topology.uniform_space.cauchy ⟷ Mathlib.Topology.UniformSpace.Cauchy

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

@@ -50,7 +50,7 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
     Cauchy f ↔ NeBot f ∧ ∀ i, p i → ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s i :=
   and_congr Iff.rfl <|
     (f.basis_sets.prod_self.le_basis_iffₓ h).trans <| by
-      simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
+      simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, forall_mem_comm]
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
 -/
 
@@ -66,7 +66,7 @@ theorem cauchy_iff' {f : Filter α} :
 #print cauchy_iff /-
 theorem cauchy_iff {f : Filter α} : Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, t ×ˢ t ⊆ s :=
   cauchy_iff'.trans <| by
-    simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
+    simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, forall_mem_comm]
 #align cauchy_iff cauchy_iff
 -/
 

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

@@ -43,7 +43,7 @@ def IsComplete (s : Set α) :=
 #align is_complete IsComplete
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 #print Filter.HasBasis.cauchy_iff /-
 theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α × α)} (h : (𝓤 α).HasBasis p s)
     {f : Filter α} :
@@ -54,7 +54,7 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 #print cauchy_iff' /-
 theorem cauchy_iff' {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s :=
@@ -378,7 +378,7 @@ theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α}
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m n «expr ≥ » N) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 #print Filter.HasBasis.cauchySeq_iff /-
 -- see Note [nolint_ge]
 @[nolint ge_or_gt]
@@ -459,7 +459,7 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
 #align is_complete.union IsComplete.union
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print isComplete_iUnion_separated /-
 theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
@@ -613,7 +613,7 @@ def TotallyBounded (s : Set α) : Prop :=
 #align totally_bounded TotallyBounded
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print TotallyBounded.exists_subset /-
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
     (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U} :=
@@ -634,7 +634,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
 #align totally_bounded.exists_subset TotallyBounded.exists_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print totallyBounded_iff_subset /-
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔

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

@@ -239,7 +239,7 @@ theorem CauchySeq.mem_entourage {β : Type _} [SemilatticeSup β] {u : β → α
     {V : Set (α × α)} (hV : V ∈ 𝓤 α) : ∃ k₀, ∀ i j, k₀ ≤ i → k₀ ≤ j → (u i, u j) ∈ V :=
   by
   haveI := h.nonempty
-  have := h.tendsto_uniformity; rw [← prod_at_top_at_top_eq] at this 
+  have := h.tendsto_uniformity; rw [← prod_at_top_at_top_eq] at this
   simpa [maps_to] using at_top_basis.prod_self.tendsto_left_iff.1 this V hV
 #align cauchy_seq.mem_entourage CauchySeq.mem_entourage
 -/
@@ -293,7 +293,7 @@ theorem CauchySeq.subseq_subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V
     (hu : CauchySeq u) {f g : ℕ → ℕ} (hf : Tendsto f atTop atTop) (hg : Tendsto g atTop atTop) :
     ∃ φ : ℕ → ℕ, StrictMono φ ∧ ∀ n, ((u ∘ f ∘ φ) n, (u ∘ g ∘ φ) n) ∈ V n :=
   by
-  rw [cauchySeq_iff_tendsto] at hu 
+  rw [cauchySeq_iff_tendsto] at hu
   exact ((hu.comp <| hf.prod_at_top hg).comp tendsto_at_top_diagonal).subseq_mem hV
 #align cauchy_seq.subseq_subseq_mem CauchySeq.subseq_subseq_mem
 -/
@@ -348,7 +348,7 @@ theorem CauchySeq.subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V n ∈ 
   have : ∀ n, ∃ N, ∀ k ≥ N, ∀ l ≥ k, (u l, u k) ∈ V n :=
     by
     intro n
-    rw [cauchySeq_iff] at hu 
+    rw [cauchySeq_iff] at hu
     rcases hu _ (hV n) with ⟨N, H⟩
     exact ⟨N, fun k hk l hl => H _ (le_trans hk hl) _ hk⟩
   obtain ⟨φ : ℕ → ℕ, φ_extr : StrictMono φ, hφ : ∀ n, ∀ l ≥ φ n, (u l, u <| φ n) ∈ V n⟩ :=
@@ -467,7 +467,7 @@ theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀
     IsComplete (⋃ i, s i) := by
   set S := ⋃ i, s i
   intro l hl hls
-  rw [le_principal_iff] at hls 
+  rw [le_principal_iff] at hls
   cases' cauchy_iff.1 hl with hl_ne hl'
   obtain ⟨t, htS, htl, htU⟩ : ∃ (t : _) (_ : t ⊆ S), t ∈ l ∧ t ×ˢ t ⊆ U :=
     by
@@ -697,7 +697,7 @@ theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs
   let ⟨c, hfc, hct⟩ := hs _ this
   ⟨f '' c, hfc.image f, by
     simp [image_subset_iff]
-    simp [subset_def] at hct 
+    simp [subset_def] at hct
     intro x hx; simp
     exact hct x hx⟩
 #align totally_bounded.image TotallyBounded.image

mathlib commit https://github.com/leanprover-community/mathlib/commit/3365b20c2ffa7c35e47e5209b89ba9abdddf3ffe

@@ -731,8 +731,9 @@ theorem totallyBounded_iff_filter {s : Set α} :
   · intro H d hd
     contrapose! H with hd_cover
     set f := ⨅ t : Finset α, 𝓟 (s \ ⋃ y ∈ t, {x | (x, y) ∈ d})
-    have : ne_bot f := by
-      refine' infi_ne_bot_of_directed' (directed_of_sup _) _
+    have : ne_bot f :=
+      by
+      refine' infi_ne_bot_of_directed' (directed_of_isDirected_le _) _
       · intro t₁ t₂ h
         exact principal_mono.2 (diff_subset_diff_right <| bUnion_subset_bUnion_left h)
       · intro t

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

@@ -3,9 +3,9 @@ Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
 -/
-import Mathbin.Topology.Algebra.Constructions
-import Mathbin.Topology.Bases
-import Mathbin.Topology.UniformSpace.Basic
+import Topology.Algebra.Constructions
+import Topology.Bases
+import Topology.UniformSpace.Basic
 
 #align_import topology.uniform_space.cauchy from "leanprover-community/mathlib"@"22131150f88a2d125713ffa0f4693e3355b1eb49"
 
@@ -43,7 +43,7 @@ def IsComplete (s : Set α) :=
 #align is_complete IsComplete
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 #print Filter.HasBasis.cauchy_iff /-
 theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α × α)} (h : (𝓤 α).HasBasis p s)
     {f : Filter α} :
@@ -54,7 +54,7 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 #print cauchy_iff' /-
 theorem cauchy_iff' {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s :=
@@ -378,7 +378,7 @@ theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α}
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m n «expr ≥ » N) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 #print Filter.HasBasis.cauchySeq_iff /-
 -- see Note [nolint_ge]
 @[nolint ge_or_gt]
@@ -459,7 +459,7 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
 #align is_complete.union IsComplete.union
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print isComplete_iUnion_separated /-
 theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
@@ -613,7 +613,7 @@ def TotallyBounded (s : Set α) : Prop :=
 #align totally_bounded TotallyBounded
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print TotallyBounded.exists_subset /-
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
     (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U} :=
@@ -634,7 +634,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
 #align totally_bounded.exists_subset TotallyBounded.exists_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print totallyBounded_iff_subset /-
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔

mathlib commit https://github.com/leanprover-community/mathlib/commit/442a83d738cb208d3600056c489be16900ba701d

@@ -684,7 +684,8 @@ theorem TotallyBounded.closure {s : Set α} (h : TotallyBounded s) : TotallyBoun
     let ⟨t, htf, hst⟩ := h V hV.1
     ⟨t, htf,
       closure_minimal hst <|
-        isClosed_biUnion htf fun y hy => hV.2.Preimage (continuous_id.prod_mk continuous_const)⟩
+        Set.Finite.isClosed_biUnion htf fun y hy =>
+          hV.2.Preimage (continuous_id.prod_mk continuous_const)⟩
 #align totally_bounded.closure TotallyBounded.closure
 -/
 

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

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
-
-! This file was ported from Lean 3 source module topology.uniform_space.cauchy
-! leanprover-community/mathlib commit 22131150f88a2d125713ffa0f4693e3355b1eb49
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.Algebra.Constructions
 import Mathbin.Topology.Bases
 import Mathbin.Topology.UniformSpace.Basic
 
+#align_import topology.uniform_space.cauchy from "leanprover-community/mathlib"@"22131150f88a2d125713ffa0f4693e3355b1eb49"
+
 /-!
 # Theory of Cauchy filters in uniform spaces. Complete uniform spaces. Totally bounded subsets.
 
@@ -46,7 +43,7 @@ def IsComplete (s : Set α) :=
 #align is_complete IsComplete
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 #print Filter.HasBasis.cauchy_iff /-
 theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α × α)} (h : (𝓤 α).HasBasis p s)
     {f : Filter α} :
@@ -57,7 +54,7 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 #print cauchy_iff' /-
 theorem cauchy_iff' {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s :=
@@ -381,7 +378,7 @@ theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α}
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m n «expr ≥ » N) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 #print Filter.HasBasis.cauchySeq_iff /-
 -- see Note [nolint_ge]
 @[nolint ge_or_gt]
@@ -462,7 +459,7 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
 #align is_complete.union IsComplete.union
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print isComplete_iUnion_separated /-
 theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
@@ -616,7 +613,7 @@ def TotallyBounded (s : Set α) : Prop :=
 #align totally_bounded TotallyBounded
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print TotallyBounded.exists_subset /-
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
     (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U} :=
@@ -637,7 +634,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
 #align totally_bounded.exists_subset TotallyBounded.exists_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 #print totallyBounded_iff_subset /-
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔

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

@@ -47,6 +47,7 @@ def IsComplete (s : Set α) :=
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+#print Filter.HasBasis.cauchy_iff /-
 theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α × α)} (h : (𝓤 α).HasBasis p s)
     {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ i, p i → ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s i :=
@@ -54,18 +55,23 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
     (f.basis_sets.prod_self.le_basis_iffₓ h).trans <| by
       simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+#print cauchy_iff' /-
 theorem cauchy_iff' {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s :=
   (𝓤 α).basis_sets.cauchy_iff
 #align cauchy_iff' cauchy_iff'
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print cauchy_iff /-
 theorem cauchy_iff {f : Filter α} : Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, t ×ˢ t ⊆ s :=
   cauchy_iff'.trans <| by
     simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
 #align cauchy_iff cauchy_iff
+-/
 
 #print Cauchy.ultrafilter_of /-
 theorem Cauchy.ultrafilter_of {l : Filter α} (h : Cauchy l) :
@@ -91,13 +97,17 @@ theorem cauchy_map_iff' {l : Filter β} [hl : NeBot l] {f : β → α} :
 #align cauchy_map_iff' cauchy_map_iff'
 -/
 
+#print Cauchy.mono /-
 theorem Cauchy.mono {f g : Filter α} [hg : NeBot g] (h_c : Cauchy f) (h_le : g ≤ f) : Cauchy g :=
   ⟨hg, le_trans (Filter.prod_mono h_le h_le) h_c.right⟩
 #align cauchy.mono Cauchy.mono
+-/
 
+#print Cauchy.mono' /-
 theorem Cauchy.mono' {f g : Filter α} (h_c : Cauchy f) (hg : NeBot g) (h_le : g ≤ f) : Cauchy g :=
   h_c.mono h_le
 #align cauchy.mono' Cauchy.mono'
+-/
 
 #print cauchy_nhds /-
 theorem cauchy_nhds {a : α} : Cauchy (𝓝 a) :=
@@ -118,6 +128,7 @@ theorem Filter.Tendsto.cauchy_map {l : Filter β} [NeBot l] {f : β → α} {a :
 #align filter.tendsto.cauchy_map Filter.Tendsto.cauchy_map
 -/
 
+#print Cauchy.prod /-
 theorem Cauchy.prod [UniformSpace β] {f : Filter α} {g : Filter β} (hf : Cauchy f) (hg : Cauchy g) :
     Cauchy (f ×ᶠ g) := by
   refine' ⟨hf.1.Prod hg.1, _⟩
@@ -126,8 +137,10 @@ theorem Cauchy.prod [UniformSpace β] {f : Filter α} {g : Filter β} (hf : Cauc
     ⟨le_trans (prod_mono tendsto_fst tendsto_fst) hf.2,
       le_trans (prod_mono tendsto_snd tendsto_snd) hg.2⟩
 #align cauchy.prod Cauchy.prod
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print le_nhds_of_cauchy_adhp_aux /-
 /-- The common part of the proofs of `le_nhds_of_cauchy_adhp` and
 `sequentially_complete.le_nhds_of_seq_tendsto_nhds`: if for any entourage `s`
 one can choose a set `t ∈ f` of diameter `s` such that it contains a point `y`
@@ -145,8 +158,10 @@ theorem le_nhds_of_cauchy_adhp_aux {f : Filter α} {x : α}
   -- Given a point `z ∈ t`, we have `(x, y) ∈ U` and `(y, z) ∈ t × t ⊆ U`, hence `z ∈ s`
   exact fun z hz => hU (prod_mk_mem_compRel hxy (ht <| mk_mem_prod hy hz)) rfl
 #align le_nhds_of_cauchy_adhp_aux le_nhds_of_cauchy_adhp_aux
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print le_nhds_of_cauchy_adhp /-
 /-- If `x` is an adherent (cluster) point for a Cauchy filter `f`, then it is a limit point
 for `f`. -/
 theorem le_nhds_of_cauchy_adhp {f : Filter α} {x : α} (hf : Cauchy f) (adhs : ClusterPt x f) :
@@ -159,11 +174,14 @@ theorem le_nhds_of_cauchy_adhp {f : Filter α} {x : α} (hf : Cauchy f) (adhs :
       use t, t_mem, ht
       exact forall_mem_nonempty_iff_ne_bot.2 adhs _ (inter_mem_inf (mem_nhds_left x hs) t_mem))
 #align le_nhds_of_cauchy_adhp le_nhds_of_cauchy_adhp
+-/
 
+#print le_nhds_iff_adhp_of_cauchy /-
 theorem le_nhds_iff_adhp_of_cauchy {f : Filter α} {x : α} (hf : Cauchy f) :
     f ≤ 𝓝 x ↔ ClusterPt x f :=
   ⟨fun h => ClusterPt.of_le_nhds' h hf.1, le_nhds_of_cauchy_adhp hf⟩
 #align le_nhds_iff_adhp_of_cauchy le_nhds_iff_adhp_of_cauchy
+-/
 
 #print Cauchy.map /-
 theorem Cauchy.map [UniformSpace β] {f : Filter α} {m : α → β} (hf : Cauchy f)
@@ -176,6 +194,7 @@ theorem Cauchy.map [UniformSpace β] {f : Filter α} {m : α → β} (hf : Cauch
 #align cauchy.map Cauchy.map
 -/
 
+#print Cauchy.comap /-
 theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cauchy f)
     (hm : comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) ≤ 𝓤 α) [NeBot (comap m f)] :
     Cauchy (comap m f) :=
@@ -186,12 +205,15 @@ theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cau
       _ ≤ comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) := (comap_mono hf.right)
       _ ≤ 𝓤 α := hm⟩
 #align cauchy.comap Cauchy.comap
+-/
 
+#print Cauchy.comap' /-
 theorem Cauchy.comap' [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cauchy f)
     (hm : comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) ≤ 𝓤 α) (hb : NeBot (comap m f)) :
     Cauchy (comap m f) :=
   hf.comap hm
 #align cauchy.comap' Cauchy.comap'
+-/
 
 #print CauchySeq /-
 /-- Cauchy sequences. Usually defined on ℕ, but often it is also useful to say that a function
@@ -202,10 +224,12 @@ def CauchySeq [SemilatticeSup β] (u : β → α) :=
 #align cauchy_seq CauchySeq
 -/
 
+#print CauchySeq.tendsto_uniformity /-
 theorem CauchySeq.tendsto_uniformity [SemilatticeSup β] {u : β → α} (h : CauchySeq u) :
     Tendsto (Prod.map u u) atTop (𝓤 α) := by
   simpa only [tendsto, prod_map_map_eq', prod_at_top_at_top_eq] using h.right
 #align cauchy_seq.tendsto_uniformity CauchySeq.tendsto_uniformity
+-/
 
 #print CauchySeq.nonempty /-
 theorem CauchySeq.nonempty [SemilatticeSup β] {u : β → α} (hu : CauchySeq u) : Nonempty β :=
@@ -213,6 +237,7 @@ theorem CauchySeq.nonempty [SemilatticeSup β] {u : β → α} (hu : CauchySeq u
 #align cauchy_seq.nonempty CauchySeq.nonempty
 -/
 
+#print CauchySeq.mem_entourage /-
 theorem CauchySeq.mem_entourage {β : Type _} [SemilatticeSup β] {u : β → α} (h : CauchySeq u)
     {V : Set (α × α)} (hV : V ∈ 𝓤 α) : ∃ k₀, ∀ i j, k₀ ≤ i → k₀ ≤ j → (u i, u j) ∈ V :=
   by
@@ -220,6 +245,7 @@ theorem CauchySeq.mem_entourage {β : Type _} [SemilatticeSup β] {u : β → α
   have := h.tendsto_uniformity; rw [← prod_at_top_at_top_eq] at this 
   simpa [maps_to] using at_top_basis.prod_self.tendsto_left_iff.1 this V hV
 #align cauchy_seq.mem_entourage CauchySeq.mem_entourage
+-/
 
 #print Filter.Tendsto.cauchySeq /-
 theorem Filter.Tendsto.cauchySeq [SemilatticeSup β] [Nonempty β] {f : β → α} {x}
@@ -234,15 +260,19 @@ theorem cauchySeq_const [SemilatticeSup β] [Nonempty β] (x : α) : CauchySeq f
 #align cauchy_seq_const cauchySeq_const
 -/
 
+#print cauchySeq_iff_tendsto /-
 theorem cauchySeq_iff_tendsto [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ Tendsto (Prod.map u u) atTop (𝓤 α) :=
   cauchy_map_iff'.trans <| by simp only [prod_at_top_at_top_eq, Prod.map_def]
 #align cauchy_seq_iff_tendsto cauchySeq_iff_tendsto
+-/
 
+#print CauchySeq.comp_tendsto /-
 theorem CauchySeq.comp_tendsto {γ} [SemilatticeSup β] [SemilatticeSup γ] [Nonempty γ] {f : β → α}
     (hf : CauchySeq f) {g : γ → β} (hg : Tendsto g atTop atTop) : CauchySeq (f ∘ g) :=
   cauchySeq_iff_tendsto.2 <| hf.tendsto_uniformity.comp (hg.prod_atTop hg)
 #align cauchy_seq.comp_tendsto CauchySeq.comp_tendsto
+-/
 
 #print CauchySeq.comp_injective /-
 theorem CauchySeq.comp_injective [SemilatticeSup β] [NoMaxOrder β] [Nonempty β] {u : ℕ → α}
@@ -271,10 +301,12 @@ theorem CauchySeq.subseq_subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V
 #align cauchy_seq.subseq_subseq_mem CauchySeq.subseq_subseq_mem
 -/
 
+#print cauchySeq_iff' /-
 theorem cauchySeq_iff' {u : ℕ → α} :
     CauchySeq u ↔ ∀ V ∈ 𝓤 α, ∀ᶠ k in atTop, k ∈ Prod.map u u ⁻¹' V := by
   simpa only [cauchySeq_iff_tendsto]
 #align cauchy_seq_iff' cauchySeq_iff'
+-/
 
 #print cauchySeq_iff /-
 theorem cauchySeq_iff {u : ℕ → α} :
@@ -283,16 +315,20 @@ theorem cauchySeq_iff {u : ℕ → α} :
 #align cauchy_seq_iff cauchySeq_iff
 -/
 
+#print CauchySeq.prod_map /-
 theorem CauchySeq.prod_map {γ δ} [UniformSpace β] [SemilatticeSup γ] [SemilatticeSup δ] {u : γ → α}
     {v : δ → β} (hu : CauchySeq u) (hv : CauchySeq v) : CauchySeq (Prod.map u v) := by
   simpa only [CauchySeq, prod_map_map_eq', prod_at_top_at_top_eq] using hu.prod hv
 #align cauchy_seq.prod_map CauchySeq.prod_map
+-/
 
+#print CauchySeq.prod /-
 theorem CauchySeq.prod {γ} [UniformSpace β] [SemilatticeSup γ] {u : γ → α} {v : γ → β}
     (hu : CauchySeq u) (hv : CauchySeq v) : CauchySeq fun x => (u x, v x) :=
   haveI := hu.nonempty
   (hu.prod hv).mono (tendsto.prod_mk le_rfl le_rfl)
 #align cauchy_seq.prod CauchySeq.prod
+-/
 
 #print CauchySeq.eventually_eventually /-
 theorem CauchySeq.eventually_eventually [SemilatticeSup β] {u : β → α} (hu : CauchySeq u)
@@ -301,10 +337,12 @@ theorem CauchySeq.eventually_eventually [SemilatticeSup β] {u : β → α} (hu
 #align cauchy_seq.eventually_eventually CauchySeq.eventually_eventually
 -/
 
+#print UniformContinuous.comp_cauchySeq /-
 theorem UniformContinuous.comp_cauchySeq {γ} [UniformSpace β] [SemilatticeSup γ] {f : α → β}
     (hf : UniformContinuous f) {u : γ → α} (hu : CauchySeq u) : CauchySeq (f ∘ u) :=
   hu.map hf
 #align uniform_continuous.comp_cauchy_seq UniformContinuous.comp_cauchySeq
+-/
 
 #print CauchySeq.subseq_mem /-
 theorem CauchySeq.subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V n ∈ 𝓤 α) {u : ℕ → α}
@@ -334,14 +372,17 @@ theorem Filter.Tendsto.subseq_mem_entourage {V : ℕ → Set (α × α)} (hV : 
 #align filter.tendsto.subseq_mem_entourage Filter.Tendsto.subseq_mem_entourage
 -/
 
+#print tendsto_nhds_of_cauchySeq_of_subseq /-
 /-- If a Cauchy sequence has a convergent subsequence, then it converges. -/
 theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α} (hu : CauchySeq u)
     {ι : Type _} {f : ι → β} {p : Filter ι} [NeBot p] (hf : Tendsto f p atTop) {a : α}
     (ha : Tendsto (u ∘ f) p (𝓝 a)) : Tendsto u atTop (𝓝 a) :=
   le_nhds_of_cauchy_adhp hu (mapClusterPt_of_comp hf ha)
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m n «expr ≥ » N) -/
+#print Filter.HasBasis.cauchySeq_iff /-
 -- see Note [nolint_ge]
 @[nolint ge_or_gt]
 theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u : β → α} {p : γ → Prop}
@@ -353,7 +394,9 @@ theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u
   simp only [exists_prop, true_and_iff, maps_to, preimage, subset_def, Prod.forall, mem_prod_eq,
     mem_set_of_eq, mem_Ici, and_imp, Prod.map, ge_iff_le, @forall_swap (_ ≤ _) β]
 #align filter.has_basis.cauchy_seq_iff Filter.HasBasis.cauchySeq_iff
+-/
 
+#print Filter.HasBasis.cauchySeq_iff' /-
 theorem Filter.HasBasis.cauchySeq_iff' {γ} [Nonempty β] [SemilatticeSup β] {u : β → α}
     {p : γ → Prop} {s : γ → Set (α × α)} (H : (𝓤 α).HasBasis p s) :
     CauchySeq u ↔ ∀ i, p i → ∃ N, ∀ n ≥ N, (u n, u N) ∈ s i :=
@@ -366,6 +409,7 @@ theorem Filter.HasBasis.cauchySeq_iff' {γ} [Nonempty β] [SemilatticeSup β] {u
     · exact hN m hm
     · exact hN n hn
 #align filter.has_basis.cauchy_seq_iff' Filter.HasBasis.cauchySeq_iff'
+-/
 
 #print cauchySeq_of_controlled /-
 theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Set (α × α))
@@ -382,11 +426,14 @@ theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Se
 #align cauchy_seq_of_controlled cauchySeq_of_controlled
 -/
 
+#print isComplete_iff_clusterPt /-
 theorem isComplete_iff_clusterPt {s : Set α} :
     IsComplete s ↔ ∀ l, Cauchy l → l ≤ 𝓟 s → ∃ x ∈ s, ClusterPt x l :=
   forall₃_congr fun l hl hls => exists₂_congr fun x hx => le_nhds_iff_adhp_of_cauchy hl
 #align is_complete_iff_cluster_pt isComplete_iff_clusterPt
+-/
 
+#print isComplete_iff_ultrafilter /-
 theorem isComplete_iff_ultrafilter {s : Set α} :
     IsComplete s ↔ ∀ l : Ultrafilter α, Cauchy (l : Filter α) → ↑l ≤ 𝓟 s → ∃ x ∈ s, ↑l ≤ 𝓝 x :=
   by
@@ -395,12 +442,16 @@ theorem isComplete_iff_ultrafilter {s : Set α} :
   rcases H (Ultrafilter.of l) hl.ultrafilter_of ((Ultrafilter.of_le l).trans hls) with ⟨x, hxs, hxl⟩
   exact ⟨x, hxs, (ClusterPt.of_le_nhds hxl).mono (Ultrafilter.of_le l)⟩
 #align is_complete_iff_ultrafilter isComplete_iff_ultrafilter
+-/
 
+#print isComplete_iff_ultrafilter' /-
 theorem isComplete_iff_ultrafilter' {s : Set α} :
     IsComplete s ↔ ∀ l : Ultrafilter α, Cauchy (l : Filter α) → s ∈ l → ∃ x ∈ s, ↑l ≤ 𝓝 x :=
   isComplete_iff_ultrafilter.trans <| by simp only [le_principal_iff, Ultrafilter.mem_coe]
 #align is_complete_iff_ultrafilter' isComplete_iff_ultrafilter'
+-/
 
+#print IsComplete.union /-
 protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsComplete t) :
     IsComplete (s ∪ t) :=
   by
@@ -409,9 +460,11 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
     ⟨fun hsl => (hs l hl hsl).imp fun x hx => ⟨Or.inl hx.fst, hx.snd⟩, fun htl =>
       (ht l hl htl).imp fun x hx => ⟨Or.inr hx.fst, hx.snd⟩⟩
 #align is_complete.union IsComplete.union
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print isComplete_iUnion_separated /-
 theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
     {U : Set (α × α)} (hU : U ∈ 𝓤 α) (hd : ∀ (i j : ι), ∀ x ∈ s i, ∀ y ∈ s j, (x, y) ∈ U → i = j) :
     IsComplete (⋃ i, s i) := by
@@ -435,6 +488,7 @@ theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀
   rcases hs i l hl (le_principal_iff.2 <| mem_of_superset htl hi) with ⟨x, hxs, hlx⟩
   exact ⟨x, mem_Union.2 ⟨i, hxs⟩, hlx⟩
 #align is_complete_Union_separated isComplete_iUnion_separated
+-/
 
 #print CompleteSpace /-
 /-- A complete space is defined here using uniformities. A uniform space
@@ -453,6 +507,7 @@ theorem complete_univ {α : Type u} [UniformSpace α] [CompleteSpace α] : IsCom
 #align complete_univ complete_univ
 -/
 
+#print CompleteSpace.prod /-
 instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace β] :
     CompleteSpace (α × β)
     where complete f hf :=
@@ -463,6 +518,7 @@ instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace
         exact
           Filter.le_lift.2 fun s hs => Filter.le_lift'.2 fun t ht => inter_mem (hx1 hs) (hx2 ht)⟩
 #align complete_space.prod CompleteSpace.prod
+-/
 
 #print CompleteSpace.mulOpposite /-
 @[to_additive]
@@ -490,15 +546,19 @@ theorem completeSpace_iff_isComplete_univ : CompleteSpace α ↔ IsComplete (uni
 #align complete_space_iff_is_complete_univ completeSpace_iff_isComplete_univ
 -/
 
+#print completeSpace_iff_ultrafilter /-
 theorem completeSpace_iff_ultrafilter :
     CompleteSpace α ↔ ∀ l : Ultrafilter α, Cauchy (l : Filter α) → ∃ x : α, ↑l ≤ 𝓝 x := by
   simp [completeSpace_iff_isComplete_univ, isComplete_iff_ultrafilter]
 #align complete_space_iff_ultrafilter completeSpace_iff_ultrafilter
+-/
 
+#print cauchy_iff_exists_le_nhds /-
 theorem cauchy_iff_exists_le_nhds [CompleteSpace α] {l : Filter α} [NeBot l] :
     Cauchy l ↔ ∃ x, l ≤ 𝓝 x :=
   ⟨CompleteSpace.complete, fun ⟨x, hx⟩ => cauchy_nhds.mono hx⟩
 #align cauchy_iff_exists_le_nhds cauchy_iff_exists_le_nhds
+-/
 
 #print cauchy_map_iff_exists_tendsto /-
 theorem cauchy_map_iff_exists_tendsto [CompleteSpace α] {l : Filter β} {f : β → α} [NeBot l] :
@@ -515,6 +575,7 @@ theorem cauchySeq_tendsto_of_complete [SemilatticeSup β] [CompleteSpace α] {u
 #align cauchy_seq_tendsto_of_complete cauchySeq_tendsto_of_complete
 -/
 
+#print cauchySeq_tendsto_of_isComplete /-
 /-- If `K` is a complete subset, then any cauchy sequence in `K` converges to a point in `K` -/
 theorem cauchySeq_tendsto_of_isComplete [SemilatticeSup β] {K : Set α} (h₁ : IsComplete K)
     {u : β → α} (h₂ : ∀ n, u n ∈ K) (h₃ : CauchySeq u) : ∃ v ∈ K, Tendsto u atTop (𝓝 v) :=
@@ -523,11 +584,14 @@ theorem cauchySeq_tendsto_of_isComplete [SemilatticeSup β] {K : Set α} (h₁ :
       mem_map_iff_exists_image.2
         ⟨univ, univ_mem, by simp only [image_univ]; rintro _ ⟨n, rfl⟩; exact h₂ n⟩
 #align cauchy_seq_tendsto_of_is_complete cauchySeq_tendsto_of_isComplete
+-/
 
+#print Cauchy.le_nhds_lim /-
 theorem Cauchy.le_nhds_lim [CompleteSpace α] [Nonempty α] {f : Filter α} (hf : Cauchy f) :
     f ≤ 𝓝 (lim f) :=
   le_nhds_lim (CompleteSpace.complete hf)
 #align cauchy.le_nhds_Lim Cauchy.le_nhds_lim
+-/
 
 #print CauchySeq.tendsto_limUnder /-
 theorem CauchySeq.tendsto_limUnder [SemilatticeSup β] [CompleteSpace α] [Nonempty α] {u : β → α}
@@ -553,6 +617,7 @@ def TotallyBounded (s : Set α) : Prop :=
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print TotallyBounded.exists_subset /-
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
     (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U} :=
   by
@@ -570,8 +635,10 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
     set z : ↥u := ⟨y, hy, ⟨x, xs, xy⟩⟩
     exact ⟨z, rU <| mem_compRel.2 ⟨y, xy, rs (hfr z)⟩⟩
 #align totally_bounded.exists_subset TotallyBounded.exists_subset
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print totallyBounded_iff_subset /-
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔
       ∀ d ∈ 𝓤 α, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ d} :=
@@ -579,13 +646,16 @@ theorem totallyBounded_iff_subset {s : Set α} :
     let ⟨t, _, ht⟩ := H d hd
     ⟨t, ht⟩⟩
 #align totally_bounded_iff_subset totallyBounded_iff_subset
+-/
 
+#print Filter.HasBasis.totallyBounded_iff /-
 theorem Filter.HasBasis.totallyBounded_iff {ι} {p : ι → Prop} {U : ι → Set (α × α)}
     (H : (𝓤 α).HasBasis p U) {s : Set α} :
     TotallyBounded s ↔ ∀ i, p i → ∃ t : Set α, Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U i} :=
   H.forall_iff fun U V hUV h =>
     h.imp fun t ht => ⟨ht.1, ht.2.trans <| iUnion₂_mono fun x hx y hy => hUV hy⟩
 #align filter.has_basis.totally_bounded_iff Filter.HasBasis.totallyBounded_iff
+-/
 
 #print totallyBounded_of_forall_symm /-
 theorem totallyBounded_of_forall_symm {s : Set α}
@@ -636,6 +706,7 @@ theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs
 -/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print Ultrafilter.cauchy_of_totallyBounded /-
 theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (hs : TotallyBounded s)
     (h : ↑f ≤ 𝓟 s) : Cauchy (f : Filter α) :=
   ⟨f.ne_bot', fun t ht =>
@@ -648,7 +719,9 @@ theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (
       fun ⟨x₁, x₂⟩ ⟨(h₁ : (x₁, y) ∈ t'), (h₂ : (x₂, y) ∈ t')⟩ => ⟨y, h₁, ht'_symm h₂⟩
     mem_of_superset (prod_mem_prod hif hif) (Subset.trans this ht'_t)⟩
 #align ultrafilter.cauchy_of_totally_bounded Ultrafilter.cauchy_of_totallyBounded
+-/
 
+#print totallyBounded_iff_filter /-
 theorem totallyBounded_iff_filter {s : Set α} :
     TotallyBounded s ↔ ∀ f, NeBot f → f ≤ 𝓟 s → ∃ c ≤ f, Cauchy c :=
   by
@@ -679,7 +752,9 @@ theorem totallyBounded_iff_filter {s : Set α} :
     refine' fun x hx hxm => hx.2 _
     simpa [ys] using hmd (mk_mem_prod hxm hym)
 #align totally_bounded_iff_filter totallyBounded_iff_filter
+-/
 
+#print totallyBounded_iff_ultrafilter /-
 theorem totallyBounded_iff_ultrafilter {s : Set α} :
     TotallyBounded s ↔ ∀ f : Ultrafilter α, ↑f ≤ 𝓟 s → Cauchy (f : Filter α) :=
   by
@@ -687,6 +762,7 @@ theorem totallyBounded_iff_ultrafilter {s : Set α} :
   intro f hf hfs
   exact ⟨Ultrafilter.of f, Ultrafilter.of_le f, H _ ((Ultrafilter.of_le f).trans hfs)⟩
 #align totally_bounded_iff_ultrafilter totallyBounded_iff_ultrafilter
+-/
 
 #print isCompact_iff_totallyBounded_isComplete /-
 theorem isCompact_iff_totallyBounded_isComplete {s : Set α} :
@@ -770,10 +846,12 @@ open Set Finset
 noncomputable section
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print SequentiallyComplete.setSeqAux /-
 /-- An auxiliary sequence of sets approximating a Cauchy filter. -/
 def setSeqAux (n : ℕ) : { s : Set α // ∃ _ : s ∈ f, s ×ˢ s ⊆ U n } :=
   indefiniteDescription _ <| (cauchy_iff.1 hf).2 (U n) (U_mem n)
 #align sequentially_complete.set_seq_aux SequentiallyComplete.setSeqAux
+-/
 
 #print SequentiallyComplete.setSeq /-
 /-- Given a Cauchy filter `f` and a sequence `U` of entourages, `set_seq` provides
@@ -835,14 +913,13 @@ theorem seq_pair_mem ⦃N m n : ℕ⦄ (hm : N ≤ m) (hn : N ≤ n) :
 #align sequentially_complete.seq_pair_mem SequentiallyComplete.seq_pair_mem
 -/
 
-include U_le
-
 #print SequentiallyComplete.seq_is_cauchySeq /-
 theorem seq_is_cauchySeq : CauchySeq <| seq hf U_mem :=
   cauchySeq_of_controlled U U_le <| seq_pair_mem hf U_mem
 #align sequentially_complete.seq_is_cauchy_seq SequentiallyComplete.seq_is_cauchySeq
 -/
 
+#print SequentiallyComplete.le_nhds_of_seq_tendsto_nhds /-
 /-- If the sequence `sequentially_complete.seq` converges to `a`, then `f ≤ 𝓝 a`. -/
 theorem le_nhds_of_seq_tendsto_nhds ⦃a : α⦄ (ha : Tendsto (seq hf U_mem) atTop (𝓝 a)) : f ≤ 𝓝 a :=
   le_nhds_of_cauchy_adhp_aux
@@ -857,6 +934,7 @@ theorem le_nhds_of_seq_tendsto_nhds ⦃a : α⦄ (ha : Tendsto (seq hf U_mem) at
         exact Set.Subset.trans (set_seq_prod_subset hf U_mem this this) hm
       · exact hm (hn _ <| le_max_right m n))
 #align sequentially_complete.le_nhds_of_seq_tendsto_nhds SequentiallyComplete.le_nhds_of_seq_tendsto_nhds
+-/
 
 end SequentiallyComplete
 

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

@@ -172,8 +172,7 @@ theorem Cauchy.map [UniformSpace β] {f : Filter α} {m : α → β} (hf : Cauch
     calc
       map m f ×ᶠ map m f = map (fun p : α × α => (m p.1, m p.2)) (f ×ᶠ f) := Filter.prod_map_map_eq
       _ ≤ map (fun p : α × α => (m p.1, m p.2)) (𝓤 α) := (map_mono hf.right)
-      _ ≤ 𝓤 β := hm
-      ⟩
+      _ ≤ 𝓤 β := hm⟩
 #align cauchy.map Cauchy.map
 -/
 
@@ -185,8 +184,7 @@ theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cau
       comap m f ×ᶠ comap m f = comap (fun p : α × α => (m p.1, m p.2)) (f ×ᶠ f) :=
         Filter.prod_comap_comap_eq
       _ ≤ comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) := (comap_mono hf.right)
-      _ ≤ 𝓤 α := hm
-      ⟩
+      _ ≤ 𝓤 α := hm⟩
 #align cauchy.comap Cauchy.comap
 
 theorem Cauchy.comap' [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cauchy f)

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

@@ -46,7 +46,7 @@ def IsComplete (s : Set α) :=
 #align is_complete IsComplete
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α × α)} (h : (𝓤 α).HasBasis p s)
     {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ i, p i → ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s i :=
@@ -55,7 +55,7 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
       simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 theorem cauchy_iff' {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s :=
   (𝓤 α).basis_sets.cauchy_iff
@@ -343,7 +343,7 @@ theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α}
   le_nhds_of_cauchy_adhp hu (mapClusterPt_of_comp hf ha)
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m n «expr ≥ » N) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 -- see Note [nolint_ge]
 @[nolint ge_or_gt]
 theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u : β → α} {p : γ → Prop}
@@ -412,7 +412,7 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
       (ht l hl htl).imp fun x hx => ⟨Or.inr hx.fst, hx.snd⟩⟩
 #align is_complete.union IsComplete.union
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
     {U : Set (α × α)} (hU : U ∈ 𝓤 α) (hd : ∀ (i j : ι), ∀ x ∈ s i, ∀ y ∈ s j, (x, y) ∈ U → i = j) :
@@ -554,7 +554,7 @@ def TotallyBounded (s : Set α) : Prop :=
 #align totally_bounded TotallyBounded
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
     (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U} :=
   by
@@ -573,7 +573,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
     exact ⟨z, rU <| mem_compRel.2 ⟨y, xy, rs (hfr z)⟩⟩
 #align totally_bounded.exists_subset TotallyBounded.exists_subset
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔
       ∀ d ∈ 𝓤 α, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ d} :=

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

@@ -550,17 +550,17 @@ theorem IsClosed.isComplete [CompleteSpace α] {s : Set α} (h : IsClosed s) : I
 /-- A set `s` is totally bounded if for every entourage `d` there is a finite
   set of points `t` such that every element of `s` is `d`-near to some element of `t`. -/
 def TotallyBounded (s : Set α) : Prop :=
-  ∀ d ∈ 𝓤 α, ∃ t : Set α, t.Finite ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ d }
+  ∀ d ∈ 𝓤 α, ∃ t : Set α, t.Finite ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ d}
 #align totally_bounded TotallyBounded
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
-    (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U } :=
+    (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U} :=
   by
   rcases comp_symm_of_uniformity hU with ⟨r, hr, rs, rU⟩
   rcases hs r hr with ⟨k, fk, ks⟩
-  let u := k ∩ { y | ∃ x ∈ s, (x, y) ∈ r }
+  let u := k ∩ {y | ∃ x ∈ s, (x, y) ∈ r}
   choose hk f hfs hfr using fun x : u => x.coe_prop
   refine' ⟨range f, _, _, _⟩
   · exact range_subset_iff.2 hfs
@@ -576,7 +576,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔
-      ∀ d ∈ 𝓤 α, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ d } :=
+      ∀ d ∈ 𝓤 α, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ d} :=
   ⟨fun H d hd => H.exists_subset hd, fun H d hd =>
     let ⟨t, _, ht⟩ := H d hd
     ⟨t, ht⟩⟩
@@ -584,7 +584,7 @@ theorem totallyBounded_iff_subset {s : Set α} :
 
 theorem Filter.HasBasis.totallyBounded_iff {ι} {p : ι → Prop} {U : ι → Set (α × α)}
     (H : (𝓤 α).HasBasis p U) {s : Set α} :
-    TotallyBounded s ↔ ∀ i, p i → ∃ t : Set α, Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U i } :=
+    TotallyBounded s ↔ ∀ i, p i → ∃ t : Set α, Set.Finite t ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U i} :=
   H.forall_iff fun U V hUV h =>
     h.imp fun t ht => ⟨ht.1, ht.2.trans <| iUnion₂_mono fun x hx y hy => hUV hy⟩
 #align filter.has_basis.totally_bounded_iff Filter.HasBasis.totallyBounded_iff
@@ -627,7 +627,7 @@ theorem TotallyBounded.closure {s : Set α} (h : TotallyBounded s) : TotallyBoun
 /-- The image of a totally bounded set under a uniformly continuous map is totally bounded. -/
 theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs : TotallyBounded s)
     (hf : UniformContinuous f) : TotallyBounded (f '' s) := fun t ht =>
-  have : { p : α × α | (f p.1, f p.2) ∈ t } ∈ 𝓤 α := hf ht
+  have : {p : α × α | (f p.1, f p.2) ∈ t} ∈ 𝓤 α := hf ht
   let ⟨c, hfc, hct⟩ := hs _ this
   ⟨f '' c, hfc.image f, by
     simp [image_subset_iff]
@@ -643,10 +643,10 @@ theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (
   ⟨f.ne_bot', fun t ht =>
     let ⟨t', ht'₁, ht'_symm, ht'_t⟩ := comp_symm_of_uniformity ht
     let ⟨i, hi, hs_union⟩ := hs t' ht'₁
-    have : (⋃ y ∈ i, { x | (x, y) ∈ t' }) ∈ f := mem_of_superset (le_principal_iff.mp h) hs_union
-    have : ∃ y ∈ i, { x | (x, y) ∈ t' } ∈ f := (Ultrafilter.finite_biUnion_mem_iff hi).1 this
+    have : (⋃ y ∈ i, {x | (x, y) ∈ t'}) ∈ f := mem_of_superset (le_principal_iff.mp h) hs_union
+    have : ∃ y ∈ i, {x | (x, y) ∈ t'} ∈ f := (Ultrafilter.finite_biUnion_mem_iff hi).1 this
     let ⟨y, hy, hif⟩ := this
-    have : { x | (x, y) ∈ t' } ×ˢ { x | (x, y) ∈ t' } ⊆ compRel t' t' :=
+    have : {x | (x, y) ∈ t'} ×ˢ {x | (x, y) ∈ t'} ⊆ compRel t' t' :=
       fun ⟨x₁, x₂⟩ ⟨(h₁ : (x₁, y) ∈ t'), (h₂ : (x₂, y) ∈ t')⟩ => ⟨y, h₁, ht'_symm h₂⟩
     mem_of_superset (prod_mem_prod hif hif) (Subset.trans this ht'_t)⟩
 #align ultrafilter.cauchy_of_totally_bounded Ultrafilter.cauchy_of_totallyBounded
@@ -661,7 +661,7 @@ theorem totallyBounded_iff_filter {s : Set α} :
         (Ultrafilter.of f).cauchy_of_totallyBounded H ((Ultrafilter.of_le f).trans hfs)⟩
   · intro H d hd
     contrapose! H with hd_cover
-    set f := ⨅ t : Finset α, 𝓟 (s \ ⋃ y ∈ t, { x | (x, y) ∈ d })
+    set f := ⨅ t : Finset α, 𝓟 (s \ ⋃ y ∈ t, {x | (x, y) ∈ d})
     have : ne_bot f := by
       refine' infi_ne_bot_of_directed' (directed_of_sup _) _
       · intro t₁ t₂ h
@@ -673,7 +673,7 @@ theorem totallyBounded_iff_filter {s : Set α} :
     rcases mem_prod_same_iff.1 (hc.2 hd) with ⟨m, hm, hmd⟩
     have : m ∩ s ∈ c := inter_mem hm (le_principal_iff.mp (hcf.trans ‹_›))
     rcases hc.1.nonempty_of_mem this with ⟨y, hym, hys⟩
-    set ys := ⋃ y' ∈ ({y} : Finset α), { x | (x, y') ∈ d }
+    set ys := ⋃ y' ∈ ({y} : Finset α), {x | (x, y') ∈ d}
     have : m ⊆ ys := by simpa [ys] using fun x hx => hmd (mk_mem_prod hx hym)
     have : c ≤ 𝓟 (s \ ys) := hcf.trans (iInf_le_of_le {y} le_rfl)
     refine' hc.1.Ne (empty_mem_iff_bot.mp _)
@@ -739,7 +739,7 @@ theorem CauchySeq.totallyBounded_range {s : ℕ → α} (hs : CauchySeq s) : Tot
   by
   refine' totallyBounded_iff_subset.2 fun a ha => _
   cases' cauchySeq_iff.1 hs a ha with n hn
-  refine' ⟨s '' { k | k ≤ n }, image_subset_range _ _, (finite_le_nat _).image _, _⟩
+  refine' ⟨s '' {k | k ≤ n}, image_subset_range _ _, (finite_le_nat _).image _, _⟩
   rw [range_subset_iff, bUnion_image]
   intro m
   rw [mem_Union₂]

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

@@ -219,7 +219,7 @@ theorem CauchySeq.mem_entourage {β : Type _} [SemilatticeSup β] {u : β → α
     {V : Set (α × α)} (hV : V ∈ 𝓤 α) : ∃ k₀, ∀ i j, k₀ ≤ i → k₀ ≤ j → (u i, u j) ∈ V :=
   by
   haveI := h.nonempty
-  have := h.tendsto_uniformity; rw [← prod_at_top_at_top_eq] at this
+  have := h.tendsto_uniformity; rw [← prod_at_top_at_top_eq] at this 
   simpa [maps_to] using at_top_basis.prod_self.tendsto_left_iff.1 this V hV
 #align cauchy_seq.mem_entourage CauchySeq.mem_entourage
 
@@ -268,7 +268,7 @@ theorem CauchySeq.subseq_subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V
     (hu : CauchySeq u) {f g : ℕ → ℕ} (hf : Tendsto f atTop atTop) (hg : Tendsto g atTop atTop) :
     ∃ φ : ℕ → ℕ, StrictMono φ ∧ ∀ n, ((u ∘ f ∘ φ) n, (u ∘ g ∘ φ) n) ∈ V n :=
   by
-  rw [cauchySeq_iff_tendsto] at hu
+  rw [cauchySeq_iff_tendsto] at hu 
   exact ((hu.comp <| hf.prod_at_top hg).comp tendsto_at_top_diagonal).subseq_mem hV
 #align cauchy_seq.subseq_subseq_mem CauchySeq.subseq_subseq_mem
 -/
@@ -315,7 +315,7 @@ theorem CauchySeq.subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V n ∈ 
   have : ∀ n, ∃ N, ∀ k ≥ N, ∀ l ≥ k, (u l, u k) ∈ V n :=
     by
     intro n
-    rw [cauchySeq_iff] at hu
+    rw [cauchySeq_iff] at hu 
     rcases hu _ (hV n) with ⟨N, H⟩
     exact ⟨N, fun k hk l hl => H _ (le_trans hk hl) _ hk⟩
   obtain ⟨φ : ℕ → ℕ, φ_extr : StrictMono φ, hφ : ∀ n, ∀ l ≥ φ n, (u l, u <| φ n) ∈ V n⟩ :=
@@ -419,9 +419,9 @@ theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀
     IsComplete (⋃ i, s i) := by
   set S := ⋃ i, s i
   intro l hl hls
-  rw [le_principal_iff] at hls
+  rw [le_principal_iff] at hls 
   cases' cauchy_iff.1 hl with hl_ne hl'
-  obtain ⟨t, htS, htl, htU⟩ : ∃ (t : _)(_ : t ⊆ S), t ∈ l ∧ t ×ˢ t ⊆ U :=
+  obtain ⟨t, htS, htl, htU⟩ : ∃ (t : _) (_ : t ⊆ S), t ∈ l ∧ t ×ˢ t ⊆ U :=
     by
     rcases hl' U hU with ⟨t, htl, htU⟩
     exact
@@ -556,7 +556,7 @@ def TotallyBounded (s : Set α) : Prop :=
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
-    (hU : U ∈ 𝓤 α) : ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U } :=
+    (hU : U ∈ 𝓤 α) : ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U } :=
   by
   rcases comp_symm_of_uniformity hU with ⟨r, hr, rs, rU⟩
   rcases hs r hr with ⟨k, fk, ks⟩
@@ -576,7 +576,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔
-      ∀ d ∈ 𝓤 α, ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ d } :=
+      ∀ d ∈ 𝓤 α, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ d } :=
   ⟨fun H d hd => H.exists_subset hd, fun H d hd =>
     let ⟨t, _, ht⟩ := H d hd
     ⟨t, ht⟩⟩
@@ -631,7 +631,7 @@ theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs
   let ⟨c, hfc, hct⟩ := hs _ this
   ⟨f '' c, hfc.image f, by
     simp [image_subset_iff]
-    simp [subset_def] at hct
+    simp [subset_def] at hct 
     intro x hx; simp
     exact hct x hx⟩
 #align totally_bounded.image TotallyBounded.image
@@ -744,7 +744,7 @@ theorem CauchySeq.totallyBounded_range {s : ℕ → α} (hs : CauchySeq s) : Tot
   intro m
   rw [mem_Union₂]
   cases' le_total m n with hm hm
-  exacts[⟨m, hm, refl_mem_uniformity ha⟩, ⟨n, le_refl n, hn m hm n le_rfl⟩]
+  exacts [⟨m, hm, refl_mem_uniformity ha⟩, ⟨n, le_refl n, hn m hm n le_rfl⟩]
 #align cauchy_seq.totally_bounded_range CauchySeq.totallyBounded_range
 -/
 

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

@@ -24,7 +24,7 @@ universe u v
 
 open Filter TopologicalSpace Set Classical UniformSpace Function
 
-open Classical uniformity Topology Filter
+open scoped Classical uniformity Topology Filter
 
 variable {α : Type u} {β : Type v} [UniformSpace α]
 
@@ -246,10 +246,12 @@ theorem CauchySeq.comp_tendsto {γ} [SemilatticeSup β] [SemilatticeSup γ] [Non
   cauchySeq_iff_tendsto.2 <| hf.tendsto_uniformity.comp (hg.prod_atTop hg)
 #align cauchy_seq.comp_tendsto CauchySeq.comp_tendsto
 
+#print CauchySeq.comp_injective /-
 theorem CauchySeq.comp_injective [SemilatticeSup β] [NoMaxOrder β] [Nonempty β] {u : ℕ → α}
     (hu : CauchySeq u) {f : β → ℕ} (hf : Injective f) : CauchySeq (u ∘ f) :=
   hu.comp_tendsto <| Nat.cofinite_eq_atTop ▸ hf.tendsto_cofinite.mono_left atTop_le_cofinite
 #align cauchy_seq.comp_injective CauchySeq.comp_injective
+-/
 
 #print Function.Bijective.cauchySeq_comp_iff /-
 theorem Function.Bijective.cauchySeq_comp_iff {f : ℕ → ℕ} (hf : Bijective f) (u : ℕ → α) :
@@ -367,6 +369,7 @@ theorem Filter.HasBasis.cauchySeq_iff' {γ} [Nonempty β] [SemilatticeSup β] {u
     · exact hN n hn
 #align filter.has_basis.cauchy_seq_iff' Filter.HasBasis.cauchySeq_iff'
 
+#print cauchySeq_of_controlled /-
 theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Set (α × α))
     (hU : ∀ s ∈ 𝓤 α, ∃ n, U n ⊆ s) {f : β → α}
     (hf : ∀ {N m n : β}, N ≤ m → N ≤ n → (f m, f n) ∈ U N) : CauchySeq f :=
@@ -379,6 +382,7 @@ theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Se
       cases' mn with m n
       exact hN (hf hmn.1 hmn.2))
 #align cauchy_seq_of_controlled cauchySeq_of_controlled
+-/
 
 theorem isComplete_iff_clusterPt {s : Set α} :
     IsComplete s ↔ ∀ l, Cauchy l → l ≤ 𝓟 s → ∃ x ∈ s, ClusterPt x l :=

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

@@ -46,12 +46,6 @@ def IsComplete (s : Set α) :=
 #align is_complete IsComplete
 -/
 
-/- warning: filter.has_basis.cauchy_iff -> Filter.HasBasis.cauchy_iff is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α × α)} (h : (𝓤 α).HasBasis p s)
     {f : Filter α} :
@@ -61,24 +55,12 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
       simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_iff' cauchy_iff'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 theorem cauchy_iff' {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s :=
   (𝓤 α).basis_sets.cauchy_iff
 #align cauchy_iff' cauchy_iff'
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_iff cauchy_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem cauchy_iff {f : Filter α} : Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, t ×ˢ t ⊆ s :=
   cauchy_iff'.trans <| by
@@ -109,22 +91,10 @@ theorem cauchy_map_iff' {l : Filter β} [hl : NeBot l] {f : β → α} :
 #align cauchy_map_iff' cauchy_map_iff'
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cauchy.mono Cauchy.monoₓ'. -/
 theorem Cauchy.mono {f g : Filter α} [hg : NeBot g] (h_c : Cauchy f) (h_le : g ≤ f) : Cauchy g :=
   ⟨hg, le_trans (Filter.prod_mono h_le h_le) h_c.right⟩
 #align cauchy.mono Cauchy.mono
 
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-Case conversion may be inaccurate. Consider using '#align cauchy.mono' Cauchy.mono'ₓ'. -/
 theorem Cauchy.mono' {f g : Filter α} (h_c : Cauchy f) (hg : NeBot g) (h_le : g ≤ f) : Cauchy g :=
   h_c.mono h_le
 #align cauchy.mono' Cauchy.mono'
@@ -148,12 +118,6 @@ theorem Filter.Tendsto.cauchy_map {l : Filter β} [NeBot l] {f : β → α} {a :
 #align filter.tendsto.cauchy_map Filter.Tendsto.cauchy_map
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cauchy.prod Cauchy.prodₓ'. -/
 theorem Cauchy.prod [UniformSpace β] {f : Filter α} {g : Filter β} (hf : Cauchy f) (hg : Cauchy g) :
     Cauchy (f ×ᶠ g) := by
   refine' ⟨hf.1.Prod hg.1, _⟩
@@ -163,12 +127,6 @@ theorem Cauchy.prod [UniformSpace β] {f : Filter α} {g : Filter β} (hf : Cauc
       le_trans (prod_mono tendsto_snd tendsto_snd) hg.2⟩
 #align cauchy.prod Cauchy.prod
 
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-Case conversion may be inaccurate. Consider using '#align le_nhds_of_cauchy_adhp_aux le_nhds_of_cauchy_adhp_auxₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- The common part of the proofs of `le_nhds_of_cauchy_adhp` and
 `sequentially_complete.le_nhds_of_seq_tendsto_nhds`: if for any entourage `s`
@@ -188,12 +146,6 @@ theorem le_nhds_of_cauchy_adhp_aux {f : Filter α} {x : α}
   exact fun z hz => hU (prod_mk_mem_compRel hxy (ht <| mk_mem_prod hy hz)) rfl
 #align le_nhds_of_cauchy_adhp_aux le_nhds_of_cauchy_adhp_aux
 
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-Case conversion may be inaccurate. Consider using '#align le_nhds_of_cauchy_adhp le_nhds_of_cauchy_adhpₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- If `x` is an adherent (cluster) point for a Cauchy filter `f`, then it is a limit point
 for `f`. -/
@@ -208,12 +160,6 @@ theorem le_nhds_of_cauchy_adhp {f : Filter α} {x : α} (hf : Cauchy f) (adhs :
       exact forall_mem_nonempty_iff_ne_bot.2 adhs _ (inter_mem_inf (mem_nhds_left x hs) t_mem))
 #align le_nhds_of_cauchy_adhp le_nhds_of_cauchy_adhp
 
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-Case conversion may be inaccurate. Consider using '#align le_nhds_iff_adhp_of_cauchy le_nhds_iff_adhp_of_cauchyₓ'. -/
 theorem le_nhds_iff_adhp_of_cauchy {f : Filter α} {x : α} (hf : Cauchy f) :
     f ≤ 𝓝 x ↔ ClusterPt x f :=
   ⟨fun h => ClusterPt.of_le_nhds' h hf.1, le_nhds_of_cauchy_adhp hf⟩
@@ -231,12 +177,6 @@ theorem Cauchy.map [UniformSpace β] {f : Filter α} {m : α → β} (hf : Cauch
 #align cauchy.map Cauchy.map
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cauchy.comap Cauchy.comapₓ'. -/
 theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cauchy f)
     (hm : comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) ≤ 𝓤 α) [NeBot (comap m f)] :
     Cauchy (comap m f) :=
@@ -249,12 +189,6 @@ theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cau
       ⟩
 #align cauchy.comap Cauchy.comap
 
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-Case conversion may be inaccurate. Consider using '#align cauchy.comap' Cauchy.comap'ₓ'. -/
 theorem Cauchy.comap' [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cauchy f)
     (hm : comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) ≤ 𝓤 α) (hb : NeBot (comap m f)) :
     Cauchy (comap m f) :=
@@ -270,12 +204,6 @@ def CauchySeq [SemilatticeSup β] (u : β → α) :=
 #align cauchy_seq CauchySeq
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq.tendsto_uniformity CauchySeq.tendsto_uniformityₓ'. -/
 theorem CauchySeq.tendsto_uniformity [SemilatticeSup β] {u : β → α} (h : CauchySeq u) :
     Tendsto (Prod.map u u) atTop (𝓤 α) := by
   simpa only [tendsto, prod_map_map_eq', prod_at_top_at_top_eq] using h.right
@@ -287,12 +215,6 @@ theorem CauchySeq.nonempty [SemilatticeSup β] {u : β → α} (hu : CauchySeq u
 #align cauchy_seq.nonempty CauchySeq.nonempty
 -/
 
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 theorem CauchySeq.mem_entourage {β : Type _} [SemilatticeSup β] {u : β → α} (h : CauchySeq u)
     {V : Set (α × α)} (hV : V ∈ 𝓤 α) : ∃ k₀, ∀ i j, k₀ ≤ i → k₀ ≤ j → (u i, u j) ∈ V :=
   by
@@ -314,34 +236,16 @@ theorem cauchySeq_const [SemilatticeSup β] [Nonempty β] (x : α) : CauchySeq f
 #align cauchy_seq_const cauchySeq_const
 -/
 
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 theorem cauchySeq_iff_tendsto [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ Tendsto (Prod.map u u) atTop (𝓤 α) :=
   cauchy_map_iff'.trans <| by simp only [prod_at_top_at_top_eq, Prod.map_def]
 #align cauchy_seq_iff_tendsto cauchySeq_iff_tendsto
 
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 theorem CauchySeq.comp_tendsto {γ} [SemilatticeSup β] [SemilatticeSup γ] [Nonempty γ] {f : β → α}
     (hf : CauchySeq f) {g : γ → β} (hg : Tendsto g atTop atTop) : CauchySeq (f ∘ g) :=
   cauchySeq_iff_tendsto.2 <| hf.tendsto_uniformity.comp (hg.prod_atTop hg)
 #align cauchy_seq.comp_tendsto CauchySeq.comp_tendsto
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq.comp_injective CauchySeq.comp_injectiveₓ'. -/
 theorem CauchySeq.comp_injective [SemilatticeSup β] [NoMaxOrder β] [Nonempty β] {u : ℕ → α}
     (hu : CauchySeq u) {f : β → ℕ} (hf : Injective f) : CauchySeq (u ∘ f) :=
   hu.comp_tendsto <| Nat.cofinite_eq_atTop ▸ hf.tendsto_cofinite.mono_left atTop_le_cofinite
@@ -367,12 +271,6 @@ theorem CauchySeq.subseq_subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V
 #align cauchy_seq.subseq_subseq_mem CauchySeq.subseq_subseq_mem
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_iff' cauchySeq_iff'ₓ'. -/
 theorem cauchySeq_iff' {u : ℕ → α} :
     CauchySeq u ↔ ∀ V ∈ 𝓤 α, ∀ᶠ k in atTop, k ∈ Prod.map u u ⁻¹' V := by
   simpa only [cauchySeq_iff_tendsto]
@@ -385,23 +283,11 @@ theorem cauchySeq_iff {u : ℕ → α} :
 #align cauchy_seq_iff cauchySeq_iff
 -/
 
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 theorem CauchySeq.prod_map {γ δ} [UniformSpace β] [SemilatticeSup γ] [SemilatticeSup δ] {u : γ → α}
     {v : δ → β} (hu : CauchySeq u) (hv : CauchySeq v) : CauchySeq (Prod.map u v) := by
   simpa only [CauchySeq, prod_map_map_eq', prod_at_top_at_top_eq] using hu.prod hv
 #align cauchy_seq.prod_map CauchySeq.prod_map
 
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 theorem CauchySeq.prod {γ} [UniformSpace β] [SemilatticeSup γ] {u : γ → α} {v : γ → β}
     (hu : CauchySeq u) (hv : CauchySeq v) : CauchySeq fun x => (u x, v x) :=
   haveI := hu.nonempty
@@ -415,12 +301,6 @@ theorem CauchySeq.eventually_eventually [SemilatticeSup β] {u : β → α} (hu
 #align cauchy_seq.eventually_eventually CauchySeq.eventually_eventually
 -/
 
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 theorem UniformContinuous.comp_cauchySeq {γ} [UniformSpace β] [SemilatticeSup γ] {f : α → β}
     (hf : UniformContinuous f) {u : γ → α} (hu : CauchySeq u) : CauchySeq (f ∘ u) :=
   hu.map hf
@@ -454,12 +334,6 @@ theorem Filter.Tendsto.subseq_mem_entourage {V : ℕ → Set (α × α)} (hV : 
 #align filter.tendsto.subseq_mem_entourage Filter.Tendsto.subseq_mem_entourage
 -/
 
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 /-- If a Cauchy sequence has a convergent subsequence, then it converges. -/
 theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α} (hu : CauchySeq u)
     {ι : Type _} {f : ι → β} {p : Filter ι} [NeBot p] (hf : Tendsto f p atTop) {a : α}
@@ -467,12 +341,6 @@ theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α}
   le_nhds_of_cauchy_adhp hu (mapClusterPt_of_comp hf ha)
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 -- see Note [nolint_ge]
 @[nolint ge_or_gt]
@@ -486,12 +354,6 @@ theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u
     mem_set_of_eq, mem_Ici, and_imp, Prod.map, ge_iff_le, @forall_swap (_ ≤ _) β]
 #align filter.has_basis.cauchy_seq_iff Filter.HasBasis.cauchySeq_iff
 
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 theorem Filter.HasBasis.cauchySeq_iff' {γ} [Nonempty β] [SemilatticeSup β] {u : β → α}
     {p : γ → Prop} {s : γ → Set (α × α)} (H : (𝓤 α).HasBasis p s) :
     CauchySeq u ↔ ∀ i, p i → ∃ N, ∀ n ≥ N, (u n, u N) ∈ s i :=
@@ -505,12 +367,6 @@ theorem Filter.HasBasis.cauchySeq_iff' {γ} [Nonempty β] [SemilatticeSup β] {u
     · exact hN n hn
 #align filter.has_basis.cauchy_seq_iff' Filter.HasBasis.cauchySeq_iff'
 
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 theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Set (α × α))
     (hU : ∀ s ∈ 𝓤 α, ∃ n, U n ⊆ s) {f : β → α}
     (hf : ∀ {N m n : β}, N ≤ m → N ≤ n → (f m, f n) ∈ U N) : CauchySeq f :=
@@ -524,23 +380,11 @@ theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Se
       exact hN (hf hmn.1 hmn.2))
 #align cauchy_seq_of_controlled cauchySeq_of_controlled
 
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 theorem isComplete_iff_clusterPt {s : Set α} :
     IsComplete s ↔ ∀ l, Cauchy l → l ≤ 𝓟 s → ∃ x ∈ s, ClusterPt x l :=
   forall₃_congr fun l hl hls => exists₂_congr fun x hx => le_nhds_iff_adhp_of_cauchy hl
 #align is_complete_iff_cluster_pt isComplete_iff_clusterPt
 
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-Case conversion may be inaccurate. Consider using '#align is_complete_iff_ultrafilter isComplete_iff_ultrafilterₓ'. -/
 theorem isComplete_iff_ultrafilter {s : Set α} :
     IsComplete s ↔ ∀ l : Ultrafilter α, Cauchy (l : Filter α) → ↑l ≤ 𝓟 s → ∃ x ∈ s, ↑l ≤ 𝓝 x :=
   by
@@ -550,23 +394,11 @@ theorem isComplete_iff_ultrafilter {s : Set α} :
   exact ⟨x, hxs, (ClusterPt.of_le_nhds hxl).mono (Ultrafilter.of_le l)⟩
 #align is_complete_iff_ultrafilter isComplete_iff_ultrafilter
 
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-Case conversion may be inaccurate. Consider using '#align is_complete_iff_ultrafilter' isComplete_iff_ultrafilter'ₓ'. -/
 theorem isComplete_iff_ultrafilter' {s : Set α} :
     IsComplete s ↔ ∀ l : Ultrafilter α, Cauchy (l : Filter α) → s ∈ l → ∃ x ∈ s, ↑l ≤ 𝓝 x :=
   isComplete_iff_ultrafilter.trans <| by simp only [le_principal_iff, Ultrafilter.mem_coe]
 #align is_complete_iff_ultrafilter' isComplete_iff_ultrafilter'
 
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-Case conversion may be inaccurate. Consider using '#align is_complete.union IsComplete.unionₓ'. -/
 protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsComplete t) :
     IsComplete (s ∪ t) :=
   by
@@ -576,12 +408,6 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
       (ht l hl htl).imp fun x hx => ⟨Or.inr hx.fst, hx.snd⟩⟩
 #align is_complete.union IsComplete.union
 
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-Case conversion may be inaccurate. Consider using '#align is_complete_Union_separated isComplete_iUnion_separatedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
@@ -625,12 +451,6 @@ theorem complete_univ {α : Type u} [UniformSpace α] [CompleteSpace α] : IsCom
 #align complete_univ complete_univ
 -/
 
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-Case conversion may be inaccurate. Consider using '#align complete_space.prod CompleteSpace.prodₓ'. -/
 instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace β] :
     CompleteSpace (α × β)
     where complete f hf :=
@@ -668,23 +488,11 @@ theorem completeSpace_iff_isComplete_univ : CompleteSpace α ↔ IsComplete (uni
 #align complete_space_iff_is_complete_univ completeSpace_iff_isComplete_univ
 -/
 
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-Case conversion may be inaccurate. Consider using '#align complete_space_iff_ultrafilter completeSpace_iff_ultrafilterₓ'. -/
 theorem completeSpace_iff_ultrafilter :
     CompleteSpace α ↔ ∀ l : Ultrafilter α, Cauchy (l : Filter α) → ∃ x : α, ↑l ≤ 𝓝 x := by
   simp [completeSpace_iff_isComplete_univ, isComplete_iff_ultrafilter]
 #align complete_space_iff_ultrafilter completeSpace_iff_ultrafilter
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_iff_exists_le_nhds cauchy_iff_exists_le_nhdsₓ'. -/
 theorem cauchy_iff_exists_le_nhds [CompleteSpace α] {l : Filter α} [NeBot l] :
     Cauchy l ↔ ∃ x, l ≤ 𝓝 x :=
   ⟨CompleteSpace.complete, fun ⟨x, hx⟩ => cauchy_nhds.mono hx⟩
@@ -705,12 +513,6 @@ theorem cauchySeq_tendsto_of_complete [SemilatticeSup β] [CompleteSpace α] {u
 #align cauchy_seq_tendsto_of_complete cauchySeq_tendsto_of_complete
 -/
 
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-Case conversion may be inaccurate. Consider using '#align cauchy_seq_tendsto_of_is_complete cauchySeq_tendsto_of_isCompleteₓ'. -/
 /-- If `K` is a complete subset, then any cauchy sequence in `K` converges to a point in `K` -/
 theorem cauchySeq_tendsto_of_isComplete [SemilatticeSup β] {K : Set α} (h₁ : IsComplete K)
     {u : β → α} (h₂ : ∀ n, u n ∈ K) (h₃ : CauchySeq u) : ∃ v ∈ K, Tendsto u atTop (𝓝 v) :=
@@ -720,12 +522,6 @@ theorem cauchySeq_tendsto_of_isComplete [SemilatticeSup β] {K : Set α} (h₁ :
         ⟨univ, univ_mem, by simp only [image_univ]; rintro _ ⟨n, rfl⟩; exact h₂ n⟩
 #align cauchy_seq_tendsto_of_is_complete cauchySeq_tendsto_of_isComplete
 
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-Case conversion may be inaccurate. Consider using '#align cauchy.le_nhds_Lim Cauchy.le_nhds_limₓ'. -/
 theorem Cauchy.le_nhds_lim [CompleteSpace α] [Nonempty α] {f : Filter α} (hf : Cauchy f) :
     f ≤ 𝓝 (lim f) :=
   le_nhds_lim (CompleteSpace.complete hf)
@@ -754,12 +550,6 @@ def TotallyBounded (s : Set α) : Prop :=
 #align totally_bounded TotallyBounded
 -/
 
-/- warning: totally_bounded.exists_subset -> TotallyBounded.exists_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align totally_bounded.exists_subset TotallyBounded.exists_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
     (hU : U ∈ 𝓤 α) : ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U } :=
@@ -779,12 +569,6 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
     exact ⟨z, rU <| mem_compRel.2 ⟨y, xy, rs (hfr z)⟩⟩
 #align totally_bounded.exists_subset TotallyBounded.exists_subset
 
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-Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_subset totallyBounded_iff_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔
@@ -794,12 +578,6 @@ theorem totallyBounded_iff_subset {s : Set α} :
     ⟨t, ht⟩⟩
 #align totally_bounded_iff_subset totallyBounded_iff_subset
 
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-Case conversion may be inaccurate. Consider using '#align filter.has_basis.totally_bounded_iff Filter.HasBasis.totallyBounded_iffₓ'. -/
 theorem Filter.HasBasis.totallyBounded_iff {ι} {p : ι → Prop} {U : ι → Set (α × α)}
     (H : (𝓤 α).HasBasis p U) {s : Set α} :
     TotallyBounded s ↔ ∀ i, p i → ∃ t : Set α, Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U i } :=
@@ -855,12 +633,6 @@ theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs
 #align totally_bounded.image TotallyBounded.image
 -/
 
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-Case conversion may be inaccurate. Consider using '#align ultrafilter.cauchy_of_totally_bounded Ultrafilter.cauchy_of_totallyBoundedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (hs : TotallyBounded s)
     (h : ↑f ≤ 𝓟 s) : Cauchy (f : Filter α) :=
@@ -875,12 +647,6 @@ theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (
     mem_of_superset (prod_mem_prod hif hif) (Subset.trans this ht'_t)⟩
 #align ultrafilter.cauchy_of_totally_bounded Ultrafilter.cauchy_of_totallyBounded
 
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-Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_filter totallyBounded_iff_filterₓ'. -/
 theorem totallyBounded_iff_filter {s : Set α} :
     TotallyBounded s ↔ ∀ f, NeBot f → f ≤ 𝓟 s → ∃ c ≤ f, Cauchy c :=
   by
@@ -912,12 +678,6 @@ theorem totallyBounded_iff_filter {s : Set α} :
     simpa [ys] using hmd (mk_mem_prod hxm hym)
 #align totally_bounded_iff_filter totallyBounded_iff_filter
 
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-Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_ultrafilter totallyBounded_iff_ultrafilterₓ'. -/
 theorem totallyBounded_iff_ultrafilter {s : Set α} :
     TotallyBounded s ↔ ∀ f : Ultrafilter α, ↑f ≤ 𝓟 s → Cauchy (f : Filter α) :=
   by
@@ -1007,12 +767,6 @@ open Set Finset
 
 noncomputable section
 
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-Case conversion may be inaccurate. Consider using '#align sequentially_complete.set_seq_aux SequentiallyComplete.setSeqAuxₓ'. -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 /-- An auxiliary sequence of sets approximating a Cauchy filter. -/
 def setSeqAux (n : ℕ) : { s : Set α // ∃ _ : s ∈ f, s ×ˢ s ⊆ U n } :=
@@ -1087,12 +841,6 @@ theorem seq_is_cauchySeq : CauchySeq <| seq hf U_mem :=
 #align sequentially_complete.seq_is_cauchy_seq SequentiallyComplete.seq_is_cauchySeq
 -/
 
-/- warning: sequentially_complete.le_nhds_of_seq_tendsto_nhds -> SequentiallyComplete.le_nhds_of_seq_tendsto_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} (hf : Cauchy.{u1} α _inst_1 f) {U : Nat -> (Set.{u1} (Prod.{u1, u1} α α))} (U_mem : forall (n : Nat), Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) (U n) (uniformity.{u1} α _inst_1)), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasSubset.{u1} (Prod.{u1, u1} α α)) (U n) s))) -> (forall {{a : α}}, (Filter.Tendsto.{0, u1} Nat α (SequentiallyComplete.seq.{u1} α _inst_1 f hf (fun (n : Nat) => U n) U_mem) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} (hf : Cauchy.{u1} α _inst_1 f) {U : Nat -> (Set.{u1} (Prod.{u1, u1} α α))} (U_mem : forall (n : Nat), Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) (U n) (uniformity.{u1} α _inst_1)), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.instHasSubsetSet.{u1} (Prod.{u1, u1} α α)) (U n) s))) -> (forall {{a : α}}, (Filter.Tendsto.{0, u1} Nat α (SequentiallyComplete.seq.{u1} α _inst_1 f hf (fun (n : Nat) => U n) U_mem) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)))
-Case conversion may be inaccurate. Consider using '#align sequentially_complete.le_nhds_of_seq_tendsto_nhds SequentiallyComplete.le_nhds_of_seq_tendsto_nhdsₓ'. -/
 /-- If the sequence `sequentially_complete.seq` converges to `a`, then `f ≤ 𝓝 a`. -/
 theorem le_nhds_of_seq_tendsto_nhds ⦃a : α⦄ (ha : Tendsto (seq hf U_mem) atTop (𝓝 a)) : f ≤ 𝓝 a :=
   le_nhds_of_cauchy_adhp_aux

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

@@ -603,8 +603,7 @@ theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀
     rcases mem_Union.1 (htS hx) with ⟨i, hi⟩
     refine' ⟨i, fun y hy => _⟩
     rcases mem_Union.1 (htS hy) with ⟨j, hj⟩
-    convert hj
-    exact hd i j x hi y hj (htU <| mk_mem_prod hx hy)
+    convert hj; exact hd i j x hi y hj (htU <| mk_mem_prod hx hy)
   rcases hs i l hl (le_principal_iff.2 <| mem_of_superset htl hi) with ⟨x, hxs, hlx⟩
   exact ⟨x, mem_Union.2 ⟨i, hxs⟩, hlx⟩
 #align is_complete_Union_separated isComplete_iUnion_separated
@@ -718,10 +717,7 @@ theorem cauchySeq_tendsto_of_isComplete [SemilatticeSup β] {K : Set α} (h₁ :
   h₁ _ h₃ <|
     le_principal_iff.2 <|
       mem_map_iff_exists_image.2
-        ⟨univ, univ_mem, by
-          simp only [image_univ]
-          rintro _ ⟨n, rfl⟩
-          exact h₂ n⟩
+        ⟨univ, univ_mem, by simp only [image_univ]; rintro _ ⟨n, rfl⟩; exact h₂ n⟩
 #align cauchy_seq_tendsto_of_is_complete cauchySeq_tendsto_of_isComplete
 
 /- warning: cauchy.le_nhds_Lim -> Cauchy.le_nhds_lim is a dubious translation:
@@ -777,8 +773,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
   · haveI : Fintype u := (fk.inter_of_left _).Fintype
     exact finite_range f
   · intro x xs
-    obtain ⟨y, hy, xy⟩ : ∃ y ∈ k, (x, y) ∈ r
-    exact mem_Union₂.1 (ks xs)
+    obtain ⟨y, hy, xy⟩ : ∃ y ∈ k, (x, y) ∈ r; exact mem_Union₂.1 (ks xs)
     rw [bUnion_range, mem_Union]
     set z : ↥u := ⟨y, hy, ⟨x, xs, xy⟩⟩
     exact ⟨z, rU <| mem_compRel.2 ⟨y, xy, rs (hfr z)⟩⟩
@@ -1154,9 +1149,7 @@ variable (α)
 
 #print UniformSpace.firstCountableTopology /-
 instance (priority := 100) firstCountableTopology : FirstCountableTopology α :=
-  ⟨fun a => by
-    rw [nhds_eq_comap_uniformity]
-    infer_instance⟩
+  ⟨fun a => by rw [nhds_eq_comap_uniformity]; infer_instance⟩
 #align uniform_space.first_countable_topology UniformSpace.firstCountableTopology
 -/
 

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

@@ -111,7 +111,7 @@ theorem cauchy_map_iff' {l : Filter β} [hl : NeBot l] {f : β → α} :
 
 /- warning: cauchy.mono -> Cauchy.mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α} [hg : Filter.NeBot.{u1} α g], (Cauchy.{u1} α _inst_1 f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (Cauchy.{u1} α _inst_1 g)
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α} [hg : Filter.NeBot.{u1} α g], (Cauchy.{u1} α _inst_1 f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (Cauchy.{u1} α _inst_1 g)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α} [hg : Filter.NeBot.{u1} α g], (Cauchy.{u1} α _inst_1 f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (Cauchy.{u1} α _inst_1 g)
 Case conversion may be inaccurate. Consider using '#align cauchy.mono Cauchy.monoₓ'. -/
@@ -121,7 +121,7 @@ theorem Cauchy.mono {f g : Filter α} [hg : NeBot g] (h_c : Cauchy f) (h_le : g
 
 /- warning: cauchy.mono' -> Cauchy.mono' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (Cauchy.{u1} α _inst_1 f) -> (Filter.NeBot.{u1} α g) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (Cauchy.{u1} α _inst_1 g)
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (Cauchy.{u1} α _inst_1 f) -> (Filter.NeBot.{u1} α g) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) g f) -> (Cauchy.{u1} α _inst_1 g)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {g : Filter.{u1} α}, (Cauchy.{u1} α _inst_1 f) -> (Filter.NeBot.{u1} α g) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) g f) -> (Cauchy.{u1} α _inst_1 g)
 Case conversion may be inaccurate. Consider using '#align cauchy.mono' Cauchy.mono'ₓ'. -/
@@ -165,7 +165,7 @@ theorem Cauchy.prod [UniformSpace β] {f : Filter α} {g : Filter β} (hf : Cauc
 
 /- warning: le_nhds_of_cauchy_adhp_aux -> le_nhds_of_cauchy_adhp_aux is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t f) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t f) => And (HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasSubset.{u1} (Prod.{u1, u1} α α)) (Set.prod.{u1, u1} α α t t) s) (Exists.{succ u1} α (fun (y : α) => And (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t))))))) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t f) (fun (H : Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) t f) => And (HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasSubset.{u1} (Prod.{u1, u1} α α)) (Set.prod.{u1, u1} α α t t) s) (Exists.{succ u1} α (fun (y : α) => And (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t))))))) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t f) (And (HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.instHasSubsetSet.{u1} (Prod.{u1, u1} α α)) (Set.prod.{u1, u1} α α t t) s) (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t))))))) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
 Case conversion may be inaccurate. Consider using '#align le_nhds_of_cauchy_adhp_aux le_nhds_of_cauchy_adhp_auxₓ'. -/
@@ -190,7 +190,7 @@ theorem le_nhds_of_cauchy_adhp_aux {f : Filter α} {x : α}
 
 /- warning: le_nhds_of_cauchy_adhp -> le_nhds_of_cauchy_adhp is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (Cauchy.{u1} α _inst_1 f) -> (ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (Cauchy.{u1} α _inst_1 f) -> (ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (Cauchy.{u1} α _inst_1 f) -> (ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))
 Case conversion may be inaccurate. Consider using '#align le_nhds_of_cauchy_adhp le_nhds_of_cauchy_adhpₓ'. -/
@@ -210,7 +210,7 @@ theorem le_nhds_of_cauchy_adhp {f : Filter α} {x : α} (hf : Cauchy f) (adhs :
 
 /- warning: le_nhds_iff_adhp_of_cauchy -> le_nhds_iff_adhp_of_cauchy is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (Cauchy.{u1} α _inst_1 f) -> (Iff (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)) (ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x f))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (Cauchy.{u1} α _inst_1 f) -> (Iff (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)) (ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} {x : α}, (Cauchy.{u1} α _inst_1 f) -> (Iff (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)) (ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x f))
 Case conversion may be inaccurate. Consider using '#align le_nhds_iff_adhp_of_cauchy le_nhds_iff_adhp_of_cauchyₓ'. -/
@@ -233,7 +233,7 @@ theorem Cauchy.map [UniformSpace β] {f : Filter α} {m : α → β} (hf : Cauch
 
 /- warning: cauchy.comap -> Cauchy.comap 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 : Filter.{u2} β} {m : α -> β}, (Cauchy.{u2} β _inst_2 f) -> (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (fun (p : Prod.{u1, u1} α α) => Prod.mk.{u2, u2} β β (m (Prod.fst.{u1, u1} α α p)) (m (Prod.snd.{u1, u1} α α p))) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)) -> (forall [_inst_3 : Filter.NeBot.{u1} α (Filter.comap.{u1, u2} α β m f)], Cauchy.{u1} α _inst_1 (Filter.comap.{u1, u2} α β m f))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : Filter.{u2} β} {m : α -> β}, (Cauchy.{u2} β _inst_2 f) -> (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toHasLe.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (fun (p : Prod.{u1, u1} α α) => Prod.mk.{u2, u2} β β (m (Prod.fst.{u1, u1} α α p)) (m (Prod.snd.{u1, u1} α α p))) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)) -> (forall [_inst_3 : Filter.NeBot.{u1} α (Filter.comap.{u1, u2} α β m f)], Cauchy.{u1} α _inst_1 (Filter.comap.{u1, u2} α β m f))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : Filter.{u2} β} {m : α -> β}, (Cauchy.{u2} β _inst_2 f) -> (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instPartialOrderFilter.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (fun (p : Prod.{u1, u1} α α) => Prod.mk.{u2, u2} β β (m (Prod.fst.{u1, u1} α α p)) (m (Prod.snd.{u1, u1} α α p))) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)) -> (forall [_inst_3 : Filter.NeBot.{u1} α (Filter.comap.{u1, u2} α β m f)], Cauchy.{u1} α _inst_1 (Filter.comap.{u1, u2} α β m f))
 Case conversion may be inaccurate. Consider using '#align cauchy.comap Cauchy.comapₓ'. -/
@@ -251,7 +251,7 @@ theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cau
 
 /- warning: cauchy.comap' -> Cauchy.comap' 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 : Filter.{u2} β} {m : α -> β}, (Cauchy.{u2} β _inst_2 f) -> (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (fun (p : Prod.{u1, u1} α α) => Prod.mk.{u2, u2} β β (m (Prod.fst.{u1, u1} α α p)) (m (Prod.snd.{u1, u1} α α p))) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)) -> (Filter.NeBot.{u1} α (Filter.comap.{u1, u2} α β m f)) -> (Cauchy.{u1} α _inst_1 (Filter.comap.{u1, u2} α β m f))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : Filter.{u2} β} {m : α -> β}, (Cauchy.{u2} β _inst_2 f) -> (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toHasLe.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.partialOrder.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (fun (p : Prod.{u1, u1} α α) => Prod.mk.{u2, u2} β β (m (Prod.fst.{u1, u1} α α p)) (m (Prod.snd.{u1, u1} α α p))) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)) -> (Filter.NeBot.{u1} α (Filter.comap.{u1, u2} α β m f)) -> (Cauchy.{u1} α _inst_1 (Filter.comap.{u1, u2} α β m f))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : UniformSpace.{u2} β] {f : Filter.{u2} β} {m : α -> β}, (Cauchy.{u2} β _inst_2 f) -> (LE.le.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Preorder.toLE.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (PartialOrder.toPreorder.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instPartialOrderFilter.{u1} (Prod.{u1, u1} α α)))) (Filter.comap.{u1, u2} (Prod.{u1, u1} α α) (Prod.{u2, u2} β β) (fun (p : Prod.{u1, u1} α α) => Prod.mk.{u2, u2} β β (m (Prod.fst.{u1, u1} α α p)) (m (Prod.snd.{u1, u1} α α p))) (uniformity.{u2} β _inst_2)) (uniformity.{u1} α _inst_1)) -> (Filter.NeBot.{u1} α (Filter.comap.{u1, u2} α β m f)) -> (Cauchy.{u1} α _inst_1 (Filter.comap.{u1, u2} α β m f))
 Case conversion may be inaccurate. Consider using '#align cauchy.comap' Cauchy.comap'ₓ'. -/
@@ -289,7 +289,7 @@ theorem CauchySeq.nonempty [SemilatticeSup β] {u : β → α} (hu : CauchySeq u
 
 /- warning: cauchy_seq.mem_entourage -> CauchySeq.mem_entourage is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {β : Type.{u2}} [_inst_2 : SemilatticeSup.{u2} β] {u : β -> α}, (CauchySeq.{u1, u2} α β _inst_1 _inst_2 u) -> (forall {V : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) V (uniformity.{u1} α _inst_1)) -> (Exists.{succ u2} β (fun (k₀ : β) => forall (i : β) (j : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) k₀ i) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) k₀ j) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (u i) (u j)) V))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {β : Type.{u2}} [_inst_2 : SemilatticeSup.{u2} β] {u : β -> α}, (CauchySeq.{u1, u2} α β _inst_1 _inst_2 u) -> (forall {V : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) V (uniformity.{u1} α _inst_1)) -> (Exists.{succ u2} β (fun (k₀ : β) => forall (i : β) (j : β), (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) k₀ i) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) k₀ j) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (u i) (u j)) V))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : UniformSpace.{u2} α] {β : Type.{u1}} [_inst_2 : SemilatticeSup.{u1} β] {u : β -> α}, (CauchySeq.{u2, u1} α β _inst_1 _inst_2 u) -> (forall {V : Set.{u2} (Prod.{u2, u2} α α)}, (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} α α)) (Filter.{u2} (Prod.{u2, u2} α α)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} α α)) V (uniformity.{u2} α _inst_1)) -> (Exists.{succ u1} β (fun (k₀ : β) => forall (i : β) (j : β), (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) k₀ i) -> (LE.le.{u1} β (Preorder.toLE.{u1} β (PartialOrder.toPreorder.{u1} β (SemilatticeSup.toPartialOrder.{u1} β _inst_2))) k₀ j) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α (u i) (u j)) V))))
 Case conversion may be inaccurate. Consider using '#align cauchy_seq.mem_entourage CauchySeq.mem_entourageₓ'. -/
@@ -336,12 +336,16 @@ theorem CauchySeq.comp_tendsto {γ} [SemilatticeSup β] [SemilatticeSup γ] [Non
   cauchySeq_iff_tendsto.2 <| hf.tendsto_uniformity.comp (hg.prod_atTop hg)
 #align cauchy_seq.comp_tendsto CauchySeq.comp_tendsto
 
-#print CauchySeq.comp_injective /-
+/- warning: cauchy_seq.comp_injective -> CauchySeq.comp_injective is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : NoMaxOrder.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] [_inst_4 : Nonempty.{succ u2} β] {u : Nat -> α}, (CauchySeq.{u1, 0} α Nat _inst_1 (CanonicallyLinearOrderedAddMonoid.semilatticeSup.{0} Nat Nat.canonicallyLinearOrderedAddMonoid) u) -> (forall {f : β -> Nat}, (Function.Injective.{succ u2, 1} β Nat f) -> (CauchySeq.{u1, u2} α β _inst_1 _inst_2 (Function.comp.{succ u2, 1, succ u1} β Nat α u f)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : NoMaxOrder.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2)))] [_inst_4 : Nonempty.{succ u2} β] {u : Nat -> α}, (CauchySeq.{u1, 0} α Nat _inst_1 (Lattice.toSemilatticeSup.{0} Nat (DistribLattice.toLattice.{0} Nat instDistribLatticeNat)) u) -> (forall {f : β -> Nat}, (Function.Injective.{succ u2, 1} β Nat f) -> (CauchySeq.{u1, u2} α β _inst_1 _inst_2 (Function.comp.{succ u2, 1, succ u1} β Nat α u f)))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq.comp_injective CauchySeq.comp_injectiveₓ'. -/
 theorem CauchySeq.comp_injective [SemilatticeSup β] [NoMaxOrder β] [Nonempty β] {u : ℕ → α}
     (hu : CauchySeq u) {f : β → ℕ} (hf : Injective f) : CauchySeq (u ∘ f) :=
   hu.comp_tendsto <| Nat.cofinite_eq_atTop ▸ hf.tendsto_cofinite.mono_left atTop_le_cofinite
 #align cauchy_seq.comp_injective CauchySeq.comp_injective
--/
 
 #print Function.Bijective.cauchySeq_comp_iff /-
 theorem Function.Bijective.cauchySeq_comp_iff {f : ℕ → ℕ} (hf : Bijective f) (u : ℕ → α) :
@@ -465,7 +469,7 @@ theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α}
 
 /- warning: filter.has_basis.cauchy_seq_iff -> Filter.HasBasis.cauchySeq_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] {γ : Sort.{u3}} [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {p : γ -> Prop} {s : γ -> (Set.{u1} (Prod.{u1, u1} α α))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) γ (uniformity.{u1} α _inst_1) p s) -> (Iff (CauchySeq.{u1, u2} α β _inst_1 _inst_3 u) (forall (i : γ), (p i) -> (Exists.{succ u2} β (fun (N : β) => forall (m : β), (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) m N) -> (forall (n : β), (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) n N) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (u m) (u n)) (s i)))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] {γ : Sort.{u3}} [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {p : γ -> Prop} {s : γ -> (Set.{u1} (Prod.{u1, u1} α α))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) γ (uniformity.{u1} α _inst_1) p s) -> (Iff (CauchySeq.{u1, u2} α β _inst_1 _inst_3 u) (forall (i : γ), (p i) -> (Exists.{succ u2} β (fun (N : β) => forall (m : β), (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) m N) -> (forall (n : β), (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) n N) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (u m) (u n)) (s i)))))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : UniformSpace.{u2} α] {γ : Sort.{u1}} [_inst_2 : Nonempty.{succ u3} β] [_inst_3 : SemilatticeSup.{u3} β] {u : β -> α} {p : γ -> Prop} {s : γ -> (Set.{u2} (Prod.{u2, u2} α α))}, (Filter.HasBasis.{u2, u1} (Prod.{u2, u2} α α) γ (uniformity.{u2} α _inst_1) p s) -> (Iff (CauchySeq.{u2, u3} α β _inst_1 _inst_3 u) (forall (i : γ), (p i) -> (Exists.{succ u3} β (fun (N : β) => forall (m : β), (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeSup.toPartialOrder.{u3} β _inst_3))) N m) -> (forall (n : β), (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeSup.toPartialOrder.{u3} β _inst_3))) N n) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α (u m) (u n)) (s i)))))))
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.cauchy_seq_iff Filter.HasBasis.cauchySeq_iffₓ'. -/
@@ -484,7 +488,7 @@ theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u
 
 /- warning: filter.has_basis.cauchy_seq_iff' -> Filter.HasBasis.cauchySeq_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] {γ : Sort.{u3}} [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {p : γ -> Prop} {s : γ -> (Set.{u1} (Prod.{u1, u1} α α))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) γ (uniformity.{u1} α _inst_1) p s) -> (Iff (CauchySeq.{u1, u2} α β _inst_1 _inst_3 u) (forall (i : γ), (p i) -> (Exists.{succ u2} β (fun (N : β) => forall (n : β), (GE.ge.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) n N) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (u n) (u N)) (s i))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] {γ : Sort.{u3}} [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {p : γ -> Prop} {s : γ -> (Set.{u1} (Prod.{u1, u1} α α))}, (Filter.HasBasis.{u1, u3} (Prod.{u1, u1} α α) γ (uniformity.{u1} α _inst_1) p s) -> (Iff (CauchySeq.{u1, u2} α β _inst_1 _inst_3 u) (forall (i : γ), (p i) -> (Exists.{succ u2} β (fun (N : β) => forall (n : β), (GE.ge.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) n N) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (u n) (u N)) (s i))))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : UniformSpace.{u2} α] {γ : Sort.{u1}} [_inst_2 : Nonempty.{succ u3} β] [_inst_3 : SemilatticeSup.{u3} β] {u : β -> α} {p : γ -> Prop} {s : γ -> (Set.{u2} (Prod.{u2, u2} α α))}, (Filter.HasBasis.{u2, u1} (Prod.{u2, u2} α α) γ (uniformity.{u2} α _inst_1) p s) -> (Iff (CauchySeq.{u2, u3} α β _inst_1 _inst_3 u) (forall (i : γ), (p i) -> (Exists.{succ u3} β (fun (N : β) => forall (n : β), (GE.ge.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeSup.toPartialOrder.{u3} β _inst_3))) n N) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α (u n) (u N)) (s i))))))
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.cauchy_seq_iff' Filter.HasBasis.cauchySeq_iff'ₓ'. -/
@@ -501,7 +505,12 @@ theorem Filter.HasBasis.cauchySeq_iff' {γ} [Nonempty β] [SemilatticeSup β] {u
     · exact hN n hn
 #align filter.has_basis.cauchy_seq_iff' Filter.HasBasis.cauchySeq_iff'
 
-#print cauchySeq_of_controlled /-
+/- warning: cauchy_seq_of_controlled -> cauchySeq_of_controlled is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : Nonempty.{succ u2} β] (U : β -> (Set.{u1} (Prod.{u1, u1} α α))), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u2} β (fun (n : β) => HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasSubset.{u1} (Prod.{u1, u1} α α)) (U n) s))) -> (forall {f : β -> α}, (forall {N : β} {m : β} {n : β}, (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) N m) -> (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) N n) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (f m) (f n)) (U N))) -> (CauchySeq.{u1, u2} α β _inst_1 _inst_2 f))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : SemilatticeSup.{u2} β] [_inst_3 : Nonempty.{succ u2} β] (U : β -> (Set.{u1} (Prod.{u1, u1} α α))), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u2} β (fun (n : β) => HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.instHasSubsetSet.{u1} (Prod.{u1, u1} α α)) (U n) s))) -> (forall {f : β -> α}, (forall {{N : β}} {{m : β}} {{n : β}}, (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) N m) -> (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_2))) N n) -> (Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α (f m) (f n)) (U N))) -> (CauchySeq.{u1, u2} α β _inst_1 _inst_2 f))
+Case conversion may be inaccurate. Consider using '#align cauchy_seq_of_controlled cauchySeq_of_controlledₓ'. -/
 theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Set (α × α))
     (hU : ∀ s ∈ 𝓤 α, ∃ n, U n ⊆ s) {f : β → α}
     (hf : ∀ {N m n : β}, N ≤ m → N ≤ n → (f m, f n) ∈ U N) : CauchySeq f :=
@@ -514,11 +523,10 @@ theorem cauchySeq_of_controlled [SemilatticeSup β] [Nonempty β] (U : β → Se
       cases' mn with m n
       exact hN (hf hmn.1 hmn.2))
 #align cauchy_seq_of_controlled cauchySeq_of_controlled
--/
 
 /- warning: is_complete_iff_cluster_pt -> isComplete_iff_clusterPt is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Filter.{u1} α), (Cauchy.{u1} α _inst_1 l) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) l (Filter.principal.{u1} α s)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x l))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Filter.{u1} α), (Cauchy.{u1} α _inst_1 l) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) l (Filter.principal.{u1} α s)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x l))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Filter.{u1} α), (Cauchy.{u1} α _inst_1 l) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) l (Filter.principal.{u1} α s)) -> (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (ClusterPt.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x l))))
 Case conversion may be inaccurate. Consider using '#align is_complete_iff_cluster_pt isComplete_iff_clusterPtₓ'. -/
@@ -529,7 +537,7 @@ theorem isComplete_iff_clusterPt {s : Set α} :
 
 /- warning: is_complete_iff_ultrafilter -> isComplete_iff_ultrafilter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (Filter.principal.{u1} α s)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (Filter.principal.{u1} α s)) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 (Ultrafilter.toFilter.{u1} α l)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Ultrafilter.toFilter.{u1} α l) (Filter.principal.{u1} α s)) -> (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Ultrafilter.toFilter.{u1} α l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))))
 Case conversion may be inaccurate. Consider using '#align is_complete_iff_ultrafilter isComplete_iff_ultrafilterₓ'. -/
@@ -544,7 +552,7 @@ theorem isComplete_iff_ultrafilter {s : Set α} :
 
 /- warning: is_complete_iff_ultrafilter' -> isComplete_iff_ultrafilter' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Ultrafilter.{u1} α) (Ultrafilter.hasMem.{u1} α) s l) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l)) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Ultrafilter.{u1} α) (Ultrafilter.hasMem.{u1} α) s l) -> (Exists.{succ u1} α (fun (x : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) => LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (IsComplete.{u1} α _inst_1 s) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 (Ultrafilter.toFilter.{u1} α l)) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Ultrafilter.{u1} α) (Ultrafilter.instMembershipSetUltrafilter.{u1} α) s l) -> (Exists.{succ u1} α (fun (x : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Ultrafilter.toFilter.{u1} α l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))))
 Case conversion may be inaccurate. Consider using '#align is_complete_iff_ultrafilter' isComplete_iff_ultrafilter'ₓ'. -/
@@ -663,7 +671,7 @@ theorem completeSpace_iff_isComplete_univ : CompleteSpace α ↔ IsComplete (uni
 
 /- warning: complete_space_iff_ultrafilter -> completeSpace_iff_ultrafilter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α], Iff (CompleteSpace.{u1} α _inst_1) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l)) -> (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α], Iff (CompleteSpace.{u1} α _inst_1) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l)) -> (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α], Iff (CompleteSpace.{u1} α _inst_1) (forall (l : Ultrafilter.{u1} α), (Cauchy.{u1} α _inst_1 (Ultrafilter.toFilter.{u1} α l)) -> (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Ultrafilter.toFilter.{u1} α l) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x))))
 Case conversion may be inaccurate. Consider using '#align complete_space_iff_ultrafilter completeSpace_iff_ultrafilterₓ'. -/
@@ -674,7 +682,7 @@ theorem completeSpace_iff_ultrafilter :
 
 /- warning: cauchy_iff_exists_le_nhds -> cauchy_iff_exists_le_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : CompleteSpace.{u1} α _inst_1] {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], Iff (Cauchy.{u1} α _inst_1 l) (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) l (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : CompleteSpace.{u1} α _inst_1] {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], Iff (Cauchy.{u1} α _inst_1 l) (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) l (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : CompleteSpace.{u1} α _inst_1] {l : Filter.{u1} α} [_inst_3 : Filter.NeBot.{u1} α l], Iff (Cauchy.{u1} α _inst_1 l) (Exists.{succ u1} α (fun (x : α) => LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) l (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) x)))
 Case conversion may be inaccurate. Consider using '#align cauchy_iff_exists_le_nhds cauchy_iff_exists_le_nhdsₓ'. -/
@@ -718,7 +726,7 @@ theorem cauchySeq_tendsto_of_isComplete [SemilatticeSup β] {K : Set α} (h₁ :
 
 /- warning: cauchy.le_nhds_Lim -> Cauchy.le_nhds_lim is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : CompleteSpace.{u1} α _inst_1] [_inst_3 : Nonempty.{succ u1} α] {f : Filter.{u1} α}, (Cauchy.{u1} α _inst_1 f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (lim.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) _inst_3 f)))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : CompleteSpace.{u1} α _inst_1] [_inst_3 : Nonempty.{succ u1} α] {f : Filter.{u1} α}, (Cauchy.{u1} α _inst_1 f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (lim.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) _inst_3 f)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] [_inst_2 : CompleteSpace.{u1} α _inst_1] [_inst_3 : Nonempty.{succ u1} α] {f : Filter.{u1} α}, (Cauchy.{u1} α _inst_1 f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) (lim.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) _inst_3 f)))
 Case conversion may be inaccurate. Consider using '#align cauchy.le_nhds_Lim Cauchy.le_nhds_limₓ'. -/
@@ -854,7 +862,7 @@ theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs
 
 /- warning: ultrafilter.cauchy_of_totally_bounded -> Ultrafilter.cauchy_of_totallyBounded is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α} (f : Ultrafilter.{u1} α), (TotallyBounded.{u1} α _inst_1 s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f) (Filter.principal.{u1} α s)) -> (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α} (f : Ultrafilter.{u1} α), (TotallyBounded.{u1} α _inst_1 s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f) (Filter.principal.{u1} α s)) -> (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α} (f : Ultrafilter.{u1} α), (TotallyBounded.{u1} α _inst_1 s) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Ultrafilter.toFilter.{u1} α f) (Filter.principal.{u1} α s)) -> (Cauchy.{u1} α _inst_1 (Ultrafilter.toFilter.{u1} α f))
 Case conversion may be inaccurate. Consider using '#align ultrafilter.cauchy_of_totally_bounded Ultrafilter.cauchy_of_totallyBoundedₓ'. -/
@@ -874,7 +882,7 @@ theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (
 
 /- warning: totally_bounded_iff_filter -> totallyBounded_iff_filter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (f : Filter.{u1} α), (Filter.NeBot.{u1} α f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (Filter.principal.{u1} α s)) -> (Exists.{succ u1} (Filter.{u1} α) (fun (c : Filter.{u1} α) => Exists.{0} (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) c f) (fun (H : LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) c f) => Cauchy.{u1} α _inst_1 c))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (f : Filter.{u1} α), (Filter.NeBot.{u1} α f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (Filter.principal.{u1} α s)) -> (Exists.{succ u1} (Filter.{u1} α) (fun (c : Filter.{u1} α) => Exists.{0} (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) c f) (fun (H : LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) c f) => Cauchy.{u1} α _inst_1 c))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (f : Filter.{u1} α), (Filter.NeBot.{u1} α f) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f (Filter.principal.{u1} α s)) -> (Exists.{succ u1} (Filter.{u1} α) (fun (c : Filter.{u1} α) => And (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) c f) (Cauchy.{u1} α _inst_1 c))))
 Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_filter totallyBounded_iff_filterₓ'. -/
@@ -911,7 +919,7 @@ theorem totallyBounded_iff_filter {s : Set α} :
 
 /- warning: totally_bounded_iff_ultrafilter -> totallyBounded_iff_ultrafilter is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (f : Ultrafilter.{u1} α), (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f) (Filter.principal.{u1} α s)) -> (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f)))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (f : Ultrafilter.{u1} α), (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f) (Filter.principal.{u1} α s)) -> (Cauchy.{u1} α _inst_1 ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Ultrafilter.{u1} α) (Filter.{u1} α) (HasLiftT.mk.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (CoeTCₓ.coe.{succ u1, succ u1} (Ultrafilter.{u1} α) (Filter.{u1} α) (Ultrafilter.Filter.hasCoeT.{u1} α))) f)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (f : Ultrafilter.{u1} α), (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) (Ultrafilter.toFilter.{u1} α f) (Filter.principal.{u1} α s)) -> (Cauchy.{u1} α _inst_1 (Ultrafilter.toFilter.{u1} α f)))
 Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_ultrafilter totallyBounded_iff_ultrafilterₓ'. -/
@@ -1086,7 +1094,7 @@ theorem seq_is_cauchySeq : CauchySeq <| seq hf U_mem :=
 
 /- warning: sequentially_complete.le_nhds_of_seq_tendsto_nhds -> SequentiallyComplete.le_nhds_of_seq_tendsto_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} (hf : Cauchy.{u1} α _inst_1 f) {U : Nat -> (Set.{u1} (Prod.{u1, u1} α α))} (U_mem : forall (n : Nat), Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) (U n) (uniformity.{u1} α _inst_1)), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasSubset.{u1} (Prod.{u1, u1} α α)) (U n) s))) -> (forall {{a : α}}, (Filter.Tendsto.{0, u1} Nat α (SequentiallyComplete.seq.{u1} α _inst_1 f hf (fun (n : Nat) => U n) U_mem) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} (hf : Cauchy.{u1} α _inst_1 f) {U : Nat -> (Set.{u1} (Prod.{u1, u1} α α))} (U_mem : forall (n : Nat), Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) (U n) (uniformity.{u1} α _inst_1)), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasSubset.{u1} (Prod.{u1, u1} α α)) (U n) s))) -> (forall {{a : α}}, (Filter.Tendsto.{0, u1} Nat α (SequentiallyComplete.seq.{u1} α _inst_1 f hf (fun (n : Nat) => U n) U_mem) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring)))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toHasLe.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.partialOrder.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α} (hf : Cauchy.{u1} α _inst_1 f) {U : Nat -> (Set.{u1} (Prod.{u1, u1} α α))} (U_mem : forall (n : Nat), Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) (U n) (uniformity.{u1} α _inst_1)), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{1} Nat (fun (n : Nat) => HasSubset.Subset.{u1} (Set.{u1} (Prod.{u1, u1} α α)) (Set.instHasSubsetSet.{u1} (Prod.{u1, u1} α α)) (U n) s))) -> (forall {{a : α}}, (Filter.Tendsto.{0, u1} Nat α (SequentiallyComplete.seq.{u1} α _inst_1 f hf (fun (n : Nat) => U n) U_mem) (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)) -> (LE.le.{u1} (Filter.{u1} α) (Preorder.toLE.{u1} (Filter.{u1} α) (PartialOrder.toPreorder.{u1} (Filter.{u1} α) (Filter.instPartialOrderFilter.{u1} α))) f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α _inst_1) a)))
 Case conversion may be inaccurate. Consider using '#align sequentially_complete.le_nhds_of_seq_tendsto_nhds SequentiallyComplete.le_nhds_of_seq_tendsto_nhdsₓ'. -/

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

@@ -568,15 +568,15 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
       (ht l hl htl).imp fun x hx => ⟨Or.inr hx.fst, hx.snd⟩⟩
 #align is_complete.union IsComplete.union
 
-/- warning: is_complete_Union_separated -> isComplete_unionᵢ_separated is a dubious translation:
+/- warning: is_complete_Union_separated -> isComplete_iUnion_separated is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {ι : Sort.{u2}} {s : ι -> (Set.{u1} α)}, (forall (i : ι), IsComplete.{u1} α _inst_1 (s i)) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (forall (i : ι) (j : ι) (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (s i)) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (s j)) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U) -> (Eq.{u2} ι i j))) -> (IsComplete.{u1} α _inst_1 (Set.unionᵢ.{u1, u2} α ι (fun (i : ι) => s i))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {ι : Sort.{u2}} {s : ι -> (Set.{u1} α)}, (forall (i : ι), IsComplete.{u1} α _inst_1 (s i)) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (forall (i : ι) (j : ι) (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (s i)) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (s j)) -> (Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U) -> (Eq.{u2} ι i j))) -> (IsComplete.{u1} α _inst_1 (Set.iUnion.{u1, u2} α ι (fun (i : ι) => s i))))
 but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : UniformSpace.{u2} α] {ι : Sort.{u1}} {s : ι -> (Set.{u2} α)}, (forall (i : ι), IsComplete.{u2} α _inst_1 (s i)) -> (forall {U : Set.{u2} (Prod.{u2, u2} α α)}, (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} α α)) (Filter.{u2} (Prod.{u2, u2} α α)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} α α)) U (uniformity.{u2} α _inst_1)) -> (forall (i : ι) (j : ι) (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (s i)) -> (forall (y : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y (s j)) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α x y) U) -> (Eq.{u1} ι i j))) -> (IsComplete.{u2} α _inst_1 (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => s i))))
-Case conversion may be inaccurate. Consider using '#align is_complete_Union_separated isComplete_unionᵢ_separatedₓ'. -/
+  forall {α : Type.{u2}} [_inst_1 : UniformSpace.{u2} α] {ι : Sort.{u1}} {s : ι -> (Set.{u2} α)}, (forall (i : ι), IsComplete.{u2} α _inst_1 (s i)) -> (forall {U : Set.{u2} (Prod.{u2, u2} α α)}, (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} α α)) (Filter.{u2} (Prod.{u2, u2} α α)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} α α)) U (uniformity.{u2} α _inst_1)) -> (forall (i : ι) (j : ι) (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (s i)) -> (forall (y : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y (s j)) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α x y) U) -> (Eq.{u1} ι i j))) -> (IsComplete.{u2} α _inst_1 (Set.iUnion.{u2, u1} α ι (fun (i : ι) => s i))))
+Case conversion may be inaccurate. Consider using '#align is_complete_Union_separated isComplete_iUnion_separatedₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem isComplete_unionᵢ_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
+theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
     {U : Set (α × α)} (hU : U ∈ 𝓤 α) (hd : ∀ (i j : ι), ∀ x ∈ s i, ∀ y ∈ s j, (x, y) ∈ U → i = j) :
     IsComplete (⋃ i, s i) := by
   set S := ⋃ i, s i
@@ -599,7 +599,7 @@ theorem isComplete_unionᵢ_separated {ι : Sort _} {s : ι → Set α} (hs : 
     exact hd i j x hi y hj (htU <| mk_mem_prod hx hy)
   rcases hs i l hl (le_principal_iff.2 <| mem_of_superset htl hi) with ⟨x, hxs, hlx⟩
   exact ⟨x, mem_Union.2 ⟨i, hxs⟩, hlx⟩
-#align is_complete_Union_separated isComplete_unionᵢ_separated
+#align is_complete_Union_separated isComplete_iUnion_separated
 
 #print CompleteSpace /-
 /-- A complete space is defined here using uniformities. A uniform space
@@ -752,9 +752,9 @@ def TotallyBounded (s : Set α) : Prop :=
 
 /- warning: totally_bounded.exists_subset -> TotallyBounded.exists_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (y : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.5698 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (y : α) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.5698 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
 Case conversion may be inaccurate. Consider using '#align totally_bounded.exists_subset TotallyBounded.exists_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
@@ -778,9 +778,9 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
 
 /- warning: totally_bounded_iff_subset -> totallyBounded_iff_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (y : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.6626 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (y : α) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.6626 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
 Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_subset totallyBounded_iff_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff_subset {s : Set α} :
@@ -793,15 +793,15 @@ theorem totallyBounded_iff_subset {s : Set α} :
 
 /- warning: filter.has_basis.totally_bounded_iff -> Filter.HasBasis.totallyBounded_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {ι : Sort.{u2}} {p : ι -> Prop} {U : ι -> (Set.{u1} (Prod.{u1, u1} α α))}, (Filter.HasBasis.{u1, u2} (Prod.{u1, u1} α α) ι (uniformity.{u1} α _inst_1) p U) -> (forall {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (i : ι), (p i) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (U i))))))))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {ι : Sort.{u2}} {p : ι -> Prop} {U : ι -> (Set.{u1} (Prod.{u1, u1} α α))}, (Filter.HasBasis.{u1, u2} (Prod.{u1, u1} α α) ι (uniformity.{u1} α _inst_1) p U) -> (forall {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (i : ι), (p i) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (y : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) (U i))))))))))
 but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : UniformSpace.{u2} α] {ι : Sort.{u1}} {p : ι -> Prop} {U : ι -> (Set.{u2} (Prod.{u2, u2} α α))}, (Filter.HasBasis.{u2, u1} (Prod.{u2, u2} α α) ι (uniformity.{u2} α _inst_1) p U) -> (forall {s : Set.{u2} α}, Iff (TotallyBounded.{u2} α _inst_1 s) (forall (i : ι), (p i) -> (Exists.{succ u2} (Set.{u2} α) (fun (t : Set.{u2} α) => And (Set.Finite.{u2} α t) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) s (Set.unionᵢ.{u2, succ u2} α α (fun (y : α) => Set.unionᵢ.{u2, 0} α (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y t) (fun (H : Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y t) => setOf.{u2} α (fun (x : α) => Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α x y) (U i))))))))))
+  forall {α : Type.{u2}} [_inst_1 : UniformSpace.{u2} α] {ι : Sort.{u1}} {p : ι -> Prop} {U : ι -> (Set.{u2} (Prod.{u2, u2} α α))}, (Filter.HasBasis.{u2, u1} (Prod.{u2, u2} α α) ι (uniformity.{u2} α _inst_1) p U) -> (forall {s : Set.{u2} α}, Iff (TotallyBounded.{u2} α _inst_1 s) (forall (i : ι), (p i) -> (Exists.{succ u2} (Set.{u2} α) (fun (t : Set.{u2} α) => And (Set.Finite.{u2} α t) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) s (Set.iUnion.{u2, succ u2} α α (fun (y : α) => Set.iUnion.{u2, 0} α (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y t) (fun (H : Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y t) => setOf.{u2} α (fun (x : α) => Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α x y) (U i))))))))))
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.totally_bounded_iff Filter.HasBasis.totallyBounded_iffₓ'. -/
 theorem Filter.HasBasis.totallyBounded_iff {ι} {p : ι → Prop} {U : ι → Set (α × α)}
     (H : (𝓤 α).HasBasis p U) {s : Set α} :
     TotallyBounded s ↔ ∀ i, p i → ∃ t : Set α, Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U i } :=
   H.forall_iff fun U V hUV h =>
-    h.imp fun t ht => ⟨ht.1, ht.2.trans <| unionᵢ₂_mono fun x hx y hy => hUV hy⟩
+    h.imp fun t ht => ⟨ht.1, ht.2.trans <| iUnion₂_mono fun x hx y hy => hUV hy⟩
 #align filter.has_basis.totally_bounded_iff Filter.HasBasis.totallyBounded_iff
 
 #print totallyBounded_of_forall_symm /-
@@ -834,7 +834,7 @@ theorem TotallyBounded.closure {s : Set α} (h : TotallyBounded s) : TotallyBoun
     let ⟨t, htf, hst⟩ := h V hV.1
     ⟨t, htf,
       closure_minimal hst <|
-        isClosed_bunionᵢ htf fun y hy => hV.2.Preimage (continuous_id.prod_mk continuous_const)⟩
+        isClosed_biUnion htf fun y hy => hV.2.Preimage (continuous_id.prod_mk continuous_const)⟩
 #align totally_bounded.closure TotallyBounded.closure
 -/
 
@@ -865,7 +865,7 @@ theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (
     let ⟨t', ht'₁, ht'_symm, ht'_t⟩ := comp_symm_of_uniformity ht
     let ⟨i, hi, hs_union⟩ := hs t' ht'₁
     have : (⋃ y ∈ i, { x | (x, y) ∈ t' }) ∈ f := mem_of_superset (le_principal_iff.mp h) hs_union
-    have : ∃ y ∈ i, { x | (x, y) ∈ t' } ∈ f := (Ultrafilter.finite_bunionᵢ_mem_iff hi).1 this
+    have : ∃ y ∈ i, { x | (x, y) ∈ t' } ∈ f := (Ultrafilter.finite_biUnion_mem_iff hi).1 this
     let ⟨y, hy, hif⟩ := this
     have : { x | (x, y) ∈ t' } ×ˢ { x | (x, y) ∈ t' } ⊆ compRel t' t' :=
       fun ⟨x₁, x₂⟩ ⟨(h₁ : (x₁, y) ∈ t'), (h₂ : (x₂, y) ∈ t')⟩ => ⟨y, h₁, ht'_symm h₂⟩
@@ -895,14 +895,14 @@ theorem totallyBounded_iff_filter {s : Set α} :
         exact principal_mono.2 (diff_subset_diff_right <| bUnion_subset_bUnion_left h)
       · intro t
         simpa [nonempty_diff] using hd_cover t t.finite_to_set
-    have : f ≤ 𝓟 s := infᵢ_le_of_le ∅ (by simp)
+    have : f ≤ 𝓟 s := iInf_le_of_le ∅ (by simp)
     refine' ⟨f, ‹_›, ‹_›, fun c hcf hc => _⟩
     rcases mem_prod_same_iff.1 (hc.2 hd) with ⟨m, hm, hmd⟩
     have : m ∩ s ∈ c := inter_mem hm (le_principal_iff.mp (hcf.trans ‹_›))
     rcases hc.1.nonempty_of_mem this with ⟨y, hym, hys⟩
     set ys := ⋃ y' ∈ ({y} : Finset α), { x | (x, y') ∈ d }
     have : m ⊆ ys := by simpa [ys] using fun x hx => hmd (mk_mem_prod hx hym)
-    have : c ≤ 𝓟 (s \ ys) := hcf.trans (infᵢ_le_of_le {y} le_rfl)
+    have : c ≤ 𝓟 (s \ ys) := hcf.trans (iInf_le_of_le {y} le_rfl)
     refine' hc.1.Ne (empty_mem_iff_bot.mp _)
     filter_upwards [le_principal_iff.1 this, hm]
     refine' fun x hx hxm => hx.2 _
@@ -1026,19 +1026,19 @@ def setSeq (n : ℕ) : Set α :=
 
 #print SequentiallyComplete.setSeq_mem /-
 theorem setSeq_mem (n : ℕ) : setSeq hf U_mem n ∈ f :=
-  (binterᵢ_mem (finite_le_nat n)).2 fun m _ => (setSeqAux hf U_mem m).2.fst
+  (biInter_mem (finite_le_nat n)).2 fun m _ => (setSeqAux hf U_mem m).2.fst
 #align sequentially_complete.set_seq_mem SequentiallyComplete.setSeq_mem
 -/
 
 #print SequentiallyComplete.setSeq_mono /-
 theorem setSeq_mono ⦃m n : ℕ⦄ (h : m ≤ n) : setSeq hf U_mem n ⊆ setSeq hf U_mem m :=
-  binterᵢ_subset_binterᵢ_left fun k hk => le_trans hk h
+  biInter_subset_biInter_left fun k hk => le_trans hk h
 #align sequentially_complete.set_seq_mono SequentiallyComplete.setSeq_mono
 -/
 
 #print SequentiallyComplete.setSeq_sub_aux /-
 theorem setSeq_sub_aux (n : ℕ) : setSeq hf U_mem n ⊆ setSeqAux hf U_mem n :=
-  binterᵢ_subset_of_mem right_mem_Iic
+  biInter_subset_of_mem right_mem_Iic
 #align sequentially_complete.set_seq_sub_aux SequentiallyComplete.setSeq_sub_aux
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/38f16f960f5006c6c0c2bac7b0aba5273188f4e5

@@ -635,6 +635,7 @@ instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace
           Filter.le_lift.2 fun s hs => Filter.le_lift'.2 fun t ht => inter_mem (hx1 hs) (hx2 ht)⟩
 #align complete_space.prod CompleteSpace.prod
 
+#print CompleteSpace.mulOpposite /-
 @[to_additive]
 instance CompleteSpace.mulOpposite [CompleteSpace α] : CompleteSpace αᵐᵒᵖ
     where complete f hf :=
@@ -642,7 +643,8 @@ instance CompleteSpace.mulOpposite [CompleteSpace α] : CompleteSpace αᵐᵒ
       let ⟨x, hx⟩ := CompleteSpace.complete (hf.map MulOpposite.uniformContinuous_unop)
       ⟨x, (map_le_iff_le_comap.mp hx).trans_eq <| MulOpposite.comap_unop_nhds _⟩
 #align complete_space.mul_opposite CompleteSpace.mulOpposite
-#align complete_space.add_opposite CompleteSpace.add_opposite
+#align complete_space.add_opposite CompleteSpace.addOpposite
+-/
 
 #print completeSpace_of_isComplete_univ /-
 /-- If `univ` is complete, the space is a complete space -/
@@ -752,7 +754,7 @@ def TotallyBounded (s : Set α) : Prop :=
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.5631 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.5698 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
 Case conversion may be inaccurate. Consider using '#align totally_bounded.exists_subset TotallyBounded.exists_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
@@ -778,7 +780,7 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
 lean 3 declaration is
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) t s) => And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.Mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.hasMem.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.6559 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
+  forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.6626 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
 Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_subset totallyBounded_iff_subsetₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff_subset {s : Set α} :

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

@@ -52,7 +52,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : UniformSpace.{u2} α] {ι : Sort.{u1}} {p : ι -> Prop} {s : ι -> (Set.{u2} (Prod.{u2, u2} α α))}, (Filter.HasBasis.{u2, u1} (Prod.{u2, u2} α α) ι (uniformity.{u2} α _inst_1) p s) -> (forall {f : Filter.{u2} α}, Iff (Cauchy.{u2} α _inst_1 f) (And (Filter.NeBot.{u2} α f) (forall (i : ι), (p i) -> (Exists.{succ u2} (Set.{u2} α) (fun (t : Set.{u2} α) => And (Membership.mem.{u2, u2} (Set.{u2} α) (Filter.{u2} α) (instMembershipSetFilter.{u2} α) t f) (forall (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x t) -> (forall (y : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y t) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α x y) (s i)))))))))
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iffₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α × α)} (h : (𝓤 α).HasBasis p s)
     {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ i, p i → ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s i :=
@@ -67,7 +67,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {f : Filter.{u1} α}, Iff (Cauchy.{u1} α _inst_1 f) (And (Filter.NeBot.{u1} α f) (forall (s : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) t f) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) s)))))))
 Case conversion may be inaccurate. Consider using '#align cauchy_iff' cauchy_iff'ₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 theorem cauchy_iff' {f : Filter α} :
     Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), (x, y) ∈ s :=
   (𝓤 α).basis_sets.cauchy_iff
@@ -225,7 +225,7 @@ theorem Cauchy.map [UniformSpace β] {f : Filter α} {m : α → β} (hf : Cauch
   ⟨hf.1.map _,
     calc
       map m f ×ᶠ map m f = map (fun p : α × α => (m p.1, m p.2)) (f ×ᶠ f) := Filter.prod_map_map_eq
-      _ ≤ map (fun p : α × α => (m p.1, m p.2)) (𝓤 α) := map_mono hf.right
+      _ ≤ map (fun p : α × α => (m p.1, m p.2)) (𝓤 α) := (map_mono hf.right)
       _ ≤ 𝓤 β := hm
       ⟩
 #align cauchy.map Cauchy.map
@@ -244,7 +244,7 @@ theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (hf : Cau
     calc
       comap m f ×ᶠ comap m f = comap (fun p : α × α => (m p.1, m p.2)) (f ×ᶠ f) :=
         Filter.prod_comap_comap_eq
-      _ ≤ comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) := comap_mono hf.right
+      _ ≤ comap (fun p : α × α => (m p.1, m p.2)) (𝓤 β) := (comap_mono hf.right)
       _ ≤ 𝓤 α := hm
       ⟩
 #align cauchy.comap Cauchy.comap
@@ -469,7 +469,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : UniformSpace.{u2} α] {γ : Sort.{u1}} [_inst_2 : Nonempty.{succ u3} β] [_inst_3 : SemilatticeSup.{u3} β] {u : β -> α} {p : γ -> Prop} {s : γ -> (Set.{u2} (Prod.{u2, u2} α α))}, (Filter.HasBasis.{u2, u1} (Prod.{u2, u2} α α) γ (uniformity.{u2} α _inst_1) p s) -> (Iff (CauchySeq.{u2, u3} α β _inst_1 _inst_3 u) (forall (i : γ), (p i) -> (Exists.{succ u3} β (fun (N : β) => forall (m : β), (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeSup.toPartialOrder.{u3} β _inst_3))) N m) -> (forall (n : β), (LE.le.{u3} β (Preorder.toLE.{u3} β (PartialOrder.toPreorder.{u3} β (SemilatticeSup.toPartialOrder.{u3} β _inst_3))) N n) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α (u m) (u n)) (s i)))))))
 Case conversion may be inaccurate. Consider using '#align filter.has_basis.cauchy_seq_iff Filter.HasBasis.cauchySeq_iffₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (m n «expr ≥ » N) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 -- see Note [nolint_ge]
 @[nolint ge_or_gt]
 theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u : β → α} {p : γ → Prop}
@@ -574,7 +574,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : UniformSpace.{u2} α] {ι : Sort.{u1}} {s : ι -> (Set.{u2} α)}, (forall (i : ι), IsComplete.{u2} α _inst_1 (s i)) -> (forall {U : Set.{u2} (Prod.{u2, u2} α α)}, (Membership.mem.{u2, u2} (Set.{u2} (Prod.{u2, u2} α α)) (Filter.{u2} (Prod.{u2, u2} α α)) (instMembershipSetFilter.{u2} (Prod.{u2, u2} α α)) U (uniformity.{u2} α _inst_1)) -> (forall (i : ι) (j : ι) (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x (s i)) -> (forall (y : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) y (s j)) -> (Membership.mem.{u2, u2} (Prod.{u2, u2} α α) (Set.{u2} (Prod.{u2, u2} α α)) (Set.instMembershipSet.{u2} (Prod.{u2, u2} α α)) (Prod.mk.{u2, u2} α α x y) U) -> (Eq.{u1} ι i j))) -> (IsComplete.{u2} α _inst_1 (Set.unionᵢ.{u2, u1} α ι (fun (i : ι) => s i))))
 Case conversion may be inaccurate. Consider using '#align is_complete_Union_separated isComplete_unionᵢ_separatedₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » S) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » S) -/
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 theorem isComplete_unionᵢ_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
     {U : Set (α × α)} (hU : U ∈ 𝓤 α) (hd : ∀ (i j : ι), ∀ x ∈ s i, ∀ y ∈ s j, (x, y) ∈ U → i = j) :
@@ -754,7 +754,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, (TotallyBounded.{u1} α _inst_1 s) -> (forall {U : Set.{u1} (Prod.{u1, u1} α α)}, (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) U (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.5631 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) U)))))))))
 Case conversion may be inaccurate. Consider using '#align totally_bounded.exists_subset TotallyBounded.exists_subsetₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : Set (α × α)}
     (hU : U ∈ 𝓤 α) : ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U } :=
   by
@@ -780,7 +780,7 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : UniformSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α _inst_1 s) (forall (d : Set.{u1} (Prod.{u1, u1} α α)), (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) d (uniformity.{u1} α _inst_1)) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) t s) (And (Set.Finite.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (y : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) (fun (h._@.Mathlib.Topology.UniformSpace.Cauchy._hyg.6559 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => setOf.{u1} α (fun (x : α) => Membership.mem.{u1, u1} (Prod.{u1, u1} α α) (Set.{u1} (Prod.{u1, u1} α α)) (Set.instMembershipSet.{u1} (Prod.{u1, u1} α α)) (Prod.mk.{u1, u1} α α x y) d)))))))))
 Case conversion may be inaccurate. Consider using '#align totally_bounded_iff_subset totallyBounded_iff_subsetₓ'. -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff_subset {s : Set α} :
     TotallyBounded s ↔
       ∀ d ∈ 𝓤 α, ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ d } :=

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

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
 
 ! This file was ported from Lean 3 source module topology.uniform_space.cauchy
-! leanprover-community/mathlib commit 4c19a16e4b705bf135cf9a80ac18fcc99c438514
+! leanprover-community/mathlib commit 22131150f88a2d125713ffa0f4693e3355b1eb49
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.Topology.Algebra.Constructions
 import Mathbin.Topology.Bases
 import Mathbin.Topology.UniformSpace.Basic
 
@@ -634,6 +635,15 @@ instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace
           Filter.le_lift.2 fun s hs => Filter.le_lift'.2 fun t ht => inter_mem (hx1 hs) (hx2 ht)⟩
 #align complete_space.prod CompleteSpace.prod
 
+@[to_additive]
+instance CompleteSpace.mulOpposite [CompleteSpace α] : CompleteSpace αᵐᵒᵖ
+    where complete f hf :=
+    MulOpposite.op_surjective.exists.mpr <|
+      let ⟨x, hx⟩ := CompleteSpace.complete (hf.map MulOpposite.uniformContinuous_unop)
+      ⟨x, (map_le_iff_le_comap.mp hx).trans_eq <| MulOpposite.comap_unop_nhds _⟩
+#align complete_space.mul_opposite CompleteSpace.mulOpposite
+#align complete_space.add_opposite CompleteSpace.add_opposite
+
 #print completeSpace_of_isComplete_univ /-
 /-- If `univ` is complete, the space is a complete space -/
 theorem completeSpace_of_isComplete_univ (h : IsComplete (univ : Set α)) : CompleteSpace α :=

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

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

@@ -722,8 +722,8 @@ theorem setSeq_sub_aux (n : ℕ) : setSeq hf U_mem n ⊆ setSeqAux hf U_mem n :=
 theorem setSeq_prod_subset {N m n} (hm : N ≤ m) (hn : N ≤ n) :
     setSeq hf U_mem m ×ˢ setSeq hf U_mem n ⊆ U N := fun p hp => by
   refine' (setSeqAux hf U_mem N).2.2 ⟨_, _⟩ <;> apply setSeq_sub_aux
-  exact setSeq_mono hf U_mem hm hp.1
-  exact setSeq_mono hf U_mem hn hp.2
+  · exact setSeq_mono hf U_mem hm hp.1
+  · exact setSeq_mono hf U_mem hn hp.2
 #align sequentially_complete.set_seq_prod_subset SequentiallyComplete.setSeq_prod_subset
 
 /-- A sequence of points such that `seq n ∈ setSeq n`. Here `setSeq` is an antitone

Follow-up to #10816.

Remaining places containing such lemmas are

• Option.bex_ne_none and Option.ball_ne_none: defined in Lean core
• Nat.decidableBallLT and Nat.decidableBallLE: defined in Lean core
• bef_def is still used in a number of places and could be renamed
• BAll.imp_{left,right}, BEx.imp_{left,right}, BEx.intro and BEx.elim

I only audited the first ~150 lemmas mentioning "ball"; too many lemmas named after Metric.ball/openBall/closedBall.

Co-authored-by: Yaël Dillies <yael.dillies@gmail.com>

@@ -43,7 +43,7 @@ theorem Filter.HasBasis.cauchy_iff {ι} {p : ι → Prop} {s : ι → Set (α ×
     Cauchy f ↔ NeBot f ∧ ∀ i, p i → ∃ t ∈ f, ∀ x ∈ t, ∀ y ∈ t, (x, y) ∈ s i :=
   and_congr Iff.rfl <|
     (f.basis_sets.prod_self.le_basis_iff h).trans <| by
-      simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
+      simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, forall_mem_comm]
 #align filter.has_basis.cauchy_iff Filter.HasBasis.cauchy_iff
 
 theorem cauchy_iff' {f : Filter α} :
@@ -53,7 +53,7 @@ theorem cauchy_iff' {f : Filter α} :
 
 theorem cauchy_iff {f : Filter α} : Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α, ∃ t ∈ f, t ×ˢ t ⊆ s :=
   cauchy_iff'.trans <| by
-    simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
+    simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, forall_mem_comm]
 #align cauchy_iff cauchy_iff
 
 lemma cauchy_iff_le {l : Filter α} [hl : l.NeBot] :

Classifies by adding issue number #11215 to porting notes claiming "TODO".

@@ -795,7 +795,7 @@ theorem complete_of_cauchySeq_tendsto (H' : ∀ u : ℕ → α, CauchySeq u →
 
 variable (α)
 
--- Porting note: todo: move to `Topology.UniformSpace.Basic`
+-- Porting note (#11215): TODO: move to `Topology.UniformSpace.Basic`
 instance (priority := 100) firstCountableTopology : FirstCountableTopology α :=
   ⟨fun a => by rw [nhds_eq_comap_uniformity]; infer_instance⟩
 #align uniform_space.first_countable_topology UniformSpace.firstCountableTopology

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.

@@ -16,9 +16,11 @@ import Mathlib.Topology.UniformSpace.Basic
 
 universe u v
 
-open Filter TopologicalSpace Set Classical UniformSpace Function
+open scoped Classical
+open Filter TopologicalSpace Set UniformSpace Function
 
-open Classical Uniformity Topology Filter
+open scoped Classical
+open Uniformity Topology Filter
 
 variable {α : Type u} {β : Type v} [uniformSpace : UniformSpace α]
 
@@ -696,7 +698,7 @@ noncomputable section
 /-- An auxiliary sequence of sets approximating a Cauchy filter. -/
 def setSeqAux (n : ℕ) : { s : Set α // s ∈ f ∧ s ×ˢ s ⊆ U n } :=
   -- Porting note: changed `∃ _ : s ∈ f, ..` to `s ∈ f ∧ ..`
-  indefiniteDescription _ <| (cauchy_iff.1 hf).2 (U n) (U_mem n)
+  Classical.indefiniteDescription _ <| (cauchy_iff.1 hf).2 (U n) (U_mem n)
 #align sequentially_complete.set_seq_aux SequentiallyComplete.setSeqAux
 
 /-- Given a Cauchy filter `f` and a sequence `U` of entourages, `set_seq` provides
@@ -728,11 +730,11 @@ theorem setSeq_prod_subset {N m n} (hm : N ≤ m) (hn : N ≤ n) :
 sequence of sets `setSeq n ∈ f` with diameters controlled by a given sequence
 of entourages. -/
 def seq (n : ℕ) : α :=
-  choose <| hf.1.nonempty_of_mem (setSeq_mem hf U_mem n)
+  (hf.1.nonempty_of_mem (setSeq_mem hf U_mem n)).choose
 #align sequentially_complete.seq SequentiallyComplete.seq
 
 theorem seq_mem (n : ℕ) : seq hf U_mem n ∈ setSeq hf U_mem n :=
-  choose_spec <| hf.1.nonempty_of_mem (setSeq_mem hf U_mem n)
+  (hf.1.nonempty_of_mem (setSeq_mem hf U_mem n)).choose_spec
 #align sequentially_complete.seq_mem SequentiallyComplete.seq_mem
 
 theorem seq_pair_mem ⦃N m n : ℕ⦄ (hm : N ≤ m) (hn : N ≤ n) :

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".

@@ -793,7 +793,7 @@ theorem complete_of_cauchySeq_tendsto (H' : ∀ u : ℕ → α, CauchySeq u →
 
 variable (α)
 
--- porting note: todo: move to `Topology.UniformSpace.Basic`
+-- Porting note: todo: move to `Topology.UniformSpace.Basic`
 instance (priority := 100) firstCountableTopology : FirstCountableTopology α :=
   ⟨fun a => by rw [nhds_eq_comap_uniformity]; infer_instance⟩
 #align uniform_space.first_countable_topology UniformSpace.firstCountableTopology

This resolves the Zulip comment here.

@@ -310,6 +310,17 @@ theorem tendsto_nhds_of_cauchySeq_of_subseq [Preorder β] {u : β → α} (hu :
   le_nhds_of_cauchy_adhp hu (mapClusterPt_of_comp hf ha)
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
 
+/-- Any shift of a Cauchy sequence is also a Cauchy sequence. -/
+theorem cauchySeq_shift {u : ℕ → α} (k : ℕ) : CauchySeq (fun n ↦ u (n + k)) ↔ CauchySeq u := by
+  constructor <;> intro h
+  · rw [cauchySeq_iff] at h ⊢
+    intro V mV
+    obtain ⟨N, h⟩ := h V mV
+    use N + k
+    intro a ha b hb
+    convert h (a - k) (Nat.le_sub_of_add_le ha) (b - k) (Nat.le_sub_of_add_le hb) <;> omega
+  · exact h.comp_tendsto (tendsto_add_atTop_nat k)
+
 theorem Filter.HasBasis.cauchySeq_iff {γ} [Nonempty β] [SemilatticeSup β] {u : β → α} {p : γ → Prop}
     {s : γ → Set (α × α)} (h : (𝓤 α).HasBasis p s) :
     CauchySeq u ↔ ∀ i, p i → ∃ N, ∀ m, N ≤ m → ∀ n, N ≤ n → (u m, u n) ∈ s i := by

Use haveI to drop unneeded Nonempty/Inhabited assumptions.

@@ -477,14 +477,14 @@ theorem cauchySeq_tendsto_of_isComplete [Preorder β] {K : Set α} (h₁ : IsCom
     ⟨univ, univ_mem, by rwa [image_univ, range_subset_iff]⟩
 #align cauchy_seq_tendsto_of_is_complete cauchySeq_tendsto_of_isComplete
 
-theorem Cauchy.le_nhds_lim [CompleteSpace α] [Nonempty α] {f : Filter α} (hf : Cauchy f) :
-    f ≤ 𝓝 (lim f) :=
+theorem Cauchy.le_nhds_lim [CompleteSpace α] {f : Filter α} (hf : Cauchy f) :
+    haveI := hf.1.nonempty; f ≤ 𝓝 (lim f) :=
   _root_.le_nhds_lim (CompleteSpace.complete hf)
 set_option linter.uppercaseLean3 false in
 #align cauchy.le_nhds_Lim Cauchy.le_nhds_lim
 
-theorem CauchySeq.tendsto_limUnder [Preorder β] [CompleteSpace α] [Nonempty α] {u : β → α}
-    (h : CauchySeq u) : Tendsto u atTop (𝓝 <| limUnder atTop u) :=
+theorem CauchySeq.tendsto_limUnder [Preorder β] [CompleteSpace α] {u : β → α} (h : CauchySeq u) :
+    haveI := h.1.nonempty; Tendsto u atTop (𝓝 <| limUnder atTop u) :=
   h.le_nhds_lim
 #align cauchy_seq.tendsto_lim CauchySeq.tendsto_limUnder
 

I literally went through and regex'd some uses of cases', replacing them with rcases; this is meant to be a low effort PR as I hope that tools can do this in the future.

rcases is an easier replacement than cases, though with better tools we could in future do a second pass converting simple rcases added here (and existing ones) to cases.

@@ -655,7 +655,7 @@ theorem CauchySeq.totallyBounded_range {s : ℕ → α} (hs : CauchySeq s) :
   rw [range_subset_iff, biUnion_image]
   intro m
   rw [mem_iUnion₂]
-  cases' le_total m n with hm hm
+  rcases le_total m n with hm | hm
   exacts [⟨m, hm, refl_mem_uniformity ha⟩, ⟨n, le_refl n, hn m hm n le_rfl⟩]
 #align cauchy_seq.totally_bounded_range CauchySeq.totallyBounded_range
 

Removes nonterminal uses of simp at. Replaces most of these with instances of simp? ... says.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -566,7 +566,8 @@ theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs
   ⟨f '' c, hfc.image f, by
     simp only [mem_image, iUnion_exists, biUnion_and', iUnion_iUnion_eq_right, image_subset_iff,
       preimage_iUnion, preimage_setOf_eq]
-    simp [subset_def] at hct
+    simp? [subset_def] at hct says
+      simp only [mem_setOf_eq, subset_def, mem_iUnion, exists_prop] at hct
     intro x hx; simp
     exact hct x hx⟩
 #align totally_bounded.image TotallyBounded.image

Mostly, this means replacing "of_open" by "of_isOpen". A few lemmas names were misleading and are corrected differently. Zulip discussion.

@@ -799,7 +799,7 @@ theorem secondCountable_of_separable [SeparableSpace α] : SecondCountableTopolo
     (@uniformity_hasBasis_open_symmetric α _).exists_antitone_subbasis
   choose ht_mem hto hts using hto
   refine' ⟨⟨⋃ x ∈ s, range fun k => ball x (t k), hsc.biUnion fun x _ => countable_range _, _⟩⟩
-  refine' (isTopologicalBasis_of_open_of_nhds _ _).eq_generateFrom
+  refine' (isTopologicalBasis_of_isOpen_of_nhds _ _).eq_generateFrom
   · simp only [mem_iUnion₂, mem_range]
     rintro _ ⟨x, _, k, rfl⟩
     exact isOpen_ball x (hto k)

@@ -193,16 +193,16 @@ theorem Cauchy.comap' [UniformSpace β] {f : Filter β} {m : α → β} (hf : Ca
 /-- Cauchy sequences. Usually defined on ℕ, but often it is also useful to say that a function
 defined on ℝ is Cauchy at +∞ to deduce convergence. Therefore, we define it in a type class that
 is general enough to cover both ℕ and ℝ, which are the main motivating examples. -/
-def CauchySeq [SemilatticeSup β] (u : β → α) :=
+def CauchySeq [Preorder β] (u : β → α) :=
   Cauchy (atTop.map u)
 #align cauchy_seq CauchySeq
 
-theorem CauchySeq.tendsto_uniformity [SemilatticeSup β] {u : β → α} (h : CauchySeq u) :
+theorem CauchySeq.tendsto_uniformity [Preorder β] {u : β → α} (h : CauchySeq u) :
     Tendsto (Prod.map u u) atTop (𝓤 α) := by
   simpa only [Tendsto, prod_map_map_eq', prod_atTop_atTop_eq] using h.right
 #align cauchy_seq.tendsto_uniformity CauchySeq.tendsto_uniformity
 
-theorem CauchySeq.nonempty [SemilatticeSup β] {u : β → α} (hu : CauchySeq u) : Nonempty β :=
+theorem CauchySeq.nonempty [Preorder β] {u : β → α} (hu : CauchySeq u) : Nonempty β :=
   @nonempty_of_neBot _ _ <| (map_neBot_iff _).1 hu.1
 #align cauchy_seq.nonempty CauchySeq.nonempty
 
@@ -227,9 +227,9 @@ theorem cauchySeq_iff_tendsto [Nonempty β] [SemilatticeSup β] {u : β → α}
   cauchy_map_iff'.trans <| by simp only [prod_atTop_atTop_eq, Prod.map_def]
 #align cauchy_seq_iff_tendsto cauchySeq_iff_tendsto
 
-theorem CauchySeq.comp_tendsto {γ} [SemilatticeSup β] [SemilatticeSup γ] [Nonempty γ] {f : β → α}
+theorem CauchySeq.comp_tendsto {γ} [Preorder β] [SemilatticeSup γ] [Nonempty γ] {f : β → α}
     (hf : CauchySeq f) {g : γ → β} (hg : Tendsto g atTop atTop) : CauchySeq (f ∘ g) :=
-  cauchySeq_iff_tendsto.2 <| hf.tendsto_uniformity.comp (hg.prod_atTop hg)
+  ⟨inferInstance, le_trans (prod_le_prod.mpr ⟨Tendsto.comp le_rfl hg, Tendsto.comp le_rfl hg⟩) hf.2⟩
 #align cauchy_seq.comp_tendsto CauchySeq.comp_tendsto
 
 theorem CauchySeq.comp_injective [SemilatticeSup β] [NoMaxOrder β] [Nonempty β] {u : ℕ → α}
@@ -262,14 +262,14 @@ theorem cauchySeq_iff {u : ℕ → α} :
   simp only [cauchySeq_iff', Filter.eventually_atTop_prod_self', mem_preimage, Prod_map]
 #align cauchy_seq_iff cauchySeq_iff
 
-theorem CauchySeq.prod_map {γ δ} [UniformSpace β] [SemilatticeSup γ] [SemilatticeSup δ] {u : γ → α}
+theorem CauchySeq.prod_map {γ δ} [UniformSpace β] [Preorder γ] [Preorder δ] {u : γ → α}
     {v : δ → β} (hu : CauchySeq u) (hv : CauchySeq v) : CauchySeq (Prod.map u v) := by
   simpa only [CauchySeq, prod_map_map_eq', prod_atTop_atTop_eq] using hu.prod hv
 #align cauchy_seq.prod_map CauchySeq.prod_map
 
-theorem CauchySeq.prod {γ} [UniformSpace β] [SemilatticeSup γ] {u : γ → α} {v : γ → β}
+theorem CauchySeq.prod {γ} [UniformSpace β] [Preorder γ] {u : γ → α} {v : γ → β}
     (hu : CauchySeq u) (hv : CauchySeq v) : CauchySeq fun x => (u x, v x) :=
-  haveI := hu.nonempty
+  haveI := hu.1.of_map
   (Cauchy.prod hu hv).mono (Tendsto.prod_mk le_rfl le_rfl)
 #align cauchy_seq.prod CauchySeq.prod
 
@@ -278,7 +278,7 @@ theorem CauchySeq.eventually_eventually [SemilatticeSup β] {u : β → α} (hu
   eventually_atTop_curry <| hu.tendsto_uniformity hV
 #align cauchy_seq.eventually_eventually CauchySeq.eventually_eventually
 
-theorem UniformContinuous.comp_cauchySeq {γ} [UniformSpace β] [SemilatticeSup γ] {f : α → β}
+theorem UniformContinuous.comp_cauchySeq {γ} [UniformSpace β] [Preorder γ] {f : α → β}
     (hf : UniformContinuous f) {u : γ → α} (hu : CauchySeq u) : CauchySeq (f ∘ u) :=
   hu.map hf
 #align uniform_continuous.comp_cauchy_seq UniformContinuous.comp_cauchySeq
@@ -304,7 +304,7 @@ theorem Filter.Tendsto.subseq_mem_entourage {V : ℕ → Set (α × α)} (hV : 
 #align filter.tendsto.subseq_mem_entourage Filter.Tendsto.subseq_mem_entourage
 
 /-- If a Cauchy sequence has a convergent subsequence, then it converges. -/
-theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α} (hu : CauchySeq u)
+theorem tendsto_nhds_of_cauchySeq_of_subseq [Preorder β] {u : β → α} (hu : CauchySeq u)
     {ι : Type*} {f : ι → β} {p : Filter ι} [NeBot p] (hf : Tendsto f p atTop) {a : α}
     (ha : Tendsto (u ∘ f) p (𝓝 a)) : Tendsto u atTop (𝓝 a) :=
   le_nhds_of_cauchy_adhp hu (mapClusterPt_of_comp hf ha)
@@ -465,13 +465,13 @@ theorem cauchy_map_iff_exists_tendsto [CompleteSpace α] {l : Filter β} {f : β
 #align cauchy_map_iff_exists_tendsto cauchy_map_iff_exists_tendsto
 
 /-- A Cauchy sequence in a complete space converges -/
-theorem cauchySeq_tendsto_of_complete [SemilatticeSup β] [CompleteSpace α] {u : β → α}
+theorem cauchySeq_tendsto_of_complete [Preorder β] [CompleteSpace α] {u : β → α}
     (H : CauchySeq u) : ∃ x, Tendsto u atTop (𝓝 x) :=
   CompleteSpace.complete H
 #align cauchy_seq_tendsto_of_complete cauchySeq_tendsto_of_complete
 
 /-- If `K` is a complete subset, then any cauchy sequence in `K` converges to a point in `K` -/
-theorem cauchySeq_tendsto_of_isComplete [SemilatticeSup β] {K : Set α} (h₁ : IsComplete K)
+theorem cauchySeq_tendsto_of_isComplete [Preorder β] {K : Set α} (h₁ : IsComplete K)
     {u : β → α} (h₂ : ∀ n, u n ∈ K) (h₃ : CauchySeq u) : ∃ v ∈ K, Tendsto u atTop (𝓝 v) :=
   h₁ _ h₃ <| le_principal_iff.2 <| mem_map_iff_exists_image.2
     ⟨univ, univ_mem, by rwa [image_univ, range_subset_iff]⟩
@@ -483,7 +483,7 @@ theorem Cauchy.le_nhds_lim [CompleteSpace α] [Nonempty α] {f : Filter α} (hf
 set_option linter.uppercaseLean3 false in
 #align cauchy.le_nhds_Lim Cauchy.le_nhds_lim
 
-theorem CauchySeq.tendsto_limUnder [SemilatticeSup β] [CompleteSpace α] [Nonempty α] {u : β → α}
+theorem CauchySeq.tendsto_limUnder [Preorder β] [CompleteSpace α] [Nonempty α] {u : β → α}
     (h : CauchySeq u) : Tendsto u atTop (𝓝 <| limUnder atTop u) :=
   h.le_nhds_lim
 #align cauchy_seq.tendsto_lim CauchySeq.tendsto_limUnder

New lemmas / instances

• An archimedean ordered semiring is directed upwards.
• Filter.hasAntitoneBasis_atTop;
• Filter.HasAntitoneBasis.iInf_principal;

Fix typos

• Docstrings: "if the agree" -> "if they agree".
• ProbabilityTheory.measure_eq_zero_or_one_of_indepSetCat_self -> ProbabilityTheory.measure_eq_zero_or_one_of_indepSet_self.

Weaken typeclass assumptions

From a semilattice to a directed type

• MeasureTheory.tendsto_measure_iUnion;
• MeasureTheory.tendsto_measure_iInter;
• Monotone.directed_le, Monotone.directed_ge;
• Antitone.directed_le, Antitone.directed_ge;
• directed_of_sup, renamed to directed_of_isDirected_le;
• directed_of_inf, renamed to directed_of_isDirected_ge;

From a strict ordered semiring to an ordered semiring

• tendsto_nat_cast_atTop_atTop;
• Filter.Eventually.nat_cast_atTop;
• atTop_hasAntitoneBasis_of_archimedean;

@@ -592,22 +592,17 @@ theorem totallyBounded_iff_filter {s : Set α} :
   · intro H d hd
     contrapose! H with hd_cover
     set f := ⨅ t : Finset α, 𝓟 (s \ ⋃ y ∈ t, { x | (x, y) ∈ d })
-    have : Filter.NeBot f := by
-      refine' iInf_neBot_of_directed' (directed_of_sup _) _
-      · intro t₁ t₂ h
-        exact principal_mono.2 (diff_subset_diff_right <| biUnion_subset_biUnion_left h)
-      · intro t
-        simpa [nonempty_diff] using hd_cover t t.finite_toSet
+    have hb : HasAntitoneBasis f fun t : Finset α ↦ s \ ⋃ y ∈ t, { x | (x, y) ∈ d } :=
+      .iInf_principal fun _ _ ↦ diff_subset_diff_right ∘ biUnion_subset_biUnion_left
+    have : Filter.NeBot f := hb.1.neBot_iff.2 fun _ ↦
+      nonempty_diff.2 <| hd_cover _ (Finset.finite_toSet _)
     have : f ≤ 𝓟 s := iInf_le_of_le ∅ (by simp)
     refine' ⟨f, ‹_›, ‹_›, fun c hcf hc => _⟩
     rcases mem_prod_same_iff.1 (hc.2 hd) with ⟨m, hm, hmd⟩
     rcases hc.1.nonempty_of_mem hm with ⟨y, hym⟩
-    set ys := ⋃ y' ∈ ({y} : Finset α), { x | (x, y') ∈ d }
-    have : c ≤ 𝓟 (s \ ys) := hcf.trans (iInf_le_of_le {y} le_rfl)
-    refine' hc.1.ne (empty_mem_iff_bot.mp _)
-    filter_upwards [le_principal_iff.1 this, hm]
-    refine' fun x hx hxm => hx.2 _
-    simpa using hmd (mk_mem_prod hxm hym)
+    have : s \ {x | (x, y) ∈ d} ∈ c := by simpa using hcf (hb.mem {y})
+    rcases hc.1.nonempty_of_mem (inter_mem hm this) with ⟨z, hzm, -, hyz⟩
+    exact hyz (hmd ⟨hzm, hym⟩)
 #align totally_bounded_iff_filter totallyBounded_iff_filter
 
 theorem totallyBounded_iff_ultrafilter {s : Set α} :

Removes nonterminal simps on lines looking like simp [...]

@@ -564,7 +564,8 @@ theorem TotallyBounded.image [UniformSpace β] {f : α → β} {s : Set α} (hs
   have : { p : α × α | (f p.1, f p.2) ∈ t } ∈ 𝓤 α := hf ht
   let ⟨c, hfc, hct⟩ := hs _ this
   ⟨f '' c, hfc.image f, by
-    simp [image_subset_iff]
+    simp only [mem_image, iUnion_exists, biUnion_and', iUnion_iUnion_eq_right, image_subset_iff,
+      preimage_iUnion, preimage_setOf_eq]
     simp [subset_def] at hct
     intro x hx; simp
     exact hct x hx⟩

Also add completeSpace_prod, integrable_prod.

@@ -413,6 +413,24 @@ instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace
     ⟨(x1, x2), by rw [nhds_prod_eq, le_prod]; constructor <;> assumption⟩
 #align complete_space.prod CompleteSpace.prod
 
+lemma CompleteSpace.fst_of_prod [UniformSpace β] [CompleteSpace (α × β)] [h : Nonempty β] :
+    CompleteSpace α where
+  complete hf :=
+    let ⟨y⟩ := h
+    let ⟨(a, b), hab⟩ := CompleteSpace.complete <| hf.prod <| cauchy_pure (a := y)
+    ⟨a, by simpa only [map_fst_prod, nhds_prod_eq] using map_mono (m := Prod.fst) hab⟩
+
+lemma CompleteSpace.snd_of_prod [UniformSpace β] [CompleteSpace (α × β)] [h : Nonempty α] :
+    CompleteSpace β where
+  complete hf :=
+    let ⟨x⟩ := h
+    let ⟨(a, b), hab⟩ := CompleteSpace.complete <| (cauchy_pure (a := x)).prod hf
+    ⟨b, by simpa only [map_snd_prod, nhds_prod_eq] using map_mono (m := Prod.snd) hab⟩
+
+lemma completeSpace_prod_of_nonempty [UniformSpace β] [Nonempty α] [Nonempty β] :
+    CompleteSpace (α × β) ↔ CompleteSpace α ∧ CompleteSpace β :=
+  ⟨fun _ ↦ ⟨.fst_of_prod (β := β), .snd_of_prod (α := α)⟩, fun ⟨_, _⟩ ↦ .prod⟩
+
 @[to_additive]
 instance CompleteSpace.mulOpposite [CompleteSpace α] : CompleteSpace αᵐᵒᵖ where
   complete hf :=

We define Alexandrov-discrete spaces as topological spaces where the intersection of a family of open sets is open.

This PR only gives a minimal API because the goal is to ensure that lemma names like isOpen_sInter are free to use for AlexandrovDiscrete. The existing lemmas are getting prefixed by Set.Finite or suffixed by _of_finite.

@@ -537,7 +537,7 @@ theorem TotallyBounded.closure {s : Set α} (h : TotallyBounded s) : TotallyBoun
     let ⟨t, htf, hst⟩ := h V hV.1
     ⟨t, htf,
       closure_minimal hst <|
-        isClosed_biUnion htf fun _ _ => hV.2.preimage (continuous_id.prod_mk continuous_const)⟩
+        htf.isClosed_biUnion fun _ _ => hV.2.preimage (continuous_id.prod_mk continuous_const)⟩
 #align totally_bounded.closure TotallyBounded.closure
 
 /-- The image of a totally bounded set under a uniformly continuous map is totally bounded. -/

Some of the lemmas are cherry-picked from leanprover-community/mathlib#17975 and will be useful for the general Arzela-Ascoli theorem, but I also filled some API holes on the way.

@@ -20,7 +20,7 @@ open Filter TopologicalSpace Set Classical UniformSpace Function
 
 open Classical Uniformity Topology Filter
 
-variable {α : Type u} {β : Type v} [UniformSpace α]
+variable {α : Type u} {β : Type v} [uniformSpace : UniformSpace α]
 
 /-- A filter `f` is Cauchy if for every entourage `r`, there exists an
   `s ∈ f` such that `s × s ⊆ r`. This is a generalization of Cauchy
@@ -54,6 +54,10 @@ theorem cauchy_iff {f : Filter α} : Cauchy f ↔ NeBot f ∧ ∀ s ∈ 𝓤 α,
     simp only [subset_def, Prod.forall, mem_prod_eq, and_imp, id, ball_mem_comm]
 #align cauchy_iff cauchy_iff
 
+lemma cauchy_iff_le {l : Filter α} [hl : l.NeBot] :
+    Cauchy l ↔ l ×ˢ l ≤ 𝓤 α := by
+  simp only [Cauchy, hl, true_and]
+
 theorem Cauchy.ultrafilter_of {l : Filter α} (h : Cauchy l) :
     Cauchy (@Ultrafilter.of _ l h.1 : Filter α) := by
   haveI := h.1
@@ -92,13 +96,40 @@ theorem Filter.Tendsto.cauchy_map {l : Filter β} [NeBot l] {f : β → α} {a :
   cauchy_nhds.mono h
 #align filter.tendsto.cauchy_map Filter.Tendsto.cauchy_map
 
+lemma Cauchy.mono_uniformSpace {u v : UniformSpace β} {F : Filter β} (huv : u ≤ v)
+    (hF : Cauchy (uniformSpace := u) F) : Cauchy (uniformSpace := v) F :=
+  ⟨hF.1, hF.2.trans huv⟩
+
+lemma cauchy_inf_uniformSpace {u v : UniformSpace β} {F : Filter β} :
+    Cauchy (uniformSpace := u ⊓ v) F ↔
+    Cauchy (uniformSpace := u) F ∧ Cauchy (uniformSpace := v) F := by
+  unfold Cauchy
+  rw [inf_uniformity (u := u), le_inf_iff, and_and_left]
+
+lemma cauchy_iInf_uniformSpace {ι : Sort*} [Nonempty ι] {u : ι → UniformSpace β}
+    {l : Filter β} :
+    Cauchy (uniformSpace := ⨅ i, u i) l ↔ ∀ i, Cauchy (uniformSpace := u i) l := by
+  unfold Cauchy
+  rw [iInf_uniformity, le_iInf_iff, forall_and, forall_const]
+
+lemma cauchy_iInf_uniformSpace' {ι : Sort*} {u : ι → UniformSpace β}
+    {l : Filter β} [l.NeBot] :
+    Cauchy (uniformSpace := ⨅ i, u i) l ↔ ∀ i, Cauchy (uniformSpace := u i) l := by
+  simp_rw [cauchy_iff_le (uniformSpace := _), iInf_uniformity, le_iInf_iff]
+
+lemma cauchy_comap_uniformSpace {u : UniformSpace β} {f : α → β} {l : Filter α} :
+    Cauchy (uniformSpace := comap f u) l ↔ Cauchy (map f l) := by
+  simp only [Cauchy, map_neBot_iff, prod_map_map_eq, map_le_iff_le_comap]
+  rfl
+
+lemma cauchy_prod_iff [UniformSpace β] {F : Filter (α × β)} :
+    Cauchy F ↔ Cauchy (map Prod.fst F) ∧ Cauchy (map Prod.snd F) := by
+  simp_rw [instUniformSpaceProd, ← cauchy_comap_uniformSpace, ← cauchy_inf_uniformSpace]
+
 theorem Cauchy.prod [UniformSpace β] {f : Filter α} {g : Filter β} (hf : Cauchy f) (hg : Cauchy g) :
     Cauchy (f ×ˢ g) := by
-  refine' ⟨hf.1.prod hg.1, _⟩
-  simp only [uniformity_prod, le_inf_iff, ← map_le_iff_le_comap, ← prod_map_map_eq]
-  exact
-    ⟨le_trans (prod_mono tendsto_fst tendsto_fst) hf.2,
-      le_trans (prod_mono tendsto_snd tendsto_snd) hg.2⟩
+  have := hf.1; have := hg.1
+  simpa [cauchy_prod_iff, hf.1] using ⟨hf, hg⟩
 #align cauchy.prod Cauchy.prod
 
 /-- The common part of the proofs of `le_nhds_of_cauchy_adhp` and
@@ -379,9 +410,7 @@ instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace
   complete hf :=
     let ⟨x1, hx1⟩ := CompleteSpace.complete <| hf.map uniformContinuous_fst
     let ⟨x2, hx2⟩ := CompleteSpace.complete <| hf.map uniformContinuous_snd
-    ⟨(x1, x2), by
-      rw [nhds_prod_eq, Filter.prod_def]
-      exact Filter.le_lift.2 fun s hs => Filter.le_lift'.2 fun t ht => inter_mem (hx1 hs) (hx2 ht)⟩
+    ⟨(x1, x2), by rw [nhds_prod_eq, le_prod]; constructor <;> assumption⟩
 #align complete_space.prod CompleteSpace.prod
 
 @[to_additive]

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

This has nice performance benefits.

@@ -175,7 +175,7 @@ theorem CauchySeq.nonempty [SemilatticeSup β] {u : β → α} (hu : CauchySeq u
   @nonempty_of_neBot _ _ <| (map_neBot_iff _).1 hu.1
 #align cauchy_seq.nonempty CauchySeq.nonempty
 
-theorem CauchySeq.mem_entourage {β : Type _} [SemilatticeSup β] {u : β → α} (h : CauchySeq u)
+theorem CauchySeq.mem_entourage {β : Type*} [SemilatticeSup β] {u : β → α} (h : CauchySeq u)
     {V : Set (α × α)} (hV : V ∈ 𝓤 α) : ∃ k₀, ∀ i j, k₀ ≤ i → k₀ ≤ j → (u i, u j) ∈ V := by
   haveI := h.nonempty
   have := h.tendsto_uniformity; rw [← prod_atTop_atTop_eq] at this
@@ -274,7 +274,7 @@ theorem Filter.Tendsto.subseq_mem_entourage {V : ℕ → Set (α × α)} (hV : 
 
 /-- If a Cauchy sequence has a convergent subsequence, then it converges. -/
 theorem tendsto_nhds_of_cauchySeq_of_subseq [SemilatticeSup β] {u : β → α} (hu : CauchySeq u)
-    {ι : Type _} {f : ι → β} {p : Filter ι} [NeBot p] (hf : Tendsto f p atTop) {a : α}
+    {ι : Type*} {f : ι → β} {p : Filter ι} [NeBot p] (hf : Tendsto f p atTop) {a : α}
     (ha : Tendsto (u ∘ f) p (𝓝 a)) : Tendsto u atTop (𝓝 a) :=
   le_nhds_of_cauchy_adhp hu (mapClusterPt_of_comp hf ha)
 #align tendsto_nhds_of_cauchy_seq_of_subseq tendsto_nhds_of_cauchySeq_of_subseq
@@ -340,7 +340,7 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
       (ht l hl htl).imp fun x hx => ⟨Or.inr hx.1, hx.2⟩⟩
 #align is_complete.union IsComplete.union
 
-theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
+theorem isComplete_iUnion_separated {ι : Sort*} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
     {U : Set (α × α)} (hU : U ∈ 𝓤 α) (hd : ∀ (i j : ι), ∀ x ∈ s i, ∀ y ∈ s j, (x, y) ∈ U → i = j) :
     IsComplete (⋃ i, s i) := by
   set S := ⋃ i, s i

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2017 Johannes Hölzl. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
-
-! This file was ported from Lean 3 source module topology.uniform_space.cauchy
-! leanprover-community/mathlib commit 22131150f88a2d125713ffa0f4693e3355b1eb49
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.Algebra.Constructions
 import Mathlib.Topology.Bases
 import Mathlib.Topology.UniformSpace.Basic
 
+#align_import topology.uniform_space.cauchy from "leanprover-community/mathlib"@"22131150f88a2d125713ffa0f4693e3355b1eb49"
+
 /-!
 # Theory of Cauchy filters in uniform spaces. Complete uniform spaces. Totally bounded subsets.
 -/

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

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

@@ -30,7 +30,7 @@ variable {α : Type u} {β : Type v} [UniformSpace α]
   sequences, because if `a : ℕ → α` then the filter of sets containing
   cofinitely many of the `a n` is Cauchy iff `a` is a Cauchy sequence. -/
 def Cauchy (f : Filter α) :=
-  NeBot f ∧ f ×ᶠ f ≤ 𝓤 α
+  NeBot f ∧ f ×ˢ f ≤ 𝓤 α
 #align cauchy Cauchy
 
 /-- A set `s` is called *complete*, if any Cauchy filter `f` such that `s ∈ f`
@@ -65,12 +65,12 @@ theorem Cauchy.ultrafilter_of {l : Filter α} (h : Cauchy l) :
 #align cauchy.ultrafilter_of Cauchy.ultrafilter_of
 
 theorem cauchy_map_iff {l : Filter β} {f : β → α} :
-    Cauchy (l.map f) ↔ NeBot l ∧ Tendsto (fun p : β × β => (f p.1, f p.2)) (l ×ᶠ l) (𝓤 α) := by
+    Cauchy (l.map f) ↔ NeBot l ∧ Tendsto (fun p : β × β => (f p.1, f p.2)) (l ×ˢ l) (𝓤 α) := by
   rw [Cauchy, map_neBot_iff, prod_map_map_eq, Tendsto]
 #align cauchy_map_iff cauchy_map_iff
 
 theorem cauchy_map_iff' {l : Filter β} [hl : NeBot l] {f : β → α} :
-    Cauchy (l.map f) ↔ Tendsto (fun p : β × β => (f p.1, f p.2)) (l ×ᶠ l) (𝓤 α) :=
+    Cauchy (l.map f) ↔ Tendsto (fun p : β × β => (f p.1, f p.2)) (l ×ˢ l) (𝓤 α) :=
   cauchy_map_iff.trans <| and_iff_right hl
 #align cauchy_map_iff' cauchy_map_iff'
 
@@ -96,7 +96,7 @@ theorem Filter.Tendsto.cauchy_map {l : Filter β} [NeBot l] {f : β → α} {a :
 #align filter.tendsto.cauchy_map Filter.Tendsto.cauchy_map
 
 theorem Cauchy.prod [UniformSpace β] {f : Filter α} {g : Filter β} (hf : Cauchy f) (hg : Cauchy g) :
-    Cauchy (f ×ᶠ g) := by
+    Cauchy (f ×ˢ g) := by
   refine' ⟨hf.1.prod hg.1, _⟩
   simp only [uniformity_prod, le_inf_iff, ← map_le_iff_le_comap, ← prod_map_map_eq]
   exact
@@ -141,7 +141,7 @@ nonrec theorem Cauchy.map [UniformSpace β] {f : Filter α} {m : α → β} (hf
     (hm : UniformContinuous m) : Cauchy (map m f) :=
   ⟨hf.1.map _,
     calc
-      map m f ×ᶠ map m f = map (Prod.map m m) (f ×ᶠ f) := Filter.prod_map_map_eq
+      map m f ×ˢ map m f = map (Prod.map m m) (f ×ˢ f) := Filter.prod_map_map_eq
       _ ≤ Filter.map (Prod.map m m) (𝓤 α) := map_mono hf.right
       _ ≤ 𝓤 β := hm⟩
 #align cauchy.map Cauchy.map
@@ -151,7 +151,7 @@ nonrec theorem Cauchy.comap [UniformSpace β] {f : Filter β} {m : α → β} (h
     Cauchy (comap m f) :=
   ⟨‹_›,
     calc
-      comap m f ×ᶠ comap m f = comap (Prod.map m m) (f ×ᶠ f) := prod_comap_comap_eq
+      comap m f ×ˢ comap m f = comap (Prod.map m m) (f ×ˢ f) := prod_comap_comap_eq
       _ ≤ comap (Prod.map m m) (𝓤 β) := comap_mono hf.right
       _ ≤ 𝓤 α := hm⟩
 #align cauchy.comap Cauchy.comap

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>

@@ -343,7 +343,7 @@ protected theorem IsComplete.union {s t : Set α} (hs : IsComplete s) (ht : IsCo
       (ht l hl htl).imp fun x hx => ⟨Or.inr hx.1, hx.2⟩⟩
 #align is_complete.union IsComplete.union
 
-theorem isComplete_unionᵢ_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
+theorem isComplete_iUnion_separated {ι : Sort _} {s : ι → Set α} (hs : ∀ i, IsComplete (s i))
     {U : Set (α × α)} (hU : U ∈ 𝓤 α) (hd : ∀ (i j : ι), ∀ x ∈ s i, ∀ y ∈ s j, (x, y) ∈ U → i = j) :
     IsComplete (⋃ i, s i) := by
   set S := ⋃ i, s i
@@ -356,13 +356,13 @@ theorem isComplete_unionᵢ_separated {ι : Sort _} {s : ι → Set α} (hs : 
       (Set.prod_mono (inter_subset_left _ _) (inter_subset_left _ _)).trans htU⟩
   obtain ⟨i, hi⟩ : ∃ i, t ⊆ s i := by
     rcases Filter.nonempty_of_mem htl with ⟨x, hx⟩
-    rcases mem_unionᵢ.1 (htS hx) with ⟨i, hi⟩
+    rcases mem_iUnion.1 (htS hx) with ⟨i, hi⟩
     refine' ⟨i, fun y hy => _⟩
-    rcases mem_unionᵢ.1 (htS hy) with ⟨j, hj⟩
+    rcases mem_iUnion.1 (htS hy) with ⟨j, hj⟩
     rwa [hd i j x hi y hj (htU <| mk_mem_prod hx hy)]
   rcases hs i l hl (le_principal_iff.2 <| mem_of_superset htl hi) with ⟨x, hxs, hlx⟩
-  exact ⟨x, mem_unionᵢ.2 ⟨i, hxs⟩, hlx⟩
-#align is_complete_Union_separated isComplete_unionᵢ_separated
+  exact ⟨x, mem_iUnion.2 ⟨i, hxs⟩, hlx⟩
+#align is_complete_Union_separated isComplete_iUnion_separated
 
 /-- A complete space is defined here using uniformities. A uniform space
   is complete if every Cauchy filter converges. -/
@@ -467,8 +467,8 @@ theorem TotallyBounded.exists_subset {s : Set α} (hs : TotallyBounded s) {U : S
   · haveI : Fintype u := (fk.inter_of_left _).fintype
     exact finite_range f
   · intro x xs
-    obtain ⟨y, hy, xy⟩ := mem_unionᵢ₂.1 (ks xs)
-    rw [bunionᵢ_range, mem_unionᵢ]
+    obtain ⟨y, hy, xy⟩ := mem_iUnion₂.1 (ks xs)
+    rw [biUnion_range, mem_iUnion]
     set z : ↥u := ⟨y, hy, ⟨x, xs, xy⟩⟩
     exact ⟨z, rU <| mem_compRel.2 ⟨y, xy, rs (hfr z)⟩⟩
 #align totally_bounded.exists_subset TotallyBounded.exists_subset
@@ -485,7 +485,7 @@ theorem Filter.HasBasis.totallyBounded_iff {ι} {p : ι → Prop} {U : ι → Se
     (H : (𝓤 α).HasBasis p U) {s : Set α} :
     TotallyBounded s ↔ ∀ i, p i → ∃ t : Set α, Set.Finite t ∧ s ⊆ ⋃ y ∈ t, { x | (x, y) ∈ U i } :=
   H.forall_iff fun _ _ hUV h =>
-    h.imp fun _ ht => ⟨ht.1, ht.2.trans <| unionᵢ₂_mono fun _ _ _ hy => hUV hy⟩
+    h.imp fun _ ht => ⟨ht.1, ht.2.trans <| iUnion₂_mono fun _ _ _ hy => hUV hy⟩
 #align filter.has_basis.totally_bounded_iff Filter.HasBasis.totallyBounded_iff
 
 theorem totallyBounded_of_forall_symm {s : Set α}
@@ -511,7 +511,7 @@ theorem TotallyBounded.closure {s : Set α} (h : TotallyBounded s) : TotallyBoun
     let ⟨t, htf, hst⟩ := h V hV.1
     ⟨t, htf,
       closure_minimal hst <|
-        isClosed_bunionᵢ htf fun _ _ => hV.2.preimage (continuous_id.prod_mk continuous_const)⟩
+        isClosed_biUnion htf fun _ _ => hV.2.preimage (continuous_id.prod_mk continuous_const)⟩
 #align totally_bounded.closure TotallyBounded.closure
 
 /-- The image of a totally bounded set under a uniformly continuous map is totally bounded. -/
@@ -532,7 +532,7 @@ theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (
     let ⟨t', ht'₁, ht'_symm, ht'_t⟩ := comp_symm_of_uniformity ht
     let ⟨i, hi, hs_union⟩ := hs t' ht'₁
     have : (⋃ y ∈ i, { x | (x, y) ∈ t' }) ∈ f := mem_of_superset (le_principal_iff.mp h) hs_union
-    have : ∃ y ∈ i, { x | (x, y) ∈ t' } ∈ f := (Ultrafilter.finite_bunionᵢ_mem_iff hi).1 this
+    have : ∃ y ∈ i, { x | (x, y) ∈ t' } ∈ f := (Ultrafilter.finite_biUnion_mem_iff hi).1 this
     let ⟨y, _, hif⟩ := this
     have : { x | (x, y) ∈ t' } ×ˢ { x | (x, y) ∈ t' } ⊆ compRel t' t' :=
       fun ⟨_, _⟩ ⟨(h₁ : (_, y) ∈ t'), (h₂ : (_, y) ∈ t')⟩ => ⟨y, h₁, ht'_symm h₂⟩
@@ -548,17 +548,17 @@ theorem totallyBounded_iff_filter {s : Set α} :
     contrapose! H with hd_cover
     set f := ⨅ t : Finset α, 𝓟 (s \ ⋃ y ∈ t, { x | (x, y) ∈ d })
     have : Filter.NeBot f := by
-      refine' infᵢ_neBot_of_directed' (directed_of_sup _) _
+      refine' iInf_neBot_of_directed' (directed_of_sup _) _
       · intro t₁ t₂ h
-        exact principal_mono.2 (diff_subset_diff_right <| bunionᵢ_subset_bunionᵢ_left h)
+        exact principal_mono.2 (diff_subset_diff_right <| biUnion_subset_biUnion_left h)
       · intro t
         simpa [nonempty_diff] using hd_cover t t.finite_toSet
-    have : f ≤ 𝓟 s := infᵢ_le_of_le ∅ (by simp)
+    have : f ≤ 𝓟 s := iInf_le_of_le ∅ (by simp)
     refine' ⟨f, ‹_›, ‹_›, fun c hcf hc => _⟩
     rcases mem_prod_same_iff.1 (hc.2 hd) with ⟨m, hm, hmd⟩
     rcases hc.1.nonempty_of_mem hm with ⟨y, hym⟩
     set ys := ⋃ y' ∈ ({y} : Finset α), { x | (x, y') ∈ d }
-    have : c ≤ 𝓟 (s \ ys) := hcf.trans (infᵢ_le_of_le {y} le_rfl)
+    have : c ≤ 𝓟 (s \ ys) := hcf.trans (iInf_le_of_le {y} le_rfl)
     refine' hc.1.ne (empty_mem_iff_bot.mp _)
     filter_upwards [le_principal_iff.1 this, hm]
     refine' fun x hx hxm => hx.2 _
@@ -611,9 +611,9 @@ theorem CauchySeq.totallyBounded_range {s : ℕ → α} (hs : CauchySeq s) :
   refine' totallyBounded_iff_subset.2 fun a ha => _
   cases' cauchySeq_iff.1 hs a ha with n hn
   refine' ⟨s '' { k | k ≤ n }, image_subset_range _ _, (finite_le_nat _).image _, _⟩
-  rw [range_subset_iff, bunionᵢ_image]
+  rw [range_subset_iff, biUnion_image]
   intro m
-  rw [mem_unionᵢ₂]
+  rw [mem_iUnion₂]
   cases' le_total m n with hm hm
   exacts [⟨m, hm, refl_mem_uniformity ha⟩, ⟨n, le_refl n, hn m hm n le_rfl⟩]
 #align cauchy_seq.totally_bounded_range CauchySeq.totallyBounded_range
@@ -654,15 +654,15 @@ def setSeq (n : ℕ) : Set α :=
 #align sequentially_complete.set_seq SequentiallyComplete.setSeq
 
 theorem setSeq_mem (n : ℕ) : setSeq hf U_mem n ∈ f :=
-  (binterᵢ_mem (finite_le_nat n)).2 fun m _ => (setSeqAux hf U_mem m).2.1
+  (biInter_mem (finite_le_nat n)).2 fun m _ => (setSeqAux hf U_mem m).2.1
 #align sequentially_complete.set_seq_mem SequentiallyComplete.setSeq_mem
 
 theorem setSeq_mono ⦃m n : ℕ⦄ (h : m ≤ n) : setSeq hf U_mem n ⊆ setSeq hf U_mem m :=
-  binterᵢ_subset_binterᵢ_left <| Iic_subset_Iic.2 h
+  biInter_subset_biInter_left <| Iic_subset_Iic.2 h
 #align sequentially_complete.set_seq_mono SequentiallyComplete.setSeq_mono
 
 theorem setSeq_sub_aux (n : ℕ) : setSeq hf U_mem n ⊆ setSeqAux hf U_mem n :=
-  binterᵢ_subset_of_mem right_mem_Iic
+  biInter_subset_of_mem right_mem_Iic
 #align sequentially_complete.set_seq_sub_aux SequentiallyComplete.setSeq_sub_aux
 
 theorem setSeq_prod_subset {N m n} (hm : N ≤ m) (hn : N ≤ n) :
@@ -758,13 +758,13 @@ theorem secondCountable_of_separable [SeparableSpace α] : SecondCountableTopolo
       h_basis : (𝓤 α).HasAntitoneBasis t⟩ :=
     (@uniformity_hasBasis_open_symmetric α _).exists_antitone_subbasis
   choose ht_mem hto hts using hto
-  refine' ⟨⟨⋃ x ∈ s, range fun k => ball x (t k), hsc.bunionᵢ fun x _ => countable_range _, _⟩⟩
+  refine' ⟨⟨⋃ x ∈ s, range fun k => ball x (t k), hsc.biUnion fun x _ => countable_range _, _⟩⟩
   refine' (isTopologicalBasis_of_open_of_nhds _ _).eq_generateFrom
-  · simp only [mem_unionᵢ₂, mem_range]
+  · simp only [mem_iUnion₂, mem_range]
     rintro _ ⟨x, _, k, rfl⟩
     exact isOpen_ball x (hto k)
   · intro x V hxV hVo
-    simp only [mem_unionᵢ₂, mem_range, exists_prop]
+    simp only [mem_iUnion₂, mem_range, exists_prop]
     rcases UniformSpace.mem_nhds_iff.1 (IsOpen.mem_nhds hVo hxV) with ⟨U, hU, hUV⟩
     rcases comp_symm_of_uniformity hU with ⟨U', hU', _, hUU'⟩
     rcases h_basis.toHasBasis.mem_iff.1 hU' with ⟨k, -, hk⟩

This PR puts, with one exception, every single remaining by that lies all by itself on its own line to the previous line, thus matching the current behaviour of start-port.sh. The exception is when the by begins the second or later argument to a tuple or anonymous constructor; see https://github.com/leanprover-community/mathlib4/pull/3825#discussion_r1186702599.

Essentially this is s/\n *by$/ by/g, but with manual editing to satisfy the linter's max-100-char-line requirement. The Python style linter is also modified to catch these "isolated bys".

@@ -267,9 +267,8 @@ theorem CauchySeq.subseq_mem {V : ℕ → Set (α × α)} (hV : ∀ n, V n ∈ 
 #align cauchy_seq.subseq_mem CauchySeq.subseq_mem
 
 theorem Filter.Tendsto.subseq_mem_entourage {V : ℕ → Set (α × α)} (hV : ∀ n, V n ∈ 𝓤 α) {u : ℕ → α}
-    {a : α} (hu : Tendsto u atTop (𝓝 a)) :
-    ∃ φ : ℕ → ℕ, StrictMono φ ∧ (u (φ 0), a) ∈ V 0 ∧ ∀ n, (u <| φ (n + 1), u <| φ n) ∈ V (n + 1) :=
-  by
+    {a : α} (hu : Tendsto u atTop (𝓝 a)) : ∃ φ : ℕ → ℕ, StrictMono φ ∧ (u (φ 0), a) ∈ V 0 ∧
+      ∀ n, (u <| φ (n + 1), u <| φ n) ∈ V (n + 1) := by
   rcases mem_atTop_sets.1 (hu (ball_mem_nhds a (symm_le_uniformity <| hV 0))) with ⟨n, hn⟩
   rcases (hu.comp (tendsto_add_atTop_nat n)).cauchySeq.subseq_mem fun n => hV (n + 1) with
     ⟨φ, φ_mono, hφV⟩

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Johannes Hölzl, Mario Carneiro
 
 ! This file was ported from Lean 3 source module topology.uniform_space.cauchy
-! leanprover-community/mathlib commit d90e4e186f1d18e375dcd4e5b5f6364b01cb3e46
+! leanprover-community/mathlib commit 22131150f88a2d125713ffa0f4693e3355b1eb49
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathlib.Topology.Algebra.Constructions
 import Mathlib.Topology.Bases
 import Mathlib.Topology.UniformSpace.Basic
 
@@ -387,6 +388,15 @@ instance CompleteSpace.prod [UniformSpace β] [CompleteSpace α] [CompleteSpace
       exact Filter.le_lift.2 fun s hs => Filter.le_lift'.2 fun t ht => inter_mem (hx1 hs) (hx2 ht)⟩
 #align complete_space.prod CompleteSpace.prod
 
+@[to_additive]
+instance CompleteSpace.mulOpposite [CompleteSpace α] : CompleteSpace αᵐᵒᵖ where
+  complete hf :=
+    MulOpposite.op_surjective.exists.mpr <|
+      let ⟨x, hx⟩ := CompleteSpace.complete (hf.map MulOpposite.uniformContinuous_unop)
+      ⟨x, (map_le_iff_le_comap.mp hx).trans_eq <| MulOpposite.comap_unop_nhds _⟩
+#align complete_space.mul_opposite CompleteSpace.mulOpposite
+#align complete_space.add_opposite CompleteSpace.addOpposite
+
 /-- If `univ` is complete, the space is a complete space -/
 theorem completeSpace_of_isComplete_univ (h : IsComplete (univ : Set α)) : CompleteSpace α :=
   ⟨fun hf => let ⟨x, _, hx⟩ := h _ hf ((@principal_univ α).symm ▸ le_top); ⟨x, hx⟩⟩

@@ -270,7 +270,7 @@ theorem Filter.Tendsto.subseq_mem_entourage {V : ℕ → Set (α × α)} (hV : 
     ∃ φ : ℕ → ℕ, StrictMono φ ∧ (u (φ 0), a) ∈ V 0 ∧ ∀ n, (u <| φ (n + 1), u <| φ n) ∈ V (n + 1) :=
   by
   rcases mem_atTop_sets.1 (hu (ball_mem_nhds a (symm_le_uniformity <| hV 0))) with ⟨n, hn⟩
-  rcases(hu.comp (tendsto_add_atTop_nat n)).cauchySeq.subseq_mem fun n => hV (n + 1) with
+  rcases (hu.comp (tendsto_add_atTop_nat n)).cauchySeq.subseq_mem fun n => hV (n + 1) with
     ⟨φ, φ_mono, hφV⟩
   exact ⟨fun k => φ k + n, φ_mono.add_const _, hn _ le_add_self, hφV⟩
 #align filter.tendsto.subseq_mem_entourage Filter.Tendsto.subseq_mem_entourage
@@ -533,7 +533,7 @@ theorem Ultrafilter.cauchy_of_totallyBounded {s : Set α} (f : Ultrafilter α) (
 theorem totallyBounded_iff_filter {s : Set α} :
     TotallyBounded s ↔ ∀ f, NeBot f → f ≤ 𝓟 s → ∃ c ≤ f, Cauchy c := by
   constructor
-  · exact fun  H f hf hfs => ⟨Ultrafilter.of f, Ultrafilter.of_le f,
+  · exact fun H f hf hfs => ⟨Ultrafilter.of f, Ultrafilter.of_le f,
       (Ultrafilter.of f).cauchy_of_totallyBounded H ((Ultrafilter.of_le f).trans hfs)⟩
   · intro H d hd
     contrapose! H with hd_cover
@@ -597,8 +597,8 @@ theorem isCompact_of_totallyBounded_isClosed [CompleteSpace α] {s : Set α} (ht
 #align is_compact_of_totally_bounded_is_closed isCompact_of_totallyBounded_isClosed
 
 /-- Every Cauchy sequence over `ℕ` is totally bounded. -/
-theorem CauchySeq.totallyBounded_range {s : ℕ → α} (hs : CauchySeq s) : TotallyBounded (range s) :=
-  by
+theorem CauchySeq.totallyBounded_range {s : ℕ → α} (hs : CauchySeq s) :
+    TotallyBounded (range s) := by
   refine' totallyBounded_iff_subset.2 fun a ha => _
   cases' cauchySeq_iff.1 hs a ha with n hn
   refine' ⟨s '' { k | k ≤ n }, image_subset_range _ _, (finite_le_nat _).image _, _⟩
@@ -606,7 +606,7 @@ theorem CauchySeq.totallyBounded_range {s : ℕ → α} (hs : CauchySeq s) : Tot
   intro m
   rw [mem_unionᵢ₂]
   cases' le_total m n with hm hm
-  exacts[⟨m, hm, refl_mem_uniformity ha⟩, ⟨n, le_refl n, hn m hm n le_rfl⟩]
+  exacts [⟨m, hm, refl_mem_uniformity ha⟩, ⟨n, le_refl n, hn m hm n le_rfl⟩]
 #align cauchy_seq.totally_bounded_range CauchySeq.totallyBounded_range
 
 /-!

@@ -126,8 +126,7 @@ theorem le_nhds_of_cauchy_adhp {f : Filter α} {x : α} (hf : Cauchy f) (adhs :
     f ≤ 𝓝 x :=
   le_nhds_of_cauchy_adhp_aux
     (fun s hs => by
-      obtain ⟨t, t_mem, ht⟩ : ∃ t ∈ f, t ×ˢ t ⊆ s
-      exact (cauchy_iff.1 hf).2 s hs
+      obtain ⟨t, t_mem, ht⟩ : ∃ t ∈ f, t ×ˢ t ⊆ s := (cauchy_iff.1 hf).2 s hs
       use t, t_mem, ht
       exact forall_mem_nonempty_iff_neBot.2 adhs _ (inter_mem_inf (mem_nhds_left x hs) t_mem))
 #align le_nhds_of_cauchy_adhp le_nhds_of_cauchy_adhp
@@ -743,7 +742,7 @@ one obtains a countable basis by taking the balls centered at points in a dense
 and with rational "radii" from a countable open symmetric antitone basis of `𝓤 α`. We do not
 register this as an instance, as there is already an instance going in the other direction
 from second countable spaces to separable spaces, and we want to avoid loops. -/
-theorem second_countable_of_separable [SeparableSpace α] : SecondCountableTopology α := by
+theorem secondCountable_of_separable [SeparableSpace α] : SecondCountableTopology α := by
   rcases exists_countable_dense α with ⟨s, hsc, hsd⟩
   obtain
     ⟨t : ℕ → Set (α × α), hto : ∀ i : ℕ, t i ∈ (𝓤 α).sets ∧ IsOpen (t i) ∧ SymmetricRel (t i),
@@ -765,6 +764,6 @@ theorem second_countable_of_separable [SeparableSpace α] : SecondCountableTopol
       ⟨y, hxy, hys⟩
     refine' ⟨_, ⟨y, hys, k, rfl⟩, (hts k).subset hxy, fun z hz => _⟩
     exact hUV (ball_subset_of_comp_subset (hk hxy) hUU' (hk hz))
-#align uniform_space.second_countable_of_separable UniformSpace.second_countable_of_separable
+#align uniform_space.second_countable_of_separable UniformSpace.secondCountable_of_separable
 
 end UniformSpace

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