topology.uniform_space.compact ⟷ Mathlib.Topology.UniformSpace.Compact

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

@@ -94,7 +94,7 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
 /- ./././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 -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y «expr ≠ » x) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (y «expr ≠ » x) -/
 #print uniformSpaceOfCompactT2 /-
 /-- The unique uniform structure inducing a given compact topological structure. -/
 def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ] : UniformSpace γ

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

@@ -126,7 +126,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     have : (x, y) ∉ interior V :=
       by
       have : (x, y) ∈ closure (Vᶜ) := by rwa [mem_closure_iff_clusterPt]
-      rwa [closure_compl] at this 
+      rwa [closure_compl] at this
     have diag_subset : diagonal γ ⊆ interior V := subset_interior_iff_mem_nhdsSet.2 V_in
     have x_ne_y : x ≠ y := mt (@diag_subset (x, y)) this
     -- Since γ is compact and Hausdorff, it is normal, hence T₃.
@@ -208,8 +208,8 @@ theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β}
     (hf : ContinuousOn f s) : UniformContinuousOn f s :=
   by
   rw [uniformContinuousOn_iff_restrict]
-  rw [isCompact_iff_compactSpace] at hs 
-  rw [continuousOn_iff_continuous_restrict] at hf 
+  rw [isCompact_iff_compactSpace] at hs
+  rw [continuousOn_iff_continuous_restrict] at hf
   skip
   exact CompactSpace.uniformContinuous_of_continuous hf
 #align is_compact.uniform_continuous_on_of_continuous IsCompact.uniformContinuousOn_of_continuous
@@ -318,7 +318,7 @@ uniformly equicontinuous. -/
 theorem CompactSpace.uniformEquicontinuous_of_equicontinuous {ι : Type _} {F : ι → β → α}
     [CompactSpace β] (h : Equicontinuous F) : UniformEquicontinuous F :=
   by
-  rw [equicontinuous_iff_continuous] at h 
+  rw [equicontinuous_iff_continuous] at h
   rw [uniformEquicontinuous_iff_uniformContinuous]
   exact CompactSpace.uniformContinuous_of_continuous h
 #align compact_space.uniform_equicontinuous_of_equicontinuous CompactSpace.uniformEquicontinuous_of_equicontinuous

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

@@ -118,7 +118,8 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     by_contra H
     haveI : ne_bot (F ⊓ 𝓟 (Vᶜ)) := ⟨H⟩
     -- Hence compactness would give us a cluster point (x, y) for F ⊓ 𝓟 Vᶜ
-    obtain ⟨⟨x, y⟩, hxy⟩ : ∃ p : γ × γ, ClusterPt p (F ⊓ 𝓟 (Vᶜ)) := cluster_point_of_compact _
+    obtain ⟨⟨x, y⟩, hxy⟩ : ∃ p : γ × γ, ClusterPt p (F ⊓ 𝓟 (Vᶜ)) :=
+      exists_clusterPt_of_compactSpace _
     -- In particular (x, y) is a cluster point of 𝓟 Vᶜ, hence is not in the interior of V,
     -- and a fortiori not in Δ, so x ≠ y
     have clV : ClusterPt (x, y) (𝓟 <| Vᶜ) := hxy.of_inf_right

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

@@ -3,10 +3,10 @@ Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Yury Kudryashov
 -/
-import Mathbin.Topology.UniformSpace.UniformConvergence
-import Mathbin.Topology.UniformSpace.Equicontinuity
-import Mathbin.Topology.Separation
-import Mathbin.Topology.Support
+import Topology.UniformSpace.UniformConvergence
+import Topology.UniformSpace.Equicontinuity
+import Topology.Separation
+import Topology.Support
 
 #align_import topology.uniform_space.compact from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
 
@@ -94,7 +94,7 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
 /- ./././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 -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » x) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (y «expr ≠ » x) -/
 #print uniformSpaceOfCompactT2 /-
 /-- The unique uniform structure inducing a given compact topological structure. -/
 def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ] : UniformSpace γ

mathlib commit https://github.com/leanprover-community/mathlib/commit/001ffdc42920050657fd45bd2b8bfbec8eaaeb29

@@ -129,7 +129,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     have diag_subset : diagonal γ ⊆ interior V := subset_interior_iff_mem_nhdsSet.2 V_in
     have x_ne_y : x ≠ y := mt (@diag_subset (x, y)) this
     -- Since γ is compact and Hausdorff, it is normal, hence T₃.
-    haveI : NormalSpace γ := normalOfCompactT2
+    haveI : NormalSpace γ := T4Space.of_compactSpace_t2Space
     -- So there are closed neighboords V₁ and V₂ of x and y contained in disjoint open neighborhoods
     -- U₁ and U₂.
     obtain

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

@@ -80,7 +80,7 @@ theorem compactSpace_uniformity [CompactSpace α] : 𝓤 α = ⨆ x, 𝓝 (x, x)
 theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
     {u u' : UniformSpace γ} (h : u.toTopologicalSpace = t) (h' : u'.toTopologicalSpace = t) :
     u = u' := by
-  apply uniformSpace_eq
+  apply UniformSpace.ext
   change uniformity _ = uniformity _
   have : @CompactSpace γ u.to_topological_space := by rwa [h]
   have : @CompactSpace γ u'.to_topological_space := by rwa [h']

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.uniform_space.compact
-! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.UniformSpace.UniformConvergence
 import Mathbin.Topology.UniformSpace.Equicontinuity
 import Mathbin.Topology.Separation
 import Mathbin.Topology.Support
 
+#align_import topology.uniform_space.compact from "leanprover-community/mathlib"@"ee05e9ce1322178f0c12004eb93c00d2c8c00ed2"
+
 /-!
 # Compact separated uniform spaces
 
@@ -97,7 +94,7 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
 /- ./././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 -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ≠ » x) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » x) -/
 #print uniformSpaceOfCompactT2 /-
 /-- The unique uniform structure inducing a given compact topological structure. -/
 def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ] : UniformSpace γ

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

@@ -54,6 +54,7 @@ variable {α β γ : Type _} [UniformSpace α] [UniformSpace β]
 
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print nhdsSet_diagonal_eq_uniformity /-
 /-- On a compact uniform space, the topology determines the uniform structure, entourages are
 exactly the neighborhoods of the diagonal. -/
 theorem nhdsSet_diagonal_eq_uniformity [CompactSpace α] : 𝓝ˢ (diagonal α) = 𝓤 α :=
@@ -68,12 +69,15 @@ theorem nhdsSet_diagonal_eq_uniformity [CompactSpace α] : 𝓝ˢ (diagonal α)
   refine' (is_compact_diagonal.nhds_set_basis_uniformity this).ge_iff.2 fun U hU => _
   exact mem_of_superset hU fun ⟨x, y⟩ hxy => mem_Union₂.2 ⟨(x, x), rfl, refl_mem_uniformity hU, hxy⟩
 #align nhds_set_diagonal_eq_uniformity nhdsSet_diagonal_eq_uniformity
+-/
 
+#print compactSpace_uniformity /-
 /-- On a compact uniform space, the topology determines the uniform structure, entourages are
 exactly the neighborhoods of the diagonal. -/
 theorem compactSpace_uniformity [CompactSpace α] : 𝓤 α = ⨆ x, 𝓝 (x, x) :=
   nhdsSet_diagonal_eq_uniformity.symm.trans (nhdsSet_diagonal _)
 #align compact_space_uniformity compactSpace_uniformity
+-/
 
 #print unique_uniformity_of_compact /-
 theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
@@ -188,6 +192,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
 -/
 
 
+#print CompactSpace.uniformContinuous_of_continuous /-
 /-- Heine-Cantor: a continuous function on a compact uniform space is uniformly
 continuous. -/
 theorem CompactSpace.uniformContinuous_of_continuous [CompactSpace α] {f : α → β}
@@ -196,7 +201,9 @@ theorem CompactSpace.uniformContinuous_of_continuous [CompactSpace α] {f : α 
     (h.Prod_map h).tendsto_nhdsSet mapsTo_prod_map_diagonal
   (this.mono_left nhdsSet_diagonal_eq_uniformity.ge).mono_right nhdsSet_diagonal_le_uniformity
 #align compact_space.uniform_continuous_of_continuous CompactSpace.uniformContinuous_of_continuous
+-/
 
+#print IsCompact.uniformContinuousOn_of_continuous /-
 /-- Heine-Cantor: a continuous function on a compact set of a uniform space is uniformly
 continuous. -/
 theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β} (hs : IsCompact s)
@@ -208,6 +215,7 @@ theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β}
   skip
   exact CompactSpace.uniformContinuous_of_continuous hf
 #align is_compact.uniform_continuous_on_of_continuous IsCompact.uniformContinuousOn_of_continuous
+-/
 
 #print IsCompact.uniformContinuousAt_of_continuousAt /-
 /-- If `s` is compact and `f` is continuous at all points of `s`, then `f` is
@@ -231,6 +239,7 @@ theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s :
 #align is_compact.uniform_continuous_at_of_continuous_at IsCompact.uniformContinuousAt_of_continuousAt
 -/
 
+#print Continuous.uniformContinuous_of_tendsto_cocompact /-
 theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : β}
     (h_cont : Continuous f) (hx : Tendsto f (cocompact α) (𝓝 x)) : UniformContinuous f :=
   uniformContinuous_def.2 fun r hr =>
@@ -248,6 +257,7 @@ theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : 
     apply htr
     exact ⟨x, htsymm.mk_mem_comm.1 (hst h₁), hst h₂⟩
 #align continuous.uniform_continuous_of_tendsto_cocompact Continuous.uniformContinuous_of_tendsto_cocompact
+-/
 
 #print HasCompactMulSupport.is_one_at_infty /-
 /-- If `f` has compact multiplicative support, then `f` tends to 1 at infinity. -/
@@ -278,6 +288,7 @@ theorem HasCompactMulSupport.uniformContinuous_of_continuous {f : α → β} [On
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print ContinuousOn.tendstoUniformly /-
 /-- A family of functions `α → β → γ` tends uniformly to its value at `x` if `α` is locally compact,
 `β` is compact and `f` is continuous on `U × (univ : set β)` for some neighborhood `U` of `x`. -/
 theorem ContinuousOn.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β] [UniformSpace γ]
@@ -290,13 +301,16 @@ theorem ContinuousOn.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β]
       (h.mono <| prod_mono hKU subset.rfl)
   exact this.tendsto_uniformly hxK
 #align continuous_on.tendsto_uniformly ContinuousOn.tendstoUniformly
+-/
 
+#print Continuous.tendstoUniformly /-
 /-- A continuous family of functions `α → β → γ` tends uniformly to its value at `x` if `α` is
 locally compact and `β` is compact. -/
 theorem Continuous.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β] [UniformSpace γ]
     (f : α → β → γ) (h : Continuous ↿f) (x : α) : TendstoUniformly f (f x) (𝓝 x) :=
   h.ContinuousOn.TendstoUniformly univ_mem
 #align continuous.tendsto_uniformly Continuous.tendstoUniformly
+-/
 
 section UniformConvergence
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/31c24aa72e7b3e5ed97a8412470e904f82b81004

@@ -93,7 +93,7 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
 /- ./././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 -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » x) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (y «expr ≠ » x) -/
 #print uniformSpaceOfCompactT2 /-
 /-- The unique uniform structure inducing a given compact topological structure. -/
 def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ] : UniformSpace γ

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

@@ -216,7 +216,7 @@ close to `x` (even if `y` is not itself in `s`, so this is a stronger assertion
 `uniform_continuous_on s`). -/
 theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s : Set α}
     (hs : IsCompact s) (f : α → β) (hf : ∀ a ∈ s, ContinuousAt f a) (hr : r ∈ 𝓤 β) :
-    { x : α × α | x.1 ∈ s → (f x.1, f x.2) ∈ r } ∈ 𝓤 α :=
+    {x : α × α | x.1 ∈ s → (f x.1, f x.2) ∈ r} ∈ 𝓤 α :=
   by
   obtain ⟨t, ht, htsymm, htr⟩ := comp_symm_mem_uniformity_sets hr
   choose U hU T hT hb using fun a ha =>

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

@@ -124,7 +124,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     have : (x, y) ∉ interior V :=
       by
       have : (x, y) ∈ closure (Vᶜ) := by rwa [mem_closure_iff_clusterPt]
-      rwa [closure_compl] at this
+      rwa [closure_compl] at this 
     have diag_subset : diagonal γ ⊆ interior V := subset_interior_iff_mem_nhdsSet.2 V_in
     have x_ne_y : x ≠ y := mt (@diag_subset (x, y)) this
     -- Since γ is compact and Hausdorff, it is normal, hence T₃.
@@ -203,8 +203,8 @@ theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β}
     (hf : ContinuousOn f s) : UniformContinuousOn f s :=
   by
   rw [uniformContinuousOn_iff_restrict]
-  rw [isCompact_iff_compactSpace] at hs
-  rw [continuousOn_iff_continuous_restrict] at hf
+  rw [isCompact_iff_compactSpace] at hs 
+  rw [continuousOn_iff_continuous_restrict] at hf 
   skip
   exact CompactSpace.uniformContinuous_of_continuous hf
 #align is_compact.uniform_continuous_on_of_continuous IsCompact.uniformContinuousOn_of_continuous
@@ -227,7 +227,7 @@ theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s :
   obtain ⟨a, ha, haU⟩ := Set.mem_iUnion₂.1 (hsU h₁)
   apply htr
   refine' ⟨f a, htsymm.mk_mem_comm.1 (hb _ _ _ haU _), hb _ _ _ haU _⟩
-  exacts[mem_ball_self _ (hT a a.2), mem_Inter₂.1 h a ha]
+  exacts [mem_ball_self _ (hT a a.2), mem_Inter₂.1 h a ha]
 #align is_compact.uniform_continuous_at_of_continuous_at IsCompact.uniformContinuousAt_of_continuousAt
 -/
 
@@ -306,7 +306,7 @@ uniformly equicontinuous. -/
 theorem CompactSpace.uniformEquicontinuous_of_equicontinuous {ι : Type _} {F : ι → β → α}
     [CompactSpace β] (h : Equicontinuous F) : UniformEquicontinuous F :=
   by
-  rw [equicontinuous_iff_continuous] at h
+  rw [equicontinuous_iff_continuous] at h 
   rw [uniformEquicontinuous_iff_uniformContinuous]
   exact CompactSpace.uniformContinuous_of_continuous h
 #align compact_space.uniform_equicontinuous_of_equicontinuous CompactSpace.uniformEquicontinuous_of_equicontinuous

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

@@ -42,7 +42,7 @@ uniform space, uniform continuity, compact space
 -/
 
 
-open Classical uniformity Topology Filter
+open scoped Classical uniformity Topology Filter
 
 open Filter UniformSpace Set
 

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

@@ -53,12 +53,6 @@ variable {α β γ : Type _} [UniformSpace α] [UniformSpace β]
 -/
 
 
-/- warning: nhds_set_diagonal_eq_uniformity -> nhdsSet_diagonal_eq_uniformity is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Set.diagonal.{u1} α)) (uniformity.{u1} α _inst_1)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Set.diagonal.{u1} α)) (uniformity.{u1} α _inst_1)
-Case conversion may be inaccurate. Consider using '#align nhds_set_diagonal_eq_uniformity nhdsSet_diagonal_eq_uniformityₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- On a compact uniform space, the topology determines the uniform structure, entourages are
 exactly the neighborhoods of the diagonal. -/
@@ -75,12 +69,6 @@ theorem nhdsSet_diagonal_eq_uniformity [CompactSpace α] : 𝓝ˢ (diagonal α)
   exact mem_of_superset hU fun ⟨x, y⟩ hxy => mem_Union₂.2 ⟨(x, x), rfl, refl_mem_uniformity hU, hxy⟩
 #align nhds_set_diagonal_eq_uniformity nhdsSet_diagonal_eq_uniformity
 
-/- warning: compact_space_uniformity -> compactSpace_uniformity is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasSup.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
-Case conversion may be inaccurate. Consider using '#align compact_space_uniformity compactSpace_uniformityₓ'. -/
 /-- On a compact uniform space, the topology determines the uniform structure, entourages are
 exactly the neighborhoods of the diagonal. -/
 theorem compactSpace_uniformity [CompactSpace α] : 𝓤 α = ⨆ x, 𝓝 (x, x) :=
@@ -200,12 +188,6 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
 -/
 
 
-/- warning: compact_space.uniform_continuous_of_continuous -> CompactSpace.uniformContinuous_of_continuous 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_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)] {f : α -> β}, (Continuous.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2) f) -> (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : UniformSpace.{u2} α] [_inst_2 : UniformSpace.{u1} β] [_inst_3 : CompactSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α _inst_1)] {f : α -> β}, (Continuous.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} β _inst_2) f) -> (UniformContinuous.{u2, u1} α β _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align compact_space.uniform_continuous_of_continuous CompactSpace.uniformContinuous_of_continuousₓ'. -/
 /-- Heine-Cantor: a continuous function on a compact uniform space is uniformly
 continuous. -/
 theorem CompactSpace.uniformContinuous_of_continuous [CompactSpace α] {f : α → β}
@@ -215,12 +197,6 @@ theorem CompactSpace.uniformContinuous_of_continuous [CompactSpace α] {f : α 
   (this.mono_left nhdsSet_diagonal_eq_uniformity.ge).mono_right nhdsSet_diagonal_le_uniformity
 #align compact_space.uniform_continuous_of_continuous CompactSpace.uniformContinuous_of_continuous
 
-/- warning: is_compact.uniform_continuous_on_of_continuous -> IsCompact.uniformContinuousOn_of_continuous 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] {s : Set.{u1} α} {f : α -> β}, (IsCompact.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) s) -> (ContinuousOn.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2) f s) -> (UniformContinuousOn.{u1, u2} α β _inst_1 _inst_2 f s)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : UniformSpace.{u2} α] [_inst_2 : UniformSpace.{u1} β] {s : Set.{u2} α} {f : α -> β}, (IsCompact.{u2} α (UniformSpace.toTopologicalSpace.{u2} α _inst_1) s) -> (ContinuousOn.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} β _inst_2) f s) -> (UniformContinuousOn.{u2, u1} α β _inst_1 _inst_2 f s)
-Case conversion may be inaccurate. Consider using '#align is_compact.uniform_continuous_on_of_continuous IsCompact.uniformContinuousOn_of_continuousₓ'. -/
 /-- Heine-Cantor: a continuous function on a compact set of a uniform space is uniformly
 continuous. -/
 theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β} (hs : IsCompact s)
@@ -255,12 +231,6 @@ theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s :
 #align is_compact.uniform_continuous_at_of_continuous_at IsCompact.uniformContinuousAt_of_continuousAt
 -/
 
-/- warning: continuous.uniform_continuous_of_tendsto_cocompact -> Continuous.uniformContinuous_of_tendsto_cocompact 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} {x : β}, (Continuous.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2) f) -> (Filter.Tendsto.{u1, u2} α β f (Filter.cocompact.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2) x)) -> (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f)
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : UniformSpace.{u2} α] [_inst_2 : UniformSpace.{u1} β] {f : α -> β} {x : β}, (Continuous.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} β _inst_2) f) -> (Filter.Tendsto.{u2, u1} α β f (Filter.cocompact.{u2} α (UniformSpace.toTopologicalSpace.{u2} α _inst_1)) (nhds.{u1} β (UniformSpace.toTopologicalSpace.{u1} β _inst_2) x)) -> (UniformContinuous.{u2, u1} α β _inst_1 _inst_2 f)
-Case conversion may be inaccurate. Consider using '#align continuous.uniform_continuous_of_tendsto_cocompact Continuous.uniformContinuous_of_tendsto_cocompactₓ'. -/
 theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : β}
     (h_cont : Continuous f) (hx : Tendsto f (cocompact α) (𝓝 x)) : UniformContinuous f :=
   uniformContinuous_def.2 fun r hr =>
@@ -306,12 +276,6 @@ theorem HasCompactMulSupport.uniformContinuous_of_continuous {f : α → β} [On
 #align has_compact_support.uniform_continuous_of_continuous HasCompactSupport.uniformContinuous_of_continuous
 -/
 
-/- warning: continuous_on.tendsto_uniformly -> ContinuousOn.tendstoUniformly is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u3} γ] {f : α -> β -> γ} {x : α} {U : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) U (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)) -> (ContinuousOn.{max u1 u2, u3} (Prod.{u1, u2} α β) γ (Prod.topologicalSpace.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u3} γ _inst_5) (Function.HasUncurry.uncurry.{max u1 u2 u3, max u1 u2, u3} (α -> β -> γ) (Prod.{u1, u2} α β) γ (Function.hasUncurryInduction.{u1, max u2 u3, u2, u3} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u3} β γ)) f) (Set.prod.{u1, u2} α β U (Set.univ.{u2} β))) -> (TendstoUniformly.{u2, u3, u1} β γ α _inst_5 f (f x) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u1} γ] {f : α -> β -> γ} {x : α} {U : Set.{u3} α}, (Membership.mem.{u3, u3} (Set.{u3} α) (Filter.{u3} α) (instMembershipSetFilter.{u3} α) U (nhds.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1) x)) -> (ContinuousOn.{max u3 u2, u1} (Prod.{u3, u2} α β) γ (instTopologicalSpaceProd.{u3, u2} α β (UniformSpace.toTopologicalSpace.{u3} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u1} γ _inst_5) (Function.HasUncurry.uncurry.{max (max u3 u2) u1, max u3 u2, u1} (α -> β -> γ) (Prod.{u3, u2} α β) γ (Function.hasUncurryInduction.{u3, max u2 u1, u2, u1} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u1} β γ)) f) (Set.prod.{u3, u2} α β U (Set.univ.{u2} β))) -> (TendstoUniformly.{u2, u1, u3} β γ α _inst_5 f (f x) (nhds.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1) x))
-Case conversion may be inaccurate. Consider using '#align continuous_on.tendsto_uniformly ContinuousOn.tendstoUniformlyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- A family of functions `α → β → γ` tends uniformly to its value at `x` if `α` is locally compact,
@@ -327,12 +291,6 @@ theorem ContinuousOn.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β]
   exact this.tendsto_uniformly hxK
 #align continuous_on.tendsto_uniformly ContinuousOn.tendstoUniformly
 
-/- warning: continuous.tendsto_uniformly -> Continuous.tendstoUniformly is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u3} γ] (f : α -> β -> γ), (Continuous.{max u1 u2, u3} (Prod.{u1, u2} α β) γ (Prod.topologicalSpace.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u3} γ _inst_5) (Function.HasUncurry.uncurry.{max u1 u2 u3, max u1 u2, u3} (α -> β -> γ) (Prod.{u1, u2} α β) γ (Function.hasUncurryInduction.{u1, max u2 u3, u2, u3} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u3} β γ)) f)) -> (forall (x : α), TendstoUniformly.{u2, u3, u1} β γ α _inst_5 f (f x) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
-but is expected to have type
-  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u1} γ] (f : α -> β -> γ), (Continuous.{max u3 u2, u1} (Prod.{u3, u2} α β) γ (instTopologicalSpaceProd.{u3, u2} α β (UniformSpace.toTopologicalSpace.{u3} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u1} γ _inst_5) (Function.HasUncurry.uncurry.{max (max u3 u2) u1, max u3 u2, u1} (α -> β -> γ) (Prod.{u3, u2} α β) γ (Function.hasUncurryInduction.{u3, max u2 u1, u2, u1} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u1} β γ)) f)) -> (forall (x : α), TendstoUniformly.{u2, u1, u3} β γ α _inst_5 f (f x) (nhds.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1) x))
-Case conversion may be inaccurate. Consider using '#align continuous.tendsto_uniformly Continuous.tendstoUniformlyₓ'. -/
 /-- A continuous family of functions `α → β → γ` tends uniformly to its value at `x` if `α` is
 locally compact and `β` is compact. -/
 theorem Continuous.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β] [UniformSpace γ]

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

@@ -77,9 +77,9 @@ theorem nhdsSet_diagonal_eq_uniformity [CompactSpace α] : 𝓝ˢ (diagonal α)
 
 /- warning: compact_space_uniformity -> compactSpace_uniformity is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (supᵢ.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasSup.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasSup.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (supᵢ.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (iSup.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
 Case conversion may be inaccurate. Consider using '#align compact_space_uniformity compactSpace_uniformityₓ'. -/
 /-- On a compact uniform space, the topology determines the uniform structure, entourages are
 exactly the neighborhoods of the diagonal. -/
@@ -188,7 +188,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
       simp_rw [isOpen_fold, isOpen_iff_mem_nhds, ← mem_comap_prod_mk, this]
     intro x
     simp_rw [nhdsSet_diagonal, comap_supr, nhds_prod_eq, comap_prod, (· ∘ ·), comap_id']
-    rw [supᵢ_split_single _ x, comap_const_of_mem fun V => mem_of_mem_nhds]
+    rw [iSup_split_single _ x, comap_const_of_mem fun V => mem_of_mem_nhds]
     suffices ∀ (y) (_ : y ≠ x), comap (fun y : γ => x) (𝓝 y) ⊓ 𝓝 y ≤ 𝓝 x by simpa
     intro y hxy
     simp [comap_const_of_not_mem (compl_singleton_mem_nhds hxy) (Classical.not_not.2 rfl)]
@@ -248,7 +248,7 @@ theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s :
   obtain ⟨fs, hsU⟩ := hs.elim_nhds_subcover' U hU
   apply mem_of_superset ((bInter_finset_mem fs).2 fun a _ => hT a a.2)
   rintro ⟨a₁, a₂⟩ h h₁
-  obtain ⟨a, ha, haU⟩ := Set.mem_unionᵢ₂.1 (hsU h₁)
+  obtain ⟨a, ha, haU⟩ := Set.mem_iUnion₂.1 (hsU h₁)
   apply htr
   refine' ⟨f a, htsymm.mk_mem_comm.1 (hb _ _ _ haU _), hb _ _ _ haU _⟩
   exacts[mem_ball_self _ (hT a a.2), mem_Inter₂.1 h a ha]

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.uniform_space.compact
-! leanprover-community/mathlib commit 735b22f8f9ff9792cf4212d7cb051c4c994bc685
+! leanprover-community/mathlib commit ee05e9ce1322178f0c12004eb93c00d2c8c00ed2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -16,6 +16,9 @@ import Mathbin.Topology.Support
 /-!
 # Compact separated uniform spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 ## Main statements
 
 * `compact_space_uniformity`: On a compact uniform space, the topology determines the

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

@@ -102,7 +102,7 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
 /- ./././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 -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (y «expr ≠ » x) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (y «expr ≠ » x) -/
 #print uniformSpaceOfCompactT2 /-
 /-- The unique uniform structure inducing a given compact topological structure. -/
 def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ] : UniformSpace γ

mathlib commit https://github.com/leanprover-community/mathlib/commit/22131150f88a2d125713ffa0f4693e3355b1eb49

@@ -50,6 +50,12 @@ variable {α β γ : Type _} [UniformSpace α] [UniformSpace β]
 -/
 
 
+/- warning: nhds_set_diagonal_eq_uniformity -> nhdsSet_diagonal_eq_uniformity is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Set.diagonal.{u1} α)) (uniformity.{u1} α _inst_1)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (nhdsSet.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Set.diagonal.{u1} α)) (uniformity.{u1} α _inst_1)
+Case conversion may be inaccurate. Consider using '#align nhds_set_diagonal_eq_uniformity nhdsSet_diagonal_eq_uniformityₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- On a compact uniform space, the topology determines the uniform structure, entourages are
 exactly the neighborhoods of the diagonal. -/
@@ -66,12 +72,19 @@ theorem nhdsSet_diagonal_eq_uniformity [CompactSpace α] : 𝓝ˢ (diagonal α)
   exact mem_of_superset hU fun ⟨x, y⟩ hxy => mem_Union₂.2 ⟨(x, x), rfl, refl_mem_uniformity hU, hxy⟩
 #align nhds_set_diagonal_eq_uniformity nhdsSet_diagonal_eq_uniformity
 
+/- warning: compact_space_uniformity -> compactSpace_uniformity is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (supᵢ.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasSup.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (Prod.topologicalSpace.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α _inst_1) (supᵢ.{u1, succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toSupSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) α (fun (x : α) => nhds.{u1} (Prod.{u1, u1} α α) (instTopologicalSpaceProd.{u1, u1} α α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (Prod.mk.{u1, u1} α α x x)))
+Case conversion may be inaccurate. Consider using '#align compact_space_uniformity compactSpace_uniformityₓ'. -/
 /-- On a compact uniform space, the topology determines the uniform structure, entourages are
 exactly the neighborhoods of the diagonal. -/
 theorem compactSpace_uniformity [CompactSpace α] : 𝓤 α = ⨆ x, 𝓝 (x, x) :=
   nhdsSet_diagonal_eq_uniformity.symm.trans (nhdsSet_diagonal _)
 #align compact_space_uniformity compactSpace_uniformity
 
+#print unique_uniformity_of_compact /-
 theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
     {u u' : UniformSpace γ} (h : u.toTopologicalSpace = t) (h' : u'.toTopologicalSpace = t) :
     u = u' := by
@@ -81,6 +94,7 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
   have : @CompactSpace γ u'.to_topological_space := by rwa [h']
   rw [compactSpace_uniformity, compactSpace_uniformity, h, h']
 #align unique_uniformity_of_compact unique_uniformity_of_compact
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
@@ -89,6 +103,7 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (y «expr ≠ » x) -/
+#print uniformSpaceOfCompactT2 /-
 /-- The unique uniform structure inducing a given compact topological structure. -/
 def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ] : UniformSpace γ
     where
@@ -175,12 +190,19 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     intro y hxy
     simp [comap_const_of_not_mem (compl_singleton_mem_nhds hxy) (Classical.not_not.2 rfl)]
 #align uniform_space_of_compact_t2 uniformSpaceOfCompactT2
+-/
 
 /-!
 ### Heine-Cantor theorem
 -/
 
 
+/- warning: compact_space.uniform_continuous_of_continuous -> CompactSpace.uniformContinuous_of_continuous 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_3 : CompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)] {f : α -> β}, (Continuous.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2) f) -> (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : UniformSpace.{u2} α] [_inst_2 : UniformSpace.{u1} β] [_inst_3 : CompactSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α _inst_1)] {f : α -> β}, (Continuous.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} β _inst_2) f) -> (UniformContinuous.{u2, u1} α β _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align compact_space.uniform_continuous_of_continuous CompactSpace.uniformContinuous_of_continuousₓ'. -/
 /-- Heine-Cantor: a continuous function on a compact uniform space is uniformly
 continuous. -/
 theorem CompactSpace.uniformContinuous_of_continuous [CompactSpace α] {f : α → β}
@@ -190,6 +212,12 @@ theorem CompactSpace.uniformContinuous_of_continuous [CompactSpace α] {f : α 
   (this.mono_left nhdsSet_diagonal_eq_uniformity.ge).mono_right nhdsSet_diagonal_le_uniformity
 #align compact_space.uniform_continuous_of_continuous CompactSpace.uniformContinuous_of_continuous
 
+/- warning: is_compact.uniform_continuous_on_of_continuous -> IsCompact.uniformContinuousOn_of_continuous 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] {s : Set.{u1} α} {f : α -> β}, (IsCompact.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) s) -> (ContinuousOn.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2) f s) -> (UniformContinuousOn.{u1, u2} α β _inst_1 _inst_2 f s)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : UniformSpace.{u2} α] [_inst_2 : UniformSpace.{u1} β] {s : Set.{u2} α} {f : α -> β}, (IsCompact.{u2} α (UniformSpace.toTopologicalSpace.{u2} α _inst_1) s) -> (ContinuousOn.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} β _inst_2) f s) -> (UniformContinuousOn.{u2, u1} α β _inst_1 _inst_2 f s)
+Case conversion may be inaccurate. Consider using '#align is_compact.uniform_continuous_on_of_continuous IsCompact.uniformContinuousOn_of_continuousₓ'. -/
 /-- Heine-Cantor: a continuous function on a compact set of a uniform space is uniformly
 continuous. -/
 theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β} (hs : IsCompact s)
@@ -202,11 +230,12 @@ theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β}
   exact CompactSpace.uniformContinuous_of_continuous hf
 #align is_compact.uniform_continuous_on_of_continuous IsCompact.uniformContinuousOn_of_continuous
 
+#print IsCompact.uniformContinuousAt_of_continuousAt /-
 /-- If `s` is compact and `f` is continuous at all points of `s`, then `f` is
 "uniformly continuous at the set `s`", i.e. `f x` is close to `f y` whenever `x ∈ s` and `y` is
 close to `x` (even if `y` is not itself in `s`, so this is a stronger assertion than
 `uniform_continuous_on s`). -/
-theorem IsCompact.uniform_continuousAt_of_continuousAt {r : Set (β × β)} {s : Set α}
+theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s : Set α}
     (hs : IsCompact s) (f : α → β) (hf : ∀ a ∈ s, ContinuousAt f a) (hr : r ∈ 𝓤 β) :
     { x : α × α | x.1 ∈ s → (f x.1, f x.2) ∈ r } ∈ 𝓤 α :=
   by
@@ -220,8 +249,15 @@ theorem IsCompact.uniform_continuousAt_of_continuousAt {r : Set (β × β)} {s :
   apply htr
   refine' ⟨f a, htsymm.mk_mem_comm.1 (hb _ _ _ haU _), hb _ _ _ haU _⟩
   exacts[mem_ball_self _ (hT a a.2), mem_Inter₂.1 h a ha]
-#align is_compact.uniform_continuous_at_of_continuous_at IsCompact.uniform_continuousAt_of_continuousAt
+#align is_compact.uniform_continuous_at_of_continuous_at IsCompact.uniformContinuousAt_of_continuousAt
+-/
 
+/- warning: continuous.uniform_continuous_of_tendsto_cocompact -> Continuous.uniformContinuous_of_tendsto_cocompact 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} {x : β}, (Continuous.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2) f) -> (Filter.Tendsto.{u1, u2} α β f (Filter.cocompact.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2) x)) -> (UniformContinuous.{u1, u2} α β _inst_1 _inst_2 f)
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u1}} [_inst_1 : UniformSpace.{u2} α] [_inst_2 : UniformSpace.{u1} β] {f : α -> β} {x : β}, (Continuous.{u2, u1} α β (UniformSpace.toTopologicalSpace.{u2} α _inst_1) (UniformSpace.toTopologicalSpace.{u1} β _inst_2) f) -> (Filter.Tendsto.{u2, u1} α β f (Filter.cocompact.{u2} α (UniformSpace.toTopologicalSpace.{u2} α _inst_1)) (nhds.{u1} β (UniformSpace.toTopologicalSpace.{u1} β _inst_2) x)) -> (UniformContinuous.{u2, u1} α β _inst_1 _inst_2 f)
+Case conversion may be inaccurate. Consider using '#align continuous.uniform_continuous_of_tendsto_cocompact Continuous.uniformContinuous_of_tendsto_cocompactₓ'. -/
 theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : β}
     (h_cont : Continuous f) (hx : Tendsto f (cocompact α) (𝓝 x)) : UniformContinuous f :=
   uniformContinuous_def.2 fun r hr =>
@@ -240,6 +276,7 @@ theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : 
     exact ⟨x, htsymm.mk_mem_comm.1 (hst h₁), hst h₂⟩
 #align continuous.uniform_continuous_of_tendsto_cocompact Continuous.uniformContinuous_of_tendsto_cocompact
 
+#print HasCompactMulSupport.is_one_at_infty /-
 /-- If `f` has compact multiplicative support, then `f` tends to 1 at infinity. -/
 @[to_additive "If `f` has compact support, then `f` tends to zero at infinity."]
 theorem HasCompactMulSupport.is_one_at_infty {f : α → γ} [TopologicalSpace γ] [One γ]
@@ -255,14 +292,23 @@ theorem HasCompactMulSupport.is_one_at_infty {f : α → γ} [TopologicalSpace 
   exact mem_of_mem_nhds hN
 #align has_compact_mul_support.is_one_at_infty HasCompactMulSupport.is_one_at_infty
 #align has_compact_support.is_zero_at_infty HasCompactSupport.is_zero_at_infty
+-/
 
+#print HasCompactMulSupport.uniformContinuous_of_continuous /-
 @[to_additive]
 theorem HasCompactMulSupport.uniformContinuous_of_continuous {f : α → β} [One β]
     (h1 : HasCompactMulSupport f) (h2 : Continuous f) : UniformContinuous f :=
   h2.uniformContinuous_of_tendsto_cocompact h1.is_one_at_infty
 #align has_compact_mul_support.uniform_continuous_of_continuous HasCompactMulSupport.uniformContinuous_of_continuous
 #align has_compact_support.uniform_continuous_of_continuous HasCompactSupport.uniformContinuous_of_continuous
+-/
 
+/- warning: continuous_on.tendsto_uniformly -> ContinuousOn.tendstoUniformly is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u3} γ] {f : α -> β -> γ} {x : α} {U : Set.{u1} α}, (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) U (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)) -> (ContinuousOn.{max u1 u2, u3} (Prod.{u1, u2} α β) γ (Prod.topologicalSpace.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u3} γ _inst_5) (Function.HasUncurry.uncurry.{max u1 u2 u3, max u1 u2, u3} (α -> β -> γ) (Prod.{u1, u2} α β) γ (Function.hasUncurryInduction.{u1, max u2 u3, u2, u3} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u3} β γ)) f) (Set.prod.{u1, u2} α β U (Set.univ.{u2} β))) -> (TendstoUniformly.{u2, u3, u1} β γ α _inst_5 f (f x) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u1} γ] {f : α -> β -> γ} {x : α} {U : Set.{u3} α}, (Membership.mem.{u3, u3} (Set.{u3} α) (Filter.{u3} α) (instMembershipSetFilter.{u3} α) U (nhds.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1) x)) -> (ContinuousOn.{max u3 u2, u1} (Prod.{u3, u2} α β) γ (instTopologicalSpaceProd.{u3, u2} α β (UniformSpace.toTopologicalSpace.{u3} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u1} γ _inst_5) (Function.HasUncurry.uncurry.{max (max u3 u2) u1, max u3 u2, u1} (α -> β -> γ) (Prod.{u3, u2} α β) γ (Function.hasUncurryInduction.{u3, max u2 u1, u2, u1} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u1} β γ)) f) (Set.prod.{u3, u2} α β U (Set.univ.{u2} β))) -> (TendstoUniformly.{u2, u1, u3} β γ α _inst_5 f (f x) (nhds.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1) x))
+Case conversion may be inaccurate. Consider using '#align continuous_on.tendsto_uniformly ContinuousOn.tendstoUniformlyₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- A family of functions `α → β → γ` tends uniformly to its value at `x` if `α` is locally compact,
@@ -278,6 +324,12 @@ theorem ContinuousOn.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β]
   exact this.tendsto_uniformly hxK
 #align continuous_on.tendsto_uniformly ContinuousOn.tendstoUniformly
 
+/- warning: continuous.tendsto_uniformly -> Continuous.tendstoUniformly is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} {γ : Type.{u3}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u3} γ] (f : α -> β -> γ), (Continuous.{max u1 u2, u3} (Prod.{u1, u2} α β) γ (Prod.topologicalSpace.{u1, u2} α β (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u3} γ _inst_5) (Function.HasUncurry.uncurry.{max u1 u2 u3, max u1 u2, u3} (α -> β -> γ) (Prod.{u1, u2} α β) γ (Function.hasUncurryInduction.{u1, max u2 u3, u2, u3} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u3} β γ)) f)) -> (forall (x : α), TendstoUniformly.{u2, u3, u1} β γ α _inst_5 f (f x) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
+but is expected to have type
+  forall {α : Type.{u3}} {β : Type.{u2}} {γ : Type.{u1}} [_inst_1 : UniformSpace.{u3} α] [_inst_2 : UniformSpace.{u2} β] [_inst_3 : LocallyCompactSpace.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1)] [_inst_4 : CompactSpace.{u2} β (UniformSpace.toTopologicalSpace.{u2} β _inst_2)] [_inst_5 : UniformSpace.{u1} γ] (f : α -> β -> γ), (Continuous.{max u3 u2, u1} (Prod.{u3, u2} α β) γ (instTopologicalSpaceProd.{u3, u2} α β (UniformSpace.toTopologicalSpace.{u3} α _inst_1) (UniformSpace.toTopologicalSpace.{u2} β _inst_2)) (UniformSpace.toTopologicalSpace.{u1} γ _inst_5) (Function.HasUncurry.uncurry.{max (max u3 u2) u1, max u3 u2, u1} (α -> β -> γ) (Prod.{u3, u2} α β) γ (Function.hasUncurryInduction.{u3, max u2 u1, u2, u1} α (β -> γ) β γ (Function.hasUncurryBase.{u2, u1} β γ)) f)) -> (forall (x : α), TendstoUniformly.{u2, u1, u3} β γ α _inst_5 f (f x) (nhds.{u3} α (UniformSpace.toTopologicalSpace.{u3} α _inst_1) x))
+Case conversion may be inaccurate. Consider using '#align continuous.tendsto_uniformly Continuous.tendstoUniformlyₓ'. -/
 /-- A continuous family of functions `α → β → γ` tends uniformly to its value at `x` if `α` is
 locally compact and `β` is compact. -/
 theorem Continuous.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β] [UniformSpace γ]
@@ -287,6 +339,7 @@ theorem Continuous.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β] [
 
 section UniformConvergence
 
+#print CompactSpace.uniformEquicontinuous_of_equicontinuous /-
 /-- An equicontinuous family of functions defined on a compact uniform space is automatically
 uniformly equicontinuous. -/
 theorem CompactSpace.uniformEquicontinuous_of_equicontinuous {ι : Type _} {F : ι → β → α}
@@ -296,6 +349,7 @@ theorem CompactSpace.uniformEquicontinuous_of_equicontinuous {ι : Type _} {F :
   rw [uniformEquicontinuous_iff_uniformContinuous]
   exact CompactSpace.uniformContinuous_of_continuous h
 #align compact_space.uniform_equicontinuous_of_equicontinuous CompactSpace.uniformEquicontinuous_of_equicontinuous
+-/
 
 end UniformConvergence
 

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

• replace isOpen_uniformity with nhds_eq_comap_uniformity as I suggested in #2028
• don't extend UniformSpace.Core so that we can drop refl, as it follows from nhds_eq_comap_uniformity;
• drop UniformSpace.mk' - can't be a match_pattern anymore;
• deprecate UniformSpace.ofNhdsEqComap.

@@ -79,7 +79,6 @@ theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
 def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ] : UniformSpace γ
     where
   uniformity := 𝓝ˢ (diagonal γ)
-  refl := principal_le_nhdsSet
   symm := continuous_swap.tendsto_nhdsSet fun x => Eq.symm
   comp := by
     /-  This is the difficult part of the proof. We need to prove that, for each neighborhood `W`
@@ -143,18 +142,12 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     -- Hence w ∈ U₁ ∩ U₂ which is empty.
     -- So we have a contradiction
     exact hU₁₂.le_bot ⟨uw_in.2, wv_in.1⟩
-  isOpen_uniformity := by
-    -- Here we need to prove the topology induced by the constructed uniformity is the
-    -- topology we started with.
-    suffices ∀ x : γ, Filter.comap (Prod.mk x) (𝓝ˢ (diagonal γ)) = 𝓝 x by
-      intro s
-      simp_rw [isOpen_iff_mem_nhds, ← mem_comap_prod_mk, this]
-    intro x
+  nhds_eq_comap_uniformity x := by
     simp_rw [nhdsSet_diagonal, comap_iSup, nhds_prod_eq, comap_prod, (· ∘ ·), comap_id']
     rw [iSup_split_single _ x, comap_const_of_mem fun V => mem_of_mem_nhds]
-    suffices ∀ (y) (_ : y ≠ x), comap (fun _ : γ => x) (𝓝 y) ⊓ 𝓝 y ≤ 𝓝 x by simpa
+    suffices ∀ y ≠ x, comap (fun _ : γ ↦ x) (𝓝 y) ⊓ 𝓝 y ≤ 𝓝 x by simpa
     intro y hxy
-    simp [comap_const_of_not_mem (compl_singleton_mem_nhds hxy) (Classical.not_not.2 rfl)]
+    simp [comap_const_of_not_mem (compl_singleton_mem_nhds hxy) (not_not_intro rfl)]
 #align uniform_space_of_compact_t2 uniformSpaceOfCompactT2
 
 /-!

We remove all but one open Classicals, instead preferring to use open scoped Classical. The only real side-effect this led to is moving a couple declarations to use Exists.choose instead of Classical.choose.

The first few commits are explicitly labelled regex replaces for ease of review.

@@ -36,7 +36,8 @@ uniform space, uniform continuity, compact space
 -/
 
 
-open Classical Uniformity Topology Filter UniformSpace Set
+open scoped Classical
+open Uniformity Topology Filter UniformSpace Set
 
 variable {α β γ : Type*} [UniformSpace α] [UniformSpace β]
 

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -221,7 +221,7 @@ theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : 
 @[to_additive "If `f` has compact support, then `f` tends to zero at infinity."]
 theorem HasCompactMulSupport.is_one_at_infty {f : α → γ} [TopologicalSpace γ] [One γ]
     (h : HasCompactMulSupport f) : Tendsto f (cocompact α) (𝓝 1) := by
-  -- porting note: move to src/topology/support.lean once the port is over
+  -- Porting note: move to src/topology/support.lean once the port is over
   intro N hN
   rw [mem_map, mem_cocompact']
   refine' ⟨mulTSupport f, h.isCompact, _⟩

Fix 1 typo, 5 lowercase, 4 header depths

@@ -30,7 +30,7 @@ import Mathlib.Topology.Support
 The construction `uniformSpace_of_compact_t2` is not declared as an instance, as it would badly
 loop.
 
-## tags
+## Tags
 
 uniform space, uniform continuity, compact space
 -/

Co-authored-by: Patrick Massot <patrickmassot@free.fr> Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -119,7 +119,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
       rintro ⟨z, z'⟩ (rfl : z = z')
       refine' IsOpen.mem_nhds _ _
       · apply_rules [IsOpen.union, IsOpen.prod]
-      · simp only [mem_union, mem_prod, and_self_iff]
+      · simp only [W, mem_union, mem_prod, and_self_iff]
         exact (_root_.em _).imp_left fun h => union_subset_union VU₁ VU₂ h
     -- So W ○ W ∈ F by definition of F
     have : W ○ W ∈ F := @mem_lift' _ _ _ (fun s => s ○ s) _ W_in

• Prove that a set is a Gdelta if and only if it is an intersection of open sets indexed by ℕ.
• Cleanup porting todos in the Gdelta file
• Rename cluster_point_of_compact to exists_clusterPt_of_compactSpace
• Generalize the class T2Space to T2OrLocallyCompactRegularSpace in the file Support.lean

@@ -94,7 +94,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     by_contra H
     haveI : NeBot (F ⊓ 𝓟 Vᶜ) := ⟨H⟩
     -- Hence compactness would give us a cluster point (x, y) for F ⊓ 𝓟 Vᶜ
-    obtain ⟨⟨x, y⟩, hxy⟩ : ∃ p : γ × γ, ClusterPt p (F ⊓ 𝓟 Vᶜ) := cluster_point_of_compact _
+    obtain ⟨⟨x, y⟩, hxy⟩ : ∃ p : γ × γ, ClusterPt p (F ⊓ 𝓟 Vᶜ) := exists_clusterPt_of_compactSpace _
     -- In particular (x, y) is a cluster point of 𝓟 Vᶜ, hence is not in the interior of V,
     -- and a fortiori not in Δ, so x ≠ y
     have clV : ClusterPt (x, y) (𝓟 <| Vᶜ) := hxy.of_inf_right

Useful to uniformize proofs for T2 spaces and regular spaces, notably to discuss regular measures in topological groups.

@@ -261,6 +261,33 @@ theorem Continuous.tendstoUniformly [WeaklyLocallyCompactSpace α] [CompactSpace
   this.tendstoUniformly hxK
 #align continuous.tendsto_uniformly Continuous.tendstoUniformly
 
+/-- In a product space `α × β`, assume that a function `f` is continuous on `s × k` where `k` is
+compact. Then, along the fiber above any `q ∈ s`, `f` is transversely uniformly continuous, i.e.,
+if `p ∈ s` is close enough to `q`, then `f p x` is uniformly close to `f q x` for all `x ∈ k`. -/
+lemma IsCompact.mem_uniformity_of_prod
+    {α β E : Type*} [TopologicalSpace α] [TopologicalSpace β] [UniformSpace E]
+    {f : α → β → E} {s : Set α} {k : Set β} {q : α} {u : Set (E × E)}
+    (hk : IsCompact k) (hf : ContinuousOn f.uncurry (s ×ˢ k)) (hq : q ∈ s) (hu : u ∈ 𝓤 E) :
+    ∃ v ∈ 𝓝[s] q, ∀ p ∈ v, ∀ x ∈ k, (f p x, f q x) ∈ u := by
+  apply hk.induction_on (p := fun t ↦ ∃ v ∈ 𝓝[s] q, ∀ p ∈ v, ∀ x ∈ t, (f p x, f q x) ∈ u)
+  · exact ⟨univ, univ_mem, by simp⟩
+  · intro t' t ht't ⟨v, v_mem, hv⟩
+    exact ⟨v, v_mem, fun p hp x hx ↦ hv p hp x (ht't hx)⟩
+  · intro t t' ⟨v, v_mem, hv⟩ ⟨v', v'_mem, hv'⟩
+    refine ⟨v ∩ v', inter_mem v_mem v'_mem, fun p hp x hx ↦ ?_⟩
+    rcases hx with h'x|h'x
+    · exact hv p hp.1 x h'x
+    · exact hv' p hp.2 x h'x
+  · rcases comp_symm_of_uniformity hu with ⟨u', u'_mem, u'_symm, hu'⟩
+    intro x hx
+    obtain ⟨v, hv, w, hw, hvw⟩ :
+      ∃ v ∈ 𝓝[s] q, ∃ w ∈ 𝓝[k] x, v ×ˢ w ⊆ f.uncurry ⁻¹' {z | (f q x, z) ∈ u'} :=
+        mem_nhdsWithin_prod_iff.1 (hf (q, x) ⟨hq, hx⟩ (mem_nhds_left (f q x) u'_mem))
+    refine ⟨w, hw, v, hv, fun p hp y hy ↦ ?_⟩
+    have A : (f q x, f p y) ∈ u' := hvw (⟨hp, hy⟩ : (p, y) ∈ v ×ˢ w)
+    have B : (f q x, f q y) ∈ u' := hvw (⟨mem_of_mem_nhdsWithin hq hv, hy⟩ : (q, y) ∈ v ×ˢ w)
+    exact hu' (prod_mk_mem_compRel (u'_symm A) B)
+
 section UniformConvergence
 
 /-- An equicontinuous family of functions defined on a compact uniform space is automatically

• Rename NormalSpace to T4Space.
• Add NormalSpace, a version without the T1Space assumption.
• Adjust some theorems.
• Supersedes thus closes #6892.
• Add some instance cycles, see #2030

@@ -103,8 +103,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
       rwa [closure_compl] at this
     have diag_subset : diagonal γ ⊆ interior V := subset_interior_iff_mem_nhdsSet.2 V_in
     have x_ne_y : x ≠ y := mt (@diag_subset (x, y)) this
-    -- Since γ is compact and Hausdorff, it is normal, hence T₃.
-    haveI : NormalSpace γ := normalOfCompactT2
+    -- Since γ is compact and Hausdorff, it is T₄, hence T₃.
     -- So there are closed neighborhoods V₁ and V₂ of x and y contained in
     -- disjoint open neighborhoods U₁ and U₂.
     obtain

@@ -252,11 +252,14 @@ theorem ContinuousOn.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β]
   exact this.tendstoUniformly hxK
 #align continuous_on.tendsto_uniformly ContinuousOn.tendstoUniformly
 
-/-- A continuous family of functions `α → β → γ` tends uniformly to its value at `x` if `α` is
-locally compact and `β` is compact. -/
-theorem Continuous.tendstoUniformly [LocallyCompactSpace α] [CompactSpace β] [UniformSpace γ]
+/-- A continuous family of functions `α → β → γ` tends uniformly to its value at `x`
+if `α` is weakly locally compact and `β` is compact. -/
+theorem Continuous.tendstoUniformly [WeaklyLocallyCompactSpace α] [CompactSpace β] [UniformSpace γ]
     (f : α → β → γ) (h : Continuous ↿f) (x : α) : TendstoUniformly f (f x) (𝓝 x) :=
-  h.continuousOn.tendstoUniformly univ_mem
+  let ⟨K, hK, hxK⟩ := exists_compact_mem_nhds x
+  have : UniformContinuousOn (↿f) (K ×ˢ univ) :=
+    IsCompact.uniformContinuousOn_of_continuous (hK.prod isCompact_univ) h.continuousOn
+  this.tendstoUniformly hxK
 #align continuous.tendsto_uniformly Continuous.tendstoUniformly
 
 section UniformConvergence

@@ -68,7 +68,7 @@ theorem compactSpace_uniformity [CompactSpace α] : 𝓤 α = ⨆ x, 𝓝 (x, x)
 theorem unique_uniformity_of_compact [t : TopologicalSpace γ] [CompactSpace γ]
     {u u' : UniformSpace γ} (h : u.toTopologicalSpace = t) (h' : u'.toTopologicalSpace = t) :
     u = u' := by
-  refine uniformSpace_eq ?_
+  refine UniformSpace.ext ?_
   have : @CompactSpace γ u.toTopologicalSpace := by rwa [h]
   have : @CompactSpace γ u'.toTopologicalSpace := by rwa [h']
   rw [@compactSpace_uniformity _ u, compactSpace_uniformity, h, h']

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

This has nice performance benefits.

@@ -38,7 +38,7 @@ uniform space, uniform continuity, compact space
 
 open Classical Uniformity Topology Filter UniformSpace Set
 
-variable {α β γ : Type _} [UniformSpace α] [UniformSpace β]
+variable {α β γ : Type*} [UniformSpace α] [UniformSpace β]
 
 /-!
 ### Uniformity on compact spaces
@@ -263,7 +263,7 @@ section UniformConvergence
 
 /-- An equicontinuous family of functions defined on a compact uniform space is automatically
 uniformly equicontinuous. -/
-theorem CompactSpace.uniformEquicontinuous_of_equicontinuous {ι : Type _} {F : ι → β → α}
+theorem CompactSpace.uniformEquicontinuous_of_equicontinuous {ι : Type*} {F : ι → β → α}
     [CompactSpace β] (h : Equicontinuous F) : UniformEquicontinuous F := by
   rw [equicontinuous_iff_continuous] at h
   rw [uniformEquicontinuous_iff_uniformContinuous]

• depends on: #5966

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

@@ -2,17 +2,14 @@
 Copyright (c) 2020 Patrick Massot. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Patrick Massot, Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.uniform_space.compact
-! leanprover-community/mathlib commit 735b22f8f9ff9792cf4212d7cb051c4c994bc685
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.UniformSpace.UniformConvergence
 import Mathlib.Topology.UniformSpace.Equicontinuity
 import Mathlib.Topology.Separation
 import Mathlib.Topology.Support
 
+#align_import topology.uniform_space.compact from "leanprover-community/mathlib"@"735b22f8f9ff9792cf4212d7cb051c4c994bc685"
+
 /-!
 # Compact separated uniform spaces
 

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

@@ -95,14 +95,14 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     rw [le_iff_forall_inf_principal_compl]
     intro V V_in
     by_contra H
-    haveI : NeBot (F ⊓ 𝓟 (Vᶜ)) := ⟨H⟩
+    haveI : NeBot (F ⊓ 𝓟 Vᶜ) := ⟨H⟩
     -- Hence compactness would give us a cluster point (x, y) for F ⊓ 𝓟 Vᶜ
-    obtain ⟨⟨x, y⟩, hxy⟩ : ∃ p : γ × γ, ClusterPt p (F ⊓ 𝓟 (Vᶜ)) := cluster_point_of_compact _
+    obtain ⟨⟨x, y⟩, hxy⟩ : ∃ p : γ × γ, ClusterPt p (F ⊓ 𝓟 Vᶜ) := cluster_point_of_compact _
     -- In particular (x, y) is a cluster point of 𝓟 Vᶜ, hence is not in the interior of V,
     -- and a fortiori not in Δ, so x ≠ y
     have clV : ClusterPt (x, y) (𝓟 <| Vᶜ) := hxy.of_inf_right
     have : (x, y) ∉ interior V := by
-      have : (x, y) ∈ closure (Vᶜ) := by rwa [mem_closure_iff_clusterPt]
+      have : (x, y) ∈ closure Vᶜ := by rwa [mem_closure_iff_clusterPt]
       rwa [closure_compl] at this
     have diag_subset : diagonal γ ⊆ interior V := subset_interior_iff_mem_nhdsSet.2 V_in
     have x_ne_y : x ≠ y := mt (@diag_subset (x, y)) this

These are all doc fixes

@@ -108,8 +108,8 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     have x_ne_y : x ≠ y := mt (@diag_subset (x, y)) this
     -- Since γ is compact and Hausdorff, it is normal, hence T₃.
     haveI : NormalSpace γ := normalOfCompactT2
-    -- So there are closed neighboords V₁ and V₂ of x and y contained in disjoint open neighborhoods
-    -- U₁ and U₂.
+    -- So there are closed neighborhoods V₁ and V₂ of x and y contained in
+    -- disjoint open neighborhoods U₁ and U₂.
     obtain
       ⟨U₁, _, V₁, V₁_in, U₂, _, V₂, V₂_in, V₁_cl, V₂_cl, U₁_op, U₂_op, VU₁, VU₂, hU₁₂⟩ :=
       disjoint_nested_nhds x_ne_y

Too often tempted to change these during other PRs, so doing a mass edit here.

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au>

@@ -201,7 +201,7 @@ theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s :
   obtain ⟨a, ha, haU⟩ := Set.mem_iUnion₂.1 (hsU h₁)
   apply htr
   refine' ⟨f a, htsymm.mk_mem_comm.1 (hb _ _ _ haU _), hb _ _ _ haU _⟩
-  exacts[mem_ball_self _ (hT a a.2), mem_iInter₂.1 h a ha]
+  exacts [mem_ball_self _ (hT a a.2), mem_iInter₂.1 h a ha]
 #align is_compact.uniform_continuous_at_of_continuous_at IsCompact.uniformContinuousAt_of_continuousAt
 
 theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : β}

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>

@@ -58,7 +58,7 @@ theorem nhdsSet_diagonal_eq_uniformity [CompactSpace α] : 𝓝ˢ (diagonal α)
     rw [uniformity_prod_eq_comap_prod]
     exact (𝓤 α).basis_sets.prod_self.comap _
   refine' (isCompact_diagonal.nhdsSet_basis_uniformity this).ge_iff.2 fun U hU => _
-  exact mem_of_superset hU fun ⟨x, y⟩ hxy => mem_unionᵢ₂.2
+  exact mem_of_superset hU fun ⟨x, y⟩ hxy => mem_iUnion₂.2
     ⟨(x, x), rfl, refl_mem_uniformity hU, hxy⟩
 #align nhds_set_diagonal_eq_uniformity nhdsSet_diagonal_eq_uniformity
 
@@ -153,8 +153,8 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
       intro s
       simp_rw [isOpen_iff_mem_nhds, ← mem_comap_prod_mk, this]
     intro x
-    simp_rw [nhdsSet_diagonal, comap_supᵢ, nhds_prod_eq, comap_prod, (· ∘ ·), comap_id']
-    rw [supᵢ_split_single _ x, comap_const_of_mem fun V => mem_of_mem_nhds]
+    simp_rw [nhdsSet_diagonal, comap_iSup, nhds_prod_eq, comap_prod, (· ∘ ·), comap_id']
+    rw [iSup_split_single _ x, comap_const_of_mem fun V => mem_of_mem_nhds]
     suffices ∀ (y) (_ : y ≠ x), comap (fun _ : γ => x) (𝓝 y) ⊓ 𝓝 y ≤ 𝓝 x by simpa
     intro y hxy
     simp [comap_const_of_not_mem (compl_singleton_mem_nhds hxy) (Classical.not_not.2 rfl)]
@@ -196,12 +196,12 @@ theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s :
   choose U hU T hT hb using fun a ha =>
     exists_mem_nhds_ball_subset_of_mem_nhds ((hf a ha).preimage_mem_nhds <| mem_nhds_left _ ht)
   obtain ⟨fs, hsU⟩ := hs.elim_nhds_subcover' U hU
-  apply mem_of_superset ((binterᵢ_finset_mem fs).2 fun a _ => hT a a.2)
+  apply mem_of_superset ((biInter_finset_mem fs).2 fun a _ => hT a a.2)
   rintro ⟨a₁, a₂⟩ h h₁
-  obtain ⟨a, ha, haU⟩ := Set.mem_unionᵢ₂.1 (hsU h₁)
+  obtain ⟨a, ha, haU⟩ := Set.mem_iUnion₂.1 (hsU h₁)
   apply htr
   refine' ⟨f a, htsymm.mk_mem_comm.1 (hb _ _ _ haU _), hb _ _ _ haU _⟩
-  exacts[mem_ball_self _ (hT a a.2), mem_interᵢ₂.1 h a ha]
+  exacts[mem_ball_self _ (hT a a.2), mem_iInter₂.1 h a ha]
 #align is_compact.uniform_continuous_at_of_continuous_at IsCompact.uniformContinuousAt_of_continuousAt
 
 theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : β}

This proof had been uglyfied in mathlib3 already.

@@ -169,9 +169,10 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
 continuous. -/
 theorem CompactSpace.uniformContinuous_of_continuous [CompactSpace α] {f : α → β}
     (h : Continuous f) : UniformContinuous f :=
-  have : Tendsto (Prod.map f f) (𝓝ˢ (diagonal α)) (𝓝ˢ (diagonal β)) :=
-    (h.prod_map h).tendsto_nhdsSet mapsTo_prod_map_diagonal
-  (this.mono_left nhdsSet_diagonal_eq_uniformity.ge).mono_right nhdsSet_diagonal_le_uniformity
+calc map (Prod.map f f) (𝓤 α)
+   = map (Prod.map f f) (𝓝ˢ (diagonal α)) := by rw [nhdsSet_diagonal_eq_uniformity]
+ _ ≤ 𝓝ˢ (diagonal β)                      := (h.prod_map h).tendsto_nhdsSet mapsTo_prod_map_diagonal
+ _ ≤ 𝓤 β                                  := nhdsSet_diagonal_le_uniformity
 #align compact_space.uniform_continuous_of_continuous CompactSpace.uniformContinuous_of_continuous
 
 /-- Heine-Cantor: a continuous function on a compact set of a uniform space is uniformly

closes #3680, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Stepping.20through.20simp_rw/near/326712986

@@ -151,7 +151,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     -- topology we started with.
     suffices ∀ x : γ, Filter.comap (Prod.mk x) (𝓝ˢ (diagonal γ)) = 𝓝 x by
       intro s
-      simp_rw [isOpen_fold, isOpen_iff_mem_nhds, ← mem_comap_prod_mk, this]
+      simp_rw [isOpen_iff_mem_nhds, ← mem_comap_prod_mk, this]
     intro x
     simp_rw [nhdsSet_diagonal, comap_supᵢ, nhds_prod_eq, comap_prod, (· ∘ ·), comap_id']
     rw [supᵢ_split_single _ x, comap_const_of_mem fun V => mem_of_mem_nhds]

@@ -39,9 +39,7 @@ uniform space, uniform continuity, compact space
 -/
 
 
-open Classical Uniformity Topology Filter
-
-open Filter UniformSpace Set
+open Classical Uniformity Topology Filter UniformSpace Set
 
 variable {α β γ : Type _} [UniformSpace α] [UniformSpace β]
 
@@ -56,8 +54,7 @@ theorem nhdsSet_diagonal_eq_uniformity [CompactSpace α] : 𝓝ˢ (diagonal α)
   refine' nhdsSet_diagonal_le_uniformity.antisymm _
   have :
     (𝓤 (α × α)).HasBasis (fun U => U ∈ 𝓤 α) fun U =>
-      (fun p : (α × α) × α × α => ((p.1.1, p.2.1), p.1.2, p.2.2)) ⁻¹' U ×ˢ U :=
-    by
+      (fun p : (α × α) × α × α => ((p.1.1, p.2.1), p.1.2, p.2.2)) ⁻¹' U ×ˢ U := by
     rw [uniformity_prod_eq_comap_prod]
     exact (𝓤 α).basis_sets.prod_self.comap _
   refine' (isCompact_diagonal.nhdsSet_basis_uniformity this).ge_iff.2 fun U hU => _
@@ -86,8 +83,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
   uniformity := 𝓝ˢ (diagonal γ)
   refl := principal_le_nhdsSet
   symm := continuous_swap.tendsto_nhdsSet fun x => Eq.symm
-  comp :=
-    by
+  comp := by
     /-  This is the difficult part of the proof. We need to prove that, for each neighborhood `W`
         of the diagonal `Δ`, there exists a smaller neighborhood `V` such that `V ○ V ⊆ W`.
         -/
@@ -105,8 +101,7 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     -- In particular (x, y) is a cluster point of 𝓟 Vᶜ, hence is not in the interior of V,
     -- and a fortiori not in Δ, so x ≠ y
     have clV : ClusterPt (x, y) (𝓟 <| Vᶜ) := hxy.of_inf_right
-    have : (x, y) ∉ interior V :=
-      by
+    have : (x, y) ∉ interior V := by
       have : (x, y) ∈ closure (Vᶜ) := by rwa [mem_closure_iff_clusterPt]
       rwa [closure_compl] at this
     have diag_subset : diagonal γ ⊆ interior V := subset_interior_iff_mem_nhdsSet.2 V_in
@@ -151,12 +146,10 @@ def uniformSpaceOfCompactT2 [TopologicalSpace γ] [CompactSpace γ] [T2Space γ]
     -- Hence w ∈ U₁ ∩ U₂ which is empty.
     -- So we have a contradiction
     exact hU₁₂.le_bot ⟨uw_in.2, wv_in.1⟩
-  isOpen_uniformity :=
-    by
+  isOpen_uniformity := by
     -- Here we need to prove the topology induced by the constructed uniformity is the
     -- topology we started with.
-    suffices ∀ x : γ, Filter.comap (Prod.mk x) (𝓝ˢ (diagonal γ)) = 𝓝 x
-      by
+    suffices ∀ x : γ, Filter.comap (Prod.mk x) (𝓝ˢ (diagonal γ)) = 𝓝 x by
       intro s
       simp_rw [isOpen_fold, isOpen_iff_mem_nhds, ← mem_comap_prod_mk, this]
     intro x
@@ -188,7 +181,6 @@ theorem IsCompact.uniformContinuousOn_of_continuous {s : Set α} {f : α → β}
   rw [uniformContinuousOn_iff_restrict]
   rw [isCompact_iff_compactSpace] at hs
   rw [continuousOn_iff_continuous_restrict] at hf
-  skip
   exact CompactSpace.uniformContinuous_of_continuous hf
 #align is_compact.uniform_continuous_on_of_continuous IsCompact.uniformContinuousOn_of_continuous
 
@@ -213,8 +205,7 @@ theorem IsCompact.uniformContinuousAt_of_continuousAt {r : Set (β × β)} {s :
 
 theorem Continuous.uniformContinuous_of_tendsto_cocompact {f : α → β} {x : β}
     (h_cont : Continuous f) (hx : Tendsto f (cocompact α) (𝓝 x)) : UniformContinuous f :=
-  uniformContinuous_def.2 fun r hr =>
-    by
+  uniformContinuous_def.2 fun r hr => by
     obtain ⟨t, ht, htsymm, htr⟩ := comp_symm_mem_uniformity_sets hr
     obtain ⟨s, hs, hst⟩ := mem_cocompact.1 (hx <| mem_nhds_left _ ht)
     apply