topology.metric_space.emetric_space ⟷ Mathlib.Topology.EMetricSpace.Basic

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

@@ -1179,7 +1179,7 @@ theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α)
 theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s) :=
   eq_of_forall_ge_iff fun d => by
     simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, iSup_le_iff,
-      zero_le, true_and_iff, forall_and, and_self_iff, ← and_assoc']
+      zero_le, true_and_iff, forall_and, and_self_iff, ← and_assoc]
 #align emetric.diam_insert EMetric.diam_insert
 -/
 

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

@@ -307,7 +307,7 @@ theorem uniformity_basis_edist_nnreal_le :
 #print uniformity_basis_edist_inv_nat /-
 theorem uniformity_basis_edist_inv_nat :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => {p : α × α | edist p.1 p.2 < (↑n)⁻¹} :=
-  EMetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun ε ε₀ =>
+  EMetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.natCast_ne_top n) fun ε ε₀ =>
     let ⟨n, hn⟩ := ENNReal.exists_inv_nat_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_nat

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 -/
 import Data.Nat.Interval
-import Data.Real.Ennreal
+import Data.ENNReal.Basic
 import Topology.UniformSpace.Pi
 import Topology.UniformSpace.UniformConvergence
 import Topology.UniformSpace.UniformEmbedding
@@ -335,7 +335,7 @@ namespace Emetric
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection {a b «expr ∈ » s} -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection {a b «expr ∈ » s} -/
 #print EMetric.uniformContinuousOn_iff /-
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
@@ -377,7 +377,7 @@ theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
 #align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbedding
 -/
 
-/- ./././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 EMetric.cauchy_iff /-
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
@@ -955,7 +955,7 @@ theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
 #align emetric.inseparable_iff EMetric.inseparable_iff
 -/
 
-/- ./././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 EMetric.cauchySeq_iff /-
 -- see Note [nolint_ge]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
@@ -994,7 +994,7 @@ theorem totallyBounded_iff {s : Set α} :
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
 -/
 
-/- ./././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 EMetric.totallyBounded_iff' /-
 theorem totallyBounded_iff' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
@@ -1007,7 +1007,7 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
-/- ./././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 EMetric.subset_countable_closure_of_almost_dense_set /-
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
@@ -1042,7 +1042,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 -/
 
-/- ./././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 EMetric.subset_countable_closure_of_compact /-
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
@@ -1440,7 +1440,7 @@ end Pi
 
 namespace Emetric
 
-/- ./././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 EMetric.countable_closure_of_compact /-
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :

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

@@ -125,7 +125,7 @@ theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y
   apply le_antisymm
   · rw [← zero_add (edist y z), ← h]
     apply edist_triangle
-  · rw [edist_comm] at h 
+  · rw [edist_comm] at h
     rw [← zero_add (edist x z), ← h]
     apply edist_triangle
 #align edist_congr_right edist_congr_right
@@ -605,7 +605,7 @@ instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetric
       preimage_set_of_eq, comap_principal]
     rw [iInf_comm]; congr; funext ε
     rw [iInf_comm]; congr; funext εpos
-    change 0 < ε at εpos 
+    change 0 < ε at εpos
     simp [Set.ext_iff, εpos]
 #align pseudo_emetric_space_pi pseudoEMetricSpacePi
 -/
@@ -1222,7 +1222,7 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       _ ≤ diam s + (edist x y + diam t) := le_self_add
       _ = diam s + edist x y + diam t := (add_assoc _ _ _).symm
   · exact A a h'a b h'b
-  · have Z := A b h'b a h'a; rwa [edist_comm] at Z 
+  · have Z := A b h'b a h'a; rwa [edist_comm] at Z
   ·
     calc
       edist a b ≤ diam t := edist_le_diam_of_mem h'a h'b
@@ -1259,7 +1259,7 @@ theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetric
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, diam (s b) ≤ c) : diam (Set.pi univ s) ≤ c :=
   by
   apply diam_le fun x hx y hy => edist_pi_le_iff.mpr _
-  rw [mem_univ_pi] at hx hy 
+  rw [mem_univ_pi] at hx hy
   exact fun b => diam_le_iff.1 (h b) (x b) (hx b) (y b) (hy b)
 #align emetric.diam_pi_le_of_le EMetric.diam_pi_le_of_le
 -/
@@ -1314,13 +1314,13 @@ theorem eq_of_forall_edist_le {x y : γ} (h : ∀ ε > 0, edist x y ≤ ε) : x
 #align eq_of_forall_edist_le eq_of_forall_edist_le
 -/
 
-#print to_separated /-
+#print EMetricSpace.instT0Space /-
 -- see Note [lower instance priority]
 /-- An emetric space is separated -/
-instance (priority := 100) to_separated : SeparatedSpace γ :=
-  separated_def.2 fun x y h =>
+instance (priority := 100) EMetricSpace.instT0Space : T0Space γ :=
+  t0Space_iff_uniformity.2 fun x y h =>
     eq_of_forall_edist_le fun ε ε0 => le_of_lt (h _ (edist_mem_uniformity ε0))
-#align to_separated to_separated
+#align to_separated EMetricSpace.instT0Space
 -/
 
 #print EMetric.uniformEmbedding_iff' /-
@@ -1431,7 +1431,7 @@ instance emetricSpacePi [∀ b, EMetricSpace (π b)] : EMetricSpace (∀ b, π b
     eq_of_edist_eq_zero := fun f g eq0 =>
       by
       have eq1 : (sup univ fun b : β => edist (f b) (g b)) ≤ 0 := le_of_eq eq0
-      simp only [Finset.sup_le_iff] at eq1 
+      simp only [Finset.sup_le_iff] at eq1
       exact funext fun b => edist_le_zero.1 <| eq1 b <| mem_univ b }
 #align emetric_space_pi emetricSpacePi
 -/
@@ -1476,25 +1476,25 @@ end Emetric
 -/
 
 
-instance [PseudoEMetricSpace X] : EDist (UniformSpace.SeparationQuotient X) :=
+instance [PseudoEMetricSpace X] : EDist (SeparationQuotient X) :=
   ⟨fun x y =>
     Quotient.liftOn₂' x y edist fun x y x' y' hx hy =>
       calc
         edist x y = edist x' y :=
-          edist_congr_right <| EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx
+          edist_congr_right <| EMetric.inseparable_iff.1 <| inseparable_iff_inseparable.1 hx
         _ = edist x' y' :=
-          edist_congr_left <| EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy⟩
+          edist_congr_left <| EMetric.inseparable_iff.1 <| inseparable_iff_inseparable.1 hy⟩
 
-#print UniformSpace.SeparationQuotient.edist_mk /-
+#print SeparationQuotient.edist_mk /-
 @[simp]
-theorem UniformSpace.SeparationQuotient.edist_mk [PseudoEMetricSpace X] (x y : X) :
-    @edist (UniformSpace.SeparationQuotient X) _ (Quot.mk _ x) (Quot.mk _ y) = edist x y :=
+theorem SeparationQuotient.edist_mk [PseudoEMetricSpace X] (x y : X) :
+    @edist (SeparationQuotient X) _ (Quot.mk _ x) (Quot.mk _ y) = edist x y :=
   rfl
-#align uniform_space.separation_quotient.edist_mk UniformSpace.SeparationQuotient.edist_mk
+#align uniform_space.separation_quotient.edist_mk SeparationQuotient.edist_mk
 -/
 
-instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient X) :=
-  @EMetricSpace.ofT0PseudoEMetricSpace (UniformSpace.SeparationQuotient X)
+instance [PseudoEMetricSpace X] : EMetricSpace (SeparationQuotient X) :=
+  @EMetricSpace.ofT0PseudoEMetricSpace (SeparationQuotient X)
     { edist_self := fun x => Quotient.inductionOn' x edist_self
       edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm
       edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle
@@ -1508,7 +1508,7 @@ instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient
                   ext ⟨⟨x⟩, ⟨y⟩⟩
                   refine' ⟨_, fun h => ⟨(x, y), h, rfl⟩⟩
                   rintro ⟨⟨x', y'⟩, h', h⟩
-                  simp only [Prod.ext_iff] at h 
+                  simp only [Prod.ext_iff] at h
                   rwa [← h.1, ← h.2]) }
     _
 

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

@@ -1161,11 +1161,13 @@ theorem diam_singleton : diam ({x} : Set α) = 0 :=
 #align emetric.diam_singleton EMetric.diam_singleton
 -/
 
+#print EMetric.diam_one /-
 @[simp, to_additive]
 theorem diam_one [One α] : diam (1 : Set α) = 0 :=
   diam_singleton
-#align emetric.diam_one Emetric.diam_one
-#align emetric.diam_zero Emetric.diam_zero
+#align emetric.diam_one EMetric.diam_one
+#align emetric.diam_zero EMetric.diam_zero
+-/
 
 #print EMetric.diam_iUnion_mem_option /-
 theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/b1abe23ae96fef89ad30d9f4362c307f72a55010

@@ -1461,7 +1461,7 @@ theorem diam_eq_zero_iff : diam s = 0 ↔ s.Subsingleton :=
 
 #print EMetric.diam_pos_iff' /-
 theorem diam_pos_iff' : 0 < diam s ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y := by
-  simp only [pos_iff_ne_zero, Ne.def, diam_eq_zero_iff, Set.Subsingleton, not_forall]
+  simp only [pos_iff_ne_zero, Ne.def, diam_eq_zero_iff, Set.Subsingleton, Classical.not_forall]
 #align emetric.diam_pos_iff EMetric.diam_pos_iff'
 -/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c8f305514e0d47dfaa710f5a52f0d21b588e6328

@@ -9,7 +9,7 @@ import Topology.UniformSpace.Pi
 import Topology.UniformSpace.UniformConvergence
 import Topology.UniformSpace.UniformEmbedding
 
-#align_import topology.metric_space.emetric_space from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+#align_import topology.metric_space.emetric_space from "leanprover-community/mathlib"@"c8f305514e0d47dfaa710f5a52f0d21b588e6328"
 
 /-!
 # Extended metric spaces
@@ -35,7 +35,7 @@ to `emetric_space` at the end.
 
 open Set Filter Classical
 
-open scoped uniformity Topology BigOperators Filter NNReal ENNReal
+open scoped uniformity Topology BigOperators Filter NNReal ENNReal Pointwise
 
 universe u v w
 
@@ -1161,6 +1161,12 @@ theorem diam_singleton : diam ({x} : Set α) = 0 :=
 #align emetric.diam_singleton EMetric.diam_singleton
 -/
 
+@[simp, to_additive]
+theorem diam_one [One α] : diam (1 : Set α) = 0 :=
+  diam_singleton
+#align emetric.diam_one Emetric.diam_one
+#align emetric.diam_zero Emetric.diam_zero
+
 #print EMetric.diam_iUnion_mem_option /-
 theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp

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

@@ -3,11 +3,11 @@ Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 -/
-import Mathbin.Data.Nat.Interval
-import Mathbin.Data.Real.Ennreal
-import Mathbin.Topology.UniformSpace.Pi
-import Mathbin.Topology.UniformSpace.UniformConvergence
-import Mathbin.Topology.UniformSpace.UniformEmbedding
+import Data.Nat.Interval
+import Data.Real.Ennreal
+import Topology.UniformSpace.Pi
+import Topology.UniformSpace.UniformConvergence
+import Topology.UniformSpace.UniformEmbedding
 
 #align_import topology.metric_space.emetric_space from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 
@@ -335,7 +335,7 @@ namespace Emetric
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection {a b «expr ∈ » s} -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection {a b «expr ∈ » s} -/
 #print EMetric.uniformContinuousOn_iff /-
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
@@ -377,7 +377,7 @@ theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
 #align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbedding
 -/
 
-/- ./././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 EMetric.cauchy_iff /-
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
@@ -955,7 +955,7 @@ theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
 #align emetric.inseparable_iff EMetric.inseparable_iff
 -/
 
-/- ./././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 EMetric.cauchySeq_iff /-
 -- see Note [nolint_ge]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
@@ -994,7 +994,7 @@ theorem totallyBounded_iff {s : Set α} :
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
 -/
 
-/- ./././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 EMetric.totallyBounded_iff' /-
 theorem totallyBounded_iff' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
@@ -1007,7 +1007,7 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
-/- ./././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 EMetric.subset_countable_closure_of_almost_dense_set /-
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
@@ -1042,7 +1042,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 -/
 
-/- ./././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 EMetric.subset_countable_closure_of_compact /-
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
@@ -1432,7 +1432,7 @@ end Pi
 
 namespace Emetric
 
-/- ./././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 EMetric.countable_closure_of_compact /-
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :

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

@@ -204,7 +204,7 @@ theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 {p : α × α | edis
 theorem uniformSpace_edist :
     ‹PseudoEMetricSpace α›.toUniformSpace =
       uniformSpaceOfEDist edist edist_self edist_comm edist_triangle :=
-  uniformSpace_eq uniformity_pseudoedist
+  UniformSpace.ext uniformity_pseudoedist
 #align uniform_space_edist uniformSpace_edist
 -/
 

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

@@ -2,11 +2,6 @@
 Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.metric_space.emetric_space
-! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Data.Nat.Interval
 import Mathbin.Data.Real.Ennreal
@@ -14,6 +9,8 @@ import Mathbin.Topology.UniformSpace.Pi
 import Mathbin.Topology.UniformSpace.UniformConvergence
 import Mathbin.Topology.UniformSpace.UniformEmbedding
 
+#align_import topology.metric_space.emetric_space from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Extended metric spaces
 
@@ -338,7 +335,7 @@ namespace Emetric
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection {a b «expr ∈ » s} -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection {a b «expr ∈ » s} -/
 #print EMetric.uniformContinuousOn_iff /-
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
@@ -380,7 +377,7 @@ theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
 #align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbedding
 -/
 
-/- ./././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 EMetric.cauchy_iff /-
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
@@ -958,7 +955,7 @@ theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
 #align emetric.inseparable_iff EMetric.inseparable_iff
 -/
 
-/- ./././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 EMetric.cauchySeq_iff /-
 -- see Note [nolint_ge]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
@@ -997,7 +994,7 @@ theorem totallyBounded_iff {s : Set α} :
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
 -/
 
-/- ./././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 EMetric.totallyBounded_iff' /-
 theorem totallyBounded_iff' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
@@ -1010,7 +1007,7 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
-/- ./././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 EMetric.subset_countable_closure_of_almost_dense_set /-
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
@@ -1045,7 +1042,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 -/
 
-/- ./././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 EMetric.subset_countable_closure_of_compact /-
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
@@ -1435,7 +1432,7 @@ end Pi
 
 namespace Emetric
 
-/- ./././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 EMetric.countable_closure_of_compact /-
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :

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

@@ -44,6 +44,7 @@ universe u v w
 
 variable {α : Type u} {β : Type v} {X : Type _}
 
+#print uniformity_dist_of_mem_uniformity /-
 /-- Characterizing uniformities associated to a (generalized) distance function `D`
 in terms of the elements of the uniformity. -/
 theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α)} (z : β)
@@ -51,6 +52,7 @@ theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α
     U = ⨅ ε > z, 𝓟 {p : α × α | D p.1 p.2 < ε} :=
   HasBasis.eq_biInf ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_set_of]⟩
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
+-/
 
 #print EDist /-
 /-- `has_edist α` means that `α` is equipped with an extended distance. -/
@@ -61,6 +63,7 @@ class EDist (α : Type _) where
 
 export EDist (edist)
 
+#print uniformSpaceOfEDist /-
 /-- Creating a uniform space from an extended distance. -/
 noncomputable def uniformSpaceOfEDist (edist : α → α → ℝ≥0∞) (edist_self : ∀ x : α, edist x x = 0)
     (edist_comm : ∀ x y : α, edist x y = edist y x)
@@ -69,6 +72,7 @@ noncomputable def uniformSpaceOfEDist (edist : α → α → ℝ≥0∞) (edist_
     ⟨ε / 2, ENNReal.half_pos ε0.lt.ne', fun _ h₁ _ h₂ =>
       (ENNReal.add_lt_add h₁ h₂).trans_eq (ENNReal.add_halves _)⟩
 #align uniform_space_of_edist uniformSpaceOfEDist
+-/
 
 #print PseudoEMetricSpace /-
 -- the uniform structure is embedded in the emetric space structure
@@ -105,15 +109,20 @@ export PseudoEMetricSpace (edist_self edist_comm edist_triangle)
 
 attribute [simp] edist_self
 
+#print edist_triangle_left /-
 /-- Triangle inequality for the extended distance -/
 theorem edist_triangle_left (x y z : α) : edist x y ≤ edist z x + edist z y := by
   rw [edist_comm z] <;> apply edist_triangle
 #align edist_triangle_left edist_triangle_left
+-/
 
+#print edist_triangle_right /-
 theorem edist_triangle_right (x y z : α) : edist x y ≤ edist x z + edist y z := by
   rw [edist_comm y] <;> apply edist_triangle
 #align edist_triangle_right edist_triangle_right
+-/
 
+#print edist_congr_right /-
 theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y z :=
   by
   apply le_antisymm
@@ -123,17 +132,23 @@ theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y
     rw [← zero_add (edist x z), ← h]
     apply edist_triangle
 #align edist_congr_right edist_congr_right
+-/
 
+#print edist_congr_left /-
 theorem edist_congr_left {x y z : α} (h : edist x y = 0) : edist z x = edist z y := by
   rw [edist_comm z x, edist_comm z y]; apply edist_congr_right h
 #align edist_congr_left edist_congr_left
+-/
 
+#print edist_triangle4 /-
 theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + edist z t :=
   calc
     edist x t ≤ edist x z + edist z t := edist_triangle x z t
     _ ≤ edist x y + edist y z + edist z t := add_le_add_right (edist_triangle x y z) _
 #align edist_triangle4 edist_triangle4
+-/
 
+#print edist_le_Ico_sum_edist /-
 /-- The triangle (polygon) inequality for sequences of points; `finset.Ico` version. -/
 theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
     edist (f m) (f n) ≤ ∑ i in Finset.Ico m n, edist (f i) (f (i + 1)) :=
@@ -150,13 +165,17 @@ theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
       _ = ∑ i in Finset.Ico m (n + 1), _ := by
         rw [Nat.Ico_succ_right_eq_insert_Ico hn, Finset.sum_insert, add_comm] <;> simp
 #align edist_le_Ico_sum_edist edist_le_Ico_sum_edist
+-/
 
+#print edist_le_range_sum_edist /-
 /-- The triangle (polygon) inequality for sequences of points; `finset.range` version. -/
 theorem edist_le_range_sum_edist (f : ℕ → α) (n : ℕ) :
     edist (f 0) (f n) ≤ ∑ i in Finset.range n, edist (f i) (f (i + 1)) :=
   Nat.Ico_zero_eq_range ▸ edist_le_Ico_sum_edist f (Nat.zero_le n)
 #align edist_le_range_sum_edist edist_le_range_sum_edist
+-/
 
+#print edist_le_Ico_sum_of_edist_le /-
 /-- A version of `edist_le_Ico_sum_edist` with each intermediate distance replaced
 with an upper estimate. -/
 theorem edist_le_Ico_sum_of_edist_le {f : ℕ → α} {m n} (hmn : m ≤ n) {d : ℕ → ℝ≥0∞}
@@ -165,7 +184,9 @@ theorem edist_le_Ico_sum_of_edist_le {f : ℕ → α} {m n} (hmn : m ≤ n) {d :
   le_trans (edist_le_Ico_sum_edist f hmn) <|
     Finset.sum_le_sum fun k hk => hd (Finset.mem_Ico.1 hk).1 (Finset.mem_Ico.1 hk).2
 #align edist_le_Ico_sum_of_edist_le edist_le_Ico_sum_of_edist_le
+-/
 
+#print edist_le_range_sum_of_edist_le /-
 /-- A version of `edist_le_range_sum_edist` with each intermediate distance replaced
 with an upper estimate. -/
 theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → ℝ≥0∞}
@@ -173,11 +194,14 @@ theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → 
     edist (f 0) (f n) ≤ ∑ i in Finset.range n, d i :=
   Nat.Ico_zero_eq_range ▸ edist_le_Ico_sum_of_edist_le (zero_le n) fun _ _ => hd
 #align edist_le_range_sum_of_edist_le edist_le_range_sum_of_edist_le
+-/
 
+#print uniformity_pseudoedist /-
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 {p : α × α | edist p.1 p.2 < ε} :=
   PseudoEMetricSpace.uniformity_edist
 #align uniformity_pseudoedist uniformity_pseudoedist
+-/
 
 #print uniformSpace_edist /-
 theorem uniformSpace_edist :
@@ -187,17 +211,22 @@ theorem uniformSpace_edist :
 #align uniform_space_edist uniformSpace_edist
 -/
 
+#print uniformity_basis_edist /-
 theorem uniformity_basis_edist :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 < ε} :=
   (@uniformSpace_edist α _).symm ▸ UniformSpace.hasBasis_ofFun ⟨1, one_pos⟩ _ _ _ _ _
 #align uniformity_basis_edist uniformity_basis_edist
+-/
 
+#print mem_uniformity_edist /-
 /-- Characterization of the elements of the uniformity in terms of the extended distance -/
 theorem mem_uniformity_edist {s : Set (α × α)} :
     s ∈ 𝓤 α ↔ ∃ ε > 0, ∀ {a b : α}, edist a b < ε → (a, b) ∈ s :=
   uniformity_basis_edist.mem_uniformity_iff
 #align mem_uniformity_edist mem_uniformity_edist
+-/
 
+#print EMetric.mk_uniformity_basis /-
 /-- Given `f : β → ℝ≥0∞`, if `f` sends `{i | p i}` to a set of positive numbers
 accumulating to zero, then `f i`-neighborhoods of the diagonal form a basis of `𝓤 α`.
 
@@ -214,7 +243,9 @@ protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f
     exact ⟨i, hi, fun x hx => hε <| lt_of_lt_of_le hx H⟩
   · exact fun ⟨i, hi, H⟩ => ⟨f i, hf₀ i hi, H⟩
 #align emetric.mk_uniformity_basis EMetric.mk_uniformity_basis
+-/
 
+#print EMetric.mk_uniformity_basis_le /-
 /-- Given `f : β → ℝ≥0∞`, if `f` sends `{i | p i}` to a set of positive numbers
 accumulating to zero, then closed `f i`-neighborhoods of the diagonal form a basis of `𝓤 α`.
 
@@ -231,47 +262,61 @@ protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop}
     exact ⟨i, hi, fun x hx => hε <| lt_of_le_of_lt (le_trans hx H) hε'.2⟩
   · exact fun ⟨i, hi, H⟩ => ⟨f i, hf₀ i hi, fun x hx => H (le_of_lt hx)⟩
 #align emetric.mk_uniformity_basis_le EMetric.mk_uniformity_basis_le
+-/
 
+#print uniformity_basis_edist_le /-
 theorem uniformity_basis_edist_le :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 ≤ ε} :=
   EMetric.mk_uniformity_basis_le (fun _ => id) fun ε ε₀ => ⟨ε, ε₀, le_refl ε⟩
 #align uniformity_basis_edist_le uniformity_basis_edist_le
+-/
 
+#print uniformity_basis_edist' /-
 theorem uniformity_basis_edist' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => {p : α × α | edist p.1 p.2 < ε} :=
   EMetric.mk_uniformity_basis (fun _ => And.left) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := exists_between hε'
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist' uniformity_basis_edist'
+-/
 
+#print uniformity_basis_edist_le' /-
 theorem uniformity_basis_edist_le' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => {p : α × α | edist p.1 p.2 ≤ ε} :=
   EMetric.mk_uniformity_basis_le (fun _ => And.left) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := exists_between hε'
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist_le' uniformity_basis_edist_le'
+-/
 
+#print uniformity_basis_edist_nnreal /-
 theorem uniformity_basis_edist_nnreal :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 < ε} :=
   EMetric.mk_uniformity_basis (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal uniformity_basis_edist_nnreal
+-/
 
+#print uniformity_basis_edist_nnreal_le /-
 theorem uniformity_basis_edist_nnreal_le :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 ≤ ε} :=
   EMetric.mk_uniformity_basis_le (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nnreal_le
+-/
 
+#print uniformity_basis_edist_inv_nat /-
 theorem uniformity_basis_edist_inv_nat :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => {p : α × α | edist p.1 p.2 < (↑n)⁻¹} :=
   EMetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun ε ε₀ =>
     let ⟨n, hn⟩ := ENNReal.exists_inv_nat_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_nat
+-/
 
+#print uniformity_basis_edist_inv_two_pow /-
 theorem uniformity_basis_edist_inv_two_pow :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => {p : α × α | edist p.1 p.2 < 2⁻¹ ^ n} :=
   EMetric.mk_uniformity_basis (fun n _ => ENNReal.pow_pos (ENNReal.inv_pos.2 ENNReal.two_ne_top) _)
@@ -279,11 +324,14 @@ theorem uniformity_basis_edist_inv_two_pow :
     let ⟨n, hn⟩ := ENNReal.exists_inv_two_pow_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_pow
+-/
 
+#print edist_mem_uniformity /-
 /-- Fixed size neighborhoods of the diagonal belong to the uniform structure -/
 theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : {p : α × α | edist p.1 p.2 < ε} ∈ 𝓤 α :=
   mem_uniformity_edist.2 ⟨ε, ε0, fun a b => id⟩
 #align edist_mem_uniformity edist_mem_uniformity
+-/
 
 namespace Emetric
 
@@ -291,19 +339,24 @@ instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection {a b «expr ∈ » s} -/
+#print EMetric.uniformContinuousOn_iff /-
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
     UniformContinuousOn f s ↔
       ∀ ε > 0, ∃ δ > 0, ∀ {a} {_ : a ∈ s} {b} {_ : b ∈ s}, edist a b < δ → edist (f a) (f b) < ε :=
   uniformity_basis_edist.uniformContinuousOn_iff uniformity_basis_edist
 #align emetric.uniform_continuous_on_iff EMetric.uniformContinuousOn_iff
+-/
 
+#print EMetric.uniformContinuous_iff /-
 /-- ε-δ characterization of uniform continuity on pseudoemetric spaces -/
 theorem uniformContinuous_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformContinuous f ↔ ∀ ε > 0, ∃ δ > 0, ∀ {a b : α}, edist a b < δ → edist (f a) (f b) < ε :=
   uniformity_basis_edist.uniformContinuous_iff uniformity_basis_edist
 #align emetric.uniform_continuous_iff EMetric.uniformContinuous_iff
+-/
 
+#print EMetric.uniformEmbedding_iff /-
 /-- ε-δ characterization of uniform embeddings on pseudoemetric spaces -/
 theorem uniformEmbedding_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformEmbedding f ↔
@@ -314,7 +367,9 @@ theorem uniformEmbedding_iff [PseudoEMetricSpace β] {f : α → β} :
   simp only [uniformity_basis_edist.uniform_embedding_iff uniformity_basis_edist, exists_prop]
   rfl
 #align emetric.uniform_embedding_iff EMetric.uniformEmbedding_iff
+-/
 
+#print EMetric.controlled_of_uniformEmbedding /-
 /-- If a map between pseudoemetric spaces is a uniform embedding then the edistance between `f x`
 and `f y` is controlled in terms of the distance between `x` and `y`. -/
 theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
@@ -323,14 +378,18 @@ theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
         ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, edist (f a) (f b) < ε → edist a b < δ :=
   fun h => ⟨uniformContinuous_iff.1 (uniformEmbedding_iff.1 h).2.1, (uniformEmbedding_iff.1 h).2.2⟩
 #align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbedding
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (x y «expr ∈ » t) -/
+#print EMetric.cauchy_iff /-
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
     Cauchy f ↔ f ≠ ⊥ ∧ ∀ ε > 0, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), edist x y < ε := by
   rw [← ne_bot_iff] <;> exact uniformity_basis_edist.cauchy_iff
 #align emetric.cauchy_iff EMetric.cauchy_iff
+-/
 
+#print EMetric.complete_of_convergent_controlled_sequences /-
 /-- A very useful criterion to show that a space is complete is to show that all sequences
 which satisfy a bound of the form `edist (u n) (u m) < B N` for all `n m ≥ N` are
 converging. This is often applied for `B N = 2^{-N}`, i.e., with a very fast convergence to
@@ -344,6 +403,7 @@ theorem complete_of_convergent_controlled_sequences (B : ℕ → ℝ≥0∞) (hB
   UniformSpace.complete_of_convergent_controlled_sequences
     (fun n => {p : α × α | edist p.1 p.2 < B n}) (fun n => edist_mem_uniformity <| hB n) H
 #align emetric.complete_of_convergent_controlled_sequences EMetric.complete_of_convergent_controlled_sequences
+-/
 
 #print EMetric.complete_of_cauchySeq_tendsto /-
 /-- A sequentially complete pseudoemetric space is complete. -/
@@ -353,6 +413,7 @@ theorem complete_of_cauchySeq_tendsto :
 #align emetric.complete_of_cauchy_seq_tendsto EMetric.complete_of_cauchySeq_tendsto
 -/
 
+#print EMetric.tendstoLocallyUniformlyOn_iff /-
 /-- Expressing locally uniform convergence on a set using `edist`. -/
 theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} {s : Set β} :
@@ -364,7 +425,9 @@ theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : 
   rcases H ε εpos x hx with ⟨t, ht, Ht⟩
   exact ⟨t, ht, Ht.mono fun n hs x hx => hε (hs x hx)⟩
 #align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iff
+-/
 
+#print EMetric.tendstoUniformlyOn_iff /-
 /-- Expressing uniform convergence on a set using `edist`. -/
 theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} {s : Set β} :
     TendstoUniformlyOn F f p s ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x ∈ s, edist (f x) (F n x) < ε :=
@@ -373,7 +436,9 @@ theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β →
   rcases mem_uniformity_edist.1 hu with ⟨ε, εpos, hε⟩
   exact (H ε εpos).mono fun n hs x hx => hε (hs x hx)
 #align emetric.tendsto_uniformly_on_iff EMetric.tendstoUniformlyOn_iff
+-/
 
+#print EMetric.tendstoLocallyUniformly_iff /-
 /-- Expressing locally uniform convergence using `edist`. -/
 theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} :
@@ -383,12 +448,15 @@ theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι
   simp only [← tendstoLocallyUniformlyOn_univ, tendsto_locally_uniformly_on_iff, mem_univ,
     forall_const, exists_prop, nhdsWithin_univ]
 #align emetric.tendsto_locally_uniformly_iff EMetric.tendstoLocallyUniformly_iff
+-/
 
+#print EMetric.tendstoUniformly_iff /-
 /-- Expressing uniform convergence using `edist`. -/
 theorem tendstoUniformly_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} :
     TendstoUniformly F f p ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x, edist (f x) (F n x) < ε := by
   simp only [← tendstoUniformlyOn_univ, tendsto_uniformly_on_iff, mem_univ, forall_const]
 #align emetric.tendsto_uniformly_iff EMetric.tendstoUniformly_iff
+-/
 
 end Emetric
 
@@ -468,14 +536,18 @@ section ULift
 instance : PseudoEMetricSpace (ULift α) :=
   PseudoEMetricSpace.induced ULift.down ‹_›
 
+#print ULift.edist_eq /-
 theorem ULift.edist_eq (x y : ULift α) : edist x y = edist x.down y.down :=
   rfl
 #align ulift.edist_eq ULift.edist_eq
+-/
 
+#print ULift.edist_up_up /-
 @[simp]
 theorem ULift.edist_up_up (x y : α) : edist (ULift.up x) (ULift.up y) = edist x y :=
   rfl
 #align ulift.edist_up_up ULift.edist_up_up
+-/
 
 end ULift
 
@@ -501,10 +573,12 @@ instance Prod.pseudoEMetricSpaceMax [PseudoEMetricSpace β] : PseudoEMetricSpace
 #align prod.pseudo_emetric_space_max Prod.pseudoEMetricSpaceMax
 -/
 
+#print Prod.edist_eq /-
 theorem Prod.edist_eq [PseudoEMetricSpace β] (x y : α × β) :
     edist x y = max (edist x.1 y.1) (edist x.2 y.2) :=
   rfl
 #align prod.edist_eq Prod.edist_eq
+-/
 
 section Pi
 
@@ -539,24 +613,32 @@ instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetric
 #align pseudo_emetric_space_pi pseudoEMetricSpacePi
 -/
 
+#print edist_pi_def /-
 theorem edist_pi_def [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b) :
     edist f g = Finset.sup univ fun b => edist (f b) (g b) :=
   rfl
 #align edist_pi_def edist_pi_def
+-/
 
+#print edist_le_pi_edist /-
 theorem edist_le_pi_edist [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b) (b : β) :
     edist (f b) (g b) ≤ edist f g :=
   Finset.le_sup (Finset.mem_univ b)
 #align edist_le_pi_edist edist_le_pi_edist
+-/
 
+#print edist_pi_le_iff /-
 theorem edist_pi_le_iff [∀ b, PseudoEMetricSpace (π b)] {f g : ∀ b, π b} {d : ℝ≥0∞} :
     edist f g ≤ d ↔ ∀ b, edist (f b) (g b) ≤ d :=
   Finset.sup_le_iff.trans <| by simp only [Finset.mem_univ, forall_const]
 #align edist_pi_le_iff edist_pi_le_iff
+-/
 
+#print edist_pi_const_le /-
 theorem edist_pi_const_le (a b : α) : (edist (fun _ : β => a) fun _ => b) ≤ edist a b :=
   edist_pi_le_iff.2 fun _ => le_rfl
 #align edist_pi_const_le edist_pi_const_le
+-/
 
 #print edist_pi_const /-
 @[simp]
@@ -578,13 +660,17 @@ def ball (x : α) (ε : ℝ≥0∞) : Set α :=
 #align emetric.ball EMetric.ball
 -/
 
+#print EMetric.mem_ball /-
 @[simp]
 theorem mem_ball : y ∈ ball x ε ↔ edist y x < ε :=
   Iff.rfl
 #align emetric.mem_ball EMetric.mem_ball
+-/
 
+#print EMetric.mem_ball' /-
 theorem mem_ball' : y ∈ ball x ε ↔ edist x y < ε := by rw [edist_comm, mem_ball]
 #align emetric.mem_ball' EMetric.mem_ball'
+-/
 
 #print EMetric.closedBall /-
 /-- `emetric.closed_ball x ε` is the set of all points `y` with `edist y x ≤ ε` -/
@@ -593,31 +679,41 @@ def closedBall (x : α) (ε : ℝ≥0∞) :=
 #align emetric.closed_ball EMetric.closedBall
 -/
 
+#print EMetric.mem_closedBall /-
 @[simp]
 theorem mem_closedBall : y ∈ closedBall x ε ↔ edist y x ≤ ε :=
   Iff.rfl
 #align emetric.mem_closed_ball EMetric.mem_closedBall
+-/
 
+#print EMetric.mem_closedBall' /-
 theorem mem_closedBall' : y ∈ closedBall x ε ↔ edist x y ≤ ε := by rw [edist_comm, mem_closed_ball]
 #align emetric.mem_closed_ball' EMetric.mem_closedBall'
+-/
 
+#print EMetric.closedBall_top /-
 @[simp]
 theorem closedBall_top (x : α) : closedBall x ∞ = univ :=
   eq_univ_of_forall fun y => le_top
 #align emetric.closed_ball_top EMetric.closedBall_top
+-/
 
 #print EMetric.ball_subset_closedBall /-
 theorem ball_subset_closedBall : ball x ε ⊆ closedBall x ε := fun y hy => le_of_lt hy
 #align emetric.ball_subset_closed_ball EMetric.ball_subset_closedBall
 -/
 
+#print EMetric.pos_of_mem_ball /-
 theorem pos_of_mem_ball (hy : y ∈ ball x ε) : 0 < ε :=
   lt_of_le_of_lt (zero_le _) hy
 #align emetric.pos_of_mem_ball EMetric.pos_of_mem_ball
+-/
 
+#print EMetric.mem_ball_self /-
 theorem mem_ball_self (h : 0 < ε) : x ∈ ball x ε :=
   show edist x x < ε by rw [edist_self] <;> assumption
 #align emetric.mem_ball_self EMetric.mem_ball_self
+-/
 
 #print EMetric.mem_closedBall_self /-
 theorem mem_closedBall_self : x ∈ closedBall x ε :=
@@ -636,19 +732,26 @@ theorem mem_closedBall_comm : x ∈ closedBall y ε ↔ y ∈ closedBall x ε :=
 #align emetric.mem_closed_ball_comm EMetric.mem_closedBall_comm
 -/
 
+#print EMetric.ball_subset_ball /-
 theorem ball_subset_ball (h : ε₁ ≤ ε₂) : ball x ε₁ ⊆ ball x ε₂ := fun y (yx : _ < ε₁) =>
   lt_of_lt_of_le yx h
 #align emetric.ball_subset_ball EMetric.ball_subset_ball
+-/
 
+#print EMetric.closedBall_subset_closedBall /-
 theorem closedBall_subset_closedBall (h : ε₁ ≤ ε₂) : closedBall x ε₁ ⊆ closedBall x ε₂ :=
   fun y (yx : _ ≤ ε₁) => le_trans yx h
 #align emetric.closed_ball_subset_closed_ball EMetric.closedBall_subset_closedBall
+-/
 
+#print EMetric.ball_disjoint /-
 theorem ball_disjoint (h : ε₁ + ε₂ ≤ edist x y) : Disjoint (ball x ε₁) (ball y ε₂) :=
   Set.disjoint_left.mpr fun z h₁ h₂ =>
     (edist_triangle_left x y z).not_lt <| (ENNReal.add_lt_add h₁ h₂).trans_le h
 #align emetric.ball_disjoint EMetric.ball_disjoint
+-/
 
+#print EMetric.ball_subset /-
 theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) : ball x ε₁ ⊆ ball y ε₂ :=
   fun z zx =>
   calc
@@ -657,28 +760,37 @@ theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) :
     _ < edist x y + ε₁ := (ENNReal.add_lt_add_left h' zx)
     _ ≤ ε₂ := h
 #align emetric.ball_subset EMetric.ball_subset
+-/
 
+#print EMetric.exists_ball_subset_ball /-
 theorem exists_ball_subset_ball (h : y ∈ ball x ε) : ∃ ε' > 0, ball y ε' ⊆ ball x ε :=
   by
   have : 0 < ε - edist y x := by simpa using h
   refine' ⟨ε - edist y x, this, ball_subset _ (ne_top_of_lt h)⟩
   exact (add_tsub_cancel_of_le (mem_ball.mp h).le).le
 #align emetric.exists_ball_subset_ball EMetric.exists_ball_subset_ball
+-/
 
+#print EMetric.ball_eq_empty_iff /-
 theorem ball_eq_empty_iff : ball x ε = ∅ ↔ ε = 0 :=
   eq_empty_iff_forall_not_mem.trans
     ⟨fun h => le_bot_iff.1 (le_of_not_gt fun ε0 => h _ (mem_ball_self ε0)), fun ε0 y h =>
       not_lt_of_le (le_of_eq ε0) (pos_of_mem_ball h)⟩
 #align emetric.ball_eq_empty_iff EMetric.ball_eq_empty_iff
+-/
 
+#print EMetric.ordConnected_setOf_closedBall_subset /-
 theorem ordConnected_setOf_closedBall_subset (x : α) (s : Set α) :
     OrdConnected {r | closedBall x r ⊆ s} :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (closedBall_subset_closedBall hr.2).trans hr₂⟩
 #align emetric.ord_connected_set_of_closed_ball_subset EMetric.ordConnected_setOf_closedBall_subset
+-/
 
+#print EMetric.ordConnected_setOf_ball_subset /-
 theorem ordConnected_setOf_ball_subset (x : α) (s : Set α) : OrdConnected {r | ball x r ⊆ s} :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (ball_subset_ball hr.2).trans hr₂⟩
 #align emetric.ord_connected_set_of_ball_subset EMetric.ordConnected_setOf_ball_subset
+-/
 
 #print EMetric.edistLtTopSetoid /-
 /-- Relation “two points are at a finite edistance” is an equivalence relation. -/
@@ -690,66 +802,90 @@ def edistLtTopSetoid : Setoid α where
 #align emetric.edist_lt_top_setoid EMetric.edistLtTopSetoid
 -/
 
+#print EMetric.ball_zero /-
 @[simp]
 theorem ball_zero : ball x 0 = ∅ := by rw [EMetric.ball_eq_empty_iff]
 #align emetric.ball_zero EMetric.ball_zero
+-/
 
+#print EMetric.nhds_basis_eball /-
 theorem nhds_basis_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) (ball x) :=
   nhds_basis_uniformity uniformity_basis_edist
 #align emetric.nhds_basis_eball EMetric.nhds_basis_eball
+-/
 
+#print EMetric.nhdsWithin_basis_eball /-
 theorem nhdsWithin_basis_eball : (𝓝[s] x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => ball x ε ∩ s :=
   nhdsWithin_hasBasis nhds_basis_eball s
 #align emetric.nhds_within_basis_eball EMetric.nhdsWithin_basis_eball
+-/
 
+#print EMetric.nhds_basis_closed_eball /-
 theorem nhds_basis_closed_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) (closedBall x) :=
   nhds_basis_uniformity uniformity_basis_edist_le
 #align emetric.nhds_basis_closed_eball EMetric.nhds_basis_closed_eball
+-/
 
+#print EMetric.nhdsWithin_basis_closed_eball /-
 theorem nhdsWithin_basis_closed_eball :
     (𝓝[s] x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => closedBall x ε ∩ s :=
   nhdsWithin_hasBasis nhds_basis_closed_eball s
 #align emetric.nhds_within_basis_closed_eball EMetric.nhdsWithin_basis_closed_eball
+-/
 
+#print EMetric.nhds_eq /-
 theorem nhds_eq : 𝓝 x = ⨅ ε > 0, 𝓟 (ball x ε) :=
   nhds_basis_eball.eq_biInf
 #align emetric.nhds_eq EMetric.nhds_eq
+-/
 
+#print EMetric.mem_nhds_iff /-
 theorem mem_nhds_iff : s ∈ 𝓝 x ↔ ∃ ε > 0, ball x ε ⊆ s :=
   nhds_basis_eball.mem_iff
 #align emetric.mem_nhds_iff EMetric.mem_nhds_iff
+-/
 
+#print EMetric.mem_nhdsWithin_iff /-
 theorem mem_nhdsWithin_iff : s ∈ 𝓝[t] x ↔ ∃ ε > 0, ball x ε ∩ t ⊆ s :=
   nhdsWithin_basis_eball.mem_iff
 #align emetric.mem_nhds_within_iff EMetric.mem_nhdsWithin_iff
+-/
 
 section
 
 variable [PseudoEMetricSpace β] {f : α → β}
 
+#print EMetric.tendsto_nhdsWithin_nhdsWithin /-
 theorem tendsto_nhdsWithin_nhdsWithin {t : Set β} {a b} :
     Tendsto f (𝓝[s] a) (𝓝[t] b) ↔
       ∀ ε > 0, ∃ δ > 0, ∀ ⦃x⦄, x ∈ s → edist x a < δ → f x ∈ t ∧ edist (f x) b < ε :=
   (nhdsWithin_basis_eball.tendsto_iffₓ nhdsWithin_basis_eball).trans <|
     forall₂_congr fun ε hε => exists₂_congr fun δ hδ => forall_congr' fun x => by simp <;> itauto
 #align emetric.tendsto_nhds_within_nhds_within EMetric.tendsto_nhdsWithin_nhdsWithin
+-/
 
+#print EMetric.tendsto_nhdsWithin_nhds /-
 theorem tendsto_nhdsWithin_nhds {a b} :
     Tendsto f (𝓝[s] a) (𝓝 b) ↔
       ∀ ε > 0, ∃ δ > 0, ∀ {x : α}, x ∈ s → edist x a < δ → edist (f x) b < ε :=
   by rw [← nhdsWithin_univ b, tendsto_nhds_within_nhds_within]; simp only [mem_univ, true_and_iff]
 #align emetric.tendsto_nhds_within_nhds EMetric.tendsto_nhdsWithin_nhds
+-/
 
+#print EMetric.tendsto_nhds_nhds /-
 theorem tendsto_nhds_nhds {a b} :
     Tendsto f (𝓝 a) (𝓝 b) ↔ ∀ ε > 0, ∃ δ > 0, ∀ ⦃x⦄, edist x a < δ → edist (f x) b < ε :=
   nhds_basis_eball.tendsto_iffₓ nhds_basis_eball
 #align emetric.tendsto_nhds_nhds EMetric.tendsto_nhds_nhds
+-/
 
 end
 
+#print EMetric.isOpen_iff /-
 theorem isOpen_iff : IsOpen s ↔ ∀ x ∈ s, ∃ ε > 0, ball x ε ⊆ s := by
   simp [isOpen_iff_nhds, mem_nhds_iff]
 #align emetric.is_open_iff EMetric.isOpen_iff
+-/
 
 #print EMetric.isOpen_ball /-
 theorem isOpen_ball : IsOpen (ball x ε) :=
@@ -757,20 +893,26 @@ theorem isOpen_ball : IsOpen (ball x ε) :=
 #align emetric.is_open_ball EMetric.isOpen_ball
 -/
 
+#print EMetric.isClosed_ball_top /-
 theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
   isOpen_compl_iff.1 <|
     isOpen_iff.2 fun y hy =>
       ⟨⊤, ENNReal.coe_lt_top,
         (ball_disjoint <| by rw [top_add]; exact le_of_not_lt hy).subset_compl_right⟩
 #align emetric.is_closed_ball_top EMetric.isClosed_ball_top
+-/
 
+#print EMetric.ball_mem_nhds /-
 theorem ball_mem_nhds (x : α) {ε : ℝ≥0∞} (ε0 : 0 < ε) : ball x ε ∈ 𝓝 x :=
   isOpen_ball.mem_nhds (mem_ball_self ε0)
 #align emetric.ball_mem_nhds EMetric.ball_mem_nhds
+-/
 
+#print EMetric.closedBall_mem_nhds /-
 theorem closedBall_mem_nhds (x : α) {ε : ℝ≥0∞} (ε0 : 0 < ε) : closedBall x ε ∈ 𝓝 x :=
   mem_of_superset (ball_mem_nhds x ε0) ball_subset_closedBall
 #align emetric.closed_ball_mem_nhds EMetric.closedBall_mem_nhds
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
 #print EMetric.ball_prod_same /-
@@ -788,27 +930,36 @@ theorem closedBall_prod_same [PseudoEMetricSpace β] (x : α) (y : β) (r : ℝ
 #align emetric.closed_ball_prod_same EMetric.closedBall_prod_same
 -/
 
+#print EMetric.mem_closure_iff /-
 /-- ε-characterization of the closure in pseudoemetric spaces -/
 theorem mem_closure_iff : x ∈ closure s ↔ ∀ ε > 0, ∃ y ∈ s, edist x y < ε :=
   (mem_closure_iff_nhds_basis nhds_basis_eball).trans <| by simp only [mem_ball, edist_comm x]
 #align emetric.mem_closure_iff EMetric.mem_closure_iff
+-/
 
+#print EMetric.tendsto_nhds /-
 theorem tendsto_nhds {f : Filter β} {u : β → α} {a : α} :
     Tendsto u f (𝓝 a) ↔ ∀ ε > 0, ∀ᶠ x in f, edist (u x) a < ε :=
   nhds_basis_eball.tendsto_right_iff
 #align emetric.tendsto_nhds EMetric.tendsto_nhds
+-/
 
+#print EMetric.tendsto_atTop /-
 theorem tendsto_atTop [Nonempty β] [SemilatticeSup β] {u : β → α} {a : α} :
     Tendsto u atTop (𝓝 a) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, edist (u n) a < ε :=
   (atTop_basis.tendsto_iffₓ nhds_basis_eball).trans <| by
     simp only [exists_prop, true_and_iff, mem_Ici, mem_ball]
 #align emetric.tendsto_at_top EMetric.tendsto_atTop
+-/
 
+#print EMetric.inseparable_iff /-
 theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
   simp [inseparable_iff_mem_closure, mem_closure_iff, edist_comm, forall_lt_iff_le']
 #align emetric.inseparable_iff EMetric.inseparable_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (m n «expr ≥ » N) -/
+#print EMetric.cauchySeq_iff /-
 -- see Note [nolint_ge]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
 the pseudoedistance between its elements is arbitrarily small -/
@@ -817,20 +968,26 @@ theorem cauchySeq_iff [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ ∀ ε > 0, ∃ N, ∀ (m) (_ : m ≥ N) (n) (_ : n ≥ N), edist (u m) (u n) < ε :=
   uniformity_basis_edist.cauchySeq_iff
 #align emetric.cauchy_seq_iff EMetric.cauchySeq_iff
+-/
 
+#print EMetric.cauchySeq_iff' /-
 /-- A variation around the emetric characterization of Cauchy sequences -/
 theorem cauchySeq_iff' [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ ∀ ε > (0 : ℝ≥0∞), ∃ N, ∀ n ≥ N, edist (u n) (u N) < ε :=
   uniformity_basis_edist.cauchySeq_iff'
 #align emetric.cauchy_seq_iff' EMetric.cauchySeq_iff'
+-/
 
+#print EMetric.cauchySeq_iff_NNReal /-
 /-- A variation of the emetric characterization of Cauchy sequences that deals with
 `ℝ≥0` upper bounds. -/
 theorem cauchySeq_iff_NNReal [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ ∀ ε : ℝ≥0, 0 < ε → ∃ N, ∀ n, N ≤ n → edist (u n) (u N) < ε :=
   uniformity_basis_edist_nnreal.cauchySeq_iff'
 #align emetric.cauchy_seq_iff_nnreal EMetric.cauchySeq_iff_NNReal
+-/
 
+#print EMetric.totallyBounded_iff /-
 theorem totallyBounded_iff {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ t : Set α, t.Finite ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => H _ (edist_mem_uniformity ε0), fun H r ru =>
@@ -838,8 +995,10 @@ theorem totallyBounded_iff {s : Set α} :
     let ⟨t, ft, h⟩ := H ε ε0
     ⟨t, ft, h.trans <| iUnion₂_mono fun y yt z => hε⟩⟩
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print EMetric.totallyBounded_iff' /-
 theorem totallyBounded_iff' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => (totallyBounded_iff_subset.1 H) _ (edist_mem_uniformity ε0), fun H r ru =>
@@ -847,10 +1006,12 @@ theorem totallyBounded_iff' {s : Set α} :
     let ⟨t, _, ft, h⟩ := H ε ε0
     ⟨t, ft, h.trans <| iUnion₂_mono fun y yt z => hε⟩⟩
 #align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'
+-/
 
 section Compact
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print EMetric.subset_countable_closure_of_almost_dense_set /-
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
 theorem subset_countable_closure_of_almost_dense_set (s : Set α)
@@ -882,8 +1043,10 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     edist x (f n⁻¹ y) ≤ n⁻¹ * 2 := hf _ _ ⟨hyx, hx⟩
     _ < ε := ENNReal.mul_lt_of_lt_div hn
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print EMetric.subset_countable_closure_of_compact /-
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
 theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
@@ -893,6 +1056,7 @@ theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
   rcases totally_bounded_iff'.1 hs.totally_bounded ε hε with ⟨t, hts, htf, hst⟩
   exact ⟨t, htf.countable, subset.trans hst <| Union₂_mono fun _ _ => ball_subset_closed_ball⟩
 #align emetric.subset_countable_closure_of_compact EMetric.subset_countable_closure_of_compact
+-/
 
 end Compact
 
@@ -918,6 +1082,7 @@ theorem secondCountable_of_sigmaCompact [SigmaCompactSpace α] : SecondCountable
 
 variable {α}
 
+#print EMetric.secondCountable_of_almost_dense_set /-
 theorem secondCountable_of_almost_dense_set
     (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ (⋃ x ∈ t, closedBall x ε) = univ) :
     SecondCountableTopology α :=
@@ -929,6 +1094,7 @@ theorem secondCountable_of_almost_dense_set
   · rcases hs ε ε0 with ⟨t, htc, ht⟩
     exact ⟨t, htc, univ_subset_iff.2 ht⟩
 #align emetric.second_countable_of_almost_dense_set EMetric.secondCountable_of_almost_dense_set
+-/
 
 end SecondCountable
 
@@ -941,56 +1107,76 @@ noncomputable def diam (s : Set α) :=
 #align emetric.diam EMetric.diam
 -/
 
+#print EMetric.diam_le_iff /-
 theorem diam_le_iff {d : ℝ≥0∞} : diam s ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d := by
   simp only [diam, iSup_le_iff]
 #align emetric.diam_le_iff EMetric.diam_le_iff
+-/
 
+#print EMetric.diam_image_le_iff /-
 theorem diam_image_le_iff {d : ℝ≥0∞} {f : β → α} {s : Set β} :
     diam (f '' s) ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist (f x) (f y) ≤ d := by
   simp only [diam_le_iff, ball_image_iff]
 #align emetric.diam_image_le_iff EMetric.diam_image_le_iff
+-/
 
+#print EMetric.edist_le_of_diam_le /-
 theorem edist_le_of_diam_le {d} (hx : x ∈ s) (hy : y ∈ s) (hd : diam s ≤ d) : edist x y ≤ d :=
   diam_le_iff.1 hd x hx y hy
 #align emetric.edist_le_of_diam_le EMetric.edist_le_of_diam_le
+-/
 
+#print EMetric.edist_le_diam_of_mem /-
 /-- If two points belong to some set, their edistance is bounded by the diameter of the set -/
 theorem edist_le_diam_of_mem (hx : x ∈ s) (hy : y ∈ s) : edist x y ≤ diam s :=
   edist_le_of_diam_le hx hy le_rfl
 #align emetric.edist_le_diam_of_mem EMetric.edist_le_diam_of_mem
+-/
 
+#print EMetric.diam_le /-
 /-- If the distance between any two points in a set is bounded by some constant, this constant
 bounds the diameter. -/
 theorem diam_le {d : ℝ≥0∞} (h : ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d) : diam s ≤ d :=
   diam_le_iff.2 h
 #align emetric.diam_le EMetric.diam_le
+-/
 
+#print EMetric.diam_subsingleton /-
 /-- The diameter of a subsingleton vanishes. -/
 theorem diam_subsingleton (hs : s.Subsingleton) : diam s = 0 :=
   nonpos_iff_eq_zero.1 <| diam_le fun x hx y hy => (hs hx hy).symm ▸ edist_self y ▸ le_rfl
 #align emetric.diam_subsingleton EMetric.diam_subsingleton
+-/
 
+#print EMetric.diam_empty /-
 /-- The diameter of the empty set vanishes -/
 @[simp]
 theorem diam_empty : diam (∅ : Set α) = 0 :=
   diam_subsingleton subsingleton_empty
 #align emetric.diam_empty EMetric.diam_empty
+-/
 
+#print EMetric.diam_singleton /-
 /-- The diameter of a singleton vanishes -/
 @[simp]
 theorem diam_singleton : diam ({x} : Set α) = 0 :=
   diam_subsingleton subsingleton_singleton
 #align emetric.diam_singleton EMetric.diam_singleton
+-/
 
+#print EMetric.diam_iUnion_mem_option /-
 theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp
 #align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_option
+-/
 
+#print EMetric.diam_insert /-
 theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s) :=
   eq_of_forall_ge_iff fun d => by
     simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, iSup_le_iff,
       zero_le, true_and_iff, forall_and, and_self_iff, ← and_assoc']
 #align emetric.diam_insert EMetric.diam_insert
+-/
 
 #print EMetric.diam_pair /-
 theorem diam_pair : diam ({x, y} : Set α) = edist x y := by
@@ -998,16 +1184,21 @@ theorem diam_pair : diam ({x, y} : Set α) = edist x y := by
 #align emetric.diam_pair EMetric.diam_pair
 -/
 
+#print EMetric.diam_triple /-
 theorem diam_triple : diam ({x, y, z} : Set α) = max (max (edist x y) (edist x z)) (edist y z) := by
   simp only [diam_insert, iSup_insert, iSup_singleton, diam_singleton, ENNReal.max_zero_right,
     ENNReal.sup_eq_max]
 #align emetric.diam_triple EMetric.diam_triple
+-/
 
+#print EMetric.diam_mono /-
 /-- The diameter is monotonous with respect to inclusion -/
 theorem diam_mono {s t : Set α} (h : s ⊆ t) : diam s ≤ diam t :=
   diam_le fun x hx y hy => edist_le_diam_of_mem (h hx) (h hy)
 #align emetric.diam_mono EMetric.diam_mono
+-/
 
+#print EMetric.diam_union /-
 /-- The diameter of a union is controlled by the diameter of the sets, and the edistance
 between two points in the sets. -/
 theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
@@ -1032,13 +1223,17 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       edist a b ≤ diam t := edist_le_diam_of_mem h'a h'b
       _ ≤ diam s + edist x y + diam t := le_add_self
 #align emetric.diam_union EMetric.diam_union
+-/
 
+#print EMetric.diam_union' /-
 theorem diam_union' {t : Set α} (h : (s ∩ t).Nonempty) : diam (s ∪ t) ≤ diam s + diam t :=
   by
   let ⟨x, ⟨xs, xt⟩⟩ := h
   simpa using diam_union xs xt
 #align emetric.diam_union' EMetric.diam_union'
+-/
 
+#print EMetric.diam_closedBall /-
 theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
   diam_le fun a ha b hb =>
     calc
@@ -1046,11 +1241,15 @@ theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
       _ ≤ r + r := (add_le_add ha hb)
       _ = 2 * r := (two_mul r).symm
 #align emetric.diam_closed_ball EMetric.diam_closedBall
+-/
 
+#print EMetric.diam_ball /-
 theorem diam_ball {r : ℝ≥0∞} : diam (ball x r) ≤ 2 * r :=
   le_trans (diam_mono ball_subset_closedBall) diam_closedBall
 #align emetric.diam_ball EMetric.diam_ball
+-/
 
+#print EMetric.diam_pi_le_of_le /-
 theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, diam (s b) ≤ c) : diam (Set.pi univ s) ≤ c :=
   by
@@ -1058,6 +1257,7 @@ theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetric
   rw [mem_univ_pi] at hx hy 
   exact fun b => diam_le_iff.1 (h b) (x b) (hx b) (y b) (hy b)
 #align emetric.diam_pi_le_of_le EMetric.diam_pi_le_of_le
+-/
 
 end Diam
 
@@ -1075,29 +1275,39 @@ variable {γ : Type w} [EMetricSpace γ]
 
 export EMetricSpace (eq_of_edist_eq_zero)
 
+#print edist_eq_zero /-
 /-- Characterize the equality of points by the vanishing of their extended distance -/
 @[simp]
 theorem edist_eq_zero {x y : γ} : edist x y = 0 ↔ x = y :=
   Iff.intro eq_of_edist_eq_zero fun this : x = y => this ▸ edist_self _
 #align edist_eq_zero edist_eq_zero
+-/
 
+#print zero_eq_edist /-
 @[simp]
 theorem zero_eq_edist {x y : γ} : 0 = edist x y ↔ x = y :=
   Iff.intro (fun h => eq_of_edist_eq_zero h.symm) fun this : x = y => this ▸ (edist_self _).symm
 #align zero_eq_edist zero_eq_edist
+-/
 
+#print edist_le_zero /-
 theorem edist_le_zero {x y : γ} : edist x y ≤ 0 ↔ x = y :=
   nonpos_iff_eq_zero.trans edist_eq_zero
 #align edist_le_zero edist_le_zero
+-/
 
+#print edist_pos /-
 @[simp]
 theorem edist_pos {x y : γ} : 0 < edist x y ↔ x ≠ y := by simp [← not_le]
 #align edist_pos edist_pos
+-/
 
+#print eq_of_forall_edist_le /-
 /-- Two points coincide if their distance is `< ε` for all positive ε -/
 theorem eq_of_forall_edist_le {x y : γ} (h : ∀ ε > 0, edist x y ≤ ε) : x = y :=
   eq_of_edist_eq_zero (eq_of_le_of_forall_le_of_dense bot_le h)
 #align eq_of_forall_edist_le eq_of_forall_edist_le
+-/
 
 #print to_separated /-
 -- see Note [lower instance priority]
@@ -1108,6 +1318,7 @@ instance (priority := 100) to_separated : SeparatedSpace γ :=
 #align to_separated to_separated
 -/
 
+#print EMetric.uniformEmbedding_iff' /-
 /-- A map between emetric spaces is a uniform embedding if and only if the edistance between `f x`
 and `f y` is controlled in terms of the distance between `x` and `y` and conversely. -/
 theorem EMetric.uniformEmbedding_iff' [EMetricSpace β] {f : γ → β} :
@@ -1119,6 +1330,7 @@ theorem EMetric.uniformEmbedding_iff' [EMetricSpace β] {f : γ → β} :
     uniformity_basis_edist.uniform_inducing_iff uniformity_basis_edist, exists_prop]
   rfl
 #align emetric.uniform_embedding_iff' EMetric.uniformEmbedding_iff'
+-/
 
 #print EMetricSpace.ofT0PseudoEMetricSpace /-
 /-- If a `pseudo_emetric_space` is a T₀ space, then it is an `emetric_space`. -/
@@ -1190,10 +1402,12 @@ instance Prod.emetricSpaceMax [EMetricSpace β] : EMetricSpace (γ × β) :=
 #align prod.emetric_space_max Prod.emetricSpaceMax
 -/
 
+#print uniformity_edist /-
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_edist : 𝓤 γ = ⨅ ε > 0, 𝓟 {p : γ × γ | edist p.1 p.2 < ε} :=
   PseudoEMetricSpace.uniformity_edist
 #align uniformity_edist uniformity_edist
+-/
 
 section Pi
 
@@ -1222,6 +1436,7 @@ end Pi
 namespace Emetric
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
+#print EMetric.countable_closure_of_compact /-
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
     ∃ (t : _) (_ : t ⊆ s), t.Countable ∧ s = closure t :=
@@ -1229,18 +1444,23 @@ theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
   rcases subset_countable_closure_of_compact hs with ⟨t, hts, htc, hsub⟩
   exact ⟨t, hts, htc, subset.antisymm hsub (closure_minimal hts hs.is_closed)⟩
 #align emetric.countable_closure_of_compact EMetric.countable_closure_of_compact
+-/
 
 section Diam
 
 variable {s : Set γ}
 
+#print EMetric.diam_eq_zero_iff /-
 theorem diam_eq_zero_iff : diam s = 0 ↔ s.Subsingleton :=
   ⟨fun h x hx y hy => edist_le_zero.1 <| h ▸ edist_le_diam_of_mem hx hy, diam_subsingleton⟩
 #align emetric.diam_eq_zero_iff EMetric.diam_eq_zero_iff
+-/
 
+#print EMetric.diam_pos_iff' /-
 theorem diam_pos_iff' : 0 < diam s ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y := by
   simp only [pos_iff_ne_zero, Ne.def, diam_eq_zero_iff, Set.Subsingleton, not_forall]
 #align emetric.diam_pos_iff EMetric.diam_pos_iff'
+-/
 
 end Diam
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/a3e83f0fa4391c8740f7d773a7a9b74e311ae2a3

@@ -146,7 +146,7 @@ theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
   · intro n hn hrec
     calc
       edist (f m) (f (n + 1)) ≤ edist (f m) (f n) + edist (f n) (f (n + 1)) := edist_triangle _ _ _
-      _ ≤ (∑ i in Finset.Ico m n, _) + _ := (add_le_add hrec le_rfl)
+      _ ≤ ∑ i in Finset.Ico m n, _ + _ := (add_le_add hrec le_rfl)
       _ = ∑ i in Finset.Ico m (n + 1), _ := by
         rw [Nat.Ico_succ_right_eq_insert_Ico hn, Finset.sum_insert, add_comm] <;> simp
 #align edist_le_Ico_sum_edist edist_le_Ico_sum_edist

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

@@ -132,7 +132,6 @@ theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + e
   calc
     edist x t ≤ edist x z + edist z t := edist_triangle x z t
     _ ≤ edist x y + edist y z + edist z t := add_le_add_right (edist_triangle x y z) _
-    
 #align edist_triangle4 edist_triangle4
 
 /-- The triangle (polygon) inequality for sequences of points; `finset.Ico` version. -/
@@ -150,7 +149,6 @@ theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
       _ ≤ (∑ i in Finset.Ico m n, _) + _ := (add_le_add hrec le_rfl)
       _ = ∑ i in Finset.Ico m (n + 1), _ := by
         rw [Nat.Ico_succ_right_eq_insert_Ico hn, Finset.sum_insert, add_comm] <;> simp
-      
 #align edist_le_Ico_sum_edist edist_le_Ico_sum_edist
 
 /-- The triangle (polygon) inequality for sequences of points; `finset.range` version. -/
@@ -658,7 +656,6 @@ theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) :
     _ = edist x y + edist z x := (add_comm _ _)
     _ < edist x y + ε₁ := (ENNReal.add_lt_add_left h' zx)
     _ ≤ ε₂ := h
-    
 #align emetric.ball_subset EMetric.ball_subset
 
 theorem exists_ball_subset_ball (h : y ∈ ball x ε) : ∃ ε' > 0, ball y ε' ⊆ ball x ε :=
@@ -873,7 +870,6 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
         edist z y ≤ edist z x + edist y x := edist_triangle_right _ _ _
         _ ≤ r + r := (add_le_add hz.1 hxy)
         _ = r * 2 := (mul_two r).symm
-        
   choose f hfs hf
   refine'
     ⟨⋃ n : ℕ, f n⁻¹ '' T n, Union_subset fun n => image_subset_iff.2 fun z hz => hfs _ _,
@@ -885,7 +881,6 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
   calc
     edist x (f n⁻¹ y) ≤ n⁻¹ * 2 := hf _ _ ⟨hyx, hx⟩
     _ < ε := ENNReal.mul_lt_of_lt_div hn
-    
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (t «expr ⊆ » s) -/
@@ -1023,7 +1018,6 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       edist a b ≤ edist a x + edist x y + edist y b := edist_triangle4 _ _ _ _
       _ ≤ diam s + edist x y + diam t :=
         add_le_add (add_le_add (edist_le_diam_of_mem ha xs) le_rfl) (edist_le_diam_of_mem yt hb)
-      
   refine' diam_le fun a ha b hb => _
   cases' (mem_union _ _ _).1 ha with h'a h'a <;> cases' (mem_union _ _ _).1 hb with h'b h'b
   ·
@@ -1031,14 +1025,12 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       edist a b ≤ diam s := edist_le_diam_of_mem h'a h'b
       _ ≤ diam s + (edist x y + diam t) := le_self_add
       _ = diam s + edist x y + diam t := (add_assoc _ _ _).symm
-      
   · exact A a h'a b h'b
   · have Z := A b h'b a h'a; rwa [edist_comm] at Z 
   ·
     calc
       edist a b ≤ diam t := edist_le_diam_of_mem h'a h'b
       _ ≤ diam s + edist x y + diam t := le_add_self
-      
 #align emetric.diam_union EMetric.diam_union
 
 theorem diam_union' {t : Set α} (h : (s ∩ t).Nonempty) : diam (s ∪ t) ≤ diam s + diam t :=
@@ -1053,7 +1045,6 @@ theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
       edist a b ≤ edist a x + edist b x := edist_triangle_right _ _ _
       _ ≤ r + r := (add_le_add ha hb)
       _ = 2 * r := (two_mul r).symm
-      
 #align emetric.diam_closed_ball EMetric.diam_closedBall
 
 theorem diam_ball {r : ℝ≥0∞} : diam (ball x r) ≤ 2 * r :=
@@ -1267,8 +1258,7 @@ instance [PseudoEMetricSpace X] : EDist (UniformSpace.SeparationQuotient X) :=
         edist x y = edist x' y :=
           edist_congr_right <| EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx
         _ = edist x' y' :=
-          edist_congr_left <| EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy
-        ⟩
+          edist_congr_left <| EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy⟩
 
 #print UniformSpace.SeparationQuotient.edist_mk /-
 @[simp]

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

@@ -292,7 +292,7 @@ namespace Emetric
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection {a b «expr ∈ » s} -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection {a b «expr ∈ » s} -/
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
     UniformContinuousOn f s ↔
@@ -326,7 +326,7 @@ theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
   fun h => ⟨uniformContinuous_iff.1 (uniformEmbedding_iff.1 h).2.1, (uniformEmbedding_iff.1 h).2.2⟩
 #align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbedding
 
-/- ./././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) -/
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
     Cauchy f ↔ f ≠ ⊥ ∧ ∀ ε > 0, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), edist x y < ε := by
@@ -811,7 +811,7 @@ theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
   simp [inseparable_iff_mem_closure, mem_closure_iff, edist_comm, forall_lt_iff_le']
 #align emetric.inseparable_iff EMetric.inseparable_iff
 
-/- ./././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]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
 the pseudoedistance between its elements is arbitrarily small -/
@@ -842,7 +842,7 @@ theorem totallyBounded_iff {s : Set α} :
     ⟨t, ft, h.trans <| iUnion₂_mono fun y yt z => hε⟩⟩
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
 
-/- ./././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' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => (totallyBounded_iff_subset.1 H) _ (edist_mem_uniformity ε0), fun H r ru =>
@@ -853,7 +853,7 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
-/- ./././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) -/
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
 theorem subset_countable_closure_of_almost_dense_set (s : Set α)
@@ -888,7 +888,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 
-/- ./././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) -/
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
 theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
@@ -1230,7 +1230,7 @@ end Pi
 
 namespace Emetric
 
-/- ./././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) -/
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
     ∃ (t : _) (_ : t ⊆ s), t.Countable ∧ s = closure t :=

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

@@ -48,7 +48,7 @@ variable {α : Type u} {β : Type v} {X : Type _}
 in terms of the elements of the uniformity. -/
 theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α)} (z : β)
     (D : α → α → β) (H : ∀ s, s ∈ U ↔ ∃ ε > z, ∀ {a b : α}, D a b < ε → (a, b) ∈ s) :
-    U = ⨅ ε > z, 𝓟 { p : α × α | D p.1 p.2 < ε } :=
+    U = ⨅ ε > z, 𝓟 {p : α × α | D p.1 p.2 < ε} :=
   HasBasis.eq_biInf ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_set_of]⟩
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
 
@@ -91,7 +91,7 @@ class PseudoEMetricSpace (α : Type u) extends EDist α : Type u where
   edist_comm : ∀ x y : α, edist x y = edist y x
   edist_triangle : ∀ x y z : α, edist x z ≤ edist x y + edist y z
   toUniformSpace : UniformSpace α := uniformSpaceOfEDist edist edist_self edist_comm edist_triangle
-  uniformity_edist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } := by intros; rfl
+  uniformity_edist : 𝓤 α = ⨅ ε > 0, 𝓟 {p : α × α | edist p.1 p.2 < ε} := by intros; rfl
 #align pseudo_emetric_space PseudoEMetricSpace
 -/
 
@@ -177,7 +177,7 @@ theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → 
 #align edist_le_range_sum_of_edist_le edist_le_range_sum_of_edist_le
 
 /-- Reformulation of the uniform structure in terms of the extended distance -/
-theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } :=
+theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 {p : α × α | edist p.1 p.2 < ε} :=
   PseudoEMetricSpace.uniformity_edist
 #align uniformity_pseudoedist uniformity_pseudoedist
 
@@ -190,7 +190,7 @@ theorem uniformSpace_edist :
 -/
 
 theorem uniformity_basis_edist :
-    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
+    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 < ε} :=
   (@uniformSpace_edist α _).symm ▸ UniformSpace.hasBasis_ofFun ⟨1, one_pos⟩ _ _ _ _ _
 #align uniformity_basis_edist uniformity_basis_edist
 
@@ -207,7 +207,7 @@ For specific bases see `uniformity_basis_edist`, `uniformity_basis_edist'`,
 `uniformity_basis_edist_nnreal`, and `uniformity_basis_edist_inv_nat`. -/
 protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
     (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _) (hx : p x), f x ≤ ε) :
-    (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 < f x } :=
+    (𝓤 α).HasBasis p fun x => {p : α × α | edist p.1 p.2 < f x} :=
   by
   refine' ⟨fun s => uniformity_basis_edist.mem_iff.trans _⟩
   constructor
@@ -223,7 +223,7 @@ accumulating to zero, then closed `f i`-neighborhoods of the diagonal form a bas
 For specific bases see `uniformity_basis_edist_le` and `uniformity_basis_edist_le'`. -/
 protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
     (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _) (hx : p x), f x ≤ ε) :
-    (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 ≤ f x } :=
+    (𝓤 α).HasBasis p fun x => {p : α × α | edist p.1 p.2 ≤ f x} :=
   by
   refine' ⟨fun s => uniformity_basis_edist.mem_iff.trans _⟩
   constructor
@@ -235,47 +235,47 @@ protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop}
 #align emetric.mk_uniformity_basis_le EMetric.mk_uniformity_basis_le
 
 theorem uniformity_basis_edist_le :
-    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
+    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 ≤ ε} :=
   EMetric.mk_uniformity_basis_le (fun _ => id) fun ε ε₀ => ⟨ε, ε₀, le_refl ε⟩
 #align uniformity_basis_edist_le uniformity_basis_edist_le
 
 theorem uniformity_basis_edist' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
-    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => { p : α × α | edist p.1 p.2 < ε } :=
+    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => {p : α × α | edist p.1 p.2 < ε} :=
   EMetric.mk_uniformity_basis (fun _ => And.left) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := exists_between hε'
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist' uniformity_basis_edist'
 
 theorem uniformity_basis_edist_le' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
-    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
+    (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => {p : α × α | edist p.1 p.2 ≤ ε} :=
   EMetric.mk_uniformity_basis_le (fun _ => And.left) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := exists_between hε'
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist_le' uniformity_basis_edist_le'
 
 theorem uniformity_basis_edist_nnreal :
-    (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
+    (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 < ε} :=
   EMetric.mk_uniformity_basis (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal uniformity_basis_edist_nnreal
 
 theorem uniformity_basis_edist_nnreal_le :
-    (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
+    (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => {p : α × α | edist p.1 p.2 ≤ ε} :=
   EMetric.mk_uniformity_basis_le (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nnreal_le
 
 theorem uniformity_basis_edist_inv_nat :
-    (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < (↑n)⁻¹ } :=
+    (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => {p : α × α | edist p.1 p.2 < (↑n)⁻¹} :=
   EMetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun ε ε₀ =>
     let ⟨n, hn⟩ := ENNReal.exists_inv_nat_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_nat
 
 theorem uniformity_basis_edist_inv_two_pow :
-    (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < 2⁻¹ ^ n } :=
+    (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => {p : α × α | edist p.1 p.2 < 2⁻¹ ^ n} :=
   EMetric.mk_uniformity_basis (fun n _ => ENNReal.pow_pos (ENNReal.inv_pos.2 ENNReal.two_ne_top) _)
     fun ε ε₀ =>
     let ⟨n, hn⟩ := ENNReal.exists_inv_two_pow_lt (ne_of_gt ε₀)
@@ -283,7 +283,7 @@ theorem uniformity_basis_edist_inv_two_pow :
 #align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_pow
 
 /-- Fixed size neighborhoods of the diagonal belong to the uniform structure -/
-theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : { p : α × α | edist p.1 p.2 < ε } ∈ 𝓤 α :=
+theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : {p : α × α | edist p.1 p.2 < ε} ∈ 𝓤 α :=
   mem_uniformity_edist.2 ⟨ε, ε0, fun a b => id⟩
 #align edist_mem_uniformity edist_mem_uniformity
 
@@ -344,7 +344,7 @@ theorem complete_of_convergent_controlled_sequences (B : ℕ → ℝ≥0∞) (hB
         (∀ N n m : ℕ, N ≤ n → N ≤ m → edist (u n) (u m) < B N) → ∃ x, Tendsto u atTop (𝓝 x)) :
     CompleteSpace α :=
   UniformSpace.complete_of_convergent_controlled_sequences
-    (fun n => { p : α × α | edist p.1 p.2 < B n }) (fun n => edist_mem_uniformity <| hB n) H
+    (fun n => {p : α × α | edist p.1 p.2 < B n}) (fun n => edist_mem_uniformity <| hB n) H
 #align emetric.complete_of_convergent_controlled_sequences EMetric.complete_of_convergent_controlled_sequences
 
 #print EMetric.complete_of_cauchySeq_tendsto /-
@@ -576,7 +576,7 @@ variable {x y z : α} {ε ε₁ ε₂ : ℝ≥0∞} {s t : Set α}
 #print EMetric.ball /-
 /-- `emetric.ball x ε` is the set of all points `y` with `edist y x < ε` -/
 def ball (x : α) (ε : ℝ≥0∞) : Set α :=
-  { y | edist y x < ε }
+  {y | edist y x < ε}
 #align emetric.ball EMetric.ball
 -/
 
@@ -591,7 +591,7 @@ theorem mem_ball' : y ∈ ball x ε ↔ edist x y < ε := by rw [edist_comm, mem
 #print EMetric.closedBall /-
 /-- `emetric.closed_ball x ε` is the set of all points `y` with `edist y x ≤ ε` -/
 def closedBall (x : α) (ε : ℝ≥0∞) :=
-  { y | edist y x ≤ ε }
+  {y | edist y x ≤ ε}
 #align emetric.closed_ball EMetric.closedBall
 -/
 
@@ -675,11 +675,11 @@ theorem ball_eq_empty_iff : ball x ε = ∅ ↔ ε = 0 :=
 #align emetric.ball_eq_empty_iff EMetric.ball_eq_empty_iff
 
 theorem ordConnected_setOf_closedBall_subset (x : α) (s : Set α) :
-    OrdConnected { r | closedBall x r ⊆ s } :=
+    OrdConnected {r | closedBall x r ⊆ s} :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (closedBall_subset_closedBall hr.2).trans hr₂⟩
 #align emetric.ord_connected_set_of_closed_ball_subset EMetric.ordConnected_setOf_closedBall_subset
 
-theorem ordConnected_setOf_ball_subset (x : α) (s : Set α) : OrdConnected { r | ball x r ⊆ s } :=
+theorem ordConnected_setOf_ball_subset (x : α) (s : Set α) : OrdConnected {r | ball x r ⊆ s} :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (ball_subset_ball hr.2).trans hr₂⟩
 #align emetric.ord_connected_set_of_ball_subset EMetric.ordConnected_setOf_ball_subset
 
@@ -1200,7 +1200,7 @@ instance Prod.emetricSpaceMax [EMetricSpace β] : EMetricSpace (γ × β) :=
 -/
 
 /-- Reformulation of the uniform structure in terms of the extended distance -/
-theorem uniformity_edist : 𝓤 γ = ⨅ ε > 0, 𝓟 { p : γ × γ | edist p.1 p.2 < ε } :=
+theorem uniformity_edist : 𝓤 γ = ⨅ ε > 0, 𝓟 {p : γ × γ | edist p.1 p.2 < ε} :=
   PseudoEMetricSpace.uniformity_edist
 #align uniformity_edist uniformity_edist
 

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

@@ -91,7 +91,7 @@ class PseudoEMetricSpace (α : Type u) extends EDist α : Type u where
   edist_comm : ∀ x y : α, edist x y = edist y x
   edist_triangle : ∀ x y z : α, edist x z ≤ edist x y + edist y z
   toUniformSpace : UniformSpace α := uniformSpaceOfEDist edist edist_self edist_comm edist_triangle
-  uniformity_edist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } := by intros ; rfl
+  uniformity_edist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } := by intros; rfl
 #align pseudo_emetric_space PseudoEMetricSpace
 -/
 
@@ -119,7 +119,7 @@ theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y
   apply le_antisymm
   · rw [← zero_add (edist y z), ← h]
     apply edist_triangle
-  · rw [edist_comm] at h
+  · rw [edist_comm] at h 
     rw [← zero_add (edist x z), ← h]
     apply edist_triangle
 #align edist_congr_right edist_congr_right
@@ -206,7 +206,7 @@ accumulating to zero, then `f i`-neighborhoods of the diagonal form a basis of `
 For specific bases see `uniformity_basis_edist`, `uniformity_basis_edist'`,
 `uniformity_basis_edist_nnreal`, and `uniformity_basis_edist_inv_nat`. -/
 protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
-    (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _)(hx : p x), f x ≤ ε) :
+    (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _) (hx : p x), f x ≤ ε) :
     (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 < f x } :=
   by
   refine' ⟨fun s => uniformity_basis_edist.mem_iff.trans _⟩
@@ -222,7 +222,7 @@ accumulating to zero, then closed `f i`-neighborhoods of the diagonal form a bas
 
 For specific bases see `uniformity_basis_edist_le` and `uniformity_basis_edist_le'`. -/
 protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
-    (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _)(hx : p x), f x ≤ ε) :
+    (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _) (hx : p x), f x ≤ ε) :
     (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 ≤ f x } :=
   by
   refine' ⟨fun s => uniformity_basis_edist.mem_iff.trans _⟩
@@ -496,8 +496,8 @@ instance Prod.pseudoEMetricSpaceMax [PseudoEMetricSpace β] : PseudoEMetricSpace
   uniformity_edist := by
     refine' uniformity_prod.trans _
     simp only [PseudoEMetricSpace.uniformity_edist, comap_infi]
-    rw [← iInf_inf_eq]; congr ; funext
-    rw [← iInf_inf_eq]; congr ; funext
+    rw [← iInf_inf_eq]; congr; funext
+    rw [← iInf_inf_eq]; congr; funext
     simp [inf_principal, ext_iff, max_lt_iff]
   toUniformSpace := Prod.uniformSpace
 #align prod.pseudo_emetric_space_max Prod.pseudoEMetricSpaceMax
@@ -534,9 +534,9 @@ instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetric
     by
     simp only [Pi.uniformity, PseudoEMetricSpace.uniformity_edist, comap_infi, gt_iff_lt,
       preimage_set_of_eq, comap_principal]
-    rw [iInf_comm]; congr ; funext ε
-    rw [iInf_comm]; congr ; funext εpos
-    change 0 < ε at εpos
+    rw [iInf_comm]; congr; funext ε
+    rw [iInf_comm]; congr; funext εpos
+    change 0 < ε at εpos 
     simp [Set.ext_iff, εpos]
 #align pseudo_emetric_space_pi pseudoEMetricSpacePi
 -/
@@ -844,7 +844,7 @@ theorem totallyBounded_iff {s : Set α} :
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff' {s : Set α} :
-    TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
+    TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _) (_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => (totallyBounded_iff_subset.1 H) _ (edist_mem_uniformity ε0), fun H r ru =>
     let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 ru
     let ⟨t, _, ft, h⟩ := H ε ε0
@@ -858,7 +858,7 @@ section Compact
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
 theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ s ⊆ ⋃ x ∈ t, closedBall x ε) :
-    ∃ (t : _)(_ : t ⊆ s), t.Countable ∧ s ⊆ closure t :=
+    ∃ (t : _) (_ : t ⊆ s), t.Countable ∧ s ⊆ closure t :=
   by
   rcases s.eq_empty_or_nonempty with (rfl | ⟨x₀, hx₀⟩)
   · exact ⟨∅, empty_subset _, countable_empty, empty_subset _⟩
@@ -892,7 +892,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
 theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
-    ∃ (t : _)(_ : t ⊆ s), t.Countable ∧ s ⊆ closure t :=
+    ∃ (t : _) (_ : t ⊆ s), t.Countable ∧ s ⊆ closure t :=
   by
   refine' subset_countable_closure_of_almost_dense_set s fun ε hε => _
   rcases totally_bounded_iff'.1 hs.totally_bounded ε hε with ⟨t, hts, htf, hst⟩
@@ -1033,7 +1033,7 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       _ = diam s + edist x y + diam t := (add_assoc _ _ _).symm
       
   · exact A a h'a b h'b
-  · have Z := A b h'b a h'a; rwa [edist_comm] at Z
+  · have Z := A b h'b a h'a; rwa [edist_comm] at Z 
   ·
     calc
       edist a b ≤ diam t := edist_le_diam_of_mem h'a h'b
@@ -1064,7 +1064,7 @@ theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetric
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, diam (s b) ≤ c) : diam (Set.pi univ s) ≤ c :=
   by
   apply diam_le fun x hx y hy => edist_pi_le_iff.mpr _
-  rw [mem_univ_pi] at hx hy
+  rw [mem_univ_pi] at hx hy 
   exact fun b => diam_le_iff.1 (h b) (x b) (hx b) (y b) (hy b)
 #align emetric.diam_pi_le_of_le EMetric.diam_pi_le_of_le
 
@@ -1221,7 +1221,7 @@ instance emetricSpacePi [∀ b, EMetricSpace (π b)] : EMetricSpace (∀ b, π b
     eq_of_edist_eq_zero := fun f g eq0 =>
       by
       have eq1 : (sup univ fun b : β => edist (f b) (g b)) ≤ 0 := le_of_eq eq0
-      simp only [Finset.sup_le_iff] at eq1
+      simp only [Finset.sup_le_iff] at eq1 
       exact funext fun b => edist_le_zero.1 <| eq1 b <| mem_univ b }
 #align emetric_space_pi emetricSpacePi
 -/
@@ -1233,7 +1233,7 @@ namespace Emetric
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
-    ∃ (t : _)(_ : t ⊆ s), t.Countable ∧ s = closure t :=
+    ∃ (t : _) (_ : t ⊆ s), t.Countable ∧ s = closure t :=
   by
   rcases subset_countable_closure_of_compact hs with ⟨t, hts, htc, hsub⟩
   exact ⟨t, hts, htc, subset.antisymm hsub (closure_minimal hts hs.is_closed)⟩
@@ -1293,7 +1293,7 @@ instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient
                   ext ⟨⟨x⟩, ⟨y⟩⟩
                   refine' ⟨_, fun h => ⟨(x, y), h, rfl⟩⟩
                   rintro ⟨⟨x', y'⟩, h', h⟩
-                  simp only [Prod.ext_iff] at h
+                  simp only [Prod.ext_iff] at h 
                   rwa [← h.1, ← h.2]) }
     _
 

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

@@ -38,7 +38,7 @@ to `emetric_space` at the end.
 
 open Set Filter Classical
 
-open uniformity Topology BigOperators Filter NNReal ENNReal
+open scoped uniformity Topology BigOperators Filter NNReal ENNReal
 
 universe u v w
 

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

@@ -44,12 +44,6 @@ universe u v w
 
 variable {α : Type u} {β : Type v} {X : Type _}
 
-/- warning: uniformity_dist_of_mem_uniformity -> uniformity_dist_of_mem_uniformity is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => Exists.{0} (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (iInf.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => And (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (iInf.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
-Case conversion may be inaccurate. Consider using '#align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformityₓ'. -/
 /-- Characterizing uniformities associated to a (generalized) distance function `D`
 in terms of the elements of the uniformity. -/
 theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α)} (z : β)
@@ -67,12 +61,6 @@ class EDist (α : Type _) where
 
 export EDist (edist)
 
-/- warning: uniform_space_of_edist -> uniformSpaceOfEDist is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align uniform_space_of_edist uniformSpaceOfEDistₓ'. -/
 /-- Creating a uniform space from an extended distance. -/
 noncomputable def uniformSpaceOfEDist (edist : α → α → ℝ≥0∞) (edist_self : ∀ x : α, edist x x = 0)
     (edist_comm : ∀ x y : α, edist x y = edist y x)
@@ -117,33 +105,15 @@ export PseudoEMetricSpace (edist_self edist_comm edist_triangle)
 
 attribute [simp] edist_self
 
-/- warning: edist_triangle_left -> edist_triangle_left is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z y))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z y))
-Case conversion may be inaccurate. Consider using '#align edist_triangle_left edist_triangle_leftₓ'. -/
 /-- Triangle inequality for the extended distance -/
 theorem edist_triangle_left (x y z : α) : edist x y ≤ edist z x + edist z y := by
   rw [edist_comm z] <;> apply edist_triangle
 #align edist_triangle_left edist_triangle_left
 
-/- warning: edist_triangle_right -> edist_triangle_right is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align edist_triangle_right edist_triangle_rightₓ'. -/
 theorem edist_triangle_right (x y z : α) : edist x y ≤ edist x z + edist y z := by
   rw [edist_comm y] <;> apply edist_triangle
 #align edist_triangle_right edist_triangle_right
 
-/- warning: edist_congr_right -> edist_congr_right is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align edist_congr_right edist_congr_rightₓ'. -/
 theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y z :=
   by
   apply le_antisymm
@@ -154,22 +124,10 @@ theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y
     apply edist_triangle
 #align edist_congr_right edist_congr_right
 
-/- warning: edist_congr_left -> edist_congr_left is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align edist_congr_left edist_congr_leftₓ'. -/
 theorem edist_congr_left {x y z : α} (h : edist x y = 0) : edist z x = edist z y := by
   rw [edist_comm z x, edist_comm z y]; apply edist_congr_right h
 #align edist_congr_left edist_congr_left
 
-/- warning: edist_triangle4 -> edist_triangle4 is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align edist_triangle4 edist_triangle4ₓ'. -/
 theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + edist z t :=
   calc
     edist x t ≤ edist x z + edist z t := edist_triangle x z t
@@ -177,12 +135,6 @@ theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + e
     
 #align edist_triangle4 edist_triangle4
 
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 /-- The triangle (polygon) inequality for sequences of points; `finset.Ico` version. -/
 theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
     edist (f m) (f n) ≤ ∑ i in Finset.Ico m n, edist (f i) (f (i + 1)) :=
@@ -201,24 +153,12 @@ theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
       
 #align edist_le_Ico_sum_edist edist_le_Ico_sum_edist
 
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 /-- The triangle (polygon) inequality for sequences of points; `finset.range` version. -/
 theorem edist_le_range_sum_edist (f : ℕ → α) (n : ℕ) :
     edist (f 0) (f n) ≤ ∑ i in Finset.range n, edist (f i) (f (i + 1)) :=
   Nat.Ico_zero_eq_range ▸ edist_le_Ico_sum_edist f (Nat.zero_le n)
 #align edist_le_range_sum_edist edist_le_range_sum_edist
 
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 /-- A version of `edist_le_Ico_sum_edist` with each intermediate distance replaced
 with an upper estimate. -/
 theorem edist_le_Ico_sum_of_edist_le {f : ℕ → α} {m n} (hmn : m ≤ n) {d : ℕ → ℝ≥0∞}
@@ -228,12 +168,6 @@ theorem edist_le_Ico_sum_of_edist_le {f : ℕ → α} {m n} (hmn : m ≤ n) {d :
     Finset.sum_le_sum fun k hk => hd (Finset.mem_Ico.1 hk).1 (Finset.mem_Ico.1 hk).2
 #align edist_le_Ico_sum_of_edist_le edist_le_Ico_sum_of_edist_le
 
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-Case conversion may be inaccurate. Consider using '#align edist_le_range_sum_of_edist_le edist_le_range_sum_of_edist_leₓ'. -/
 /-- A version of `edist_le_range_sum_edist` with each intermediate distance replaced
 with an upper estimate. -/
 theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → ℝ≥0∞}
@@ -242,12 +176,6 @@ theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → 
   Nat.Ico_zero_eq_range ▸ edist_le_Ico_sum_of_edist_le (zero_le n) fun _ _ => hd
 #align edist_le_range_sum_of_edist_le edist_le_range_sum_of_edist_le
 
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-Case conversion may be inaccurate. Consider using '#align uniformity_pseudoedist uniformity_pseudoedistₓ'. -/
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } :=
   PseudoEMetricSpace.uniformity_edist
@@ -261,35 +189,17 @@ theorem uniformSpace_edist :
 #align uniform_space_edist uniformSpace_edist
 -/
 
-/- warning: uniformity_basis_edist -> uniformity_basis_edist is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist uniformity_basis_edistₓ'. -/
 theorem uniformity_basis_edist :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
   (@uniformSpace_edist α _).symm ▸ UniformSpace.hasBasis_ofFun ⟨1, one_pos⟩ _ _ _ _ _
 #align uniformity_basis_edist uniformity_basis_edist
 
-/- warning: mem_uniformity_edist -> mem_uniformity_edist is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align mem_uniformity_edist mem_uniformity_edistₓ'. -/
 /-- Characterization of the elements of the uniformity in terms of the extended distance -/
 theorem mem_uniformity_edist {s : Set (α × α)} :
     s ∈ 𝓤 α ↔ ∃ ε > 0, ∀ {a b : α}, edist a b < ε → (a, b) ∈ s :=
   uniformity_basis_edist.mem_uniformity_iff
 #align mem_uniformity_edist mem_uniformity_edist
 
-/- warning: emetric.mk_uniformity_basis -> EMetric.mk_uniformity_basis is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.mk_uniformity_basis EMetric.mk_uniformity_basisₓ'. -/
 /-- Given `f : β → ℝ≥0∞`, if `f` sends `{i | p i}` to a set of positive numbers
 accumulating to zero, then `f i`-neighborhoods of the diagonal form a basis of `𝓤 α`.
 
@@ -307,12 +217,6 @@ protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f
   · exact fun ⟨i, hi, H⟩ => ⟨f i, hf₀ i hi, H⟩
 #align emetric.mk_uniformity_basis EMetric.mk_uniformity_basis
 
-/- warning: emetric.mk_uniformity_basis_le -> EMetric.mk_uniformity_basis_le is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align emetric.mk_uniformity_basis_le EMetric.mk_uniformity_basis_leₓ'. -/
 /-- Given `f : β → ℝ≥0∞`, if `f` sends `{i | p i}` to a set of positive numbers
 accumulating to zero, then closed `f i`-neighborhoods of the diagonal form a basis of `𝓤 α`.
 
@@ -330,23 +234,11 @@ protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop}
   · exact fun ⟨i, hi, H⟩ => ⟨f i, hf₀ i hi, fun x hx => H (le_of_lt hx)⟩
 #align emetric.mk_uniformity_basis_le EMetric.mk_uniformity_basis_le
 
-/- warning: uniformity_basis_edist_le -> uniformity_basis_edist_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_le uniformity_basis_edist_leₓ'. -/
 theorem uniformity_basis_edist_le :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
   EMetric.mk_uniformity_basis_le (fun _ => id) fun ε ε₀ => ⟨ε, ε₀, le_refl ε⟩
 #align uniformity_basis_edist_le uniformity_basis_edist_le
 
-/- warning: uniformity_basis_edist' -> uniformity_basis_edist' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.instMembershipSet.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist' uniformity_basis_edist'ₓ'. -/
 theorem uniformity_basis_edist' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => { p : α × α | edist p.1 p.2 < ε } :=
   EMetric.mk_uniformity_basis (fun _ => And.left) fun ε ε₀ =>
@@ -354,12 +246,6 @@ theorem uniformity_basis_edist' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist' uniformity_basis_edist'
 
-/- warning: uniformity_basis_edist_le' -> uniformity_basis_edist_le' is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.instMembershipSet.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_le' uniformity_basis_edist_le'ₓ'. -/
 theorem uniformity_basis_edist_le' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
   EMetric.mk_uniformity_basis_le (fun _ => And.left) fun ε ε₀ =>
@@ -367,12 +253,6 @@ theorem uniformity_basis_edist_le' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist_le' uniformity_basis_edist_le'
 
-/- warning: uniformity_basis_edist_nnreal -> uniformity_basis_edist_nnreal is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (ENNReal.some ε)))
-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_nnreal uniformity_basis_edist_nnrealₓ'. -/
 theorem uniformity_basis_edist_nnreal :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
   EMetric.mk_uniformity_basis (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
@@ -380,12 +260,6 @@ theorem uniformity_basis_edist_nnreal :
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal uniformity_basis_edist_nnreal
 
-/- warning: uniformity_basis_edist_nnreal_le -> uniformity_basis_edist_nnreal_le is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (ENNReal.some ε)))
-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nnreal_leₓ'. -/
 theorem uniformity_basis_edist_nnreal_le :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
   EMetric.mk_uniformity_basis_le (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
@@ -393,12 +267,6 @@ theorem uniformity_basis_edist_nnreal_le :
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nnreal_le
 
-/- warning: uniformity_basis_edist_inv_nat -> uniformity_basis_edist_inv_nat is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (Inv.inv.{0} ENNReal ENNReal.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) n))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (Nat.cast.{0} ENNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) n))))
-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_natₓ'. -/
 theorem uniformity_basis_edist_inv_nat :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < (↑n)⁻¹ } :=
   EMetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun ε ε₀ =>
@@ -406,12 +274,6 @@ theorem uniformity_basis_edist_inv_nat :
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_nat
 
-/- warning: uniformity_basis_edist_inv_two_pow -> uniformity_basis_edist_inv_two_pow is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (Inv.inv.{0} ENNReal ENNReal.hasInv (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))))) n)))
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n)))
-Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_powₓ'. -/
 theorem uniformity_basis_edist_inv_two_pow :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < 2⁻¹ ^ n } :=
   EMetric.mk_uniformity_basis (fun n _ => ENNReal.pow_pos (ENNReal.inv_pos.2 ENNReal.two_ne_top) _)
@@ -420,12 +282,6 @@ theorem uniformity_basis_edist_inv_two_pow :
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_pow
 
-/- warning: edist_mem_uniformity -> edist_mem_uniformity is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (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)) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (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)) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
-Case conversion may be inaccurate. Consider using '#align edist_mem_uniformity edist_mem_uniformityₓ'. -/
 /-- Fixed size neighborhoods of the diagonal belong to the uniform structure -/
 theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : { p : α × α | edist p.1 p.2 < ε } ∈ 𝓤 α :=
   mem_uniformity_edist.2 ⟨ε, ε0, fun a b => id⟩
@@ -436,12 +292,6 @@ namespace Emetric
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
-/- warning: emetric.uniform_continuous_on_iff -> EMetric.uniformContinuousOn_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.uniform_continuous_on_iff EMetric.uniformContinuousOn_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection {a b «expr ∈ » s} -/
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
@@ -450,24 +300,12 @@ theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set
   uniformity_basis_edist.uniformContinuousOn_iff uniformity_basis_edist
 #align emetric.uniform_continuous_on_iff EMetric.uniformContinuousOn_iff
 
-/- warning: emetric.uniform_continuous_iff -> EMetric.uniformContinuous_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.uniform_continuous_iff EMetric.uniformContinuous_iffₓ'. -/
 /-- ε-δ characterization of uniform continuity on pseudoemetric spaces -/
 theorem uniformContinuous_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformContinuous f ↔ ∀ ε > 0, ∃ δ > 0, ∀ {a b : α}, edist a b < δ → edist (f a) (f b) < ε :=
   uniformity_basis_edist.uniformContinuous_iff uniformity_basis_edist
 #align emetric.uniform_continuous_iff EMetric.uniformContinuous_iff
 
-/- warning: emetric.uniform_embedding_iff -> EMetric.uniformEmbedding_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.uniform_embedding_iff EMetric.uniformEmbedding_iffₓ'. -/
 /-- ε-δ characterization of uniform embeddings on pseudoemetric spaces -/
 theorem uniformEmbedding_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformEmbedding f ↔
@@ -479,12 +317,6 @@ theorem uniformEmbedding_iff [PseudoEMetricSpace β] {f : α → β} :
   rfl
 #align emetric.uniform_embedding_iff EMetric.uniformEmbedding_iff
 
-/- warning: emetric.controlled_of_uniform_embedding -> EMetric.controlled_of_uniformEmbedding is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbeddingₓ'. -/
 /-- If a map between pseudoemetric spaces is a uniform embedding then the edistance between `f x`
 and `f y` is controlled in terms of the distance between `x` and `y`. -/
 theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
@@ -494,12 +326,6 @@ theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
   fun h => ⟨uniformContinuous_iff.1 (uniformEmbedding_iff.1 h).2.1, (uniformEmbedding_iff.1 h).2.2⟩
 #align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbedding
 
-/- warning: emetric.cauchy_iff -> EMetric.cauchy_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.cauchy_iff EMetric.cauchy_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
@@ -507,12 +333,6 @@ protected theorem cauchy_iff {f : Filter α} :
   rw [← ne_bot_iff] <;> exact uniformity_basis_edist.cauchy_iff
 #align emetric.cauchy_iff EMetric.cauchy_iff
 
-/- warning: emetric.complete_of_convergent_controlled_sequences -> EMetric.complete_of_convergent_controlled_sequences is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.complete_of_convergent_controlled_sequences EMetric.complete_of_convergent_controlled_sequencesₓ'. -/
 /-- A very useful criterion to show that a space is complete is to show that all sequences
 which satisfy a bound of the form `edist (u n) (u m) < B N` for all `n m ≥ N` are
 converging. This is often applied for `B N = 2^{-N}`, i.e., with a very fast convergence to
@@ -535,9 +355,6 @@ theorem complete_of_cauchySeq_tendsto :
 #align emetric.complete_of_cauchy_seq_tendsto EMetric.complete_of_cauchySeq_tendsto
 -/
 
-/- warning: emetric.tendsto_locally_uniformly_on_iff -> EMetric.tendstoLocallyUniformlyOn_iff is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iffₓ'. -/
 /-- Expressing locally uniform convergence on a set using `edist`. -/
 theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} {s : Set β} :
@@ -550,12 +367,6 @@ theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : 
   exact ⟨t, ht, Ht.mono fun n hs x hx => hε (hs x hx)⟩
 #align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iff
 
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-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_uniformly_on_iff EMetric.tendstoUniformlyOn_iffₓ'. -/
 /-- Expressing uniform convergence on a set using `edist`. -/
 theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} {s : Set β} :
     TendstoUniformlyOn F f p s ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x ∈ s, edist (f x) (F n x) < ε :=
@@ -565,12 +376,6 @@ theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β →
   exact (H ε εpos).mono fun n hs x hx => hε (hs x hx)
 #align emetric.tendsto_uniformly_on_iff EMetric.tendstoUniformlyOn_iff
 
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-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_locally_uniformly_iff EMetric.tendstoLocallyUniformly_iffₓ'. -/
 /-- Expressing locally uniform convergence using `edist`. -/
 theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} :
@@ -581,12 +386,6 @@ theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι
     forall_const, exists_prop, nhdsWithin_univ]
 #align emetric.tendsto_locally_uniformly_iff EMetric.tendstoLocallyUniformly_iff
 
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-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_uniformly_iff EMetric.tendstoUniformly_iffₓ'. -/
 /-- Expressing uniform convergence using `edist`. -/
 theorem tendstoUniformly_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} :
     TendstoUniformly F f p ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x, edist (f x) (F n x) < ε := by
@@ -671,22 +470,10 @@ section ULift
 instance : PseudoEMetricSpace (ULift α) :=
   PseudoEMetricSpace.induced ULift.down ‹_›
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align ulift.edist_eq ULift.edist_eqₓ'. -/
 theorem ULift.edist_eq (x y : ULift α) : edist x y = edist x.down y.down :=
   rfl
 #align ulift.edist_eq ULift.edist_eq
 
-/- warning: ulift.edist_up_up -> ULift.edist_up_up is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align ulift.edist_up_up ULift.edist_up_upₓ'. -/
 @[simp]
 theorem ULift.edist_up_up (x y : α) : edist (ULift.up x) (ULift.up y) = edist x y :=
   rfl
@@ -716,12 +503,6 @@ instance Prod.pseudoEMetricSpaceMax [PseudoEMetricSpace β] : PseudoEMetricSpace
 #align prod.pseudo_emetric_space_max Prod.pseudoEMetricSpaceMax
 -/
 
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-Case conversion may be inaccurate. Consider using '#align prod.edist_eq Prod.edist_eqₓ'. -/
 theorem Prod.edist_eq [PseudoEMetricSpace β] (x y : α × β) :
     edist x y = max (edist x.1 y.1) (edist x.2 y.2) :=
   rfl
@@ -760,45 +541,21 @@ instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetric
 #align pseudo_emetric_space_pi pseudoEMetricSpacePi
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align edist_pi_def edist_pi_defₓ'. -/
 theorem edist_pi_def [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b) :
     edist f g = Finset.sup univ fun b => edist (f b) (g b) :=
   rfl
 #align edist_pi_def edist_pi_def
 
-/- warning: edist_le_pi_edist -> edist_le_pi_edist is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align edist_le_pi_edist edist_le_pi_edistₓ'. -/
 theorem edist_le_pi_edist [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b) (b : β) :
     edist (f b) (g b) ≤ edist f g :=
   Finset.le_sup (Finset.mem_univ b)
 #align edist_le_pi_edist edist_le_pi_edist
 
-/- warning: edist_pi_le_iff -> edist_pi_le_iff is a dubious translation:
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-  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {f : forall (b : β), π b} {g : forall (b : β), π b} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g) d) (forall (b : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)) d)
-but is expected to have type
-  forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), EDist.{u1} (π b)] {f : forall (b : β), π b} {g : forall (b : β), π b} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{max u2 u1} (forall (b : β), π b) (instEDistForAll.{u2, u1} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b)) f g) d) (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} (π b) (_inst_3 b) (f b) (g b)) d)
-Case conversion may be inaccurate. Consider using '#align edist_pi_le_iff edist_pi_le_iffₓ'. -/
 theorem edist_pi_le_iff [∀ b, PseudoEMetricSpace (π b)] {f g : ∀ b, π b} {d : ℝ≥0∞} :
     edist f g ≤ d ↔ ∀ b, edist (f b) (g b) ≤ d :=
   Finset.sup_le_iff.trans <| by simp only [Finset.mem_univ, forall_const]
 #align edist_pi_le_iff edist_pi_le_iff
 
-/- warning: edist_pi_const_le -> edist_pi_const_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align edist_pi_const_le edist_pi_const_leₓ'. -/
 theorem edist_pi_const_le (a b : α) : (edist (fun _ : β => a) fun _ => b) ≤ edist a b :=
   edist_pi_le_iff.2 fun _ => le_rfl
 #align edist_pi_const_le edist_pi_const_le
@@ -823,23 +580,11 @@ def ball (x : α) (ε : ℝ≥0∞) : Set α :=
 #align emetric.ball EMetric.ball
 -/
 
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align emetric.mem_ball EMetric.mem_ballₓ'. -/
 @[simp]
 theorem mem_ball : y ∈ ball x ε ↔ edist y x < ε :=
   Iff.rfl
 #align emetric.mem_ball EMetric.mem_ball
 
-/- warning: emetric.mem_ball' -> EMetric.mem_ball' is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align emetric.mem_ball' EMetric.mem_ball'ₓ'. -/
 theorem mem_ball' : y ∈ ball x ε ↔ edist x y < ε := by rw [edist_comm, mem_ball]
 #align emetric.mem_ball' EMetric.mem_ball'
 
@@ -850,32 +595,14 @@ def closedBall (x : α) (ε : ℝ≥0∞) :=
 #align emetric.closed_ball EMetric.closedBall
 -/
 
-/- warning: emetric.mem_closed_ball -> EMetric.mem_closedBall is a dubious translation:
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-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align emetric.mem_closed_ball EMetric.mem_closedBallₓ'. -/
 @[simp]
 theorem mem_closedBall : y ∈ closedBall x ε ↔ edist y x ≤ ε :=
   Iff.rfl
 #align emetric.mem_closed_ball EMetric.mem_closedBall
 
-/- warning: emetric.mem_closed_ball' -> EMetric.mem_closedBall' is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align emetric.mem_closed_ball' EMetric.mem_closedBall'ₓ'. -/
 theorem mem_closedBall' : y ∈ closedBall x ε ↔ edist x y ≤ ε := by rw [edist_comm, mem_closed_ball]
 #align emetric.mem_closed_ball' EMetric.mem_closedBall'
 
-/- warning: emetric.closed_ball_top -> EMetric.closedBall_top is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_top EMetric.closedBall_topₓ'. -/
 @[simp]
 theorem closedBall_top (x : α) : closedBall x ∞ = univ :=
   eq_univ_of_forall fun y => le_top
@@ -886,22 +613,10 @@ theorem ball_subset_closedBall : ball x ε ⊆ closedBall x ε := fun y hy => le
 #align emetric.ball_subset_closed_ball EMetric.ball_subset_closedBall
 -/
 
-/- warning: emetric.pos_of_mem_ball -> EMetric.pos_of_mem_ball is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.pos_of_mem_ball EMetric.pos_of_mem_ballₓ'. -/
 theorem pos_of_mem_ball (hy : y ∈ ball x ε) : 0 < ε :=
   lt_of_le_of_lt (zero_le _) hy
 #align emetric.pos_of_mem_ball EMetric.pos_of_mem_ball
 
-/- warning: emetric.mem_ball_self -> EMetric.mem_ball_self is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.mem_ball_self EMetric.mem_ball_selfₓ'. -/
 theorem mem_ball_self (h : 0 < ε) : x ∈ ball x ε :=
   show edist x x < ε by rw [edist_self] <;> assumption
 #align emetric.mem_ball_self EMetric.mem_ball_self
@@ -923,43 +638,19 @@ theorem mem_closedBall_comm : x ∈ closedBall y ε ↔ y ∈ closedBall x ε :=
 #align emetric.mem_closed_ball_comm EMetric.mem_closedBall_comm
 -/
 
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-Case conversion may be inaccurate. Consider using '#align emetric.ball_subset_ball EMetric.ball_subset_ballₓ'. -/
 theorem ball_subset_ball (h : ε₁ ≤ ε₂) : ball x ε₁ ⊆ ball x ε₂ := fun y (yx : _ < ε₁) =>
   lt_of_lt_of_le yx h
 #align emetric.ball_subset_ball EMetric.ball_subset_ball
 
-/- warning: emetric.closed_ball_subset_closed_ball -> EMetric.closedBall_subset_closedBall is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_subset_closed_ball EMetric.closedBall_subset_closedBallₓ'. -/
 theorem closedBall_subset_closedBall (h : ε₁ ≤ ε₂) : closedBall x ε₁ ⊆ closedBall x ε₂ :=
   fun y (yx : _ ≤ ε₁) => le_trans yx h
 #align emetric.closed_ball_subset_closed_ball EMetric.closedBall_subset_closedBall
 
-/- warning: emetric.ball_disjoint -> EMetric.ball_disjoint is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ε₁ ε₂) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)) -> (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
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-Case conversion may be inaccurate. Consider using '#align emetric.ball_disjoint EMetric.ball_disjointₓ'. -/
 theorem ball_disjoint (h : ε₁ + ε₂ ≤ edist x y) : Disjoint (ball x ε₁) (ball y ε₂) :=
   Set.disjoint_left.mpr fun z h₁ h₂ =>
     (edist_triangle_left x y z).not_lt <| (ENNReal.add_lt_add h₁ h₂).trans_le h
 #align emetric.ball_disjoint EMetric.ball_disjoint
 
-/- warning: emetric.ball_subset -> EMetric.ball_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.ball_subset EMetric.ball_subsetₓ'. -/
 theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) : ball x ε₁ ⊆ ball y ε₂ :=
   fun z zx =>
   calc
@@ -970,12 +661,6 @@ theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) :
     
 #align emetric.ball_subset EMetric.ball_subset
 
-/- warning: emetric.exists_ball_subset_ball -> EMetric.exists_ball_subset_ball is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (Exists.{1} ENNReal (fun (ε' : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε' (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 y ε') (EMetric.ball.{u1} α _inst_1 x ε))))
-Case conversion may be inaccurate. Consider using '#align emetric.exists_ball_subset_ball EMetric.exists_ball_subset_ballₓ'. -/
 theorem exists_ball_subset_ball (h : y ∈ ball x ε) : ∃ ε' > 0, ball y ε' ⊆ ball x ε :=
   by
   have : 0 < ε - edist y x := by simpa using h
@@ -983,35 +668,17 @@ theorem exists_ball_subset_ball (h : y ∈ ball x ε) : ∃ ε' > 0, ball y ε'
   exact (add_tsub_cancel_of_le (mem_ball.mp h).le).le
 #align emetric.exists_ball_subset_ball EMetric.exists_ball_subset_ball
 
-/- warning: emetric.ball_eq_empty_iff -> EMetric.ball_eq_empty_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, Iff (Eq.{succ u1} (Set.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Eq.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, Iff (Eq.{succ u1} (Set.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Eq.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
-Case conversion may be inaccurate. Consider using '#align emetric.ball_eq_empty_iff EMetric.ball_eq_empty_iffₓ'. -/
 theorem ball_eq_empty_iff : ball x ε = ∅ ↔ ε = 0 :=
   eq_empty_iff_forall_not_mem.trans
     ⟨fun h => le_bot_iff.1 (le_of_not_gt fun ε0 => h _ (mem_ball_self ε0)), fun ε0 y h =>
       not_lt_of_le (le_of_eq ε0) (pos_of_mem_ball h)⟩
 #align emetric.ball_eq_empty_iff EMetric.ball_eq_empty_iff
 
-/- warning: emetric.ord_connected_set_of_closed_ball_subset -> EMetric.ordConnected_setOf_closedBall_subset is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (s : Set.{u1} α), Set.OrdConnected.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (setOf.{0} ENNReal (fun (r : ENNReal) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x r) s))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align emetric.ord_connected_set_of_closed_ball_subset EMetric.ordConnected_setOf_closedBall_subsetₓ'. -/
 theorem ordConnected_setOf_closedBall_subset (x : α) (s : Set α) :
     OrdConnected { r | closedBall x r ⊆ s } :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (closedBall_subset_closedBall hr.2).trans hr₂⟩
 #align emetric.ord_connected_set_of_closed_ball_subset EMetric.ordConnected_setOf_closedBall_subset
 
-/- warning: emetric.ord_connected_set_of_ball_subset -> EMetric.ordConnected_setOf_ball_subset is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.ord_connected_set_of_ball_subset EMetric.ordConnected_setOf_ball_subsetₓ'. -/
 theorem ordConnected_setOf_ball_subset (x : α) (s : Set α) : OrdConnected { r | ball x r ⊆ s } :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (ball_subset_ball hr.2).trans hr₂⟩
 #align emetric.ord_connected_set_of_ball_subset EMetric.ordConnected_setOf_ball_subset
@@ -1026,83 +693,35 @@ def edistLtTopSetoid : Setoid α where
 #align emetric.edist_lt_top_setoid EMetric.edistLtTopSetoid
 -/
 
-/- warning: emetric.ball_zero -> EMetric.ball_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.ball_zero EMetric.ball_zeroₓ'. -/
 @[simp]
 theorem ball_zero : ball x 0 = ∅ := by rw [EMetric.ball_eq_empty_iff]
 #align emetric.ball_zero EMetric.ball_zero
 
-/- warning: emetric.nhds_basis_eball -> EMetric.nhds_basis_eball is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.nhds_basis_eball EMetric.nhds_basis_eballₓ'. -/
 theorem nhds_basis_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) (ball x) :=
   nhds_basis_uniformity uniformity_basis_edist
 #align emetric.nhds_basis_eball EMetric.nhds_basis_eball
 
-/- warning: emetric.nhds_within_basis_eball -> EMetric.nhdsWithin_basis_eball is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)
-Case conversion may be inaccurate. Consider using '#align emetric.nhds_within_basis_eball EMetric.nhdsWithin_basis_eballₓ'. -/
 theorem nhdsWithin_basis_eball : (𝓝[s] x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => ball x ε ∩ s :=
   nhdsWithin_hasBasis nhds_basis_eball s
 #align emetric.nhds_within_basis_eball EMetric.nhdsWithin_basis_eball
 
-/- warning: emetric.nhds_basis_closed_eball -> EMetric.nhds_basis_closed_eball is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (EMetric.closedBall.{u1} α _inst_1 x)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (EMetric.closedBall.{u1} α _inst_1 x)
-Case conversion may be inaccurate. Consider using '#align emetric.nhds_basis_closed_eball EMetric.nhds_basis_closed_eballₓ'. -/
 theorem nhds_basis_closed_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) (closedBall x) :=
   nhds_basis_uniformity uniformity_basis_edist_le
 #align emetric.nhds_basis_closed_eball EMetric.nhds_basis_closed_eball
 
-/- warning: emetric.nhds_within_basis_closed_eball -> EMetric.nhdsWithin_basis_closed_eball is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) s)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) s)
-Case conversion may be inaccurate. Consider using '#align emetric.nhds_within_basis_closed_eball EMetric.nhdsWithin_basis_closed_eballₓ'. -/
 theorem nhdsWithin_basis_closed_eball :
     (𝓝[s] x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => closedBall x ε ∩ s :=
   nhdsWithin_hasBasis nhds_basis_closed_eball s
 #align emetric.nhds_within_basis_closed_eball EMetric.nhdsWithin_basis_closed_eball
 
-/- warning: emetric.nhds_eq -> EMetric.nhds_eq is a dubious translation:
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-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (iInf.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
-Case conversion may be inaccurate. Consider using '#align emetric.nhds_eq EMetric.nhds_eqₓ'. -/
 theorem nhds_eq : 𝓝 x = ⨅ ε > 0, 𝓟 (ball x ε) :=
   nhds_basis_eball.eq_biInf
 #align emetric.nhds_eq EMetric.nhds_eq
 
-/- warning: emetric.mem_nhds_iff -> EMetric.mem_nhds_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)))
-Case conversion may be inaccurate. Consider using '#align emetric.mem_nhds_iff EMetric.mem_nhds_iffₓ'. -/
 theorem mem_nhds_iff : s ∈ 𝓝 x ↔ ∃ ε > 0, ball x ε ⊆ s :=
   nhds_basis_eball.mem_iff
 #align emetric.mem_nhds_iff EMetric.mem_nhds_iff
 
-/- warning: emetric.mem_nhds_within_iff -> EMetric.mem_nhdsWithin_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x t)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) t) s)))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x t)) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) t) s)))
-Case conversion may be inaccurate. Consider using '#align emetric.mem_nhds_within_iff EMetric.mem_nhdsWithin_iffₓ'. -/
 theorem mem_nhdsWithin_iff : s ∈ 𝓝[t] x ↔ ∃ ε > 0, ball x ε ∩ t ⊆ s :=
   nhdsWithin_basis_eball.mem_iff
 #align emetric.mem_nhds_within_iff EMetric.mem_nhdsWithin_iff
@@ -1111,12 +730,6 @@ section
 
 variable [PseudoEMetricSpace β] {f : α → β}
 
-/- warning: emetric.tendsto_nhds_within_nhds_within -> EMetric.tendsto_nhdsWithin_nhdsWithin is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {t : Set.{u2} β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhdsWithin.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b t)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (f x) t) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε))))))
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-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_within_nhds_within EMetric.tendsto_nhdsWithin_nhdsWithinₓ'. -/
 theorem tendsto_nhdsWithin_nhdsWithin {t : Set β} {a b} :
     Tendsto f (𝓝[s] a) (𝓝[t] b) ↔
       ∀ ε > 0, ∃ δ > 0, ∀ ⦃x⦄, x ∈ s → edist x a < δ → f x ∈ t ∧ edist (f x) b < ε :=
@@ -1124,24 +737,12 @@ theorem tendsto_nhdsWithin_nhdsWithin {t : Set β} {a b} :
     forall₂_congr fun ε hε => exists₂_congr fun δ hδ => forall_congr' fun x => by simp <;> itauto
 #align emetric.tendsto_nhds_within_nhds_within EMetric.tendsto_nhdsWithin_nhdsWithin
 
-/- warning: emetric.tendsto_nhds_within_nhds -> EMetric.tendsto_nhdsWithin_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
-but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε)))))
-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_within_nhds EMetric.tendsto_nhdsWithin_nhdsₓ'. -/
 theorem tendsto_nhdsWithin_nhds {a b} :
     Tendsto f (𝓝[s] a) (𝓝 b) ↔
       ∀ ε > 0, ∃ δ > 0, ∀ {x : α}, x ∈ s → edist x a < δ → edist (f x) b < ε :=
   by rw [← nhdsWithin_univ b, tendsto_nhds_within_nhds_within]; simp only [mem_univ, true_and_iff]
 #align emetric.tendsto_nhds_within_nhds EMetric.tendsto_nhdsWithin_nhds
 
-/- warning: emetric.tendsto_nhds_nhds -> EMetric.tendsto_nhds_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
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-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {{x : α}}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε)))))
-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_nhds EMetric.tendsto_nhds_nhdsₓ'. -/
 theorem tendsto_nhds_nhds {a b} :
     Tendsto f (𝓝 a) (𝓝 b) ↔ ∀ ε > 0, ∃ δ > 0, ∀ ⦃x⦄, edist x a < δ → edist (f x) b < ε :=
   nhds_basis_eball.tendsto_iffₓ nhds_basis_eball
@@ -1149,12 +750,6 @@ theorem tendsto_nhds_nhds {a b} :
 
 end
 
-/- warning: emetric.is_open_iff -> EMetric.isOpen_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (IsOpen.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (IsOpen.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s))))
-Case conversion may be inaccurate. Consider using '#align emetric.is_open_iff EMetric.isOpen_iffₓ'. -/
 theorem isOpen_iff : IsOpen s ↔ ∀ x ∈ s, ∃ ε > 0, ball x ε ⊆ s := by
   simp [isOpen_iff_nhds, mem_nhds_iff]
 #align emetric.is_open_iff EMetric.isOpen_iff
@@ -1165,12 +760,6 @@ theorem isOpen_ball : IsOpen (ball x ε) :=
 #align emetric.is_open_ball EMetric.isOpen_ball
 -/
 
-/- warning: emetric.is_closed_ball_top -> EMetric.isClosed_ball_top is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, IsClosed.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (EMetric.ball.{u1} α _inst_1 x (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, IsClosed.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (EMetric.ball.{u1} α _inst_1 x (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
-Case conversion may be inaccurate. Consider using '#align emetric.is_closed_ball_top EMetric.isClosed_ball_topₓ'. -/
 theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
   isOpen_compl_iff.1 <|
     isOpen_iff.2 fun y hy =>
@@ -1178,22 +767,10 @@ theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
         (ball_disjoint <| by rw [top_add]; exact le_of_not_lt hy).subset_compl_right⟩
 #align emetric.is_closed_ball_top EMetric.isClosed_ball_top
 
-/- warning: emetric.ball_mem_nhds -> EMetric.ball_mem_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
-Case conversion may be inaccurate. Consider using '#align emetric.ball_mem_nhds EMetric.ball_mem_nhdsₓ'. -/
 theorem ball_mem_nhds (x : α) {ε : ℝ≥0∞} (ε0 : 0 < ε) : ball x ε ∈ 𝓝 x :=
   isOpen_ball.mem_nhds (mem_ball_self ε0)
 #align emetric.ball_mem_nhds EMetric.ball_mem_nhds
 
-/- warning: emetric.closed_ball_mem_nhds -> EMetric.closedBall_mem_nhds is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
-Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_mem_nhds EMetric.closedBall_mem_nhdsₓ'. -/
 theorem closedBall_mem_nhds (x : α) {ε : ℝ≥0∞} (ε0 : 0 < ε) : closedBall x ε ∈ 𝓝 x :=
   mem_of_superset (ball_mem_nhds x ε0) ball_subset_closedBall
 #align emetric.closed_ball_mem_nhds EMetric.closedBall_mem_nhds
@@ -1214,56 +791,26 @@ theorem closedBall_prod_same [PseudoEMetricSpace β] (x : α) (y : β) (r : ℝ
 #align emetric.closed_ball_prod_same EMetric.closedBall_prod_same
 -/
 
-/- warning: emetric.mem_closure_iff -> EMetric.mem_closure_iff is a dubious translation:
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 /-- ε-characterization of the closure in pseudoemetric spaces -/
 theorem mem_closure_iff : x ∈ closure s ↔ ∀ ε > 0, ∃ y ∈ s, edist x y < ε :=
   (mem_closure_iff_nhds_basis nhds_basis_eball).trans <| by simp only [mem_ball, edist_comm x]
 #align emetric.mem_closure_iff EMetric.mem_closure_iff
 
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 theorem tendsto_nhds {f : Filter β} {u : β → α} {a : α} :
     Tendsto u f (𝓝 a) ↔ ∀ ε > 0, ∀ᶠ x in f, edist (u x) a < ε :=
   nhds_basis_eball.tendsto_right_iff
 #align emetric.tendsto_nhds EMetric.tendsto_nhds
 
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-Case conversion may be inaccurate. Consider using '#align emetric.tendsto_at_top EMetric.tendsto_atTopₓ'. -/
 theorem tendsto_atTop [Nonempty β] [SemilatticeSup β] {u : β → α} {a : α} :
     Tendsto u atTop (𝓝 a) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, edist (u n) a < ε :=
   (atTop_basis.tendsto_iffₓ nhds_basis_eball).trans <| by
     simp only [exists_prop, true_and_iff, mem_Ici, mem_ball]
 #align emetric.tendsto_at_top EMetric.tendsto_atTop
 
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-Case conversion may be inaccurate. Consider using '#align emetric.inseparable_iff EMetric.inseparable_iffₓ'. -/
 theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
   simp [inseparable_iff_mem_closure, mem_closure_iff, edist_comm, forall_lt_iff_le']
 #align emetric.inseparable_iff EMetric.inseparable_iff
 
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 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 -- see Note [nolint_ge]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
@@ -1274,24 +821,12 @@ theorem cauchySeq_iff [Nonempty β] [SemilatticeSup β] {u : β → α} :
   uniformity_basis_edist.cauchySeq_iff
 #align emetric.cauchy_seq_iff EMetric.cauchySeq_iff
 
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-Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff' EMetric.cauchySeq_iff'ₓ'. -/
 /-- A variation around the emetric characterization of Cauchy sequences -/
 theorem cauchySeq_iff' [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ ∀ ε > (0 : ℝ≥0∞), ∃ N, ∀ n ≥ N, edist (u n) (u N) < ε :=
   uniformity_basis_edist.cauchySeq_iff'
 #align emetric.cauchy_seq_iff' EMetric.cauchySeq_iff'
 
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-Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff_nnreal EMetric.cauchySeq_iff_NNRealₓ'. -/
 /-- A variation of the emetric characterization of Cauchy sequences that deals with
 `ℝ≥0` upper bounds. -/
 theorem cauchySeq_iff_NNReal [Nonempty β] [SemilatticeSup β] {u : β → α} :
@@ -1299,12 +834,6 @@ theorem cauchySeq_iff_NNReal [Nonempty β] [SemilatticeSup β] {u : β → α} :
   uniformity_basis_edist_nnreal.cauchySeq_iff'
 #align emetric.cauchy_seq_iff_nnreal EMetric.cauchySeq_iff_NNReal
 
-/- warning: emetric.totally_bounded_iff -> EMetric.totallyBounded_iff is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff EMetric.totallyBounded_iffₓ'. -/
 theorem totallyBounded_iff {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ t : Set α, t.Finite ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => H _ (edist_mem_uniformity ε0), fun H r ru =>
@@ -1313,12 +842,6 @@ theorem totallyBounded_iff {s : Set α} :
     ⟨t, ft, h.trans <| iUnion₂_mono fun y yt z => hε⟩⟩
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
 
-/- warning: emetric.totally_bounded_iff' -> EMetric.totallyBounded_iff' is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
@@ -1330,12 +853,6 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
-/- warning: emetric.subset_countable_closure_of_almost_dense_set -> EMetric.subset_countable_closure_of_almost_dense_set is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_setₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
@@ -1371,12 +888,6 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 
-/- warning: emetric.subset_countable_closure_of_compact -> EMetric.subset_countable_closure_of_compact is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.subset_countable_closure_of_compact EMetric.subset_countable_closure_of_compactₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
@@ -1412,12 +923,6 @@ theorem secondCountable_of_sigmaCompact [SigmaCompactSpace α] : SecondCountable
 
 variable {α}
 
-/- warning: emetric.second_countable_of_almost_dense_set -> EMetric.secondCountable_of_almost_dense_set is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.second_countable_of_almost_dense_set EMetric.secondCountable_of_almost_dense_setₓ'. -/
 theorem secondCountable_of_almost_dense_set
     (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ (⋃ x ∈ t, closedBall x ε) = univ) :
     SecondCountableTopology α :=
@@ -1441,111 +946,51 @@ noncomputable def diam (s : Set α) :=
 #align emetric.diam EMetric.diam
 -/
 
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_le_iff EMetric.diam_le_iffₓ'. -/
 theorem diam_le_iff {d : ℝ≥0∞} : diam s ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d := by
   simp only [diam, iSup_le_iff]
 #align emetric.diam_le_iff EMetric.diam_le_iff
 
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_image_le_iff EMetric.diam_image_le_iffₓ'. -/
 theorem diam_image_le_iff {d : ℝ≥0∞} {f : β → α} {s : Set β} :
     diam (f '' s) ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist (f x) (f y) ≤ d := by
   simp only [diam_le_iff, ball_image_iff]
 #align emetric.diam_image_le_iff EMetric.diam_image_le_iff
 
-/- warning: emetric.edist_le_of_diam_le -> EMetric.edist_le_of_diam_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.edist_le_of_diam_le EMetric.edist_le_of_diam_leₓ'. -/
 theorem edist_le_of_diam_le {d} (hx : x ∈ s) (hy : y ∈ s) (hd : diam s ≤ d) : edist x y ≤ d :=
   diam_le_iff.1 hd x hx y hy
 #align emetric.edist_le_of_diam_le EMetric.edist_le_of_diam_le
 
-/- warning: emetric.edist_le_diam_of_mem -> EMetric.edist_le_diam_of_mem is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.edist_le_diam_of_mem EMetric.edist_le_diam_of_memₓ'. -/
 /-- If two points belong to some set, their edistance is bounded by the diameter of the set -/
 theorem edist_le_diam_of_mem (hx : x ∈ s) (hy : y ∈ s) : edist x y ≤ diam s :=
   edist_le_of_diam_le hx hy le_rfl
 #align emetric.edist_le_diam_of_mem EMetric.edist_le_diam_of_mem
 
-/- warning: emetric.diam_le -> EMetric.diam_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_le EMetric.diam_leₓ'. -/
 /-- If the distance between any two points in a set is bounded by some constant, this constant
 bounds the diameter. -/
 theorem diam_le {d : ℝ≥0∞} (h : ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d) : diam s ≤ d :=
   diam_le_iff.2 h
 #align emetric.diam_le EMetric.diam_le
 
-/- warning: emetric.diam_subsingleton -> EMetric.diam_subsingleton is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_subsingleton EMetric.diam_subsingletonₓ'. -/
 /-- The diameter of a subsingleton vanishes. -/
 theorem diam_subsingleton (hs : s.Subsingleton) : diam s = 0 :=
   nonpos_iff_eq_zero.1 <| diam_le fun x hx y hy => (hs hx hy).symm ▸ edist_self y ▸ le_rfl
 #align emetric.diam_subsingleton EMetric.diam_subsingleton
 
-/- warning: emetric.diam_empty -> EMetric.diam_empty is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_empty EMetric.diam_emptyₓ'. -/
 /-- The diameter of the empty set vanishes -/
 @[simp]
 theorem diam_empty : diam (∅ : Set α) = 0 :=
   diam_subsingleton subsingleton_empty
 #align emetric.diam_empty EMetric.diam_empty
 
-/- warning: emetric.diam_singleton -> EMetric.diam_singleton is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_singleton EMetric.diam_singletonₓ'. -/
 /-- The diameter of a singleton vanishes -/
 @[simp]
 theorem diam_singleton : diam ({x} : Set α) = 0 :=
   diam_subsingleton subsingleton_singleton
 #align emetric.diam_singleton EMetric.diam_singleton
 
-/- warning: emetric.diam_Union_mem_option -> EMetric.diam_iUnion_mem_option is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_optionₓ'. -/
 theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp
 #align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_option
 
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_insert EMetric.diam_insertₓ'. -/
 theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s) :=
   eq_of_forall_ge_iff fun d => by
     simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, iSup_le_iff,
@@ -1558,34 +1003,16 @@ theorem diam_pair : diam ({x, y} : Set α) = edist x y := by
 #align emetric.diam_pair EMetric.diam_pair
 -/
 
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_triple EMetric.diam_tripleₓ'. -/
 theorem diam_triple : diam ({x, y, z} : Set α) = max (max (edist x y) (edist x z)) (edist y z) := by
   simp only [diam_insert, iSup_insert, iSup_singleton, diam_singleton, ENNReal.max_zero_right,
     ENNReal.sup_eq_max]
 #align emetric.diam_triple EMetric.diam_triple
 
-/- warning: emetric.diam_mono -> EMetric.diam_mono is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_mono EMetric.diam_monoₓ'. -/
 /-- The diameter is monotonous with respect to inclusion -/
 theorem diam_mono {s t : Set α} (h : s ⊆ t) : diam s ≤ diam t :=
   diam_le fun x hx y hy => edist_le_diam_of_mem (h hx) (h hy)
 #align emetric.diam_mono EMetric.diam_mono
 
-/- warning: emetric.diam_union -> EMetric.diam_union is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_union EMetric.diam_unionₓ'. -/
 /-- The diameter of a union is controlled by the diameter of the sets, and the edistance
 between two points in the sets. -/
 theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
@@ -1614,24 +1041,12 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       
 #align emetric.diam_union EMetric.diam_union
 
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_union' EMetric.diam_union'ₓ'. -/
 theorem diam_union' {t : Set α} (h : (s ∩ t).Nonempty) : diam (s ∪ t) ≤ diam s + diam t :=
   by
   let ⟨x, ⟨xs, xt⟩⟩ := h
   simpa using diam_union xs xt
 #align emetric.diam_union' EMetric.diam_union'
 
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_closed_ball EMetric.diam_closedBallₓ'. -/
 theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
   diam_le fun a ha b hb =>
     calc
@@ -1641,22 +1056,10 @@ theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
       
 #align emetric.diam_closed_ball EMetric.diam_closedBall
 
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_ball EMetric.diam_ballₓ'. -/
 theorem diam_ball {r : ℝ≥0∞} : diam (ball x r) ≤ 2 * r :=
   le_trans (diam_mono ball_subset_closedBall) diam_closedBall
 #align emetric.diam_ball EMetric.diam_ball
 
-/- warning: emetric.diam_pi_le_of_le -> EMetric.diam_pi_le_of_le is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align emetric.diam_pi_le_of_le EMetric.diam_pi_le_of_leₓ'. -/
 theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, diam (s b) ≤ c) : diam (Set.pi univ s) ≤ c :=
   by
@@ -1681,55 +1084,25 @@ variable {γ : Type w} [EMetricSpace γ]
 
 export EMetricSpace (eq_of_edist_eq_zero)
 
-/- warning: edist_eq_zero -> edist_eq_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align edist_eq_zero edist_eq_zeroₓ'. -/
 /-- Characterize the equality of points by the vanishing of their extended distance -/
 @[simp]
 theorem edist_eq_zero {x y : γ} : edist x y = 0 ↔ x = y :=
   Iff.intro eq_of_edist_eq_zero fun this : x = y => this ▸ edist_self _
 #align edist_eq_zero edist_eq_zero
 
-/- warning: zero_eq_edist -> zero_eq_edist is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align zero_eq_edist zero_eq_edistₓ'. -/
 @[simp]
 theorem zero_eq_edist {x y : γ} : 0 = edist x y ↔ x = y :=
   Iff.intro (fun h => eq_of_edist_eq_zero h.symm) fun this : x = y => this ▸ (edist_self _).symm
 #align zero_eq_edist zero_eq_edist
 
-/- warning: edist_le_zero -> edist_le_zero is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align edist_le_zero edist_le_zeroₓ'. -/
 theorem edist_le_zero {x y : γ} : edist x y ≤ 0 ↔ x = y :=
   nonpos_iff_eq_zero.trans edist_eq_zero
 #align edist_le_zero edist_le_zero
 
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-Case conversion may be inaccurate. Consider using '#align edist_pos edist_posₓ'. -/
 @[simp]
 theorem edist_pos {x y : γ} : 0 < edist x y ↔ x ≠ y := by simp [← not_le]
 #align edist_pos edist_pos
 
-/- warning: eq_of_forall_edist_le -> eq_of_forall_edist_le is a dubious translation:
-lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) ε)) -> (Eq.{succ u1} γ x y)
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align eq_of_forall_edist_le eq_of_forall_edist_leₓ'. -/
 /-- Two points coincide if their distance is `< ε` for all positive ε -/
 theorem eq_of_forall_edist_le {x y : γ} (h : ∀ ε > 0, edist x y ≤ ε) : x = y :=
   eq_of_edist_eq_zero (eq_of_le_of_forall_le_of_dense bot_le h)
@@ -1744,12 +1117,6 @@ instance (priority := 100) to_separated : SeparatedSpace γ :=
 #align to_separated to_separated
 -/
 
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-Case conversion may be inaccurate. Consider using '#align emetric.uniform_embedding_iff' EMetric.uniformEmbedding_iff'ₓ'. -/
 /-- A map between emetric spaces is a uniform embedding if and only if the edistance between `f x`
 and `f y` is controlled in terms of the distance between `x` and `y` and conversely. -/
 theorem EMetric.uniformEmbedding_iff' [EMetricSpace β] {f : γ → β} :
@@ -1832,12 +1199,6 @@ instance Prod.emetricSpaceMax [EMetricSpace β] : EMetricSpace (γ × β) :=
 #align prod.emetric_space_max Prod.emetricSpaceMax
 -/
 
-/- warning: uniformity_edist -> uniformity_edist is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align uniformity_edist uniformity_edistₓ'. -/
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_edist : 𝓤 γ = ⨅ ε > 0, 𝓟 { p : γ × γ | edist p.1 p.2 < ε } :=
   PseudoEMetricSpace.uniformity_edist
@@ -1869,12 +1230,6 @@ end Pi
 
 namespace Emetric
 
-/- warning: emetric.countable_closure_of_compact -> EMetric.countable_closure_of_compact is a dubious translation:
-lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, (IsCompact.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) s) -> (Exists.{succ u1} (Set.{u1} γ) (fun (t : Set.{u1} γ) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} γ) (Set.hasSubset.{u1} γ) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} γ) (Set.hasSubset.{u1} γ) t s) => And (Set.Countable.{u1} γ t) (Eq.{succ u1} (Set.{u1} γ) s (closure.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) t)))))
-but is expected to have type
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, (IsCompact.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) s) -> (Exists.{succ u1} (Set.{u1} γ) (fun (t : Set.{u1} γ) => And (HasSubset.Subset.{u1} (Set.{u1} γ) (Set.instHasSubsetSet.{u1} γ) t s) (And (Set.Countable.{u1} γ t) (Eq.{succ u1} (Set.{u1} γ) s (closure.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) t)))))
-Case conversion may be inaccurate. Consider using '#align emetric.countable_closure_of_compact EMetric.countable_closure_of_compactₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
@@ -1888,22 +1243,10 @@ section Diam
 
 variable {s : Set γ}
 
-/- warning: emetric.diam_eq_zero_iff -> EMetric.diam_eq_zero_iff is a dubious translation:
-lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (Eq.{1} ENNReal (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2) s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Set.Subsingleton.{u1} γ s)
-but is expected to have type
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (Eq.{1} ENNReal (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2) s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Set.Subsingleton.{u1} γ s)
-Case conversion may be inaccurate. Consider using '#align emetric.diam_eq_zero_iff EMetric.diam_eq_zero_iffₓ'. -/
 theorem diam_eq_zero_iff : diam s = 0 ↔ s.Subsingleton :=
   ⟨fun h x hx y hy => edist_le_zero.1 <| h ▸ edist_le_diam_of_mem hx hy, diam_subsingleton⟩
 #align emetric.diam_eq_zero_iff EMetric.diam_eq_zero_iff
 
-/- warning: emetric.diam_pos_iff -> EMetric.diam_pos_iff' is a dubious translation:
-lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2) s)) (Exists.{succ u1} γ (fun (x : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) => Exists.{succ u1} γ (fun (y : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) => Ne.{succ u1} γ x y)))))
-but is expected to have type
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2) s)) (Exists.{succ u1} γ (fun (x : γ) => And (Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) (Exists.{succ u1} γ (fun (y : γ) => And (Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) y s) (Ne.{succ u1} γ x y)))))
-Case conversion may be inaccurate. Consider using '#align emetric.diam_pos_iff EMetric.diam_pos_iff'ₓ'. -/
 theorem diam_pos_iff' : 0 < diam s ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y := by
   simp only [pos_iff_ne_zero, Ne.def, diam_eq_zero_iff, Set.Subsingleton, not_forall]
 #align emetric.diam_pos_iff EMetric.diam_pos_iff'

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

@@ -103,11 +103,7 @@ class PseudoEMetricSpace (α : Type u) extends EDist α : Type u where
   edist_comm : ∀ x y : α, edist x y = edist y x
   edist_triangle : ∀ x y z : α, edist x z ≤ edist x y + edist y z
   toUniformSpace : UniformSpace α := uniformSpaceOfEDist edist edist_self edist_comm edist_triangle
-  uniformity_edist :
-    𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α |
-            edist p.1 p.2 < ε } := by
-    intros
-    rfl
+  uniformity_edist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } := by intros ; rfl
 #align pseudo_emetric_space PseudoEMetricSpace
 -/
 
@@ -164,10 +160,8 @@ lean 3 declaration is
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z y))
 Case conversion may be inaccurate. Consider using '#align edist_congr_left edist_congr_leftₓ'. -/
-theorem edist_congr_left {x y z : α} (h : edist x y = 0) : edist z x = edist z y :=
-  by
-  rw [edist_comm z x, edist_comm z y]
-  apply edist_congr_right h
+theorem edist_congr_left {x y z : α} (h : edist x y = 0) : edist z x = edist z y := by
+  rw [edist_comm z x, edist_comm z y]; apply edist_congr_right h
 #align edist_congr_left edist_congr_left
 
 /- warning: edist_triangle4 -> edist_triangle4 is a dubious translation:
@@ -1027,10 +1021,8 @@ theorem ordConnected_setOf_ball_subset (x : α) (s : Set α) : OrdConnected { r
 def edistLtTopSetoid : Setoid α where
   R x y := edist x y < ⊤
   iseqv :=
-    ⟨fun x => by
-      rw [edist_self]
-      exact ENNReal.coe_lt_top, fun x y h => by rwa [edist_comm], fun x y z hxy hyz =>
-      lt_of_le_of_lt (edist_triangle x y z) (ENNReal.add_lt_top.2 ⟨hxy, hyz⟩)⟩
+    ⟨fun x => by rw [edist_self]; exact ENNReal.coe_lt_top, fun x y h => by rwa [edist_comm],
+      fun x y z hxy hyz => lt_of_le_of_lt (edist_triangle x y z) (ENNReal.add_lt_top.2 ⟨hxy, hyz⟩)⟩
 #align emetric.edist_lt_top_setoid EMetric.edistLtTopSetoid
 -/
 
@@ -1141,9 +1133,7 @@ Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_w
 theorem tendsto_nhdsWithin_nhds {a b} :
     Tendsto f (𝓝[s] a) (𝓝 b) ↔
       ∀ ε > 0, ∃ δ > 0, ∀ {x : α}, x ∈ s → edist x a < δ → edist (f x) b < ε :=
-  by
-  rw [← nhdsWithin_univ b, tendsto_nhds_within_nhds_within]
-  simp only [mem_univ, true_and_iff]
+  by rw [← nhdsWithin_univ b, tendsto_nhds_within_nhds_within]; simp only [mem_univ, true_and_iff]
 #align emetric.tendsto_nhds_within_nhds EMetric.tendsto_nhdsWithin_nhds
 
 /- warning: emetric.tendsto_nhds_nhds -> EMetric.tendsto_nhds_nhds is a dubious translation:
@@ -1185,9 +1175,7 @@ theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
   isOpen_compl_iff.1 <|
     isOpen_iff.2 fun y hy =>
       ⟨⊤, ENNReal.coe_lt_top,
-        (ball_disjoint <| by
-            rw [top_add]
-            exact le_of_not_lt hy).subset_compl_right⟩
+        (ball_disjoint <| by rw [top_add]; exact le_of_not_lt hy).subset_compl_right⟩
 #align emetric.is_closed_ball_top EMetric.isClosed_ball_top
 
 /- warning: emetric.ball_mem_nhds -> EMetric.ball_mem_nhds is a dubious translation:
@@ -1362,9 +1350,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     by
     intro r x
     rcases(closed_ball x r ∩ s).eq_empty_or_nonempty with (he | ⟨y, hxy, hys⟩)
-    · refine' ⟨x₀, hx₀, _⟩
-      rw [he]
-      exact empty_subset _
+    · refine' ⟨x₀, hx₀, _⟩; rw [he]; exact empty_subset _
     · refine' ⟨y, hys, fun z hz => _⟩
       calc
         edist z y ≤ edist z x + edist y x := edist_triangle_right _ _ _
@@ -1620,8 +1606,7 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       _ = diam s + edist x y + diam t := (add_assoc _ _ _).symm
       
   · exact A a h'a b h'b
-  · have Z := A b h'b a h'a
-    rwa [edist_comm] at Z
+  · have Z := A b h'b a h'a; rwa [edist_comm] at Z
   ·
     calc
       edist a b ≤ diam t := edist_le_diam_of_mem h'a h'b

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

@@ -542,10 +542,7 @@ theorem complete_of_cauchySeq_tendsto :
 -/
 
 /- warning: emetric.tendsto_locally_uniformly_on_iff -> EMetric.tendstoLocallyUniformlyOn_iff is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι} {s : Set.{u2} β}, Iff (TendstoLocallyUniformlyOn.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (Exists.{succ u2} (Set.{u2} β) (fun (t : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f y) (F n y)) ε)) p)))))
-but is expected to have type
-  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} [_inst_2 : TopologicalSpace.{u3} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι} {s : Set.{u3} β}, Iff (TendstoLocallyUniformlyOn.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) _inst_2 F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (x : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) x s) -> (Exists.{succ u3} (Set.{u3} β) (fun (t : Set.{u3} β) => And (Membership.mem.{u3, u3} (Set.{u3} β) (Filter.{u3} β) (instMembershipSetFilter.{u3} β) t (nhdsWithin.{u3} β _inst_2 x s)) (Filter.Eventually.{u1} ι (fun (n : ι) => forall (y : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f y) (F n y)) ε)) p)))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iffₓ'. -/
 /-- Expressing locally uniform convergence on a set using `edist`. -/
 theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}

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

@@ -46,7 +46,7 @@ variable {α : Type u} {β : Type v} {X : Type _}
 
 /- warning: uniformity_dist_of_mem_uniformity -> uniformity_dist_of_mem_uniformity is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => Exists.{0} (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (iInf.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => Exists.{0} (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (iInf.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toHasLt.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => And (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (iInf.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
 Case conversion may be inaccurate. Consider using '#align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformityₓ'. -/
@@ -69,7 +69,7 @@ export EDist (edist)
 
 /- warning: uniform_space_of_edist -> uniformSpaceOfEDist is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} (edist : α -> α -> ENNReal), (forall (x : α), Eq.{1} ENNReal (edist x x) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : α) (y : α), Eq.{1} ENNReal (edist x y) (edist y x)) -> (forall (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (edist x z) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (edist x y) (edist y z))) -> (UniformSpace.{u1} α)
+  forall {α : Type.{u1}} (edist : α -> α -> ENNReal), (forall (x : α), Eq.{1} ENNReal (edist x x) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : α) (y : α), Eq.{1} ENNReal (edist x y) (edist y x)) -> (forall (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (edist x z) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (edist x y) (edist y z))) -> (UniformSpace.{u1} α)
 but is expected to have type
   forall {α : Type.{u1}} (edist : α -> α -> ENNReal), (forall (x : α), Eq.{1} ENNReal (edist x x) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (x : α) (y : α), Eq.{1} ENNReal (edist x y) (edist y x)) -> (forall (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (edist x z) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (edist x y) (edist y z))) -> (UniformSpace.{u1} α)
 Case conversion may be inaccurate. Consider using '#align uniform_space_of_edist uniformSpaceOfEDistₓ'. -/
@@ -123,7 +123,7 @@ attribute [simp] edist_self
 
 /- warning: edist_triangle_left -> edist_triangle_left is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z y))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z y))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z y))
 Case conversion may be inaccurate. Consider using '#align edist_triangle_left edist_triangle_leftₓ'. -/
@@ -134,7 +134,7 @@ theorem edist_triangle_left (x y z : α) : edist x y ≤ edist z x + edist z y :
 
 /- warning: edist_triangle_right -> edist_triangle_right is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z))
 Case conversion may be inaccurate. Consider using '#align edist_triangle_right edist_triangle_rightₓ'. -/
@@ -172,7 +172,7 @@ theorem edist_congr_left {x y z : α} (h : edist x y = 0) : edist z x = edist z
 
 /- warning: edist_triangle4 -> edist_triangle4 is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α) (t : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x t) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z t))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α) (t : α), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x t) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α) (t : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x t) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z t))
 Case conversion may be inaccurate. Consider using '#align edist_triangle4 edist_triangle4ₓ'. -/
@@ -185,7 +185,7 @@ theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + e
 
 /- warning: edist_le_Ico_sum_edist -> edist_le_Ico_sum_edist is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
 Case conversion may be inaccurate. Consider using '#align edist_le_Ico_sum_edist edist_le_Ico_sum_edistₓ'. -/
@@ -209,7 +209,7 @@ theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
 
 /- warning: edist_le_range_sum_edist -> edist_le_range_sum_edist is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.range n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) (n : Nat), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.range n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.range n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
 Case conversion may be inaccurate. Consider using '#align edist_le_range_sum_edist edist_le_range_sum_edistₓ'. -/
@@ -221,7 +221,7 @@ theorem edist_le_range_sum_edist (f : ℕ → α) (n : ℕ) :
 
 /- warning: edist_le_Ico_sum_of_edist_le -> edist_le_Ico_sum_of_edist_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (forall {d : Nat -> ENNReal}, (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe m k) -> (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => d i))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (forall {d : Nat -> ENNReal}, (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe m k) -> (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => d i))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (forall {d : Nat -> ENNReal}, (forall {k : Nat}, (LE.le.{0} Nat instLENat m k) -> (LT.lt.{0} Nat instLTNat k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m n) (fun (i : Nat) => d i))))
 Case conversion may be inaccurate. Consider using '#align edist_le_Ico_sum_of_edist_le edist_le_Ico_sum_of_edist_leₓ'. -/
@@ -236,7 +236,7 @@ theorem edist_le_Ico_sum_of_edist_le {f : ℕ → α} {m n} (hmn : m ≤ n) {d :
 
 /- warning: edist_le_range_sum_of_edist_le -> edist_le_range_sum_of_edist_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} (n : Nat) {d : Nat -> ENNReal}, (forall {k : Nat}, (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.range n) (fun (i : Nat) => d i)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} (n : Nat) {d : Nat -> ENNReal}, (forall {k : Nat}, (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.range n) (fun (i : Nat) => d i)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} (n : Nat) {d : Nat -> ENNReal}, (forall {k : Nat}, (LT.lt.{0} Nat instLTNat k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.range n) (fun (i : Nat) => d i)))
 Case conversion may be inaccurate. Consider using '#align edist_le_range_sum_of_edist_le edist_le_range_sum_of_edist_leₓ'. -/
@@ -250,7 +250,7 @@ theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → 
 
 /- warning: uniformity_pseudoedist -> uniformity_pseudoedist is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
 Case conversion may be inaccurate. Consider using '#align uniformity_pseudoedist uniformity_pseudoedistₓ'. -/
@@ -269,7 +269,7 @@ theorem uniformSpace_edist :
 
 /- warning: uniformity_basis_edist -> uniformity_basis_edist is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist uniformity_basis_edistₓ'. -/
@@ -280,7 +280,7 @@ theorem uniformity_basis_edist :
 
 /- warning: mem_uniformity_edist -> mem_uniformity_edist is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} (Prod.{u1, u1} α α)}, Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) ε) -> (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 a b) s))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} (Prod.{u1, u1} α α)}, Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) ε) -> (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 a b) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} (Prod.{u1, u1} α α)}, Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) ε) -> (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 a b) s))))
 Case conversion may be inaccurate. Consider using '#align mem_uniformity_edist mem_uniformity_edistₓ'. -/
@@ -292,7 +292,7 @@ theorem mem_uniformity_edist {s : Set (α × α)} :
 
 /- warning: emetric.mk_uniformity_basis -> EMetric.mk_uniformity_basis is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {β : Type.{u2}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Exists.{succ u2} β (fun (x : β) => Exists.{0} (p x) (fun (hx : p x) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (f x) ε)))) -> (Filter.HasBasis.{u1, succ u2} (Prod.{u1, u1} α α) β (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) p (fun (x : β) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (f x))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {β : Type.{u2}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Exists.{succ u2} β (fun (x : β) => Exists.{0} (p x) (fun (hx : p x) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (f x) ε)))) -> (Filter.HasBasis.{u1, succ u2} (Prod.{u1, u1} α α) β (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) p (fun (x : β) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (f x))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] {β : Type.{u1}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Exists.{succ u1} β (fun (x : β) => And (p x) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (f x) ε)))) -> (Filter.HasBasis.{u2, succ u1} (Prod.{u2, u2} α α) β (uniformity.{u2} α (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1)) p (fun (x : β) => setOf.{u2} (Prod.{u2, u2} α α) (fun (p : Prod.{u2, u2} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (Prod.fst.{u2, u2} α α p) (Prod.snd.{u2, u2} α α p)) (f x))))
 Case conversion may be inaccurate. Consider using '#align emetric.mk_uniformity_basis EMetric.mk_uniformity_basisₓ'. -/
@@ -315,7 +315,7 @@ protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f
 
 /- warning: emetric.mk_uniformity_basis_le -> EMetric.mk_uniformity_basis_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {β : Type.{u2}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Exists.{succ u2} β (fun (x : β) => Exists.{0} (p x) (fun (hx : p x) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (f x) ε)))) -> (Filter.HasBasis.{u1, succ u2} (Prod.{u1, u1} α α) β (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) p (fun (x : β) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (f x))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {β : Type.{u2}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Exists.{succ u2} β (fun (x : β) => Exists.{0} (p x) (fun (hx : p x) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (f x) ε)))) -> (Filter.HasBasis.{u1, succ u2} (Prod.{u1, u1} α α) β (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) p (fun (x : β) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (f x))))
 but is expected to have type
   forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] {β : Type.{u1}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Exists.{succ u1} β (fun (x : β) => And (p x) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (f x) ε)))) -> (Filter.HasBasis.{u2, succ u1} (Prod.{u2, u2} α α) β (uniformity.{u2} α (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1)) p (fun (x : β) => setOf.{u2} (Prod.{u2, u2} α α) (fun (p : Prod.{u2, u2} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (Prod.fst.{u2, u2} α α p) (Prod.snd.{u2, u2} α α p)) (f x))))
 Case conversion may be inaccurate. Consider using '#align emetric.mk_uniformity_basis_le EMetric.mk_uniformity_basis_leₓ'. -/
@@ -338,7 +338,7 @@ protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop}
 
 /- warning: uniformity_basis_edist_le -> uniformity_basis_edist_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_le uniformity_basis_edist_leₓ'. -/
@@ -349,7 +349,7 @@ theorem uniformity_basis_edist_le :
 
 /- warning: uniformity_basis_edist' -> uniformity_basis_edist' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.instMembershipSet.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist' uniformity_basis_edist'ₓ'. -/
@@ -362,7 +362,7 @@ theorem uniformity_basis_edist' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
 
 /- warning: uniformity_basis_edist_le' -> uniformity_basis_edist_le' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.instMembershipSet.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_le' uniformity_basis_edist_le'ₓ'. -/
@@ -375,7 +375,7 @@ theorem uniformity_basis_edist_le' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
 
 /- warning: uniformity_basis_edist_nnreal -> uniformity_basis_edist_nnreal is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (ENNReal.some ε)))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_nnreal uniformity_basis_edist_nnrealₓ'. -/
@@ -388,7 +388,7 @@ theorem uniformity_basis_edist_nnreal :
 
 /- warning: uniformity_basis_edist_nnreal_le -> uniformity_basis_edist_nnreal_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (ENNReal.some ε)))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nnreal_leₓ'. -/
@@ -401,7 +401,7 @@ theorem uniformity_basis_edist_nnreal_le :
 
 /- warning: uniformity_basis_edist_inv_nat -> uniformity_basis_edist_inv_nat is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (Inv.inv.{0} ENNReal ENNReal.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) n))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (Inv.inv.{0} ENNReal ENNReal.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) n))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (Nat.cast.{0} ENNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) n))))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_natₓ'. -/
@@ -414,7 +414,7 @@ theorem uniformity_basis_edist_inv_nat :
 
 /- warning: uniformity_basis_edist_inv_two_pow -> uniformity_basis_edist_inv_two_pow is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (Inv.inv.{0} ENNReal ENNReal.hasInv (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))))) n)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (Inv.inv.{0} ENNReal ENNReal.hasInv (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))))) n)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n)))
 Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_powₓ'. -/
@@ -428,7 +428,7 @@ theorem uniformity_basis_edist_inv_two_pow :
 
 /- warning: edist_mem_uniformity -> edist_mem_uniformity is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (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)) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (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)) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (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)) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align edist_mem_uniformity edist_mem_uniformityₓ'. -/
@@ -444,7 +444,7 @@ instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
 
 /- warning: emetric.uniform_continuous_on_iff -> EMetric.uniformContinuousOn_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {s : Set.{u1} α}, Iff (UniformContinuousOn.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s} {b : α} {H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {s : Set.{u1} α}, Iff (UniformContinuousOn.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s} {b : α} {H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {s : Set.{u1} α}, Iff (UniformContinuousOn.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (forall {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε))))))
 Case conversion may be inaccurate. Consider using '#align emetric.uniform_continuous_on_iff EMetric.uniformContinuousOn_iffₓ'. -/
@@ -458,7 +458,7 @@ theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set
 
 /- warning: emetric.uniform_continuous_iff -> EMetric.uniformContinuous_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε)))))
 Case conversion may be inaccurate. Consider using '#align emetric.uniform_continuous_iff EMetric.uniformContinuous_iffₓ'. -/
@@ -470,7 +470,7 @@ theorem uniformContinuous_iff [PseudoEMetricSpace β] {f : α → β} :
 
 /- warning: emetric.uniform_embedding_iff -> EMetric.uniformEmbedding_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ)))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ)))))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ)))))))
 Case conversion may be inaccurate. Consider using '#align emetric.uniform_embedding_iff EMetric.uniformEmbedding_iffₓ'. -/
@@ -487,7 +487,7 @@ theorem uniformEmbedding_iff [PseudoEMetricSpace β] {f : α → β} :
 
 /- warning: emetric.controlled_of_uniform_embedding -> EMetric.controlled_of_uniformEmbedding is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) -> (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) -> (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ))))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) -> (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ))))))
 Case conversion may be inaccurate. Consider using '#align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbeddingₓ'. -/
@@ -502,7 +502,7 @@ theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
 
 /- warning: emetric.cauchy_iff -> EMetric.cauchy_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u1} α}, Iff (Cauchy.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) f) (And (Ne.{succ u1} (Filter.{u1} α) f (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u1} α}, Iff (Cauchy.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) f) (And (Ne.{succ u1} (Filter.{u1} α) f (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u1} α}, Iff (Cauchy.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) f) (And (Ne.{succ u1} (Filter.{u1} α) f (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε)))))))
 Case conversion may be inaccurate. Consider using '#align emetric.cauchy_iff EMetric.cauchy_iffₓ'. -/
@@ -515,7 +515,7 @@ protected theorem cauchy_iff {f : Filter α} :
 
 /- warning: emetric.complete_of_convergent_controlled_sequences -> EMetric.complete_of_convergent_controlled_sequences is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (B : Nat -> ENNReal), (forall (n : Nat), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (B n)) -> (forall (u : Nat -> α), (forall (N : Nat) (n : Nat) (m : Nat), (LE.le.{0} Nat Nat.hasLe N n) -> (LE.le.{0} Nat Nat.hasLe N m) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u m)) (B N))) -> (Exists.{succ u1} α (fun (x : α) => Filter.Tendsto.{0, u1} Nat α u (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 (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)))) -> (CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (B : Nat -> ENNReal), (forall (n : Nat), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (B n)) -> (forall (u : Nat -> α), (forall (N : Nat) (n : Nat) (m : Nat), (LE.le.{0} Nat Nat.hasLe N n) -> (LE.le.{0} Nat Nat.hasLe N m) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u m)) (B N))) -> (Exists.{succ u1} α (fun (x : α) => Filter.Tendsto.{0, u1} Nat α u (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 (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)))) -> (CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (B : Nat -> ENNReal), (forall (n : Nat), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (B n)) -> (forall (u : Nat -> α), (forall (N : Nat) (n : Nat) (m : Nat), (LE.le.{0} Nat instLENat N n) -> (LE.le.{0} Nat instLENat N m) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) (u m)) (B N))) -> (Exists.{succ u1} α (fun (x : α) => Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)))) -> (CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))
 Case conversion may be inaccurate. Consider using '#align emetric.complete_of_convergent_controlled_sequences EMetric.complete_of_convergent_controlled_sequencesₓ'. -/
@@ -543,7 +543,7 @@ theorem complete_of_cauchySeq_tendsto :
 
 /- warning: emetric.tendsto_locally_uniformly_on_iff -> EMetric.tendstoLocallyUniformlyOn_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι} {s : Set.{u2} β}, Iff (TendstoLocallyUniformlyOn.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (Exists.{succ u2} (Set.{u2} β) (fun (t : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f y) (F n y)) ε)) p)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι} {s : Set.{u2} β}, Iff (TendstoLocallyUniformlyOn.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (Exists.{succ u2} (Set.{u2} β) (fun (t : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f y) (F n y)) ε)) p)))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} [_inst_2 : TopologicalSpace.{u3} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι} {s : Set.{u3} β}, Iff (TendstoLocallyUniformlyOn.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) _inst_2 F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (x : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) x s) -> (Exists.{succ u3} (Set.{u3} β) (fun (t : Set.{u3} β) => And (Membership.mem.{u3, u3} (Set.{u3} β) (Filter.{u3} β) (instMembershipSetFilter.{u3} β) t (nhdsWithin.{u3} β _inst_2 x s)) (Filter.Eventually.{u1} ι (fun (n : ι) => forall (y : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f y) (F n y)) ε)) p)))))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iffₓ'. -/
@@ -561,7 +561,7 @@ theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : 
 
 /- warning: emetric.tendsto_uniformly_on_iff -> EMetric.tendstoUniformlyOn_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι} {s : Set.{u2} β}, Iff (TendstoUniformlyOn.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u3} ι (fun (n : ι) => forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (F n x)) ε)) p))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι} {s : Set.{u2} β}, Iff (TendstoUniformlyOn.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u3} ι (fun (n : ι) => forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (F n x)) ε)) p))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι} {s : Set.{u3} β}, Iff (TendstoUniformlyOn.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Filter.Eventually.{u1} ι (fun (n : ι) => forall (x : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f x) (F n x)) ε)) p))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_uniformly_on_iff EMetric.tendstoUniformlyOn_iffₓ'. -/
@@ -576,7 +576,7 @@ theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β →
 
 /- warning: emetric.tendsto_locally_uniformly_iff -> EMetric.tendstoLocallyUniformly_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι}, Iff (TendstoLocallyUniformly.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : β), Exists.{succ u2} (Set.{u2} β) (fun (t : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhds.{u2} β _inst_2 x)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhds.{u2} β _inst_2 x)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f y) (F n y)) ε)) p))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι}, Iff (TendstoLocallyUniformly.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : β), Exists.{succ u2} (Set.{u2} β) (fun (t : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhds.{u2} β _inst_2 x)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhds.{u2} β _inst_2 x)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f y) (F n y)) ε)) p))))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} [_inst_2 : TopologicalSpace.{u3} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι}, Iff (TendstoLocallyUniformly.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) _inst_2 F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (x : β), Exists.{succ u3} (Set.{u3} β) (fun (t : Set.{u3} β) => And (Membership.mem.{u3, u3} (Set.{u3} β) (Filter.{u3} β) (instMembershipSetFilter.{u3} β) t (nhds.{u3} β _inst_2 x)) (Filter.Eventually.{u1} ι (fun (n : ι) => forall (y : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f y) (F n y)) ε)) p))))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_locally_uniformly_iff EMetric.tendstoLocallyUniformly_iffₓ'. -/
@@ -592,7 +592,7 @@ theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι
 
 /- warning: emetric.tendsto_uniformly_iff -> EMetric.tendstoUniformly_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι}, Iff (TendstoUniformly.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u3} ι (fun (n : ι) => forall (x : β), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (F n x)) ε) p))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι}, Iff (TendstoUniformly.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u3} ι (fun (n : ι) => forall (x : β), LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (F n x)) ε) p))
 but is expected to have type
   forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι}, Iff (TendstoUniformly.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Filter.Eventually.{u1} ι (fun (n : ι) => forall (x : β), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f x) (F n x)) ε) p))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_uniformly_iff EMetric.tendstoUniformly_iffₓ'. -/
@@ -782,7 +782,7 @@ theorem edist_pi_def [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b) :
 
 /- warning: edist_le_pi_edist -> edist_le_pi_edist is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] (f : forall (b : β), π b) (g : forall (b : β), π b) (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)) (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g)
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] (f : forall (b : β), π b) (g : forall (b : β), π b) (b : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)) (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g)
 but is expected to have type
   forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), EDist.{u1} (π b)] (f : forall (b : β), π b) (g : forall (b : β), π b) (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} (π b) (_inst_3 b) (f b) (g b)) (EDist.edist.{max u2 u1} (forall (b : β), π b) (instEDistForAll.{u2, u1} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b)) f g)
 Case conversion may be inaccurate. Consider using '#align edist_le_pi_edist edist_le_pi_edistₓ'. -/
@@ -793,7 +793,7 @@ theorem edist_le_pi_edist [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b)
 
 /- warning: edist_pi_le_iff -> edist_pi_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {f : forall (b : β), π b} {g : forall (b : β), π b} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g) d) (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)) d)
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {f : forall (b : β), π b} {g : forall (b : β), π b} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g) d) (forall (b : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)) d)
 but is expected to have type
   forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), EDist.{u1} (π b)] {f : forall (b : β), π b} {g : forall (b : β), π b} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{max u2 u1} (forall (b : β), π b) (instEDistForAll.{u2, u1} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b)) f g) d) (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} (π b) (_inst_3 b) (f b) (g b)) d)
 Case conversion may be inaccurate. Consider using '#align edist_pi_le_iff edist_pi_le_iffₓ'. -/
@@ -804,7 +804,7 @@ theorem edist_pi_le_iff [∀ b, PseudoEMetricSpace (π b)] {f g : ∀ b, π b} {
 
 /- warning: edist_pi_const_le -> edist_pi_const_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Fintype.{u2} β] (a : α) (b : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{max u2 u1} (β -> α) (PseudoEMetricSpace.toHasEdist.{max u2 u1} (β -> α) (pseudoEMetricSpacePi.{u2, u1} β (fun (_x : β) => α) _inst_2 (fun (b : β) => _inst_1))) (fun (_x : β) => a) (fun (_x : β) => b)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b)
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Fintype.{u2} β] (a : α) (b : α), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{max u2 u1} (β -> α) (PseudoEMetricSpace.toHasEdist.{max u2 u1} (β -> α) (pseudoEMetricSpacePi.{u2, u1} β (fun (_x : β) => α) _inst_2 (fun (b : β) => _inst_1))) (fun (_x : β) => a) (fun (_x : β) => b)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b)
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Fintype.{u2} β] (a : α) (b : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{max u1 u2} (β -> α) (instEDistForAll.{u2, u1} β (fun (x._@.Mathlib.Topology.MetricSpace.EMetricSpace._hyg.5043 : β) => α) _inst_2 (fun (b : β) => PseudoEMetricSpace.toEDist.{u1} α _inst_1)) (fun (_x : β) => a) (fun (_x : β) => b)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b)
 Case conversion may be inaccurate. Consider using '#align edist_pi_const_le edist_pi_const_leₓ'. -/
@@ -834,7 +834,7 @@ def ball (x : α) (ε : ℝ≥0∞) : Set α :=
 
 /- warning: emetric.mem_ball -> EMetric.mem_ball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y x) ε)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y x) ε)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y x) ε)
 Case conversion may be inaccurate. Consider using '#align emetric.mem_ball EMetric.mem_ballₓ'. -/
@@ -845,7 +845,7 @@ theorem mem_ball : y ∈ ball x ε ↔ edist y x < ε :=
 
 /- warning: emetric.mem_ball' -> EMetric.mem_ball' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε)
 Case conversion may be inaccurate. Consider using '#align emetric.mem_ball' EMetric.mem_ball'ₓ'. -/
@@ -861,7 +861,7 @@ def closedBall (x : α) (ε : ℝ≥0∞) :=
 
 /- warning: emetric.mem_closed_ball -> EMetric.mem_closedBall is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y x) ε)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y x) ε)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y x) ε)
 Case conversion may be inaccurate. Consider using '#align emetric.mem_closed_ball EMetric.mem_closedBallₓ'. -/
@@ -872,7 +872,7 @@ theorem mem_closedBall : y ∈ closedBall x ε ↔ edist y x ≤ ε :=
 
 /- warning: emetric.mem_closed_ball' -> EMetric.mem_closedBall' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε)
 Case conversion may be inaccurate. Consider using '#align emetric.mem_closed_ball' EMetric.mem_closedBall'ₓ'. -/
@@ -897,7 +897,7 @@ theorem ball_subset_closedBall : ball x ε ⊆ closedBall x ε := fun y hy => le
 
 /- warning: emetric.pos_of_mem_ball -> EMetric.pos_of_mem_ball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε)
 Case conversion may be inaccurate. Consider using '#align emetric.pos_of_mem_ball EMetric.pos_of_mem_ballₓ'. -/
@@ -907,7 +907,7 @@ theorem pos_of_mem_ball (hy : y ∈ ball x ε) : 0 < ε :=
 
 /- warning: emetric.mem_ball_self -> EMetric.mem_ball_self is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (EMetric.ball.{u1} α _inst_1 x ε))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (EMetric.ball.{u1} α _inst_1 x ε))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (EMetric.ball.{u1} α _inst_1 x ε))
 Case conversion may be inaccurate. Consider using '#align emetric.mem_ball_self EMetric.mem_ball_selfₓ'. -/
@@ -934,7 +934,7 @@ theorem mem_closedBall_comm : x ∈ closedBall y ε ↔ y ∈ closedBall x ε :=
 
 /- warning: emetric.ball_subset_ball -> EMetric.ball_subset_ball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 x ε₂))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 x ε₂))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 x ε₂))
 Case conversion may be inaccurate. Consider using '#align emetric.ball_subset_ball EMetric.ball_subset_ballₓ'. -/
@@ -944,7 +944,7 @@ theorem ball_subset_ball (h : ε₁ ≤ ε₂) : ball x ε₁ ⊆ ball x ε₂ :
 
 /- warning: emetric.closed_ball_subset_closed_ball -> EMetric.closedBall_subset_closedBall is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε₁) (EMetric.closedBall.{u1} α _inst_1 x ε₂))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε₁) (EMetric.closedBall.{u1} α _inst_1 x ε₂))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε₁) (EMetric.closedBall.{u1} α _inst_1 x ε₂))
 Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_subset_closed_ball EMetric.closedBall_subset_closedBallₓ'. -/
@@ -954,7 +954,7 @@ theorem closedBall_subset_closedBall (h : ε₁ ≤ ε₂) : closedBall x ε₁
 
 /- warning: emetric.ball_disjoint -> EMetric.ball_disjoint is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ε₁ ε₂) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)) -> (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ε₁ ε₂) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)) -> (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) ε₁ ε₂) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y)) -> (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
 Case conversion may be inaccurate. Consider using '#align emetric.ball_disjoint EMetric.ball_disjointₓ'. -/
@@ -965,7 +965,7 @@ theorem ball_disjoint (h : ε₁ + ε₂ ≤ edist x y) : Disjoint (ball x ε₁
 
 /- warning: emetric.ball_subset -> EMetric.ball_subset is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε₁) ε₂) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε₁) ε₂) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε₁) ε₂) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
 Case conversion may be inaccurate. Consider using '#align emetric.ball_subset EMetric.ball_subsetₓ'. -/
@@ -981,7 +981,7 @@ theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) :
 
 /- warning: emetric.exists_ball_subset_ball -> EMetric.exists_ball_subset_ball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (Exists.{1} ENNReal (fun (ε' : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε' (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε' (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 y ε') (EMetric.ball.{u1} α _inst_1 x ε))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (Exists.{1} ENNReal (fun (ε' : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε' (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε' (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 y ε') (EMetric.ball.{u1} α _inst_1 x ε))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (Exists.{1} ENNReal (fun (ε' : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε' (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 y ε') (EMetric.ball.{u1} α _inst_1 x ε))))
 Case conversion may be inaccurate. Consider using '#align emetric.exists_ball_subset_ball EMetric.exists_ball_subset_ballₓ'. -/
@@ -1049,7 +1049,7 @@ theorem ball_zero : ball x 0 = ∅ := by rw [EMetric.ball_eq_empty_iff]
 
 /- warning: emetric.nhds_basis_eball -> EMetric.nhds_basis_eball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (EMetric.ball.{u1} α _inst_1 x)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (EMetric.ball.{u1} α _inst_1 x)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (EMetric.ball.{u1} α _inst_1 x)
 Case conversion may be inaccurate. Consider using '#align emetric.nhds_basis_eball EMetric.nhds_basis_eballₓ'. -/
@@ -1059,7 +1059,7 @@ theorem nhds_basis_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) (ba
 
 /- warning: emetric.nhds_within_basis_eball -> EMetric.nhdsWithin_basis_eball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)
 Case conversion may be inaccurate. Consider using '#align emetric.nhds_within_basis_eball EMetric.nhdsWithin_basis_eballₓ'. -/
@@ -1069,7 +1069,7 @@ theorem nhdsWithin_basis_eball : (𝓝[s] x).HasBasis (fun ε : ℝ≥0∞ => 0
 
 /- warning: emetric.nhds_basis_closed_eball -> EMetric.nhds_basis_closed_eball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (EMetric.closedBall.{u1} α _inst_1 x)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (EMetric.closedBall.{u1} α _inst_1 x)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (EMetric.closedBall.{u1} α _inst_1 x)
 Case conversion may be inaccurate. Consider using '#align emetric.nhds_basis_closed_eball EMetric.nhds_basis_closed_eballₓ'. -/
@@ -1079,7 +1079,7 @@ theorem nhds_basis_closed_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 <
 
 /- warning: emetric.nhds_within_basis_closed_eball -> EMetric.nhdsWithin_basis_closed_eball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) s)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) s)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) s)
 Case conversion may be inaccurate. Consider using '#align emetric.nhds_within_basis_closed_eball EMetric.nhdsWithin_basis_closed_eballₓ'. -/
@@ -1090,7 +1090,7 @@ theorem nhdsWithin_basis_closed_eball :
 
 /- warning: emetric.nhds_eq -> EMetric.nhds_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (iInf.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (iInf.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (iInf.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
 Case conversion may be inaccurate. Consider using '#align emetric.nhds_eq EMetric.nhds_eqₓ'. -/
@@ -1100,7 +1100,7 @@ theorem nhds_eq : 𝓝 x = ⨅ ε > 0, 𝓟 (ball x ε) :=
 
 /- warning: emetric.mem_nhds_iff -> EMetric.mem_nhds_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)))
 Case conversion may be inaccurate. Consider using '#align emetric.mem_nhds_iff EMetric.mem_nhds_iffₓ'. -/
@@ -1110,7 +1110,7 @@ theorem mem_nhds_iff : s ∈ 𝓝 x ↔ ∃ ε > 0, ball x ε ⊆ s :=
 
 /- warning: emetric.mem_nhds_within_iff -> EMetric.mem_nhdsWithin_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x t)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) t) s)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x t)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) t) s)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x t)) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) t) s)))
 Case conversion may be inaccurate. Consider using '#align emetric.mem_nhds_within_iff EMetric.mem_nhdsWithin_iffₓ'. -/
@@ -1124,7 +1124,7 @@ variable [PseudoEMetricSpace β] {f : α → β}
 
 /- warning: emetric.tendsto_nhds_within_nhds_within -> EMetric.tendsto_nhdsWithin_nhdsWithin is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {t : Set.{u2} β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhdsWithin.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b t)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (f x) t) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {t : Set.{u2} β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhdsWithin.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b t)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (f x) t) (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε))))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {t : Set.{u2} β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhdsWithin.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b t)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {{x : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (And (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) (f x) t) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε))))))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_within_nhds_within EMetric.tendsto_nhdsWithin_nhdsWithinₓ'. -/
@@ -1137,7 +1137,7 @@ theorem tendsto_nhdsWithin_nhdsWithin {t : Set β} {a b} :
 
 /- warning: emetric.tendsto_nhds_within_nhds -> EMetric.tendsto_nhdsWithin_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε)))))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_within_nhds EMetric.tendsto_nhdsWithin_nhdsₓ'. -/
@@ -1151,7 +1151,7 @@ theorem tendsto_nhdsWithin_nhds {a b} :
 
 /- warning: emetric.tendsto_nhds_nhds -> EMetric.tendsto_nhds_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {{x : α}}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε)))))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_nhds EMetric.tendsto_nhds_nhdsₓ'. -/
@@ -1164,7 +1164,7 @@ end
 
 /- warning: emetric.is_open_iff -> EMetric.isOpen_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (IsOpen.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (IsOpen.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (IsOpen.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s))))
 Case conversion may be inaccurate. Consider using '#align emetric.is_open_iff EMetric.isOpen_iffₓ'. -/
@@ -1195,7 +1195,7 @@ theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
 
 /- warning: emetric.ball_mem_nhds -> EMetric.ball_mem_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
 Case conversion may be inaccurate. Consider using '#align emetric.ball_mem_nhds EMetric.ball_mem_nhdsₓ'. -/
@@ -1205,7 +1205,7 @@ theorem ball_mem_nhds (x : α) {ε : ℝ≥0∞} (ε0 : 0 < ε) : ball x ε ∈
 
 /- warning: emetric.closed_ball_mem_nhds -> EMetric.closedBall_mem_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
 Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_mem_nhds EMetric.closedBall_mem_nhdsₓ'. -/
@@ -1231,7 +1231,7 @@ theorem closedBall_prod_same [PseudoEMetricSpace β] (x : α) (y : β) (r : ℝ
 
 /- warning: emetric.mem_closure_iff -> EMetric.mem_closure_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε))))
 Case conversion may be inaccurate. Consider using '#align emetric.mem_closure_iff EMetric.mem_closure_iffₓ'. -/
@@ -1242,7 +1242,7 @@ theorem mem_closure_iff : x ∈ closure s ↔ ∀ ε > 0, ∃ y ∈ s, edist x y
 
 /- warning: emetric.tendsto_nhds -> EMetric.tendsto_nhds is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u2} β (fun (x : β) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u x) a) ε) f))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u2} β (fun (x : β) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u x) a) ε) f))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Filter.Eventually.{u2} β (fun (x : β) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u x) a) ε) f))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds EMetric.tendsto_nhdsₓ'. -/
@@ -1253,7 +1253,7 @@ theorem tendsto_nhds {f : Filter β} {u : β → α} {a : α} :
 
 /- warning: emetric.tendsto_at_top -> EMetric.tendsto_atTop is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) a) ε))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) a) ε))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) a) ε))))
 Case conversion may be inaccurate. Consider using '#align emetric.tendsto_at_top EMetric.tendsto_atTopₓ'. -/
@@ -1275,7 +1275,7 @@ theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
 
 /- warning: emetric.cauchy_seq_iff -> EMetric.cauchySeq_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u m) (u n)) ε)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u m) (u n)) ε)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u2} β (fun (N : β) => forall (m : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N m) -> (forall (n : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N n) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u m) (u n)) ε)))))
 Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff EMetric.cauchySeq_iffₓ'. -/
@@ -1291,7 +1291,7 @@ theorem cauchySeq_iff [Nonempty β] [SemilatticeSup β] {u : β → α} :
 
 /- warning: emetric.cauchy_seq_iff' -> EMetric.cauchySeq_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u N)) ε))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u N)) ε))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) (u N)) ε))))
 Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff' EMetric.cauchySeq_iff'ₓ'. -/
@@ -1303,7 +1303,7 @@ theorem cauchySeq_iff' [Nonempty β] [SemilatticeSup β] {u : β → α} :
 
 /- warning: emetric.cauchy_seq_iff_nnreal -> EMetric.cauchySeq_iff_NNReal is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (Exists.{succ u2} β (fun (N : β) => forall (n : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N n) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u N)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toHasLt.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (Exists.{succ u2} β (fun (N : β) => forall (n : β), (LE.le.{u2} β (Preorder.toHasLe.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N n) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u N)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (Exists.{succ u2} β (fun (N : β) => forall (n : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N n) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) (u N)) (ENNReal.some ε)))))
 Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff_nnreal EMetric.cauchySeq_iff_NNRealₓ'. -/
@@ -1316,7 +1316,7 @@ theorem cauchySeq_iff_NNReal [Nonempty β] [SemilatticeSup β] {u : β → α} :
 
 /- warning: emetric.totally_bounded_iff -> EMetric.totallyBounded_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε)))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε)))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => 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 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε)))))))
 Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff EMetric.totallyBounded_iffₓ'. -/
@@ -1330,7 +1330,7 @@ theorem totallyBounded_iff {s : Set α} :
 
 /- warning: emetric.totally_bounded_iff' -> EMetric.totallyBounded_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε))))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε))))))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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.MetricSpace.EMetricSpace._hyg.9103 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε))))))))
 Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'ₓ'. -/
@@ -1347,7 +1347,7 @@ section Compact
 
 /- warning: emetric.subset_countable_closure_of_almost_dense_set -> EMetric.subset_countable_closure_of_almost_dense_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
 Case conversion may be inaccurate. Consider using '#align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_setₓ'. -/
@@ -1431,7 +1431,7 @@ variable {α}
 
 /- warning: emetric.second_countable_of_almost_dense_set -> EMetric.secondCountable_of_almost_dense_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align emetric.second_countable_of_almost_dense_set EMetric.secondCountable_of_almost_dense_setₓ'. -/
@@ -1460,7 +1460,7 @@ noncomputable def diam (s : Set α) :=
 
 /- warning: emetric.diam_le_iff -> EMetric.diam_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) d) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) d)))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_le_iff EMetric.diam_le_iffₓ'. -/
@@ -1470,7 +1470,7 @@ theorem diam_le_iff {d : ℝ≥0∞} : diam s ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s
 
 /- warning: emetric.diam_image_le_iff -> EMetric.diam_image_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Set.image.{u2, u1} β α f s)) d) (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (f y)) d)))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Set.image.{u2, u1} β α f s)) d) (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y s) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (f y)) d)))
 but is expected to have type
   forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (Set.image.{u2, u1} β α f s)) d) (forall (x : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) -> (forall (y : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f x) (f y)) d)))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_image_le_iff EMetric.diam_image_le_iffₓ'. -/
@@ -1481,7 +1481,7 @@ theorem diam_image_le_iff {d : ℝ≥0∞} {f : β → α} {s : Set β} :
 
 /- warning: emetric.edist_le_of_diam_le -> EMetric.edist_le_of_diam_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {d : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {d : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {d : ENNReal}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) d)
 Case conversion may be inaccurate. Consider using '#align emetric.edist_le_of_diam_le EMetric.edist_le_of_diam_leₓ'. -/
@@ -1491,7 +1491,7 @@ theorem edist_le_of_diam_le {d} (hx : x ∈ s) (hy : y ∈ s) (hd : diam s ≤ d
 
 /- warning: emetric.edist_le_diam_of_mem -> EMetric.edist_le_diam_of_mem is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EMetric.diam.{u1} α _inst_1 s))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EMetric.diam.{u1} α _inst_1 s))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (EMetric.diam.{u1} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align emetric.edist_le_diam_of_mem EMetric.edist_le_diam_of_memₓ'. -/
@@ -1502,7 +1502,7 @@ theorem edist_le_diam_of_mem (hx : x ∈ s) (hy : y ∈ s) : edist x y ≤ diam
 
 /- warning: emetric.diam_le -> EMetric.diam_le is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) d))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) d)
 Case conversion may be inaccurate. Consider using '#align emetric.diam_le EMetric.diam_leₓ'. -/
@@ -1588,7 +1588,7 @@ theorem diam_triple : diam ({x, y, z} : Set α) = max (max (edist x y) (edist x
 
 /- warning: emetric.diam_mono -> EMetric.diam_mono is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_mono EMetric.diam_monoₓ'. -/
@@ -1599,7 +1599,7 @@ theorem diam_mono {s t : Set α} (h : s ⊆ t) : diam s ≤ diam t :=
 
 /- warning: emetric.diam_union -> EMetric.diam_union is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {t : Set.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EMetric.diam.{u1} α _inst_1 s) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)) (EMetric.diam.{u1} α _inst_1 t)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {t : Set.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EMetric.diam.{u1} α _inst_1 s) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)) (EMetric.diam.{u1} α _inst_1 t)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {t : Set.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EMetric.diam.{u1} α _inst_1 s) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y)) (EMetric.diam.{u1} α _inst_1 t)))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_union EMetric.diam_unionₓ'. -/
@@ -1634,7 +1634,7 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
 
 /- warning: emetric.diam_union' -> EMetric.diam_union' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t)))
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t)))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_union' EMetric.diam_union'ₓ'. -/
@@ -1646,7 +1646,7 @@ theorem diam_union' {t : Set α} (h : (s ∩ t).Nonempty) : diam (s ∪ t) ≤ d
 
 /- warning: emetric.diam_closed_ball -> EMetric.diam_closedBall is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (EMetric.closedBall.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) r)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (EMetric.closedBall.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) r)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (EMetric.closedBall.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) r)
 Case conversion may be inaccurate. Consider using '#align emetric.diam_closed_ball EMetric.diam_closedBallₓ'. -/
@@ -1661,7 +1661,7 @@ theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
 
 /- warning: emetric.diam_ball -> EMetric.diam_ball is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (EMetric.ball.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) r)
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (EMetric.ball.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) r)
 but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (EMetric.ball.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) r)
 Case conversion may be inaccurate. Consider using '#align emetric.diam_ball EMetric.diam_ballₓ'. -/
@@ -1671,7 +1671,7 @@ theorem diam_ball {r : ℝ≥0∞} : diam (ball x r) ≤ 2 * r :=
 
 /- warning: emetric.diam_pi_le_of_le -> EMetric.diam_pi_le_of_le is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u2} (π b) (_inst_3 b) (s b)) c) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b)) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)) c)
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u2} (π b) (_inst_3 b) (s b)) c) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b)) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)) c)
 but is expected to have type
   forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u1} (π b)] {s : forall (b : β), Set.{u1} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} (π b) (_inst_3 b) (s b)) c) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u2, u1} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b)) (Set.pi.{u2, u1} β (fun (b : β) => π b) (Set.univ.{u2} β) s)) c)
 Case conversion may be inaccurate. Consider using '#align emetric.diam_pi_le_of_le EMetric.diam_pi_le_of_leₓ'. -/
@@ -1724,7 +1724,7 @@ theorem zero_eq_edist {x y : γ} : 0 = edist x y ↔ x = y :=
 
 /- warning: edist_le_zero -> edist_le_zero is a dubious translation:
 lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Eq.{succ u1} γ x y)
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Eq.{succ u1} γ x y)
 but is expected to have type
   forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Eq.{succ u1} γ x y)
 Case conversion may be inaccurate. Consider using '#align edist_le_zero edist_le_zeroₓ'. -/
@@ -1734,7 +1734,7 @@ theorem edist_le_zero {x y : γ} : edist x y ≤ 0 ↔ x = y :=
 
 /- warning: edist_pos -> edist_pos is a dubious translation:
 lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y)) (Ne.{succ u1} γ x y)
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y)) (Ne.{succ u1} γ x y)
 but is expected to have type
   forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y)) (Ne.{succ u1} γ x y)
 Case conversion may be inaccurate. Consider using '#align edist_pos edist_posₓ'. -/
@@ -1744,7 +1744,7 @@ theorem edist_pos {x y : γ} : 0 < edist x y ↔ x ≠ y := by simp [← not_le]
 
 /- warning: eq_of_forall_edist_le -> eq_of_forall_edist_le is a dubious translation:
 lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) ε)) -> (Eq.{succ u1} γ x y)
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (LE.le.{0} ENNReal (Preorder.toHasLe.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) ε)) -> (Eq.{succ u1} γ x y)
 but is expected to have type
   forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y) ε)) -> (Eq.{succ u1} γ x y)
 Case conversion may be inaccurate. Consider using '#align eq_of_forall_edist_le eq_of_forall_edist_leₓ'. -/
@@ -1764,7 +1764,7 @@ instance (priority := 100) to_separated : SeparatedSpace γ :=
 
 /- warning: emetric.uniform_embedding_iff' -> EMetric.uniformEmbedding_iff' is a dubious translation:
 lean 3 declaration is
-  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : EMetricSpace.{u2} γ] [_inst_3 : EMetricSpace.{u1} β] {f : γ -> β}, Iff (UniformEmbedding.{u2, u1} γ β (PseudoEMetricSpace.toUniformSpace.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) (PseudoEMetricSpace.toUniformSpace.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) f) (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toHasEdist.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toHasEdist.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toHasEdist.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toHasEdist.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) a b) δ))))))
+  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : EMetricSpace.{u2} γ] [_inst_3 : EMetricSpace.{u1} β] {f : γ -> β}, Iff (UniformEmbedding.{u2, u1} γ β (PseudoEMetricSpace.toUniformSpace.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) (PseudoEMetricSpace.toUniformSpace.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) f) (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toHasEdist.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toHasEdist.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toHasEdist.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toHasEdist.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) a b) δ))))))
 but is expected to have type
   forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : EMetricSpace.{u2} γ] [_inst_3 : EMetricSpace.{u1} β] {f : γ -> β}, Iff (UniformEmbedding.{u2, u1} γ β (PseudoEMetricSpace.toUniformSpace.{u2} γ (EMetricSpace.toPseudoEMetricSpace.{u2} γ _inst_2)) (PseudoEMetricSpace.toUniformSpace.{u1} β (EMetricSpace.toPseudoEMetricSpace.{u1} β _inst_3)) f) (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toEDist.{u2} γ (EMetricSpace.toPseudoEMetricSpace.{u2} γ _inst_2)) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toEDist.{u1} β (EMetricSpace.toPseudoEMetricSpace.{u1} β _inst_3)) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toEDist.{u1} β (EMetricSpace.toPseudoEMetricSpace.{u1} β _inst_3)) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toEDist.{u2} γ (EMetricSpace.toPseudoEMetricSpace.{u2} γ _inst_2)) a b) δ))))))
 Case conversion may be inaccurate. Consider using '#align emetric.uniform_embedding_iff' EMetric.uniformEmbedding_iff'ₓ'. -/
@@ -1852,7 +1852,7 @@ instance Prod.emetricSpaceMax [EMetricSpace β] : EMetricSpace (γ × β) :=
 
 /- warning: uniformity_edist -> uniformity_edist is a dubious translation:
 lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
 but is expected to have type
   forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
 Case conversion may be inaccurate. Consider using '#align uniformity_edist uniformity_edistₓ'. -/
@@ -1918,7 +1918,7 @@ theorem diam_eq_zero_iff : diam s = 0 ↔ s.Subsingleton :=
 
 /- warning: emetric.diam_pos_iff -> EMetric.diam_pos_iff' is a dubious translation:
 lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2) s)) (Exists.{succ u1} γ (fun (x : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) => Exists.{succ u1} γ (fun (y : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) => Ne.{succ u1} γ x y)))))
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (LT.lt.{0} ENNReal (Preorder.toHasLt.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2) s)) (Exists.{succ u1} γ (fun (x : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) => Exists.{succ u1} γ (fun (y : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) => Ne.{succ u1} γ x y)))))
 but is expected to have type
   forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2) s)) (Exists.{succ u1} γ (fun (x : γ) => And (Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) (Exists.{succ u1} γ (fun (y : γ) => And (Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) y s) (Ne.{succ u1} γ x y)))))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_pos_iff EMetric.diam_pos_iff'ₓ'. -/

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

@@ -46,16 +46,16 @@ variable {α : Type u} {β : Type v} {X : Type _}
 
 /- warning: uniformity_dist_of_mem_uniformity -> uniformity_dist_of_mem_uniformity is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => Exists.{0} (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (infᵢ.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => Exists.{0} (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (iInf.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
 but is expected to have type
-  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => And (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (infᵢ.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => And (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (iInf.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
 Case conversion may be inaccurate. Consider using '#align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformityₓ'. -/
 /-- Characterizing uniformities associated to a (generalized) distance function `D`
 in terms of the elements of the uniformity. -/
 theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α)} (z : β)
     (D : α → α → β) (H : ∀ s, s ∈ U ↔ ∃ ε > z, ∀ {a b : α}, D a b < ε → (a, b) ∈ s) :
     U = ⨅ ε > z, 𝓟 { p : α × α | D p.1 p.2 < ε } :=
-  HasBasis.eq_binfᵢ ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_set_of]⟩
+  HasBasis.eq_biInf ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_set_of]⟩
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
 
 #print EDist /-
@@ -250,9 +250,9 @@ theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → 
 
 /- warning: uniformity_pseudoedist -> uniformity_pseudoedist is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
 Case conversion may be inaccurate. Consider using '#align uniformity_pseudoedist uniformity_pseudoedistₓ'. -/
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } :=
@@ -440,7 +440,7 @@ theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : { p : α × α |
 namespace Emetric
 
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
-  isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_infᵢ⟩
+  isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
 /- warning: emetric.uniform_continuous_on_iff -> EMetric.uniformContinuousOn_iff is a dubious translation:
 lean 3 declaration is
@@ -634,7 +634,7 @@ def PseudoEMetricSpace.induced {α β} (f : α → β) (m : PseudoEMetricSpace 
   edist_comm x y := edist_comm _ _
   edist_triangle x y z := edist_triangle _ _ _
   toUniformSpace := UniformSpace.comap f m.toUniformSpace
-  uniformity_edist := (uniformity_basis_edist.comap _).eq_binfᵢ
+  uniformity_edist := (uniformity_basis_edist.comap _).eq_biInf
 #align pseudo_emetric_space.induced PseudoEMetricSpace.induced
 -/
 
@@ -718,8 +718,8 @@ instance Prod.pseudoEMetricSpaceMax [PseudoEMetricSpace β] : PseudoEMetricSpace
   uniformity_edist := by
     refine' uniformity_prod.trans _
     simp only [PseudoEMetricSpace.uniformity_edist, comap_infi]
-    rw [← infᵢ_inf_eq]; congr ; funext
-    rw [← infᵢ_inf_eq]; congr ; funext
+    rw [← iInf_inf_eq]; congr ; funext
+    rw [← iInf_inf_eq]; congr ; funext
     simp [inf_principal, ext_iff, max_lt_iff]
   toUniformSpace := Prod.uniformSpace
 #align prod.pseudo_emetric_space_max Prod.pseudoEMetricSpaceMax
@@ -762,8 +762,8 @@ instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetric
     by
     simp only [Pi.uniformity, PseudoEMetricSpace.uniformity_edist, comap_infi, gt_iff_lt,
       preimage_set_of_eq, comap_principal]
-    rw [infᵢ_comm]; congr ; funext ε
-    rw [infᵢ_comm]; congr ; funext εpos
+    rw [iInf_comm]; congr ; funext ε
+    rw [iInf_comm]; congr ; funext εpos
     change 0 < ε at εpos
     simp [Set.ext_iff, εpos]
 #align pseudo_emetric_space_pi pseudoEMetricSpacePi
@@ -1090,12 +1090,12 @@ theorem nhdsWithin_basis_closed_eball :
 
 /- warning: emetric.nhds_eq -> EMetric.nhds_eq is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (infᵢ.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (iInf.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (infᵢ.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (iInf.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
 Case conversion may be inaccurate. Consider using '#align emetric.nhds_eq EMetric.nhds_eqₓ'. -/
 theorem nhds_eq : 𝓝 x = ⨅ ε > 0, 𝓟 (ball x ε) :=
-  nhds_basis_eball.eq_binfᵢ
+  nhds_basis_eball.eq_biInf
 #align emetric.nhds_eq EMetric.nhds_eq
 
 /- warning: emetric.mem_nhds_iff -> EMetric.mem_nhds_iff is a dubious translation:
@@ -1316,23 +1316,23 @@ theorem cauchySeq_iff_NNReal [Nonempty β] [SemilatticeSup β] {u : β → α} :
 
 /- warning: emetric.totally_bounded_iff -> EMetric.totallyBounded_iff is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε)))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε)))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => 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 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε)))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => 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 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε)))))))
 Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff EMetric.totallyBounded_iffₓ'. -/
 theorem totallyBounded_iff {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ t : Set α, t.Finite ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => H _ (edist_mem_uniformity ε0), fun H r ru =>
     let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 ru
     let ⟨t, ft, h⟩ := H ε ε0
-    ⟨t, ft, h.trans <| unionᵢ₂_mono fun y yt z => hε⟩⟩
+    ⟨t, ft, h.trans <| iUnion₂_mono fun y yt z => hε⟩⟩
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
 
 /- warning: emetric.totally_bounded_iff' -> EMetric.totallyBounded_iff' is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε))))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε))))))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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.MetricSpace.EMetricSpace._hyg.9103 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε))))))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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.MetricSpace.EMetricSpace._hyg.9103 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε))))))))
 Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff' {s : Set α} :
@@ -1340,16 +1340,16 @@ theorem totallyBounded_iff' {s : Set α} :
   ⟨fun H ε ε0 => (totallyBounded_iff_subset.1 H) _ (edist_mem_uniformity ε0), fun H r ru =>
     let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 ru
     let ⟨t, _, ft, h⟩ := H ε ε0
-    ⟨t, ft, h.trans <| unionᵢ₂_mono fun y yt z => hε⟩⟩
+    ⟨t, ft, h.trans <| iUnion₂_mono fun y yt z => hε⟩⟩
 #align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'
 
 section Compact
 
 /- warning: emetric.subset_countable_closure_of_almost_dense_set -> EMetric.subset_countable_closure_of_almost_dense_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
 Case conversion may be inaccurate. Consider using '#align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_setₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
@@ -1422,7 +1422,7 @@ theorem secondCountable_of_sigmaCompact [SigmaCompactSpace α] : SecondCountable
   choose T hTsub hTc hsubT using fun n =>
     subset_countable_closure_of_compact (isCompact_compactCovering α n)
   refine' ⟨⟨⋃ n, T n, countable_Union hTc, fun x => _⟩⟩
-  rcases Union_eq_univ_iff.1 (unionᵢ_compactCovering α) x with ⟨n, hn⟩
+  rcases Union_eq_univ_iff.1 (iUnion_compactCovering α) x with ⟨n, hn⟩
   exact closure_mono (subset_Union _ n) (hsubT _ hn)
 #align emetric.second_countable_of_sigma_compact EMetric.secondCountable_of_sigmaCompact
 -/
@@ -1431,9 +1431,9 @@ variable {α}
 
 /- warning: emetric.second_countable_of_almost_dense_set -> EMetric.secondCountable_of_almost_dense_set is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.iUnion.{u1, succ u1} α α (fun (x : α) => Set.iUnion.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
 Case conversion may be inaccurate. Consider using '#align emetric.second_countable_of_almost_dense_set EMetric.secondCountable_of_almost_dense_setₓ'. -/
 theorem secondCountable_of_almost_dense_set
     (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ (⋃ x ∈ t, closedBall x ε) = univ) :
@@ -1465,7 +1465,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) d) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) d)))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_le_iff EMetric.diam_le_iffₓ'. -/
 theorem diam_le_iff {d : ℝ≥0∞} : diam s ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d := by
-  simp only [diam, supᵢ_le_iff]
+  simp only [diam, iSup_le_iff]
 #align emetric.diam_le_iff EMetric.diam_le_iff
 
 /- warning: emetric.diam_image_le_iff -> EMetric.diam_image_le_iff is a dubious translation:
@@ -1547,31 +1547,31 @@ theorem diam_singleton : diam ({x} : Set α) = 0 :=
   diam_subsingleton subsingleton_singleton
 #align emetric.diam_singleton EMetric.diam_singleton
 
-/- warning: emetric.diam_Union_mem_option -> EMetric.diam_unionᵢ_mem_option is a dubious translation:
+/- warning: emetric.diam_Union_mem_option -> EMetric.diam_iUnion_mem_option is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => s i)))) (supᵢ.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => EMetric.diam.{u1} α _inst_1 (s i))))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Set.iUnion.{u1, succ u2} α ι (fun (i : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => s i)))) (iSup.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => iSup.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => EMetric.diam.{u1} α _inst_1 (s i))))
 but is expected to have type
-  forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} (o : Option.{u1} ι) (s : ι -> (Set.{u2} α)), Eq.{1} ENNReal (EMetric.diam.{u2} α _inst_1 (Set.unionᵢ.{u2, succ u1} α ι (fun (i : ι) => Set.unionᵢ.{u2, 0} α (Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) (fun (H : Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) => s i)))) (supᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) (fun (H : Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) => EMetric.diam.{u2} α _inst_1 (s i))))
-Case conversion may be inaccurate. Consider using '#align emetric.diam_Union_mem_option EMetric.diam_unionᵢ_mem_optionₓ'. -/
-theorem diam_unionᵢ_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
+  forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} (o : Option.{u1} ι) (s : ι -> (Set.{u2} α)), Eq.{1} ENNReal (EMetric.diam.{u2} α _inst_1 (Set.iUnion.{u2, succ u1} α ι (fun (i : ι) => Set.iUnion.{u2, 0} α (Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) (fun (H : Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) => s i)))) (iSup.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => iSup.{0, 0} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) (fun (H : Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) => EMetric.diam.{u2} α _inst_1 (s i))))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_optionₓ'. -/
+theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp
-#align emetric.diam_Union_mem_option EMetric.diam_unionᵢ_mem_option
+#align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_option
 
 /- warning: emetric.diam_insert -> EMetric.diam_insert is a dubious translation:
 lean 3 declaration is
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (LinearOrder.max.{0} ENNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.completeLinearOrder))) (supᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y))) (EMetric.diam.{u1} α _inst_1 s))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (LinearOrder.max.{0} ENNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.completeLinearOrder))) (iSup.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => iSup.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y))) (EMetric.diam.{u1} α _inst_1 s))
 but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (supᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y))) (EMetric.diam.{u1} α _inst_1 s))
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (iSup.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => iSup.{0, 0} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y))) (EMetric.diam.{u1} α _inst_1 s))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_insert EMetric.diam_insertₓ'. -/
 theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s) :=
   eq_of_forall_ge_iff fun d => by
-    simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, supᵢ_le_iff,
+    simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, iSup_le_iff,
       zero_le, true_and_iff, forall_and, and_self_iff, ← and_assoc']
 #align emetric.diam_insert EMetric.diam_insert
 
 #print EMetric.diam_pair /-
 theorem diam_pair : diam ({x, y} : Set α) = edist x y := by
-  simp only [supᵢ_singleton, diam_insert, diam_singleton, ENNReal.max_zero_right]
+  simp only [iSup_singleton, diam_insert, diam_singleton, ENNReal.max_zero_right]
 #align emetric.diam_pair EMetric.diam_pair
 -/
 
@@ -1582,7 +1582,7 @@ but is expected to have type
   forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) y (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) z)))) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z))
 Case conversion may be inaccurate. Consider using '#align emetric.diam_triple EMetric.diam_tripleₓ'. -/
 theorem diam_triple : diam ({x, y, z} : Set α) = max (max (edist x y) (edist x z)) (edist y z) := by
-  simp only [diam_insert, supᵢ_insert, supᵢ_singleton, diam_singleton, ENNReal.max_zero_right,
+  simp only [diam_insert, iSup_insert, iSup_singleton, diam_singleton, ENNReal.max_zero_right,
     ENNReal.sup_eq_max]
 #align emetric.diam_triple EMetric.diam_triple
 
@@ -1819,7 +1819,7 @@ def EMetricSpace.induced {γ β} (f : γ → β) (hf : Function.Injective f) (m
   edist_comm x y := edist_comm _ _
   edist_triangle x y z := edist_triangle _ _ _
   toUniformSpace := UniformSpace.comap f m.toUniformSpace
-  uniformity_edist := (uniformity_basis_edist.comap _).eq_binfᵢ
+  uniformity_edist := (uniformity_basis_edist.comap _).eq_biInf
 #align emetric_space.induced EMetricSpace.induced
 -/
 
@@ -1852,9 +1852,9 @@ instance Prod.emetricSpaceMax [EMetricSpace β] : EMetricSpace (γ × β) :=
 
 /- warning: uniformity_edist -> uniformity_edist is a dubious translation:
 lean 3 declaration is
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
 but is expected to have type
-  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) (iInf.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => iInf.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
 Case conversion may be inaccurate. Consider using '#align uniformity_edist uniformity_edistₓ'. -/
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_edist : 𝓤 γ = ⨅ ε > 0, 𝓟 { p : γ × γ | edist p.1 p.2 < ε } :=
@@ -1960,9 +1960,9 @@ instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient
       edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle
       toUniformSpace := inferInstance
       uniformity_edist :=
-        (uniformity_basis_edist.map _).eq_binfᵢ.trans <|
-          infᵢ_congr fun ε =>
-            infᵢ_congr fun hε =>
+        (uniformity_basis_edist.map _).eq_biInf.trans <|
+          iInf_congr fun ε =>
+            iInf_congr fun hε =>
               congr_arg 𝓟
                 (by
                   ext ⟨⟨x⟩, ⟨y⟩⟩

mathlib commit https://github.com/leanprover-community/mathlib/commit/21e3562c5e12d846c7def5eff8cdbc520d7d4936

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.metric_space.emetric_space
-! leanprover-community/mathlib commit 195fcd60ff2bfe392543bceb0ec2adcdb472db4c
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Topology.UniformSpace.UniformEmbedding
 /-!
 # Extended metric spaces
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 This file is devoted to the definition and study of `emetric_spaces`, i.e., metric
 spaces in which the distance is allowed to take the value ∞. This extended distance is
 called `edist`, and takes values in `ℝ≥0∞`.

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

@@ -41,6 +41,12 @@ universe u v w
 
 variable {α : Type u} {β : Type v} {X : Type _}
 
+/- warning: uniformity_dist_of_mem_uniformity -> uniformity_dist_of_mem_uniformity is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => Exists.{0} (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (infᵢ.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (LinearOrder.toLattice.{u2} β _inst_1))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : LinearOrder.{u2} β] {U : Filter.{u1} (Prod.{u1, u1} α α)} (z : β) (D : α -> α -> β), (forall (s : Set.{u1} (Prod.{u1, u1} α α)), Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s U) (Exists.{succ u2} β (fun (ε : β) => And (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (forall {a : α} {b : α}, (LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D a b) ε) -> (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 a b) s))))) -> (Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) U (infᵢ.{u1, succ u2} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) β (fun (ε : β) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) (fun (H : GT.gt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) ε z) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{u2} β (Preorder.toLT.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeInf.toPartialOrder.{u2} β (Lattice.toSemilatticeInf.{u2} β (DistribLattice.toLattice.{u2} β (instDistribLattice.{u2} β _inst_1)))))) (D (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))))))
+Case conversion may be inaccurate. Consider using '#align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformityₓ'. -/
 /-- Characterizing uniformities associated to a (generalized) distance function `D`
 in terms of the elements of the uniformity. -/
 theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α)} (z : β)
@@ -49,22 +55,31 @@ theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α
   HasBasis.eq_binfᵢ ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_set_of]⟩
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
 
+#print EDist /-
 /-- `has_edist α` means that `α` is equipped with an extended distance. -/
-class HasEdist (α : Type _) where
+class EDist (α : Type _) where
   edist : α → α → ℝ≥0∞
-#align has_edist HasEdist
+#align has_edist EDist
+-/
 
-export HasEdist (edist)
+export EDist (edist)
 
+/- warning: uniform_space_of_edist -> uniformSpaceOfEDist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} (edist : α -> α -> ENNReal), (forall (x : α), Eq.{1} ENNReal (edist x x) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : α) (y : α), Eq.{1} ENNReal (edist x y) (edist y x)) -> (forall (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (edist x z) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (edist x y) (edist y z))) -> (UniformSpace.{u1} α)
+but is expected to have type
+  forall {α : Type.{u1}} (edist : α -> α -> ENNReal), (forall (x : α), Eq.{1} ENNReal (edist x x) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (x : α) (y : α), Eq.{1} ENNReal (edist x y) (edist y x)) -> (forall (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (edist x z) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (edist x y) (edist y z))) -> (UniformSpace.{u1} α)
+Case conversion may be inaccurate. Consider using '#align uniform_space_of_edist uniformSpaceOfEDistₓ'. -/
 /-- Creating a uniform space from an extended distance. -/
-noncomputable def uniformSpaceOfEdist (edist : α → α → ℝ≥0∞) (edist_self : ∀ x : α, edist x x = 0)
+noncomputable def uniformSpaceOfEDist (edist : α → α → ℝ≥0∞) (edist_self : ∀ x : α, edist x x = 0)
     (edist_comm : ∀ x y : α, edist x y = edist y x)
     (edist_triangle : ∀ x y z : α, edist x z ≤ edist x y + edist y z) : UniformSpace α :=
   UniformSpace.ofFun edist edist_self edist_comm edist_triangle fun ε ε0 =>
     ⟨ε / 2, ENNReal.half_pos ε0.lt.ne', fun _ h₁ _ h₂ =>
       (ENNReal.add_lt_add h₁ h₂).trans_eq (ENNReal.add_halves _)⟩
-#align uniform_space_of_edist uniformSpaceOfEdist
+#align uniform_space_of_edist uniformSpaceOfEDist
 
+#print PseudoEMetricSpace /-
 -- the uniform structure is embedded in the emetric space structure
 -- to avoid instance diamond issues. See Note [forgetful inheritance].
 /-- Extended (pseudo) metric spaces, with an extended distance `edist` possibly taking the
@@ -80,37 +95,56 @@ on a product.
 
 Continuity of `edist` is proved in `topology.instances.ennreal`
 -/
-class PseudoEmetricSpace (α : Type u) extends HasEdist α : Type u where
+class PseudoEMetricSpace (α : Type u) extends EDist α : Type u where
   edist_self : ∀ x : α, edist x x = 0
   edist_comm : ∀ x y : α, edist x y = edist y x
   edist_triangle : ∀ x y z : α, edist x z ≤ edist x y + edist y z
-  toUniformSpace : UniformSpace α := uniformSpaceOfEdist edist edist_self edist_comm edist_triangle
+  toUniformSpace : UniformSpace α := uniformSpaceOfEDist edist edist_self edist_comm edist_triangle
   uniformity_edist :
     𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α |
             edist p.1 p.2 < ε } := by
     intros
     rfl
-#align pseudo_emetric_space PseudoEmetricSpace
+#align pseudo_emetric_space PseudoEMetricSpace
+-/
 
-attribute [instance] PseudoEmetricSpace.toUniformSpace
+attribute [instance] PseudoEMetricSpace.toUniformSpace
 
 /- Pseudoemetric spaces are less common than metric spaces. Therefore, we work in a dedicated
 namespace, while notions associated to metric spaces are mostly in the root namespace. -/
-variable [PseudoEmetricSpace α]
+variable [PseudoEMetricSpace α]
 
-export PseudoEmetricSpace (edist_self edist_comm edist_triangle)
+export PseudoEMetricSpace (edist_self edist_comm edist_triangle)
 
 attribute [simp] edist_self
 
+/- warning: edist_triangle_left -> edist_triangle_left is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z y))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z y))
+Case conversion may be inaccurate. Consider using '#align edist_triangle_left edist_triangle_leftₓ'. -/
 /-- Triangle inequality for the extended distance -/
 theorem edist_triangle_left (x y z : α) : edist x y ≤ edist z x + edist z y := by
   rw [edist_comm z] <;> apply edist_triangle
 #align edist_triangle_left edist_triangle_left
 
+/- warning: edist_triangle_right -> edist_triangle_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z))
+Case conversion may be inaccurate. Consider using '#align edist_triangle_right edist_triangle_rightₓ'. -/
 theorem edist_triangle_right (x y z : α) : edist x y ≤ edist x z + edist y z := by
   rw [edist_comm y] <;> apply edist_triangle
 #align edist_triangle_right edist_triangle_right
 
+/- warning: edist_congr_right -> edist_congr_right is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x z) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z))
+Case conversion may be inaccurate. Consider using '#align edist_congr_right edist_congr_rightₓ'. -/
 theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y z :=
   by
   apply le_antisymm
@@ -121,12 +155,24 @@ theorem edist_congr_right {x y z : α} (h : edist x y = 0) : edist x z = edist y
     apply edist_triangle
 #align edist_congr_right edist_congr_right
 
+/- warning: edist_congr_left -> edist_congr_left is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z y))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z x) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z y))
+Case conversion may be inaccurate. Consider using '#align edist_congr_left edist_congr_leftₓ'. -/
 theorem edist_congr_left {x y z : α} (h : edist x y = 0) : edist z x = edist z y :=
   by
   rw [edist_comm z x, edist_comm z y]
   apply edist_congr_right h
 #align edist_congr_left edist_congr_left
 
+/- warning: edist_triangle4 -> edist_triangle4 is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α) (t : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x t) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) z t))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α) (z : α) (t : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x t) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) z t))
+Case conversion may be inaccurate. Consider using '#align edist_triangle4 edist_triangle4ₓ'. -/
 theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + edist z t :=
   calc
     edist x t ≤ edist x z + edist z t := edist_triangle x z t
@@ -134,6 +180,12 @@ theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + e
     
 #align edist_triangle4 edist_triangle4
 
+/- warning: edist_le_Ico_sum_edist -> edist_le_Ico_sum_edist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1)))))))
+Case conversion may be inaccurate. Consider using '#align edist_le_Ico_sum_edist edist_le_Ico_sum_edistₓ'. -/
 /-- The triangle (polygon) inequality for sequences of points; `finset.Ico` version. -/
 theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
     edist (f m) (f n) ≤ ∑ i in Finset.Ico m n, edist (f i) (f (i + 1)) :=
@@ -152,12 +204,24 @@ theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
       
 #align edist_le_Ico_sum_edist edist_le_Ico_sum_edist
 
+/- warning: edist_le_range_sum_edist -> edist_le_range_sum_edist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.range n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) i (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (f : Nat -> α) (n : Nat), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.range n) (fun (i : Nat) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f i) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) i (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))))
+Case conversion may be inaccurate. Consider using '#align edist_le_range_sum_edist edist_le_range_sum_edistₓ'. -/
 /-- The triangle (polygon) inequality for sequences of points; `finset.range` version. -/
 theorem edist_le_range_sum_edist (f : ℕ → α) (n : ℕ) :
     edist (f 0) (f n) ≤ ∑ i in Finset.range n, edist (f i) (f (i + 1)) :=
   Nat.Ico_zero_eq_range ▸ edist_le_Ico_sum_edist f (Nat.zero_le n)
 #align edist_le_range_sum_edist edist_le_range_sum_edist
 
+/- warning: edist_le_Ico_sum_of_edist_le -> edist_le_Ico_sum_of_edist_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} {m : Nat} {n : Nat}, (LE.le.{0} Nat Nat.hasLe m n) -> (forall {d : Nat -> ENNReal}, (forall {k : Nat}, (LE.le.{0} Nat Nat.hasLe m k) -> (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (OrderedCancelAddCommMonoid.toPartialOrder.{0} Nat (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} Nat Nat.strictOrderedSemiring))) Nat.locallyFiniteOrder m n) (fun (i : Nat) => d i))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} {m : Nat} {n : Nat}, (LE.le.{0} Nat instLENat m n) -> (forall {d : Nat -> ENNReal}, (forall {k : Nat}, (LE.le.{0} Nat instLENat m k) -> (LT.lt.{0} Nat instLTNat k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f m) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.Ico.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring)) instLocallyFiniteOrderNatToPreorderToPartialOrderStrictOrderedSemiring m n) (fun (i : Nat) => d i))))
+Case conversion may be inaccurate. Consider using '#align edist_le_Ico_sum_of_edist_le edist_le_Ico_sum_of_edist_leₓ'. -/
 /-- A version of `edist_le_Ico_sum_edist` with each intermediate distance replaced
 with an upper estimate. -/
 theorem edist_le_Ico_sum_of_edist_le {f : ℕ → α} {m n} (hmn : m ≤ n) {d : ℕ → ℝ≥0∞}
@@ -167,6 +231,12 @@ theorem edist_le_Ico_sum_of_edist_le {f : ℕ → α} {m n} (hmn : m ≤ n) {d :
     Finset.sum_le_sum fun k hk => hd (Finset.mem_Ico.1 hk).1 (Finset.mem_Ico.1 hk).2
 #align edist_le_Ico_sum_of_edist_le edist_le_Ico_sum_of_edist_le
 
+/- warning: edist_le_range_sum_of_edist_le -> edist_le_range_sum_of_edist_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} (n : Nat) {d : Nat -> ENNReal}, (forall {k : Nat}, (LT.lt.{0} Nat Nat.hasLt k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat Nat.hasAdd) k (OfNat.ofNat.{0} Nat 1 (OfNat.mk.{0} Nat 1 (One.one.{0} Nat Nat.hasOne)))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (OfNat.mk.{0} Nat 0 (Zero.zero.{0} Nat Nat.hasZero)))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (OrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (OrderedSemiring.toOrderedAddCommMonoid.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))) (Finset.range n) (fun (i : Nat) => d i)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Nat -> α} (n : Nat) {d : Nat -> ENNReal}, (forall {k : Nat}, (LT.lt.{0} Nat instLTNat k n) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f k) (f (HAdd.hAdd.{0, 0, 0} Nat Nat Nat (instHAdd.{0} Nat instAddNat) k (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (d k))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))) (f n)) (Finset.sum.{0, 0} ENNReal Nat (LinearOrderedAddCommMonoid.toAddCommMonoid.{0} ENNReal (LinearOrderedAddCommMonoidWithTop.toLinearOrderedAddCommMonoid.{0} ENNReal ENNReal.instLinearOrderedAddCommMonoidWithTopENNReal)) (Finset.range n) (fun (i : Nat) => d i)))
+Case conversion may be inaccurate. Consider using '#align edist_le_range_sum_of_edist_le edist_le_range_sum_of_edist_leₓ'. -/
 /-- A version of `edist_le_range_sum_edist` with each intermediate distance replaced
 with an upper estimate. -/
 theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → ℝ≥0∞}
@@ -175,34 +245,60 @@ theorem edist_le_range_sum_of_edist_le {f : ℕ → α} (n : ℕ) {d : ℕ → 
   Nat.Ico_zero_eq_range ▸ edist_le_Ico_sum_of_edist_le (zero_le n) fun _ _ => hd
 #align edist_le_range_sum_of_edist_le edist_le_range_sum_of_edist_le
 
+/- warning: uniformity_pseudoedist -> uniformity_pseudoedist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.completeLattice.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} α α)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} α α)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} α α)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} α α) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))))
+Case conversion may be inaccurate. Consider using '#align uniformity_pseudoedist uniformity_pseudoedistₓ'. -/
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε } :=
-  PseudoEmetricSpace.uniformity_edist
+  PseudoEMetricSpace.uniformity_edist
 #align uniformity_pseudoedist uniformity_pseudoedist
 
+#print uniformSpace_edist /-
 theorem uniformSpace_edist :
-    ‹PseudoEmetricSpace α›.toUniformSpace =
-      uniformSpaceOfEdist edist edist_self edist_comm edist_triangle :=
+    ‹PseudoEMetricSpace α›.toUniformSpace =
+      uniformSpaceOfEDist edist edist_self edist_comm edist_triangle :=
   uniformSpace_eq uniformity_pseudoedist
 #align uniform_space_edist uniformSpace_edist
+-/
 
+/- warning: uniformity_basis_edist -> uniformity_basis_edist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist uniformity_basis_edistₓ'. -/
 theorem uniformity_basis_edist :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
   (@uniformSpace_edist α _).symm ▸ UniformSpace.hasBasis_ofFun ⟨1, one_pos⟩ _ _ _ _ _
 #align uniformity_basis_edist uniformity_basis_edist
 
+/- warning: mem_uniformity_edist -> mem_uniformity_edist is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} (Prod.{u1, u1} α α)}, Iff (Membership.Mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (Filter.hasMem.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) ε) -> (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 a b) s))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} (Prod.{u1, u1} α α)}, Iff (Membership.mem.{u1, u1} (Set.{u1} (Prod.{u1, u1} α α)) (Filter.{u1} (Prod.{u1, u1} α α)) (instMembershipSetFilter.{u1} (Prod.{u1, u1} α α)) s (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) ε) -> (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 a b) s))))
+Case conversion may be inaccurate. Consider using '#align mem_uniformity_edist mem_uniformity_edistₓ'. -/
 /-- Characterization of the elements of the uniformity in terms of the extended distance -/
 theorem mem_uniformity_edist {s : Set (α × α)} :
     s ∈ 𝓤 α ↔ ∃ ε > 0, ∀ {a b : α}, edist a b < ε → (a, b) ∈ s :=
   uniformity_basis_edist.mem_uniformity_iff
 #align mem_uniformity_edist mem_uniformity_edist
 
+/- warning: emetric.mk_uniformity_basis -> EMetric.mk_uniformity_basis is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {β : Type.{u2}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Exists.{succ u2} β (fun (x : β) => Exists.{0} (p x) (fun (hx : p x) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (f x) ε)))) -> (Filter.HasBasis.{u1, succ u2} (Prod.{u1, u1} α α) β (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) p (fun (x : β) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (f x))))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] {β : Type.{u1}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Exists.{succ u1} β (fun (x : β) => And (p x) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (f x) ε)))) -> (Filter.HasBasis.{u2, succ u1} (Prod.{u2, u2} α α) β (uniformity.{u2} α (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1)) p (fun (x : β) => setOf.{u2} (Prod.{u2, u2} α α) (fun (p : Prod.{u2, u2} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (Prod.fst.{u2, u2} α α p) (Prod.snd.{u2, u2} α α p)) (f x))))
+Case conversion may be inaccurate. Consider using '#align emetric.mk_uniformity_basis EMetric.mk_uniformity_basisₓ'. -/
 /-- Given `f : β → ℝ≥0∞`, if `f` sends `{i | p i}` to a set of positive numbers
 accumulating to zero, then `f i`-neighborhoods of the diagonal form a basis of `𝓤 α`.
 
 For specific bases see `uniformity_basis_edist`, `uniformity_basis_edist'`,
 `uniformity_basis_edist_nnreal`, and `uniformity_basis_edist_inv_nat`. -/
-protected theorem Emetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
+protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
     (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _)(hx : p x), f x ≤ ε) :
     (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 < f x } :=
   by
@@ -212,13 +308,19 @@ protected theorem Emetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f
     rcases hf ε ε₀ with ⟨i, hi, H⟩
     exact ⟨i, hi, fun x hx => hε <| lt_of_lt_of_le hx H⟩
   · exact fun ⟨i, hi, H⟩ => ⟨f i, hf₀ i hi, H⟩
-#align emetric.mk_uniformity_basis Emetric.mk_uniformity_basis
-
+#align emetric.mk_uniformity_basis EMetric.mk_uniformity_basis
+
+/- warning: emetric.mk_uniformity_basis_le -> EMetric.mk_uniformity_basis_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {β : Type.{u2}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Exists.{succ u2} β (fun (x : β) => Exists.{0} (p x) (fun (hx : p x) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (f x) ε)))) -> (Filter.HasBasis.{u1, succ u2} (Prod.{u1, u1} α α) β (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) p (fun (x : β) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (f x))))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] {β : Type.{u1}} {p : β -> Prop} {f : β -> ENNReal}, (forall (x : β), (p x) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (f x))) -> (forall (ε : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Exists.{succ u1} β (fun (x : β) => And (p x) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (f x) ε)))) -> (Filter.HasBasis.{u2, succ u1} (Prod.{u2, u2} α α) β (uniformity.{u2} α (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1)) p (fun (x : β) => setOf.{u2} (Prod.{u2, u2} α α) (fun (p : Prod.{u2, u2} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (Prod.fst.{u2, u2} α α p) (Prod.snd.{u2, u2} α α p)) (f x))))
+Case conversion may be inaccurate. Consider using '#align emetric.mk_uniformity_basis_le EMetric.mk_uniformity_basis_leₓ'. -/
 /-- Given `f : β → ℝ≥0∞`, if `f` sends `{i | p i}` to a set of positive numbers
 accumulating to zero, then closed `f i`-neighborhoods of the diagonal form a basis of `𝓤 α`.
 
 For specific bases see `uniformity_basis_edist_le` and `uniformity_basis_edist_le'`. -/
-protected theorem Emetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
+protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
     (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ (x : _)(hx : p x), f x ≤ ε) :
     (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 ≤ f x } :=
   by
@@ -229,56 +331,104 @@ protected theorem Emetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop}
     rcases hf ε' hε'.1 with ⟨i, hi, H⟩
     exact ⟨i, hi, fun x hx => hε <| lt_of_le_of_lt (le_trans hx H) hε'.2⟩
   · exact fun ⟨i, hi, H⟩ => ⟨f i, hf₀ i hi, fun x hx => H (le_of_lt hx)⟩
-#align emetric.mk_uniformity_basis_le Emetric.mk_uniformity_basis_le
-
+#align emetric.mk_uniformity_basis_le EMetric.mk_uniformity_basis_le
+
+/- warning: uniformity_basis_edist_le -> uniformity_basis_edist_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_le uniformity_basis_edist_leₓ'. -/
 theorem uniformity_basis_edist_le :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
-  Emetric.mk_uniformity_basis_le (fun _ => id) fun ε ε₀ => ⟨ε, ε₀, le_refl ε⟩
+  EMetric.mk_uniformity_basis_le (fun _ => id) fun ε ε₀ => ⟨ε, ε₀, le_refl ε⟩
 #align uniformity_basis_edist_le uniformity_basis_edist_le
 
+/- warning: uniformity_basis_edist' -> uniformity_basis_edist' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.instMembershipSet.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist' uniformity_basis_edist'ₓ'. -/
 theorem uniformity_basis_edist' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => { p : α × α | edist p.1 p.2 < ε } :=
-  Emetric.mk_uniformity_basis (fun _ => And.left) fun ε ε₀ =>
+  EMetric.mk_uniformity_basis (fun _ => And.left) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := exists_between hε'
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist' uniformity_basis_edist'
 
+/- warning: uniformity_basis_edist_le' -> uniformity_basis_edist_le' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.Mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.hasMem.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (ε' : ENNReal), (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε') -> (Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) ENNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : ENNReal) => Membership.mem.{0, 0} ENNReal (Set.{0} ENNReal) (Set.instMembershipSet.{0} ENNReal) ε (Set.Ioo.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε')) (fun (ε : ENNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_le' uniformity_basis_edist_le'ₓ'. -/
 theorem uniformity_basis_edist_le' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => ε ∈ Ioo 0 ε') fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
-  Emetric.mk_uniformity_basis_le (fun _ => And.left) fun ε ε₀ =>
+  EMetric.mk_uniformity_basis_le (fun _ => And.left) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := exists_between hε'
     ⟨min ε δ, ⟨lt_min ε₀ hδ.1, lt_of_le_of_lt (min_le_right _ _) hδ.2⟩, min_le_left _ _⟩
 #align uniformity_basis_edist_le' uniformity_basis_edist_le'
 
-theorem uniformity_basis_edist_nNReal :
+/- warning: uniformity_basis_edist_nnreal -> uniformity_basis_edist_nnreal is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (ENNReal.some ε)))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_nnreal uniformity_basis_edist_nnrealₓ'. -/
+theorem uniformity_basis_edist_nnreal :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
-  Emetric.mk_uniformity_basis (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
+  EMetric.mk_uniformity_basis (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
-#align uniformity_basis_edist_nnreal uniformity_basis_edist_nNReal
-
-theorem uniformity_basis_edist_nNReal_le :
+#align uniformity_basis_edist_nnreal uniformity_basis_edist_nnreal
+
+/- warning: uniformity_basis_edist_nnreal_le -> uniformity_basis_edist_nnreal_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) NNReal (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (ε : NNReal) => LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) (fun (ε : NNReal) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (ENNReal.some ε)))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nnreal_leₓ'. -/
+theorem uniformity_basis_edist_nnreal_le :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
-  Emetric.mk_uniformity_basis_le (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
+  EMetric.mk_uniformity_basis_le (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
     let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
     ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
-#align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nNReal_le
-
+#align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nnreal_le
+
+/- warning: uniformity_basis_edist_inv_nat -> uniformity_basis_edist_inv_nat is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (Inv.inv.{0} ENNReal ENNReal.hasInv ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) Nat ENNReal (HasLiftT.mk.{1, 1} Nat ENNReal (CoeTCₓ.coe.{1, 1} Nat ENNReal (Nat.castCoe.{0} ENNReal (AddMonoidWithOne.toNatCast.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))) n))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (Nat.cast.{0} ENNReal (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) n))))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_natₓ'. -/
 theorem uniformity_basis_edist_inv_nat :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < (↑n)⁻¹ } :=
-  Emetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun ε ε₀ =>
+  EMetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun ε ε₀ =>
     let ⟨n, hn⟩ := ENNReal.exists_inv_nat_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_nat
 
+/- warning: uniformity_basis_edist_inv_two_pow -> uniformity_basis_edist_inv_two_pow is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (Inv.inv.{0} ENNReal ENNReal.hasInv (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne))))))) n)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Filter.HasBasis.{u1, 1} (Prod.{u1, u1} α α) Nat (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (fun (_x : Nat) => True) (fun (n : Nat) => setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) (HPow.hPow.{0, 0, 0} ENNReal Nat ENNReal (instHPow.{0, 0} ENNReal Nat (Monoid.Pow.{0} ENNReal (MonoidWithZero.toMonoid.{0} ENNReal (Semiring.toMonoidWithZero.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal))))))) (Inv.inv.{0} ENNReal ENNReal.instInvENNReal (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))) n)))
+Case conversion may be inaccurate. Consider using '#align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_powₓ'. -/
 theorem uniformity_basis_edist_inv_two_pow :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < 2⁻¹ ^ n } :=
-  Emetric.mk_uniformity_basis (fun n _ => ENNReal.pow_pos (ENNReal.inv_pos.2 ENNReal.two_ne_top) _)
+  EMetric.mk_uniformity_basis (fun n _ => ENNReal.pow_pos (ENNReal.inv_pos.2 ENNReal.two_ne_top) _)
     fun ε ε₀ =>
     let ⟨n, hn⟩ := ENNReal.exists_inv_two_pow_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_pow
 
+/- warning: edist_mem_uniformity -> edist_mem_uniformity is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (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)) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (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)) (setOf.{u1} (Prod.{u1, u1} α α) (fun (p : Prod.{u1, u1} α α) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u1} α α p) (Prod.snd.{u1, u1} α α p)) ε)) (uniformity.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align edist_mem_uniformity edist_mem_uniformityₓ'. -/
 /-- Fixed size neighborhoods of the diagonal belong to the uniform structure -/
 theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : { p : α × α | edist p.1 p.2 < ε } ∈ 𝓤 α :=
   mem_uniformity_edist.2 ⟨ε, ε0, fun a b => id⟩
@@ -289,22 +439,40 @@ namespace Emetric
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_infᵢ⟩
 
+/- warning: emetric.uniform_continuous_on_iff -> EMetric.uniformContinuousOn_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {s : Set.{u1} α}, Iff (UniformContinuousOn.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) a s} {b : α} {H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) b s}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {s : Set.{u1} α}, Iff (UniformContinuousOn.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) a s) -> (forall {b : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) b s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε))))))
+Case conversion may be inaccurate. Consider using '#align emetric.uniform_continuous_on_iff EMetric.uniformContinuousOn_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection {a b «expr ∈ » s} -/
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
-theorem uniformContinuousOn_iff [PseudoEmetricSpace β] {f : α → β} {s : Set α} :
+theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
     UniformContinuousOn f s ↔
       ∀ ε > 0, ∃ δ > 0, ∀ {a} {_ : a ∈ s} {b} {_ : b ∈ s}, edist a b < δ → edist (f a) (f b) < ε :=
   uniformity_basis_edist.uniformContinuousOn_iff uniformity_basis_edist
-#align emetric.uniform_continuous_on_iff Emetric.uniformContinuousOn_iff
-
+#align emetric.uniform_continuous_on_iff EMetric.uniformContinuousOn_iff
+
+/- warning: emetric.uniform_continuous_iff -> EMetric.uniformContinuous_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε)))))
+Case conversion may be inaccurate. Consider using '#align emetric.uniform_continuous_iff EMetric.uniformContinuous_iffₓ'. -/
 /-- ε-δ characterization of uniform continuity on pseudoemetric spaces -/
-theorem uniformContinuous_iff [PseudoEmetricSpace β] {f : α → β} :
+theorem uniformContinuous_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformContinuous f ↔ ∀ ε > 0, ∃ δ > 0, ∀ {a b : α}, edist a b < δ → edist (f a) (f b) < ε :=
   uniformity_basis_edist.uniformContinuous_iff uniformity_basis_edist
-#align emetric.uniform_continuous_iff Emetric.uniformContinuous_iff
-
+#align emetric.uniform_continuous_iff EMetric.uniformContinuous_iff
+
+/- warning: emetric.uniform_embedding_iff -> EMetric.uniformEmbedding_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ)))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, Iff (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (And (Function.Injective.{succ u1, succ u2} α β f) (And (UniformContinuous.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ)))))))
+Case conversion may be inaccurate. Consider using '#align emetric.uniform_embedding_iff EMetric.uniformEmbedding_iffₓ'. -/
 /-- ε-δ characterization of uniform embeddings on pseudoemetric spaces -/
-theorem uniformEmbedding_iff [PseudoEmetricSpace β] {f : α → β} :
+theorem uniformEmbedding_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformEmbedding f ↔
       Function.Injective f ∧
         UniformContinuous f ∧
@@ -312,24 +480,42 @@ theorem uniformEmbedding_iff [PseudoEmetricSpace β] {f : α → β} :
   by
   simp only [uniformity_basis_edist.uniform_embedding_iff uniformity_basis_edist, exists_prop]
   rfl
-#align emetric.uniform_embedding_iff Emetric.uniformEmbedding_iff
-
+#align emetric.uniform_embedding_iff EMetric.uniformEmbedding_iff
+
+/- warning: emetric.controlled_of_uniform_embedding -> EMetric.controlled_of_uniformEmbedding is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) -> (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b) δ))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β}, (UniformEmbedding.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2) f) -> (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : α} {b : α}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b) δ))))))
+Case conversion may be inaccurate. Consider using '#align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbeddingₓ'. -/
 /-- If a map between pseudoemetric spaces is a uniform embedding then the edistance between `f x`
 and `f y` is controlled in terms of the distance between `x` and `y`. -/
-theorem controlled_of_uniformEmbedding [PseudoEmetricSpace β] {f : α → β} :
+theorem controlled_of_uniformEmbedding [PseudoEMetricSpace β] {f : α → β} :
     UniformEmbedding f →
       (∀ ε > 0, ∃ δ > 0, ∀ {a b : α}, edist a b < δ → edist (f a) (f b) < ε) ∧
         ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, edist (f a) (f b) < ε → edist a b < δ :=
   fun h => ⟨uniformContinuous_iff.1 (uniformEmbedding_iff.1 h).2.1, (uniformEmbedding_iff.1 h).2.2⟩
-#align emetric.controlled_of_uniform_embedding Emetric.controlled_of_uniformEmbedding
-
+#align emetric.controlled_of_uniform_embedding EMetric.controlled_of_uniformEmbedding
+
+/- warning: emetric.cauchy_iff -> EMetric.cauchy_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u1} α}, Iff (Cauchy.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) f) (And (Ne.{succ u1} (Filter.{u1} α) f (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toHasBot.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α)))) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u1} α}, Iff (Cauchy.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) f) (And (Ne.{succ u1} (Filter.{u1} α) f (Bot.bot.{u1} (Filter.{u1} α) (CompleteLattice.toBot.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α)))) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε)))))))
+Case conversion may be inaccurate. Consider using '#align emetric.cauchy_iff EMetric.cauchy_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
     Cauchy f ↔ f ≠ ⊥ ∧ ∀ ε > 0, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), edist x y < ε := by
   rw [← ne_bot_iff] <;> exact uniformity_basis_edist.cauchy_iff
-#align emetric.cauchy_iff Emetric.cauchy_iff
-
+#align emetric.cauchy_iff EMetric.cauchy_iff
+
+/- warning: emetric.complete_of_convergent_controlled_sequences -> EMetric.complete_of_convergent_controlled_sequences is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (B : Nat -> ENNReal), (forall (n : Nat), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (B n)) -> (forall (u : Nat -> α), (forall (N : Nat) (n : Nat) (m : Nat), (LE.le.{0} Nat Nat.hasLe N n) -> (LE.le.{0} Nat Nat.hasLe N m) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u m)) (B N))) -> (Exists.{succ u1} α (fun (x : α) => Filter.Tendsto.{0, u1} Nat α u (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 (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)))) -> (CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (B : Nat -> ENNReal), (forall (n : Nat), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (B n)) -> (forall (u : Nat -> α), (forall (N : Nat) (n : Nat) (m : Nat), (LE.le.{0} Nat instLENat N n) -> (LE.le.{0} Nat instLENat N m) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) (u m)) (B N))) -> (Exists.{succ u1} α (fun (x : α) => Filter.Tendsto.{0, u1} Nat α u (Filter.atTop.{0} Nat (PartialOrder.toPreorder.{0} Nat (StrictOrderedSemiring.toPartialOrder.{0} Nat Nat.strictOrderedSemiring))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)))) -> (CompleteSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1))
+Case conversion may be inaccurate. Consider using '#align emetric.complete_of_convergent_controlled_sequences EMetric.complete_of_convergent_controlled_sequencesₓ'. -/
 /-- A very useful criterion to show that a space is complete is to show that all sequences
 which satisfy a bound of the form `edist (u n) (u m) < B N` for all `n m ≥ N` are
 converging. This is often applied for `B N = 2^{-N}`, i.e., with a very fast convergence to
@@ -342,14 +528,22 @@ theorem complete_of_convergent_controlled_sequences (B : ℕ → ℝ≥0∞) (hB
     CompleteSpace α :=
   UniformSpace.complete_of_convergent_controlled_sequences
     (fun n => { p : α × α | edist p.1 p.2 < B n }) (fun n => edist_mem_uniformity <| hB n) H
-#align emetric.complete_of_convergent_controlled_sequences Emetric.complete_of_convergent_controlled_sequences
+#align emetric.complete_of_convergent_controlled_sequences EMetric.complete_of_convergent_controlled_sequences
 
+#print EMetric.complete_of_cauchySeq_tendsto /-
 /-- A sequentially complete pseudoemetric space is complete. -/
 theorem complete_of_cauchySeq_tendsto :
     (∀ u : ℕ → α, CauchySeq u → ∃ a, Tendsto u atTop (𝓝 a)) → CompleteSpace α :=
   UniformSpace.complete_of_cauchySeq_tendsto
-#align emetric.complete_of_cauchy_seq_tendsto Emetric.complete_of_cauchySeq_tendsto
+#align emetric.complete_of_cauchy_seq_tendsto EMetric.complete_of_cauchySeq_tendsto
+-/
 
+/- warning: emetric.tendsto_locally_uniformly_on_iff -> EMetric.tendstoLocallyUniformlyOn_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι} {s : Set.{u2} β}, Iff (TendstoLocallyUniformlyOn.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (Exists.{succ u2} (Set.{u2} β) (fun (t : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhdsWithin.{u2} β _inst_2 x s)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f y) (F n y)) ε)) p)))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} [_inst_2 : TopologicalSpace.{u3} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι} {s : Set.{u3} β}, Iff (TendstoLocallyUniformlyOn.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) _inst_2 F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (x : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) x s) -> (Exists.{succ u3} (Set.{u3} β) (fun (t : Set.{u3} β) => And (Membership.mem.{u3, u3} (Set.{u3} β) (Filter.{u3} β) (instMembershipSetFilter.{u3} β) t (nhdsWithin.{u3} β _inst_2 x s)) (Filter.Eventually.{u1} ι (fun (n : ι) => forall (y : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f y) (F n y)) ε)) p)))))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iffₓ'. -/
 /-- Expressing locally uniform convergence on a set using `edist`. -/
 theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} {s : Set β} :
@@ -360,8 +554,14 @@ theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : 
   rcases mem_uniformity_edist.1 hu with ⟨ε, εpos, hε⟩
   rcases H ε εpos x hx with ⟨t, ht, Ht⟩
   exact ⟨t, ht, Ht.mono fun n hs x hx => hε (hs x hx)⟩
-#align emetric.tendsto_locally_uniformly_on_iff Emetric.tendstoLocallyUniformlyOn_iff
-
+#align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iff
+
+/- warning: emetric.tendsto_uniformly_on_iff -> EMetric.tendstoUniformlyOn_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι} {s : Set.{u2} β}, Iff (TendstoUniformlyOn.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u3} ι (fun (n : ι) => forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (F n x)) ε)) p))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι} {s : Set.{u3} β}, Iff (TendstoUniformlyOn.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) F f p s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Filter.Eventually.{u1} ι (fun (n : ι) => forall (x : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f x) (F n x)) ε)) p))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_uniformly_on_iff EMetric.tendstoUniformlyOn_iffₓ'. -/
 /-- Expressing uniform convergence on a set using `edist`. -/
 theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} {s : Set β} :
     TendstoUniformlyOn F f p s ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x ∈ s, edist (f x) (F n x) < ε :=
@@ -369,8 +569,14 @@ theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β →
   refine' ⟨fun H ε hε => H _ (edist_mem_uniformity hε), fun H u hu => _⟩
   rcases mem_uniformity_edist.1 hu with ⟨ε, εpos, hε⟩
   exact (H ε εpos).mono fun n hs x hx => hε (hs x hx)
-#align emetric.tendsto_uniformly_on_iff Emetric.tendstoUniformlyOn_iff
-
+#align emetric.tendsto_uniformly_on_iff EMetric.tendstoUniformlyOn_iff
+
+/- warning: emetric.tendsto_locally_uniformly_iff -> EMetric.tendstoLocallyUniformly_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} [_inst_2 : TopologicalSpace.{u2} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι}, Iff (TendstoLocallyUniformly.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_2 F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (forall (x : β), Exists.{succ u2} (Set.{u2} β) (fun (t : Set.{u2} β) => Exists.{0} (Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhds.{u2} β _inst_2 x)) (fun (H : Membership.Mem.{u2, u2} (Set.{u2} β) (Filter.{u2} β) (Filter.hasMem.{u2} β) t (nhds.{u2} β _inst_2 x)) => Filter.Eventually.{u3} ι (fun (n : ι) => forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f y) (F n y)) ε)) p))))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} [_inst_2 : TopologicalSpace.{u3} β] {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι}, Iff (TendstoLocallyUniformly.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) _inst_2 F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (forall (x : β), Exists.{succ u3} (Set.{u3} β) (fun (t : Set.{u3} β) => And (Membership.mem.{u3, u3} (Set.{u3} β) (Filter.{u3} β) (instMembershipSetFilter.{u3} β) t (nhds.{u3} β _inst_2 x)) (Filter.Eventually.{u1} ι (fun (n : ι) => forall (y : β), (Membership.mem.{u3, u3} β (Set.{u3} β) (Set.instMembershipSet.{u3} β) y t) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f y) (F n y)) ε)) p))))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_locally_uniformly_iff EMetric.tendstoLocallyUniformly_iffₓ'. -/
 /-- Expressing locally uniform convergence using `edist`. -/
 theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} :
@@ -379,37 +585,46 @@ theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι
   by
   simp only [← tendstoLocallyUniformlyOn_univ, tendsto_locally_uniformly_on_iff, mem_univ,
     forall_const, exists_prop, nhdsWithin_univ]
-#align emetric.tendsto_locally_uniformly_iff Emetric.tendstoLocallyUniformly_iff
-
+#align emetric.tendsto_locally_uniformly_iff EMetric.tendstoLocallyUniformly_iff
+
+/- warning: emetric.tendsto_uniformly_iff -> EMetric.tendstoUniformly_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u3}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u3} ι}, Iff (TendstoUniformly.{u2, u1, u3} β α ι (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u3} ι (fun (n : ι) => forall (x : β), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (F n x)) ε) p))
+but is expected to have type
+  forall {α : Type.{u2}} {β : Type.{u3}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} {F : ι -> β -> α} {f : β -> α} {p : Filter.{u1} ι}, Iff (TendstoUniformly.{u3, u2, u1} β α ι (PseudoEMetricSpace.toUniformSpace.{u2} α _inst_1) F f p) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Filter.Eventually.{u1} ι (fun (n : ι) => forall (x : β), LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (f x) (F n x)) ε) p))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_uniformly_iff EMetric.tendstoUniformly_iffₓ'. -/
 /-- Expressing uniform convergence using `edist`. -/
 theorem tendstoUniformly_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} :
     TendstoUniformly F f p ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x, edist (f x) (F n x) < ε := by
   simp only [← tendstoUniformlyOn_univ, tendsto_uniformly_on_iff, mem_univ, forall_const]
-#align emetric.tendsto_uniformly_iff Emetric.tendstoUniformly_iff
+#align emetric.tendsto_uniformly_iff EMetric.tendstoUniformly_iff
 
 end Emetric
 
 open Emetric
 
+#print PseudoEMetricSpace.replaceUniformity /-
 /-- Auxiliary function to replace the uniformity on a pseudoemetric space with
 a uniformity which is equal to the original one, but maybe not defeq.
 This is useful if one wants to construct a pseudoemetric space with a
 specified uniformity. See Note [forgetful inheritance] explaining why having definitionally
 the right uniformity is often important.
 -/
-def PseudoEmetricSpace.replaceUniformity {α} [U : UniformSpace α] (m : PseudoEmetricSpace α)
-    (H : 𝓤[U] = 𝓤[PseudoEmetricSpace.toUniformSpace]) : PseudoEmetricSpace α
+def PseudoEMetricSpace.replaceUniformity {α} [U : UniformSpace α] (m : PseudoEMetricSpace α)
+    (H : 𝓤[U] = 𝓤[PseudoEMetricSpace.toUniformSpace]) : PseudoEMetricSpace α
     where
   edist := @edist _ m.toHasEdist
   edist_self := edist_self
   edist_comm := edist_comm
   edist_triangle := edist_triangle
   toUniformSpace := U
-  uniformity_edist := H.trans (@PseudoEmetricSpace.uniformity_edist α _)
-#align pseudo_emetric_space.replace_uniformity PseudoEmetricSpace.replaceUniformity
+  uniformity_edist := H.trans (@PseudoEMetricSpace.uniformity_edist α _)
+#align pseudo_emetric_space.replace_uniformity PseudoEMetricSpace.replaceUniformity
+-/
 
+#print PseudoEMetricSpace.induced /-
 /-- The extended pseudometric induced by a function taking values in a pseudoemetric space. -/
-def PseudoEmetricSpace.induced {α β} (f : α → β) (m : PseudoEmetricSpace β) : PseudoEmetricSpace α
+def PseudoEMetricSpace.induced {α β} (f : α → β) (m : PseudoEMetricSpace β) : PseudoEMetricSpace α
     where
   edist x y := edist (f x) (f y)
   edist_self x := edist_self _
@@ -417,48 +632,67 @@ def PseudoEmetricSpace.induced {α β} (f : α → β) (m : PseudoEmetricSpace 
   edist_triangle x y z := edist_triangle _ _ _
   toUniformSpace := UniformSpace.comap f m.toUniformSpace
   uniformity_edist := (uniformity_basis_edist.comap _).eq_binfᵢ
-#align pseudo_emetric_space.induced PseudoEmetricSpace.induced
+#align pseudo_emetric_space.induced PseudoEMetricSpace.induced
+-/
 
 /-- Pseudoemetric space instance on subsets of pseudoemetric spaces -/
-instance {α : Type _} {p : α → Prop} [PseudoEmetricSpace α] : PseudoEmetricSpace (Subtype p) :=
-  PseudoEmetricSpace.induced coe ‹_›
+instance {α : Type _} {p : α → Prop} [PseudoEMetricSpace α] : PseudoEMetricSpace (Subtype p) :=
+  PseudoEMetricSpace.induced coe ‹_›
 
+#print Subtype.edist_eq /-
 /-- The extended psuedodistance on a subset of a pseudoemetric space is the restriction of
 the original pseudodistance, by definition -/
 theorem Subtype.edist_eq {p : α → Prop} (x y : Subtype p) : edist x y = edist (x : α) y :=
   rfl
 #align subtype.edist_eq Subtype.edist_eq
+-/
 
 namespace MulOpposite
 
 /-- Pseudoemetric space instance on the multiplicative opposite of a pseudoemetric space. -/
 @[to_additive "Pseudoemetric space instance on the additive opposite of a pseudoemetric space."]
-instance {α : Type _} [PseudoEmetricSpace α] : PseudoEmetricSpace αᵐᵒᵖ :=
-  PseudoEmetricSpace.induced unop ‹_›
+instance {α : Type _} [PseudoEMetricSpace α] : PseudoEMetricSpace αᵐᵒᵖ :=
+  PseudoEMetricSpace.induced unop ‹_›
 
+#print MulOpposite.edist_unop /-
 @[to_additive]
 theorem edist_unop (x y : αᵐᵒᵖ) : edist (unop x) (unop y) = edist x y :=
   rfl
 #align mul_opposite.edist_unop MulOpposite.edist_unop
 #align add_opposite.edist_unop AddOpposite.edist_unop
+-/
 
+#print MulOpposite.edist_op /-
 @[to_additive]
 theorem edist_op (x y : α) : edist (op x) (op y) = edist x y :=
   rfl
 #align mul_opposite.edist_op MulOpposite.edist_op
 #align add_opposite.edist_op AddOpposite.edist_op
+-/
 
 end MulOpposite
 
 section ULift
 
-instance : PseudoEmetricSpace (ULift α) :=
-  PseudoEmetricSpace.induced ULift.down ‹_›
+instance : PseudoEMetricSpace (ULift α) :=
+  PseudoEMetricSpace.induced ULift.down ‹_›
 
+/- warning: ulift.edist_eq -> ULift.edist_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : ULift.{u2, u1} α) (y : ULift.{u2, u1} α), Eq.{1} ENNReal (EDist.edist.{max u1 u2} (ULift.{u2, u1} α) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (ULift.{u2, u1} α) (ULift.pseudoEmetricSpace.{u1, u2} α _inst_1)) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (ULift.down.{u2, u1} α x) (ULift.down.{u2, u1} α y))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] (x : ULift.{u1, u2} α) (y : ULift.{u1, u2} α), Eq.{1} ENNReal (EDist.edist.{max u2 u1} (ULift.{u1, u2} α) (PseudoEMetricSpace.toEDist.{max u2 u1} (ULift.{u1, u2} α) (instPseudoEMetricSpaceULift.{u2, u1} α _inst_1)) x y) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) (ULift.down.{u1, u2} α x) (ULift.down.{u1, u2} α y))
+Case conversion may be inaccurate. Consider using '#align ulift.edist_eq ULift.edist_eqₓ'. -/
 theorem ULift.edist_eq (x y : ULift α) : edist x y = edist x.down y.down :=
   rfl
 #align ulift.edist_eq ULift.edist_eq
 
+/- warning: ulift.edist_up_up -> ULift.edist_up_up is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (y : α), Eq.{1} ENNReal (EDist.edist.{max u1 u2} (ULift.{u2, u1} α) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (ULift.{u2, u1} α) (ULift.pseudoEmetricSpace.{u1, u2} α _inst_1)) (ULift.up.{u2, u1} α x) (ULift.up.{u2, u1} α y)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] (x : α) (y : α), Eq.{1} ENNReal (EDist.edist.{max u2 u1} (ULift.{u1, u2} α) (PseudoEMetricSpace.toEDist.{max u2 u1} (ULift.{u1, u2} α) (instPseudoEMetricSpaceULift.{u2, u1} α _inst_1)) (ULift.up.{u1, u2} α x) (ULift.up.{u1, u2} α y)) (EDist.edist.{u2} α (PseudoEMetricSpace.toEDist.{u2} α _inst_1) x y)
+Case conversion may be inaccurate. Consider using '#align ulift.edist_up_up ULift.edist_up_upₓ'. -/
 @[simp]
 theorem ULift.edist_up_up (x y : α) : edist (ULift.up x) (ULift.up y) = edist x y :=
   rfl
@@ -466,10 +700,11 @@ theorem ULift.edist_up_up (x y : α) : edist (ULift.up x) (ULift.up y) = edist x
 
 end ULift
 
+#print Prod.pseudoEMetricSpaceMax /-
 /-- The product of two pseudoemetric spaces, with the max distance, is an extended
 pseudometric spaces. We make sure that the uniform structure thus constructed is the one
 corresponding to the product of uniform spaces, to avoid diamond problems. -/
-instance Prod.pseudoEmetricSpaceMax [PseudoEmetricSpace β] : PseudoEmetricSpace (α × β)
+instance Prod.pseudoEMetricSpaceMax [PseudoEMetricSpace β] : PseudoEMetricSpace (α × β)
     where
   edist x y := edist x.1 y.1 ⊔ edist x.2 y.2
   edist_self x := by simp
@@ -479,14 +714,21 @@ instance Prod.pseudoEmetricSpaceMax [PseudoEmetricSpace β] : PseudoEmetricSpace
       (le_trans (edist_triangle _ _ _) (add_le_add (le_max_right _ _) (le_max_right _ _)))
   uniformity_edist := by
     refine' uniformity_prod.trans _
-    simp only [PseudoEmetricSpace.uniformity_edist, comap_infi]
+    simp only [PseudoEMetricSpace.uniformity_edist, comap_infi]
     rw [← infᵢ_inf_eq]; congr ; funext
     rw [← infᵢ_inf_eq]; congr ; funext
     simp [inf_principal, ext_iff, max_lt_iff]
   toUniformSpace := Prod.uniformSpace
-#align prod.pseudo_emetric_space_max Prod.pseudoEmetricSpaceMax
+#align prod.pseudo_emetric_space_max Prod.pseudoEMetricSpaceMax
+-/
 
-theorem Prod.edist_eq [PseudoEmetricSpace β] (x y : α × β) :
+/- warning: prod.edist_eq -> Prod.edist_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] (x : Prod.{u1, u2} α β) (y : Prod.{u1, u2} α β), Eq.{1} ENNReal (EDist.edist.{max u1 u2} (Prod.{u1, u2} α β) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (Prod.{u1, u2} α β) (Prod.pseudoEMetricSpaceMax.{u1, u2} α β _inst_1 _inst_2)) x y) (LinearOrder.max.{0} ENNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.completeLinearOrder))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (Prod.fst.{u1, u2} α β x) (Prod.fst.{u1, u2} α β y)) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (Prod.snd.{u1, u2} α β x) (Prod.snd.{u1, u2} α β y)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] (x : Prod.{u1, u2} α β) (y : Prod.{u1, u2} α β), Eq.{1} ENNReal (EDist.edist.{max u1 u2} (Prod.{u1, u2} α β) (PseudoEMetricSpace.toEDist.{max u1 u2} (Prod.{u1, u2} α β) (Prod.pseudoEMetricSpaceMax.{u1, u2} α β _inst_1 _inst_2)) x y) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (Prod.fst.{u1, u2} α β x) (Prod.fst.{u1, u2} α β y)) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (Prod.snd.{u1, u2} α β x) (Prod.snd.{u1, u2} α β y)))
+Case conversion may be inaccurate. Consider using '#align prod.edist_eq Prod.edist_eqₓ'. -/
+theorem Prod.edist_eq [PseudoEMetricSpace β] (x y : α × β) :
     edist x y = max (edist x.1 y.1) (edist x.2 y.2) :=
   rfl
 #align prod.edist_eq Prod.edist_eq
@@ -497,12 +739,13 @@ open Finset
 
 variable {π : β → Type _} [Fintype β]
 
+#print pseudoEMetricSpacePi /-
 /-- The product of a finite number of pseudoemetric spaces, with the max distance, is still
 a pseudoemetric space.
 This construction would also work for infinite products, but it would not give rise
 to the product topology. Hence, we only formalize it in the good situation of finitely many
 spaces. -/
-instance pseudoEmetricSpacePi [∀ b, PseudoEmetricSpace (π b)] : PseudoEmetricSpace (∀ b, π b)
+instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetricSpace (∀ b, π b)
     where
   edist f g := Finset.sup univ fun b => edist (f b) (g b)
   edist_self f := bot_unique <| Finset.sup_le <| by simp
@@ -514,37 +757,64 @@ instance pseudoEmetricSpacePi [∀ b, PseudoEmetricSpace (π b)] : PseudoEmetric
   toUniformSpace := Pi.uniformSpace _
   uniformity_edist :=
     by
-    simp only [Pi.uniformity, PseudoEmetricSpace.uniformity_edist, comap_infi, gt_iff_lt,
+    simp only [Pi.uniformity, PseudoEMetricSpace.uniformity_edist, comap_infi, gt_iff_lt,
       preimage_set_of_eq, comap_principal]
     rw [infᵢ_comm]; congr ; funext ε
     rw [infᵢ_comm]; congr ; funext εpos
     change 0 < ε at εpos
     simp [Set.ext_iff, εpos]
-#align pseudo_emetric_space_pi pseudoEmetricSpacePi
+#align pseudo_emetric_space_pi pseudoEMetricSpacePi
+-/
 
-theorem edist_pi_def [∀ b, PseudoEmetricSpace (π b)] (f g : ∀ b, π b) :
+/- warning: edist_pi_def -> edist_pi_def is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] (f : forall (b : β), π b) (g : forall (b : β), π b), Eq.{1} ENNReal (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g) (Finset.sup.{0, u1} ENNReal β ENNReal.semilatticeSup ENNReal.orderBot (Finset.univ.{u1} β _inst_2) (fun (b : β) => EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)))
+but is expected to have type
+  forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), EDist.{u1} (π b)] (f : forall (b : β), π b) (g : forall (b : β), π b), Eq.{1} ENNReal (EDist.edist.{max u2 u1} (forall (b : β), π b) (instEDistForAll.{u2, u1} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b)) f g) (Finset.sup.{0, u2} ENNReal β instENNRealSemilatticeSup ENNReal.instOrderBotENNRealToLEToPreorderToPartialOrderToSemilatticeInfToLatticeInstENNRealDistribLattice (Finset.univ.{u2} β _inst_2) (fun (b : β) => EDist.edist.{u1} (π b) (_inst_3 b) (f b) (g b)))
+Case conversion may be inaccurate. Consider using '#align edist_pi_def edist_pi_defₓ'. -/
+theorem edist_pi_def [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b) :
     edist f g = Finset.sup univ fun b => edist (f b) (g b) :=
   rfl
 #align edist_pi_def edist_pi_def
 
-theorem edist_le_pi_edist [∀ b, PseudoEmetricSpace (π b)] (f g : ∀ b, π b) (b : β) :
+/- warning: edist_le_pi_edist -> edist_le_pi_edist is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] (f : forall (b : β), π b) (g : forall (b : β), π b) (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)) (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g)
+but is expected to have type
+  forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), EDist.{u1} (π b)] (f : forall (b : β), π b) (g : forall (b : β), π b) (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} (π b) (_inst_3 b) (f b) (g b)) (EDist.edist.{max u2 u1} (forall (b : β), π b) (instEDistForAll.{u2, u1} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b)) f g)
+Case conversion may be inaccurate. Consider using '#align edist_le_pi_edist edist_le_pi_edistₓ'. -/
+theorem edist_le_pi_edist [∀ b, PseudoEMetricSpace (π b)] (f g : ∀ b, π b) (b : β) :
     edist (f b) (g b) ≤ edist f g :=
   Finset.le_sup (Finset.mem_univ b)
 #align edist_le_pi_edist edist_le_pi_edist
 
-theorem edist_pi_le_iff [∀ b, PseudoEmetricSpace (π b)] {f g : ∀ b, π b} {d : ℝ≥0∞} :
+/- warning: edist_pi_le_iff -> edist_pi_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {f : forall (b : β), π b} {g : forall (b : β), π b} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{max u1 u2} (forall (b : β), π b) (PseudoEMetricSpace.toHasEdist.{max u1 u2} (forall (b : β), π b) (pseudoEMetricSpacePi.{u1, u2} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b))) f g) d) (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} (π b) (PseudoEMetricSpace.toHasEdist.{u2} (π b) (_inst_3 b)) (f b) (g b)) d)
+but is expected to have type
+  forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), EDist.{u1} (π b)] {f : forall (b : β), π b} {g : forall (b : β), π b} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{max u2 u1} (forall (b : β), π b) (instEDistForAll.{u2, u1} β (fun (b : β) => π b) _inst_2 (fun (b : β) => _inst_3 b)) f g) d) (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} (π b) (_inst_3 b) (f b) (g b)) d)
+Case conversion may be inaccurate. Consider using '#align edist_pi_le_iff edist_pi_le_iffₓ'. -/
+theorem edist_pi_le_iff [∀ b, PseudoEMetricSpace (π b)] {f g : ∀ b, π b} {d : ℝ≥0∞} :
     edist f g ≤ d ↔ ∀ b, edist (f b) (g b) ≤ d :=
   Finset.sup_le_iff.trans <| by simp only [Finset.mem_univ, forall_const]
 #align edist_pi_le_iff edist_pi_le_iff
 
+/- warning: edist_pi_const_le -> edist_pi_const_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Fintype.{u2} β] (a : α) (b : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{max u2 u1} (β -> α) (PseudoEMetricSpace.toHasEdist.{max u2 u1} (β -> α) (pseudoEMetricSpacePi.{u2, u1} β (fun (_x : β) => α) _inst_2 (fun (b : β) => _inst_1))) (fun (_x : β) => a) (fun (_x : β) => b)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) a b)
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Fintype.{u2} β] (a : α) (b : α), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{max u1 u2} (β -> α) (instEDistForAll.{u2, u1} β (fun (x._@.Mathlib.Topology.MetricSpace.EMetricSpace._hyg.5043 : β) => α) _inst_2 (fun (b : β) => PseudoEMetricSpace.toEDist.{u1} α _inst_1)) (fun (_x : β) => a) (fun (_x : β) => b)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) a b)
+Case conversion may be inaccurate. Consider using '#align edist_pi_const_le edist_pi_const_leₓ'. -/
 theorem edist_pi_const_le (a b : α) : (edist (fun _ : β => a) fun _ => b) ≤ edist a b :=
   edist_pi_le_iff.2 fun _ => le_rfl
 #align edist_pi_const_le edist_pi_const_le
 
+#print edist_pi_const /-
 @[simp]
 theorem edist_pi_const [Nonempty β] (a b : α) : (edist (fun x : β => a) fun _ => b) = edist a b :=
   Finset.sup_const univ_nonempty (edist a b)
 #align edist_pi_const edist_pi_const
+-/
 
 end Pi
 
@@ -552,72 +822,150 @@ namespace Emetric
 
 variable {x y z : α} {ε ε₁ ε₂ : ℝ≥0∞} {s t : Set α}
 
+#print EMetric.ball /-
 /-- `emetric.ball x ε` is the set of all points `y` with `edist y x < ε` -/
 def ball (x : α) (ε : ℝ≥0∞) : Set α :=
   { y | edist y x < ε }
-#align emetric.ball Emetric.ball
+#align emetric.ball EMetric.ball
+-/
 
+/- warning: emetric.mem_ball -> EMetric.mem_ball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y x) ε)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y x) ε)
+Case conversion may be inaccurate. Consider using '#align emetric.mem_ball EMetric.mem_ballₓ'. -/
 @[simp]
 theorem mem_ball : y ∈ ball x ε ↔ edist y x < ε :=
   Iff.rfl
-#align emetric.mem_ball Emetric.mem_ball
-
+#align emetric.mem_ball EMetric.mem_ball
+
+/- warning: emetric.mem_ball' -> EMetric.mem_ball' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε)
+Case conversion may be inaccurate. Consider using '#align emetric.mem_ball' EMetric.mem_ball'ₓ'. -/
 theorem mem_ball' : y ∈ ball x ε ↔ edist x y < ε := by rw [edist_comm, mem_ball]
-#align emetric.mem_ball' Emetric.mem_ball'
+#align emetric.mem_ball' EMetric.mem_ball'
 
+#print EMetric.closedBall /-
 /-- `emetric.closed_ball x ε` is the set of all points `y` with `edist y x ≤ ε` -/
 def closedBall (x : α) (ε : ℝ≥0∞) :=
   { y | edist y x ≤ ε }
-#align emetric.closed_ball Emetric.closedBall
+#align emetric.closed_ball EMetric.closedBall
+-/
 
+/- warning: emetric.mem_closed_ball -> EMetric.mem_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y x) ε)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y x) ε)
+Case conversion may be inaccurate. Consider using '#align emetric.mem_closed_ball EMetric.mem_closedBallₓ'. -/
 @[simp]
 theorem mem_closedBall : y ∈ closedBall x ε ↔ edist y x ≤ ε :=
   Iff.rfl
-#align emetric.mem_closed_ball Emetric.mem_closedBall
-
-theorem mem_closed_ball' : y ∈ closedBall x ε ↔ edist x y ≤ ε := by rw [edist_comm, mem_closed_ball]
-#align emetric.mem_closed_ball' Emetric.mem_closed_ball'
-
+#align emetric.mem_closed_ball EMetric.mem_closedBall
+
+/- warning: emetric.mem_closed_ball' -> EMetric.mem_closedBall' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.closedBall.{u1} α _inst_1 x ε)) (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε)
+Case conversion may be inaccurate. Consider using '#align emetric.mem_closed_ball' EMetric.mem_closedBall'ₓ'. -/
+theorem mem_closedBall' : y ∈ closedBall x ε ↔ edist x y ≤ ε := by rw [edist_comm, mem_closed_ball]
+#align emetric.mem_closed_ball' EMetric.mem_closedBall'
+
+/- warning: emetric.closed_ball_top -> EMetric.closedBall_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α), Eq.{succ u1} (Set.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (Set.univ.{u1} α)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α), Eq.{succ u1} (Set.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Set.univ.{u1} α)
+Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_top EMetric.closedBall_topₓ'. -/
 @[simp]
 theorem closedBall_top (x : α) : closedBall x ∞ = univ :=
   eq_univ_of_forall fun y => le_top
-#align emetric.closed_ball_top Emetric.closedBall_top
+#align emetric.closed_ball_top EMetric.closedBall_top
 
+#print EMetric.ball_subset_closedBall /-
 theorem ball_subset_closedBall : ball x ε ⊆ closedBall x ε := fun y hy => le_of_lt hy
-#align emetric.ball_subset_closed_ball Emetric.ball_subset_closedBall
+#align emetric.ball_subset_closed_ball EMetric.ball_subset_closedBall
+-/
 
+/- warning: emetric.pos_of_mem_ball -> EMetric.pos_of_mem_ball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε)
+Case conversion may be inaccurate. Consider using '#align emetric.pos_of_mem_ball EMetric.pos_of_mem_ballₓ'. -/
 theorem pos_of_mem_ball (hy : y ∈ ball x ε) : 0 < ε :=
   lt_of_le_of_lt (zero_le _) hy
-#align emetric.pos_of_mem_ball Emetric.pos_of_mem_ball
-
+#align emetric.pos_of_mem_ball EMetric.pos_of_mem_ball
+
+/- warning: emetric.mem_ball_self -> EMetric.mem_ball_self is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (EMetric.ball.{u1} α _inst_1 x ε))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (EMetric.ball.{u1} α _inst_1 x ε))
+Case conversion may be inaccurate. Consider using '#align emetric.mem_ball_self EMetric.mem_ball_selfₓ'. -/
 theorem mem_ball_self (h : 0 < ε) : x ∈ ball x ε :=
   show edist x x < ε by rw [edist_self] <;> assumption
-#align emetric.mem_ball_self Emetric.mem_ball_self
+#align emetric.mem_ball_self EMetric.mem_ball_self
 
+#print EMetric.mem_closedBall_self /-
 theorem mem_closedBall_self : x ∈ closedBall x ε :=
   show edist x x ≤ ε by rw [edist_self] <;> exact bot_le
-#align emetric.mem_closed_ball_self Emetric.mem_closedBall_self
+#align emetric.mem_closed_ball_self EMetric.mem_closedBall_self
+-/
 
+#print EMetric.mem_ball_comm /-
 theorem mem_ball_comm : x ∈ ball y ε ↔ y ∈ ball x ε := by rw [mem_ball', mem_ball]
-#align emetric.mem_ball_comm Emetric.mem_ball_comm
+#align emetric.mem_ball_comm EMetric.mem_ball_comm
+-/
 
+#print EMetric.mem_closedBall_comm /-
 theorem mem_closedBall_comm : x ∈ closedBall y ε ↔ y ∈ closedBall x ε := by
   rw [mem_closed_ball', mem_closed_ball]
-#align emetric.mem_closed_ball_comm Emetric.mem_closedBall_comm
+#align emetric.mem_closed_ball_comm EMetric.mem_closedBall_comm
+-/
 
+/- warning: emetric.ball_subset_ball -> EMetric.ball_subset_ball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 x ε₂))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 x ε₂))
+Case conversion may be inaccurate. Consider using '#align emetric.ball_subset_ball EMetric.ball_subset_ballₓ'. -/
 theorem ball_subset_ball (h : ε₁ ≤ ε₂) : ball x ε₁ ⊆ ball x ε₂ := fun y (yx : _ < ε₁) =>
   lt_of_lt_of_le yx h
-#align emetric.ball_subset_ball Emetric.ball_subset_ball
-
+#align emetric.ball_subset_ball EMetric.ball_subset_ball
+
+/- warning: emetric.closed_ball_subset_closed_ball -> EMetric.closedBall_subset_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε₁) (EMetric.closedBall.{u1} α _inst_1 x ε₂))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε₁ ε₂) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε₁) (EMetric.closedBall.{u1} α _inst_1 x ε₂))
+Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_subset_closed_ball EMetric.closedBall_subset_closedBallₓ'. -/
 theorem closedBall_subset_closedBall (h : ε₁ ≤ ε₂) : closedBall x ε₁ ⊆ closedBall x ε₂ :=
   fun y (yx : _ ≤ ε₁) => le_trans yx h
-#align emetric.closed_ball_subset_closed_ball Emetric.closedBall_subset_closedBall
-
+#align emetric.closed_ball_subset_closed_ball EMetric.closedBall_subset_closedBall
+
+/- warning: emetric.ball_disjoint -> EMetric.ball_disjoint is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) ε₁ ε₂) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)) -> (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.completeBooleanAlgebra.{u1} α)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} α) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α))) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) ε₁ ε₂) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y)) -> (Disjoint.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} α) (Preorder.toLE.{u1} (Set.{u1} α) (PartialOrder.toPreorder.{u1} (Set.{u1} α) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} α) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} α) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} α) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} α) (Set.instCompleteBooleanAlgebraSet.{u1} α)))))) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
+Case conversion may be inaccurate. Consider using '#align emetric.ball_disjoint EMetric.ball_disjointₓ'. -/
 theorem ball_disjoint (h : ε₁ + ε₂ ≤ edist x y) : Disjoint (ball x ε₁) (ball y ε₂) :=
   Set.disjoint_left.mpr fun z h₁ h₂ =>
     (edist_triangle_left x y z).not_lt <| (ENNReal.add_lt_add h₁ h₂).trans_le h
-#align emetric.ball_disjoint Emetric.ball_disjoint
-
+#align emetric.ball_disjoint EMetric.ball_disjoint
+
+/- warning: emetric.ball_subset -> EMetric.ball_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε₁) ε₂) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε₁ : ENNReal} {ε₂ : ENNReal}, (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε₁) ε₂) -> (Ne.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε₁) (EMetric.ball.{u1} α _inst_1 y ε₂))
+Case conversion may be inaccurate. Consider using '#align emetric.ball_subset EMetric.ball_subsetₓ'. -/
 theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) : ball x ε₁ ⊆ ball y ε₂ :=
   fun z zx =>
   calc
@@ -626,30 +974,55 @@ theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) :
     _ < edist x y + ε₁ := (ENNReal.add_lt_add_left h' zx)
     _ ≤ ε₂ := h
     
-#align emetric.ball_subset Emetric.ball_subset
-
+#align emetric.ball_subset EMetric.ball_subset
+
+/- warning: emetric.exists_ball_subset_ball -> EMetric.exists_ball_subset_ball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (Exists.{1} ENNReal (fun (ε' : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε' (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε' (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 y ε') (EMetric.ball.{u1} α _inst_1 x ε))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {ε : ENNReal}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y (EMetric.ball.{u1} α _inst_1 x ε)) -> (Exists.{1} ENNReal (fun (ε' : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε' (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 y ε') (EMetric.ball.{u1} α _inst_1 x ε))))
+Case conversion may be inaccurate. Consider using '#align emetric.exists_ball_subset_ball EMetric.exists_ball_subset_ballₓ'. -/
 theorem exists_ball_subset_ball (h : y ∈ ball x ε) : ∃ ε' > 0, ball y ε' ⊆ ball x ε :=
   by
   have : 0 < ε - edist y x := by simpa using h
   refine' ⟨ε - edist y x, this, ball_subset _ (ne_top_of_lt h)⟩
   exact (add_tsub_cancel_of_le (mem_ball.mp h).le).le
-#align emetric.exists_ball_subset_ball Emetric.exists_ball_subset_ball
-
+#align emetric.exists_ball_subset_ball EMetric.exists_ball_subset_ball
+
+/- warning: emetric.ball_eq_empty_iff -> EMetric.ball_eq_empty_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, Iff (Eq.{succ u1} (Set.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (Eq.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {ε : ENNReal}, Iff (Eq.{succ u1} (Set.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (Eq.{1} ENNReal ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align emetric.ball_eq_empty_iff EMetric.ball_eq_empty_iffₓ'. -/
 theorem ball_eq_empty_iff : ball x ε = ∅ ↔ ε = 0 :=
   eq_empty_iff_forall_not_mem.trans
     ⟨fun h => le_bot_iff.1 (le_of_not_gt fun ε0 => h _ (mem_ball_self ε0)), fun ε0 y h =>
       not_lt_of_le (le_of_eq ε0) (pos_of_mem_ball h)⟩
-#align emetric.ball_eq_empty_iff Emetric.ball_eq_empty_iff
-
+#align emetric.ball_eq_empty_iff EMetric.ball_eq_empty_iff
+
+/- warning: emetric.ord_connected_set_of_closed_ball_subset -> EMetric.ordConnected_setOf_closedBall_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (s : Set.{u1} α), Set.OrdConnected.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (setOf.{0} ENNReal (fun (r : ENNReal) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x r) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (s : Set.{u1} α), Set.OrdConnected.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (setOf.{0} ENNReal (fun (r : ENNReal) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x r) s))
+Case conversion may be inaccurate. Consider using '#align emetric.ord_connected_set_of_closed_ball_subset EMetric.ordConnected_setOf_closedBall_subsetₓ'. -/
 theorem ordConnected_setOf_closedBall_subset (x : α) (s : Set α) :
     OrdConnected { r | closedBall x r ⊆ s } :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (closedBall_subset_closedBall hr.2).trans hr₂⟩
-#align emetric.ord_connected_set_of_closed_ball_subset Emetric.ordConnected_setOf_closedBall_subset
-
+#align emetric.ord_connected_set_of_closed_ball_subset EMetric.ordConnected_setOf_closedBall_subset
+
+/- warning: emetric.ord_connected_set_of_ball_subset -> EMetric.ordConnected_setOf_ball_subset is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (s : Set.{u1} α), Set.OrdConnected.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder)))) (setOf.{0} ENNReal (fun (r : ENNReal) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x r) s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) (s : Set.{u1} α), Set.OrdConnected.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (setOf.{0} ENNReal (fun (r : ENNReal) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x r) s))
+Case conversion may be inaccurate. Consider using '#align emetric.ord_connected_set_of_ball_subset EMetric.ordConnected_setOf_ball_subsetₓ'. -/
 theorem ordConnected_setOf_ball_subset (x : α) (s : Set α) : OrdConnected { r | ball x r ⊆ s } :=
   ⟨fun r₁ hr₁ r₂ hr₂ r hr => (ball_subset_ball hr.2).trans hr₂⟩
-#align emetric.ord_connected_set_of_ball_subset Emetric.ordConnected_setOf_ball_subset
+#align emetric.ord_connected_set_of_ball_subset EMetric.ordConnected_setOf_ball_subset
 
+#print EMetric.edistLtTopSetoid /-
 /-- Relation “two points are at a finite edistance” is an equivalence relation. -/
 def edistLtTopSetoid : Setoid α where
   R x y := edist x y < ⊤
@@ -658,75 +1031,156 @@ def edistLtTopSetoid : Setoid α where
       rw [edist_self]
       exact ENNReal.coe_lt_top, fun x y h => by rwa [edist_comm], fun x y z hxy hyz =>
       lt_of_le_of_lt (edist_triangle x y z) (ENNReal.add_lt_top.2 ⟨hxy, hyz⟩)⟩
-#align emetric.edist_lt_top_setoid Emetric.edistLtTopSetoid
+#align emetric.edist_lt_top_setoid EMetric.edistLtTopSetoid
+-/
 
+/- warning: emetric.ball_zero -> EMetric.ball_zero is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Set.{u1} α) (EMetric.ball.{u1} α _inst_1 x (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Set.{u1} α) (EMetric.ball.{u1} α _inst_1 x (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))
+Case conversion may be inaccurate. Consider using '#align emetric.ball_zero EMetric.ball_zeroₓ'. -/
 @[simp]
-theorem ball_zero : ball x 0 = ∅ := by rw [Emetric.ball_eq_empty_iff]
-#align emetric.ball_zero Emetric.ball_zero
-
+theorem ball_zero : ball x 0 = ∅ := by rw [EMetric.ball_eq_empty_iff]
+#align emetric.ball_zero EMetric.ball_zero
+
+/- warning: emetric.nhds_basis_eball -> EMetric.nhds_basis_eball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (EMetric.ball.{u1} α _inst_1 x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (EMetric.ball.{u1} α _inst_1 x)
+Case conversion may be inaccurate. Consider using '#align emetric.nhds_basis_eball EMetric.nhds_basis_eballₓ'. -/
 theorem nhds_basis_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) (ball x) :=
   nhds_basis_uniformity uniformity_basis_edist
-#align emetric.nhds_basis_eball Emetric.nhds_basis_eball
-
+#align emetric.nhds_basis_eball EMetric.nhds_basis_eball
+
+/- warning: emetric.nhds_within_basis_eball -> EMetric.nhdsWithin_basis_eball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)
+Case conversion may be inaccurate. Consider using '#align emetric.nhds_within_basis_eball EMetric.nhdsWithin_basis_eballₓ'. -/
 theorem nhdsWithin_basis_eball : (𝓝[s] x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => ball x ε ∩ s :=
   nhdsWithin_hasBasis nhds_basis_eball s
-#align emetric.nhds_within_basis_eball Emetric.nhdsWithin_basis_eball
-
+#align emetric.nhds_within_basis_eball EMetric.nhdsWithin_basis_eball
+
+/- warning: emetric.nhds_basis_closed_eball -> EMetric.nhds_basis_closed_eball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (EMetric.closedBall.{u1} α _inst_1 x)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Filter.HasBasis.{u1, 1} α ENNReal (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (EMetric.closedBall.{u1} α _inst_1 x)
+Case conversion may be inaccurate. Consider using '#align emetric.nhds_basis_closed_eball EMetric.nhds_basis_closed_eballₓ'. -/
 theorem nhds_basis_closed_eball : (𝓝 x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) (closedBall x) :=
   nhds_basis_uniformity uniformity_basis_edist_le
-#align emetric.nhds_basis_closed_eball Emetric.nhds_basis_closed_eball
-
+#align emetric.nhds_basis_closed_eball EMetric.nhds_basis_closed_eball
+
+/- warning: emetric.nhds_within_basis_closed_eball -> EMetric.nhdsWithin_basis_closed_eball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) s)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Filter.HasBasis.{u1, 1} α ENNReal (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x s) (fun (ε : ENNReal) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) (fun (ε : ENNReal) => Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) s)
+Case conversion may be inaccurate. Consider using '#align emetric.nhds_within_basis_closed_eball EMetric.nhdsWithin_basis_closed_eballₓ'. -/
 theorem nhdsWithin_basis_closed_eball :
     (𝓝[s] x).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => closedBall x ε ∩ s :=
   nhdsWithin_hasBasis nhds_basis_closed_eball s
-#align emetric.nhds_within_basis_closed_eball Emetric.nhdsWithin_basis_closed_eball
-
+#align emetric.nhds_within_basis_closed_eball EMetric.nhdsWithin_basis_closed_eball
+
+/- warning: emetric.nhds_eq -> EMetric.nhds_eq is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (infᵢ.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.completeLattice.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{succ u1} (Filter.{u1} α) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x) (infᵢ.{u1, 1} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} α) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} α) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} α) (Filter.instCompleteLatticeFilter.{u1} α))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} α (EMetric.ball.{u1} α _inst_1 x ε))))
+Case conversion may be inaccurate. Consider using '#align emetric.nhds_eq EMetric.nhds_eqₓ'. -/
 theorem nhds_eq : 𝓝 x = ⨅ ε > 0, 𝓟 (ball x ε) :=
   nhds_basis_eball.eq_binfᵢ
-#align emetric.nhds_eq Emetric.nhds_eq
-
+#align emetric.nhds_eq EMetric.nhds_eq
+
+/- warning: emetric.mem_nhds_iff -> EMetric.mem_nhds_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x)) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s)))
+Case conversion may be inaccurate. Consider using '#align emetric.mem_nhds_iff EMetric.mem_nhds_iffₓ'. -/
 theorem mem_nhds_iff : s ∈ 𝓝 x ↔ ∃ ε > 0, ball x ε ⊆ s :=
   nhds_basis_eball.mem_iff
-#align emetric.mem_nhds_iff Emetric.mem_nhds_iff
-
+#align emetric.mem_nhds_iff EMetric.mem_nhds_iff
+
+/- warning: emetric.mem_nhds_within_iff -> EMetric.mem_nhdsWithin_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) s (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x t)) (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) t) s)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α} {t : Set.{u1} α}, Iff (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) s (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x t)) (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) t) s)))
+Case conversion may be inaccurate. Consider using '#align emetric.mem_nhds_within_iff EMetric.mem_nhdsWithin_iffₓ'. -/
 theorem mem_nhdsWithin_iff : s ∈ 𝓝[t] x ↔ ∃ ε > 0, ball x ε ∩ t ⊆ s :=
   nhdsWithin_basis_eball.mem_iff
-#align emetric.mem_nhds_within_iff Emetric.mem_nhdsWithin_iff
+#align emetric.mem_nhds_within_iff EMetric.mem_nhdsWithin_iff
 
 section
 
-variable [PseudoEmetricSpace β] {f : α → β}
+variable [PseudoEMetricSpace β] {f : α → β}
 
+/- warning: emetric.tendsto_nhds_within_nhds_within -> EMetric.tendsto_nhdsWithin_nhdsWithin is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {t : Set.{u2} β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhdsWithin.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b t)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (And (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) (f x) t) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε))))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {t : Set.{u2} β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhdsWithin.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b t)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {{x : α}}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (And (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) (f x) t) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε))))))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_within_nhds_within EMetric.tendsto_nhdsWithin_nhdsWithinₓ'. -/
 theorem tendsto_nhdsWithin_nhdsWithin {t : Set β} {a b} :
     Tendsto f (𝓝[s] a) (𝓝[t] b) ↔
       ∀ ε > 0, ∃ δ > 0, ∀ ⦃x⦄, x ∈ s → edist x a < δ → f x ∈ t ∧ edist (f x) b < ε :=
   (nhdsWithin_basis_eball.tendsto_iffₓ nhdsWithin_basis_eball).trans <|
     forall₂_congr fun ε hε => exists₂_congr fun δ hδ => forall_congr' fun x => by simp <;> itauto
-#align emetric.tendsto_nhds_within_nhds_within Emetric.tendsto_nhdsWithin_nhdsWithin
-
+#align emetric.tendsto_nhds_within_nhds_within EMetric.tendsto_nhdsWithin_nhdsWithin
+
+/- warning: emetric.tendsto_nhds_within_nhds -> EMetric.tendsto_nhdsWithin_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {x : α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhdsWithin.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a s) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {x : α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε)))))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_within_nhds EMetric.tendsto_nhdsWithin_nhdsₓ'. -/
 theorem tendsto_nhdsWithin_nhds {a b} :
     Tendsto f (𝓝[s] a) (𝓝 b) ↔
       ∀ ε > 0, ∃ δ > 0, ∀ {x : α}, x ∈ s → edist x a < δ → edist (f x) b < ε :=
   by
   rw [← nhdsWithin_univ b, tendsto_nhds_within_nhds_within]
   simp only [mem_univ, true_and_iff]
-#align emetric.tendsto_nhds_within_nhds Emetric.tendsto_nhdsWithin_nhds
-
+#align emetric.tendsto_nhds_within_nhds EMetric.tendsto_nhdsWithin_nhds
+
+/- warning: emetric.tendsto_nhds_nhds -> EMetric.tendsto_nhds_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {{x : α}}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toHasEdist.{u2} β _inst_2) (f x) b) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : PseudoEMetricSpace.{u2} β] {f : α -> β} {a : α} {b : β}, Iff (Filter.Tendsto.{u1, u2} α β f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a) (nhds.{u2} β (UniformSpace.toTopologicalSpace.{u2} β (PseudoEMetricSpace.toUniformSpace.{u2} β _inst_2)) b)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {{x : α}}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x a) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} β (PseudoEMetricSpace.toEDist.{u2} β _inst_2) (f x) b) ε)))))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds_nhds EMetric.tendsto_nhds_nhdsₓ'. -/
 theorem tendsto_nhds_nhds {a b} :
     Tendsto f (𝓝 a) (𝓝 b) ↔ ∀ ε > 0, ∃ δ > 0, ∀ ⦃x⦄, edist x a < δ → edist (f x) b < ε :=
   nhds_basis_eball.tendsto_iffₓ nhds_basis_eball
-#align emetric.tendsto_nhds_nhds Emetric.tendsto_nhds_nhds
+#align emetric.tendsto_nhds_nhds EMetric.tendsto_nhds_nhds
 
 end
 
+/- warning: emetric.is_open_iff -> EMetric.isOpen_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (IsOpen.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (IsOpen.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) s))))
+Case conversion may be inaccurate. Consider using '#align emetric.is_open_iff EMetric.isOpen_iffₓ'. -/
 theorem isOpen_iff : IsOpen s ↔ ∀ x ∈ s, ∃ ε > 0, ball x ε ⊆ s := by
   simp [isOpen_iff_nhds, mem_nhds_iff]
-#align emetric.is_open_iff Emetric.isOpen_iff
+#align emetric.is_open_iff EMetric.isOpen_iff
 
+#print EMetric.isOpen_ball /-
 theorem isOpen_ball : IsOpen (ball x ε) :=
   isOpen_iff.2 fun y => exists_ball_subset_ball
-#align emetric.is_open_ball Emetric.isOpen_ball
+#align emetric.is_open_ball EMetric.isOpen_ball
+-/
 
+/- warning: emetric.is_closed_ball_top -> EMetric.isClosed_ball_top is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, IsClosed.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (EMetric.ball.{u1} α _inst_1 x (Top.top.{0} ENNReal (CompleteLattice.toHasTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, IsClosed.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) (EMetric.ball.{u1} α _inst_1 x (Top.top.{0} ENNReal (CompleteLattice.toTop.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))
+Case conversion may be inaccurate. Consider using '#align emetric.is_closed_ball_top EMetric.isClosed_ball_topₓ'. -/
 theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
   isOpen_compl_iff.1 <|
     isOpen_iff.2 fun y hy =>
@@ -734,48 +1188,94 @@ theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
         (ball_disjoint <| by
             rw [top_add]
             exact le_of_not_lt hy).subset_compl_right⟩
-#align emetric.is_closed_ball_top Emetric.isClosed_ball_top
-
+#align emetric.is_closed_ball_top EMetric.isClosed_ball_top
+
+/- warning: emetric.ball_mem_nhds -> EMetric.ball_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (EMetric.ball.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
+Case conversion may be inaccurate. Consider using '#align emetric.ball_mem_nhds EMetric.ball_mem_nhdsₓ'. -/
 theorem ball_mem_nhds (x : α) {ε : ℝ≥0∞} (ε0 : 0 < ε) : ball x ε ∈ 𝓝 x :=
   isOpen_ball.mem_nhds (mem_ball_self ε0)
-#align emetric.ball_mem_nhds Emetric.ball_mem_nhds
-
+#align emetric.ball_mem_nhds EMetric.ball_mem_nhds
+
+/- warning: emetric.closed_ball_mem_nhds -> EMetric.closedBall_mem_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) ε) -> (Membership.Mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (Filter.hasMem.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (x : α) {ε : ENNReal}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) ε) -> (Membership.mem.{u1, u1} (Set.{u1} α) (Filter.{u1} α) (instMembershipSetFilter.{u1} α) (EMetric.closedBall.{u1} α _inst_1 x ε) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x))
+Case conversion may be inaccurate. Consider using '#align emetric.closed_ball_mem_nhds EMetric.closedBall_mem_nhdsₓ'. -/
 theorem closedBall_mem_nhds (x : α) {ε : ℝ≥0∞} (ε0 : 0 < ε) : closedBall x ε ∈ 𝓝 x :=
   mem_of_superset (ball_mem_nhds x ε0) ball_subset_closedBall
-#align emetric.closed_ball_mem_nhds Emetric.closedBall_mem_nhds
+#align emetric.closed_ball_mem_nhds EMetric.closedBall_mem_nhds
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem ball_prod_same [PseudoEmetricSpace β] (x : α) (y : β) (r : ℝ≥0∞) :
+#print EMetric.ball_prod_same /-
+theorem ball_prod_same [PseudoEMetricSpace β] (x : α) (y : β) (r : ℝ≥0∞) :
     ball x r ×ˢ ball y r = ball (x, y) r :=
   ext fun z => max_lt_iff.symm
-#align emetric.ball_prod_same Emetric.ball_prod_same
+#align emetric.ball_prod_same EMetric.ball_prod_same
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
-theorem closedBall_prod_same [PseudoEmetricSpace β] (x : α) (y : β) (r : ℝ≥0∞) :
+#print EMetric.closedBall_prod_same /-
+theorem closedBall_prod_same [PseudoEMetricSpace β] (x : α) (y : β) (r : ℝ≥0∞) :
     closedBall x r ×ˢ closedBall y r = closedBall (x, y) r :=
   ext fun z => max_le_iff.symm
-#align emetric.closed_ball_prod_same Emetric.closedBall_prod_same
+#align emetric.closed_ball_prod_same EMetric.closedBall_prod_same
+-/
 
+/- warning: emetric.mem_closure_iff -> EMetric.mem_closure_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} α (fun (y : α) => Exists.{0} (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) ε))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Iff (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} α (fun (y : α) => And (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) ε))))
+Case conversion may be inaccurate. Consider using '#align emetric.mem_closure_iff EMetric.mem_closure_iffₓ'. -/
 /-- ε-characterization of the closure in pseudoemetric spaces -/
 theorem mem_closure_iff : x ∈ closure s ↔ ∀ ε > 0, ∃ y ∈ s, edist x y < ε :=
   (mem_closure_iff_nhds_basis nhds_basis_eball).trans <| by simp only [mem_ball, edist_comm x]
-#align emetric.mem_closure_iff Emetric.mem_closure_iff
-
+#align emetric.mem_closure_iff EMetric.mem_closure_iff
+
+/- warning: emetric.tendsto_nhds -> EMetric.tendsto_nhds is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Filter.Eventually.{u2} β (fun (x : β) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u x) a) ε) f))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {f : Filter.{u2} β} {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u f (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Filter.Eventually.{u2} β (fun (x : β) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u x) a) ε) f))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_nhds EMetric.tendsto_nhdsₓ'. -/
 theorem tendsto_nhds {f : Filter β} {u : β → α} {a : α} :
     Tendsto u f (𝓝 a) ↔ ∀ ε > 0, ∀ᶠ x in f, edist (u x) a < ε :=
   nhds_basis_eball.tendsto_right_iff
-#align emetric.tendsto_nhds Emetric.tendsto_nhds
-
+#align emetric.tendsto_nhds EMetric.tendsto_nhds
+
+/- warning: emetric.tendsto_at_top -> EMetric.tendsto_atTop is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) a) ε))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α} {a : α}, Iff (Filter.Tendsto.{u2, u1} β α u (Filter.atTop.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) (nhds.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) a)) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) a) ε))))
+Case conversion may be inaccurate. Consider using '#align emetric.tendsto_at_top EMetric.tendsto_atTopₓ'. -/
 theorem tendsto_atTop [Nonempty β] [SemilatticeSup β] {u : β → α} {a : α} :
     Tendsto u atTop (𝓝 a) ↔ ∀ ε > 0, ∃ N, ∀ n ≥ N, edist (u n) a < ε :=
   (atTop_basis.tendsto_iffₓ nhds_basis_eball).trans <| by
     simp only [exists_prop, true_and_iff, mem_Ici, mem_ball]
-#align emetric.tendsto_at_top Emetric.tendsto_atTop
-
+#align emetric.tendsto_at_top EMetric.tendsto_atTop
+
+/- warning: emetric.inseparable_iff -> EMetric.inseparable_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α}, Iff (Inseparable.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x y) (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α}, Iff (Inseparable.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) x y) (Eq.{1} ENNReal (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align emetric.inseparable_iff EMetric.inseparable_iffₓ'. -/
 theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
   simp [inseparable_iff_mem_closure, mem_closure_iff, edist_comm, forall_lt_iff_le']
-#align emetric.inseparable_iff Emetric.inseparable_iff
-
+#align emetric.inseparable_iff EMetric.inseparable_iff
+
+/- warning: emetric.cauchy_seq_iff -> EMetric.cauchySeq_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u m) (u n)) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u2} β (fun (N : β) => forall (m : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N m) -> (forall (n : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N n) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u m) (u n)) ε)))))
+Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff EMetric.cauchySeq_iffₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (m n «expr ≥ » N) -/
 -- see Note [nolint_ge]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
@@ -784,29 +1284,53 @@ the pseudoedistance between its elements is arbitrarily small -/
 theorem cauchySeq_iff [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ ∀ ε > 0, ∃ N, ∀ (m) (_ : m ≥ N) (n) (_ : n ≥ N), edist (u m) (u n) < ε :=
   uniformity_basis_edist.cauchySeq_iff
-#align emetric.cauchy_seq_iff Emetric.cauchySeq_iff
-
+#align emetric.cauchy_seq_iff EMetric.cauchySeq_iff
+
+/- warning: emetric.cauchy_seq_iff' -> EMetric.cauchySeq_iff' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u N)) ε))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) (u N)) ε))))
+Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff' EMetric.cauchySeq_iff'ₓ'. -/
 /-- A variation around the emetric characterization of Cauchy sequences -/
 theorem cauchySeq_iff' [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ ∀ ε > (0 : ℝ≥0∞), ∃ N, ∀ n ≥ N, edist (u n) (u N) < ε :=
   uniformity_basis_edist.cauchySeq_iff'
-#align emetric.cauchy_seq_iff' Emetric.cauchySeq_iff'
-
+#align emetric.cauchy_seq_iff' EMetric.cauchySeq_iff'
+
+/- warning: emetric.cauchy_seq_iff_nnreal -> EMetric.cauchySeq_iff_NNReal is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring))))))) ε) -> (Exists.{succ u2} β (fun (N : β) => forall (n : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N n) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (u n) (u N)) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) NNReal ENNReal (HasLiftT.mk.{1, 1} NNReal ENNReal (CoeTCₓ.coe.{1, 1} NNReal ENNReal (coeBase.{1, 1} NNReal ENNReal ENNReal.hasCoe))) ε)))))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] [_inst_2 : Nonempty.{succ u2} β] [_inst_3 : SemilatticeSup.{u2} β] {u : β -> α}, Iff (CauchySeq.{u1, u2} α β (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) _inst_3 u) (forall (ε : NNReal), (LT.lt.{0} NNReal (Preorder.toLT.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero)) ε) -> (Exists.{succ u2} β (fun (N : β) => forall (n : β), (LE.le.{u2} β (Preorder.toLE.{u2} β (PartialOrder.toPreorder.{u2} β (SemilatticeSup.toPartialOrder.{u2} β _inst_3))) N n) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (u n) (u N)) (ENNReal.some ε)))))
+Case conversion may be inaccurate. Consider using '#align emetric.cauchy_seq_iff_nnreal EMetric.cauchySeq_iff_NNRealₓ'. -/
 /-- A variation of the emetric characterization of Cauchy sequences that deals with
 `ℝ≥0` upper bounds. -/
-theorem cauchySeq_iff_nNReal [Nonempty β] [SemilatticeSup β] {u : β → α} :
+theorem cauchySeq_iff_NNReal [Nonempty β] [SemilatticeSup β] {u : β → α} :
     CauchySeq u ↔ ∀ ε : ℝ≥0, 0 < ε → ∃ N, ∀ n, N ≤ n → edist (u n) (u N) < ε :=
-  uniformity_basis_edist_nNReal.cauchySeq_iff'
-#align emetric.cauchy_seq_iff_nnreal Emetric.cauchySeq_iff_nNReal
-
+  uniformity_basis_edist_nnreal.cauchySeq_iff'
+#align emetric.cauchy_seq_iff_nnreal EMetric.cauchySeq_iff_NNReal
+
+/- warning: emetric.totally_bounded_iff -> EMetric.totallyBounded_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε)))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => 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 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε)))))))
+Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff EMetric.totallyBounded_iffₓ'. -/
 theorem totallyBounded_iff {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ t : Set α, t.Finite ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => H _ (edist_mem_uniformity ε0), fun H r ru =>
     let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 ru
     let ⟨t, ft, h⟩ := H ε ε0
     ⟨t, ft, h.trans <| unionᵢ₂_mono fun y yt z => hε⟩⟩
-#align emetric.totally_bounded_iff Emetric.totallyBounded_iff
-
+#align emetric.totally_bounded_iff EMetric.totallyBounded_iff
+
+/- warning: emetric.totally_bounded_iff' -> EMetric.totallyBounded_iff' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (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) => EMetric.ball.{u1} α _inst_1 y ε))))))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, Iff (TotallyBounded.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1) s) (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (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.MetricSpace.EMetricSpace._hyg.9103 : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) => EMetric.ball.{u1} α _inst_1 y ε))))))))
+Case conversion may be inaccurate. Consider using '#align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'ₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 theorem totallyBounded_iff' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
@@ -814,10 +1338,16 @@ theorem totallyBounded_iff' {s : Set α} :
     let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 ru
     let ⟨t, _, ft, h⟩ := H ε ε0
     ⟨t, ft, h.trans <| unionᵢ₂_mono fun y yt z => hε⟩⟩
-#align emetric.totally_bounded_iff' Emetric.totallyBounded_iff'
+#align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'
 
 section Compact
 
+/- warning: emetric.subset_countable_closure_of_almost_dense_set -> EMetric.subset_countable_closure_of_almost_dense_set is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] (s : Set.{u1} α), (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))))))) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
+Case conversion may be inaccurate. Consider using '#align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_setₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
@@ -853,8 +1383,14 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     edist x (f n⁻¹ y) ≤ n⁻¹ * 2 := hf _ _ ⟨hyx, hx⟩
     _ < ε := ENNReal.mul_lt_of_lt_div hn
     
-#align emetric.subset_countable_closure_of_almost_dense_set Emetric.subset_countable_closure_of_almost_dense_set
-
+#align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
+
+/- warning: emetric.subset_countable_closure_of_compact -> EMetric.subset_countable_closure_of_compact is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, (IsCompact.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, (IsCompact.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) s) -> (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.Countable.{u1} α t) (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s (closure.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)) t)))))
+Case conversion may be inaccurate. Consider using '#align emetric.subset_countable_closure_of_compact EMetric.subset_countable_closure_of_compactₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
@@ -864,7 +1400,7 @@ theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
   refine' subset_countable_closure_of_almost_dense_set s fun ε hε => _
   rcases totally_bounded_iff'.1 hs.totally_bounded ε hε with ⟨t, hts, htf, hst⟩
   exact ⟨t, htf.countable, subset.trans hst <| Union₂_mono fun _ _ => ball_subset_closed_ball⟩
-#align emetric.subset_countable_closure_of_compact Emetric.subset_countable_closure_of_compact
+#align emetric.subset_countable_closure_of_compact EMetric.subset_countable_closure_of_compact
 
 end Compact
 
@@ -874,9 +1410,10 @@ open _Root_.TopologicalSpace
 
 variable (α)
 
+#print EMetric.secondCountable_of_sigmaCompact /-
 /-- A sigma compact pseudo emetric space has second countable topology. This is not an instance
 to avoid a loop with `sigma_compact_space_of_locally_compact_second_countable`.  -/
-theorem second_countable_of_sigma_compact [SigmaCompactSpace α] : SecondCountableTopology α :=
+theorem secondCountable_of_sigmaCompact [SigmaCompactSpace α] : SecondCountableTopology α :=
   by
   suffices separable_space α by exact UniformSpace.secondCountable_of_separable α
   choose T hTsub hTc hsubT using fun n =>
@@ -884,11 +1421,18 @@ theorem second_countable_of_sigma_compact [SigmaCompactSpace α] : SecondCountab
   refine' ⟨⟨⋃ n, T n, countable_Union hTc, fun x => _⟩⟩
   rcases Union_eq_univ_iff.1 (unionᵢ_compactCovering α) x with ⟨n, hn⟩
   exact closure_mono (subset_Union _ n) (hsubT _ hn)
-#align emetric.second_countable_of_sigma_compact Emetric.second_countable_of_sigma_compact
+#align emetric.second_countable_of_sigma_compact EMetric.secondCountable_of_sigmaCompact
+-/
 
 variable {α}
 
-theorem second_countable_of_almost_dense_set
+/- warning: emetric.second_countable_of_almost_dense_set -> EMetric.secondCountable_of_almost_dense_set is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{succ u1} (Set.{u1} α) (fun (t : Set.{u1} α) => And (Set.Countable.{u1} α t) (Eq.{succ u1} (Set.{u1} α) (Set.unionᵢ.{u1, succ u1} α α (fun (x : α) => Set.unionᵢ.{u1, 0} α (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x t) => EMetric.closedBall.{u1} α _inst_1 x ε))) (Set.univ.{u1} α))))) -> (TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoEMetricSpace.toUniformSpace.{u1} α _inst_1)))
+Case conversion may be inaccurate. Consider using '#align emetric.second_countable_of_almost_dense_set EMetric.secondCountable_of_almost_dense_setₓ'. -/
+theorem secondCountable_of_almost_dense_set
     (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ (⋃ x ∈ t, closedBall x ε) = univ) :
     SecondCountableTopology α :=
   by
@@ -898,82 +1442,164 @@ theorem second_countable_of_almost_dense_set
   · exact ⟨⟨t, htc, fun x => ht (mem_univ x)⟩⟩
   · rcases hs ε ε0 with ⟨t, htc, ht⟩
     exact ⟨t, htc, univ_subset_iff.2 ht⟩
-#align emetric.second_countable_of_almost_dense_set Emetric.second_countable_of_almost_dense_set
+#align emetric.second_countable_of_almost_dense_set EMetric.secondCountable_of_almost_dense_set
 
 end SecondCountable
 
 section Diam
 
+#print EMetric.diam /-
 /-- The diameter of a set in a pseudoemetric space, named `emetric.diam` -/
 noncomputable def diam (s : Set α) :=
   ⨆ (x ∈ s) (y ∈ s), edist x y
-#align emetric.diam Emetric.diam
+#align emetric.diam EMetric.diam
+-/
 
+/- warning: emetric.diam_le_iff -> EMetric.diam_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d) (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) d) (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) d)))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_le_iff EMetric.diam_le_iffₓ'. -/
 theorem diam_le_iff {d : ℝ≥0∞} : diam s ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d := by
   simp only [diam, supᵢ_le_iff]
-#align emetric.diam_le_iff Emetric.diam_le_iff
-
+#align emetric.diam_le_iff EMetric.diam_le_iff
+
+/- warning: emetric.diam_image_le_iff -> EMetric.diam_image_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Set.image.{u2, u1} β α f s)) d) (forall (x : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) x s) -> (forall (y : β), (Membership.Mem.{u2, u2} β (Set.{u2} β) (Set.hasMem.{u2} β) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) (f x) (f y)) d)))
+but is expected to have type
+  forall {α : Type.{u1}} {β : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u1} α] {d : ENNReal} {f : β -> α} {s : Set.{u2} β}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (Set.image.{u2, u1} β α f s)) d) (forall (x : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) x s) -> (forall (y : β), (Membership.mem.{u2, u2} β (Set.{u2} β) (Set.instMembershipSet.{u2} β) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) (f x) (f y)) d)))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_image_le_iff EMetric.diam_image_le_iffₓ'. -/
 theorem diam_image_le_iff {d : ℝ≥0∞} {f : β → α} {s : Set β} :
     diam (f '' s) ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist (f x) (f y) ≤ d := by
   simp only [diam_le_iff, ball_image_iff]
-#align emetric.diam_image_le_iff Emetric.diam_image_le_iff
-
+#align emetric.diam_image_le_iff EMetric.diam_image_le_iff
+
+/- warning: emetric.edist_le_of_diam_le -> EMetric.edist_le_of_diam_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {d : ENNReal}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {d : ENNReal}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) d) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) d)
+Case conversion may be inaccurate. Consider using '#align emetric.edist_le_of_diam_le EMetric.edist_le_of_diam_leₓ'. -/
 theorem edist_le_of_diam_le {d} (hx : x ∈ s) (hy : y ∈ s) (hd : diam s ≤ d) : edist x y ≤ d :=
   diam_le_iff.1 hd x hx y hy
-#align emetric.edist_le_of_diam_le Emetric.edist_le_of_diam_le
-
+#align emetric.edist_le_of_diam_le EMetric.edist_le_of_diam_le
+
+/- warning: emetric.edist_le_diam_of_mem -> EMetric.edist_le_diam_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EMetric.diam.{u1} α _inst_1 s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (EMetric.diam.{u1} α _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align emetric.edist_le_diam_of_mem EMetric.edist_le_diam_of_memₓ'. -/
 /-- If two points belong to some set, their edistance is bounded by the diameter of the set -/
 theorem edist_le_diam_of_mem (hx : x ∈ s) (hy : y ∈ s) : edist x y ≤ diam s :=
   edist_le_of_diam_le hx hy le_rfl
-#align emetric.edist_le_diam_of_mem Emetric.edist_le_diam_of_mem
-
+#align emetric.edist_le_diam_of_mem EMetric.edist_le_diam_of_mem
+
+/- warning: emetric.diam_le -> EMetric.diam_le is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (y : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) d))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) d)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {d : ENNReal}, (forall (x : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (forall (y : α), (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) d))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) d)
+Case conversion may be inaccurate. Consider using '#align emetric.diam_le EMetric.diam_leₓ'. -/
 /-- If the distance between any two points in a set is bounded by some constant, this constant
 bounds the diameter. -/
 theorem diam_le {d : ℝ≥0∞} (h : ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d) : diam s ≤ d :=
   diam_le_iff.2 h
-#align emetric.diam_le Emetric.diam_le
-
+#align emetric.diam_le EMetric.diam_le
+
+/- warning: emetric.diam_subsingleton -> EMetric.diam_subsingleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α}, (Set.Subsingleton.{u1} α s) -> (Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_subsingleton EMetric.diam_subsingletonₓ'. -/
 /-- The diameter of a subsingleton vanishes. -/
 theorem diam_subsingleton (hs : s.Subsingleton) : diam s = 0 :=
   nonpos_iff_eq_zero.1 <| diam_le fun x hx y hy => (hs hx hy).symm ▸ edist_self y ▸ le_rfl
-#align emetric.diam_subsingleton Emetric.diam_subsingleton
-
+#align emetric.diam_subsingleton EMetric.diam_subsingleton
+
+/- warning: emetric.diam_empty -> EMetric.diam_empty is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.hasEmptyc.{u1} α))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α], Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (EmptyCollection.emptyCollection.{u1} (Set.{u1} α) (Set.instEmptyCollectionSet.{u1} α))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_empty EMetric.diam_emptyₓ'. -/
 /-- The diameter of the empty set vanishes -/
 @[simp]
 theorem diam_empty : diam (∅ : Set α) = 0 :=
   diam_subsingleton subsingleton_empty
-#align emetric.diam_empty Emetric.diam_empty
-
+#align emetric.diam_empty EMetric.diam_empty
+
+/- warning: emetric.diam_singleton -> EMetric.diam_singleton is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) x)) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) x)) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_singleton EMetric.diam_singletonₓ'. -/
 /-- The diameter of a singleton vanishes -/
 @[simp]
 theorem diam_singleton : diam ({x} : Set α) = 0 :=
   diam_subsingleton subsingleton_singleton
-#align emetric.diam_singleton Emetric.diam_singleton
-
+#align emetric.diam_singleton EMetric.diam_singleton
+
+/- warning: emetric.diam_Union_mem_option -> EMetric.diam_unionᵢ_mem_option is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {ι : Type.{u2}} (o : Option.{u2} ι) (s : ι -> (Set.{u1} α)), Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Set.unionᵢ.{u1, succ u2} α ι (fun (i : ι) => Set.unionᵢ.{u1, 0} α (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => s i)))) (supᵢ.{0, succ u2} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) ι (fun (i : ι) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) (fun (H : Membership.Mem.{u2, u2} ι (Option.{u2} ι) (Option.hasMem.{u2} ι) i o) => EMetric.diam.{u1} α _inst_1 (s i))))
+but is expected to have type
+  forall {α : Type.{u2}} [_inst_1 : PseudoEMetricSpace.{u2} α] {ι : Type.{u1}} (o : Option.{u1} ι) (s : ι -> (Set.{u2} α)), Eq.{1} ENNReal (EMetric.diam.{u2} α _inst_1 (Set.unionᵢ.{u2, succ u1} α ι (fun (i : ι) => Set.unionᵢ.{u2, 0} α (Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) (fun (H : Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) => s i)))) (supᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) ι (fun (i : ι) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) (fun (H : Membership.mem.{u1, u1} ι (Option.{u1} ι) (Option.instMembershipOption.{u1} ι) i o) => EMetric.diam.{u2} α _inst_1 (s i))))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_Union_mem_option EMetric.diam_unionᵢ_mem_optionₓ'. -/
 theorem diam_unionᵢ_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp
-#align emetric.diam_Union_mem_option Emetric.diam_unionᵢ_mem_option
-
+#align emetric.diam_Union_mem_option EMetric.diam_unionᵢ_mem_option
+
+/- warning: emetric.diam_insert -> EMetric.diam_insert is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x s)) (LinearOrder.max.{0} ENNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.completeLinearOrder))) (supᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) α (fun (y : α) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toHasSup.{0} ENNReal (CompleteLattice.toConditionallyCompleteLattice.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))) (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) (fun (H : Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y s) => EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y))) (EMetric.diam.{u1} α _inst_1 s))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {s : Set.{u1} α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x s)) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (supᵢ.{0, succ u1} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) α (fun (y : α) => supᵢ.{0, 0} ENNReal (ConditionallyCompleteLattice.toSupSet.{0} ENNReal (ConditionallyCompleteLinearOrder.toConditionallyCompleteLattice.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal)))) (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) (fun (H : Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y s) => EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y))) (EMetric.diam.{u1} α _inst_1 s))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_insert EMetric.diam_insertₓ'. -/
 theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s) :=
   eq_of_forall_ge_iff fun d => by
     simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, supᵢ_le_iff,
       zero_le, true_and_iff, forall_and, and_self_iff, ← and_assoc']
-#align emetric.diam_insert Emetric.diam_insert
+#align emetric.diam_insert EMetric.diam_insert
 
+#print EMetric.diam_pair /-
 theorem diam_pair : diam ({x, y} : Set α) = edist x y := by
   simp only [supᵢ_singleton, diam_insert, diam_singleton, ENNReal.max_zero_right]
-#align emetric.diam_pair Emetric.diam_pair
+#align emetric.diam_pair EMetric.diam_pair
+-/
 
+/- warning: emetric.diam_triple -> EMetric.diam_triple is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) x (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.hasInsert.{u1} α) y (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.hasSingleton.{u1} α) z)))) (LinearOrder.max.{0} ENNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.completeLinearOrder))) (LinearOrder.max.{0} ENNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} ENNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} ENNReal (CompleteLinearOrder.toConditionallyCompleteLinearOrderBot.{0} ENNReal ENNReal.completeLinearOrder))) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) y z))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {z : α}, Eq.{1} ENNReal (EMetric.diam.{u1} α _inst_1 (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) x (Insert.insert.{u1, u1} α (Set.{u1} α) (Set.instInsertSet.{u1} α) y (Singleton.singleton.{u1, u1} α (Set.{u1} α) (Set.instSingletonSet.{u1} α) z)))) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (Max.max.{0} ENNReal (CanonicallyLinearOrderedAddMonoid.toMax.{0} ENNReal ENNReal.instCanonicallyLinearOrderedAddMonoidENNReal) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x z)) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) y z))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_triple EMetric.diam_tripleₓ'. -/
 theorem diam_triple : diam ({x, y, z} : Set α) = max (max (edist x y) (edist x z)) (edist y z) := by
   simp only [diam_insert, supᵢ_insert, supᵢ_singleton, diam_singleton, ENNReal.max_zero_right,
     ENNReal.sup_eq_max]
-#align emetric.diam_triple Emetric.diam_triple
-
+#align emetric.diam_triple EMetric.diam_triple
+
+/- warning: emetric.diam_mono -> EMetric.diam_mono is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (HasSubset.Subset.{u1} (Set.{u1} α) (Set.instHasSubsetSet.{u1} α) s t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_mono EMetric.diam_monoₓ'. -/
 /-- The diameter is monotonous with respect to inclusion -/
 theorem diam_mono {s t : Set α} (h : s ⊆ t) : diam s ≤ diam t :=
   diam_le fun x hx y hy => edist_le_diam_of_mem (h hx) (h hy)
-#align emetric.diam_mono Emetric.diam_mono
-
+#align emetric.diam_mono EMetric.diam_mono
+
+/- warning: emetric.diam_union -> EMetric.diam_union is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {t : Set.{u1} α}, (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) y t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EMetric.diam.{u1} α _inst_1 s) (EDist.edist.{u1} α (PseudoEMetricSpace.toHasEdist.{u1} α _inst_1) x y)) (EMetric.diam.{u1} α _inst_1 t)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {y : α} {s : Set.{u1} α} {t : Set.{u1} α}, (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) x s) -> (Membership.mem.{u1, u1} α (Set.{u1} α) (Set.instMembershipSet.{u1} α) y t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EMetric.diam.{u1} α _inst_1 s) (EDist.edist.{u1} α (PseudoEMetricSpace.toEDist.{u1} α _inst_1) x y)) (EMetric.diam.{u1} α _inst_1 t)))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_union EMetric.diam_unionₓ'. -/
 /-- The diameter of a union is controlled by the diameter of the sets, and the edistance
 between two points in the sets. -/
 theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
@@ -1001,14 +1627,26 @@ theorem diam_union {t : Set α} (xs : x ∈ s) (yt : y ∈ t) :
       edist a b ≤ diam t := edist_le_diam_of_mem h'a h'b
       _ ≤ diam s + edist x y + diam t := le_add_self
       
-#align emetric.diam_union Emetric.diam_union
-
+#align emetric.diam_union EMetric.diam_union
+
+/- warning: emetric.diam_union' -> EMetric.diam_union' is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) s t)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.hasUnion.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t)))
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {s : Set.{u1} α} {t : Set.{u1} α}, (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.instInterSet.{u1} α) s t)) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (Union.union.{u1} (Set.{u1} α) (Set.instUnionSet.{u1} α) s t)) (HAdd.hAdd.{0, 0, 0} ENNReal ENNReal ENNReal (instHAdd.{0} ENNReal (Distrib.toAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)))))))) (EMetric.diam.{u1} α _inst_1 s) (EMetric.diam.{u1} α _inst_1 t)))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_union' EMetric.diam_union'ₓ'. -/
 theorem diam_union' {t : Set α} (h : (s ∩ t).Nonempty) : diam (s ∪ t) ≤ diam s + diam t :=
   by
   let ⟨x, ⟨xs, xt⟩⟩ := h
   simpa using diam_union xs xt
-#align emetric.diam_union' Emetric.diam_union'
-
+#align emetric.diam_union' EMetric.diam_union'
+
+/- warning: emetric.diam_closed_ball -> EMetric.diam_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (EMetric.closedBall.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) r)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (EMetric.closedBall.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) r)
+Case conversion may be inaccurate. Consider using '#align emetric.diam_closed_ball EMetric.diam_closedBallₓ'. -/
 theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
   diam_le fun a ha b hb =>
     calc
@@ -1016,68 +1654,120 @@ theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
       _ ≤ r + r := (add_le_add ha hb)
       _ = 2 * r := (two_mul r).symm
       
-#align emetric.diam_closed_ball Emetric.diam_closedBall
-
+#align emetric.diam_closed_ball EMetric.diam_closedBall
+
+/- warning: emetric.diam_ball -> EMetric.diam_ball is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u1} α _inst_1 (EMetric.ball.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (Distrib.toHasMul.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring)))))))) (OfNat.ofNat.{0} ENNReal 2 (OfNat.mk.{0} ENNReal 2 (bit0.{0} ENNReal (Distrib.toHasAdd.{0} ENNReal (NonUnitalNonAssocSemiring.toDistrib.{0} ENNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} ENNReal (Semiring.toNonAssocSemiring.{0} ENNReal (OrderedSemiring.toSemiring.{0} ENNReal (OrderedCommSemiring.toOrderedSemiring.{0} ENNReal (CanonicallyOrderedCommSemiring.toOrderedCommSemiring.{0} ENNReal ENNReal.canonicallyOrderedCommSemiring))))))) (One.one.{0} ENNReal (AddMonoidWithOne.toOne.{0} ENNReal (AddCommMonoidWithOne.toAddMonoidWithOne.{0} ENNReal ENNReal.addCommMonoidWithOne)))))) r)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : PseudoEMetricSpace.{u1} α] {x : α} {r : ENNReal}, LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} α _inst_1 (EMetric.ball.{u1} α _inst_1 x r)) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (OfNat.ofNat.{0} ENNReal 2 (instOfNat.{0} ENNReal 2 (CanonicallyOrderedCommSemiring.toNatCast.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal) (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) r)
+Case conversion may be inaccurate. Consider using '#align emetric.diam_ball EMetric.diam_ballₓ'. -/
 theorem diam_ball {r : ℝ≥0∞} : diam (ball x r) ≤ 2 * r :=
   le_trans (diam_mono ball_subset_closedBall) diam_closedBall
-#align emetric.diam_ball Emetric.diam_ball
-
-theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEmetricSpace (π b)]
+#align emetric.diam_ball EMetric.diam_ball
+
+/- warning: emetric.diam_pi_le_of_le -> EMetric.diam_pi_le_of_le is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {π : β -> Type.{u2}} [_inst_2 : Fintype.{u1} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u2} (π b)] {s : forall (b : β), Set.{u2} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{u2} (π b) (_inst_3 b) (s b)) c) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EMetric.diam.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u1, u2} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b)) (Set.pi.{u1, u2} β (fun (b : β) => π b) (Set.univ.{u1} β) s)) c)
+but is expected to have type
+  forall {β : Type.{u2}} {π : β -> Type.{u1}} [_inst_2 : Fintype.{u2} β] [_inst_3 : forall (b : β), PseudoEMetricSpace.{u1} (π b)] {s : forall (b : β), Set.{u1} (π b)} {c : ENNReal}, (forall (b : β), LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{u1} (π b) (_inst_3 b) (s b)) c) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EMetric.diam.{max u1 u2} (forall (i : β), π i) (pseudoEMetricSpacePi.{u2, u1} β (fun (i : β) => π i) _inst_2 (fun (b : β) => _inst_3 b)) (Set.pi.{u2, u1} β (fun (b : β) => π b) (Set.univ.{u2} β) s)) c)
+Case conversion may be inaccurate. Consider using '#align emetric.diam_pi_le_of_le EMetric.diam_pi_le_of_leₓ'. -/
+theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, diam (s b) ≤ c) : diam (Set.pi univ s) ≤ c :=
   by
   apply diam_le fun x hx y hy => edist_pi_le_iff.mpr _
   rw [mem_univ_pi] at hx hy
   exact fun b => diam_le_iff.1 (h b) (x b) (hx b) (y b) (hy b)
-#align emetric.diam_pi_le_of_le Emetric.diam_pi_le_of_le
+#align emetric.diam_pi_le_of_le EMetric.diam_pi_le_of_le
 
 end Diam
 
 end Emetric
 
+#print EMetricSpace /-
 --namespace
 /-- We now define `emetric_space`, extending `pseudo_emetric_space`. -/
-class EmetricSpace (α : Type u) extends PseudoEmetricSpace α : Type u where
+class EMetricSpace (α : Type u) extends PseudoEMetricSpace α : Type u where
   eq_of_edist_eq_zero : ∀ {x y : α}, edist x y = 0 → x = y
-#align emetric_space EmetricSpace
+#align emetric_space EMetricSpace
+-/
 
-variable {γ : Type w} [EmetricSpace γ]
+variable {γ : Type w} [EMetricSpace γ]
 
-export EmetricSpace (eq_of_edist_eq_zero)
+export EMetricSpace (eq_of_edist_eq_zero)
 
+/- warning: edist_eq_zero -> edist_eq_zero is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (Eq.{1} ENNReal (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Eq.{succ u1} γ x y)
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (Eq.{1} ENNReal (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Eq.{succ u1} γ x y)
+Case conversion may be inaccurate. Consider using '#align edist_eq_zero edist_eq_zeroₓ'. -/
 /-- Characterize the equality of points by the vanishing of their extended distance -/
 @[simp]
 theorem edist_eq_zero {x y : γ} : edist x y = 0 ↔ x = y :=
   Iff.intro eq_of_edist_eq_zero fun this : x = y => this ▸ edist_self _
 #align edist_eq_zero edist_eq_zero
 
+/- warning: zero_eq_edist -> zero_eq_edist is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (Eq.{1} ENNReal (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y)) (Eq.{succ u1} γ x y)
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (Eq.{1} ENNReal (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y)) (Eq.{succ u1} γ x y)
+Case conversion may be inaccurate. Consider using '#align zero_eq_edist zero_eq_edistₓ'. -/
 @[simp]
 theorem zero_eq_edist {x y : γ} : 0 = edist x y ↔ x = y :=
   Iff.intro (fun h => eq_of_edist_eq_zero h.symm) fun this : x = y => this ▸ (edist_self _).symm
 #align zero_eq_edist zero_eq_edist
 
+/- warning: edist_le_zero -> edist_le_zero is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Eq.{succ u1} γ x y)
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Eq.{succ u1} γ x y)
+Case conversion may be inaccurate. Consider using '#align edist_le_zero edist_le_zeroₓ'. -/
 theorem edist_le_zero {x y : γ} : edist x y ≤ 0 ↔ x = y :=
   nonpos_iff_eq_zero.trans edist_eq_zero
 #align edist_le_zero edist_le_zero
 
+/- warning: edist_pos -> edist_pos is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y)) (Ne.{succ u1} γ x y)
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y)) (Ne.{succ u1} γ x y)
+Case conversion may be inaccurate. Consider using '#align edist_pos edist_posₓ'. -/
 @[simp]
 theorem edist_pos {x y : γ} : 0 < edist x y ↔ x ≠ y := by simp [← not_le]
 #align edist_pos edist_pos
 
+/- warning: eq_of_forall_edist_le -> eq_of_forall_edist_le is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) x y) ε)) -> (Eq.{succ u1} γ x y)
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {x : γ} {y : γ}, (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) x y) ε)) -> (Eq.{succ u1} γ x y)
+Case conversion may be inaccurate. Consider using '#align eq_of_forall_edist_le eq_of_forall_edist_leₓ'. -/
 /-- Two points coincide if their distance is `< ε` for all positive ε -/
 theorem eq_of_forall_edist_le {x y : γ} (h : ∀ ε > 0, edist x y ≤ ε) : x = y :=
   eq_of_edist_eq_zero (eq_of_le_of_forall_le_of_dense bot_le h)
 #align eq_of_forall_edist_le eq_of_forall_edist_le
 
+#print to_separated /-
 -- see Note [lower instance priority]
 /-- An emetric space is separated -/
 instance (priority := 100) to_separated : SeparatedSpace γ :=
   separated_def.2 fun x y h =>
     eq_of_forall_edist_le fun ε ε0 => le_of_lt (h _ (edist_mem_uniformity ε0))
 #align to_separated to_separated
+-/
 
+/- warning: emetric.uniform_embedding_iff' -> EMetric.uniformEmbedding_iff' is a dubious translation:
+lean 3 declaration is
+  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : EMetricSpace.{u2} γ] [_inst_3 : EMetricSpace.{u1} β] {f : γ -> β}, Iff (UniformEmbedding.{u2, u1} γ β (PseudoEMetricSpace.toUniformSpace.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) (PseudoEMetricSpace.toUniformSpace.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) f) (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toHasEdist.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toHasEdist.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) δ (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => Exists.{0} (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toHasEdist.{u1} β (EMetricSpace.toPseudoEmetricSpace.{u1} β _inst_3)) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toHasEdist.{u2} γ (EMetricSpace.toPseudoEmetricSpace.{u2} γ _inst_2)) a b) δ))))))
+but is expected to have type
+  forall {β : Type.{u1}} {γ : Type.{u2}} [_inst_2 : EMetricSpace.{u2} γ] [_inst_3 : EMetricSpace.{u1} β] {f : γ -> β}, Iff (UniformEmbedding.{u2, u1} γ β (PseudoEMetricSpace.toUniformSpace.{u2} γ (EMetricSpace.toPseudoEMetricSpace.{u2} γ _inst_2)) (PseudoEMetricSpace.toUniformSpace.{u1} β (EMetricSpace.toPseudoEMetricSpace.{u1} β _inst_3)) f) (And (forall (ε : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (δ : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toEDist.{u2} γ (EMetricSpace.toPseudoEMetricSpace.{u2} γ _inst_2)) a b) δ) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toEDist.{u1} β (EMetricSpace.toPseudoEMetricSpace.{u1} β _inst_3)) (f a) (f b)) ε))))) (forall (δ : ENNReal), (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) δ (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) -> (Exists.{1} ENNReal (fun (ε : ENNReal) => And (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (forall {a : γ} {b : γ}, (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} β (PseudoEMetricSpace.toEDist.{u1} β (EMetricSpace.toPseudoEMetricSpace.{u1} β _inst_3)) (f a) (f b)) ε) -> (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u2} γ (PseudoEMetricSpace.toEDist.{u2} γ (EMetricSpace.toPseudoEMetricSpace.{u2} γ _inst_2)) a b) δ))))))
+Case conversion may be inaccurate. Consider using '#align emetric.uniform_embedding_iff' EMetric.uniformEmbedding_iff'ₓ'. -/
 /-- A map between emetric spaces is a uniform embedding if and only if the edistance between `f x`
 and `f y` is controlled in terms of the distance between `x` and `y` and conversely. -/
-theorem Emetric.uniformEmbedding_iff' [EmetricSpace β] {f : γ → β} :
+theorem EMetric.uniformEmbedding_iff' [EMetricSpace β] {f : γ → β} :
     UniformEmbedding f ↔
       (∀ ε > 0, ∃ δ > 0, ∀ {a b : γ}, edist a b < δ → edist (f a) (f b) < ε) ∧
         ∀ δ > 0, ∃ ε > 0, ∀ {a b : γ}, edist (f a) (f b) < ε → edist a b < δ :=
@@ -1085,23 +1775,26 @@ theorem Emetric.uniformEmbedding_iff' [EmetricSpace β] {f : γ → β} :
   simp only [uniformEmbedding_iff_uniformInducing,
     uniformity_basis_edist.uniform_inducing_iff uniformity_basis_edist, exists_prop]
   rfl
-#align emetric.uniform_embedding_iff' Emetric.uniformEmbedding_iff'
+#align emetric.uniform_embedding_iff' EMetric.uniformEmbedding_iff'
 
+#print EMetricSpace.ofT0PseudoEMetricSpace /-
 /-- If a `pseudo_emetric_space` is a T₀ space, then it is an `emetric_space`. -/
-def EmetricSpace.ofT0PseudoEmetricSpace (α : Type _) [PseudoEmetricSpace α] [T0Space α] :
-    EmetricSpace α :=
-  { ‹PseudoEmetricSpace α› with
-    eq_of_edist_eq_zero := fun x y hdist => (Emetric.inseparable_iff.2 hdist).Eq }
-#align emetric_space.of_t0_pseudo_emetric_space EmetricSpace.ofT0PseudoEmetricSpace
+def EMetricSpace.ofT0PseudoEMetricSpace (α : Type _) [PseudoEMetricSpace α] [T0Space α] :
+    EMetricSpace α :=
+  { ‹PseudoEMetricSpace α› with
+    eq_of_edist_eq_zero := fun x y hdist => (EMetric.inseparable_iff.2 hdist).Eq }
+#align emetric_space.of_t0_pseudo_emetric_space EMetricSpace.ofT0PseudoEMetricSpace
+-/
 
+#print EMetricSpace.replaceUniformity /-
 /-- Auxiliary function to replace the uniformity on an emetric space with
 a uniformity which is equal to the original one, but maybe not defeq.
 This is useful if one wants to construct an emetric space with a
 specified uniformity. See Note [forgetful inheritance] explaining why having definitionally
 the right uniformity is often important.
 -/
-def EmetricSpace.replaceUniformity {γ} [U : UniformSpace γ] (m : EmetricSpace γ)
-    (H : 𝓤[U] = 𝓤[PseudoEmetricSpace.toUniformSpace]) : EmetricSpace γ
+def EMetricSpace.replaceUniformity {γ} [U : UniformSpace γ] (m : EMetricSpace γ)
+    (H : 𝓤[U] = 𝓤[PseudoEMetricSpace.toUniformSpace]) : EMetricSpace γ
     where
   edist := @edist _ m.toHasEdist
   edist_self := edist_self
@@ -1109,12 +1802,14 @@ def EmetricSpace.replaceUniformity {γ} [U : UniformSpace γ] (m : EmetricSpace
   edist_comm := edist_comm
   edist_triangle := edist_triangle
   toUniformSpace := U
-  uniformity_edist := H.trans (@PseudoEmetricSpace.uniformity_edist γ _)
-#align emetric_space.replace_uniformity EmetricSpace.replaceUniformity
+  uniformity_edist := H.trans (@PseudoEMetricSpace.uniformity_edist γ _)
+#align emetric_space.replace_uniformity EMetricSpace.replaceUniformity
+-/
 
+#print EMetricSpace.induced /-
 /-- The extended metric induced by an injective function taking values in a emetric space. -/
-def EmetricSpace.induced {γ β} (f : γ → β) (hf : Function.Injective f) (m : EmetricSpace β) :
-    EmetricSpace γ where
+def EMetricSpace.induced {γ β} (f : γ → β) (hf : Function.Injective f) (m : EMetricSpace β) :
+    EMetricSpace γ where
   edist x y := edist (f x) (f y)
   edist_self x := edist_self _
   eq_of_edist_eq_zero x y h := hf (edist_eq_zero.1 h)
@@ -1122,25 +1817,27 @@ def EmetricSpace.induced {γ β} (f : γ → β) (hf : Function.Injective f) (m
   edist_triangle x y z := edist_triangle _ _ _
   toUniformSpace := UniformSpace.comap f m.toUniformSpace
   uniformity_edist := (uniformity_basis_edist.comap _).eq_binfᵢ
-#align emetric_space.induced EmetricSpace.induced
+#align emetric_space.induced EMetricSpace.induced
+-/
 
 /-- Emetric space instance on subsets of emetric spaces -/
-instance {α : Type _} {p : α → Prop} [EmetricSpace α] : EmetricSpace (Subtype p) :=
-  EmetricSpace.induced coe Subtype.coe_injective ‹_›
+instance {α : Type _} {p : α → Prop} [EMetricSpace α] : EMetricSpace (Subtype p) :=
+  EMetricSpace.induced coe Subtype.coe_injective ‹_›
 
 /-- Emetric space instance on the multiplicative opposite of an emetric space. -/
 @[to_additive "Emetric space instance on the additive opposite of an emetric space."]
-instance {α : Type _} [EmetricSpace α] : EmetricSpace αᵐᵒᵖ :=
-  EmetricSpace.induced MulOpposite.unop MulOpposite.unop_injective ‹_›
+instance {α : Type _} [EMetricSpace α] : EMetricSpace αᵐᵒᵖ :=
+  EMetricSpace.induced MulOpposite.unop MulOpposite.unop_injective ‹_›
 
-instance {α : Type _} [EmetricSpace α] : EmetricSpace (ULift α) :=
-  EmetricSpace.induced ULift.down ULift.down_injective ‹_›
+instance {α : Type _} [EMetricSpace α] : EMetricSpace (ULift α) :=
+  EMetricSpace.induced ULift.down ULift.down_injective ‹_›
 
+#print Prod.emetricSpaceMax /-
 /-- The product of two emetric spaces, with the max distance, is an extended
 metric spaces. We make sure that the uniform structure thus constructed is the one
 corresponding to the product of uniform spaces, to avoid diamond problems. -/
-instance Prod.emetricSpaceMax [EmetricSpace β] : EmetricSpace (γ × β) :=
-  { Prod.pseudoEmetricSpaceMax with
+instance Prod.emetricSpaceMax [EMetricSpace β] : EMetricSpace (γ × β) :=
+  { Prod.pseudoEMetricSpaceMax with
     eq_of_edist_eq_zero := fun x y h =>
       by
       cases' max_le_iff.1 (le_of_eq h) with h₁ h₂
@@ -1148,10 +1845,17 @@ instance Prod.emetricSpaceMax [EmetricSpace β] : EmetricSpace (γ × β) :=
       have B : x.snd = y.snd := edist_le_zero.1 h₂
       exact Prod.ext_iff.2 ⟨A, B⟩ }
 #align prod.emetric_space_max Prod.emetricSpaceMax
+-/
 
+/- warning: uniformity_edist -> uniformity_edist is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toHasInf.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.completeLattice.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) ε (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toHasEdist.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ], Eq.{succ u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (uniformity.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) (infᵢ.{u1, 1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) ENNReal (fun (ε : ENNReal) => infᵢ.{u1, 0} (Filter.{u1} (Prod.{u1, u1} γ γ)) (ConditionallyCompleteLattice.toInfSet.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (CompleteLattice.toConditionallyCompleteLattice.{u1} (Filter.{u1} (Prod.{u1, u1} γ γ)) (Filter.instCompleteLatticeFilter.{u1} (Prod.{u1, u1} γ γ)))) (GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (fun (H : GT.gt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) ε (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) => Filter.principal.{u1} (Prod.{u1, u1} γ γ) (setOf.{u1} (Prod.{u1, u1} γ γ) (fun (p : Prod.{u1, u1} γ γ) => LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (EDist.edist.{u1} γ (PseudoEMetricSpace.toEDist.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2)) (Prod.fst.{u1, u1} γ γ p) (Prod.snd.{u1, u1} γ γ p)) ε)))))
+Case conversion may be inaccurate. Consider using '#align uniformity_edist uniformity_edistₓ'. -/
 /-- Reformulation of the uniform structure in terms of the extended distance -/
 theorem uniformity_edist : 𝓤 γ = ⨅ ε > 0, 𝓟 { p : γ × γ | edist p.1 p.2 < ε } :=
-  PseudoEmetricSpace.uniformity_edist
+  PseudoEMetricSpace.uniformity_edist
 #align uniformity_edist uniformity_edist
 
 section Pi
@@ -1160,24 +1864,32 @@ open Finset
 
 variable {π : β → Type _} [Fintype β]
 
+#print emetricSpacePi /-
 /-- The product of a finite number of emetric spaces, with the max distance, is still
 an emetric space.
 This construction would also work for infinite products, but it would not give rise
 to the product topology. Hence, we only formalize it in the good situation of finitely many
 spaces. -/
-instance emetricSpacePi [∀ b, EmetricSpace (π b)] : EmetricSpace (∀ b, π b) :=
-  { pseudoEmetricSpacePi with
+instance emetricSpacePi [∀ b, EMetricSpace (π b)] : EMetricSpace (∀ b, π b) :=
+  { pseudoEMetricSpacePi with
     eq_of_edist_eq_zero := fun f g eq0 =>
       by
       have eq1 : (sup univ fun b : β => edist (f b) (g b)) ≤ 0 := le_of_eq eq0
       simp only [Finset.sup_le_iff] at eq1
       exact funext fun b => edist_le_zero.1 <| eq1 b <| mem_univ b }
 #align emetric_space_pi emetricSpacePi
+-/
 
 end Pi
 
 namespace Emetric
 
+/- warning: emetric.countable_closure_of_compact -> EMetric.countable_closure_of_compact is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, (IsCompact.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) s) -> (Exists.{succ u1} (Set.{u1} γ) (fun (t : Set.{u1} γ) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} γ) (Set.hasSubset.{u1} γ) t s) (fun (H : HasSubset.Subset.{u1} (Set.{u1} γ) (Set.hasSubset.{u1} γ) t s) => And (Set.Countable.{u1} γ t) (Eq.{succ u1} (Set.{u1} γ) s (closure.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2))) t)))))
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, (IsCompact.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) s) -> (Exists.{succ u1} (Set.{u1} γ) (fun (t : Set.{u1} γ) => And (HasSubset.Subset.{u1} (Set.{u1} γ) (Set.instHasSubsetSet.{u1} γ) t s) (And (Set.Countable.{u1} γ t) (Eq.{succ u1} (Set.{u1} γ) s (closure.{u1} γ (UniformSpace.toTopologicalSpace.{u1} γ (PseudoEMetricSpace.toUniformSpace.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2))) t)))))
+Case conversion may be inaccurate. Consider using '#align emetric.countable_closure_of_compact EMetric.countable_closure_of_compactₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (t «expr ⊆ » s) -/
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
@@ -1185,19 +1897,31 @@ theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
   by
   rcases subset_countable_closure_of_compact hs with ⟨t, hts, htc, hsub⟩
   exact ⟨t, hts, htc, subset.antisymm hsub (closure_minimal hts hs.is_closed)⟩
-#align emetric.countable_closure_of_compact Emetric.countable_closure_of_compact
+#align emetric.countable_closure_of_compact EMetric.countable_closure_of_compact
 
 section Diam
 
 variable {s : Set γ}
 
+/- warning: emetric.diam_eq_zero_iff -> EMetric.diam_eq_zero_iff is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (Eq.{1} ENNReal (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2) s) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero)))) (Set.Subsingleton.{u1} γ s)
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (Eq.{1} ENNReal (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2) s) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero))) (Set.Subsingleton.{u1} γ s)
+Case conversion may be inaccurate. Consider using '#align emetric.diam_eq_zero_iff EMetric.diam_eq_zero_iffₓ'. -/
 theorem diam_eq_zero_iff : diam s = 0 ↔ s.Subsingleton :=
   ⟨fun h x hx y hy => edist_le_zero.1 <| h ▸ edist_le_diam_of_mem hx hy, diam_subsingleton⟩
-#align emetric.diam_eq_zero_iff Emetric.diam_eq_zero_iff
-
-theorem diam_pos_iff : 0 < diam s ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y := by
+#align emetric.diam_eq_zero_iff EMetric.diam_eq_zero_iff
+
+/- warning: emetric.diam_pos_iff -> EMetric.diam_pos_iff' is a dubious translation:
+lean 3 declaration is
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.completeLinearOrder))))) (OfNat.ofNat.{0} ENNReal 0 (OfNat.mk.{0} ENNReal 0 (Zero.zero.{0} ENNReal ENNReal.hasZero))) (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEmetricSpace.{u1} γ _inst_2) s)) (Exists.{succ u1} γ (fun (x : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) x s) => Exists.{succ u1} γ (fun (y : γ) => Exists.{0} (Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) (fun (H : Membership.Mem.{u1, u1} γ (Set.{u1} γ) (Set.hasMem.{u1} γ) y s) => Ne.{succ u1} γ x y)))))
+but is expected to have type
+  forall {γ : Type.{u1}} [_inst_2 : EMetricSpace.{u1} γ] {s : Set.{u1} γ}, Iff (LT.lt.{0} ENNReal (Preorder.toLT.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (CompleteSemilatticeInf.toPartialOrder.{0} ENNReal (CompleteLattice.toCompleteSemilatticeInf.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)) (EMetric.diam.{u1} γ (EMetricSpace.toPseudoEMetricSpace.{u1} γ _inst_2) s)) (Exists.{succ u1} γ (fun (x : γ) => And (Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) x s) (Exists.{succ u1} γ (fun (y : γ) => And (Membership.mem.{u1, u1} γ (Set.{u1} γ) (Set.instMembershipSet.{u1} γ) y s) (Ne.{succ u1} γ x y)))))
+Case conversion may be inaccurate. Consider using '#align emetric.diam_pos_iff EMetric.diam_pos_iff'ₓ'. -/
+theorem diam_pos_iff' : 0 < diam s ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y := by
   simp only [pos_iff_ne_zero, Ne.def, diam_eq_zero_iff, Set.Subsingleton, not_forall]
-#align emetric.diam_pos_iff Emetric.diam_pos_iff
+#align emetric.diam_pos_iff EMetric.diam_pos_iff'
 
 end Diam
 
@@ -1208,24 +1932,26 @@ end Emetric
 -/
 
 
-instance [PseudoEmetricSpace X] : HasEdist (UniformSpace.SeparationQuotient X) :=
+instance [PseudoEMetricSpace X] : EDist (UniformSpace.SeparationQuotient X) :=
   ⟨fun x y =>
     Quotient.liftOn₂' x y edist fun x y x' y' hx hy =>
       calc
         edist x y = edist x' y :=
-          edist_congr_right <| Emetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx
+          edist_congr_right <| EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx
         _ = edist x' y' :=
-          edist_congr_left <| Emetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy
+          edist_congr_left <| EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy
         ⟩
 
+#print UniformSpace.SeparationQuotient.edist_mk /-
 @[simp]
-theorem UniformSpace.SeparationQuotient.edist_mk [PseudoEmetricSpace X] (x y : X) :
+theorem UniformSpace.SeparationQuotient.edist_mk [PseudoEMetricSpace X] (x y : X) :
     @edist (UniformSpace.SeparationQuotient X) _ (Quot.mk _ x) (Quot.mk _ y) = edist x y :=
   rfl
 #align uniform_space.separation_quotient.edist_mk UniformSpace.SeparationQuotient.edist_mk
+-/
 
-instance [PseudoEmetricSpace X] : EmetricSpace (UniformSpace.SeparationQuotient X) :=
-  @EmetricSpace.ofT0PseudoEmetricSpace (UniformSpace.SeparationQuotient X)
+instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient X) :=
+  @EMetricSpace.ofT0PseudoEMetricSpace (UniformSpace.SeparationQuotient X)
     { edist_self := fun x => Quotient.inductionOn' x edist_self
       edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm
       edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle
@@ -1254,47 +1980,55 @@ open Additive Multiplicative
 
 section
 
-variable [HasEdist X]
+variable [EDist X]
 
-instance : HasEdist (Additive X) :=
-  ‹HasEdist X›
+instance : EDist (Additive X) :=
+  ‹EDist X›
 
-instance : HasEdist (Multiplicative X) :=
-  ‹HasEdist X›
+instance : EDist (Multiplicative X) :=
+  ‹EDist X›
 
+#print edist_ofMul /-
 @[simp]
 theorem edist_ofMul (a b : X) : edist (ofMul a) (ofMul b) = edist a b :=
   rfl
 #align edist_of_mul edist_ofMul
+-/
 
+#print edist_ofAdd /-
 @[simp]
 theorem edist_ofAdd (a b : X) : edist (ofAdd a) (ofAdd b) = edist a b :=
   rfl
 #align edist_of_add edist_ofAdd
+-/
 
+#print edist_toMul /-
 @[simp]
 theorem edist_toMul (a b : Additive X) : edist (toMul a) (toMul b) = edist a b :=
   rfl
 #align edist_to_mul edist_toMul
+-/
 
+#print edist_toAdd /-
 @[simp]
 theorem edist_toAdd (a b : Multiplicative X) : edist (toAdd a) (toAdd b) = edist a b :=
   rfl
 #align edist_to_add edist_toAdd
+-/
 
 end
 
-instance [PseudoEmetricSpace X] : PseudoEmetricSpace (Additive X) :=
-  ‹PseudoEmetricSpace X›
+instance [PseudoEMetricSpace X] : PseudoEMetricSpace (Additive X) :=
+  ‹PseudoEMetricSpace X›
 
-instance [PseudoEmetricSpace X] : PseudoEmetricSpace (Multiplicative X) :=
-  ‹PseudoEmetricSpace X›
+instance [PseudoEMetricSpace X] : PseudoEMetricSpace (Multiplicative X) :=
+  ‹PseudoEMetricSpace X›
 
-instance [EmetricSpace X] : EmetricSpace (Additive X) :=
-  ‹EmetricSpace X›
+instance [EMetricSpace X] : EMetricSpace (Additive X) :=
+  ‹EMetricSpace X›
 
-instance [EmetricSpace X] : EmetricSpace (Multiplicative X) :=
-  ‹EmetricSpace X›
+instance [EMetricSpace X] : EMetricSpace (Multiplicative X) :=
+  ‹EMetricSpace X›
 
 /-!
 ### Order dual
@@ -1307,26 +2041,30 @@ open OrderDual
 
 section
 
-variable [HasEdist X]
+variable [EDist X]
 
-instance : HasEdist Xᵒᵈ :=
-  ‹HasEdist X›
+instance : EDist Xᵒᵈ :=
+  ‹EDist X›
 
+#print edist_toDual /-
 @[simp]
 theorem edist_toDual (a b : X) : edist (toDual a) (toDual b) = edist a b :=
   rfl
 #align edist_to_dual edist_toDual
+-/
 
+#print edist_ofDual /-
 @[simp]
 theorem edist_ofDual (a b : Xᵒᵈ) : edist (ofDual a) (ofDual b) = edist a b :=
   rfl
 #align edist_of_dual edist_ofDual
+-/
 
 end
 
-instance [PseudoEmetricSpace X] : PseudoEmetricSpace Xᵒᵈ :=
-  ‹PseudoEmetricSpace X›
+instance [PseudoEMetricSpace X] : PseudoEMetricSpace Xᵒᵈ :=
+  ‹PseudoEMetricSpace X›
 
-instance [EmetricSpace X] : EmetricSpace Xᵒᵈ :=
-  ‹EmetricSpace X›
+instance [EMetricSpace X] : EMetricSpace Xᵒᵈ :=
+  ‹EMetricSpace X›
 

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.metric_space.emetric_space
-! leanprover-community/mathlib commit e1a7bdeb4fd826b7e71d130d34988f0a2d26a177
+! leanprover-community/mathlib commit 195fcd60ff2bfe392543bceb0ec2adcdb472db4c
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -309,17 +309,9 @@ theorem uniformEmbedding_iff [PseudoEmetricSpace β] {f : α → β} :
       Function.Injective f ∧
         UniformContinuous f ∧
           ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, edist (f a) (f b) < ε → edist a b < δ :=
-  uniformEmbedding_def'.trans <|
-    and_congr Iff.rfl <|
-      and_congr Iff.rfl
-        ⟨fun H δ δ0 =>
-          let ⟨t, tu, ht⟩ := H _ (edist_mem_uniformity δ0)
-          let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 tu
-          ⟨ε, ε0, fun a b h => ht _ _ (hε h)⟩,
-          fun H s su =>
-          let ⟨δ, δ0, hδ⟩ := mem_uniformity_edist.1 su
-          let ⟨ε, ε0, hε⟩ := H _ δ0
-          ⟨_, edist_mem_uniformity ε0, fun a b h => hδ (hε h)⟩⟩
+  by
+  simp only [uniformity_basis_edist.uniform_embedding_iff uniformity_basis_edist, exists_prop]
+  rfl
 #align emetric.uniform_embedding_iff Emetric.uniformEmbedding_iff
 
 /-- If a map between pseudoemetric spaces is a uniform embedding then the edistance between `f x`
@@ -328,9 +320,7 @@ theorem controlled_of_uniformEmbedding [PseudoEmetricSpace β] {f : α → β} :
     UniformEmbedding f →
       (∀ ε > 0, ∃ δ > 0, ∀ {a b : α}, edist a b < δ → edist (f a) (f b) < ε) ∧
         ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, edist (f a) (f b) < ε → edist a b < δ :=
-  by
-  intro h
-  exact ⟨uniformContinuous_iff.1 (uniform_embedding_iff.1 h).2.1, (uniform_embedding_iff.1 h).2.2⟩
+  fun h => ⟨uniformContinuous_iff.1 (uniformEmbedding_iff.1 h).2.1, (uniformEmbedding_iff.1 h).2.2⟩
 #align emetric.controlled_of_uniform_embedding Emetric.controlled_of_uniformEmbedding
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (x y «expr ∈ » t) -/
@@ -1078,29 +1068,6 @@ theorem eq_of_forall_edist_le {x y : γ} (h : ∀ ε > 0, edist x y ≤ ε) : x
   eq_of_edist_eq_zero (eq_of_le_of_forall_le_of_dense bot_le h)
 #align eq_of_forall_edist_le eq_of_forall_edist_le
 
-/-- A map between emetric spaces is a uniform embedding if and only if the edistance between `f x`
-and `f y` is controlled in terms of the distance between `x` and `y` and conversely. -/
-theorem uniformEmbedding_iff' [EmetricSpace β] {f : γ → β} :
-    UniformEmbedding f ↔
-      (∀ ε > 0, ∃ δ > 0, ∀ {a b : γ}, edist a b < δ → edist (f a) (f b) < ε) ∧
-        ∀ δ > 0, ∃ ε > 0, ∀ {a b : γ}, edist (f a) (f b) < ε → edist a b < δ :=
-  by
-  constructor
-  · intro h
-    exact
-      ⟨Emetric.uniformContinuous_iff.1 (uniform_embedding_iff.1 h).2.1,
-        (uniform_embedding_iff.1 h).2.2⟩
-  · rintro ⟨h₁, h₂⟩
-    refine' uniform_embedding_iff.2 ⟨_, Emetric.uniformContinuous_iff.2 h₁, h₂⟩
-    intro x y hxy
-    have : edist x y ≤ 0 := by
-      refine' le_of_forall_lt' fun δ δpos => _
-      rcases h₂ δ δpos with ⟨ε, εpos, hε⟩
-      have : edist (f x) (f y) < ε := by simpa [hxy]
-      exact hε this
-    simpa using this
-#align uniform_embedding_iff' uniformEmbedding_iff'
-
 -- see Note [lower instance priority]
 /-- An emetric space is separated -/
 instance (priority := 100) to_separated : SeparatedSpace γ :=
@@ -1108,12 +1075,24 @@ instance (priority := 100) to_separated : SeparatedSpace γ :=
     eq_of_forall_edist_le fun ε ε0 => le_of_lt (h _ (edist_mem_uniformity ε0))
 #align to_separated to_separated
 
+/-- A map between emetric spaces is a uniform embedding if and only if the edistance between `f x`
+and `f y` is controlled in terms of the distance between `x` and `y` and conversely. -/
+theorem Emetric.uniformEmbedding_iff' [EmetricSpace β] {f : γ → β} :
+    UniformEmbedding f ↔
+      (∀ ε > 0, ∃ δ > 0, ∀ {a b : γ}, edist a b < δ → edist (f a) (f b) < ε) ∧
+        ∀ δ > 0, ∃ ε > 0, ∀ {a b : γ}, edist (f a) (f b) < ε → edist a b < δ :=
+  by
+  simp only [uniformEmbedding_iff_uniformInducing,
+    uniformity_basis_edist.uniform_inducing_iff uniformity_basis_edist, exists_prop]
+  rfl
+#align emetric.uniform_embedding_iff' Emetric.uniformEmbedding_iff'
+
 /-- If a `pseudo_emetric_space` is a T₀ space, then it is an `emetric_space`. -/
-def Emetric.ofT0PseudoEmetricSpace (α : Type _) [PseudoEmetricSpace α] [T0Space α] :
+def EmetricSpace.ofT0PseudoEmetricSpace (α : Type _) [PseudoEmetricSpace α] [T0Space α] :
     EmetricSpace α :=
   { ‹PseudoEmetricSpace α› with
-    eq_of_edist_eq_zero := fun x y hdist => Inseparable.eq <| Emetric.inseparable_iff.2 hdist }
-#align emetric.of_t0_pseudo_emetric_space Emetric.ofT0PseudoEmetricSpace
+    eq_of_edist_eq_zero := fun x y hdist => (Emetric.inseparable_iff.2 hdist).Eq }
+#align emetric_space.of_t0_pseudo_emetric_space EmetricSpace.ofT0PseudoEmetricSpace
 
 /-- Auxiliary function to replace the uniformity on an emetric space with
 a uniformity which is equal to the original one, but maybe not defeq.
@@ -1246,7 +1225,7 @@ theorem UniformSpace.SeparationQuotient.edist_mk [PseudoEmetricSpace X] (x y : X
 #align uniform_space.separation_quotient.edist_mk UniformSpace.SeparationQuotient.edist_mk
 
 instance [PseudoEmetricSpace X] : EmetricSpace (UniformSpace.SeparationQuotient X) :=
-  @Emetric.ofT0PseudoEmetricSpace (UniformSpace.SeparationQuotient X)
+  @EmetricSpace.ofT0PseudoEmetricSpace (UniformSpace.SeparationQuotient X)
     { edist_self := fun x => Quotient.inductionOn' x edist_self
       edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm
       edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle

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

@@ -146,7 +146,7 @@ theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
   · intro n hn hrec
     calc
       edist (f m) (f (n + 1)) ≤ edist (f m) (f n) + edist (f n) (f (n + 1)) := edist_triangle _ _ _
-      _ ≤ (∑ i in Finset.Ico m n, _) + _ := add_le_add hrec le_rfl
+      _ ≤ (∑ i in Finset.Ico m n, _) + _ := (add_le_add hrec le_rfl)
       _ = ∑ i in Finset.Ico m (n + 1), _ := by
         rw [Nat.Ico_succ_right_eq_insert_Ico hn, Finset.sum_insert, add_comm] <;> simp
       
@@ -289,7 +289,7 @@ namespace Emetric
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_infᵢ⟩
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection {a b «expr ∈ » s} -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection {a b «expr ∈ » s} -/
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEmetricSpace β] {f : α → β} {s : Set α} :
     UniformContinuousOn f s ↔
@@ -333,7 +333,7 @@ theorem controlled_of_uniformEmbedding [PseudoEmetricSpace β] {f : α → β} :
   exact ⟨uniformContinuous_iff.1 (uniform_embedding_iff.1 h).2.1, (uniform_embedding_iff.1 h).2.2⟩
 #align emetric.controlled_of_uniform_embedding Emetric.controlled_of_uniformEmbedding
 
-/- ./././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) -/
 /-- ε-δ characterization of Cauchy sequences on pseudoemetric spaces -/
 protected theorem cauchy_iff {f : Filter α} :
     Cauchy f ↔ f ≠ ⊥ ∧ ∀ ε > 0, ∃ t ∈ f, ∀ (x) (_ : x ∈ t) (y) (_ : y ∈ t), edist x y < ε := by
@@ -632,8 +632,8 @@ theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) :
   fun z zx =>
   calc
     edist z y ≤ edist z x + edist x y := edist_triangle _ _ _
-    _ = edist x y + edist z x := add_comm _ _
-    _ < edist x y + ε₁ := ENNReal.add_lt_add_left h' zx
+    _ = edist x y + edist z x := (add_comm _ _)
+    _ < edist x y + ε₁ := (ENNReal.add_lt_add_left h' zx)
     _ ≤ ε₂ := h
     
 #align emetric.ball_subset Emetric.ball_subset
@@ -786,7 +786,7 @@ theorem inseparable_iff : Inseparable x y ↔ edist x y = 0 := by
   simp [inseparable_iff_mem_closure, mem_closure_iff, edist_comm, forall_lt_iff_le']
 #align emetric.inseparable_iff Emetric.inseparable_iff
 
-/- ./././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]
 /-- In a pseudoemetric space, Cauchy sequences are characterized by the fact that, eventually,
 the pseudoedistance between its elements is arbitrarily small -/
@@ -817,7 +817,7 @@ theorem totallyBounded_iff {s : Set α} :
     ⟨t, ft, h.trans <| unionᵢ₂_mono fun y yt z => hε⟩⟩
 #align emetric.totally_bounded_iff Emetric.totallyBounded_iff
 
-/- ./././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' {s : Set α} :
     TotallyBounded s ↔ ∀ ε > 0, ∃ (t : _)(_ : t ⊆ s), Set.Finite t ∧ s ⊆ ⋃ y ∈ t, ball y ε :=
   ⟨fun H ε ε0 => (totallyBounded_iff_subset.1 H) _ (edist_mem_uniformity ε0), fun H r ru =>
@@ -828,7 +828,7 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
-/- ./././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) -/
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
 theorem subset_countable_closure_of_almost_dense_set (s : Set α)
@@ -848,7 +848,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     · refine' ⟨y, hys, fun z hz => _⟩
       calc
         edist z y ≤ edist z x + edist y x := edist_triangle_right _ _ _
-        _ ≤ r + r := add_le_add hz.1 hxy
+        _ ≤ r + r := (add_le_add hz.1 hxy)
         _ = r * 2 := (mul_two r).symm
         
   choose f hfs hf
@@ -865,7 +865,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     
 #align emetric.subset_countable_closure_of_almost_dense_set Emetric.subset_countable_closure_of_almost_dense_set
 
-/- ./././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) -/
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
 theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
@@ -1023,7 +1023,7 @@ theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
   diam_le fun a ha b hb =>
     calc
       edist a b ≤ edist a x + edist b x := edist_triangle_right _ _ _
-      _ ≤ r + r := add_le_add ha hb
+      _ ≤ r + r := (add_le_add ha hb)
       _ = 2 * r := (two_mul r).symm
       
 #align emetric.diam_closed_ball Emetric.diam_closedBall
@@ -1199,7 +1199,7 @@ end Pi
 
 namespace Emetric
 
-/- ./././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) -/
 /-- A compact set in an emetric space is separable, i.e., it is the closure of a countable set. -/
 theorem countable_closure_of_compact {s : Set γ} (hs : IsCompact s) :
     ∃ (t : _)(_ : t ⊆ s), t.Countable ∧ s = closure t :=

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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.metric_space.emetric_space
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit e1a7bdeb4fd826b7e71d130d34988f0a2d26a177
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -46,11 +46,7 @@ in terms of the elements of the uniformity. -/
 theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α)} (z : β)
     (D : α → α → β) (H : ∀ s, s ∈ U ↔ ∃ ε > z, ∀ {a b : α}, D a b < ε → (a, b) ∈ s) :
     U = ⨅ ε > z, 𝓟 { p : α × α | D p.1 p.2 < ε } :=
-  le_antisymm
-    (le_infᵢ fun ε => le_infᵢ fun ε0 => le_principal_iff.2 <| (H _).2 ⟨ε, ε0, fun a b => id⟩)
-    fun r ur =>
-    let ⟨ε, ε0, h⟩ := (H _).1 ur
-    mem_infᵢ_of_mem ε <| mem_infᵢ_of_mem ε0 <| mem_principal.2 fun ⟨a, b⟩ => h
+  HasBasis.eq_binfᵢ ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_set_of]⟩
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
 
 /-- `has_edist α` means that `α` is equipped with an extended distance. -/
@@ -61,36 +57,12 @@ class HasEdist (α : Type _) where
 export HasEdist (edist)
 
 /-- Creating a uniform space from an extended distance. -/
-def uniformSpaceOfEdist (edist : α → α → ℝ≥0∞) (edist_self : ∀ x : α, edist x x = 0)
+noncomputable def uniformSpaceOfEdist (edist : α → α → ℝ≥0∞) (edist_self : ∀ x : α, edist x x = 0)
     (edist_comm : ∀ x y : α, edist x y = edist y x)
     (edist_triangle : ∀ x y z : α, edist x z ≤ edist x y + edist y z) : UniformSpace α :=
-  UniformSpace.ofCore
-    { uniformity := ⨅ ε > 0, 𝓟 { p : α × α | edist p.1 p.2 < ε }
-      refl :=
-        le_infᵢ fun ε =>
-          le_infᵢ <| by
-            simp (config := { contextual := true }) [Set.subset_def, idRel, edist_self, (· > ·)]
-      comp :=
-        le_infᵢ fun ε =>
-          le_infᵢ fun h =>
-            have : (2 : ℝ≥0∞) = (2 : ℕ) := by simp
-            have A : 0 < ε / 2 :=
-              ENNReal.div_pos_iff.2 ⟨ne_of_gt h, by convert ENNReal.nat_ne_top 2⟩
-            lift'_le (mem_infᵢ_of_mem (ε / 2) <| mem_infᵢ_of_mem A (Subset.refl _)) <|
-              by
-              have : ∀ a b c : α, edist a c < ε / 2 → edist c b < ε / 2 → edist a b < ε :=
-                fun a b c hac hcb =>
-                calc
-                  edist a b ≤ edist a c + edist c b := edist_triangle _ _ _
-                  _ < ε / 2 + ε / 2 := ENNReal.add_lt_add hac hcb
-                  _ = ε := by rw [ENNReal.add_halves]
-                  
-              simpa [compRel]
-      symm :=
-        tendsto_infᵢ.2 fun ε =>
-          tendsto_infᵢ.2 fun h =>
-            tendsto_infᵢ' ε <|
-              tendsto_infᵢ' h <| tendsto_principal_principal.2 <| by simp [edist_comm] }
+  UniformSpace.ofFun edist edist_self edist_comm edist_triangle fun ε ε0 =>
+    ⟨ε / 2, ENNReal.half_pos ε0.lt.ne', fun _ h₁ _ h₂ =>
+      (ENNReal.add_lt_add h₁ h₂).trans_eq (ENNReal.add_halves _)⟩
 #align uniform_space_of_edist uniformSpaceOfEdist
 
 -- the uniform structure is embedded in the emetric space structure
@@ -208,14 +180,15 @@ theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edi
   PseudoEmetricSpace.uniformity_edist
 #align uniformity_pseudoedist uniformity_pseudoedist
 
+theorem uniformSpace_edist :
+    ‹PseudoEmetricSpace α›.toUniformSpace =
+      uniformSpaceOfEdist edist edist_self edist_comm edist_triangle :=
+  uniformSpace_eq uniformity_pseudoedist
+#align uniform_space_edist uniformSpace_edist
+
 theorem uniformity_basis_edist :
     (𝓤 α).HasBasis (fun ε : ℝ≥0∞ => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
-  (@uniformity_pseudoedist α _).symm ▸
-    hasBasis_binfᵢ_principal
-      (fun r hr p hp =>
-        ⟨min r p, lt_min hr hp, fun x hx => lt_of_lt_of_le hx (min_le_left _ _), fun x hx =>
-          lt_of_lt_of_le hx (min_le_right _ _)⟩)
-      ⟨1, zero_lt_one⟩
+  (@uniformSpace_edist α _).symm ▸ UniformSpace.hasBasis_ofFun ⟨1, one_pos⟩ _ _ _ _ _
 #align uniformity_basis_edist uniformity_basis_edist
 
 /-- Characterization of the elements of the uniformity in terms of the extended distance -/
@@ -453,17 +426,7 @@ def PseudoEmetricSpace.induced {α β} (f : α → β) (m : PseudoEmetricSpace 
   edist_comm x y := edist_comm _ _
   edist_triangle x y z := edist_triangle _ _ _
   toUniformSpace := UniformSpace.comap f m.toUniformSpace
-  uniformity_edist :=
-    by
-    apply @uniformity_dist_of_mem_uniformity _ _ _ _ _ fun x y => edist (f x) (f y)
-    refine' fun s => mem_comap.trans _
-    constructor <;> intro H
-    · rcases H with ⟨r, ru, rs⟩
-      rcases mem_uniformity_edist.1 ru with ⟨ε, ε0, hε⟩
-      refine' ⟨ε, ε0, fun a b h => rs (hε _)⟩
-      exact h
-    · rcases H with ⟨ε, ε0, hε⟩
-      exact ⟨_, edist_mem_uniformity ε0, fun ⟨a, b⟩ => hε⟩
+  uniformity_edist := (uniformity_basis_edist.comap _).eq_binfᵢ
 #align pseudo_emetric_space.induced PseudoEmetricSpace.induced
 
 /-- Pseudoemetric space instance on subsets of pseudoemetric spaces -/
@@ -1179,17 +1142,7 @@ def EmetricSpace.induced {γ β} (f : γ → β) (hf : Function.Injective f) (m
   edist_comm x y := edist_comm _ _
   edist_triangle x y z := edist_triangle _ _ _
   toUniformSpace := UniformSpace.comap f m.toUniformSpace
-  uniformity_edist :=
-    by
-    apply @uniformity_dist_of_mem_uniformity _ _ _ _ _ fun x y => edist (f x) (f y)
-    refine' fun s => mem_comap.trans _
-    constructor <;> intro H
-    · rcases H with ⟨r, ru, rs⟩
-      rcases mem_uniformity_edist.1 ru with ⟨ε, ε0, hε⟩
-      refine' ⟨ε, ε0, fun a b h => rs (hε _)⟩
-      exact h
-    · rcases H with ⟨ε, ε0, hε⟩
-      exact ⟨_, edist_mem_uniformity ε0, fun ⟨a, b⟩ => hε⟩
+  uniformity_edist := (uniformity_basis_edist.comap _).eq_binfᵢ
 #align emetric_space.induced EmetricSpace.induced
 
 /-- Emetric space instance on subsets of emetric spaces -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/9da1b3534b65d9661eb8f42443598a92bbb49211

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module topology.metric_space.emetric_space
-! leanprover-community/mathlib commit bcfa726826abd57587355b4b5b7e78ad6527b7e4
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -215,7 +215,7 @@ theorem uniformity_basis_edist :
       (fun r hr p hp =>
         ⟨min r p, lt_min hr hp, fun x hx => lt_of_lt_of_le hx (min_le_left _ _), fun x hx =>
           lt_of_lt_of_le hx (min_le_right _ _)⟩)
-      ⟨1, ENNReal.zero_lt_one⟩
+      ⟨1, zero_lt_one⟩
 #align uniformity_basis_edist uniformity_basis_edist
 
 /-- Characterization of the elements of the uniformity in terms of the extended distance -/
@@ -779,7 +779,7 @@ theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
     isOpen_iff.2 fun y hy =>
       ⟨⊤, ENNReal.coe_lt_top,
         (ball_disjoint <| by
-            rw [ENNReal.top_add]
+            rw [top_add]
             exact le_of_not_lt hy).subset_compl_right⟩
 #align emetric.is_closed_ball_top Emetric.isClosed_ball_top
 
@@ -1271,6 +1271,46 @@ end Diam
 
 end Emetric
 
+/-!
+### Separation quotient
+-/
+
+
+instance [PseudoEmetricSpace X] : HasEdist (UniformSpace.SeparationQuotient X) :=
+  ⟨fun x y =>
+    Quotient.liftOn₂' x y edist fun x y x' y' hx hy =>
+      calc
+        edist x y = edist x' y :=
+          edist_congr_right <| Emetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx
+        _ = edist x' y' :=
+          edist_congr_left <| Emetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy
+        ⟩
+
+@[simp]
+theorem UniformSpace.SeparationQuotient.edist_mk [PseudoEmetricSpace X] (x y : X) :
+    @edist (UniformSpace.SeparationQuotient X) _ (Quot.mk _ x) (Quot.mk _ y) = edist x y :=
+  rfl
+#align uniform_space.separation_quotient.edist_mk UniformSpace.SeparationQuotient.edist_mk
+
+instance [PseudoEmetricSpace X] : EmetricSpace (UniformSpace.SeparationQuotient X) :=
+  @Emetric.ofT0PseudoEmetricSpace (UniformSpace.SeparationQuotient X)
+    { edist_self := fun x => Quotient.inductionOn' x edist_self
+      edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm
+      edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle
+      toUniformSpace := inferInstance
+      uniformity_edist :=
+        (uniformity_basis_edist.map _).eq_binfᵢ.trans <|
+          infᵢ_congr fun ε =>
+            infᵢ_congr fun hε =>
+              congr_arg 𝓟
+                (by
+                  ext ⟨⟨x⟩, ⟨y⟩⟩
+                  refine' ⟨_, fun h => ⟨(x, y), h, rfl⟩⟩
+                  rintro ⟨⟨x', y'⟩, h', h⟩
+                  simp only [Prod.ext_iff] at h
+                  rwa [← h.1, ← h.2]) }
+    _
+
 /-!
 ### `additive`, `multiplicative`
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/eb0cb4511aaef0da2462207b67358a0e1fe1e2ee

@@ -35,7 +35,7 @@ to `emetric_space` at the end.
 
 open Set Filter Classical
 
-open uniformity Topology BigOperators Filter NNReal Ennreal
+open uniformity Topology BigOperators Filter NNReal ENNReal
 
 universe u v w
 
@@ -75,15 +75,15 @@ def uniformSpaceOfEdist (edist : α → α → ℝ≥0∞) (edist_self : ∀ x :
           le_infᵢ fun h =>
             have : (2 : ℝ≥0∞) = (2 : ℕ) := by simp
             have A : 0 < ε / 2 :=
-              Ennreal.div_pos_iff.2 ⟨ne_of_gt h, by convert Ennreal.nat_ne_top 2⟩
+              ENNReal.div_pos_iff.2 ⟨ne_of_gt h, by convert ENNReal.nat_ne_top 2⟩
             lift'_le (mem_infᵢ_of_mem (ε / 2) <| mem_infᵢ_of_mem A (Subset.refl _)) <|
               by
               have : ∀ a b c : α, edist a c < ε / 2 → edist c b < ε / 2 → edist a b < ε :=
                 fun a b c hac hcb =>
                 calc
                   edist a b ≤ edist a c + edist c b := edist_triangle _ _ _
-                  _ < ε / 2 + ε / 2 := Ennreal.add_lt_add hac hcb
-                  _ = ε := by rw [Ennreal.add_halves]
+                  _ < ε / 2 + ε / 2 := ENNReal.add_lt_add hac hcb
+                  _ = ε := by rw [ENNReal.add_halves]
                   
               simpa [compRel]
       symm :=
@@ -215,7 +215,7 @@ theorem uniformity_basis_edist :
       (fun r hr p hp =>
         ⟨min r p, lt_min hr hp, fun x hx => lt_of_lt_of_le hx (min_le_left _ _), fun x hx =>
           lt_of_lt_of_le hx (min_le_right _ _)⟩)
-      ⟨1, Ennreal.zero_lt_one⟩
+      ⟨1, ENNReal.zero_lt_one⟩
 #align uniformity_basis_edist uniformity_basis_edist
 
 /-- Characterization of the elements of the uniformity in terms of the extended distance -/
@@ -279,30 +279,30 @@ theorem uniformity_basis_edist_le' (ε' : ℝ≥0∞) (hε' : 0 < ε') :
 
 theorem uniformity_basis_edist_nNReal :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 < ε } :=
-  Emetric.mk_uniformity_basis (fun _ => Ennreal.coe_pos.2) fun ε ε₀ =>
-    let ⟨δ, hδ⟩ := Ennreal.lt_iff_exists_nNReal_btwn.1 ε₀
-    ⟨δ, Ennreal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
+  Emetric.mk_uniformity_basis (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
+    let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
+    ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal uniformity_basis_edist_nNReal
 
 theorem uniformity_basis_edist_nNReal_le :
     (𝓤 α).HasBasis (fun ε : ℝ≥0 => 0 < ε) fun ε => { p : α × α | edist p.1 p.2 ≤ ε } :=
-  Emetric.mk_uniformity_basis_le (fun _ => Ennreal.coe_pos.2) fun ε ε₀ =>
-    let ⟨δ, hδ⟩ := Ennreal.lt_iff_exists_nNReal_btwn.1 ε₀
-    ⟨δ, Ennreal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
+  Emetric.mk_uniformity_basis_le (fun _ => ENNReal.coe_pos.2) fun ε ε₀ =>
+    let ⟨δ, hδ⟩ := ENNReal.lt_iff_exists_nnreal_btwn.1 ε₀
+    ⟨δ, ENNReal.coe_pos.1 hδ.1, le_of_lt hδ.2⟩
 #align uniformity_basis_edist_nnreal_le uniformity_basis_edist_nNReal_le
 
 theorem uniformity_basis_edist_inv_nat :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < (↑n)⁻¹ } :=
-  Emetric.mk_uniformity_basis (fun n _ => Ennreal.inv_pos.2 <| Ennreal.nat_ne_top n) fun ε ε₀ =>
-    let ⟨n, hn⟩ := Ennreal.exists_inv_nat_lt (ne_of_gt ε₀)
+  Emetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun ε ε₀ =>
+    let ⟨n, hn⟩ := ENNReal.exists_inv_nat_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_nat
 
 theorem uniformity_basis_edist_inv_two_pow :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < 2⁻¹ ^ n } :=
-  Emetric.mk_uniformity_basis (fun n _ => Ennreal.pow_pos (Ennreal.inv_pos.2 Ennreal.two_ne_top) _)
+  Emetric.mk_uniformity_basis (fun n _ => ENNReal.pow_pos (ENNReal.inv_pos.2 ENNReal.two_ne_top) _)
     fun ε ε₀ =>
-    let ⟨n, hn⟩ := Ennreal.exists_inv_two_pow_lt (ne_of_gt ε₀)
+    let ⟨n, hn⟩ := ENNReal.exists_inv_two_pow_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_two_pow uniformity_basis_edist_inv_two_pow
 
@@ -662,7 +662,7 @@ theorem closedBall_subset_closedBall (h : ε₁ ≤ ε₂) : closedBall x ε₁
 
 theorem ball_disjoint (h : ε₁ + ε₂ ≤ edist x y) : Disjoint (ball x ε₁) (ball y ε₂) :=
   Set.disjoint_left.mpr fun z h₁ h₂ =>
-    (edist_triangle_left x y z).not_lt <| (Ennreal.add_lt_add h₁ h₂).trans_le h
+    (edist_triangle_left x y z).not_lt <| (ENNReal.add_lt_add h₁ h₂).trans_le h
 #align emetric.ball_disjoint Emetric.ball_disjoint
 
 theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) : ball x ε₁ ⊆ ball y ε₂ :=
@@ -670,7 +670,7 @@ theorem ball_subset (h : edist x y + ε₁ ≤ ε₂) (h' : edist x y ≠ ∞) :
   calc
     edist z y ≤ edist z x + edist x y := edist_triangle _ _ _
     _ = edist x y + edist z x := add_comm _ _
-    _ < edist x y + ε₁ := Ennreal.add_lt_add_left h' zx
+    _ < edist x y + ε₁ := ENNReal.add_lt_add_left h' zx
     _ ≤ ε₂ := h
     
 #align emetric.ball_subset Emetric.ball_subset
@@ -703,8 +703,8 @@ def edistLtTopSetoid : Setoid α where
   iseqv :=
     ⟨fun x => by
       rw [edist_self]
-      exact Ennreal.coe_lt_top, fun x y h => by rwa [edist_comm], fun x y z hxy hyz =>
-      lt_of_le_of_lt (edist_triangle x y z) (Ennreal.add_lt_top.2 ⟨hxy, hyz⟩)⟩
+      exact ENNReal.coe_lt_top, fun x y h => by rwa [edist_comm], fun x y z hxy hyz =>
+      lt_of_le_of_lt (edist_triangle x y z) (ENNReal.add_lt_top.2 ⟨hxy, hyz⟩)⟩
 #align emetric.edist_lt_top_setoid Emetric.edistLtTopSetoid
 
 @[simp]
@@ -777,9 +777,9 @@ theorem isOpen_ball : IsOpen (ball x ε) :=
 theorem isClosed_ball_top : IsClosed (ball x ⊤) :=
   isOpen_compl_iff.1 <|
     isOpen_iff.2 fun y hy =>
-      ⟨⊤, Ennreal.coe_lt_top,
+      ⟨⊤, ENNReal.coe_lt_top,
         (ball_disjoint <| by
-            rw [Ennreal.top_add]
+            rw [ENNReal.top_add]
             exact le_of_not_lt hy).subset_compl_right⟩
 #align emetric.is_closed_ball_top Emetric.isClosed_ball_top
 
@@ -893,12 +893,12 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     ⟨⋃ n : ℕ, f n⁻¹ '' T n, Union_subset fun n => image_subset_iff.2 fun z hz => hfs _ _,
       countable_Union fun n => (hTc n).image _, _⟩
   refine' fun x hx => mem_closure_iff.2 fun ε ε0 => _
-  rcases Ennreal.exists_inv_nat_lt (Ennreal.half_pos ε0.lt.ne').ne' with ⟨n, hn⟩
+  rcases ENNReal.exists_inv_nat_lt (ENNReal.half_pos ε0.lt.ne').ne' with ⟨n, hn⟩
   rcases mem_Union₂.1 (hsT n hx) with ⟨y, hyn, hyx⟩
   refine' ⟨f n⁻¹ y, mem_Union.2 ⟨n, mem_image_of_mem _ hyn⟩, _⟩
   calc
     edist x (f n⁻¹ y) ≤ n⁻¹ * 2 := hf _ _ ⟨hyx, hx⟩
-    _ < ε := Ennreal.mul_lt_of_lt_div hn
+    _ < ε := ENNReal.mul_lt_of_lt_div hn
     
 #align emetric.subset_countable_closure_of_almost_dense_set Emetric.subset_countable_closure_of_almost_dense_set
 
@@ -1008,12 +1008,12 @@ theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s)
 #align emetric.diam_insert Emetric.diam_insert
 
 theorem diam_pair : diam ({x, y} : Set α) = edist x y := by
-  simp only [supᵢ_singleton, diam_insert, diam_singleton, Ennreal.max_zero_right]
+  simp only [supᵢ_singleton, diam_insert, diam_singleton, ENNReal.max_zero_right]
 #align emetric.diam_pair Emetric.diam_pair
 
 theorem diam_triple : diam ({x, y, z} : Set α) = max (max (edist x y) (edist x z)) (edist y z) := by
-  simp only [diam_insert, supᵢ_insert, supᵢ_singleton, diam_singleton, Ennreal.max_zero_right,
-    Ennreal.sup_eq_max]
+  simp only [diam_insert, supᵢ_insert, supᵢ_singleton, diam_singleton, ENNReal.max_zero_right,
+    ENNReal.sup_eq_max]
 #align emetric.diam_triple Emetric.diam_triple
 
 /-- The diameter is monotonous with respect to inclusion -/

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

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -806,7 +806,7 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     · refine' ⟨y, hys, fun z hz => _⟩
       calc
         edist z y ≤ edist z x + edist y x := edist_triangle_right _ _ _
-        _ ≤ r + r := (add_le_add hz.1 hxy)
+        _ ≤ r + r := add_le_add hz.1 hxy
         _ = r * 2 := (mul_two r).symm
   choose f hfs hf using this
   refine'
@@ -1001,7 +1001,7 @@ theorem diam_closedBall {r : ℝ≥0∞} : diam (closedBall x r) ≤ 2 * r :=
   diam_le fun a ha b hb =>
     calc
       edist a b ≤ edist a x + edist b x := edist_triangle_right _ _ _
-      _ ≤ r + r := (add_le_add ha hb)
+      _ ≤ r + r := add_le_add ha hb
       _ = 2 * r := (two_mul r).symm
 #align emetric.diam_closed_ball EMetric.diam_closedBall
 

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>

@@ -951,7 +951,7 @@ theorem diam_iUnion_mem_option {ι : Type*} (o : Option ι) (s : ι → Set α)
 
 theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s) :=
   eq_of_forall_ge_iff fun d => by
-    simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, iSup_le_iff,
+    simp only [diam_le_iff, forall_mem_insert, edist_self, edist_comm x, max_le_iff, iSup_le_iff,
       zero_le, true_and_iff, forall_and, and_self_iff, ← and_assoc]
 #align emetric.diam_insert EMetric.diam_insert
 

This is less exhaustive than its sibling #11486 because edge cases are harder to classify. No fundamental difficulty, just me being a bit fast and lazy.

Reduce the diff of #11203

@@ -265,7 +265,7 @@ theorem uniformity_basis_edist_nnreal_le :
 
 theorem uniformity_basis_edist_inv_nat :
     (𝓤 α).HasBasis (fun _ => True) fun n : ℕ => { p : α × α | edist p.1 p.2 < (↑n)⁻¹ } :=
-  EMetric.mk_uniformity_basis (fun n _ => ENNReal.inv_pos.2 <| ENNReal.nat_ne_top n) fun _ε ε₀ =>
+  EMetric.mk_uniformity_basis (fun n _ ↦ ENNReal.inv_pos.2 <| ENNReal.natCast_ne_top n) fun _ε ε₀ ↦
     let ⟨n, hn⟩ := ENNReal.exists_inv_nat_lt (ne_of_gt ε₀)
     ⟨n, trivial, le_of_lt hn⟩
 #align uniformity_basis_edist_inv_nat uniformity_basis_edist_inv_nat

@@ -1169,7 +1169,7 @@ theorem diam_eq_zero_iff : diam s = 0 ↔ s.Subsingleton :=
 #align emetric.diam_eq_zero_iff EMetric.diam_eq_zero_iff
 
 theorem diam_pos_iff : 0 < diam s ↔ s.Nontrivial := by
-  simp only [pos_iff_ne_zero, Ne.def, diam_eq_zero_iff, Set.not_subsingleton_iff]
+  simp only [pos_iff_ne_zero, Ne, diam_eq_zero_iff, Set.not_subsingleton_iff]
 
 theorem diam_pos_iff' : 0 < diam s ↔ ∃ x ∈ s, ∃ y ∈ s, x ≠ y := by
   simp only [diam_pos_iff, Set.Nontrivial, exists_prop]

previously the ext tactic would fail for these classes. now it won't.

@@ -47,6 +47,7 @@ theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
 
 /-- `EDist α` means that `α` is equipped with an extended distance. -/
+@[ext]
 class EDist (α : Type*) where
   edist : α → α → ℝ≥0∞
 #align has_edist EDist
@@ -89,6 +90,16 @@ attribute [instance] PseudoEMetricSpace.toUniformSpace
 
 /- Pseudoemetric spaces are less common than metric spaces. Therefore, we work in a dedicated
 namespace, while notions associated to metric spaces are mostly in the root namespace. -/
+
+/-- Two pseudo emetric space structures with the same edistance function coincide. -/
+@[ext]
+protected theorem PseudoEMetricSpace.ext {α : Type*} {m m' : PseudoEMetricSpace α}
+    (h : m.toEDist = m'.toEDist) : m = m' := by
+  cases' m with ed  _ _ _ U hU
+  cases' m' with ed' _ _ _ U' hU'
+  congr 1
+  exact UniformSpace.ext (((show ed = ed' from h) ▸ hU).trans hU'.symm)
+
 variable [PseudoEMetricSpace α]
 
 export PseudoEMetricSpace (edist_self edist_comm edist_triangle)
@@ -1015,6 +1026,15 @@ class EMetricSpace (α : Type u) extends PseudoEMetricSpace α : Type u where
   eq_of_edist_eq_zero : ∀ {x y : α}, edist x y = 0 → x = y
 #align emetric_space EMetricSpace
 
+@[ext]
+protected theorem EMetricSpace.ext
+    {α : Type*} {m m' : EMetricSpace α} (h : m.toEDist = m'.toEDist) : m = m' := by
+  cases m
+  cases m'
+  congr
+  ext1
+  assumption
+
 variable {γ : Type w} [EMetricSpace γ]
 
 export EMetricSpace (eq_of_edist_eq_zero)

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

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

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

Fixes #2031

@@ -1044,10 +1044,9 @@ theorem eq_of_forall_edist_le {x y : γ} (h : ∀ ε > 0, edist x y ≤ ε) : x
 
 -- see Note [lower instance priority]
 /-- An emetric space is separated -/
-instance (priority := 100) to_separated : SeparatedSpace γ :=
-  separated_def.2 fun _ _ h =>
-    eq_of_forall_edist_le fun _ ε0 => le_of_lt (h _ (edist_mem_uniformity ε0))
-#align to_separated to_separated
+instance (priority := 100) EMetricSpace.instT0Space : T0Space γ where
+  t0 _ _ h := eq_of_edist_eq_zero <| inseparable_iff.1 h
+#align to_separated EMetricSpace.instT0Space
 
 /-- A map between emetric spaces is a uniform embedding if and only if the edistance between `f x`
 and `f y` is controlled in terms of the distance between `x` and `y` and conversely. -/
@@ -1164,30 +1163,24 @@ end EMetric
 ### Separation quotient
 -/
 
-instance [PseudoEMetricSpace X] : EDist (UniformSpace.SeparationQuotient X) where
-  edist x y := Quotient.liftOn₂' x y edist fun _ _ _ _ hx hy =>
-    edist_congr
-      (EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx)
-      (EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy)
+instance [PseudoEMetricSpace X] : EDist (SeparationQuotient X) where
+  edist := SeparationQuotient.lift₂ edist fun _ _ _ _ hx hy =>
+    edist_congr (EMetric.inseparable_iff.1 hx) (EMetric.inseparable_iff.1 hy)
 
-@[simp] theorem UniformSpace.SeparationQuotient.edist_mk [PseudoEMetricSpace X] (x y : X) :
-    @edist (UniformSpace.SeparationQuotient X) _ (Quot.mk _ x) (Quot.mk _ y) = edist x y :=
+@[simp] theorem SeparationQuotient.edist_mk [PseudoEMetricSpace X] (x y : X) :
+    edist (mk x) (mk y) = edist x y :=
   rfl
-#align uniform_space.separation_quotient.edist_mk UniformSpace.SeparationQuotient.edist_mk
-
-instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient X) :=
-  @EMetricSpace.ofT0PseudoEMetricSpace (UniformSpace.SeparationQuotient X)
-    { edist_self := fun x => Quotient.inductionOn' x edist_self,
-      edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm,
-      edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle,
+#align uniform_space.separation_quotient.edist_mk SeparationQuotient.edist_mk
+
+open SeparationQuotient in
+instance [PseudoEMetricSpace X] : EMetricSpace (SeparationQuotient X) :=
+  @EMetricSpace.ofT0PseudoEMetricSpace (SeparationQuotient X)
+    { edist_self := surjective_mk.forall.2 edist_self,
+      edist_comm := surjective_mk.forall₂.2 edist_comm,
+      edist_triangle := surjective_mk.forall₃.2 edist_triangle,
       toUniformSpace := inferInstance,
-      uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans <| iInf_congr fun ε =>
-        iInf_congr fun _ => congr_arg 𝓟 <| by
-          ext ⟨⟨x⟩, ⟨y⟩⟩
-          refine ⟨?_, fun h => ⟨(x, y), h, rfl⟩⟩
-          rintro ⟨⟨x', y'⟩, h', h⟩
-          simp only [Prod.ext_iff] at h
-          rwa [← h.1, ← h.2] } _
+      uniformity_edist := comap_injective (surjective_mk.Prod_map surjective_mk) <| by
+        simp [comap_mk_uniformity, PseudoEMetricSpace.uniformity_edist] } _
 
 /-!
 ### `Additive`, `Multiplicative`

Classifies by adding issue number #10756 to porting notes claiming anything semantically equivalent to:

• "new lemma"
• "added lemma"

@@ -291,7 +291,7 @@ theorem uniformContinuous_iff [PseudoEMetricSpace β] {f : α → β} :
   uniformity_basis_edist.uniformContinuous_iff uniformity_basis_edist
 #align emetric.uniform_continuous_iff EMetric.uniformContinuous_iff
 
--- Porting note: new lemma
+-- Porting note (#10756): new lemma
 theorem uniformInducing_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformInducing f ↔ UniformContinuous f ∧
       ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, edist (f a) (f b) < ε → edist a b < δ :=

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

@@ -778,7 +778,7 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
--- Porting note: todo: generalize to a uniform space with metrizable uniformity
+-- Porting note (#11215): TODO: generalize to a uniform space with metrizable uniformity
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
 theorem subset_countable_closure_of_almost_dense_set (s : Set α)
@@ -835,7 +835,7 @@ theorem _root_.TopologicalSpace.IsSeparable.separableSpace {s : Set α} (hs : Is
   rwa [inducing_subtype_val.dense_iff, Subtype.forall]
 #align topological_space.is_separable.separable_space TopologicalSpace.IsSeparable.separableSpace
 
--- Porting note: todo: generalize to metrizable spaces
+-- Porting note (#11215): TODO: generalize to metrizable spaces
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
 theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
@@ -1059,7 +1059,8 @@ theorem EMetric.uniformEmbedding_iff' [EMetricSpace β] {f : γ → β} :
 #align emetric.uniform_embedding_iff' EMetric.uniformEmbedding_iff'
 
 /-- If a `PseudoEMetricSpace` is a T₀ space, then it is an `EMetricSpace`. -/
-@[reducible] -- Porting note: made `reducible`; todo: make it an instance?
+@[reducible] -- Porting note: made `reducible`;
+-- Porting note (#11215): TODO: make it an instance?
 def EMetricSpace.ofT0PseudoEMetricSpace (α : Type*) [PseudoEMetricSpace α] [T0Space α] :
     EMetricSpace α :=
   { ‹PseudoEMetricSpace α› with

ball for "bounded forall" and bex for "bounded exists" are from experience very confusing abbreviations. This PR renames them to forall_mem and exists_mem in the few Set lemma names that mention them.

Also deprecate ball_image_of_ball, mem_image_elim, mem_image_elim_on since those lemmas are duplicates of the renamed lemmas (apart from argument order and implicitness, which I am also fixing by making the binder in the RHS of forall_mem_image semi-implicit), have obscure names and are completely unused.

@@ -893,7 +893,7 @@ theorem diam_le_iff {d : ℝ≥0∞} : diam s ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s
 
 theorem diam_image_le_iff {d : ℝ≥0∞} {f : β → α} {s : Set β} :
     diam (f '' s) ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist (f x) (f y) ≤ d := by
-  simp only [diam_le_iff, ball_image_iff]
+  simp only [diam_le_iff, forall_mem_image]
 #align emetric.diam_image_le_iff EMetric.diam_image_le_iff
 
 theorem edist_le_of_diam_le {d} (hx : x ∈ s) (hy : y ∈ s) (hd : diam s ≤ d) : edist x y ≤ d :=

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".

@@ -277,7 +277,7 @@ namespace EMetric
 instance (priority := 900) instIsCountablyGeneratedUniformity : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
--- porting note: changed explicit/implicit
+-- Porting note: changed explicit/implicit
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
 theorem uniformContinuousOn_iff [PseudoEMetricSpace β] {f : α → β} {s : Set α} :
     UniformContinuousOn f s ↔
@@ -291,7 +291,7 @@ theorem uniformContinuous_iff [PseudoEMetricSpace β] {f : α → β} :
   uniformity_basis_edist.uniformContinuous_iff uniformity_basis_edist
 #align emetric.uniform_continuous_iff EMetric.uniformContinuous_iff
 
--- porting note: new lemma
+-- Porting note: new lemma
 theorem uniformInducing_iff [PseudoEMetricSpace β] {f : α → β} :
     UniformInducing f ↔ UniformContinuous f ∧
       ∀ δ > 0, ∃ ε > 0, ∀ {a b : α}, edist (f a) (f b) < ε → edist a b < δ :=
@@ -474,7 +474,7 @@ open Finset
 
 variable {π : β → Type*} [Fintype β]
 
--- porting note: reordered instances
+-- Porting note: reordered instances
 instance [∀ b, EDist (π b)] : EDist (∀ b, π b) where
   edist f g := Finset.sup univ fun b => edist (f b) (g b)
 
@@ -778,7 +778,7 @@ theorem totallyBounded_iff' {s : Set α} :
 
 section Compact
 
--- porting note: todo: generalize to a uniform space with metrizable uniformity
+-- Porting note: todo: generalize to a uniform space with metrizable uniformity
 /-- For a set `s` in a pseudo emetric space, if for every `ε > 0` there exists a countable
 set that is `ε`-dense in `s`, then there exists a countable subset `t ⊆ s` that is dense in `s`. -/
 theorem subset_countable_closure_of_almost_dense_set (s : Set α)
@@ -835,7 +835,7 @@ theorem _root_.TopologicalSpace.IsSeparable.separableSpace {s : Set α} (hs : Is
   rwa [inducing_subtype_val.dense_iff, Subtype.forall]
 #align topological_space.is_separable.separable_space TopologicalSpace.IsSeparable.separableSpace
 
--- porting note: todo: generalize to metrizable spaces
+-- Porting note: todo: generalize to metrizable spaces
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/
 theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
@@ -1059,7 +1059,7 @@ theorem EMetric.uniformEmbedding_iff' [EMetricSpace β] {f : γ → β} :
 #align emetric.uniform_embedding_iff' EMetric.uniformEmbedding_iff'
 
 /-- If a `PseudoEMetricSpace` is a T₀ space, then it is an `EMetricSpace`. -/
-@[reducible] -- porting note: made `reducible`; todo: make it an instance?
+@[reducible] -- Porting note: made `reducible`; todo: make it an instance?
 def EMetricSpace.ofT0PseudoEMetricSpace (α : Type*) [PseudoEMetricSpace α] [T0Space α] :
     EMetricSpace α :=
   { ‹PseudoEMetricSpace α› with

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

This follows on from #6964.

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

@@ -870,8 +870,8 @@ theorem secondCountable_of_almost_dense_set
     (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ ⋃ x ∈ t, closedBall x ε = univ) :
     SecondCountableTopology α := by
   suffices SeparableSpace α from UniformSpace.secondCountable_of_separable α
-  have : ∀ ε > 0, ∃ t : Set α, Set.Countable t ∧ univ ⊆ ⋃ x ∈ t, closedBall x ε
-  · simpa only [univ_subset_iff] using hs
+  have : ∀ ε > 0, ∃ t : Set α, Set.Countable t ∧ univ ⊆ ⋃ x ∈ t, closedBall x ε := by
+    simpa only [univ_subset_iff] using hs
   rcases subset_countable_closure_of_almost_dense_set (univ : Set α) this with ⟨t, -, htc, ht⟩
   exact ⟨⟨t, htc, fun x => ht (mem_univ x)⟩⟩
 #align emetric.second_countable_of_almost_dense_set EMetric.secondCountable_of_almost_dense_set

Co-authored-by: Jireh Loreaux <loreaujy@gmail.com>

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 -/
 import Mathlib.Data.Nat.Interval
-import Mathlib.Data.ENNReal.Basic
+import Mathlib.Data.ENNReal.Real
 import Mathlib.Topology.UniformSpace.Pi
 import Mathlib.Topology.UniformSpace.UniformConvergence
 import Mathlib.Topology.UniformSpace.UniformEmbedding

In preparation for splitting that file. Location suggested by @j-loreaux on zulip.

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 -/
 import Mathlib.Data.Nat.Interval
-import Mathlib.Data.Real.ENNReal
+import Mathlib.Data.ENNReal.Basic
 import Mathlib.Topology.UniformSpace.Pi
 import Mathlib.Topology.UniformSpace.UniformConvergence
 import Mathlib.Topology.UniformSpace.UniformEmbedding

See Zulip thread for the discussion.

@@ -1180,7 +1180,7 @@ instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient
       edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm,
       edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle,
       toUniformSpace := inferInstance,
-      uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans $ iInf_congr fun ε =>
+      uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans <| iInf_congr fun ε =>
         iInf_congr fun _ => congr_arg 𝓟 <| by
           ext ⟨⟨x⟩, ⟨y⟩⟩
           refine ⟨?_, fun h => ⟨(x, y), h, rfl⟩⟩

Subset of #9319

@@ -510,7 +510,7 @@ spaces. -/
 instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetricSpace (∀ b, π b) where
   edist_self f := bot_unique <| Finset.sup_le <| by simp
   edist_comm f g := by simp [edist_pi_def, edist_comm]
-  edist_triangle f g h := edist_pi_le_iff.2 <| fun b => le_trans (edist_triangle _ (g b) _)
+  edist_triangle f g h := edist_pi_le_iff.2 fun b => le_trans (edist_triangle _ (g b) _)
     (add_le_add (edist_le_pi_edist _ _ _) (edist_le_pi_edist _ _ _))
   toUniformSpace := Pi.uniformSpace _
   uniformity_edist := by
@@ -1180,8 +1180,8 @@ instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient
       edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm,
       edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle,
       toUniformSpace := inferInstance,
-      uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans $ iInf_congr $ fun ε =>
-        iInf_congr $ fun _ => congr_arg 𝓟 <| by
+      uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans $ iInf_congr fun ε =>
+        iInf_congr fun _ => congr_arg 𝓟 <| by
           ext ⟨⟨x⟩, ⟨y⟩⟩
           refine ⟨?_, fun h => ⟨(x, y), h, rfl⟩⟩
           rintro ⟨⟨x', y'⟩, h', h⟩

This converts usages of the pattern

cases h
case inl h' => ...
case inr h' => ...

which derive from mathported code, to the "structured cases" syntax:

cases h with
| inl h' => ...
| inr h' => ...

The case where the subgoals are handled with · instead of case is more contentious (and much more numerous) so I left those alone. This pattern also appears with cases', induction, induction', and rcases. Furthermore, there is a similar transformation for by_cases:

by_cases h : cond
case pos => ...
case neg => ...

is replaced by:

if h : cond then
  ...
else
  ...

Co-authored-by: Mario Carneiro <di.gama@gmail.com>

@@ -132,9 +132,9 @@ theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + e
 /-- The triangle (polygon) inequality for sequences of points; `Finset.Ico` version. -/
 theorem edist_le_Ico_sum_edist (f : ℕ → α) {m n} (h : m ≤ n) :
     edist (f m) (f n) ≤ ∑ i in Finset.Ico m n, edist (f i) (f (i + 1)) := by
-  induction n, h using Nat.le_induction
-  case base => rw [Finset.Ico_self, Finset.sum_empty, edist_self]
-  case succ n hle ihn =>
+  induction n, h using Nat.le_induction with
+  | base => rw [Finset.Ico_self, Finset.sum_empty, edist_self]
+  | succ n hle ihn =>
     calc
       edist (f m) (f (n + 1)) ≤ edist (f m) (f n) + edist (f n) (f (n + 1)) := edist_triangle _ _ _
       _ ≤ (∑ i in Finset.Ico m n, _) + _ := add_le_add ihn le_rfl

This reduces the file from ~2600 lines to ~1600 lines.

Co-authored-by: Vierkantor <vierkantor@vierkantor.com> Co-authored-by: Floris van Doorn <fpvdoorn@gmail.com>

@@ -3,6 +3,7 @@ Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 -/
+import Mathlib.Data.Nat.Interval
 import Mathlib.Data.Real.ENNReal
 import Mathlib.Topology.UniformSpace.Pi
 import Mathlib.Topology.UniformSpace.UniformConvergence

Also change a few theorems to instances, as instance loops are not a problem any more.

@@ -852,9 +852,9 @@ open TopologicalSpace
 
 variable (α)
 
-/-- A sigma compact pseudo emetric space has second countable topology. This is not an instance
-to avoid a loop with `sigmaCompactSpace_of_locally_compact_second_countable`.  -/
-theorem secondCountable_of_sigmaCompact [SigmaCompactSpace α] : SecondCountableTopology α := by
+/-- A sigma compact pseudo emetric space has second countable topology. -/
+instance (priority := 90) secondCountable_of_sigmaCompact [SigmaCompactSpace α] :
+    SecondCountableTopology α := by
   suffices SeparableSpace α by exact UniformSpace.secondCountable_of_separable α
   choose T _ hTc hsubT using fun n =>
     subset_countable_closure_of_compact (isCompact_compactCovering α n)

This was "feat(topology/metric_space): diameter of pointwise zero and addition"

@@ -8,7 +8,7 @@ import Mathlib.Topology.UniformSpace.Pi
 import Mathlib.Topology.UniformSpace.UniformConvergence
 import Mathlib.Topology.UniformSpace.UniformEmbedding
 
-#align_import topology.metric_space.emetric_space from "leanprover-community/mathlib"@"195fcd60ff2bfe392543bceb0ec2adcdb472db4c"
+#align_import topology.metric_space.emetric_space from "leanprover-community/mathlib"@"c8f305514e0d47dfaa710f5a52f0d21b588e6328"
 
 /-!
 # Extended metric spaces
@@ -29,7 +29,9 @@ to `EMetricSpace` at the end.
 -/
 
 
-open Set Filter Classical Uniformity Topology BigOperators NNReal ENNReal
+open Set Filter Classical
+
+open scoped Uniformity Topology BigOperators Filter NNReal ENNReal Pointwise
 
 universe u v w
 
@@ -925,6 +927,12 @@ theorem diam_singleton : diam ({x} : Set α) = 0 :=
   diam_subsingleton subsingleton_singleton
 #align emetric.diam_singleton EMetric.diam_singleton
 
+@[to_additive (attr := simp)]
+theorem diam_one [One α] : diam (1 : Set α) = 0 :=
+  diam_singleton
+#align emetric.diam_one EMetric.diam_one
+#align emetric.diam_zero EMetric.diam_zero
+
 theorem diam_iUnion_mem_option {ι : Type*} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp
 #align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_option

For faster build times and clearer dependencies. No attempt at being exhaustive.

The new import in Clopen.lean had been transitively imported before.

@@ -3,7 +3,6 @@ Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
 -/
-import Mathlib.Data.Nat.Interval
 import Mathlib.Data.Real.ENNReal
 import Mathlib.Topology.UniformSpace.Pi
 import Mathlib.Topology.UniformSpace.UniformConvergence

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -813,7 +813,7 @@ open TopologicalSpace in
 subset. This is not obvious, as the countable set whose closure covers `s` given by the definition
 of separability does not need in general to be contained in `s`. -/
 theorem _root_.TopologicalSpace.IsSeparable.exists_countable_dense_subset
-   {s : Set α} (hs : IsSeparable s) : ∃ t, t ⊆ s ∧ t.Countable ∧ s ⊆ closure t := by
+    {s : Set α} (hs : IsSeparable s) : ∃ t, t ⊆ s ∧ t.Countable ∧ s ⊆ closure t := by
   have : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ s ⊆ ⋃ x ∈ t, closedBall x ε := fun ε ε0 => by
     rcases hs with ⟨t, htc, hst⟩
     refine ⟨t, htc, hst.trans fun x hx => ?_⟩

@@ -809,17 +809,25 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 
 open TopologicalSpace in
-/-- If a set `s` is separable, then the corresponding subtype is separable in a (pseudo extended)
-metric space.  This is not obvious, as the countable set whose closure covers `s` does not need in
-general to be contained in `s`. -/
-theorem _root_.TopologicalSpace.IsSeparable.separableSpace {s : Set α} (hs : IsSeparable s) :
-    SeparableSpace s := by
+/-- If a set `s` is separable in a (pseudo extended) metric space, then it admits a countable dense
+subset. This is not obvious, as the countable set whose closure covers `s` given by the definition
+of separability does not need in general to be contained in `s`. -/
+theorem _root_.TopologicalSpace.IsSeparable.exists_countable_dense_subset
+   {s : Set α} (hs : IsSeparable s) : ∃ t, t ⊆ s ∧ t.Countable ∧ s ⊆ closure t := by
   have : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ s ⊆ ⋃ x ∈ t, closedBall x ε := fun ε ε0 => by
     rcases hs with ⟨t, htc, hst⟩
     refine ⟨t, htc, hst.trans fun x hx => ?_⟩
     rcases mem_closure_iff.1 hx ε ε0 with ⟨y, hyt, hxy⟩
     exact mem_iUnion₂.2 ⟨y, hyt, mem_closedBall.2 hxy.le⟩
-  rcases subset_countable_closure_of_almost_dense_set _ this with ⟨t, hts, htc, hst⟩
+  exact subset_countable_closure_of_almost_dense_set _ this
+
+open TopologicalSpace in
+/-- If a set `s` is separable, then the corresponding subtype is separable in a (pseudo extended)
+metric space.  This is not obvious, as the countable set whose closure covers `s` does not need in
+general to be contained in `s`. -/
+theorem _root_.TopologicalSpace.IsSeparable.separableSpace {s : Set α} (hs : IsSeparable s) :
+    SeparableSpace s := by
+  rcases hs.exists_countable_dense_subset with ⟨t, hts, htc, hst⟩
   lift t to Set s using hts
   refine ⟨⟨t, countable_of_injective_of_countable_image (Subtype.coe_injective.injOn _) htc, ?_⟩⟩
   rwa [inducing_subtype_val.dense_iff, Subtype.forall]

@@ -171,7 +171,7 @@ theorem uniformity_pseudoedist : 𝓤 α = ⨅ ε > 0, 𝓟 { p : α × α | edi
 theorem uniformSpace_edist :
     ‹PseudoEMetricSpace α›.toUniformSpace =
       uniformSpaceOfEDist edist edist_self edist_comm edist_triangle :=
-  uniformSpace_eq uniformity_pseudoedist
+  UniformSpace.ext uniformity_pseudoedist
 #align uniform_space_edist uniformSpace_edist
 
 theorem uniformity_basis_edist :

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

This has nice performance benefits.

@@ -34,7 +34,7 @@ open Set Filter Classical Uniformity Topology BigOperators NNReal ENNReal
 
 universe u v w
 
-variable {α : Type u} {β : Type v} {X : Type _}
+variable {α : Type u} {β : Type v} {X : Type*}
 
 /-- Characterizing uniformities associated to a (generalized) distance function `D`
 in terms of the elements of the uniformity. -/
@@ -45,7 +45,7 @@ theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
 
 /-- `EDist α` means that `α` is equipped with an extended distance. -/
-class EDist (α : Type _) where
+class EDist (α : Type*) where
   edist : α → α → ℝ≥0∞
 #align has_edist EDist
 
@@ -190,7 +190,7 @@ accumulating to zero, then `f i`-neighborhoods of the diagonal form a basis of `
 
 For specific bases see `uniformity_basis_edist`, `uniformity_basis_edist'`,
 `uniformity_basis_edist_nnreal`, and `uniformity_basis_edist_inv_nat`. -/
-protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
+protected theorem EMetric.mk_uniformity_basis {β : Type*} {p : β → Prop} {f : β → ℝ≥0∞}
     (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ x, p x ∧ f x ≤ ε) :
     (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 < f x } := by
   refine' ⟨fun s => uniformity_basis_edist.mem_iff.trans _⟩
@@ -205,7 +205,7 @@ protected theorem EMetric.mk_uniformity_basis {β : Type _} {p : β → Prop} {f
 accumulating to zero, then closed `f i`-neighborhoods of the diagonal form a basis of `𝓤 α`.
 
 For specific bases see `uniformity_basis_edist_le` and `uniformity_basis_edist_le'`. -/
-protected theorem EMetric.mk_uniformity_basis_le {β : Type _} {p : β → Prop} {f : β → ℝ≥0∞}
+protected theorem EMetric.mk_uniformity_basis_le {β : Type*} {p : β → Prop} {f : β → ℝ≥0∞}
     (hf₀ : ∀ x, p x → 0 < f x) (hf : ∀ ε, 0 < ε → ∃ x, p x ∧ f x ≤ ε) :
     (𝓤 α).HasBasis p fun x => { p : α × α | edist p.1 p.2 ≤ f x } := by
   refine' ⟨fun s => uniformity_basis_edist.mem_iff.trans _⟩
@@ -341,7 +341,7 @@ theorem complete_of_cauchySeq_tendsto :
 #align emetric.complete_of_cauchy_seq_tendsto EMetric.complete_of_cauchySeq_tendsto
 
 /-- Expressing locally uniform convergence on a set using `edist`. -/
-theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
+theorem tendstoLocallyUniformlyOn_iff {ι : Type*} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} {s : Set β} :
     TendstoLocallyUniformlyOn F f p s ↔
       ∀ ε > 0, ∀ x ∈ s, ∃ t ∈ 𝓝[s] x, ∀ᶠ n in p, ∀ y ∈ t, edist (f y) (F n y) < ε := by
@@ -352,7 +352,7 @@ theorem tendstoLocallyUniformlyOn_iff {ι : Type _} [TopologicalSpace β] {F : 
 #align emetric.tendsto_locally_uniformly_on_iff EMetric.tendstoLocallyUniformlyOn_iff
 
 /-- Expressing uniform convergence on a set using `edist`. -/
-theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} {s : Set β} :
+theorem tendstoUniformlyOn_iff {ι : Type*} {F : ι → β → α} {f : β → α} {p : Filter ι} {s : Set β} :
     TendstoUniformlyOn F f p s ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x ∈ s, edist (f x) (F n x) < ε := by
   refine' ⟨fun H ε hε => H _ (edist_mem_uniformity hε), fun H u hu => _⟩
   rcases mem_uniformity_edist.1 hu with ⟨ε, εpos, hε⟩
@@ -360,7 +360,7 @@ theorem tendstoUniformlyOn_iff {ι : Type _} {F : ι → β → α} {f : β →
 #align emetric.tendsto_uniformly_on_iff EMetric.tendstoUniformlyOn_iff
 
 /-- Expressing locally uniform convergence using `edist`. -/
-theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
+theorem tendstoLocallyUniformly_iff {ι : Type*} [TopologicalSpace β] {F : ι → β → α} {f : β → α}
     {p : Filter ι} :
     TendstoLocallyUniformly F f p ↔
       ∀ ε > 0, ∀ x : β, ∃ t ∈ 𝓝 x, ∀ᶠ n in p, ∀ y ∈ t, edist (f y) (F n y) < ε := by
@@ -369,7 +369,7 @@ theorem tendstoLocallyUniformly_iff {ι : Type _} [TopologicalSpace β] {F : ι
 #align emetric.tendsto_locally_uniformly_iff EMetric.tendstoLocallyUniformly_iff
 
 /-- Expressing uniform convergence using `edist`. -/
-theorem tendstoUniformly_iff {ι : Type _} {F : ι → β → α} {f : β → α} {p : Filter ι} :
+theorem tendstoUniformly_iff {ι : Type*} {F : ι → β → α} {f : β → α} {p : Filter ι} :
     TendstoUniformly F f p ↔ ∀ ε > 0, ∀ᶠ n in p, ∀ x, edist (f x) (F n x) < ε := by
   simp only [← tendstoUniformlyOn_univ, tendstoUniformlyOn_iff, mem_univ, forall_const]
 #align emetric.tendsto_uniformly_iff EMetric.tendstoUniformly_iff
@@ -406,7 +406,7 @@ def PseudoEMetricSpace.induced {α β} (f : α → β) (m : PseudoEMetricSpace 
 #align pseudo_emetric_space.induced PseudoEMetricSpace.induced
 
 /-- Pseudoemetric space instance on subsets of pseudoemetric spaces -/
-instance {α : Type _} {p : α → Prop} [PseudoEMetricSpace α] : PseudoEMetricSpace (Subtype p) :=
+instance {α : Type*} {p : α → Prop} [PseudoEMetricSpace α] : PseudoEMetricSpace (Subtype p) :=
   PseudoEMetricSpace.induced Subtype.val ‹_›
 
 /-- The extended pseudodistance on a subset of a pseudoemetric space is the restriction of
@@ -418,7 +418,7 @@ namespace MulOpposite
 
 /-- Pseudoemetric space instance on the multiplicative opposite of a pseudoemetric space. -/
 @[to_additive "Pseudoemetric space instance on the additive opposite of a pseudoemetric space."]
-instance {α : Type _} [PseudoEMetricSpace α] : PseudoEMetricSpace αᵐᵒᵖ :=
+instance {α : Type*} [PseudoEMetricSpace α] : PseudoEMetricSpace αᵐᵒᵖ :=
   PseudoEMetricSpace.induced unop ‹_›
 
 @[to_additive]
@@ -470,7 +470,7 @@ section Pi
 
 open Finset
 
-variable {π : β → Type _} [Fintype β]
+variable {π : β → Type*} [Fintype β]
 
 -- porting note: reordered instances
 instance [∀ b, EDist (π b)] : EDist (∀ b, π b) where
@@ -918,7 +918,7 @@ theorem diam_singleton : diam ({x} : Set α) = 0 :=
   diam_subsingleton subsingleton_singleton
 #align emetric.diam_singleton EMetric.diam_singleton
 
-theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
+theorem diam_iUnion_mem_option {ι : Type*} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp
 #align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_option
 
@@ -982,7 +982,7 @@ theorem diam_ball {r : ℝ≥0∞} : diam (ball x r) ≤ 2 * r :=
   le_trans (diam_mono ball_subset_closedBall) diam_closedBall
 #align emetric.diam_ball EMetric.diam_ball
 
-theorem diam_pi_le_of_le {π : β → Type _} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
+theorem diam_pi_le_of_le {π : β → Type*} [Fintype β] [∀ b, PseudoEMetricSpace (π b)]
     {s : ∀ b : β, Set (π b)} {c : ℝ≥0∞} (h : ∀ b, diam (s b) ≤ c) : diam (Set.pi univ s) ≤ c := by
   refine diam_le fun x hx y hy => edist_pi_le_iff.mpr ?_
   rw [mem_univ_pi] at hx hy
@@ -1044,7 +1044,7 @@ theorem EMetric.uniformEmbedding_iff' [EMetricSpace β] {f : γ → β} :
 
 /-- If a `PseudoEMetricSpace` is a T₀ space, then it is an `EMetricSpace`. -/
 @[reducible] -- porting note: made `reducible`; todo: make it an instance?
-def EMetricSpace.ofT0PseudoEMetricSpace (α : Type _) [PseudoEMetricSpace α] [T0Space α] :
+def EMetricSpace.ofT0PseudoEMetricSpace (α : Type*) [PseudoEMetricSpace α] [T0Space α] :
     EMetricSpace α :=
   { ‹PseudoEMetricSpace α› with
     eq_of_edist_eq_zero := fun h => (EMetric.inseparable_iff.2 h).eq }
@@ -1075,15 +1075,15 @@ def EMetricSpace.induced {γ β} (f : γ → β) (hf : Function.Injective f) (m
 #align emetric_space.induced EMetricSpace.induced
 
 /-- EMetric space instance on subsets of emetric spaces -/
-instance {α : Type _} {p : α → Prop} [EMetricSpace α] : EMetricSpace (Subtype p) :=
+instance {α : Type*} {p : α → Prop} [EMetricSpace α] : EMetricSpace (Subtype p) :=
   EMetricSpace.induced Subtype.val Subtype.coe_injective ‹_›
 
 /-- EMetric space instance on the multiplicative opposite of an emetric space. -/
 @[to_additive "EMetric space instance on the additive opposite of an emetric space."]
-instance {α : Type _} [EMetricSpace α] : EMetricSpace αᵐᵒᵖ :=
+instance {α : Type*} [EMetricSpace α] : EMetricSpace αᵐᵒᵖ :=
   EMetricSpace.induced MulOpposite.unop MulOpposite.unop_injective ‹_›
 
-instance {α : Type _} [EMetricSpace α] : EMetricSpace (ULift α) :=
+instance {α : Type*} [EMetricSpace α] : EMetricSpace (ULift α) :=
   EMetricSpace.induced ULift.down ULift.down_injective ‹_›
 
 /-- The product of two emetric spaces, with the max distance, is an extended
@@ -1102,7 +1102,7 @@ section Pi
 
 open Finset
 
-variable {π : β → Type _} [Fintype β]
+variable {π : β → Type*} [Fintype β]
 
 /-- The product of a finite number of emetric spaces, with the max distance, is still
 an emetric space.

Per https://github.com/leanprover/lean4/issues/2343, we are going to need to change the automatic generation of instance names, as they become too long.

This PR ensures that everywhere in Mathlib that refers to an instance by name, that name is given explicitly, rather than being automatically generated.

There are four exceptions, which are now commented, with links to https://github.com/leanprover/lean4/issues/2343.

This was implemented by running Mathlib against a modified Lean that appended _ᾰ to all automatically generated names, and fixing everything.

Co-authored-by: Scott Morrison <scott.morrison@gmail.com>

@@ -272,7 +272,7 @@ theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : { p : α × α |
 
 namespace EMetric
 
-instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
+instance (priority := 900) instIsCountablyGeneratedUniformity : IsCountablyGenerated (𝓤 α) :=
   isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
 -- porting note: changed explicit/implicit

• depends on: #5966

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

@@ -2,11 +2,6 @@
 Copyright (c) 2015, 2017 Jeremy Avigad. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Jeremy Avigad, Robert Y. Lewis, Johannes Hölzl, Mario Carneiro, Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module topology.metric_space.emetric_space
-! leanprover-community/mathlib commit 195fcd60ff2bfe392543bceb0ec2adcdb472db4c
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Data.Nat.Interval
 import Mathlib.Data.Real.ENNReal
@@ -14,6 +9,8 @@ import Mathlib.Topology.UniformSpace.Pi
 import Mathlib.Topology.UniformSpace.UniformConvergence
 import Mathlib.Topology.UniformSpace.UniformEmbedding
 
+#align_import topology.metric_space.emetric_space from "leanprover-community/mathlib"@"195fcd60ff2bfe392543bceb0ec2adcdb472db4c"
+
 /-!
 # Extended metric spaces
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -517,8 +517,8 @@ instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetric
   uniformity_edist := by
     simp only [Pi.uniformity, PseudoEMetricSpace.uniformity_edist, comap_iInf, gt_iff_lt,
       preimage_setOf_eq, comap_principal, edist_pi_def]
-    rw [iInf_comm]; congr ; funext ε
-    rw [iInf_comm]; congr ; funext εpos
+    rw [iInf_comm]; congr; funext ε
+    rw [iInf_comm]; congr; funext εpos
     simp [setOf_forall, εpos]
 #align pseudo_emetric_space_pi pseudoEMetricSpacePi
 

@@ -860,7 +860,7 @@ theorem secondCountable_of_sigmaCompact [SigmaCompactSpace α] : SecondCountable
 variable {α}
 
 theorem secondCountable_of_almost_dense_set
-    (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ (⋃ x ∈ t, closedBall x ε) = univ) :
+    (hs : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ ⋃ x ∈ t, closedBall x ε = univ) :
     SecondCountableTopology α := by
   suffices SeparableSpace α from UniformSpace.secondCountable_of_separable α
   have : ∀ ε > 0, ∃ t : Set α, Set.Countable t ∧ univ ⊆ ⋃ x ∈ t, closedBall x ε

@@ -119,6 +119,11 @@ theorem edist_congr_left {x y z : α} (h : edist x y = 0) : edist z x = edist z
   apply edist_congr_right h
 #align edist_congr_left edist_congr_left
 
+-- new theorem
+theorem edist_congr {w x y z : α} (hl : edist w x = 0) (hr : edist y z = 0) :
+    edist w y = edist x z :=
+  (edist_congr_right hl).trans (edist_congr_left hr)
+
 theorem edist_triangle4 (x y z t : α) : edist x t ≤ edist x y + edist y z + edist z t :=
   calc
     edist x t ≤ edist x z + edist z t := edist_triangle x z t
@@ -1146,11 +1151,10 @@ end EMetric
 -/
 
 instance [PseudoEMetricSpace X] : EDist (UniformSpace.SeparationQuotient X) where
-  edist x y := Quotient.liftOn₂' x y edist fun x y x' y' hx hy =>
-    calc edist x y = edist x' y := edist_congr_right $
-      EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx
-    _ = edist x' y' := edist_congr_left $
-      EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy
+  edist x y := Quotient.liftOn₂' x y edist fun _ _ _ _ hx hy =>
+    edist_congr
+      (EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hx)
+      (EMetric.inseparable_iff.1 <| separationRel_iff_inseparable.1 hy)
 
 @[simp] theorem UniformSpace.SeparationQuotient.edist_mk [PseudoEMetricSpace X] (x y : X) :
     @edist (UniformSpace.SeparationQuotient X) _ (Quot.mk _ x) (Quot.mk _ y) = edist x y :=

Part 3 of #5001

@@ -1065,7 +1065,7 @@ def EMetricSpace.replaceUniformity {γ} [U : UniformSpace γ] (m : EMetricSpace
   uniformity_edist := H.trans (@PseudoEMetricSpace.uniformity_edist γ _)
 #align emetric_space.replace_uniformity EMetricSpace.replaceUniformity
 
-/-- The extended metric induced by an injective function taking values in a emetric space. -/
+/-- The extended metric induced by an injective function taking values in an emetric space. -/
 def EMetricSpace.induced {γ β} (f : γ → β) (hf : Function.Injective f) (m : EMetricSpace β) :
     EMetricSpace γ :=
   { PseudoEMetricSpace.induced f m.toPseudoEMetricSpace with

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -1158,18 +1158,18 @@ instance [PseudoEMetricSpace X] : EDist (UniformSpace.SeparationQuotient X) wher
 #align uniform_space.separation_quotient.edist_mk UniformSpace.SeparationQuotient.edist_mk
 
 instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient X) :=
-@EMetricSpace.ofT0PseudoEMetricSpace (UniformSpace.SeparationQuotient X)
-  { edist_self := fun x => Quotient.inductionOn' x edist_self,
-    edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm,
-    edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle,
-    toUniformSpace := inferInstance,
-    uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans $ iInf_congr $ fun ε =>
-      iInf_congr $ fun _ => congr_arg 𝓟 <| by
-        ext ⟨⟨x⟩, ⟨y⟩⟩
-        refine ⟨?_, fun h => ⟨(x, y), h, rfl⟩⟩
-        rintro ⟨⟨x', y'⟩, h', h⟩
-        simp only [Prod.ext_iff] at h
-        rwa [← h.1, ← h.2] } _
+  @EMetricSpace.ofT0PseudoEMetricSpace (UniformSpace.SeparationQuotient X)
+    { edist_self := fun x => Quotient.inductionOn' x edist_self,
+      edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm,
+      edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle,
+      toUniformSpace := inferInstance,
+      uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans $ iInf_congr $ fun ε =>
+        iInf_congr $ fun _ => congr_arg 𝓟 <| by
+          ext ⟨⟨x⟩, ⟨y⟩⟩
+          refine ⟨?_, fun h => ⟨(x, y), h, rfl⟩⟩
+          rintro ⟨⟨x', y'⟩, h', h⟩
+          simp only [Prod.ext_iff] at h
+          rwa [← h.1, ← h.2] } _
 
 /-!
 ### `Additive`, `Multiplicative`

These are all doc fixes

@@ -407,7 +407,7 @@ def PseudoEMetricSpace.induced {α β} (f : α → β) (m : PseudoEMetricSpace 
 instance {α : Type _} {p : α → Prop} [PseudoEMetricSpace α] : PseudoEMetricSpace (Subtype p) :=
   PseudoEMetricSpace.induced Subtype.val ‹_›
 
-/-- The extended psuedodistance on a subset of a pseudoemetric space is the restriction of
+/-- The extended pseudodistance on a subset of a pseudoemetric space is the restriction of
 the original pseudodistance, by definition -/
 theorem Subtype.edist_eq {p : α → Prop} (x y : Subtype p) : edist x y = edist (x : α) y := rfl
 #align subtype.edist_eq Subtype.edist_eq

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>

@@ -44,7 +44,7 @@ in terms of the elements of the uniformity. -/
 theorem uniformity_dist_of_mem_uniformity [LinearOrder β] {U : Filter (α × α)} (z : β)
     (D : α → α → β) (H : ∀ s, s ∈ U ↔ ∃ ε > z, ∀ {a b : α}, D a b < ε → (a, b) ∈ s) :
     U = ⨅ ε > z, 𝓟 { p : α × α | D p.1 p.2 < ε } :=
-  HasBasis.eq_binfᵢ ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_setOf]⟩
+  HasBasis.eq_biInf ⟨fun s => by simp only [H, subset_def, Prod.forall, mem_setOf]⟩
 #align uniformity_dist_of_mem_uniformity uniformity_dist_of_mem_uniformity
 
 /-- `EDist α` means that `α` is equipped with an extended distance. -/
@@ -271,7 +271,7 @@ theorem edist_mem_uniformity {ε : ℝ≥0∞} (ε0 : 0 < ε) : { p : α × α |
 namespace EMetric
 
 instance (priority := 900) : IsCountablyGenerated (𝓤 α) :=
-  isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_infᵢ⟩
+  isCountablyGenerated_of_seq ⟨_, uniformity_basis_edist_inv_nat.eq_iInf⟩
 
 -- porting note: changed explicit/implicit
 /-- ε-δ characterization of uniform continuity on a set for pseudoemetric spaces -/
@@ -400,7 +400,7 @@ def PseudoEMetricSpace.induced {α β} (f : α → β) (m : PseudoEMetricSpace 
   edist_comm _ _ := edist_comm _ _
   edist_triangle _ _ _ := edist_triangle _ _ _
   toUniformSpace := UniformSpace.comap f m.toUniformSpace
-  uniformity_edist := (uniformity_basis_edist.comap (Prod.map f f)).eq_binfᵢ
+  uniformity_edist := (uniformity_basis_edist.comap (Prod.map f f)).eq_biInf
 #align pseudo_emetric_space.induced PseudoEMetricSpace.induced
 
 /-- Pseudoemetric space instance on subsets of pseudoemetric spaces -/
@@ -455,7 +455,7 @@ instance Prod.pseudoEMetricSpaceMax [PseudoEMetricSpace β] : PseudoEMetricSpace
     max_le (le_trans (edist_triangle _ _ _) (add_le_add (le_max_left _ _) (le_max_left _ _)))
       (le_trans (edist_triangle _ _ _) (add_le_add (le_max_right _ _) (le_max_right _ _)))
   uniformity_edist := uniformity_prod.trans <| by
-    simp [PseudoEMetricSpace.uniformity_edist, ← infᵢ_inf_eq, setOf_and]
+    simp [PseudoEMetricSpace.uniformity_edist, ← iInf_inf_eq, setOf_and]
   toUniformSpace := inferInstance
 #align prod.pseudo_emetric_space_max Prod.pseudoEMetricSpaceMax
 
@@ -510,10 +510,10 @@ instance pseudoEMetricSpacePi [∀ b, PseudoEMetricSpace (π b)] : PseudoEMetric
     (add_le_add (edist_le_pi_edist _ _ _) (edist_le_pi_edist _ _ _))
   toUniformSpace := Pi.uniformSpace _
   uniformity_edist := by
-    simp only [Pi.uniformity, PseudoEMetricSpace.uniformity_edist, comap_infᵢ, gt_iff_lt,
+    simp only [Pi.uniformity, PseudoEMetricSpace.uniformity_edist, comap_iInf, gt_iff_lt,
       preimage_setOf_eq, comap_principal, edist_pi_def]
-    rw [infᵢ_comm]; congr ; funext ε
-    rw [infᵢ_comm]; congr ; funext εpos
+    rw [iInf_comm]; congr ; funext ε
+    rw [iInf_comm]; congr ; funext εpos
     simp [setOf_forall, εpos]
 #align pseudo_emetric_space_pi pseudoEMetricSpacePi
 
@@ -646,7 +646,7 @@ theorem nhdsWithin_basis_closed_eball :
 #align emetric.nhds_within_basis_closed_eball EMetric.nhdsWithin_basis_closed_eball
 
 theorem nhds_eq : 𝓝 x = ⨅ ε > 0, 𝓟 (ball x ε) :=
-  nhds_basis_eball.eq_binfᵢ
+  nhds_basis_eball.eq_biInf
 #align emetric.nhds_eq EMetric.nhds_eq
 
 theorem mem_nhds_iff : s ∈ 𝓝 x ↔ ∃ ε > 0, ball x ε ⊆ s :=
@@ -761,7 +761,7 @@ theorem totallyBounded_iff {s : Set α} :
   ⟨fun H _ε ε0 => H _ (edist_mem_uniformity ε0), fun H _r ru =>
     let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 ru
     let ⟨t, ft, h⟩ := H ε ε0
-    ⟨t, ft, h.trans <| unionᵢ₂_mono fun _ _ _ => hε⟩⟩
+    ⟨t, ft, h.trans <| iUnion₂_mono fun _ _ _ => hε⟩⟩
 #align emetric.totally_bounded_iff EMetric.totallyBounded_iff
 
 theorem totallyBounded_iff' {s : Set α} :
@@ -769,7 +769,7 @@ theorem totallyBounded_iff' {s : Set α} :
   ⟨fun H _ε ε0 => (totallyBounded_iff_subset.1 H) _ (edist_mem_uniformity ε0), fun H _r ru =>
     let ⟨ε, ε0, hε⟩ := mem_uniformity_edist.1 ru
     let ⟨t, _, ft, h⟩ := H ε ε0
-    ⟨t, ft, h.trans <| unionᵢ₂_mono fun _ _ _ => hε⟩⟩
+    ⟨t, ft, h.trans <| iUnion₂_mono fun _ _ _ => hε⟩⟩
 #align emetric.totally_bounded_iff' EMetric.totallyBounded_iff'
 
 section Compact
@@ -795,12 +795,12 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
         _ = r * 2 := (mul_two r).symm
   choose f hfs hf using this
   refine'
-    ⟨⋃ n : ℕ, f n⁻¹ '' T n, unionᵢ_subset fun n => image_subset_iff.2 fun z _ => hfs _ _,
-      countable_unionᵢ fun n => (hTc n).image _, _⟩
+    ⟨⋃ n : ℕ, f n⁻¹ '' T n, iUnion_subset fun n => image_subset_iff.2 fun z _ => hfs _ _,
+      countable_iUnion fun n => (hTc n).image _, _⟩
   refine' fun x hx => mem_closure_iff.2 fun ε ε0 => _
   rcases ENNReal.exists_inv_nat_lt (ENNReal.half_pos ε0.lt.ne').ne' with ⟨n, hn⟩
-  rcases mem_unionᵢ₂.1 (hsT n hx) with ⟨y, hyn, hyx⟩
-  refine' ⟨f n⁻¹ y, mem_unionᵢ.2 ⟨n, mem_image_of_mem _ hyn⟩, _⟩
+  rcases mem_iUnion₂.1 (hsT n hx) with ⟨y, hyn, hyx⟩
+  refine' ⟨f n⁻¹ y, mem_iUnion.2 ⟨n, mem_image_of_mem _ hyn⟩, _⟩
   calc
     edist x (f n⁻¹ y) ≤ (n : ℝ≥0∞)⁻¹ * 2 := hf _ _ ⟨hyx, hx⟩
     _ < ε := ENNReal.mul_lt_of_lt_div hn
@@ -816,7 +816,7 @@ theorem _root_.TopologicalSpace.IsSeparable.separableSpace {s : Set α} (hs : Is
     rcases hs with ⟨t, htc, hst⟩
     refine ⟨t, htc, hst.trans fun x hx => ?_⟩
     rcases mem_closure_iff.1 hx ε ε0 with ⟨y, hyt, hxy⟩
-    exact mem_unionᵢ₂.2 ⟨y, hyt, mem_closedBall.2 hxy.le⟩
+    exact mem_iUnion₂.2 ⟨y, hyt, mem_closedBall.2 hxy.le⟩
   rcases subset_countable_closure_of_almost_dense_set _ this with ⟨t, hts, htc, hst⟩
   lift t to Set s using hts
   refine ⟨⟨t, countable_of_injective_of_countable_image (Subtype.coe_injective.injOn _) htc, ?_⟩⟩
@@ -830,7 +830,7 @@ theorem subset_countable_closure_of_compact {s : Set α} (hs : IsCompact s) :
     ∃ t, t ⊆ s ∧ t.Countable ∧ s ⊆ closure t := by
   refine' subset_countable_closure_of_almost_dense_set s fun ε hε => _
   rcases totallyBounded_iff'.1 hs.totallyBounded ε hε with ⟨t, -, htf, hst⟩
-  exact ⟨t, htf.countable, hst.trans <| unionᵢ₂_mono fun _ _ => ball_subset_closedBall⟩
+  exact ⟨t, htf.countable, hst.trans <| iUnion₂_mono fun _ _ => ball_subset_closedBall⟩
 #align emetric.subset_countable_closure_of_compact EMetric.subset_countable_closure_of_compact
 
 end Compact
@@ -847,9 +847,9 @@ theorem secondCountable_of_sigmaCompact [SigmaCompactSpace α] : SecondCountable
   suffices SeparableSpace α by exact UniformSpace.secondCountable_of_separable α
   choose T _ hTc hsubT using fun n =>
     subset_countable_closure_of_compact (isCompact_compactCovering α n)
-  refine' ⟨⟨⋃ n, T n, countable_unionᵢ hTc, fun x => _⟩⟩
-  rcases unionᵢ_eq_univ_iff.1 (unionᵢ_compactCovering α) x with ⟨n, hn⟩
-  exact closure_mono (subset_unionᵢ _ n) (hsubT _ hn)
+  refine' ⟨⟨⋃ n, T n, countable_iUnion hTc, fun x => _⟩⟩
+  rcases iUnion_eq_univ_iff.1 (iUnion_compactCovering α) x with ⟨n, hn⟩
+  exact closure_mono (subset_iUnion _ n) (hsubT _ hn)
 #align emetric.second_countable_of_sigma_compact EMetric.secondCountable_of_sigmaCompact
 
 variable {α}
@@ -873,10 +873,10 @@ noncomputable def diam (s : Set α) :=
   ⨆ (x ∈ s) (y ∈ s), edist x y
 #align emetric.diam EMetric.diam
 
-theorem diam_eq_supₛ (s : Set α) : diam s = supₛ (image2 edist s s) := supₛ_image2.symm
+theorem diam_eq_sSup (s : Set α) : diam s = sSup (image2 edist s s) := sSup_image2.symm
 
 theorem diam_le_iff {d : ℝ≥0∞} : diam s ≤ d ↔ ∀ x ∈ s, ∀ y ∈ s, edist x y ≤ d := by
-  simp only [diam, supᵢ_le_iff]
+  simp only [diam, iSup_le_iff]
 #align emetric.diam_le_iff EMetric.diam_le_iff
 
 theorem diam_image_le_iff {d : ℝ≥0∞} {f : β → α} {s : Set β} :
@@ -916,22 +916,22 @@ theorem diam_singleton : diam ({x} : Set α) = 0 :=
   diam_subsingleton subsingleton_singleton
 #align emetric.diam_singleton EMetric.diam_singleton
 
-theorem diam_unionᵢ_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
+theorem diam_iUnion_mem_option {ι : Type _} (o : Option ι) (s : ι → Set α) :
     diam (⋃ i ∈ o, s i) = ⨆ i ∈ o, diam (s i) := by cases o <;> simp
-#align emetric.diam_Union_mem_option EMetric.diam_unionᵢ_mem_option
+#align emetric.diam_Union_mem_option EMetric.diam_iUnion_mem_option
 
 theorem diam_insert : diam (insert x s) = max (⨆ y ∈ s, edist x y) (diam s) :=
   eq_of_forall_ge_iff fun d => by
-    simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, supᵢ_le_iff,
+    simp only [diam_le_iff, ball_insert_iff, edist_self, edist_comm x, max_le_iff, iSup_le_iff,
       zero_le, true_and_iff, forall_and, and_self_iff, ← and_assoc]
 #align emetric.diam_insert EMetric.diam_insert
 
 theorem diam_pair : diam ({x, y} : Set α) = edist x y := by
-  simp only [supᵢ_singleton, diam_insert, diam_singleton, ENNReal.max_zero_right]
+  simp only [iSup_singleton, diam_insert, diam_singleton, ENNReal.max_zero_right]
 #align emetric.diam_pair EMetric.diam_pair
 
 theorem diam_triple : diam ({x, y, z} : Set α) = max (max (edist x y) (edist x z)) (edist y z) := by
-  simp only [diam_insert, supᵢ_insert, supᵢ_singleton, diam_singleton, ENNReal.max_zero_right,
+  simp only [diam_insert, iSup_insert, iSup_singleton, diam_singleton, ENNReal.max_zero_right,
     ENNReal.sup_eq_max]
 #align emetric.diam_triple EMetric.diam_triple
 
@@ -1163,8 +1163,8 @@ instance [PseudoEMetricSpace X] : EMetricSpace (UniformSpace.SeparationQuotient
     edist_comm := fun x y => Quotient.inductionOn₂' x y edist_comm,
     edist_triangle := fun x y z => Quotient.inductionOn₃' x y z edist_triangle,
     toUniformSpace := inferInstance,
-    uniformity_edist := (uniformity_basis_edist.map _).eq_binfᵢ.trans $ infᵢ_congr $ fun ε =>
-      infᵢ_congr $ fun _ => congr_arg 𝓟 <| by
+    uniformity_edist := (uniformity_basis_edist.map _).eq_biInf.trans $ iInf_congr $ fun ε =>
+      iInf_congr $ fun _ => congr_arg 𝓟 <| by
         ext ⟨⟨x⟩, ⟨y⟩⟩
         refine ⟨?_, fun h => ⟨(x, y), h, rfl⟩⟩
         rintro ⟨⟨x', y'⟩, h', h⟩

Co-authored-by: Moritz Firsching <firsching@google.com>

@@ -76,7 +76,7 @@ will be filled in by default. There is a default value for the uniformity, that
 in cases of interest, for instance when instantiating a `PseudoEMetricSpace` structure
 on a product.
 
-Continuity of `edist` is proved in `topology.instances.ennreal`
+Continuity of `edist` is proved in `Topology.Instances.ENNReal`
 -/
 class PseudoEMetricSpace (α : Type u) extends EDist α : Type u where
   edist_self : ∀ x : α, edist x x = 0

@@ -806,6 +806,23 @@ theorem subset_countable_closure_of_almost_dense_set (s : Set α)
     _ < ε := ENNReal.mul_lt_of_lt_div hn
 #align emetric.subset_countable_closure_of_almost_dense_set EMetric.subset_countable_closure_of_almost_dense_set
 
+open TopologicalSpace in
+/-- If a set `s` is separable, then the corresponding subtype is separable in a (pseudo extended)
+metric space.  This is not obvious, as the countable set whose closure covers `s` does not need in
+general to be contained in `s`. -/
+theorem _root_.TopologicalSpace.IsSeparable.separableSpace {s : Set α} (hs : IsSeparable s) :
+    SeparableSpace s := by
+  have : ∀ ε > 0, ∃ t : Set α, t.Countable ∧ s ⊆ ⋃ x ∈ t, closedBall x ε := fun ε ε0 => by
+    rcases hs with ⟨t, htc, hst⟩
+    refine ⟨t, htc, hst.trans fun x hx => ?_⟩
+    rcases mem_closure_iff.1 hx ε ε0 with ⟨y, hyt, hxy⟩
+    exact mem_unionᵢ₂.2 ⟨y, hyt, mem_closedBall.2 hxy.le⟩
+  rcases subset_countable_closure_of_almost_dense_set _ this with ⟨t, hts, htc, hst⟩
+  lift t to Set s using hts
+  refine ⟨⟨t, countable_of_injective_of_countable_image (Subtype.coe_injective.injOn _) htc, ?_⟩⟩
+  rwa [inducing_subtype_val.dense_iff, Subtype.forall]
+#align topological_space.is_separable.separable_space TopologicalSpace.IsSeparable.separableSpace
+
 -- porting note: todo: generalize to metrizable spaces
 /-- A compact set in a pseudo emetric space is separable, i.e., it is a subset of the closure of a
 countable set.  -/