topology.metric_space.metric_separated ⟷ Mathlib.Topology.MetricSpace.MetricSeparated

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Topology.MetricSpace.EmetricSpace
+import Topology.EMetricSpace.Basic
 
 #align_import topology.metric_space.metric_separated from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 
@@ -25,7 +25,7 @@ open Emetric Set
 
 noncomputable section
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (r «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (r «expr ≠ » 0) -/
 #print IsMetricSeparated /-
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/

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

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Topology.MetricSpace.EmetricSpace
+import Topology.MetricSpace.EmetricSpace
 
 #align_import topology.metric_space.metric_separated from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
 
@@ -25,7 +25,7 @@ open Emetric Set
 
 noncomputable section
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (r «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (r «expr ≠ » 0) -/
 #print IsMetricSeparated /-
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/

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

@@ -145,7 +145,7 @@ theorem finite_iUnion_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : 
 #align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_iUnion_left_iff
 -/
 
-alias finite_Union_left_iff ↔ _ finite_Union_left
+alias ⟨_, finite_Union_left⟩ := finite_Union_left_iff
 #align is_metric_separated.finite_Union_left IsMetricSeparated.finite_iUnion_left
 
 #print IsMetricSeparated.finite_iUnion_right_iff /-
@@ -163,7 +163,7 @@ theorem finset_iUnion_left_iff {ι : Type _} {I : Finset ι} {s : ι → Set X}
 #align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_iUnion_left_iff
 -/
 
-alias finset_Union_left_iff ↔ _ finset_Union_left
+alias ⟨_, finset_Union_left⟩ := finset_Union_left_iff
 #align is_metric_separated.finset_Union_left IsMetricSeparated.finset_iUnion_left
 
 #print IsMetricSeparated.finset_iUnion_right_iff /-
@@ -174,7 +174,7 @@ theorem finset_iUnion_right_iff {ι : Type _} {I : Finset ι} {s : Set X} {t : 
 #align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_iUnion_right_iff
 -/
 
-alias finset_Union_right_iff ↔ _ finset_Union_right
+alias ⟨_, finset_Union_right⟩ := finset_Union_right_iff
 #align is_metric_separated.finset_Union_right IsMetricSeparated.finset_iUnion_right
 
 end IsMetricSeparated

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.metric_space.metric_separated
-! 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.Topology.MetricSpace.EmetricSpace
 
+#align_import topology.metric_space.metric_separated from "leanprover-community/mathlib"@"f47581155c818e6361af4e4fda60d27d020c226b"
+
 /-!
 # Metric separated pairs of sets
 
@@ -28,7 +25,7 @@ open Emetric Set
 
 noncomputable section
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (r «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (r «expr ≠ » 0) -/
 #print IsMetricSeparated /-
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/

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

@@ -69,14 +69,18 @@ theorem empty_right (s : Set X) : IsMetricSeparated s ∅ :=
 #align is_metric_separated.empty_right IsMetricSeparated.empty_right
 -/
 
+#print IsMetricSeparated.disjoint /-
 protected theorem disjoint (h : IsMetricSeparated s t) : Disjoint s t :=
   let ⟨r, r0, hr⟩ := h
   Set.disjoint_left.mpr fun x hx1 hx2 => r0 <| by simpa using hr x hx1 x hx2
 #align is_metric_separated.disjoint IsMetricSeparated.disjoint
+-/
 
+#print IsMetricSeparated.subset_compl_right /-
 theorem subset_compl_right (h : IsMetricSeparated s t) : s ⊆ tᶜ := fun x hs ht =>
   h.Disjoint.le_bot ⟨hs, ht⟩
 #align is_metric_separated.subset_compl_right IsMetricSeparated.subset_compl_right
+-/
 
 #print IsMetricSeparated.mono /-
 @[mono]
@@ -98,6 +102,7 @@ theorem mono_right {t'} (h' : IsMetricSeparated s t') (ht : t ⊆ t') : IsMetric
 #align is_metric_separated.mono_right IsMetricSeparated.mono_right
 -/
 
+#print IsMetricSeparated.union_left /-
 theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t) :
     IsMetricSeparated (s ∪ s') t :=
   by
@@ -108,24 +113,31 @@ theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t
   · exact fun hx => (min_le_left _ _).trans (hr _ hx _ hy)
   · exact fun hx => (min_le_right _ _).trans (hr' _ hx _ hy)
 #align is_metric_separated.union_left IsMetricSeparated.union_left
+-/
 
+#print IsMetricSeparated.union_left_iff /-
 @[simp]
 theorem union_left_iff {s'} :
     IsMetricSeparated (s ∪ s') t ↔ IsMetricSeparated s t ∧ IsMetricSeparated s' t :=
   ⟨fun h => ⟨h.mono_left (subset_union_left _ _), h.mono_left (subset_union_right _ _)⟩, fun h =>
     h.1.union_left h.2⟩
 #align is_metric_separated.union_left_iff IsMetricSeparated.union_left_iff
+-/
 
+#print IsMetricSeparated.union_right /-
 theorem union_right {t'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s t') :
     IsMetricSeparated s (t ∪ t') :=
   (h.symm.union_left h'.symm).symm
 #align is_metric_separated.union_right IsMetricSeparated.union_right
+-/
 
+#print IsMetricSeparated.union_right_iff /-
 @[simp]
 theorem union_right_iff {t'} :
     IsMetricSeparated s (t ∪ t') ↔ IsMetricSeparated s t ∧ IsMetricSeparated s t' :=
   comm.trans <| union_left_iff.trans <| and_congr comm comm
 #align is_metric_separated.union_right_iff IsMetricSeparated.union_right_iff
+-/
 
 #print IsMetricSeparated.finite_iUnion_left_iff /-
 theorem finite_iUnion_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : ι → Set X}

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

@@ -28,7 +28,7 @@ open Emetric Set
 
 noncomputable section
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (r «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (r «expr ≠ » 0) -/
 #print IsMetricSeparated /-
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/

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

@@ -33,7 +33,7 @@ noncomputable section
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/
 def IsMetricSeparated {X : Type _} [EMetricSpace X] (s t : Set X) :=
-  ∃ (r : _)(_ : r ≠ 0), ∀ x ∈ s, ∀ y ∈ t, r ≤ edist x y
+  ∃ (r : _) (_ : r ≠ 0), ∀ x ∈ s, ∀ y ∈ t, r ≤ edist x y
 #align is_metric_separated IsMetricSeparated
 -/
 
@@ -103,7 +103,7 @@ theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t
   by
   rcases h, h' with ⟨⟨r, r0, hr⟩, ⟨r', r0', hr'⟩⟩
   refine' ⟨min r r', _, fun x hx y hy => hx.elim _ _⟩
-  · rw [← pos_iff_ne_zero] at r0 r0'⊢
+  · rw [← pos_iff_ne_zero] at r0 r0' ⊢
     exact lt_min r0 r0'
   · exact fun hx => (min_le_left _ _).trans (hr _ hx _ hy)
   · exact fun hx => (min_le_right _ _).trans (hr' _ hx _ hy)

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

@@ -69,23 +69,11 @@ theorem empty_right (s : Set X) : IsMetricSeparated s ∅ :=
 #align is_metric_separated.empty_right IsMetricSeparated.empty_right
 -/
 
-/- warning: is_metric_separated.disjoint -> IsMetricSeparated.disjoint is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s t)
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s t)
-Case conversion may be inaccurate. Consider using '#align is_metric_separated.disjoint IsMetricSeparated.disjointₓ'. -/
 protected theorem disjoint (h : IsMetricSeparated s t) : Disjoint s t :=
   let ⟨r, r0, hr⟩ := h
   Set.disjoint_left.mpr fun x hx1 hx2 => r0 <| by simpa using hr x hx1 x hx2
 #align is_metric_separated.disjoint IsMetricSeparated.disjoint
 
-/- warning: is_metric_separated.subset_compl_right -> IsMetricSeparated.subset_compl_right is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) s (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X)) t))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) s (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.instBooleanAlgebraSet.{u1} X)) t))
-Case conversion may be inaccurate. Consider using '#align is_metric_separated.subset_compl_right IsMetricSeparated.subset_compl_rightₓ'. -/
 theorem subset_compl_right (h : IsMetricSeparated s t) : s ⊆ tᶜ := fun x hs ht =>
   h.Disjoint.le_bot ⟨hs, ht⟩
 #align is_metric_separated.subset_compl_right IsMetricSeparated.subset_compl_right
@@ -110,12 +98,6 @@ theorem mono_right {t'} (h' : IsMetricSeparated s t') (ht : t ⊆ t') : IsMetric
 #align is_metric_separated.mono_right IsMetricSeparated.mono_right
 -/
 
-/- warning: is_metric_separated.union_left -> IsMetricSeparated.union_left is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s' t) -> (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) s s') t)
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s' t) -> (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) s s') t)
-Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_left IsMetricSeparated.union_leftₓ'. -/
 theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t) :
     IsMetricSeparated (s ∪ s') t :=
   by
@@ -127,12 +109,6 @@ theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t
   · exact fun hx => (min_le_right _ _).trans (hr' _ hx _ hy)
 #align is_metric_separated.union_left IsMetricSeparated.union_left
 
-/- warning: is_metric_separated.union_left_iff -> IsMetricSeparated.union_left_iff is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) s s') t) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s' t))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) s s') t) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s' t))
-Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_left_iff IsMetricSeparated.union_left_iffₓ'. -/
 @[simp]
 theorem union_left_iff {s'} :
     IsMetricSeparated (s ∪ s') t ↔ IsMetricSeparated s t ∧ IsMetricSeparated s' t :=
@@ -140,23 +116,11 @@ theorem union_left_iff {s'} :
     h.1.union_left h.2⟩
 #align is_metric_separated.union_left_iff IsMetricSeparated.union_left_iff
 
-/- warning: is_metric_separated.union_right -> IsMetricSeparated.union_right is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s t') -> (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) t t'))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s t') -> (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) t t'))
-Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_right IsMetricSeparated.union_rightₓ'. -/
 theorem union_right {t'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s t') :
     IsMetricSeparated s (t ∪ t') :=
   (h.symm.union_left h'.symm).symm
 #align is_metric_separated.union_right IsMetricSeparated.union_right
 
-/- warning: is_metric_separated.union_right_iff -> IsMetricSeparated.union_right_iff is a dubious translation:
-lean 3 declaration is
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) t t')) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s t'))
-but is expected to have type
-  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) t t')) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s t'))
-Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_right_iff IsMetricSeparated.union_right_iffₓ'. -/
 @[simp]
 theorem union_right_iff {t'} :
     IsMetricSeparated s (t ∪ t') ↔ IsMetricSeparated s t ∧ IsMetricSeparated s t' :=

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

@@ -163,46 +163,46 @@ theorem union_right_iff {t'} :
   comm.trans <| union_left_iff.trans <| and_congr comm comm
 #align is_metric_separated.union_right_iff IsMetricSeparated.union_right_iff
 
-#print IsMetricSeparated.finite_unionᵢ_left_iff /-
-theorem finite_unionᵢ_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
+#print IsMetricSeparated.finite_iUnion_left_iff /-
+theorem finite_iUnion_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
     {t : Set X} : IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t :=
   by
   refine' finite.induction_on hI (by simp) fun i I hi _ hI => _
   rw [bUnion_insert, ball_insert_iff, union_left_iff, hI]
-#align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_unionᵢ_left_iff
+#align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_iUnion_left_iff
 -/
 
 alias finite_Union_left_iff ↔ _ finite_Union_left
-#align is_metric_separated.finite_Union_left IsMetricSeparated.finite_unionᵢ_left
+#align is_metric_separated.finite_Union_left IsMetricSeparated.finite_iUnion_left
 
-#print IsMetricSeparated.finite_unionᵢ_right_iff /-
-theorem finite_unionᵢ_right_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : Set X}
+#print IsMetricSeparated.finite_iUnion_right_iff /-
+theorem finite_iUnion_right_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : Set X}
     {t : ι → Set X} : IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) := by
   simpa only [@comm _ _ s] using finite_Union_left_iff hI
-#align is_metric_separated.finite_Union_right_iff IsMetricSeparated.finite_unionᵢ_right_iff
+#align is_metric_separated.finite_Union_right_iff IsMetricSeparated.finite_iUnion_right_iff
 -/
 
-#print IsMetricSeparated.finset_unionᵢ_left_iff /-
+#print IsMetricSeparated.finset_iUnion_left_iff /-
 @[simp]
-theorem finset_unionᵢ_left_iff {ι : Type _} {I : Finset ι} {s : ι → Set X} {t : Set X} :
+theorem finset_iUnion_left_iff {ι : Type _} {I : Finset ι} {s : ι → Set X} {t : Set X} :
     IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t :=
-  finite_unionᵢ_left_iff I.finite_toSet
-#align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_unionᵢ_left_iff
+  finite_iUnion_left_iff I.finite_toSet
+#align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_iUnion_left_iff
 -/
 
 alias finset_Union_left_iff ↔ _ finset_Union_left
-#align is_metric_separated.finset_Union_left IsMetricSeparated.finset_unionᵢ_left
+#align is_metric_separated.finset_Union_left IsMetricSeparated.finset_iUnion_left
 
-#print IsMetricSeparated.finset_unionᵢ_right_iff /-
+#print IsMetricSeparated.finset_iUnion_right_iff /-
 @[simp]
-theorem finset_unionᵢ_right_iff {ι : Type _} {I : Finset ι} {s : Set X} {t : ι → Set X} :
+theorem finset_iUnion_right_iff {ι : Type _} {I : Finset ι} {s : Set X} {t : ι → Set X} :
     IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) :=
-  finite_unionᵢ_right_iff I.finite_toSet
-#align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_unionᵢ_right_iff
+  finite_iUnion_right_iff I.finite_toSet
+#align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_iUnion_right_iff
 -/
 
 alias finset_Union_right_iff ↔ _ finset_Union_right
-#align is_metric_separated.finset_Union_right IsMetricSeparated.finset_unionᵢ_right
+#align is_metric_separated.finset_Union_right IsMetricSeparated.finset_iUnion_right
 
 end IsMetricSeparated
 

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: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.metric_space.metric_separated
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit f47581155c818e6361af4e4fda60d27d020c226b
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Topology.MetricSpace.EmetricSpace
 /-!
 # Metric separated pairs of sets
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the predicate `is_metric_separated`. We say that two sets in an (extended)
 metric space are *metric separated* if the (extended) distance between `x ∈ s` and `y ∈ t` is
 bounded from below by a positive constant.

mathlib commit https://github.com/leanprover-community/mathlib/commit/62e8311c791f02c47451bf14aa2501048e7c2f33

@@ -26,59 +26,93 @@ open Emetric Set
 noncomputable section
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (r «expr ≠ » 0) -/
+#print IsMetricSeparated /-
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/
 def IsMetricSeparated {X : Type _} [EMetricSpace X] (s t : Set X) :=
   ∃ (r : _)(_ : r ≠ 0), ∀ x ∈ s, ∀ y ∈ t, r ≤ edist x y
 #align is_metric_separated IsMetricSeparated
+-/
 
 namespace IsMetricSeparated
 
 variable {X : Type _} [EMetricSpace X] {s t : Set X} {x y : X}
 
+#print IsMetricSeparated.symm /-
 @[symm]
 theorem symm (h : IsMetricSeparated s t) : IsMetricSeparated t s :=
   let ⟨r, r0, hr⟩ := h
   ⟨r, r0, fun y hy x hx => edist_comm x y ▸ hr x hx y hy⟩
 #align is_metric_separated.symm IsMetricSeparated.symm
+-/
 
+#print IsMetricSeparated.comm /-
 theorem comm : IsMetricSeparated s t ↔ IsMetricSeparated t s :=
   ⟨symm, symm⟩
 #align is_metric_separated.comm IsMetricSeparated.comm
+-/
 
+#print IsMetricSeparated.empty_left /-
 @[simp]
 theorem empty_left (s : Set X) : IsMetricSeparated ∅ s :=
   ⟨1, one_ne_zero, fun x => False.elim⟩
 #align is_metric_separated.empty_left IsMetricSeparated.empty_left
+-/
 
+#print IsMetricSeparated.empty_right /-
 @[simp]
 theorem empty_right (s : Set X) : IsMetricSeparated s ∅ :=
   (empty_left s).symm
 #align is_metric_separated.empty_right IsMetricSeparated.empty_right
+-/
 
+/- warning: is_metric_separated.disjoint -> IsMetricSeparated.disjoint is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.completeBooleanAlgebra.{u1} X)))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} X) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X))) s t)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (Disjoint.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} X) (Preorder.toLE.{u1} (Set.{u1} X) (PartialOrder.toPreorder.{u1} (Set.{u1} X) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} X) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} X) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} X) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} X) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} X) (Set.instCompleteBooleanAlgebraSet.{u1} X)))))) s t)
+Case conversion may be inaccurate. Consider using '#align is_metric_separated.disjoint IsMetricSeparated.disjointₓ'. -/
 protected theorem disjoint (h : IsMetricSeparated s t) : Disjoint s t :=
   let ⟨r, r0, hr⟩ := h
   Set.disjoint_left.mpr fun x hx1 hx2 => r0 <| by simpa using hr x hx1 x hx2
 #align is_metric_separated.disjoint IsMetricSeparated.disjoint
 
+/- warning: is_metric_separated.subset_compl_right -> IsMetricSeparated.subset_compl_right is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.hasSubset.{u1} X) s (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.booleanAlgebra.{u1} X)) t))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (HasSubset.Subset.{u1} (Set.{u1} X) (Set.instHasSubsetSet.{u1} X) s (HasCompl.compl.{u1} (Set.{u1} X) (BooleanAlgebra.toHasCompl.{u1} (Set.{u1} X) (Set.instBooleanAlgebraSet.{u1} X)) t))
+Case conversion may be inaccurate. Consider using '#align is_metric_separated.subset_compl_right IsMetricSeparated.subset_compl_rightₓ'. -/
 theorem subset_compl_right (h : IsMetricSeparated s t) : s ⊆ tᶜ := fun x hs ht =>
   h.Disjoint.le_bot ⟨hs, ht⟩
 #align is_metric_separated.subset_compl_right IsMetricSeparated.subset_compl_right
 
+#print IsMetricSeparated.mono /-
 @[mono]
 theorem mono {s' t'} (hs : s ⊆ s') (ht : t ⊆ t') :
     IsMetricSeparated s' t' → IsMetricSeparated s t := fun ⟨r, r0, hr⟩ =>
   ⟨r, r0, fun x hx y hy => hr x (hs hx) y (ht hy)⟩
 #align is_metric_separated.mono IsMetricSeparated.mono
+-/
 
+#print IsMetricSeparated.mono_left /-
 theorem mono_left {s'} (h' : IsMetricSeparated s' t) (hs : s ⊆ s') : IsMetricSeparated s t :=
   h'.mono hs Subset.rfl
 #align is_metric_separated.mono_left IsMetricSeparated.mono_left
+-/
 
+#print IsMetricSeparated.mono_right /-
 theorem mono_right {t'} (h' : IsMetricSeparated s t') (ht : t ⊆ t') : IsMetricSeparated s t :=
   h'.mono Subset.rfl ht
 #align is_metric_separated.mono_right IsMetricSeparated.mono_right
+-/
 
+/- warning: is_metric_separated.union_left -> IsMetricSeparated.union_left is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s' t) -> (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) s s') t)
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s' t) -> (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) s s') t)
+Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_left IsMetricSeparated.union_leftₓ'. -/
 theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t) :
     IsMetricSeparated (s ∪ s') t :=
   by
@@ -90,6 +124,12 @@ theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t
   · exact fun hx => (min_le_right _ _).trans (hr' _ hx _ hy)
 #align is_metric_separated.union_left IsMetricSeparated.union_left
 
+/- warning: is_metric_separated.union_left_iff -> IsMetricSeparated.union_left_iff is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) s s') t) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s' t))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {s' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) s s') t) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s' t))
+Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_left_iff IsMetricSeparated.union_left_iffₓ'. -/
 @[simp]
 theorem union_left_iff {s'} :
     IsMetricSeparated (s ∪ s') t ↔ IsMetricSeparated s t ∧ IsMetricSeparated s' t :=
@@ -97,46 +137,66 @@ theorem union_left_iff {s'} :
     h.1.union_left h.2⟩
 #align is_metric_separated.union_left_iff IsMetricSeparated.union_left_iff
 
+/- warning: is_metric_separated.union_right -> IsMetricSeparated.union_right is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s t') -> (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) t t'))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, (IsMetricSeparated.{u1} X _inst_1 s t) -> (IsMetricSeparated.{u1} X _inst_1 s t') -> (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) t t'))
+Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_right IsMetricSeparated.union_rightₓ'. -/
 theorem union_right {t'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s t') :
     IsMetricSeparated s (t ∪ t') :=
   (h.symm.union_left h'.symm).symm
 #align is_metric_separated.union_right IsMetricSeparated.union_right
 
+/- warning: is_metric_separated.union_right_iff -> IsMetricSeparated.union_right_iff is a dubious translation:
+lean 3 declaration is
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.hasUnion.{u1} X) t t')) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s t'))
+but is expected to have type
+  forall {X : Type.{u1}} [_inst_1 : EMetricSpace.{u1} X] {s : Set.{u1} X} {t : Set.{u1} X} {t' : Set.{u1} X}, Iff (IsMetricSeparated.{u1} X _inst_1 s (Union.union.{u1} (Set.{u1} X) (Set.instUnionSet.{u1} X) t t')) (And (IsMetricSeparated.{u1} X _inst_1 s t) (IsMetricSeparated.{u1} X _inst_1 s t'))
+Case conversion may be inaccurate. Consider using '#align is_metric_separated.union_right_iff IsMetricSeparated.union_right_iffₓ'. -/
 @[simp]
 theorem union_right_iff {t'} :
     IsMetricSeparated s (t ∪ t') ↔ IsMetricSeparated s t ∧ IsMetricSeparated s t' :=
   comm.trans <| union_left_iff.trans <| and_congr comm comm
 #align is_metric_separated.union_right_iff IsMetricSeparated.union_right_iff
 
+#print IsMetricSeparated.finite_unionᵢ_left_iff /-
 theorem finite_unionᵢ_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
     {t : Set X} : IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t :=
   by
   refine' finite.induction_on hI (by simp) fun i I hi _ hI => _
   rw [bUnion_insert, ball_insert_iff, union_left_iff, hI]
 #align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_unionᵢ_left_iff
+-/
 
 alias finite_Union_left_iff ↔ _ finite_Union_left
 #align is_metric_separated.finite_Union_left IsMetricSeparated.finite_unionᵢ_left
 
+#print IsMetricSeparated.finite_unionᵢ_right_iff /-
 theorem finite_unionᵢ_right_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : Set X}
     {t : ι → Set X} : IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) := by
   simpa only [@comm _ _ s] using finite_Union_left_iff hI
 #align is_metric_separated.finite_Union_right_iff IsMetricSeparated.finite_unionᵢ_right_iff
+-/
 
+#print IsMetricSeparated.finset_unionᵢ_left_iff /-
 @[simp]
 theorem finset_unionᵢ_left_iff {ι : Type _} {I : Finset ι} {s : ι → Set X} {t : Set X} :
     IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t :=
   finite_unionᵢ_left_iff I.finite_toSet
 #align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_unionᵢ_left_iff
+-/
 
 alias finset_Union_left_iff ↔ _ finset_Union_left
 #align is_metric_separated.finset_Union_left IsMetricSeparated.finset_unionᵢ_left
 
+#print IsMetricSeparated.finset_unionᵢ_right_iff /-
 @[simp]
 theorem finset_unionᵢ_right_iff {ι : Type _} {I : Finset ι} {s : Set X} {t : ι → Set X} :
     IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) :=
   finite_unionᵢ_right_iff I.finite_toSet
 #align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_unionᵢ_right_iff
+-/
 
 alias finset_Union_right_iff ↔ _ finset_Union_right
 #align is_metric_separated.finset_Union_right IsMetricSeparated.finset_unionᵢ_right

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

@@ -28,13 +28,13 @@ noncomputable section
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (r «expr ≠ » 0) -/
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/
-def IsMetricSeparated {X : Type _} [EmetricSpace X] (s t : Set X) :=
+def IsMetricSeparated {X : Type _} [EMetricSpace X] (s t : Set X) :=
   ∃ (r : _)(_ : r ≠ 0), ∀ x ∈ s, ∀ y ∈ t, r ≤ edist x y
 #align is_metric_separated IsMetricSeparated
 
 namespace IsMetricSeparated
 
-variable {X : Type _} [EmetricSpace X] {s t : Set X} {x y : X}
+variable {X : Type _} [EMetricSpace X] {s t : Set X} {x y : X}
 
 @[symm]
 theorem symm (h : IsMetricSeparated s t) : IsMetricSeparated t s :=

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

@@ -25,7 +25,7 @@ open Emetric Set
 
 noncomputable section
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (r «expr ≠ » 0) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (r «expr ≠ » 0) -/
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/
 def IsMetricSeparated {X : Type _} [EmetricSpace X] (s t : Set X) :=

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: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module topology.metric_space.metric_separated
-! leanprover-community/mathlib commit 6ca1a09bc9aa75824bf97388c9e3b441fc4ccf3f
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -48,7 +48,7 @@ theorem comm : IsMetricSeparated s t ↔ IsMetricSeparated t s :=
 
 @[simp]
 theorem empty_left (s : Set X) : IsMetricSeparated ∅ s :=
-  ⟨1, ENNReal.zero_lt_one.ne', fun x => False.elim⟩
+  ⟨1, one_ne_zero, fun x => False.elim⟩
 #align is_metric_separated.empty_left IsMetricSeparated.empty_left
 
 @[simp]

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

@@ -48,7 +48,7 @@ theorem comm : IsMetricSeparated s t ↔ IsMetricSeparated t s :=
 
 @[simp]
 theorem empty_left (s : Set X) : IsMetricSeparated ∅ s :=
-  ⟨1, Ennreal.zero_lt_one.ne', fun x => False.elim⟩
+  ⟨1, ENNReal.zero_lt_one.ne', fun x => False.elim⟩
 #align is_metric_separated.empty_left IsMetricSeparated.empty_left
 
 @[simp]

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

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>

@@ -106,7 +106,7 @@ theorem union_right_iff {t'} :
 theorem finite_iUnion_left_iff {ι : Type*} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
     {t : Set X} : IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t := by
   refine' Finite.induction_on hI (by simp) @fun i I _ _ hI => _
-  rw [biUnion_insert, ball_insert_iff, union_left_iff, hI]
+  rw [biUnion_insert, forall_mem_insert, union_left_iff, hI]
 #align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_iUnion_left_iff
 
 alias ⟨_, finite_iUnion_left⟩ := finite_iUnion_left_iff

Later I'm going to split files like Lipschitz into 2: one in EMetricSpace/ and one in MetricSpace/.

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathlib.Topology.MetricSpace.EMetricSpace
+import Mathlib.Topology.EMetricSpace.Basic
 
 #align_import topology.metric_space.metric_separated from "leanprover-community/mathlib"@"57ac39bd365c2f80589a700f9fbb664d3a1a30c2"
 

@@ -109,7 +109,7 @@ theorem finite_iUnion_left_iff {ι : Type*} {I : Set ι} (hI : I.Finite) {s : ι
   rw [biUnion_insert, ball_insert_iff, union_left_iff, hI]
 #align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_iUnion_left_iff
 
-alias finite_iUnion_left_iff ↔ _ finite_iUnion_left
+alias ⟨_, finite_iUnion_left⟩ := finite_iUnion_left_iff
 #align is_metric_separated.finite_Union_left IsMetricSeparated.finite_iUnion_left
 
 theorem finite_iUnion_right_iff {ι : Type*} {I : Set ι} (hI : I.Finite) {s : Set X}
@@ -123,7 +123,7 @@ theorem finset_iUnion_left_iff {ι : Type*} {I : Finset ι} {s : ι → Set X} {
   finite_iUnion_left_iff I.finite_toSet
 #align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_iUnion_left_iff
 
-alias finset_iUnion_left_iff ↔ _ finset_iUnion_left
+alias ⟨_, finset_iUnion_left⟩ := finset_iUnion_left_iff
 #align is_metric_separated.finset_Union_left IsMetricSeparated.finset_iUnion_left
 
 @[simp]
@@ -132,7 +132,7 @@ theorem finset_iUnion_right_iff {ι : Type*} {I : Finset ι} {s : Set X} {t : ι
   finite_iUnion_right_iff I.finite_toSet
 #align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_iUnion_right_iff
 
-alias finset_iUnion_right_iff ↔ _ finset_iUnion_right
+alias ⟨_, finset_iUnion_right⟩ := finset_iUnion_right_iff
 #align is_metric_separated.finset_Union_right IsMetricSeparated.finset_iUnion_right
 
 end IsMetricSeparated

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

This has nice performance benefits.

@@ -24,13 +24,13 @@ noncomputable section
 
 /-- Two sets in an (extended) metric space are called *metric separated* if the (extended) distance
 between `x ∈ s` and `y ∈ t` is bounded from below by a positive constant. -/
-def IsMetricSeparated {X : Type _} [EMetricSpace X] (s t : Set X) :=
+def IsMetricSeparated {X : Type*} [EMetricSpace X] (s t : Set X) :=
   ∃ r, r ≠ 0 ∧ ∀ x ∈ s, ∀ y ∈ t, r ≤ edist x y
 #align is_metric_separated IsMetricSeparated
 
 namespace IsMetricSeparated
 
-variable {X : Type _} [EMetricSpace X] {s t : Set X} {x y : X}
+variable {X : Type*} [EMetricSpace X] {s t : Set X} {x y : X}
 
 @[symm]
 theorem symm (h : IsMetricSeparated s t) : IsMetricSeparated t s :=
@@ -103,7 +103,7 @@ theorem union_right_iff {t'} :
   comm.trans <| union_left_iff.trans <| and_congr comm comm
 #align is_metric_separated.union_right_iff IsMetricSeparated.union_right_iff
 
-theorem finite_iUnion_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
+theorem finite_iUnion_left_iff {ι : Type*} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
     {t : Set X} : IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t := by
   refine' Finite.induction_on hI (by simp) @fun i I _ _ hI => _
   rw [biUnion_insert, ball_insert_iff, union_left_iff, hI]
@@ -112,13 +112,13 @@ theorem finite_iUnion_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : 
 alias finite_iUnion_left_iff ↔ _ finite_iUnion_left
 #align is_metric_separated.finite_Union_left IsMetricSeparated.finite_iUnion_left
 
-theorem finite_iUnion_right_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : Set X}
+theorem finite_iUnion_right_iff {ι : Type*} {I : Set ι} (hI : I.Finite) {s : Set X}
     {t : ι → Set X} : IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) := by
   simpa only [@comm _ _ s] using finite_iUnion_left_iff hI
 #align is_metric_separated.finite_Union_right_iff IsMetricSeparated.finite_iUnion_right_iff
 
 @[simp]
-theorem finset_iUnion_left_iff {ι : Type _} {I : Finset ι} {s : ι → Set X} {t : Set X} :
+theorem finset_iUnion_left_iff {ι : Type*} {I : Finset ι} {s : ι → Set X} {t : Set X} :
     IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t :=
   finite_iUnion_left_iff I.finite_toSet
 #align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_iUnion_left_iff
@@ -127,7 +127,7 @@ alias finset_iUnion_left_iff ↔ _ finset_iUnion_left
 #align is_metric_separated.finset_Union_left IsMetricSeparated.finset_iUnion_left
 
 @[simp]
-theorem finset_iUnion_right_iff {ι : Type _} {I : Finset ι} {s : Set X} {t : ι → Set X} :
+theorem finset_iUnion_right_iff {ι : Type*} {I : Finset ι} {s : Set X} {t : ι → Set X} :
     IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) :=
   finite_iUnion_right_iff I.finite_toSet
 #align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_iUnion_right_iff

• depends on: #5966

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

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module topology.metric_space.metric_separated
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.MetricSpace.EMetricSpace
 
+#align_import topology.metric_space.metric_separated from "leanprover-community/mathlib"@"57ac39bd365c2f80589a700f9fbb664d3a1a30c2"
+
 /-!
 # Metric separated pairs of sets
 

Changes are of the form

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

@@ -82,7 +82,7 @@ theorem union_left {s'} (h : IsMetricSeparated s t) (h' : IsMetricSeparated s' t
     IsMetricSeparated (s ∪ s') t := by
   rcases h, h' with ⟨⟨r, r0, hr⟩, ⟨r', r0', hr'⟩⟩
   refine' ⟨min r r', _, fun x hx y hy => hx.elim _ _⟩
-  · rw [← pos_iff_ne_zero] at r0 r0'⊢
+  · rw [← pos_iff_ne_zero] at r0 r0' ⊢
     exact lt_min r0 r0'
   · exact fun hx => (min_le_left _ _).trans (hr _ hx _ hy)
   · exact fun hx => (min_le_right _ _).trans (hr' _ hx _ hy)

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>

@@ -106,36 +106,36 @@ theorem union_right_iff {t'} :
   comm.trans <| union_left_iff.trans <| and_congr comm comm
 #align is_metric_separated.union_right_iff IsMetricSeparated.union_right_iff
 
-theorem finite_unionᵢ_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
+theorem finite_iUnion_left_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : ι → Set X}
     {t : Set X} : IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t := by
   refine' Finite.induction_on hI (by simp) @fun i I _ _ hI => _
-  rw [bunionᵢ_insert, ball_insert_iff, union_left_iff, hI]
-#align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_unionᵢ_left_iff
+  rw [biUnion_insert, ball_insert_iff, union_left_iff, hI]
+#align is_metric_separated.finite_Union_left_iff IsMetricSeparated.finite_iUnion_left_iff
 
-alias finite_unionᵢ_left_iff ↔ _ finite_unionᵢ_left
-#align is_metric_separated.finite_Union_left IsMetricSeparated.finite_unionᵢ_left
+alias finite_iUnion_left_iff ↔ _ finite_iUnion_left
+#align is_metric_separated.finite_Union_left IsMetricSeparated.finite_iUnion_left
 
-theorem finite_unionᵢ_right_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : Set X}
+theorem finite_iUnion_right_iff {ι : Type _} {I : Set ι} (hI : I.Finite) {s : Set X}
     {t : ι → Set X} : IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) := by
-  simpa only [@comm _ _ s] using finite_unionᵢ_left_iff hI
-#align is_metric_separated.finite_Union_right_iff IsMetricSeparated.finite_unionᵢ_right_iff
+  simpa only [@comm _ _ s] using finite_iUnion_left_iff hI
+#align is_metric_separated.finite_Union_right_iff IsMetricSeparated.finite_iUnion_right_iff
 
 @[simp]
-theorem finset_unionᵢ_left_iff {ι : Type _} {I : Finset ι} {s : ι → Set X} {t : Set X} :
+theorem finset_iUnion_left_iff {ι : Type _} {I : Finset ι} {s : ι → Set X} {t : Set X} :
     IsMetricSeparated (⋃ i ∈ I, s i) t ↔ ∀ i ∈ I, IsMetricSeparated (s i) t :=
-  finite_unionᵢ_left_iff I.finite_toSet
-#align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_unionᵢ_left_iff
+  finite_iUnion_left_iff I.finite_toSet
+#align is_metric_separated.finset_Union_left_iff IsMetricSeparated.finset_iUnion_left_iff
 
-alias finset_unionᵢ_left_iff ↔ _ finset_unionᵢ_left
-#align is_metric_separated.finset_Union_left IsMetricSeparated.finset_unionᵢ_left
+alias finset_iUnion_left_iff ↔ _ finset_iUnion_left
+#align is_metric_separated.finset_Union_left IsMetricSeparated.finset_iUnion_left
 
 @[simp]
-theorem finset_unionᵢ_right_iff {ι : Type _} {I : Finset ι} {s : Set X} {t : ι → Set X} :
+theorem finset_iUnion_right_iff {ι : Type _} {I : Finset ι} {s : Set X} {t : ι → Set X} :
     IsMetricSeparated s (⋃ i ∈ I, t i) ↔ ∀ i ∈ I, IsMetricSeparated s (t i) :=
-  finite_unionᵢ_right_iff I.finite_toSet
-#align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_unionᵢ_right_iff
+  finite_iUnion_right_iff I.finite_toSet
+#align is_metric_separated.finset_Union_right_iff IsMetricSeparated.finset_iUnion_right_iff
 
-alias finset_unionᵢ_right_iff ↔ _ finset_unionᵢ_right
-#align is_metric_separated.finset_Union_right IsMetricSeparated.finset_unionᵢ_right
+alias finset_iUnion_right_iff ↔ _ finset_iUnion_right
+#align is_metric_separated.finset_Union_right IsMetricSeparated.finset_iUnion_right
 
 end IsMetricSeparated

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