicalSpace β] {e : α → β} {p : β → Prop
 -/
 
 theorem isClosed_property2 [TopologicalSpace β] {e : α → β} {p : β → β → Prop} (he : DenseRange e)
-    (hp : IsClosed { q : β × β | p q.1 q.2 }) (h : ∀ a₁ a₂, p (e a₁) (e a₂)) : ∀ b₁ b₂, p b₁ b₂ :=
+    (hp : IsClosed {q : β × β | p q.1 q.2}) (h : ∀ a₁ a₂, p (e a₁) (e a₂)) : ∀ b₁ b₂, p b₁ b₂ :=
   have : ∀ q : β × β, p q.1 q.2 := isClosed_property (he.Prod_map he) hp fun _ => h _ _
   fun b₁ b₂ => this ⟨b₁, b₂⟩
 #align is_closed_property2 isClosed_property2
 
 theorem isClosed_property3 [TopologicalSpace β] {e : α → β} {p : β → β → β → Prop}
-    (he : DenseRange e) (hp : IsClosed { q : β × β × β | p q.1 q.2.1 q.2.2 })
+    (he : DenseRange e) (hp : IsClosed {q : β × β × β | p q.1 q.2.1 q.2.2})
     (h : ∀ a₁ a₂ a₃, p (e a₁) (e a₂) (e a₃)) : ∀ b₁ b₂ b₃, p b₁ b₂ b₃ :=
   have : ∀ q : β × β × β, p q.1 q.2.1 q.2.2 :=
     isClosed_property (he.Prod_map <| he.Prod_map he) hp fun _ => h _ _ _
@@ -366,21 +366,21 @@ theorem isClosed_property3 [TopologicalSpace β] {e : α → β} {p : β → β
 #print DenseRange.induction_on /-
 @[elab_as_elim]
 theorem DenseRange.induction_on [TopologicalSpace β] {e : α → β} (he : DenseRange e) {p : β → Prop}
-    (b₀ : β) (hp : IsClosed { b | p b }) (ih : ∀ a : α, p <| e a) : p b₀ :=
+    (b₀ : β) (hp : IsClosed {b | p b}) (ih : ∀ a : α, p <| e a) : p b₀ :=
   isClosed_property he hp ih b₀
 #align dense_range.induction_on DenseRange.induction_on
 -/
 
 @[elab_as_elim]
 theorem DenseRange.induction_on₂ [TopologicalSpace β] {e : α → β} {p : β → β → Prop}
-    (he : DenseRange e) (hp : IsClosed { q : β × β | p q.1 q.2 }) (h : ∀ a₁ a₂, p (e a₁) (e a₂))
+    (he : DenseRange e) (hp : IsClosed {q : β × β | p q.1 q.2}) (h : ∀ a₁ a₂, p (e a₁) (e a₂))
     (b₁ b₂ : β) : p b₁ b₂ :=
   isClosed_property2 he hp h _ _
 #align dense_range.induction_on₂ DenseRange.induction_on₂
 
 @[elab_as_elim]
 theorem DenseRange.induction_on₃ [TopologicalSpace β] {e : α → β} {p : β → β → β → Prop}
-    (he : DenseRange e) (hp : IsClosed { q : β × β × β | p q.1 q.2.1 q.2.2 })
+    (he : DenseRange e) (hp : IsClosed {q : β × β × β | p q.1 q.2.1 q.2.2})
     (h : ∀ a₁ a₂ a₃, p (e a₁) (e a₂) (e a₃)) (b₁ b₂ b₃ : β) : p b₁ b₂ b₃ :=
   isClosed_property3 he hp h _ _ _
 #align dense_range.induction_on₃ DenseRange.induction_on₃
@@ -417,7 +417,7 @@ theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [Topolog
         (closure_mono (image_subset f hi')).trans
           (subset.trans (closure_minimal (image_subset_iff.mpr subset.rfl) hT₂) hT₃)⟩
   · obtain ⟨i, hi, hi'⟩ := hT
-    suffices closure (f '' s i) ∈ 𝓝 (f x) by filter_upwards [this]using hi'
+    suffices closure (f '' s i) ∈ 𝓝 (f x) by filter_upwards [this] using hi'
     replace h := (h (s i)).mpr ⟨i, hi, subset.rfl⟩
     exact hf.closure_image_mem_nhds h
 #align filter.has_basis.has_basis_of_dense_inducing Filter.HasBasis.hasBasis_of_denseInducing

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

@@ -44,7 +44,7 @@ variable {α : Type _} {β : Type _} {γ : Type _} {δ : Type _}
   is the one induced by `i` from the topology on `β`. -/
 @[protect_proj]
 structure DenseInducing [TopologicalSpace α] [TopologicalSpace β] (i : α → β) extends Inducing i :
-  Prop where
+    Prop where
   dense : DenseRange i
 #align dense_inducing DenseInducing
 -/
@@ -77,7 +77,7 @@ protected theorem preconnectedSpace [PreconnectedSpace α] (di : DenseInducing i
 theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs : s ∈ 𝓝 a) :
     closure (i '' s) ∈ 𝓝 (i a) :=
   by
-  rw [di.nhds_eq_comap a, ((nhds_basis_opens _).comap _).mem_iff] at hs
+  rw [di.nhds_eq_comap a, ((nhds_basis_opens _).comap _).mem_iff] at hs 
   rcases hs with ⟨U, ⟨haU, hUo⟩, sub : i ⁻¹' U ⊆ s⟩
   refine' mem_of_superset (hUo.mem_nhds haU) _
   calc
@@ -99,9 +99,9 @@ theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dens
     {s : Set α} (hs : IsCompact s) : interior s = ∅ :=
   by
   refine' eq_empty_iff_forall_not_mem.2 fun x hx => _
-  rw [mem_interior_iff_mem_nhds] at hx
+  rw [mem_interior_iff_mem_nhds] at hx 
   have := di.closure_image_mem_nhds hx
-  rw [(hs.image di.continuous).IsClosed.closure_eq] at this
+  rw [(hs.image di.continuous).IsClosed.closure_eq] at this 
   rcases hd.inter_nhds_nonempty this with ⟨y, hyi, hys⟩
   exact hyi (image_subset_range _ _ hys)
 #align dense_inducing.interior_compact_eq_empty DenseInducing.interior_compact_eq_empty
@@ -134,9 +134,9 @@ theorem tendsto_comap_nhds_nhds {d : δ} {a : α} (di : DenseInducing i)
   by
   have lim1 : map g (comap g (𝓝 d)) ≤ 𝓝 d := map_comap_le
   replace lim1 : map h (map g (comap g (𝓝 d))) ≤ map h (𝓝 d) := map_mono lim1
-  rw [Filter.map_map, comm, ← Filter.map_map, map_le_iff_le_comap] at lim1
+  rw [Filter.map_map, comm, ← Filter.map_map, map_le_iff_le_comap] at lim1 
   have lim2 : comap i (map h (𝓝 d)) ≤ comap i (𝓝 (i a)) := comap_mono H
-  rw [← di.nhds_eq_comap] at lim2
+  rw [← di.nhds_eq_comap] at lim2 
   exact le_trans lim1 lim2
 #align dense_inducing.tendsto_comap_nhds_nhds DenseInducing.tendsto_comap_nhds_nhds
 
@@ -190,7 +190,7 @@ theorem extend_eq' [T2Space γ] {f : α → γ} (di : DenseInducing i)
   by
   rcases hf (i a) with ⟨b, hb⟩
   refine' di.extend_eq_at' b _
-  rwa [← di.to_inducing.nhds_eq_comap] at hb
+  rwa [← di.to_inducing.nhds_eq_comap] at hb 
 #align dense_inducing.extend_eq' DenseInducing.extend_eq'
 
 theorem extend_unique_at [T2Space γ] {b : β} {f : α → γ} {g : β → γ} (di : DenseInducing i)
@@ -253,7 +253,7 @@ end DenseInducing
 #print DenseEmbedding /-
 /-- A dense embedding is an embedding with dense image. -/
 structure DenseEmbedding [TopologicalSpace α] [TopologicalSpace β] (e : α → β) extends
-  DenseInducing e : Prop where
+    DenseInducing e : Prop where
   inj : Function.Injective e
 #align dense_embedding DenseEmbedding
 -/
@@ -308,7 +308,7 @@ protected theorem subtype (p : α → Prop) : DenseEmbedding (subtypeEmb p e) :=
   { dense :=
       dense_iff_closure_eq.2 <| by
         ext ⟨x, hx⟩
-        rw [image_eq_range] at hx
+        rw [image_eq_range] at hx 
         simpa [closure_subtype, ← range_comp, (· ∘ ·)]
     inj := (de.inj.comp Subtype.coe_injective).codRestrict _
     induced :=
@@ -404,7 +404,7 @@ theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [Topolog
     [T3Space β] {ι : Type _} {s : ι → Set α} {p : ι → Prop} {x : α} (h : (𝓝 x).HasBasis p s)
     {f : α → β} (hf : DenseInducing f) : (𝓝 (f x)).HasBasis p fun i => closure <| f '' s i :=
   by
-  rw [Filter.hasBasis_iff] at h⊢
+  rw [Filter.hasBasis_iff] at h ⊢
   intro T
   refine' ⟨fun hT => _, fun hT => _⟩
   · obtain ⟨T', hT₁, hT₂, hT₃⟩ := exists_mem_nhds_isClosed_subset hT

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

@@ -35,7 +35,7 @@ noncomputable section
 
 open Set Filter
 
-open Classical Topology Filter
+open scoped Classical Topology Filter
 
 variable {α : Type _} {β : Type _} {γ : Type _} {δ : Type _}
 

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

@@ -55,22 +55,10 @@ variable [TopologicalSpace α] [TopologicalSpace β]
 
 variable {i : α → β} (di : DenseInducing i)
 
-/- warning: dense_inducing.nhds_eq_comap -> DenseInducing.nhds_eq_comap is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {i : α -> β}, (DenseInducing.{u1, u2} α β _inst_1 _inst_2 i) -> (forall (a : α), Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α _inst_1 a) (Filter.comap.{u1, u2} α β i (nhds.{u2} β _inst_2 (i a))))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {i : α -> β}, (DenseInducing.{u2, u1} α β _inst_1 _inst_2 i) -> (forall (a : α), Eq.{succ u2} (Filter.{u2} α) (nhds.{u2} α _inst_1 a) (Filter.comap.{u2, u1} α β i (nhds.{u1} β _inst_2 (i a))))
-Case conversion may be inaccurate. Consider using '#align dense_inducing.nhds_eq_comap DenseInducing.nhds_eq_comapₓ'. -/
 theorem nhds_eq_comap (di : DenseInducing i) : ∀ a : α, 𝓝 a = comap i (𝓝 <| i a) :=
   di.to_inducing.nhds_eq_comap
 #align dense_inducing.nhds_eq_comap DenseInducing.nhds_eq_comap
 
-/- warning: dense_inducing.continuous -> DenseInducing.continuous is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {i : α -> β}, (DenseInducing.{u1, u2} α β _inst_1 _inst_2 i) -> (Continuous.{u1, u2} α β _inst_1 _inst_2 i)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {i : α -> β}, (DenseInducing.{u2, u1} α β _inst_1 _inst_2 i) -> (Continuous.{u2, u1} α β _inst_1 _inst_2 i)
-Case conversion may be inaccurate. Consider using '#align dense_inducing.continuous DenseInducing.continuousₓ'. -/
 protected theorem continuous (di : DenseInducing i) : Continuous i :=
   di.to_inducing.Continuous
 #align dense_inducing.continuous DenseInducing.continuous
@@ -81,23 +69,11 @@ theorem closure_range : closure (range i) = univ :=
 #align dense_inducing.closure_range DenseInducing.closure_range
 -/
 
-/- warning: dense_inducing.preconnected_space -> DenseInducing.preconnectedSpace is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {i : α -> β} [_inst_3 : PreconnectedSpace.{u1} α _inst_1], (DenseInducing.{u1, u2} α β _inst_1 _inst_2 i) -> (PreconnectedSpace.{u2} β _inst_2)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {i : α -> β} [_inst_3 : PreconnectedSpace.{u2} α _inst_1], (DenseInducing.{u2, u1} α β _inst_1 _inst_2 i) -> (PreconnectedSpace.{u1} β _inst_2)
-Case conversion may be inaccurate. Consider using '#align dense_inducing.preconnected_space DenseInducing.preconnectedSpaceₓ'. -/
 protected theorem preconnectedSpace [PreconnectedSpace α] (di : DenseInducing i) :
     PreconnectedSpace β :=
   di.dense.PreconnectedSpace di.Continuous
 #align dense_inducing.preconnected_space DenseInducing.preconnectedSpace
 
-/- warning: dense_inducing.closure_image_mem_nhds -> DenseInducing.closure_image_mem_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {i : α -> β} {s : Set.{u1} α} {a : α}, (DenseInducing.{u1, u2} α β _inst_1 _inst_2 i) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α _inst_1 a)) -> (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) (closure.{u2} β _inst_2 (Set.image.{u1, u2} α β i s)) (nhds.{u2} β _inst_2 (i a)))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {i : α -> β} {s : Set.{u2} α} {a : α}, (DenseInducing.{u2, u1} α β _inst_1 _inst_2 i) -> (Membership.mem.{u2, u2} (Set.{u2} α) (Filter.{u2} α) (instMembershipSetFilter.{u2} α) s (nhds.{u2} α _inst_1 a)) -> (Membership.mem.{u1, u1} (Set.{u1} β) (Filter.{u1} β) (instMembershipSetFilter.{u1} β) (closure.{u1} β _inst_2 (Set.image.{u2, u1} α β i s)) (nhds.{u1} β _inst_2 (i a)))
-Case conversion may be inaccurate. Consider using '#align dense_inducing.closure_image_mem_nhds DenseInducing.closure_image_mem_nhdsₓ'. -/
 theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs : s ∈ 𝓝 a) :
     closure (i '' s) ∈ 𝓝 (i a) :=
   by
@@ -110,12 +86,6 @@ theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs
     
 #align dense_inducing.closure_image_mem_nhds DenseInducing.closure_image_mem_nhds
 
-/- warning: dense_inducing.dense_image -> DenseInducing.dense_image is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {i : α -> β}, (DenseInducing.{u1, u2} α β _inst_1 _inst_2 i) -> (forall {s : Set.{u1} α}, Iff (Dense.{u2} β _inst_2 (Set.image.{u1, u2} α β i s)) (Dense.{u1} α _inst_1 s))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {i : α -> β}, (DenseInducing.{u2, u1} α β _inst_1 _inst_2 i) -> (forall {s : Set.{u2} α}, Iff (Dense.{u1} β _inst_2 (Set.image.{u2, u1} α β i s)) (Dense.{u2} α _inst_1 s))
-Case conversion may be inaccurate. Consider using '#align dense_inducing.dense_image DenseInducing.dense_imageₓ'. -/
 theorem dense_image (di : DenseInducing i) {s : Set α} : Dense (i '' s) ↔ Dense s :=
   by
   refine' ⟨fun H x => _, di.dense.dense_image di.continuous⟩
@@ -123,12 +93,6 @@ theorem dense_image (di : DenseInducing i) {s : Set α} : Dense (i '' s) ↔ Den
   trivial
 #align dense_inducing.dense_image DenseInducing.dense_image
 
-/- warning: dense_inducing.interior_compact_eq_empty -> DenseInducing.interior_compact_eq_empty is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {i : α -> β} [_inst_3 : T2Space.{u2} β _inst_2], (DenseInducing.{u1, u2} α β _inst_1 _inst_2 i) -> (Dense.{u2} β _inst_2 (HasCompl.compl.{u2} (Set.{u2} β) (BooleanAlgebra.toHasCompl.{u2} (Set.{u2} β) (Set.booleanAlgebra.{u2} β)) (Set.range.{u2, succ u1} β α i))) -> (forall {s : Set.{u1} α}, (IsCompact.{u1} α _inst_1 s) -> (Eq.{succ u1} (Set.{u1} α) (interior.{u1} α _inst_1 s) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.interior_compact_eq_empty DenseInducing.interior_compact_eq_emptyₓ'. -/
 /-- If `i : α → β` is a dense embedding with dense complement of the range, then any compact set in
 `α` has empty interior. -/
 theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dense (range iᶜ))
@@ -142,12 +106,6 @@ theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dens
   exact hyi (image_subset_range _ _ hys)
 #align dense_inducing.interior_compact_eq_empty DenseInducing.interior_compact_eq_empty
 
-/- warning: dense_inducing.prod -> DenseInducing.prod is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.prod DenseInducing.prodₓ'. -/
 /-- The product of two dense inducings is a dense inducing -/
 protected theorem prod [TopologicalSpace γ] [TopologicalSpace δ] {e₁ : α → β} {e₂ : γ → δ}
     (de₁ : DenseInducing e₁) (de₂ : DenseInducing e₂) :
@@ -158,12 +116,6 @@ protected theorem prod [TopologicalSpace γ] [TopologicalSpace δ] {e₁ : α 
 
 open TopologicalSpace
 
-/- warning: dense_inducing.separable_space -> DenseInducing.separableSpace 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 dense_inducing.separable_space DenseInducing.separableSpaceₓ'. -/
 /-- If the domain of a `dense_inducing` map is a separable space, then so is the codomain. -/
 protected theorem separableSpace [SeparableSpace α] : SeparableSpace β :=
   di.dense.SeparableSpace di.Continuous
@@ -171,12 +123,6 @@ protected theorem separableSpace [SeparableSpace α] : SeparableSpace β :=
 
 variable [TopologicalSpace δ] {f : γ → α} {g : γ → δ} {h : δ → β}
 
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.tendsto_comap_nhds_nhds DenseInducing.tendsto_comap_nhds_nhdsₓ'. -/
 /-- ```
  γ -f→ α
 g↓     ↓e
@@ -194,22 +140,10 @@ theorem tendsto_comap_nhds_nhds {d : δ} {a : α} (di : DenseInducing i)
   exact le_trans lim1 lim2
 #align dense_inducing.tendsto_comap_nhds_nhds DenseInducing.tendsto_comap_nhds_nhds
 
-/- warning: dense_inducing.nhds_within_ne_bot -> DenseInducing.nhdsWithin_neBot is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {i : α -> β}, (DenseInducing.{u1, u2} α β _inst_1 _inst_2 i) -> (forall (b : β), Filter.NeBot.{u2} β (nhdsWithin.{u2} β _inst_2 b (Set.range.{u2, succ u1} β α i)))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.nhds_within_ne_bot DenseInducing.nhdsWithin_neBotₓ'. -/
 protected theorem nhdsWithin_neBot (di : DenseInducing i) (b : β) : NeBot (𝓝[range i] b) :=
   di.dense.nhdsWithin_neBot b
 #align dense_inducing.nhds_within_ne_bot DenseInducing.nhdsWithin_neBot
 
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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 dense_inducing.comap_nhds_ne_bot DenseInducing.comap_nhds_neBotₓ'. -/
 theorem comap_nhds_neBot (di : DenseInducing i) (b : β) : NeBot (comap i (𝓝 b)) :=
   comap_neBot fun s hs =>
     let ⟨_, ⟨ha, a, rfl⟩⟩ := mem_closure_iff_nhds.1 (di.dense b) s hs
@@ -228,56 +162,26 @@ def extend (di : DenseInducing i) (f : α → γ) (b : β) : γ :=
 #align dense_inducing.extend DenseInducing.extend
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.extend_eq_of_tendsto DenseInducing.extend_eq_of_tendstoₓ'. -/
 theorem extend_eq_of_tendsto [T2Space γ] {b : β} {c : γ} {f : α → γ}
     (hf : Tendsto f (comap i (𝓝 b)) (𝓝 c)) : di.extend f b = c :=
   haveI := di.comap_nhds_ne_bot
   hf.lim_eq
 #align dense_inducing.extend_eq_of_tendsto DenseInducing.extend_eq_of_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.extend_eq_at DenseInducing.extend_eq_atₓ'. -/
 theorem extend_eq_at [T2Space γ] {f : α → γ} {a : α} (hf : ContinuousAt f a) :
     di.extend f (i a) = f a :=
   extend_eq_of_tendsto _ <| di.nhds_eq_comap a ▸ hf
 #align dense_inducing.extend_eq_at DenseInducing.extend_eq_at
 
-/- warning: dense_inducing.extend_eq_at' -> DenseInducing.extend_eq_at' is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.extend_eq_at' DenseInducing.extend_eq_at'ₓ'. -/
 theorem extend_eq_at' [T2Space γ] {f : α → γ} {a : α} (c : γ) (hf : Tendsto f (𝓝 a) (𝓝 c)) :
     di.extend f (i a) = f a :=
   di.extend_eq_at (continuousAt_of_tendsto_nhds hf)
 #align dense_inducing.extend_eq_at' DenseInducing.extend_eq_at'
 
-/- warning: dense_inducing.extend_eq -> DenseInducing.extend_eq is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.extend_eq DenseInducing.extend_eqₓ'. -/
 theorem extend_eq [T2Space γ] {f : α → γ} (hf : Continuous f) (a : α) : di.extend f (i a) = f a :=
   di.extend_eq_at hf.ContinuousAt
 #align dense_inducing.extend_eq DenseInducing.extend_eq
 
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-Case conversion may be inaccurate. Consider using '#align dense_inducing.extend_eq' DenseInducing.extend_eq'ₓ'. -/
 /-- Variation of `extend_eq` where we ask that `f` has a limit along `comap i (𝓝 b)` for each
 `b : β`. This is a strictly stronger assumption than continuity of `f`, but in a lot of cases
 you'd have to prove it anyway to use `continuous_extend`, so this avoids doing the work twice. -/
@@ -289,12 +193,6 @@ theorem extend_eq' [T2Space γ] {f : α → γ} (di : DenseInducing i)
   rwa [← di.to_inducing.nhds_eq_comap] at hb
 #align dense_inducing.extend_eq' DenseInducing.extend_eq'
 
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 theorem extend_unique_at [T2Space γ] {b : β} {f : α → γ} {g : β → γ} (di : DenseInducing i)
     (hf : ∀ᶠ x in comap i (𝓝 b), g (i x) = f x) (hg : ContinuousAt g b) : di.extend f b = g b :=
   by
@@ -307,23 +205,11 @@ theorem extend_unique_at [T2Space γ] {b : β} {f : α → γ} {g : β → γ} (
   exact hxs
 #align dense_inducing.extend_unique_at DenseInducing.extend_unique_at
 
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 theorem extend_unique [T2Space γ] {f : α → γ} {g : β → γ} (di : DenseInducing i)
     (hf : ∀ x, g (i x) = f x) (hg : Continuous g) : di.extend f = g :=
   funext fun b => extend_unique_at di (eventually_of_forall hf) hg.ContinuousAt
 #align dense_inducing.extend_unique DenseInducing.extend_unique
 
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 theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInducing i)
     (hf : ∀ᶠ x in 𝓝 b, ∃ c, Tendsto f (comap i <| 𝓝 x) (𝓝 c)) : ContinuousAt (di.extend f) b :=
   by
@@ -349,23 +235,11 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
   tauto
 #align dense_inducing.continuous_at_extend DenseInducing.continuousAt_extend
 
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 theorem continuous_extend [T3Space γ] {f : α → γ} (di : DenseInducing i)
     (hf : ∀ b, ∃ c, Tendsto f (comap i (𝓝 b)) (𝓝 c)) : Continuous (di.extend f) :=
   continuous_iff_continuousAt.mpr fun b => di.continuousAt_extend <| univ_mem' hf
 #align dense_inducing.continuous_extend DenseInducing.continuous_extend
 
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 theorem mk' (i : α → β) (c : Continuous i) (dense : ∀ x, x ∈ closure (range i))
     (H : ∀ (a : α), ∀ s ∈ 𝓝 a, ∃ t ∈ 𝓝 (i a), ∀ b, i b ∈ t → b ∈ s) : DenseInducing i :=
   { induced :=
@@ -384,12 +258,6 @@ structure DenseEmbedding [TopologicalSpace α] [TopologicalSpace β] (e : α →
 #align dense_embedding DenseEmbedding
 -/
 
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 theorem DenseEmbedding.mk' [TopologicalSpace α] [TopologicalSpace β] (e : α → β) (c : Continuous e)
     (dense : DenseRange e) (inj : Function.Injective e)
     (H : ∀ (a : α), ∀ s ∈ 𝓝 a, ∃ t ∈ 𝓝 (e a), ∀ b, e b ∈ t → b ∈ s) : DenseEmbedding e :=
@@ -410,34 +278,16 @@ theorem inj_iff {x y} : e x = e y ↔ x = y :=
 #align dense_embedding.inj_iff DenseEmbedding.inj_iff
 -/
 
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-Case conversion may be inaccurate. Consider using '#align dense_embedding.to_embedding DenseEmbedding.to_embeddingₓ'. -/
 theorem to_embedding : Embedding e :=
   { induced := de.induced
     inj := de.inj }
 #align dense_embedding.to_embedding DenseEmbedding.to_embedding
 
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 /-- If the domain of a `dense_embedding` is a separable space, then so is its codomain. -/
 protected theorem separableSpace [SeparableSpace α] : SeparableSpace β :=
   de.to_denseInducing.SeparableSpace
 #align dense_embedding.separable_space DenseEmbedding.separableSpace
 
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-Case conversion may be inaccurate. Consider using '#align dense_embedding.prod DenseEmbedding.prodₓ'. -/
 /-- The product of two dense embeddings is a dense embedding. -/
 protected theorem prod {e₁ : α → β} {e₂ : γ → δ} (de₁ : DenseEmbedding e₁)
     (de₂ : DenseEmbedding e₂) : DenseEmbedding fun p : α × γ => (e₁ p.1, e₂ p.2) :=
@@ -454,12 +304,6 @@ def subtypeEmb {α : Type _} (p : α → Prop) (e : α → β) (x : { x // p x }
 #align dense_embedding.subtype_emb DenseEmbedding.subtypeEmb
 -/
 
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 protected theorem subtype (p : α → Prop) : DenseEmbedding (subtypeEmb p e) :=
   { dense :=
       dense_iff_closure_eq.2 <| by
@@ -473,12 +317,6 @@ protected theorem subtype (p : α → Prop) : DenseEmbedding (subtypeEmb p e) :=
           (· ∘ ·)] }
 #align dense_embedding.subtype DenseEmbedding.subtype
 
-/- warning: dense_embedding.dense_image -> DenseEmbedding.dense_image is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] {e : α -> β}, (DenseEmbedding.{u1, u2} α β _inst_1 _inst_2 e) -> (forall {s : Set.{u1} α}, Iff (Dense.{u2} β _inst_2 (Set.image.{u1, u2} α β e s)) (Dense.{u1} α _inst_1 s))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : TopologicalSpace.{u2} α] [_inst_2 : TopologicalSpace.{u1} β] {e : α -> β}, (DenseEmbedding.{u2, u1} α β _inst_1 _inst_2 e) -> (forall {s : Set.{u2} α}, Iff (Dense.{u1} β _inst_2 (Set.image.{u2, u1} α β e s)) (Dense.{u2} α _inst_1 s))
-Case conversion may be inaccurate. Consider using '#align dense_embedding.dense_image DenseEmbedding.dense_imageₓ'. -/
 theorem dense_image {s : Set α} : Dense (e '' s) ↔ Dense s :=
   de.to_denseInducing.dense_image
 #align dense_embedding.dense_image DenseEmbedding.dense_image
@@ -511,24 +349,12 @@ theorem isClosed_property [TopologicalSpace β] {e : α → β} {p : β → Prop
 #align is_closed_property isClosed_property
 -/
 
-/- warning: is_closed_property2 -> isClosed_property2 is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β β) (Prod.topologicalSpace.{u2, u2} β β _inst_1 _inst_1) (setOf.{u2} (Prod.{u2, u2} β β) (fun (q : Prod.{u2, u2} β β) => p (Prod.fst.{u2, u2} β β q) (Prod.snd.{u2, u2} β β q)))) -> (forall (a₁ : α) (a₂ : α), p (e a₁) (e a₂)) -> (forall (b₁ : β) (b₂ : β), p b₁ b₂)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β β) (instTopologicalSpaceProd.{u2, u2} β β _inst_1 _inst_1) (setOf.{u2} (Prod.{u2, u2} β β) (fun (q : Prod.{u2, u2} β β) => p (Prod.fst.{u2, u2} β β q) (Prod.snd.{u2, u2} β β q)))) -> (forall (a₁ : α) (a₂ : α), p (e a₁) (e a₂)) -> (forall (b₁ : β) (b₂ : β), p b₁ b₂)
-Case conversion may be inaccurate. Consider using '#align is_closed_property2 isClosed_property2ₓ'. -/
 theorem isClosed_property2 [TopologicalSpace β] {e : α → β} {p : β → β → Prop} (he : DenseRange e)
     (hp : IsClosed { q : β × β | p q.1 q.2 }) (h : ∀ a₁ a₂, p (e a₁) (e a₂)) : ∀ b₁ b₂, p b₁ b₂ :=
   have : ∀ q : β × β, p q.1 q.2 := isClosed_property (he.Prod_map he) hp fun _ => h _ _
   fun b₁ b₂ => this ⟨b₁, b₂⟩
 #align is_closed_property2 isClosed_property2
 
-/- warning: is_closed_property3 -> isClosed_property3 is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (Prod.topologicalSpace.{u2, u2} β (Prod.{u2, u2} β β) _inst_1 (Prod.topologicalSpace.{u2, u2} β β _inst_1 _inst_1)) (setOf.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (fun (q : Prod.{u2, u2} β (Prod.{u2, u2} β β)) => p (Prod.fst.{u2, u2} β (Prod.{u2, u2} β β) q) (Prod.fst.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q)) (Prod.snd.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q))))) -> (forall (a₁ : α) (a₂ : α) (a₃ : α), p (e a₁) (e a₂) (e a₃)) -> (forall (b₁ : β) (b₂ : β) (b₃ : β), p b₁ b₂ b₃)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (instTopologicalSpaceProd.{u2, u2} β (Prod.{u2, u2} β β) _inst_1 (instTopologicalSpaceProd.{u2, u2} β β _inst_1 _inst_1)) (setOf.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (fun (q : Prod.{u2, u2} β (Prod.{u2, u2} β β)) => p (Prod.fst.{u2, u2} β (Prod.{u2, u2} β β) q) (Prod.fst.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q)) (Prod.snd.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q))))) -> (forall (a₁ : α) (a₂ : α) (a₃ : α), p (e a₁) (e a₂) (e a₃)) -> (forall (b₁ : β) (b₂ : β) (b₃ : β), p b₁ b₂ b₃)
-Case conversion may be inaccurate. Consider using '#align is_closed_property3 isClosed_property3ₓ'. -/
 theorem isClosed_property3 [TopologicalSpace β] {e : α → β} {p : β → β → β → Prop}
     (he : DenseRange e) (hp : IsClosed { q : β × β × β | p q.1 q.2.1 q.2.2 })
     (h : ∀ a₁ a₂ a₃, p (e a₁) (e a₂) (e a₃)) : ∀ b₁ b₂ b₃, p b₁ b₂ b₃ :=
@@ -545,12 +371,6 @@ theorem DenseRange.induction_on [TopologicalSpace β] {e : α → β} (he : Dens
 #align dense_range.induction_on DenseRange.induction_on
 -/
 
-/- warning: dense_range.induction_on₂ -> DenseRange.induction_on₂ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β β) (Prod.topologicalSpace.{u2, u2} β β _inst_1 _inst_1) (setOf.{u2} (Prod.{u2, u2} β β) (fun (q : Prod.{u2, u2} β β) => p (Prod.fst.{u2, u2} β β q) (Prod.snd.{u2, u2} β β q)))) -> (forall (a₁ : α) (a₂ : α), p (e a₁) (e a₂)) -> (forall (b₁ : β) (b₂ : β), p b₁ b₂)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β β) (instTopologicalSpaceProd.{u2, u2} β β _inst_1 _inst_1) (setOf.{u2} (Prod.{u2, u2} β β) (fun (q : Prod.{u2, u2} β β) => p (Prod.fst.{u2, u2} β β q) (Prod.snd.{u2, u2} β β q)))) -> (forall (a₁ : α) (a₂ : α), p (e a₁) (e a₂)) -> (forall (b₁ : β) (b₂ : β), p b₁ b₂)
-Case conversion may be inaccurate. Consider using '#align dense_range.induction_on₂ DenseRange.induction_on₂ₓ'. -/
 @[elab_as_elim]
 theorem DenseRange.induction_on₂ [TopologicalSpace β] {e : α → β} {p : β → β → Prop}
     (he : DenseRange e) (hp : IsClosed { q : β × β | p q.1 q.2 }) (h : ∀ a₁ a₂, p (e a₁) (e a₂))
@@ -558,12 +378,6 @@ theorem DenseRange.induction_on₂ [TopologicalSpace β] {e : α → β} {p : β
   isClosed_property2 he hp h _ _
 #align dense_range.induction_on₂ DenseRange.induction_on₂
 
-/- warning: dense_range.induction_on₃ -> DenseRange.induction_on₃ is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (Prod.topologicalSpace.{u2, u2} β (Prod.{u2, u2} β β) _inst_1 (Prod.topologicalSpace.{u2, u2} β β _inst_1 _inst_1)) (setOf.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (fun (q : Prod.{u2, u2} β (Prod.{u2, u2} β β)) => p (Prod.fst.{u2, u2} β (Prod.{u2, u2} β β) q) (Prod.fst.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q)) (Prod.snd.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q))))) -> (forall (a₁ : α) (a₂ : α) (a₃ : α), p (e a₁) (e a₂) (e a₃)) -> (forall (b₁ : β) (b₂ : β) (b₃ : β), p b₁ b₂ b₃)
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u2} β] {e : α -> β} {p : β -> β -> β -> Prop}, (DenseRange.{u2, u1} β _inst_1 α e) -> (IsClosed.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (instTopologicalSpaceProd.{u2, u2} β (Prod.{u2, u2} β β) _inst_1 (instTopologicalSpaceProd.{u2, u2} β β _inst_1 _inst_1)) (setOf.{u2} (Prod.{u2, u2} β (Prod.{u2, u2} β β)) (fun (q : Prod.{u2, u2} β (Prod.{u2, u2} β β)) => p (Prod.fst.{u2, u2} β (Prod.{u2, u2} β β) q) (Prod.fst.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q)) (Prod.snd.{u2, u2} β β (Prod.snd.{u2, u2} β (Prod.{u2, u2} β β) q))))) -> (forall (a₁ : α) (a₂ : α) (a₃ : α), p (e a₁) (e a₂) (e a₃)) -> (forall (b₁ : β) (b₂ : β) (b₃ : β), p b₁ b₂ b₃)
-Case conversion may be inaccurate. Consider using '#align dense_range.induction_on₃ DenseRange.induction_on₃ₓ'. -/
 @[elab_as_elim]
 theorem DenseRange.induction_on₃ [TopologicalSpace β] {e : α → β} {p : β → β → β → Prop}
     (he : DenseRange e) (hp : IsClosed { q : β × β × β | p q.1 q.2.1 q.2.2 })
@@ -577,12 +391,6 @@ variable [TopologicalSpace β] [TopologicalSpace γ] [T2Space γ]
 
 variable {f : α → β}
 
-/- warning: dense_range.equalizer -> DenseRange.equalizer is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : TopologicalSpace.{u2} β] [_inst_2 : TopologicalSpace.{u3} γ] [_inst_3 : T2Space.{u3} γ _inst_2] {f : α -> β}, (DenseRange.{u2, u1} β _inst_1 α f) -> (forall {g : β -> γ} {h : β -> γ}, (Continuous.{u2, u3} β γ _inst_1 _inst_2 g) -> (Continuous.{u2, u3} β γ _inst_1 _inst_2 h) -> (Eq.{max (succ u1) (succ u3)} (α -> γ) (Function.comp.{succ u1, succ u2, succ u3} α β γ g f) (Function.comp.{succ u1, succ u2, succ u3} α β γ h f)) -> (Eq.{max (succ u2) (succ u3)} (β -> γ) g h))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} {γ : Type.{u1}} [_inst_1 : TopologicalSpace.{u3} β] [_inst_2 : TopologicalSpace.{u1} γ] [_inst_3 : T2Space.{u1} γ _inst_2] {f : α -> β}, (DenseRange.{u3, u2} β _inst_1 α f) -> (forall {g : β -> γ} {h : β -> γ}, (Continuous.{u3, u1} β γ _inst_1 _inst_2 g) -> (Continuous.{u3, u1} β γ _inst_1 _inst_2 h) -> (Eq.{max (succ u2) (succ u1)} (α -> γ) (Function.comp.{succ u2, succ u3, succ u1} α β γ g f) (Function.comp.{succ u2, succ u3, succ u1} α β γ h f)) -> (Eq.{max (succ u3) (succ u1)} (β -> γ) g h))
-Case conversion may be inaccurate. Consider using '#align dense_range.equalizer DenseRange.equalizerₓ'. -/
 /-- Two continuous functions to a t2-space that agree on the dense range of a function are equal. -/
 theorem DenseRange.equalizer (hfd : DenseRange f) {g h : β → γ} (hg : Continuous g)
     (hh : Continuous h) (H : g ∘ f = h ∘ f) : g = h :=
@@ -591,12 +399,6 @@ theorem DenseRange.equalizer (hfd : DenseRange f) {g h : β → γ} (hg : Contin
 
 end
 
-/- warning: filter.has_basis.has_basis_of_dense_inducing -> Filter.HasBasis.hasBasis_of_denseInducing is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u1} α] [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : T3Space.{u2} β _inst_2] {ι : Type.{u3}} {s : ι -> (Set.{u1} α)} {p : ι -> Prop} {x : α}, (Filter.HasBasis.{u1, succ u3} α ι (nhds.{u1} α _inst_1 x) p s) -> (forall {f : α -> β}, (DenseInducing.{u1, u2} α β _inst_1 _inst_2 f) -> (Filter.HasBasis.{u2, succ u3} β ι (nhds.{u2} β _inst_2 (f x)) p (fun (i : ι) => closure.{u2} β _inst_2 (Set.image.{u1, u2} α β f (s i)))))
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} [_inst_1 : TopologicalSpace.{u3} α] [_inst_2 : TopologicalSpace.{u2} β] [_inst_3 : T3Space.{u2} β _inst_2] {ι : Type.{u1}} {s : ι -> (Set.{u3} α)} {p : ι -> Prop} {x : α}, (Filter.HasBasis.{u3, succ u1} α ι (nhds.{u3} α _inst_1 x) p s) -> (forall {f : α -> β}, (DenseInducing.{u3, u2} α β _inst_1 _inst_2 f) -> (Filter.HasBasis.{u2, succ u1} β ι (nhds.{u2} β _inst_2 (f x)) p (fun (i : ι) => closure.{u2} β _inst_2 (Set.image.{u3, u2} α β f (s i)))))
-Case conversion may be inaccurate. Consider using '#align filter.has_basis.has_basis_of_dense_inducing Filter.HasBasis.hasBasis_of_denseInducingₓ'. -/
 -- Bourbaki GT III §3 no.4 Proposition 7 (generalised to any dense-inducing map to a T₃ space)
 theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [TopologicalSpace β]
     [T3Space β] {ι : Type _} {s : ι → Set α} {p : ι → Prop} {x : α} (h : (𝓝 x).HasBasis p s)

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

@@ -504,7 +504,7 @@ theorem isClosed_property [TopologicalSpace β] {e : α → β} {p : β → Prop
   have : univ ⊆ { b | p b } :=
     calc
       univ = closure (range e) := he.closure_range.symm
-      _ ⊆ closure { b | p b } := closure_mono <| range_subset_iff.mpr h
+      _ ⊆ closure { b | p b } := (closure_mono <| range_subset_iff.mpr h)
       _ = _ := hp.closure_eq
       
   fun b => this trivial

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

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -43,7 +43,6 @@ structure DenseInducing [TopologicalSpace α] [TopologicalSpace β] (i : α →
 namespace DenseInducing
 
 variable [TopologicalSpace α] [TopologicalSpace β]
-
 variable {i : α → β} (di : DenseInducing i)
 
 theorem nhds_eq_comap (di : DenseInducing i) : ∀ a : α, 𝓝 a = comap i (𝓝 <| i a) :=
@@ -245,7 +244,6 @@ namespace DenseEmbedding
 open TopologicalSpace
 
 variable [TopologicalSpace α] [TopologicalSpace β] [TopologicalSpace γ] [TopologicalSpace δ]
-
 variable {e : α → β} (de : DenseEmbedding e)
 
 theorem inj_iff {x y} : e x = e y ↔ x = y :=
@@ -352,7 +350,6 @@ theorem DenseRange.induction_on₃ [TopologicalSpace β] {e : α → β} {p : β
 section
 
 variable [TopologicalSpace β] [TopologicalSpace γ] [T2Space γ]
-
 variable {f : α → β}
 
 /-- Two continuous functions to a t2-space that agree on the dense range of a function are equal. -/

No changes to tactic file, it's just boring fixes throughout the library.

This follows on from #6964.

Co-authored-by: sgouezel <sebastien.gouezel@univ-rennes1.fr> Co-authored-by: Eric Wieser <wieser.eric@gmail.com>

@@ -108,7 +108,8 @@ protected theorem separableSpace [SeparableSpace α] : SeparableSpace β :=
 
 variable [TopologicalSpace δ] {f : γ → α} {g : γ → δ} {h : δ → β}
 
-/-- ```
+/--
+```
  γ -f→ α
 g↓     ↓e
  δ -h→ β
@@ -176,8 +177,8 @@ theorem extend_eq' [T2Space γ] {f : α → γ} (di : DenseInducing i)
 theorem extend_unique_at [T2Space γ] {b : β} {f : α → γ} {g : β → γ} (di : DenseInducing i)
     (hf : ∀ᶠ x in comap i (𝓝 b), g (i x) = f x) (hg : ContinuousAt g b) : di.extend f b = g b := by
   refine' di.extend_eq_of_tendsto fun s hs => mem_map.2 _
-  suffices : ∀ᶠ x : α in comap i (𝓝 b), g (i x) ∈ s
-  exact hf.mp (this.mono fun x hgx hfx => hfx ▸ hgx)
+  suffices ∀ᶠ x : α in comap i (𝓝 b), g (i x) ∈ s from
+    hf.mp (this.mono fun x hgx hfx => hfx ▸ hgx)
   clear hf f
   refine' eventually_comap.2 ((hg.eventually hs).mono _)
   rintro _ hxs x rfl

Salvaged from #9981.

@@ -28,8 +28,7 @@ has to be `DenseInducing` (not necessarily injective).
 noncomputable section
 
 open Set Filter
-
-open Classical Topology Filter
+open scoped Topology
 
 variable {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
 

This incorporates changes from

• #7845
• #7847
• #7853
• #7872 (was never actually made to work, but the diffs in nightly-testing are unexciting: we need to fully qualify a few names)

They can all be closed when this is merged.

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

@@ -201,8 +201,7 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
   have V₁_in : V₁ ∈ 𝓝 b := by
     filter_upwards [hf]
     rintro x ⟨c, hc⟩
-    unfold_let φ
-    rwa [di.extend_eq_of_tendsto hc]
+    rwa [← di.extend_eq_of_tendsto hc] at hc
   obtain ⟨V₂, V₂_in, V₂_op, hV₂⟩ : ∃ V₂ ∈ 𝓝 b, IsOpen V₂ ∧ ∀ x ∈ i ⁻¹' V₂, f x ∈ V' := by
     simpa [and_assoc] using
       ((nhds_basis_opens' b).comap i).tendsto_left_iff.mp (mem_of_mem_nhds V₁_in : b ∈ V₁) V' V'_in

mathport was forgetting a space in filter_upwards [...]with instead of filter_upwards [...] with.

@@ -206,7 +206,7 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
   obtain ⟨V₂, V₂_in, V₂_op, hV₂⟩ : ∃ V₂ ∈ 𝓝 b, IsOpen V₂ ∧ ∀ x ∈ i ⁻¹' V₂, f x ∈ V' := by
     simpa [and_assoc] using
       ((nhds_basis_opens' b).comap i).tendsto_left_iff.mp (mem_of_mem_nhds V₁_in : b ∈ V₁) V' V'_in
-  suffices ∀ x ∈ V₁ ∩ V₂, φ x ∈ V' by filter_upwards [inter_mem V₁_in V₂_in]using this
+  suffices ∀ x ∈ V₁ ∩ V₂, φ x ∈ V' by filter_upwards [inter_mem V₁_in V₂_in] using this
   rintro x ⟨x_in₁, x_in₂⟩
   have hV₂x : V₂ ∈ 𝓝 x := IsOpen.mem_nhds V₂_op x_in₂
   apply V'_closed.mem_of_tendsto x_in₁
@@ -381,7 +381,7 @@ theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [Topolog
         (closure_mono (image_subset f hi')).trans
           (Subset.trans (closure_minimal (image_preimage_subset _ _) hT₂) hT₃)⟩
   · obtain ⟨i, hi, hi'⟩ := hT
-    suffices closure (f '' s i) ∈ 𝓝 (f x) by filter_upwards [this]using hi'
+    suffices closure (f '' s i) ∈ 𝓝 (f x) by filter_upwards [this] using hi'
     replace h := (h (s i)).mpr ⟨i, hi, Subset.rfl⟩
     exact hf.closure_image_mem_nhds h
 #align filter.has_basis.has_basis_of_dense_inducing Filter.HasBasis.hasBasis_of_denseInducing

@@ -201,6 +201,7 @@ theorem continuousAt_extend [T3Space γ] {b : β} {f : α → γ} (di : DenseInd
   have V₁_in : V₁ ∈ 𝓝 b := by
     filter_upwards [hf]
     rintro x ⟨c, hc⟩
+    unfold_let φ
     rwa [di.extend_eq_of_tendsto hc]
   obtain ⟨V₂, V₂_in, V₂_op, hV₂⟩ : ∃ V₂ ∈ 𝓝 b, IsOpen V₂ ∧ ∀ x ∈ i ⁻¹' V₂, f x ∈ V' := by
     simpa [and_assoc] using

Match https://github.com/leanprover-community/mathlib/pull/18134

@@ -6,7 +6,7 @@ Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
 import Mathlib.Topology.Separation
 import Mathlib.Topology.Bases
 
-#align_import topology.dense_embedding from "leanprover-community/mathlib"@"d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46"
+#align_import topology.dense_embedding from "leanprover-community/mathlib"@"148aefbd371a25f1cff33c85f20c661ce3155def"
 
 /-!
 # Dense embeddings
@@ -14,8 +14,8 @@ import Mathlib.Topology.Bases
 This file defines three properties of functions:
 
 * `DenseRange f`      means `f` has dense image;
-* `DenseInducing i`   means `i` is also `Inducing`;
-* `DenseEmbedding e`  means `e` is also an `Embedding`.
+* `DenseInducing i`   means `i` is also `Inducing`, namely it induces the topology on its codomain;
+* `DenseEmbedding e`  means `e` is further an `Embedding`, namely it is injective and `Inducing`.
 
 The main theorem `continuous_extend` gives a criterion for a function
 `f : X → Z` to a T₃ space Z to extend along a dense embedding

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

This has nice performance benefits.

@@ -31,7 +31,7 @@ open Set Filter
 
 open Classical Topology Filter
 
-variable {α : Type _} {β : Type _} {γ : Type _} {δ : Type _}
+variable {α : Type*} {β : Type*} {γ : Type*} {δ : Type*}
 
 /-- `i : α → β` is "dense inducing" if it has dense range and the topology on `α`
   is the one induced by `i` from the topology on `β`. -/
@@ -271,7 +271,7 @@ protected theorem prod {e₁ : α → β} {e₂ : γ → δ} (de₁ : DenseEmbed
 
 /-- The dense embedding of a subtype inside its closure. -/
 @[simps]
-def subtypeEmb {α : Type _} (p : α → Prop) (e : α → β) (x : { x // p x }) :
+def subtypeEmb {α : Type*} (p : α → Prop) (e : α → β) (x : { x // p x }) :
     { x // x ∈ closure (e '' { x | p x }) } :=
   ⟨e x, subset_closure <| mem_image_of_mem e x.prop⟩
 #align dense_embedding.subtype_emb DenseEmbedding.subtypeEmb
@@ -295,7 +295,7 @@ theorem dense_image {s : Set α} : Dense (e '' s) ↔ Dense s :=
 
 end DenseEmbedding
 
-theorem denseEmbedding_id {α : Type _} [TopologicalSpace α] : DenseEmbedding (id : α → α) :=
+theorem denseEmbedding_id {α : Type*} [TopologicalSpace α] : DenseEmbedding (id : α → α) :=
   { embedding_id with dense := denseRange_id }
 #align dense_embedding_id denseEmbedding_id
 
@@ -365,7 +365,7 @@ end
 
 -- Bourbaki GT III §3 no.4 Proposition 7 (generalised to any dense-inducing map to a T₃ space)
 theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [TopologicalSpace β]
-    [T3Space β] {ι : Type _} {s : ι → Set α} {p : ι → Prop} {x : α} (h : (𝓝 x).HasBasis p s)
+    [T3Space β] {ι : Type*} {s : ι → Set α} {p : ι → Prop} {x : α} (h : (𝓝 x).HasBasis p s)
     {f : α → β} (hf : DenseInducing f) : (𝓝 (f x)).HasBasis p fun i => closure <| f '' s i := by
   rw [Filter.hasBasis_iff] at h ⊢
   intro T

• depends on: #5966

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

@@ -2,15 +2,12 @@
 Copyright (c) 2019 Reid Barton. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro, Patrick Massot
-
-! This file was ported from Lean 3 source module topology.dense_embedding
-! leanprover-community/mathlib commit d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Separation
 import Mathlib.Topology.Bases
 
+#align_import topology.dense_embedding from "leanprover-community/mathlib"@"d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46"
+
 /-!
 # Dense embeddings
 

Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>

@@ -85,7 +85,7 @@ theorem dense_image (di : DenseInducing i) {s : Set α} : Dense (i '' s) ↔ Den
 
 /-- If `i : α → β` is a dense embedding with dense complement of the range, then any compact set in
 `α` has empty interior. -/
-theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dense (range iᶜ))
+theorem interior_compact_eq_empty [T2Space β] (di : DenseInducing i) (hd : Dense (range i)ᶜ)
     {s : Set α} (hs : IsCompact s) : interior s = ∅ := by
   refine' eq_empty_iff_forall_not_mem.2 fun x hx => _
   rw [mem_interior_iff_mem_nhds] at hx

Changes are of the form

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

@@ -370,7 +370,7 @@ end
 theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [TopologicalSpace β]
     [T3Space β] {ι : Type _} {s : ι → Set α} {p : ι → Prop} {x : α} (h : (𝓝 x).HasBasis p s)
     {f : α → β} (hf : DenseInducing f) : (𝓝 (f x)).HasBasis p fun i => closure <| f '' s i := by
-  rw [Filter.hasBasis_iff] at h⊢
+  rw [Filter.hasBasis_iff] at h ⊢
   intro T
   refine' ⟨fun hT => _, fun hT => _⟩
   · obtain ⟨T', hT₁, hT₂, hT₃⟩ := exists_mem_nhds_isClosed_subset hT

This PR fixes two things:

• Most align statements for definitions and theorems and instances that are separated by two newlines from the relevant declaration (s/\n\n#align/\n#align). This is often seen in the mathport output after ending calc blocks.
• All remaining more-than-one-line #align statements. (This was needed for a script I wrote for #3630.)

@@ -75,7 +75,6 @@ theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs
   calc
     U ⊆ closure (i '' (i ⁻¹' U)) := di.dense.subset_closure_image_preimage_of_isOpen hUo
     _ ⊆ closure (i '' s) := closure_mono (image_subset i sub)
-
 #align dense_inducing.closure_image_mem_nhds DenseInducing.closure_image_mem_nhds
 
 theorem dense_image (di : DenseInducing i) {s : Set α} : Dense (i '' s) ↔ Dense s := by

vscode is already configured by .vscode/settings.json to trim these on save. It's not clear how they've managed to stick around.

By doing this all in one PR now, it avoids getting random whitespace diffs in PRs later.

This was done with a regex search in vscode,

@@ -75,7 +75,7 @@ theorem closure_image_mem_nhds {s : Set α} {a : α} (di : DenseInducing i) (hs
   calc
     U ⊆ closure (i '' (i ⁻¹' U)) := di.dense.subset_closure_image_preimage_of_isOpen hUo
     _ ⊆ closure (i '' s) := closure_mono (image_subset i sub)
-    
+
 #align dense_inducing.closure_image_mem_nhds DenseInducing.closure_image_mem_nhds
 
 theorem dense_image (di : DenseInducing i) {s : Set α} : Dense (i '' s) ↔ Dense s := by
@@ -315,7 +315,7 @@ theorem isClosed_property [TopologicalSpace β] {e : α → β} {p : β → Prop
       univ = closure (range e) := he.closure_range.symm
       _ ⊆ closure { b | p b } := closure_mono <| range_subset_iff.mpr h
       _ = _ := hp.closure_eq
-      
+
   fun _ => this trivial
 #align is_closed_property isClosed_property
 
@@ -388,4 +388,3 @@ theorem Filter.HasBasis.hasBasis_of_denseInducing [TopologicalSpace α] [Topolog
     replace h := (h (s i)).mpr ⟨i, hi, Subset.rfl⟩
     exact hf.closure_image_mem_nhds h
 #align filter.has_basis.has_basis_of_dense_inducing Filter.HasBasis.hasBasis_of_denseInducing
-