measure_theory.covering.vitali ⟷ Mathlib.MeasureTheory.Covering.Vitali

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

@@ -47,7 +47,7 @@ open scoped NNReal Classical ENNReal Topology
 
 namespace Vitali
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_subfamily_covering_enlargment /-
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
@@ -167,7 +167,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall /-
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
@@ -209,8 +209,8 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t') -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (u «expr ⊆ » t') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_covering_ae /-
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
 nonempty interior, such that each `a ∈ t` is included in a ball `B (x, r)` and covers a definite

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

@@ -106,7 +106,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     by
     intro c hc
     by_contra
-    rw [not_disjoint_iff_nonempty_inter] at h 
+    rw [not_disjoint_iff_nonempty_inter] at h
     obtain ⟨d, du, ad, hd⟩ : ∃ (d : ι) (H : d ∈ u), (B a ∩ B d).Nonempty ∧ δ a ≤ τ * δ d :=
       uT.2.2 a hat c hc h
     exact lt_irrefl _ ((hu d du ad).trans_le hd)
@@ -154,15 +154,15 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     -- otherwise, `c` belongs to `A`. The element of `u ∪ {a'}` that it intersects has to be `a'`.
     -- moreover, `δ c` is smaller than the maximum `m` of `δ` over `A`, which is `≤ δ a' / τ`
     -- thanks to the good choice of `a'`. This is the desired inequality.
-    · push_neg at H 
-      simp only [← not_disjoint_iff_nonempty_inter, Classical.not_not] at H 
+    · push_neg at H
+      simp only [← not_disjoint_iff_nonempty_inter, Classical.not_not] at H
       rcases mem_insert_iff.1 ba'u with (rfl | H')
       · refine' ⟨b, mem_insert _ _, hcb, _⟩
         calc
           δ c ≤ m := le_csSup bddA (mem_image_of_mem _ ⟨ct, H⟩)
           _ = τ * (m / τ) := by field_simp [(zero_lt_one.trans hτ).ne']; ring
           _ ≤ τ * δ b := mul_le_mul_of_nonneg_left ha' (zero_le_one.trans hτ.le)
-      · rw [← not_disjoint_iff_nonempty_inter] at hcb 
+      · rw [← not_disjoint_iff_nonempty_inter] at hcb
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 -/
@@ -186,7 +186,7 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
       ⟨t, subset.rfl, fun a ha b hb hab => by
         simp only [Function.onFun, closed_ball_eq_empty.2 (ht a ha), empty_disjoint], fun a ha =>
         ⟨a, ha, by simp only [closed_ball_eq_empty.2 (ht a ha), empty_subset]⟩⟩
-  push_neg at ht 
+  push_neg at ht
   let t' := {a ∈ t | 0 ≤ r a}
   rcases exists_disjoint_subfamily_covering_enlargment (fun a => closed_ball (x a) (r a)) t' r 2
       one_lt_two (fun a ha => ha.2) R (fun a ha => hr a ha.1) fun a ha =>
@@ -315,8 +315,8 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     · have R0pos : 0 < R0 := (hR0 x).trans_le H
       have vnonempty : v.nonempty := by
         by_contra
-        rw [nonempty_iff_ne_empty, Classical.not_not] at h 
-        simp only [h, Real.sSup_empty, image_empty] at R0_def 
+        rw [nonempty_iff_ne_empty, Classical.not_not] at h
+        simp only [h, Real.sSup_empty, image_empty] at R0_def
         exact lt_irrefl _ (R0pos.trans_le (le_of_eq R0_def))
       obtain ⟨a, hav, R0a⟩ : ∃ a ∈ v, R0 / 2 < r a :=
         by

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

@@ -3,9 +3,9 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathbin.Topology.MetricSpace.Basic
-import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
-import Mathbin.MeasureTheory.Covering.VitaliFamily
+import Topology.MetricSpace.Basic
+import MeasureTheory.Constructions.BorelSpace.Basic
+import MeasureTheory.Covering.VitaliFamily
 
 #align_import measure_theory.covering.vitali from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
 
@@ -47,7 +47,7 @@ open scoped NNReal Classical ENNReal Topology
 
 namespace Vitali
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_subfamily_covering_enlargment /-
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
@@ -167,7 +167,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall /-
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
@@ -209,8 +209,8 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t') -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_covering_ae /-
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
 nonempty interior, such that each `a ∈ t` is included in a ball `B (x, r)` and covers a definite

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

@@ -361,7 +361,8 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     by
     intro z hz
     set k := ⋃ (a : v) (ha : a ∈ w), B a with hk
-    have k_closed : IsClosed k := isClosed_biUnion w.finite_to_set fun i hi => h't _ (ut (vu i.2))
+    have k_closed : IsClosed k :=
+      Set.Finite.isClosed_biUnion w.finite_to_set fun i hi => h't _ (ut (vu i.2))
     have z_notmem_k : z ∉ k :=
       by
       simp only [not_exists, exists_prop, mem_Union, mem_sep_iff, forall_exists_index,

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.covering.vitali
-! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Topology.MetricSpace.Basic
 import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathbin.MeasureTheory.Covering.VitaliFamily
 
+#align_import measure_theory.covering.vitali from "leanprover-community/mathlib"@"38df578a6450a8c5142b3727e3ae894c2300cae0"
+
 /-!
 # Vitali covering theorems
 
@@ -50,7 +47,7 @@ open scoped NNReal Classical ENNReal Topology
 
 namespace Vitali
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_subfamily_covering_enlargment /-
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
@@ -170,7 +167,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall /-
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
@@ -212,8 +209,8 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t') -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 #print Vitali.exists_disjoint_covering_ae /-
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
 nonempty interior, such that each `a ∈ t` is included in a ball `B (x, r)` and covers a definite

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

@@ -51,6 +51,7 @@ open scoped NNReal Classical ENNReal Topology
 namespace Vitali
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+#print Vitali.exists_disjoint_subfamily_covering_enlargment /-
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
 is any fixed number.
@@ -167,8 +168,10 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
       · rw [← not_disjoint_iff_nonempty_inter] at hcb 
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+#print Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall /-
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
 dilations of balls in `u`. -/
@@ -207,9 +210,11 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
     rcases A b ⟨rb.1, rb.2⟩ with ⟨c, cu, hc⟩
     refine' ⟨c, cu, by simp only [closed_ball_eq_empty.2 h'a, empty_subset]⟩
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t') -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+#print Vitali.exists_disjoint_covering_ae /-
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
 nonempty interior, such that each `a ∈ t` is included in a ball `B (x, r)` and covers a definite
 proportion of the ball `B (x, 3 r)` for a given measure `μ` (think of the situation where `μ` is
@@ -427,7 +432,9 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     _ ≤ C * (ε / C) := (mul_le_mul_left' hw.le _)
     _ ≤ ε := ENNReal.mul_div_le
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae
+-/
 
+#print Vitali.vitaliFamily /-
 /-- Assume that around every point there are arbitrarily small scales at which the measure is
 doubling. Then the set of closed sets `a` with nonempty interior contained in `closed_ball x r` and
 covering a fixed proportion `1/C` of the ball `closed_ball x (3 * r)` forms a Vitali family.
@@ -480,6 +487,7 @@ protected def vitaliFamily [MetricSpace α] [MeasurableSpace α] [OpensMeasurabl
     · convert μt' using 3
       rw [bUnion_image]
 #align vitali.vitali_family Vitali.vitaliFamily
+-/
 
 end Vitali
 

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

@@ -338,9 +338,9 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
       nonpos_iff_eq_zero.mp (le_of_forall_le_of_dense fun ε εpos => _)⟩
   -- the elements of `v` are disjoint and all contained in a finite volume ball, hence the sum
   -- of their measures is finite.
-  have I : (∑' a : v, μ (B a)) < ∞ := by
+  have I : ∑' a : v, μ (B a) < ∞ := by
     calc
-      (∑' a : v, μ (B a)) = μ (⋃ a ∈ v, B a) :=
+      ∑' a : v, μ (B a) = μ (⋃ a ∈ v, B a) :=
         by
         rw [measure_bUnion (u_count.mono vu) _ fun a ha => (h't _ (vu.trans ut ha)).MeasurableSet]
         exact u_disj.subset vu
@@ -348,7 +348,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
       _ < ∞ := μK
   -- we can obtain a finite subfamily of `v`, such that the measures of the remaining elements
   -- add up to an arbitrarily small number, say `ε / C`.
-  obtain ⟨w, hw⟩ : ∃ w : Finset ↥v, (∑' a : { a // a ∉ w }, μ (B a)) < ε / C :=
+  obtain ⟨w, hw⟩ : ∃ w : Finset ↥v, ∑' a : { a // a ∉ w }, μ (B a) < ε / C :=
     haveI : 0 < ε / C := by
       simp only [ENNReal.div_pos_iff, εpos.ne', ENNReal.coe_ne_top, Ne.def, not_false_iff,
         and_self_iff]

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

@@ -164,7 +164,6 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
           δ c ≤ m := le_csSup bddA (mem_image_of_mem _ ⟨ct, H⟩)
           _ = τ * (m / τ) := by field_simp [(zero_lt_one.trans hτ).ne']; ring
           _ ≤ τ * δ b := mul_le_mul_of_nonneg_left ha' (zero_le_one.trans hτ.le)
-          
       · rw [← not_disjoint_iff_nonempty_inter] at hcb 
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
@@ -261,7 +260,6 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
         20 * min 1 (R / 20) ≤ 20 * (R / 20) :=
           mul_le_mul_of_nonneg_left (min_le_right _ _) (by norm_num)
         _ = R := by ring
-        
   choose R hR0 hR1 hRμ
   -- we restrict to a subfamily `t'` of `t`, made of elements small enough to ensure that
   -- they only see a finite part of the measure, and with a doubling property
@@ -348,7 +346,6 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
         exact u_disj.subset vu
       _ ≤ μ (closed_ball x K) := (measure_mono (Union₂_subset fun a ha => hK a (vu ha) ha.2))
       _ < ∞ := μK
-      
   -- we can obtain a finite subfamily of `v`, such that the measures of the remaining elements
   -- add up to an arbitrarily small number, say `ε / C`.
   obtain ⟨w, hw⟩ : ∃ w : Finset ↥v, (∑' a : { a // a ∉ w }, μ (B a)) < ε / C :=
@@ -429,7 +426,6 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     _ = C * ∑' a : { a // a ∉ w }, μ (B a) := ENNReal.tsum_mul_left
     _ ≤ C * (ε / C) := (mul_le_mul_left' hw.le _)
     _ ≤ ε := ENNReal.mul_div_le
-    
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae
 
 /-- Assume that around every point there are arbitrarily small scales at which the measure is

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

@@ -50,7 +50,7 @@ open scoped NNReal Classical ENNReal Topology
 
 namespace Vitali
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
 is any fixed number.
@@ -169,7 +169,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
 dilations of balls in `u`. -/
@@ -209,8 +209,8 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
     refine' ⟨c, cu, by simp only [closed_ball_eq_empty.2 h'a, empty_subset]⟩
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t') -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
 nonempty interior, such that each `a ∈ t` is included in a ball `B (x, r)` and covers a definite
 proportion of the ball `B (x, 3 r)` for a given measure `μ` (think of the situation where `μ` is

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

@@ -83,10 +83,10 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     intersects all elements of `t`, and by definition it satisfies all the desired properties.
     -/
   let T : Set (Set ι) :=
-    { u |
+    {u |
       u ⊆ t ∧
         u.PairwiseDisjoint B ∧
-          ∀ a ∈ t, ∀ b ∈ u, (B a ∩ B b).Nonempty → ∃ c ∈ u, (B a ∩ B c).Nonempty ∧ δ a ≤ τ * δ c }
+          ∀ a ∈ t, ∀ b ∈ u, (B a ∩ B b).Nonempty → ∃ c ∈ u, (B a ∩ B c).Nonempty ∧ δ a ≤ τ * δ c}
   -- By Zorn, choose a maximal family in the good set `T` of disjoint families.
   obtain ⟨u, uT, hu⟩ : ∃ u ∈ T, ∀ v ∈ T, u ⊆ v → v = u :=
     by
@@ -114,7 +114,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     exact lt_irrefl _ ((hu d du ad).trans_le hd)
   -- Let `A` be all the elements of `t` which do not intersect the family `u`. It is nonempty as it
   -- contains `a`. We will pick an element `a'` of `A` with `δ a'` almost as large as possible.
-  let A := { a' | a' ∈ t ∧ ∀ c ∈ u, Disjoint (B a') (B c) }
+  let A := {a' | a' ∈ t ∧ ∀ c ∈ u, Disjoint (B a') (B c)}
   have Anonempty : A.nonempty := ⟨a, hat, a_disj⟩
   let m := Sup (δ '' A)
   have bddA : BddAbove (δ '' A) := by
@@ -156,7 +156,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     -- otherwise, `c` belongs to `A`. The element of `u ∪ {a'}` that it intersects has to be `a'`.
     -- moreover, `δ c` is smaller than the maximum `m` of `δ` over `A`, which is `≤ δ a' / τ`
     -- thanks to the good choice of `a'`. This is the desired inequality.
-    · push_neg  at H 
+    · push_neg at H 
       simp only [← not_disjoint_iff_nonempty_inter, Classical.not_not] at H 
       rcases mem_insert_iff.1 ba'u with (rfl | H')
       · refine' ⟨b, mem_insert _ _, hcb, _⟩
@@ -187,8 +187,8 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
       ⟨t, subset.rfl, fun a ha b hb hab => by
         simp only [Function.onFun, closed_ball_eq_empty.2 (ht a ha), empty_disjoint], fun a ha =>
         ⟨a, ha, by simp only [closed_ball_eq_empty.2 (ht a ha), empty_subset]⟩⟩
-  push_neg  at ht 
-  let t' := { a ∈ t | 0 ≤ r a }
+  push_neg at ht 
+  let t' := {a ∈ t | 0 ≤ r a}
   rcases exists_disjoint_subfamily_covering_enlargment (fun a => closed_ball (x a) (r a)) t' r 2
       one_lt_two (fun a ha => ha.2) R (fun a ha => hr a ha.1) fun a ha =>
       ⟨x a, mem_closed_ball_self ha.2⟩ with
@@ -221,7 +221,7 @@ Then one can extract from `t` a disjoint subfamily that covers almost all `s`.
 For more flexibility, we give a statement with a parameterized family of sets.
 -/
 theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [OpensMeasurableSpace α]
-    [SecondCountableTopology α] (μ : Measure α) [LocallyFiniteMeasure μ] (s : Set α) (t : Set ι)
+    [SecondCountableTopology α] (μ : Measure α) [IsLocallyFiniteMeasure μ] (s : Set α) (t : Set ι)
     (C : ℝ≥0) (r : ι → ℝ) (c : ι → α) (B : ι → Set α) (hB : ∀ a ∈ t, B a ⊆ closedBall (c a) (r a))
     (μB : ∀ a ∈ t, μ (closedBall (c a) (3 * r a)) ≤ C * μ (B a))
     (ht : ∀ a ∈ t, (interior (B a)).Nonempty) (h't : ∀ a ∈ t, IsClosed (B a))
@@ -265,7 +265,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   choose R hR0 hR1 hRμ
   -- we restrict to a subfamily `t'` of `t`, made of elements small enough to ensure that
   -- they only see a finite part of the measure, and with a doubling property
-  let t' := { a ∈ t | r a ≤ R (c a) }
+  let t' := {a ∈ t | r a ≤ R (c a)}
   -- extract a disjoint subfamily `u` of `t'` thanks to the abstract Vitali covering theorem.
   obtain ⟨u, ut', u_disj, hu⟩ :
     ∃ (u : _) (_ : u ⊆ t'),
@@ -287,7 +287,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   -- it suffices to show that it covers almost all `s` locally around each point `x`.
   refine' null_of_locally_null _ fun x hx => _
   -- let `v` be the subfamily of `u` made of those sets intersecting the small ball `ball x (r x)`
-  let v := { a ∈ u | (B a ∩ ball x (R x)).Nonempty }
+  let v := {a ∈ u | (B a ∩ ball x (R x)).Nonempty}
   have vu : v ⊆ u := fun a ha => ha.1
   -- they are all contained in a fixed ball of finite measure, thanks to our choice of `t'`
   obtain ⟨K, μK, hK⟩ :
@@ -437,13 +437,13 @@ doubling. Then the set of closed sets `a` with nonempty interior contained in `c
 covering a fixed proportion `1/C` of the ball `closed_ball x (3 * r)` forms a Vitali family.
 This is essentially a restatement of the measurable Vitali theorem. -/
 protected def vitaliFamily [MetricSpace α] [MeasurableSpace α] [OpensMeasurableSpace α]
-    [SecondCountableTopology α] (μ : Measure α) [LocallyFiniteMeasure μ] (C : ℝ≥0)
+    [SecondCountableTopology α] (μ : Measure α) [IsLocallyFiniteMeasure μ] (C : ℝ≥0)
     (h : ∀ x, ∃ᶠ r in 𝓝[>] 0, μ (closedBall x (3 * r)) ≤ C * μ (closedBall x r)) : VitaliFamily μ
     where
   setsAt x :=
-    { a |
+    {a |
       IsClosed a ∧
-        (interior a).Nonempty ∧ ∃ r, a ⊆ closedBall x r ∧ μ (closedBall x (3 * r)) ≤ C * μ a }
+        (interior a).Nonempty ∧ ∃ r, a ⊆ closedBall x r ∧ μ (closedBall x (3 * r)) ≤ C * μ a}
   MeasurableSet' x a ha := ha.1.MeasurableSet
   nonempty_interior x a ha := ha.2.1
   Nontrivial x ε εpos :=
@@ -457,10 +457,10 @@ protected def vitaliFamily [MetricSpace α] [MeasurableSpace α] [OpensMeasurabl
   covering := by
     intro s f fsubset ffine
     let t : Set (ℝ × α × Set α) :=
-      { p |
+      {p |
         p.2.2 ⊆ closed_ball p.2.1 p.1 ∧
           μ (closed_ball p.2.1 (3 * p.1)) ≤ C * μ p.2.2 ∧
-            (interior p.2.2).Nonempty ∧ IsClosed p.2.2 ∧ p.2.2 ∈ f p.2.1 ∧ p.2.1 ∈ s }
+            (interior p.2.2).Nonempty ∧ IsClosed p.2.2 ∧ p.2.2 ∈ f p.2.1 ∧ p.2.1 ∈ s}
     have A : ∀ x ∈ s, ∀ ε : ℝ, ε > 0 → ∃ (p : ℝ × α × Set α) (Hp : p ∈ t), p.1 ≤ ε ∧ p.2.1 = x :=
       by
       intro x xs ε εpos

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

@@ -66,7 +66,7 @@ wider applicability.
 theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : Set ι) (δ : ι → ℝ)
     (τ : ℝ) (hτ : 1 < τ) (δnonneg : ∀ a ∈ t, 0 ≤ δ a) (R : ℝ) (δle : ∀ a ∈ t, δ a ≤ R)
     (hne : ∀ a ∈ t, (B a).Nonempty) :
-    ∃ (u : _)(_ : u ⊆ t),
+    ∃ (u : _) (_ : u ⊆ t),
       u.PairwiseDisjoint B ∧ ∀ a ∈ t, ∃ b ∈ u, (B a ∩ B b).Nonempty ∧ δ a ≤ τ * δ b :=
   by
   /- The proof could be formulated as a transfinite induction. First pick an element of `t` with `δ`
@@ -97,7 +97,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     refine'
       ⟨fun u hu => (UT hu).1, (pairwise_disjoint_sUnion hU.directed_on).2 fun u hu => (UT hu).2.1,
         fun a hat b u uU hbu hab => _⟩
-    obtain ⟨c, cu, ac, hc⟩ : ∃ (c : ι)(H : c ∈ u), (B a ∩ B c).Nonempty ∧ δ a ≤ τ * δ c :=
+    obtain ⟨c, cu, ac, hc⟩ : ∃ (c : ι) (H : c ∈ u), (B a ∩ B c).Nonempty ∧ δ a ≤ τ * δ c :=
       (UT uU).2.2 a hat b hbu hab
     exact ⟨c, ⟨u, uU, cu⟩, ac, hc⟩
   -- the only nontrivial bit is to check that every `a ∈ t` intersects an element `b ∈ u` with
@@ -108,8 +108,8 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     by
     intro c hc
     by_contra
-    rw [not_disjoint_iff_nonempty_inter] at h
-    obtain ⟨d, du, ad, hd⟩ : ∃ (d : ι)(H : d ∈ u), (B a ∩ B d).Nonempty ∧ δ a ≤ τ * δ d :=
+    rw [not_disjoint_iff_nonempty_inter] at h 
+    obtain ⟨d, du, ad, hd⟩ : ∃ (d : ι) (H : d ∈ u), (B a ∩ B d).Nonempty ∧ δ a ≤ τ * δ d :=
       uT.2.2 a hat c hc h
     exact lt_irrefl _ ((hu d du ad).trans_le hd)
   -- Let `A` be all the elements of `t` which do not intersect the family `u`. It is nonempty as it
@@ -156,16 +156,16 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     -- otherwise, `c` belongs to `A`. The element of `u ∪ {a'}` that it intersects has to be `a'`.
     -- moreover, `δ c` is smaller than the maximum `m` of `δ` over `A`, which is `≤ δ a' / τ`
     -- thanks to the good choice of `a'`. This is the desired inequality.
-    · push_neg  at H
-      simp only [← not_disjoint_iff_nonempty_inter, Classical.not_not] at H
+    · push_neg  at H 
+      simp only [← not_disjoint_iff_nonempty_inter, Classical.not_not] at H 
       rcases mem_insert_iff.1 ba'u with (rfl | H')
       · refine' ⟨b, mem_insert _ _, hcb, _⟩
         calc
           δ c ≤ m := le_csSup bddA (mem_image_of_mem _ ⟨ct, H⟩)
-          _ = τ * (m / τ) := by field_simp [(zero_lt_one.trans hτ).ne'] ; ring
+          _ = τ * (m / τ) := by field_simp [(zero_lt_one.trans hτ).ne']; ring
           _ ≤ τ * δ b := mul_le_mul_of_nonneg_left ha' (zero_le_one.trans hτ.le)
           
-      · rw [← not_disjoint_iff_nonempty_inter] at hcb
+      · rw [← not_disjoint_iff_nonempty_inter] at hcb 
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 
@@ -175,7 +175,7 @@ extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by t
 dilations of balls in `u`. -/
 theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α] (t : Set ι)
     (x : ι → α) (r : ι → ℝ) (R : ℝ) (hr : ∀ a ∈ t, r a ≤ R) :
-    ∃ (u : _)(_ : u ⊆ t),
+    ∃ (u : _) (_ : u ⊆ t),
       (u.PairwiseDisjoint fun a => closedBall (x a) (r a)) ∧
         ∀ a ∈ t, ∃ b ∈ u, closedBall (x a) (r a) ⊆ closedBall (x b) (5 * r b) :=
   by
@@ -187,7 +187,7 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
       ⟨t, subset.rfl, fun a ha b hb hab => by
         simp only [Function.onFun, closed_ball_eq_empty.2 (ht a ha), empty_disjoint], fun a ha =>
         ⟨a, ha, by simp only [closed_ball_eq_empty.2 (ht a ha), empty_subset]⟩⟩
-  push_neg  at ht
+  push_neg  at ht 
   let t' := { a ∈ t | 0 ≤ r a }
   rcases exists_disjoint_subfamily_covering_enlargment (fun a => closed_ball (x a) (r a)) t' r 2
       one_lt_two (fun a ha => ha.2) R (fun a ha => hr a ha.1) fun a ha =>
@@ -226,7 +226,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     (μB : ∀ a ∈ t, μ (closedBall (c a) (3 * r a)) ≤ C * μ (B a))
     (ht : ∀ a ∈ t, (interior (B a)).Nonempty) (h't : ∀ a ∈ t, IsClosed (B a))
     (hf : ∀ x ∈ s, ∀ ε > (0 : ℝ), ∃ a ∈ t, r a ≤ ε ∧ c a = x) :
-    ∃ (u : _)(_ : u ⊆ t), u.Countable ∧ u.PairwiseDisjoint B ∧ μ (s \ ⋃ a ∈ u, B a) = 0 :=
+    ∃ (u : _) (_ : u ⊆ t), u.Countable ∧ u.PairwiseDisjoint B ∧ μ (s \ ⋃ a ∈ u, B a) = 0 :=
   by
   /- The idea of the proof is the following. Assume for simplicity that `μ` is finite. Applying the
     abstract Vitali covering theorem with `δ = r` given by `hf`, one obtains a disjoint subfamily `u`,
@@ -250,7 +250,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   have : ∀ x, ∃ R, 0 < R ∧ R ≤ 1 ∧ μ (closed_ball x (20 * R)) < ∞ :=
     by
     intro x
-    obtain ⟨R, Rpos, μR⟩ : ∃ (R : ℝ)(hR : 0 < R), μ (closed_ball x R) < ∞ :=
+    obtain ⟨R, Rpos, μR⟩ : ∃ (R : ℝ) (hR : 0 < R), μ (closed_ball x R) < ∞ :=
       (μ.finite_at_nhds x).exists_mem_basis nhds_basis_closed_ball
     refine' ⟨min 1 (R / 20), _, min_le_left _ _, _⟩
     · simp only [true_and_iff, lt_min_iff, zero_lt_one]
@@ -268,7 +268,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   let t' := { a ∈ t | r a ≤ R (c a) }
   -- extract a disjoint subfamily `u` of `t'` thanks to the abstract Vitali covering theorem.
   obtain ⟨u, ut', u_disj, hu⟩ :
-    ∃ (u : _)(_ : u ⊆ t'),
+    ∃ (u : _) (_ : u ⊆ t'),
       u.PairwiseDisjoint B ∧ ∀ a ∈ t', ∃ b ∈ u, (B a ∩ B b).Nonempty ∧ r a ≤ 2 * r b :=
     by
     have A : ∀ a ∈ t', r a ≤ 1 := by
@@ -315,8 +315,8 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     · have R0pos : 0 < R0 := (hR0 x).trans_le H
       have vnonempty : v.nonempty := by
         by_contra
-        rw [nonempty_iff_ne_empty, Classical.not_not] at h
-        simp only [h, Real.sSup_empty, image_empty] at R0_def
+        rw [nonempty_iff_ne_empty, Classical.not_not] at h 
+        simp only [h, Real.sSup_empty, image_empty] at R0_def 
         exact lt_irrefl _ (R0pos.trans_le (le_of_eq R0_def))
       obtain ⟨a, hav, R0a⟩ : ∃ a ∈ v, R0 / 2 < r a :=
         by
@@ -377,7 +377,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
       by
       apply IsOpen.mem_nhds (is_open_ball.sdiff k_closed) _
       exact (mem_diff _).2 ⟨mem_of_mem_inter_right hz, z_notmem_k⟩
-    obtain ⟨d, dpos, hd⟩ : ∃ (d : ℝ)(dpos : 0 < d), closed_ball z d ⊆ ball x (R x) \ k :=
+    obtain ⟨d, dpos, hd⟩ : ∃ (d : ℝ) (dpos : 0 < d), closed_ball z d ⊆ ball x (R x) \ k :=
       nhds_basis_closed_ball.mem_iff.1 this
     -- choose an element `a` of the family `t` contained in this small ball
     obtain ⟨a, hat, ad, rfl⟩ : ∃ a ∈ t, r a ≤ min d (R z) ∧ c a = z
@@ -461,7 +461,7 @@ protected def vitaliFamily [MetricSpace α] [MeasurableSpace α] [OpensMeasurabl
         p.2.2 ⊆ closed_ball p.2.1 p.1 ∧
           μ (closed_ball p.2.1 (3 * p.1)) ≤ C * μ p.2.2 ∧
             (interior p.2.2).Nonempty ∧ IsClosed p.2.2 ∧ p.2.2 ∈ f p.2.1 ∧ p.2.1 ∈ s }
-    have A : ∀ x ∈ s, ∀ ε : ℝ, ε > 0 → ∃ (p : ℝ × α × Set α)(Hp : p ∈ t), p.1 ≤ ε ∧ p.2.1 = x :=
+    have A : ∀ x ∈ s, ∀ ε : ℝ, ε > 0 → ∃ (p : ℝ × α × Set α) (Hp : p ∈ t), p.1 ≤ ε ∧ p.2.1 = x :=
       by
       intro x xs ε εpos
       rcases ffine x xs ε εpos with ⟨a, ha, h'a⟩

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

@@ -46,7 +46,7 @@ variable {α ι : Type _}
 
 open Set Metric MeasureTheory TopologicalSpace Filter
 
-open NNReal Classical ENNReal Topology
+open scoped NNReal Classical ENNReal Topology
 
 namespace Vitali
 

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

@@ -50,9 +50,6 @@ open NNReal Classical ENNReal Topology
 
 namespace Vitali
 
-/- warning: vitali.exists_disjoint_subfamily_covering_enlargment -> Vitali.exists_disjoint_subfamily_covering_enlargment is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargmentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
@@ -172,12 +169,6 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 
-/- warning: vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball -> Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] (t : Set.{u2} ι) (x : ι -> α) (r : ι -> Real) (R : Real), (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (LE.le.{0} Real Real.hasLe (r a) R)) -> (Exists.{succ u2} (Set.{u2} ι) (fun (u : Set.{u2} ι) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) => And (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (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))) u (fun (a : ι) => Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (x a) (r a))) (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Exists.{succ u2} ι (fun (b : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (x a) (r a)) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (x b) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 5 (OfNat.mk.{0} Real 5 (bit1.{0} Real Real.hasOne Real.hasAdd (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (r b))))))))))
-but is expected to have type
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-Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBallₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
@@ -218,9 +209,6 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
     refine' ⟨c, cu, by simp only [closed_ball_eq_empty.2 h'a, empty_subset]⟩
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 
-/- warning: vitali.exists_disjoint_covering_ae -> Vitali.exists_disjoint_covering_ae is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_aeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t') -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
@@ -444,12 +432,6 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae
 
-/- warning: vitali.vitali_family -> Vitali.vitaliFamily is a dubious translation:
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-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : MeasurableSpace.{u1} α] [_inst_3 : OpensMeasurableSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] (μ : MeasureTheory.Measure.{u1} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u1} α _inst_2 (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) μ] (C : NNReal), (forall (x : α), Filter.Frequently.{0} Real (fun (r : Real) => 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))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 3 (OfNat.mk.{0} Real 3 (bit1.{0} Real Real.hasOne Real.hasAdd (One.one.{0} Real Real.hasOne)))) 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)))))))) ((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))) C) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x r)))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> (VitaliFamily.{u1} α _inst_1 _inst_2 μ)
-but is expected to have type
-  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : MeasurableSpace.{u1} α] [_inst_3 : OpensMeasurableSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] (μ : MeasureTheory.Measure.{u1} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u1} α _inst_2 (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) μ] (C : NNReal), (forall (x : α), Filter.Frequently.{0} Real (fun (r : Real) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_2 μ) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 3 (instOfNat.{0} Real 3 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) r))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_2 μ) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x r)))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) -> (VitaliFamily.{u1} α _inst_1 _inst_2 μ)
-Case conversion may be inaccurate. Consider using '#align vitali.vitali_family Vitali.vitaliFamilyₓ'. -/
 /-- Assume that around every point there are arbitrarily small scales at which the measure is
 doubling. Then the set of closed sets `a` with nonempty interior contained in `closed_ball x r` and
 covering a fixed proportion `1/C` of the ball `closed_ball x (3 * r)` forms a Vitali family.

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

@@ -165,9 +165,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
       · refine' ⟨b, mem_insert _ _, hcb, _⟩
         calc
           δ c ≤ m := le_csSup bddA (mem_image_of_mem _ ⟨ct, H⟩)
-          _ = τ * (m / τ) := by
-            field_simp [(zero_lt_one.trans hτ).ne']
-            ring
+          _ = τ * (m / τ) := by field_simp [(zero_lt_one.trans hτ).ne'] ; ring
           _ ≤ τ * δ b := mul_le_mul_of_nonneg_left ha' (zero_le_one.trans hτ.le)
           
       · rw [← not_disjoint_iff_nonempty_inter] at hcb

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

@@ -51,10 +51,7 @@ open NNReal Classical ENNReal Topology
 namespace Vitali
 
 /- warning: vitali.exists_disjoint_subfamily_covering_enlargment -> Vitali.exists_disjoint_subfamily_covering_enlargment is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} (B : ι -> (Set.{u1} α)) (t : Set.{u2} ι) (δ : ι -> Real) (τ : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) τ) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (δ a))) -> (forall (R : Real), (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (LE.le.{0} Real Real.hasLe (δ a) R)) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Set.Nonempty.{u1} α (B a))) -> (Exists.{succ u2} (Set.{u2} ι) (fun (u : Set.{u2} ι) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) => And (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (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))) u B) (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Exists.{succ u2} ι (fun (b : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) => And (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (B a) (B b))) (LE.le.{0} Real Real.hasLe (δ a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) τ (δ b)))))))))))
-but is expected to have type
-  forall {α : Type.{u2}} {ι : Type.{u1}} (B : ι -> (Set.{u2} α)) (t : Set.{u1} ι) (δ : ι -> Real) (τ : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) τ) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (δ a))) -> (forall (R : Real), (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (LE.le.{0} Real Real.instLEReal (δ a) R)) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (Set.Nonempty.{u2} α (B a))) -> (Exists.{succ u1} (Set.{u1} ι) (fun (u : Set.{u1} ι) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) (fun (H : HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) => And (Set.PairwiseDisjoint.{u2, u1} (Set.{u2} α) ι (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) u B) (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (Exists.{succ u1} ι (fun (b : ι) => And (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) b u) (And (Set.Nonempty.{u2} α (Inter.inter.{u2} (Set.{u2} α) (Set.instInterSet.{u2} α) (B a) (B b))) (LE.le.{0} Real Real.instLEReal (δ a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) τ (δ b)))))))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargmentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
@@ -224,10 +221,7 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 
 /- warning: vitali.exists_disjoint_covering_ae -> Vitali.exists_disjoint_covering_ae is a dubious translation:
-lean 3 declaration is
-  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : MeasurableSpace.{u1} α] [_inst_3 : OpensMeasurableSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] (μ : MeasureTheory.Measure.{u1} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u1} α _inst_2 (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) μ] (s : Set.{u1} α) (t : Set.{u2} ι) (C : NNReal) (r : ι -> Real) (c : ι -> α) (B : ι -> (Set.{u1} α)), (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (B a) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (c a) (r a)))) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a 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))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (c a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 3 (OfNat.mk.{0} Real 3 (bit1.{0} Real Real.hasOne Real.hasAdd (One.one.{0} Real Real.hasOne)))) (r a)))) (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)))))))) ((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))) C) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (B a))))) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Set.Nonempty.{u1} α (interior.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (B a)))) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (IsClosed.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (B a))) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{succ u2} ι (fun (a : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) => And (LE.le.{0} Real Real.hasLe (r a) ε) (Eq.{succ u1} α (c a) x)))))) -> (Exists.{succ u2} (Set.{u2} ι) (fun (u : Set.{u2} ι) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) => And (Set.Countable.{u2} ι u) (And (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (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))) u B) (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Set.iUnion.{u1, succ u2} α ι (fun (a : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a u) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a u) => B a))))) (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.{u2}} {ι : Type.{u1}} [_inst_1 : MetricSpace.{u2} α] [_inst_2 : MeasurableSpace.{u2} α] [_inst_3 : OpensMeasurableSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)))] (μ : MeasureTheory.Measure.{u2} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u2} α _inst_2 (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) μ] (s : Set.{u2} α) (t : Set.{u1} ι) (C : NNReal) (r : ι -> Real) (c : ι -> α) (B : ι -> (Set.{u2} α)), (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (B a) (Metric.closedBall.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1) (c a) (r a)))) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_2 μ) (Metric.closedBall.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1) (c a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 3 (instOfNat.{0} Real 3 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (r a)))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_2 μ) (B a))))) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (Set.Nonempty.{u2} α (interior.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (B a)))) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (IsClosed.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (B a))) -> (forall (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{succ u1} ι (fun (a : ι) => And (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) (And (LE.le.{0} Real Real.instLEReal (r a) ε) (Eq.{succ u2} α (c a) x)))))) -> (Exists.{succ u1} (Set.{u1} ι) (fun (u : Set.{u1} ι) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) (fun (H : HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) => And (Set.Countable.{u1} ι u) (And (Set.PairwiseDisjoint.{u2, u1} (Set.{u2} α) ι (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) u B) (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_2 μ) (SDiff.sdiff.{u2} (Set.{u2} α) (Set.instSDiffSet.{u2} α) s (Set.iUnion.{u2, succ u1} α ι (fun (a : ι) => Set.iUnion.{u2, 0} α (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a u) (fun (H : Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a u) => B a))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))))
+<too large>
 Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_aeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t') -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/8d33f09cd7089ecf074b4791907588245aec5d1b

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.covering.vitali
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
+! leanprover-community/mathlib commit 38df578a6450a8c5142b3727e3ae894c2300cae0
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -15,6 +15,9 @@ import Mathbin.MeasureTheory.Covering.VitaliFamily
 /-!
 # Vitali covering theorems
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 The topological Vitali covering theorem, in its most classical version, states the following.
 Consider a family of balls `(B (x_i, r_i))_{i ∈ I}` in a metric space, with uniformly bounded
 radii. Then one can extract a disjoint subfamily indexed by `J ⊆ I`, such that any `B (x_i, r_i)`

mathlib commit https://github.com/leanprover-community/mathlib/commit/75e7fca56381d056096ce5d05e938f63a6567828

@@ -47,6 +47,12 @@ open NNReal Classical ENNReal Topology
 
 namespace Vitali
 
+/- warning: vitali.exists_disjoint_subfamily_covering_enlargment -> Vitali.exists_disjoint_subfamily_covering_enlargment is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {ι : Type.{u2}} (B : ι -> (Set.{u1} α)) (t : Set.{u2} ι) (δ : ι -> Real) (τ : Real), (LT.lt.{0} Real Real.hasLt (OfNat.ofNat.{0} Real 1 (OfNat.mk.{0} Real 1 (One.one.{0} Real Real.hasOne))) τ) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (LE.le.{0} Real Real.hasLe (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (δ a))) -> (forall (R : Real), (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (LE.le.{0} Real Real.hasLe (δ a) R)) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Set.Nonempty.{u1} α (B a))) -> (Exists.{succ u2} (Set.{u2} ι) (fun (u : Set.{u2} ι) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) => And (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (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))) u B) (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Exists.{succ u2} ι (fun (b : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) => And (Set.Nonempty.{u1} α (Inter.inter.{u1} (Set.{u1} α) (Set.hasInter.{u1} α) (B a) (B b))) (LE.le.{0} Real Real.hasLe (δ a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) τ (δ b)))))))))))
+but is expected to have type
+  forall {α : Type.{u2}} {ι : Type.{u1}} (B : ι -> (Set.{u2} α)) (t : Set.{u1} ι) (δ : ι -> Real) (τ : Real), (LT.lt.{0} Real Real.instLTReal (OfNat.ofNat.{0} Real 1 (One.toOfNat1.{0} Real Real.instOneReal)) τ) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (LE.le.{0} Real Real.instLEReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (δ a))) -> (forall (R : Real), (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (LE.le.{0} Real Real.instLEReal (δ a) R)) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (Set.Nonempty.{u2} α (B a))) -> (Exists.{succ u1} (Set.{u1} ι) (fun (u : Set.{u1} ι) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) (fun (H : HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) => And (Set.PairwiseDisjoint.{u2, u1} (Set.{u2} α) ι (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) u B) (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (Exists.{succ u1} ι (fun (b : ι) => And (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) b u) (And (Set.Nonempty.{u2} α (Inter.inter.{u2} (Set.{u2} α) (Set.instInterSet.{u2} α) (B a) (B b))) (LE.le.{0} Real Real.instLEReal (δ a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) τ (δ b)))))))))))
+Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargmentₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
@@ -168,6 +174,12 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 
+/- warning: vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball -> Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] (t : Set.{u2} ι) (x : ι -> α) (r : ι -> Real) (R : Real), (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (LE.le.{0} Real Real.hasLe (r a) R)) -> (Exists.{succ u2} (Set.{u2} ι) (fun (u : Set.{u2} ι) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) => And (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (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))) u (fun (a : ι) => Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (x a) (r a))) (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Exists.{succ u2} ι (fun (b : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) b u) => HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (x a) (r a)) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (x b) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 5 (OfNat.mk.{0} Real 5 (bit1.{0} Real Real.hasOne Real.hasAdd (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))) (r b))))))))))
+but is expected to have type
+  forall {α : Type.{u2}} {ι : Type.{u1}} [_inst_1 : MetricSpace.{u2} α] (t : Set.{u1} ι) (x : ι -> α) (r : ι -> Real) (R : Real), (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (LE.le.{0} Real Real.instLEReal (r a) R)) -> (Exists.{succ u1} (Set.{u1} ι) (fun (u : Set.{u1} ι) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) (fun (H : HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) => And (Set.PairwiseDisjoint.{u2, u1} (Set.{u2} α) ι (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) u (fun (a : ι) => Metric.closedBall.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1) (x a) (r a))) (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (Exists.{succ u1} ι (fun (b : ι) => And (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) b u) (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (Metric.closedBall.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1) (x a) (r a)) (Metric.closedBall.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1) (x b) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 5 (instOfNat.{0} Real 5 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 3 (instOfNatNat 3))))) (r b))))))))))
+Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBallₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
@@ -208,6 +220,12 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
     refine' ⟨c, cu, by simp only [closed_ball_eq_empty.2 h'a, empty_subset]⟩
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 
+/- warning: vitali.exists_disjoint_covering_ae -> Vitali.exists_disjoint_covering_ae is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} {ι : Type.{u2}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : MeasurableSpace.{u1} α] [_inst_3 : OpensMeasurableSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] (μ : MeasureTheory.Measure.{u1} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u1} α _inst_2 (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) μ] (s : Set.{u1} α) (t : Set.{u2} ι) (C : NNReal) (r : ι -> Real) (c : ι -> α) (B : ι -> (Set.{u1} α)), (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (HasSubset.Subset.{u1} (Set.{u1} α) (Set.hasSubset.{u1} α) (B a) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (c a) (r a)))) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a 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))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) (c a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 3 (OfNat.mk.{0} Real 3 (bit1.{0} Real Real.hasOne Real.hasAdd (One.one.{0} Real Real.hasOne)))) (r a)))) (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)))))))) ((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))) C) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (B a))))) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (Set.Nonempty.{u1} α (interior.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (B a)))) -> (forall (a : ι), (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) -> (IsClosed.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) (B a))) -> (forall (x : α), (Membership.Mem.{u1, u1} α (Set.{u1} α) (Set.hasMem.{u1} α) x s) -> (forall (ε : Real), (GT.gt.{0} Real Real.hasLt ε (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))) -> (Exists.{succ u2} ι (fun (a : ι) => Exists.{0} (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a t) => And (LE.le.{0} Real Real.hasLe (r a) ε) (Eq.{succ u1} α (c a) x)))))) -> (Exists.{succ u2} (Set.{u2} ι) (fun (u : Set.{u2} ι) => Exists.{0} (HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) (fun (H : HasSubset.Subset.{u2} (Set.{u2} ι) (Set.hasSubset.{u2} ι) u t) => And (Set.Countable.{u2} ι u) (And (Set.PairwiseDisjoint.{u1, u2} (Set.{u1} α) ι (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))) u B) (Eq.{1} ENNReal (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (SDiff.sdiff.{u1} (Set.{u1} α) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} α) (Set.booleanAlgebra.{u1} α)) s (Set.iUnion.{u1, succ u2} α ι (fun (a : ι) => Set.iUnion.{u1, 0} α (Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a u) (fun (H : Membership.Mem.{u2, u2} ι (Set.{u2} ι) (Set.hasMem.{u2} ι) a u) => B a))))) (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.{u2}} {ι : Type.{u1}} [_inst_1 : MetricSpace.{u2} α] [_inst_2 : MeasurableSpace.{u2} α] [_inst_3 : OpensMeasurableSpace.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1)))] (μ : MeasureTheory.Measure.{u2} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u2} α _inst_2 (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) μ] (s : Set.{u2} α) (t : Set.{u1} ι) (C : NNReal) (r : ι -> Real) (c : ι -> α) (B : ι -> (Set.{u2} α)), (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (HasSubset.Subset.{u2} (Set.{u2} α) (Set.instHasSubsetSet.{u2} α) (B a) (Metric.closedBall.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1) (c a) (r a)))) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_2 μ) (Metric.closedBall.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1) (c a) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 3 (instOfNat.{0} Real 3 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) (r a)))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_2 μ) (B a))))) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (Set.Nonempty.{u2} α (interior.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (B a)))) -> (forall (a : ι), (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) -> (IsClosed.{u2} α (UniformSpace.toTopologicalSpace.{u2} α (PseudoMetricSpace.toUniformSpace.{u2} α (MetricSpace.toPseudoMetricSpace.{u2} α _inst_1))) (B a))) -> (forall (x : α), (Membership.mem.{u2, u2} α (Set.{u2} α) (Set.instMembershipSet.{u2} α) x s) -> (forall (ε : Real), (GT.gt.{0} Real Real.instLTReal ε (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))) -> (Exists.{succ u1} ι (fun (a : ι) => And (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a t) (And (LE.le.{0} Real Real.instLEReal (r a) ε) (Eq.{succ u2} α (c a) x)))))) -> (Exists.{succ u1} (Set.{u1} ι) (fun (u : Set.{u1} ι) => Exists.{0} (HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) (fun (H : HasSubset.Subset.{u1} (Set.{u1} ι) (Set.instHasSubsetSet.{u1} ι) u t) => And (Set.Countable.{u1} ι u) (And (Set.PairwiseDisjoint.{u2, u1} (Set.{u2} α) ι (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) (BoundedOrder.toOrderBot.{u2} (Set.{u2} α) (Preorder.toLE.{u2} (Set.{u2} α) (PartialOrder.toPreorder.{u2} (Set.{u2} α) (OmegaCompletePartialOrder.toPartialOrder.{u2} (Set.{u2} α) (CompleteLattice.instOmegaCompletePartialOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))))) (CompleteLattice.toBoundedOrder.{u2} (Set.{u2} α) (Order.Coframe.toCompleteLattice.{u2} (Set.{u2} α) (CompleteDistribLattice.toCoframe.{u2} (Set.{u2} α) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u2} (Set.{u2} α) (Set.instCompleteBooleanAlgebraSet.{u2} α)))))) u B) (Eq.{1} ENNReal (MeasureTheory.OuterMeasure.measureOf.{u2} α (MeasureTheory.Measure.toOuterMeasure.{u2} α _inst_2 μ) (SDiff.sdiff.{u2} (Set.{u2} α) (Set.instSDiffSet.{u2} α) s (Set.iUnion.{u2, succ u1} α ι (fun (a : ι) => Set.iUnion.{u2, 0} α (Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a u) (fun (H : Membership.mem.{u1, u1} ι (Set.{u1} ι) (Set.instMembershipSet.{u1} ι) a u) => B a))))) (OfNat.ofNat.{0} ENNReal 0 (Zero.toOfNat0.{0} ENNReal instENNRealZero)))))))
+Case conversion may be inaccurate. Consider using '#align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_aeₓ'. -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t') -/
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
@@ -431,6 +449,12 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae
 
+/- warning: vitali.vitali_family -> Vitali.vitaliFamily is a dubious translation:
+lean 3 declaration is
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : MeasurableSpace.{u1} α] [_inst_3 : OpensMeasurableSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] (μ : MeasureTheory.Measure.{u1} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u1} α _inst_2 (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) μ] (C : NNReal), (forall (x : α), Filter.Frequently.{0} Real (fun (r : Real) => 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))))) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 3 (OfNat.mk.{0} Real 3 (bit1.{0} Real Real.hasOne Real.hasAdd (One.one.{0} Real Real.hasOne)))) 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)))))))) ((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))) C) (coeFn.{succ u1, succ u1} (MeasureTheory.Measure.{u1} α _inst_2) (fun (_x : MeasureTheory.Measure.{u1} α _inst_2) => (Set.{u1} α) -> ENNReal) (MeasureTheory.Measure.instCoeFun.{u1} α _inst_2) μ (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x r)))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> (VitaliFamily.{u1} α _inst_1 _inst_2 μ)
+but is expected to have type
+  forall {α : Type.{u1}} [_inst_1 : MetricSpace.{u1} α] [_inst_2 : MeasurableSpace.{u1} α] [_inst_3 : OpensMeasurableSpace.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) _inst_2] [_inst_4 : TopologicalSpace.SecondCountableTopology.{u1} α (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1)))] (μ : MeasureTheory.Measure.{u1} α _inst_2) [_inst_5 : MeasureTheory.LocallyFiniteMeasure.{u1} α _inst_2 (UniformSpace.toTopologicalSpace.{u1} α (PseudoMetricSpace.toUniformSpace.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1))) μ] (C : NNReal), (forall (x : α), Filter.Frequently.{0} Real (fun (r : Real) => LE.le.{0} ENNReal (Preorder.toLE.{0} ENNReal (PartialOrder.toPreorder.{0} ENNReal (OmegaCompletePartialOrder.toPartialOrder.{0} ENNReal (CompleteLattice.instOmegaCompletePartialOrder.{0} ENNReal (CompleteLinearOrder.toCompleteLattice.{0} ENNReal ENNReal.instCompleteLinearOrderENNReal))))) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_2 μ) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 3 (instOfNat.{0} Real 3 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 1 (instOfNatNat 1))))) r))) (HMul.hMul.{0, 0, 0} ENNReal ENNReal ENNReal (instHMul.{0} ENNReal (CanonicallyOrderedCommSemiring.toMul.{0} ENNReal ENNReal.instCanonicallyOrderedCommSemiringENNReal)) (ENNReal.some C) (MeasureTheory.OuterMeasure.measureOf.{u1} α (MeasureTheory.Measure.toOuterMeasure.{u1} α _inst_2 μ) (Metric.closedBall.{u1} α (MetricSpace.toPseudoMetricSpace.{u1} α _inst_1) x r)))) (nhdsWithin.{0} Real (UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace)) (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)) (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) -> (VitaliFamily.{u1} α _inst_1 _inst_2 μ)
+Case conversion may be inaccurate. Consider using '#align vitali.vitali_family Vitali.vitaliFamilyₓ'. -/
 /-- Assume that around every point there are arbitrarily small scales at which the measure is
 doubling. Then the set of closed sets `a` with nonempty interior contained in `closed_ball x r` and
 covering a fixed proportion `1/C` of the ball `closed_ball x (3 * r)` forms a Vitali family.

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

@@ -4,12 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.covering.vitali
-! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
+! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.Topology.MetricSpace.Basic
-import Mathbin.MeasureTheory.Constructions.BorelSpace
+import Mathbin.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathbin.MeasureTheory.Covering.VitaliFamily
 
 /-!

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

@@ -89,7 +89,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     by
     refine' zorn_subset _ fun U UT hU => _
     refine' ⟨⋃₀ U, _, fun s hs => subset_sUnion_of_mem hs⟩
-    simp only [Set.unionₛ_subset_iff, and_imp, exists_prop, forall_exists_index, mem_sUnion,
+    simp only [Set.sUnion_subset_iff, and_imp, exists_prop, forall_exists_index, mem_sUnion,
       Set.mem_setOf_eq]
     refine'
       ⟨fun u hu => (UT hu).1, (pairwise_disjoint_sUnion hU.directed_on).2 fun u hu => (UT hu).2.1,
@@ -120,7 +120,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
     exact δle a' ha'.1
   obtain ⟨a', a'A, ha'⟩ : ∃ a' ∈ A, m / τ ≤ δ a' :=
     by
-    have : 0 ≤ m := (δnonneg a hat).trans (le_csupₛ bddA (mem_image_of_mem _ ⟨hat, a_disj⟩))
+    have : 0 ≤ m := (δnonneg a hat).trans (le_csSup bddA (mem_image_of_mem _ ⟨hat, a_disj⟩))
     rcases eq_or_lt_of_le this with (mzero | mpos)
     · refine' ⟨a, ⟨hat, a_disj⟩, _⟩
       simpa only [← mzero, zero_div] using δnonneg a hat
@@ -128,7 +128,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
         rw [div_lt_iff (zero_lt_one.trans hτ)]
         conv_lhs => rw [← mul_one m]
         exact (mul_lt_mul_left mpos).2 hτ
-      rcases exists_lt_of_lt_csupₛ (nonempty_image_iff.2 Anonempty) I with ⟨x, xA, hx⟩
+      rcases exists_lt_of_lt_csSup (nonempty_image_iff.2 Anonempty) I with ⟨x, xA, hx⟩
       rcases(mem_image _ _ _).1 xA with ⟨a', ha', rfl⟩
       exact ⟨a', ha', hx.le⟩
   clear hat hu a_disj a
@@ -158,7 +158,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
       rcases mem_insert_iff.1 ba'u with (rfl | H')
       · refine' ⟨b, mem_insert _ _, hcb, _⟩
         calc
-          δ c ≤ m := le_csupₛ bddA (mem_image_of_mem _ ⟨ct, H⟩)
+          δ c ≤ m := le_csSup bddA (mem_image_of_mem _ ⟨ct, H⟩)
           _ = τ * (m / τ) := by
             field_simp [(zero_lt_one.trans hτ).ne']
             ring
@@ -309,18 +309,18 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     · refine' ⟨20 * R x, hRμ x, fun a au hax => _⟩
       refine' (hB a (ut au)).trans _
       apply closed_ball_subset_closed_ball'
-      have : r a ≤ R0 := le_csupₛ R0_bdd (mem_image_of_mem _ ⟨au, hax⟩)
+      have : r a ≤ R0 := le_csSup R0_bdd (mem_image_of_mem _ ⟨au, hax⟩)
       linarith [Idist_v a ⟨au, hax⟩, hR0 x]
     · have R0pos : 0 < R0 := (hR0 x).trans_le H
       have vnonempty : v.nonempty := by
         by_contra
         rw [nonempty_iff_ne_empty, Classical.not_not] at h
-        simp only [h, Real.supₛ_empty, image_empty] at R0_def
+        simp only [h, Real.sSup_empty, image_empty] at R0_def
         exact lt_irrefl _ (R0pos.trans_le (le_of_eq R0_def))
       obtain ⟨a, hav, R0a⟩ : ∃ a ∈ v, R0 / 2 < r a :=
         by
         obtain ⟨r', r'mem, hr'⟩ : ∃ r' ∈ r '' v, R0 / 2 < r' :=
-          exists_lt_of_lt_csupₛ (nonempty_image_iff.2 vnonempty) (half_lt_self R0pos)
+          exists_lt_of_lt_csSup (nonempty_image_iff.2 vnonempty) (half_lt_self R0pos)
         rcases(mem_image _ _ _).1 r'mem with ⟨a, hav, rfl⟩
         exact ⟨a, hav, hr'⟩
       refine' ⟨8 * R0, _, _⟩
@@ -331,7 +331,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
       · intro b bu hbx
         refine' (hB b (ut bu)).trans _
         apply closed_ball_subset_closed_ball'
-        have : r b ≤ R0 := le_csupₛ R0_bdd (mem_image_of_mem _ ⟨bu, hbx⟩)
+        have : r b ≤ R0 := le_csSup R0_bdd (mem_image_of_mem _ ⟨bu, hbx⟩)
         linarith [Idist_v b ⟨bu, hbx⟩]
   -- we will show that, in `ball x (R x)`, almost all `s` is covered by the family `u`.
   refine'
@@ -361,7 +361,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     by
     intro z hz
     set k := ⋃ (a : v) (ha : a ∈ w), B a with hk
-    have k_closed : IsClosed k := isClosed_bunionᵢ w.finite_to_set fun i hi => h't _ (ut (vu i.2))
+    have k_closed : IsClosed k := isClosed_biUnion w.finite_to_set fun i hi => h't _ (ut (vu i.2))
     have z_notmem_k : z ∉ k :=
       by
       simp only [not_exists, exists_prop, mem_Union, mem_sep_iff, forall_exists_index,
@@ -397,7 +397,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     -- contrary to `b`
     have b'_notmem_w : b' ∉ w := by
       intro b'w
-      have b'k : B b' ⊆ k := @Finset.subset_set_bunionᵢ_of_mem _ _ _ (fun y : v => B y) _ b'w
+      have b'k : B b' ⊆ k := @Finset.subset_set_biUnion_of_mem _ _ _ (fun y : v => B y) _ b'w
       have : (ball x (R x) \ k ∩ k).Nonempty :=
         by
         apply ab.mono (inter_subset_inter _ b'k)

mathlib commit https://github.com/leanprover-community/mathlib/commit/d4437c68c8d350fc9d4e95e1e174409db35e30d7

@@ -220,7 +220,7 @@ Then one can extract from `t` a disjoint subfamily that covers almost all `s`.
 For more flexibility, we give a statement with a parameterized family of sets.
 -/
 theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [OpensMeasurableSpace α]
-    [SecondCountableTopology α] (μ : Measure α) [IsLocallyFiniteMeasure μ] (s : Set α) (t : Set ι)
+    [SecondCountableTopology α] (μ : Measure α) [LocallyFiniteMeasure μ] (s : Set α) (t : Set ι)
     (C : ℝ≥0) (r : ι → ℝ) (c : ι → α) (B : ι → Set α) (hB : ∀ a ∈ t, B a ⊆ closedBall (c a) (r a))
     (μB : ∀ a ∈ t, μ (closedBall (c a) (3 * r a)) ≤ C * μ (B a))
     (ht : ∀ a ∈ t, (interior (B a)).Nonempty) (h't : ∀ a ∈ t, IsClosed (B a))
@@ -436,7 +436,7 @@ doubling. Then the set of closed sets `a` with nonempty interior contained in `c
 covering a fixed proportion `1/C` of the ball `closed_ball x (3 * r)` forms a Vitali family.
 This is essentially a restatement of the measurable Vitali theorem. -/
 protected def vitaliFamily [MetricSpace α] [MeasurableSpace α] [OpensMeasurableSpace α]
-    [SecondCountableTopology α] (μ : Measure α) [IsLocallyFiniteMeasure μ] (C : ℝ≥0)
+    [SecondCountableTopology α] (μ : Measure α) [LocallyFiniteMeasure μ] (C : ℝ≥0)
     (h : ∀ x, ∃ᶠ r in 𝓝[>] 0, μ (closedBall x (3 * r)) ≤ C * μ (closedBall x r)) : VitaliFamily μ
     where
   setsAt x :=

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

@@ -47,7 +47,7 @@ open NNReal Classical ENNReal Topology
 
 namespace Vitali
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
 is any fixed number.
@@ -168,7 +168,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
         exact (hcb (H _ H')).elim
 #align vitali.exists_disjoint_subfamily_covering_enlargment Vitali.exists_disjoint_subfamily_covering_enlargment
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- Vitali covering theorem, closed balls version: given a family `t` of closed balls, one can
 extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by the 5-times
 dilations of balls in `u`. -/
@@ -208,8 +208,8 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
     refine' ⟨c, cu, by simp only [closed_ball_eq_empty.2 h'a, empty_subset]⟩
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (u «expr ⊆ » t') -/
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (u «expr ⊆ » t) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t') -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (u «expr ⊆ » t) -/
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets with
 nonempty interior, such that each `a ∈ t` is included in a ball `B (x, r)` and covers a definite
 proportion of the ball `B (x, 3 r)` for a given measure `μ` (think of the situation where `μ` is
@@ -345,7 +345,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
         by
         rw [measure_bUnion (u_count.mono vu) _ fun a ha => (h't _ (vu.trans ut ha)).MeasurableSet]
         exact u_disj.subset vu
-      _ ≤ μ (closed_ball x K) := measure_mono (Union₂_subset fun a ha => hK a (vu ha) ha.2)
+      _ ≤ μ (closed_ball x K) := (measure_mono (Union₂_subset fun a ha => hK a (vu ha) ha.2))
       _ < ∞ := μK
       
   -- we can obtain a finite subfamily of `v`, such that the measures of the remaining elements
@@ -423,10 +423,10 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   calc
     μ ((s \ ⋃ a ∈ u, B a) ∩ ball x (R x)) ≤ μ (⋃ a : { a // a ∉ w }, closed_ball (c a) (3 * r a)) :=
       measure_mono M
-    _ ≤ ∑' a : { a // a ∉ w }, μ (closed_ball (c a) (3 * r a)) := measure_Union_le _
-    _ ≤ ∑' a : { a // a ∉ w }, C * μ (B a) := ENNReal.tsum_le_tsum fun a => μB a (ut (vu a.1.2))
+    _ ≤ ∑' a : { a // a ∉ w }, μ (closed_ball (c a) (3 * r a)) := (measure_Union_le _)
+    _ ≤ ∑' a : { a // a ∉ w }, C * μ (B a) := (ENNReal.tsum_le_tsum fun a => μB a (ut (vu a.1.2)))
     _ = C * ∑' a : { a // a ∉ w }, μ (B a) := ENNReal.tsum_mul_left
-    _ ≤ C * (ε / C) := mul_le_mul_left' hw.le _
+    _ ≤ C * (ε / C) := (mul_le_mul_left' hw.le _)
     _ ≤ ε := ENNReal.mul_div_le
     
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae

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: Sébastien Gouëzel
 
 ! This file was ported from Lean 3 source module measure_theory.covering.vitali
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 57ac39bd365c2f80589a700f9fbb664d3a1a30c2
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -426,7 +426,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     _ ≤ ∑' a : { a // a ∉ w }, μ (closed_ball (c a) (3 * r a)) := measure_Union_le _
     _ ≤ ∑' a : { a // a ∉ w }, C * μ (B a) := ENNReal.tsum_le_tsum fun a => μB a (ut (vu a.1.2))
     _ = C * ∑' a : { a // a ∉ w }, μ (B a) := ENNReal.tsum_mul_left
-    _ ≤ C * (ε / C) := ENNReal.mul_le_mul le_rfl hw.le
+    _ ≤ C * (ε / C) := mul_le_mul_left' hw.le _
     _ ≤ ε := ENNReal.mul_div_le
     
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae

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

@@ -43,7 +43,7 @@ variable {α ι : Type _}
 
 open Set Metric MeasureTheory TopologicalSpace Filter
 
-open NNReal Classical Ennreal Topology
+open NNReal Classical ENNReal Topology
 
 namespace Vitali
 
@@ -352,9 +352,9 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   -- add up to an arbitrarily small number, say `ε / C`.
   obtain ⟨w, hw⟩ : ∃ w : Finset ↥v, (∑' a : { a // a ∉ w }, μ (B a)) < ε / C :=
     haveI : 0 < ε / C := by
-      simp only [Ennreal.div_pos_iff, εpos.ne', Ennreal.coe_ne_top, Ne.def, not_false_iff,
+      simp only [ENNReal.div_pos_iff, εpos.ne', ENNReal.coe_ne_top, Ne.def, not_false_iff,
         and_self_iff]
-    ((tendsto_order.1 (Ennreal.tendsto_tsum_compl_atTop_zero I.ne)).2 _ this).exists
+    ((tendsto_order.1 (ENNReal.tendsto_tsum_compl_atTop_zero I.ne)).2 _ this).exists
   -- main property: the points `z` of `s` which are not covered by `u` are contained in the
   -- enlargements of the elements not in `w`.
   have M : (s \ ⋃ a ∈ u, B a) ∩ ball x (R x) ⊆ ⋃ a : { a // a ∉ w }, closed_ball (c a) (3 * r a) :=
@@ -424,10 +424,10 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     μ ((s \ ⋃ a ∈ u, B a) ∩ ball x (R x)) ≤ μ (⋃ a : { a // a ∉ w }, closed_ball (c a) (3 * r a)) :=
       measure_mono M
     _ ≤ ∑' a : { a // a ∉ w }, μ (closed_ball (c a) (3 * r a)) := measure_Union_le _
-    _ ≤ ∑' a : { a // a ∉ w }, C * μ (B a) := Ennreal.tsum_le_tsum fun a => μB a (ut (vu a.1.2))
-    _ = C * ∑' a : { a // a ∉ w }, μ (B a) := Ennreal.tsum_mul_left
-    _ ≤ C * (ε / C) := Ennreal.mul_le_mul le_rfl hw.le
-    _ ≤ ε := Ennreal.mul_div_le
+    _ ≤ ∑' a : { a // a ∉ w }, C * μ (B a) := ENNReal.tsum_le_tsum fun a => μB a (ut (vu a.1.2))
+    _ = C * ∑' a : { a // a ∉ w }, μ (B a) := ENNReal.tsum_mul_left
+    _ ≤ C * (ε / C) := ENNReal.mul_le_mul le_rfl hw.le
+    _ ≤ ε := ENNReal.mul_div_le
     
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae
 

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

This lets us unify a few lemmas between GroupWithZero and EuclideanDomain and two lemmas that were previously proved separately for Nat, Int, Polynomial.

@@ -149,9 +149,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
       · refine' ⟨b, mem_insert _ _, hcb, _⟩
         calc
           δ c ≤ m := le_csSup bddA (mem_image_of_mem _ ⟨ct, H⟩)
-          _ = τ * (m / τ) := by
-            field_simp [(zero_lt_one.trans hτ).ne']
-            ring
+          _ = τ * (m / τ) := by field_simp [(zero_lt_one.trans hτ).ne']
           _ ≤ τ * δ b := mul_le_mul_of_nonneg_left ha' (zero_le_one.trans hτ.le)
       · rw [← not_disjoint_iff_nonempty_inter] at hcb
         exact (hcb (H _ H')).elim

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

@@ -380,10 +380,10 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   calc
     μ ((s \ ⋃ a ∈ u, B a) ∩ ball x (R x)) ≤ μ (⋃ a : { a // a ∉ w }, closedBall (c a) (3 * r a)) :=
       measure_mono M
-    _ ≤ ∑' a : { a // a ∉ w }, μ (closedBall (c a) (3 * r a)) := (measure_iUnion_le _)
+    _ ≤ ∑' a : { a // a ∉ w }, μ (closedBall (c a) (3 * r a)) := measure_iUnion_le _
     _ ≤ ∑' a : { a // a ∉ w }, C * μ (B a) := (ENNReal.tsum_le_tsum fun a => μB a (ut (vu a.1.2)))
     _ = C * ∑' a : { a // a ∉ w }, μ (B a) := ENNReal.tsum_mul_left
-    _ ≤ C * (ε / C) := (mul_le_mul_left' hw.le _)
+    _ ≤ C * (ε / C) := mul_le_mul_left' hw.le _
     _ ≤ ε := ENNReal.mul_div_le
 #align vitali.exists_disjoint_covering_ae Vitali.exists_disjoint_covering_ae
 

@@ -313,7 +313,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   -- add up to an arbitrarily small number, say `ε / C`.
   obtain ⟨w, hw⟩ : ∃ w : Finset v, (∑' a : { a // a ∉ w }, μ (B a)) < ε / C :=
     haveI : 0 < ε / C := by
-      simp only [ENNReal.div_pos_iff, εpos.ne', ENNReal.coe_ne_top, Ne.def, not_false_iff,
+      simp only [ENNReal.div_pos_iff, εpos.ne', ENNReal.coe_ne_top, Ne, not_false_iff,
         and_self_iff]
     ((tendsto_order.1 (ENNReal.tendsto_tsum_compl_atTop_zero I.ne)).2 _ this).exists
   -- main property: the points `z` of `s` which are not covered by `u` are contained in the

Use it to golf Vitali.exists_disjoint_covering_ae

@@ -227,19 +227,10 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   the family is assumed to be fine at every point of `s`).
   -/
   -- choose around each `x` a small ball on which the measure is finite
-  have : ∀ x, ∃ R, 0 < R ∧ R ≤ 1 ∧ μ (closedBall x (20 * R)) < ∞ := by
-    intro x
-    obtain ⟨R, Rpos, μR⟩ : ∃ R, 0 < R ∧ μ (closedBall x R) < ∞ :=
-      (μ.finiteAt_nhds x).exists_mem_basis nhds_basis_closedBall
-    refine' ⟨min 1 (R / 20), _, min_le_left _ _, _⟩
-    · simp only [true_and_iff, lt_min_iff, zero_lt_one]
-      linarith
-    · apply lt_of_le_of_lt (measure_mono _) μR
-      apply closedBall_subset_closedBall
-      calc
-        20 * min 1 (R / 20) ≤ 20 * (R / 20) :=
-          mul_le_mul_of_nonneg_left (min_le_right _ _) (by norm_num)
-        _ = R := by ring
+  have : ∀ x, ∃ R, 0 < R ∧ R ≤ 1 ∧ μ (closedBall x (20 * R)) < ∞ := fun x ↦ by
+    refine ((eventually_le_nhds one_pos).and ?_).exists_gt
+    refine (tendsto_closedBall_smallSets x).comp ?_ (μ.finiteAt_nhds x).eventually
+    exact Continuous.tendsto' (by fun_prop) _ _ (mul_zero _)
   choose R hR0 hR1 hRμ using this
   -- we restrict to a subfamily `t'` of `t`, made of elements small enough to ensure that
   -- they only see a finite part of the measure, and with a doubling property
@@ -385,7 +376,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     exact subset_iUnion (fun a : { a // a ∉ w } => closedBall (c a) (3 * r a)) b''
   -- now that we have proved our main inclusion, we can use it to estimate the measure of the points
   -- in `ball x (r x)` not covered by `u`.
-  haveI : Encodable v := (u_count.mono vu).toEncodable
+  haveI : Countable v := (u_count.mono vu).to_subtype
   calc
     μ ((s \ ⋃ a ∈ u, B a) ∩ ball x (R x)) ≤ μ (⋃ a : { a // a ∉ w }, closedBall (c a) (3 * r a)) :=
       measure_mono M

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

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

@@ -40,7 +40,8 @@ variable {α ι : Type*}
 
 open Set Metric MeasureTheory TopologicalSpace Filter
 
-open NNReal Classical ENNReal Topology
+open scoped Classical
+open NNReal ENNReal Topology
 
 namespace Vitali
 

This covers many instances, but is not exhaustive.

Independently of whether that syntax should be avoided (similar to #10534), I think all these changes are small improvements.

@@ -346,15 +346,15 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     obtain ⟨d, dpos, hd⟩ : ∃ d, 0 < d ∧ closedBall z d ⊆ ball x (R x) \ k :=
       nhds_basis_closedBall.mem_iff.1 this
     -- choose an element `a` of the family `t` contained in this small ball
-    obtain ⟨a, hat, ad, rfl⟩ : ∃ a ∈ t, r a ≤ min d (R z) ∧ c a = z
-    exact hf z ((mem_diff _).1 (mem_of_mem_inter_left hz)).1 (min d (R z)) (lt_min dpos (hR0 z))
+    obtain ⟨a, hat, ad, rfl⟩ : ∃ a ∈ t, r a ≤ min d (R z) ∧ c a = z :=
+      hf z ((mem_diff _).1 (mem_of_mem_inter_left hz)).1 (min d (R z)) (lt_min dpos (hR0 z))
     have ax : B a ⊆ ball x (R x) := by
       refine' (hB a hat).trans _
       refine' Subset.trans _ (hd.trans (diff_subset (ball x (R x)) k))
       exact closedBall_subset_closedBall (ad.trans (min_le_left _ _))
     -- it intersects an element `b` of `u` with comparable diameter, by definition of `u`
-    obtain ⟨b, bu, ab, bdiam⟩ : ∃ b ∈ u, (B a ∩ B b).Nonempty ∧ r a ≤ 2 * r b
-    exact hu a ⟨hat, ad.trans (min_le_right _ _)⟩
+    obtain ⟨b, bu, ab, bdiam⟩ : ∃ b ∈ u, (B a ∩ B b).Nonempty ∧ r a ≤ 2 * r b :=
+      hu a ⟨hat, ad.trans (min_le_right _ _)⟩
     have bv : b ∈ v := by
       refine' ⟨bu, ab.mono _⟩
       rw [inter_comm]

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

@@ -80,7 +80,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
   obtain ⟨u, uT, hu⟩ : ∃ u ∈ T, ∀ v ∈ T, u ⊆ v → v = u := by
     refine' zorn_subset _ fun U UT hU => _
     refine' ⟨⋃₀ U, _, fun s hs => subset_sUnion_of_mem hs⟩
-    simp only [Set.sUnion_subset_iff, and_imp, exists_prop, forall_exists_index, mem_sUnion,
+    simp only [T, Set.sUnion_subset_iff, and_imp, exists_prop, forall_exists_index, mem_sUnion,
       Set.mem_setOf_eq]
     refine'
       ⟨fun u hu => (UT hu).1, (pairwiseDisjoint_sUnion hU.directedOn).2 fun u hu => (UT hu).2.1,
@@ -332,7 +332,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     set k := ⋃ (a : v) (_ : a ∈ w), B a
     have k_closed : IsClosed k := isClosed_biUnion_finset fun i _ => h't _ (ut (vu i.2))
     have z_notmem_k : z ∉ k := by
-      simp only [not_exists, exists_prop, mem_iUnion, mem_sep_iff, forall_exists_index,
+      simp only [k, not_exists, exists_prop, mem_iUnion, mem_sep_iff, forall_exists_index,
         SetCoe.exists, not_and, exists_and_right, Subtype.coe_mk]
       intro b hbv _ h'z
       have : z ∈ (s \ ⋃ a ∈ u, B a) ∩ ⋃ a ∈ u, B a :=

I replaced a few "terminal" refine/refine's with exact.

The strategy was very simple-minded: essentially any refine whose following line had smaller indentation got replaced by exact and then I cleaned up the mess.

This PR certainly leaves some further terminal refines, but maybe the current change is beneficial.

@@ -188,7 +188,7 @@ theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α
   · exact A a ⟨ha, h'a⟩
   · rcases ht with ⟨b, rb⟩
     rcases A b ⟨rb.1, rb.2⟩ with ⟨c, cu, _⟩
-    refine' ⟨c, cu, by simp only [closedBall_eq_empty.2 h'a, empty_subset]⟩
+    exact ⟨c, cu, by simp only [closedBall_eq_empty.2 h'a, empty_subset]⟩
 #align vitali.exists_disjoint_subfamily_covering_enlargment_closed_ball Vitali.exists_disjoint_subfamily_covering_enlargment_closedBall
 
 /-- The measurable Vitali covering theorem. Assume one is given a family `t` of closed sets 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>

@@ -379,8 +379,8 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
       have B : dist e (c b) ≤ r b := mem_closedBall.1 (hB b (ut bu) eb)
       simp only [mem_closedBall]
       linarith only [dist_triangle (c a) e (c b), A, B, bdiam]
-    suffices H : closedBall (c b'') (3 * r b'') ⊆ ⋃ a : { a // a ∉ w }, closedBall (c a) (3 * r a)
-    exact H zb
+    suffices H : closedBall (c b'') (3 * r b'')
+        ⊆ ⋃ a : { a // a ∉ w }, closedBall (c a) (3 * r a) from H zb
     exact subset_iUnion (fun a : { a // a ∉ w } => closedBall (c a) (3 * r a)) b''
   -- now that we have proved our main inclusion, we can use it to estimate the measure of the points
   -- in `ball x (r x)` not covered by `u`.

This uses the improved shake script from #9772 to reduce imports across mathlib. The corresponding noshake.json file has been added to #9772.

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

@@ -5,6 +5,7 @@ Authors: Sébastien Gouëzel
 -/
 import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathlib.MeasureTheory.Covering.VitaliFamily
+import Mathlib.Data.Set.Pairwise.Lattice
 
 #align_import measure_theory.covering.vitali from "leanprover-community/mathlib"@"bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf"
 

Rename VitaliFamily.MeasurableSet' → VitaliFamily.measurableSet and VitaliFamily.Nontrivial → VitaliFamily.nontrivial.

Also add docstrings.

@@ -404,9 +404,9 @@ protected def vitaliFamily [MetricSpace α] [MeasurableSpace α] [OpensMeasurabl
     VitaliFamily μ where
   setsAt x := { a | IsClosed a ∧ (interior a).Nonempty ∧
     ∃ r, a ⊆ closedBall x r ∧ μ (closedBall x (3 * r)) ≤ C * μ a }
-  MeasurableSet' x a ha := ha.1.measurableSet
+  measurableSet x a ha := ha.1.measurableSet
   nonempty_interior x a ha := ha.2.1
-  Nontrivial x ε εpos := by
+  nontrivial x ε εpos := by
     obtain ⟨r, μr, rpos, rε⟩ :
         ∃ r, μ (closedBall x (3 * r)) ≤ C * μ (closedBall x r) ∧ r ∈ Ioc (0 : ℝ) ε :=
       ((h x).and_eventually (Ioc_mem_nhdsWithin_Ioi ⟨le_rfl, εpos⟩)).exists

• rename Finset.Nonempty.image_iff to Finset.image_nonempty, deprecate the old version;
• rename Set.nonempty_image_iff to Set.image_nonempty, deprecate the old version;
• drop unneeded Finset.Nonempty arguments here and there;
• add versions of some lemmas that assume Nonempty s instead of Nonempty (s.image f) or Nonempty (s.map f).

@@ -116,7 +116,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
         rw [div_lt_iff (zero_lt_one.trans hτ)]
         conv_lhs => rw [← mul_one m]
         exact (mul_lt_mul_left mpos).2 hτ
-      rcases exists_lt_of_lt_csSup (nonempty_image_iff.2 Anonempty) I with ⟨x, xA, hx⟩
+      rcases exists_lt_of_lt_csSup (Anonempty.image _) I with ⟨x, xA, hx⟩
       rcases (mem_image _ _ _).1 xA with ⟨a', ha', rfl⟩
       exact ⟨a', ha', hx.le⟩
   clear hat hu a_disj a
@@ -291,7 +291,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
         exact lt_irrefl _ (R0pos.trans_le (le_of_eq R0_def))
       obtain ⟨a, hav, R0a⟩ : ∃ a ∈ v, R0 / 2 < r a := by
         obtain ⟨r', r'mem, hr'⟩ : ∃ r' ∈ r '' v, R0 / 2 < r' :=
-          exists_lt_of_lt_csSup (nonempty_image_iff.2 vnonempty) (half_lt_self R0pos)
+          exists_lt_of_lt_csSup (vnonempty.image _) (half_lt_self R0pos)
         rcases (mem_image _ _ _).1 r'mem with ⟨a, hav, rfl⟩
         exact ⟨a, hav, hr'⟩
       refine' ⟨8 * R0, _, _⟩

Follow-up #9184

@@ -58,7 +58,7 @@ wider applicability.
 theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : Set ι) (δ : ι → ℝ)
     (τ : ℝ) (hτ : 1 < τ) (δnonneg : ∀ a ∈ t, 0 ≤ δ a) (R : ℝ) (δle : ∀ a ∈ t, δ a ≤ R)
     (hne : ∀ a ∈ t, (B a).Nonempty) :
-    ∃ (u : _) (_ : u ⊆ t),
+    ∃ u ⊆ t,
       u.PairwiseDisjoint B ∧ ∀ a ∈ t, ∃ b ∈ u, (B a ∩ B b).Nonempty ∧ δ a ≤ τ * δ b := by
   /- The proof could be formulated as a transfinite induction. First pick an element of `t` with `δ`
   as large as possible (up to a factor of `τ`). Then among the remaining elements not intersecting
@@ -160,7 +160,7 @@ extract a disjoint subfamily `u ⊆ t` so that all balls in `t` are covered by t
 dilations of balls in `u`. -/
 theorem exists_disjoint_subfamily_covering_enlargment_closedBall [MetricSpace α] (t : Set ι)
     (x : ι → α) (r : ι → ℝ) (R : ℝ) (hr : ∀ a ∈ t, r a ≤ R) :
-    ∃ (u : _) (_ : u ⊆ t),
+    ∃ u ⊆ t,
       (u.PairwiseDisjoint fun a => closedBall (x a) (r a)) ∧
         ∀ a ∈ t, ∃ b ∈ u, closedBall (x a) (r a) ⊆ closedBall (x b) (5 * r b) := by
   rcases eq_empty_or_nonempty t with (rfl | _)
@@ -205,7 +205,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
     (μB : ∀ a ∈ t, μ (closedBall (c a) (3 * r a)) ≤ C * μ (B a))
     (ht : ∀ a ∈ t, (interior (B a)).Nonempty) (h't : ∀ a ∈ t, IsClosed (B a))
     (hf : ∀ x ∈ s, ∀ ε > (0 : ℝ), ∃ a ∈ t, r a ≤ ε ∧ c a = x) :
-    ∃ (u : _) (_ : u ⊆ t), u.Countable ∧ u.PairwiseDisjoint B ∧ μ (s \ ⋃ a ∈ u, B a) = 0 := by
+    ∃ u ⊆ t, u.Countable ∧ u.PairwiseDisjoint B ∧ μ (s \ ⋃ a ∈ u, B a) = 0 := by
   /- The idea of the proof is the following. Assume for simplicity that `μ` is finite. Applying the
   abstract Vitali covering theorem with `δ = r` given by `hf`, one obtains a disjoint subfamily `u`,
   such that any element of `t` intersects an element of `u` with comparable radius. Fix `ε > 0`.
@@ -243,7 +243,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   -- they only see a finite part of the measure, and with a doubling property
   let t' := { a ∈ t | r a ≤ R (c a) }
   -- extract a disjoint subfamily `u` of `t'` thanks to the abstract Vitali covering theorem.
-  obtain ⟨u, ut', u_disj, hu⟩ : ∃ (u : _) (_ : u ⊆ t'),
+  obtain ⟨u, ut', u_disj, hu⟩ : ∃ u ⊆ t',
       u.PairwiseDisjoint B ∧ ∀ a ∈ t', ∃ b ∈ u, (B a ∩ B b).Nonempty ∧ r a ≤ 2 * r b := by
     have A : ∀ a ∈ t', r a ≤ 1 := by
       intro a ha

@@ -43,7 +43,7 @@ open NNReal Classical ENNReal Topology
 
 namespace Vitali
 
-/-- Vitali covering theorem: given a set `t` of subsets of a type, one may extract a disjoint
+/-- **Vitali covering theorem**: given a set `t` of subsets of a type, one may extract a disjoint
 subfamily `u` such that the `τ`-enlargment of this family covers all elements of `t`, where `τ > 1`
 is any fixed number.
 

Co-authored-by: Kyle Miller <kmill31415@gmail.com>

@@ -142,7 +142,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
       -- Moreover, `δ c` is smaller than the maximum `m` of `δ` over `A`, which is `≤ δ a' / τ`
       -- thanks to the good choice of `a'`. This is the desired inequality.
       push_neg at H
-      simp only [← not_disjoint_iff_nonempty_inter, Classical.not_not] at H
+      simp only [← disjoint_iff_inter_eq_empty] at H
       rcases mem_insert_iff.1 ba'u with (rfl | H')
       · refine' ⟨b, mem_insert _ _, hcb, _⟩
         calc

This reduces the main file from 3340 to 2220 lines. The remaining file is somewhat entangled, so splitting is less obvious. Help is welcome, though a follow-up PR is probably better :-)

I've kept copyright and authors as they were originally.

@@ -3,7 +3,6 @@ Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
 -/
-import Mathlib.Topology.MetricSpace.Basic
 import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathlib.MeasureTheory.Covering.VitaliFamily
 

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

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

@@ -330,7 +330,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
       ball x (R x) ⊆ ⋃ a : { a // a ∉ w }, closedBall (c a) (3 * r a) := by
     intro z hz
     set k := ⋃ (a : v) (_ : a ∈ w), B a
-    have k_closed : IsClosed k := isClosed_biUnion w.finite_toSet fun i _ => h't _ (ut (vu i.2))
+    have k_closed : IsClosed k := isClosed_biUnion_finset fun i _ => h't _ (ut (vu i.2))
     have z_notmem_k : z ∉ k := by
       simp only [not_exists, exists_prop, mem_iUnion, mem_sep_iff, forall_exists_index,
         SetCoe.exists, not_and, exists_and_right, Subtype.coe_mk]

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

This has nice performance benefits.

@@ -36,7 +36,7 @@ This version is given in `Vitali.vitaliFamily`.
 -/
 
 
-variable {α ι : Type _}
+variable {α ι : Type*}
 
 open Set Metric MeasureTheory TopologicalSpace Filter
 

• depends on: #5966

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

@@ -2,16 +2,13 @@
 Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Sébastien Gouëzel
-
-! This file was ported from Lean 3 source module measure_theory.covering.vitali
-! leanprover-community/mathlib commit bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Topology.MetricSpace.Basic
 import Mathlib.MeasureTheory.Constructions.BorelSpace.Basic
 import Mathlib.MeasureTheory.Covering.VitaliFamily
 
+#align_import measure_theory.covering.vitali from "leanprover-community/mathlib"@"bf6a01357ff5684b1ebcd0f1a13be314fc82c0bf"
+
 /-!
 # Vitali covering theorems
 

Fix the set tactic to not time out when dealing with slow to elaborate terms and many local hypotheses.

The root cause of this is that the rewrite [blah] at * tactic causes blah to be elaborated again and again for each local hypothesis, this is possibly a core issue that should be fixed separately, but in set we have the elaborated term already so we can just use it.

We also add some functionality to simply test / demonstrate failures when elaboration takes too long, namely sleepAtLeastHeartbeats and a sleep_heartbeats tactic.

@urkud was facing some slow running set's in https://github.com/leanprover-community/mathlib4/pull/4912, see https://leanprover.zulipchat.com/#narrow/stream/287929-mathlib4/topic/Timeout.20in.20.60set.20.2E.2E.20with.60/near/367958828 that this issue was minimized from and should fix.

Some other linter failures show up due to changes to the set internals so fix these too.

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com>

@@ -332,7 +332,7 @@ theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [Opens
   have M : (s \ ⋃ a ∈ u, B a) ∩
       ball x (R x) ⊆ ⋃ a : { a // a ∉ w }, closedBall (c a) (3 * r a) := by
     intro z hz
-    set k := ⋃ (a : v) (ha : a ∈ w), B a
+    set k := ⋃ (a : v) (_ : a ∈ w), B a
     have k_closed : IsClosed k := isClosed_biUnion w.finite_toSet fun i _ => h't _ (ut (vu i.2))
     have z_notmem_k : z ∉ k := by
       simp only [not_exists, exists_prop, mem_iUnion, mem_sep_iff, forall_exists_index,

Currently, (for both Set and Finset) insert_subset is an iff lemma stating that insert a s ⊆ t if and only if a ∈ t and s ⊆ t. For both types, this PR renames this lemma to insert_subset_iff, and adds an insert_subset lemma that gives the implication just in the reverse direction : namely theorem insert_subset (ha : a ∈ t) (hs : s ⊆ t) : insert a s ⊆ t .

This both aligns the naming with union_subset and union_subset_iff, and removes the need for the awkward insert_subset.mpr ⟨_,_⟩ idiom. It touches a lot of files (too many to list), but in a trivial way.

@@ -128,7 +128,7 @@ theorem exists_disjoint_subfamily_covering_enlargment (B : ι → Set α) (t : S
   -- we claim that `u ∪ {a'}` still belongs to `T`, contradicting the maximality of `u`.
   refine' ⟨insert a' u, ⟨_, _, _⟩, subset_insert _ _, (ne_insert_of_not_mem _ a'_ne_u).symm⟩
   · -- check that `u ∪ {a'}` is made of elements of `t`.
-    rw [insert_subset]
+    rw [insert_subset_iff]
     exact ⟨a'A.1, uT.1⟩
   · -- Check that `u ∪ {a'}` is a disjoint family. This follows from the fact that `a'` does not
     -- intersect `u`.

I have misported is_foo to Foo because I misunderstood the rule for IsLawfulFoo. This PR recover Is of Foo which is ported from is_foo. This PR also renames some misported theorems.

@@ -204,7 +204,7 @@ Then one can extract from `t` a disjoint subfamily that covers almost all `s`.
 For more flexibility, we give a statement with a parameterized family of sets.
 -/
 theorem exists_disjoint_covering_ae [MetricSpace α] [MeasurableSpace α] [OpensMeasurableSpace α]
-    [SecondCountableTopology α] (μ : Measure α) [LocallyFiniteMeasure μ] (s : Set α) (t : Set ι)
+    [SecondCountableTopology α] (μ : Measure α) [IsLocallyFiniteMeasure μ] (s : Set α) (t : Set ι)
     (C : ℝ≥0) (r : ι → ℝ) (c : ι → α) (B : ι → Set α) (hB : ∀ a ∈ t, B a ⊆ closedBall (c a) (r a))
     (μB : ∀ a ∈ t, μ (closedBall (c a) (3 * r a)) ≤ C * μ (B a))
     (ht : ∀ a ∈ t, (interior (B a)).Nonempty) (h't : ∀ a ∈ t, IsClosed (B a))
@@ -403,7 +403,7 @@ doubling. Then the set of closed sets `a` with nonempty interior contained in `c
 covering a fixed proportion `1/C` of the ball `closedBall x (3 * r)` forms a Vitali family.
 This is essentially a restatement of the measurable Vitali theorem. -/
 protected def vitaliFamily [MetricSpace α] [MeasurableSpace α] [OpensMeasurableSpace α]
-    [SecondCountableTopology α] (μ : Measure α) [LocallyFiniteMeasure μ] (C : ℝ≥0)
+    [SecondCountableTopology α] (μ : Measure α) [IsLocallyFiniteMeasure μ] (C : ℝ≥0)
     (h : ∀ x, ∃ᶠ r in 𝓝[>] 0, μ (closedBall x (3 * r)) ≤ C * μ (closedBall x r)) :
     VitaliFamily μ where
   setsAt x := { a | IsClosed a ∧ (interior a).Nonempty ∧