analysis.box_integral.partition.tagged

Changes since the initial port

The following section lists changes to this file in mathlib3 and mathlib4 that occured after the initial port. Most recent changes are shown first. Hovering over a commit will show all commits associated with the same mathlib3 commit.

Changes in mathlib3

6ca1a09b

(last sync)

Changes in mathlib3port

mathlib3

mathlib3port

2ed2c631

bump to nightly-2024-04-10-08

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

cd0c1af5

Diff

@@ -201,7 +201,7 @@ theorem forall_biUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepar
     (∀ J ∈ π.biUnionTagged πi, p ((π.biUnionTagged πi).Tag J) J) ↔
       ∀ J ∈ π, ∀ J' ∈ πi J, p ((πi J).Tag J') J' :=
   by
-  simp only [bex_imp, mem_bUnion_tagged]
+  simp only [exists₂_imp, mem_bUnion_tagged]
   refine' ⟨fun H J hJ J' hJ' => _, fun H J' J hJ hJ' => _⟩
   · rw [← π.tag_bUnion_tagged hJ hJ']; exact H J' J hJ hJ'
   · rw [π.tag_bUnion_tagged hJ hJ']; exact H J hJ J' hJ'

2ed2c631

bump to nightly-2023-12-28-06

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

c30f5587

Diff

@@ -303,7 +303,7 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
     (π.boxes.filterₓ fun J => π.Tag J = x).card ≤
         (π.boxes.filterₓ fun J : Box ι => x ∈ J.Icc).card :=
       by
-      refine' Finset.card_le_of_subset fun J hJ => _
+      refine' Finset.card_le_card fun J hJ => _
       rw [Finset.mem_filter] at hJ ⊢; rcases hJ with ⟨hJ, rfl⟩
       exact ⟨hJ, h J hJ⟩
     _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_Icc_le x

2ed2c631

bump to nightly-2023-09-24-06

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

5655435f

Diff

@@ -3,7 +3,7 @@ Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
-import Mathbin.Analysis.BoxIntegral.Partition.Basic
+import Analysis.BoxIntegral.Partition.Basic
 
 #align_import analysis.box_integral.partition.tagged from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"

2ed2c631

bump to nightly-2023-09-20-06

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

e28e6964

Diff

@@ -362,7 +362,8 @@ theorem IsSubordinate.mono [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.
 theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.IsSubordinate r)
     (hJ : J ∈ π.boxes) : diam J.Icc ≤ 2 * r (π.Tag J) :=
   calc
-    diam J.Icc ≤ diam (closedBall (π.Tag J) (r <| π.Tag J)) := diam_mono (h J hJ) bounded_closedBall
+    diam J.Icc ≤ diam (closedBall (π.Tag J) (r <| π.Tag J)) :=
+      diam_mono (h J hJ) isBounded_closedBall
     _ ≤ 2 * r (π.Tag J) := diam_closedBall (le_of_lt (r _).2)
 #align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le
 -/

2ed2c631

bump to nightly-2023-07-20-09

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

9c56d0dd

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.box_integral.partition.tagged
-! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.BoxIntegral.Partition.Basic
 
+#align_import analysis.box_integral.partition.tagged from "leanprover-community/mathlib"@"2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe"
+
 /-!
 # Tagged partitions

2ed2c631

bump to nightly-2023-06-13-21

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

829520ac

Diff

@@ -65,10 +65,12 @@ theorem mem_toPrepartition {π : TaggedPrepartition I} : J ∈ π.toPrepartition
 #align box_integral.tagged_prepartition.mem_to_prepartition BoxIntegral.TaggedPrepartition.mem_toPrepartition
 -/
 
+#print BoxIntegral.TaggedPrepartition.mem_mk /-
 @[simp]
 theorem mem_mk (π : Prepartition I) (f h) : J ∈ mk π f h ↔ J ∈ π :=
   Iff.rfl
 #align box_integral.tagged_prepartition.mem_mk BoxIntegral.TaggedPrepartition.mem_mk
+-/
 
 #print BoxIntegral.TaggedPrepartition.iUnion /-
 /-- Union of all boxes of a tagged prepartition. -/
@@ -83,10 +85,12 @@ theorem iUnion_def : π.iUnion = ⋃ J ∈ π, ↑J :=
 #align box_integral.tagged_prepartition.Union_def BoxIntegral.TaggedPrepartition.iUnion_def
 -/
 
+#print BoxIntegral.TaggedPrepartition.iUnion_mk /-
 @[simp]
 theorem iUnion_mk (π : Prepartition I) (f h) : (mk π f h).iUnion = π.iUnion :=
   rfl
 #align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.iUnion_mk
+-/
 
 #print BoxIntegral.TaggedPrepartition.iUnion_toPrepartition /-
 @[simp]
@@ -95,10 +99,12 @@ theorem iUnion_toPrepartition : π.toPrepartition.iUnion = π.iUnion :=
 #align box_integral.tagged_prepartition.Union_to_prepartition BoxIntegral.TaggedPrepartition.iUnion_toPrepartition
 -/
 
+#print BoxIntegral.TaggedPrepartition.mem_iUnion /-
 @[simp]
 theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
   Set.mem_iUnion₂
 #align box_integral.tagged_prepartition.mem_Union BoxIntegral.TaggedPrepartition.mem_iUnion
+-/
 
 #print BoxIntegral.TaggedPrepartition.subset_iUnion /-
 theorem subset_iUnion (h : J ∈ π) : ↑J ⊆ π.iUnion :=
@@ -140,11 +146,13 @@ theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧
 #align box_integral.tagged_prepartition.mem_filter BoxIntegral.TaggedPrepartition.mem_filter
 -/
 
+#print BoxIntegral.TaggedPrepartition.iUnion_filter_not /-
 @[simp]
 theorem iUnion_filter_not (π : TaggedPrepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
   π.toPrepartition.iUnion_filter_not p
 #align box_integral.tagged_prepartition.Union_filter_not BoxIntegral.TaggedPrepartition.iUnion_filter_not
+-/
 
 end TaggedPrepartition
 
@@ -164,11 +172,13 @@ def biUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : Ta
 #align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.biUnionTagged
 -/
 
+#print BoxIntegral.Prepartition.mem_biUnionTagged /-
 @[simp]
 theorem mem_biUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} :
     J ∈ π.biUnionTagged πi ↔ ∃ J' ∈ π, J ∈ πi J' :=
   π.mem_biUnion
 #align box_integral.prepartition.mem_bUnion_tagged BoxIntegral.Prepartition.mem_biUnionTagged
+-/
 
 #print BoxIntegral.Prepartition.tag_biUnionTagged /-
 theorem tag_biUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} (hJ : J ∈ π) {J'}
@@ -303,98 +313,131 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
 #align box_integral.tagged_prepartition.is_Henstock.card_filter_tag_eq_le BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le
 -/
 
+#print BoxIntegral.TaggedPrepartition.IsSubordinate /-
 /-- A tagged partition `π` is subordinate to `r : (ι → ℝ) → ℝ` if each box `J ∈ π` is included in
 the closed ball with center `π.tag J` and radius `r (π.tag J)`. -/
 def IsSubordinate [Fintype ι] (π : TaggedPrepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) : Prop :=
   ∀ J ∈ π, (J : _).Icc ⊆ closedBall (π.Tag J) (r <| π.Tag J)
 #align box_integral.tagged_prepartition.is_subordinate BoxIntegral.TaggedPrepartition.IsSubordinate
+-/
 
 variable {r r₁ r₂ : (ι → ℝ) → Ioi (0 : ℝ)}
 
+#print BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged /-
 @[simp]
 theorem isSubordinate_biUnionTagged [Fintype ι] {π : Prepartition I}
     {πi : ∀ J, TaggedPrepartition J} :
     IsSubordinate (π.biUnionTagged πi) r ↔ ∀ J ∈ π, (πi J).IsSubordinate r :=
   π.forall_biUnionTagged (fun x J => J.Icc ⊆ closedBall x (r x)) πi
 #align box_integral.tagged_prepartition.is_subordinate_bUnion_tagged BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartition /-
 theorem IsSubordinate.biUnionPrepartition [Fintype ι] (h : IsSubordinate π r)
     (πi : ∀ J, Prepartition J) : IsSubordinate (π.biUnionPrepartition πi) r := fun J hJ =>
   Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_biUnionIndex hJ) <|
     h _ <| π.toPrepartition.biUnionIndex_mem hJ
 #align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartition
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition /-
 theorem IsSubordinate.infPrepartition [Fintype ι] (h : IsSubordinate π r) (π' : Prepartition I) :
     IsSubordinate (π.infPrepartition π') r :=
   h.biUnionPrepartition _
 #align box_integral.tagged_prepartition.is_subordinate.inf_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsSubordinate.mono' /-
 theorem IsSubordinate.mono' [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ J ∈ π, r₁ (π.Tag J) ≤ r₂ (π.Tag J)) : π.IsSubordinate r₂ := fun J hJ x hx =>
   closedBall_subset_closedBall (h _ hJ) (hr₁ _ hJ hx)
 #align box_integral.tagged_prepartition.is_subordinate.mono' BoxIntegral.TaggedPrepartition.IsSubordinate.mono'
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsSubordinate.mono /-
 theorem IsSubordinate.mono [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ x ∈ I.Icc, r₁ x ≤ r₂ x) : π.IsSubordinate r₂ :=
   hr₁.mono' fun J _ => h _ <| π.tag_mem_Icc J
 #align box_integral.tagged_prepartition.is_subordinate.mono BoxIntegral.TaggedPrepartition.IsSubordinate.mono
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le /-
 theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.IsSubordinate r)
     (hJ : J ∈ π.boxes) : diam J.Icc ≤ 2 * r (π.Tag J) :=
   calc
     diam J.Icc ≤ diam (closedBall (π.Tag J) (r <| π.Tag J)) := diam_mono (h J hJ) bounded_closedBall
     _ ≤ 2 * r (π.Tag J) := diam_closedBall (le_of_lt (r _).2)
 #align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le
+-/
 
+#print BoxIntegral.TaggedPrepartition.single /-
 /-- Tagged prepartition with single box and prescribed tag. -/
 @[simps (config := { fullyApplied := false })]
 def single (I J : Box ι) (hJ : J ≤ I) (x : ι → ℝ) (h : x ∈ I.Icc) : TaggedPrepartition I :=
   ⟨Prepartition.single I J hJ, fun J => x, fun J => h⟩
 #align box_integral.tagged_prepartition.single BoxIntegral.TaggedPrepartition.single
+-/
 
+#print BoxIntegral.TaggedPrepartition.mem_single /-
 @[simp]
 theorem mem_single {J'} (hJ : J ≤ I) (h : x ∈ I.Icc) : J' ∈ single I J hJ x h ↔ J' = J :=
   Finset.mem_singleton
 #align box_integral.tagged_prepartition.mem_single BoxIntegral.TaggedPrepartition.mem_single
+-/
 
 instance (I : Box ι) : Inhabited (TaggedPrepartition I) :=
   ⟨single I I le_rfl I.upper I.upper_mem_Icc⟩
 
+#print BoxIntegral.TaggedPrepartition.isPartition_single_iff /-
 theorem isPartition_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (single I J hJ x h).IsPartition ↔ J = I :=
   Prepartition.isPartition_single_iff hJ
 #align box_integral.tagged_prepartition.is_partition_single_iff BoxIntegral.TaggedPrepartition.isPartition_single_iff
+-/
 
+#print BoxIntegral.TaggedPrepartition.isPartition_single /-
 theorem isPartition_single (h : x ∈ I.Icc) : (single I I le_rfl x h).IsPartition :=
   Prepartition.isPartitionTop I
 #align box_integral.tagged_prepartition.is_partition_single BoxIntegral.TaggedPrepartition.isPartition_single
+-/
 
+#print BoxIntegral.TaggedPrepartition.forall_mem_single /-
 theorem forall_mem_single (p : (ι → ℝ) → Box ι → Prop) (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (∀ J' ∈ single I J hJ x h, p ((single I J hJ x h).Tag J') J') ↔ p x J := by simp
 #align box_integral.tagged_prepartition.forall_mem_single BoxIntegral.TaggedPrepartition.forall_mem_single
+-/
 
+#print BoxIntegral.TaggedPrepartition.isHenstock_single_iff /-
 @[simp]
 theorem isHenstock_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     IsHenstock (single I J hJ x h) ↔ x ∈ J.Icc :=
   forall_mem_single (fun x J => x ∈ J.Icc) hJ h
 #align box_integral.tagged_prepartition.is_Henstock_single_iff BoxIntegral.TaggedPrepartition.isHenstock_single_iff
+-/
 
+#print BoxIntegral.TaggedPrepartition.isHenstock_single /-
 @[simp]
 theorem isHenstock_single (h : x ∈ I.Icc) : IsHenstock (single I I le_rfl x h) :=
   (isHenstock_single_iff (le_refl I) h).2 h
 #align box_integral.tagged_prepartition.is_Henstock_single BoxIntegral.TaggedPrepartition.isHenstock_single
+-/
 
+#print BoxIntegral.TaggedPrepartition.isSubordinate_single /-
 @[simp]
 theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
     IsSubordinate (single I J hJ x h) r ↔ J.Icc ⊆ closedBall x (r x) :=
   forall_mem_single (fun x J => J.Icc ⊆ closedBall x (r x)) hJ h
 #align box_integral.tagged_prepartition.is_subordinate_single BoxIntegral.TaggedPrepartition.isSubordinate_single
+-/
 
+#print BoxIntegral.TaggedPrepartition.iUnion_single /-
 @[simp]
 theorem iUnion_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).iUnion = J :=
   Prepartition.iUnion_single hJ
 #align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.iUnion_single
+-/
 
+#print BoxIntegral.TaggedPrepartition.disjUnion /-
 /-- Union of two tagged prepartitions with disjoint unions of boxes. -/
 def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) :
     TaggedPrepartition I
@@ -405,35 +448,47 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π
     dsimp only [Finset.piecewise]; split_ifs
     exacts [π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
 #align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnion
+-/
 
+#print BoxIntegral.TaggedPrepartition.disjUnion_boxes /-
 @[simp]
 theorem disjUnion_boxes (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).boxes = π₁.boxes ∪ π₂.boxes :=
   rfl
 #align box_integral.tagged_prepartition.disj_union_boxes BoxIntegral.TaggedPrepartition.disjUnion_boxes
+-/
 
+#print BoxIntegral.TaggedPrepartition.mem_disjUnion /-
 @[simp]
 theorem mem_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     J ∈ π₁.disjUnion π₂ h ↔ J ∈ π₁ ∨ J ∈ π₂ :=
   Finset.mem_union
 #align box_integral.tagged_prepartition.mem_disj_union BoxIntegral.TaggedPrepartition.mem_disjUnion
+-/
 
+#print BoxIntegral.TaggedPrepartition.iUnion_disjUnion /-
 @[simp]
 theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion :=
   Prepartition.iUnion_disjUnion _
 #align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.iUnion_disjUnion
+-/
 
+#print BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left /-
 theorem disjUnion_tag_of_mem_left (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₁) :
     (π₁.disjUnion π₂ h).Tag J = π₁.Tag J :=
   dif_pos hJ
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_left BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left
+-/
 
+#print BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right /-
 theorem disjUnion_tag_of_mem_right (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₂) :
     (π₁.disjUnion π₂ h).Tag J = π₂.Tag J :=
   dif_neg fun h₁ => h.le_bot ⟨π₁.subset_iUnion h₁ J.upper_mem, π₂.subset_iUnion hJ J.upper_mem⟩
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_right BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion /-
 theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h₂ : IsSubordinate π₂ r)
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsSubordinate (π₁.disjUnion π₂ h) r :=
   by
@@ -441,7 +496,9 @@ theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h
   · rw [disj_union_tag_of_mem_left _ hJ]; exact h₁ _ hJ
   · rw [disj_union_tag_of_mem_right _ hJ]; exact h₂ _ hJ
 #align box_integral.tagged_prepartition.is_subordinate.disj_union BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion /-
 theorem IsHenstock.disjUnion (h₁ : IsHenstock π₁) (h₂ : IsHenstock π₂)
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsHenstock (π₁.disjUnion π₂ h) :=
   by
@@ -449,6 +506,7 @@ theorem IsHenstock.disjUnion (h₁ : IsHenstock π₁) (h₂ : IsHenstock π₂)
   · rw [disj_union_tag_of_mem_left _ hJ]; exact h₁ _ hJ
   · rw [disj_union_tag_of_mem_right _ hJ]; exact h₂ _ hJ
 #align box_integral.tagged_prepartition.is_Henstock.disj_union BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion
+-/
 
 #print BoxIntegral.TaggedPrepartition.embedBox /-
 /-- If `I ≤ J`, then every tagged prepartition of `I` is a tagged prepartition of `J`. -/
@@ -487,24 +545,30 @@ theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π,
 #align box_integral.tagged_prepartition.distortion_le_iff BoxIntegral.TaggedPrepartition.distortion_le_iff
 -/
 
+#print BoxIntegral.Prepartition.distortion_biUnionTagged /-
 @[simp]
 theorem BoxIntegral.Prepartition.distortion_biUnionTagged (π : Prepartition I)
     (πi : ∀ J, TaggedPrepartition J) :
     (π.biUnionTagged πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_biUnion _ _
 #align box_integral.prepartition.distortion_bUnion_tagged BoxIntegral.Prepartition.distortion_biUnionTagged
+-/
 
+#print BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition /-
 @[simp]
 theorem distortion_biUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) :
     (π.biUnionPrepartition πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_biUnion _ _
 #align box_integral.tagged_prepartition.distortion_bUnion_prepartition BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition
+-/
 
+#print BoxIntegral.TaggedPrepartition.distortion_disjUnion /-
 @[simp]
 theorem distortion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).distortion = max π₁.distortion π₂.distortion :=
   sup_union
 #align box_integral.tagged_prepartition.distortion_disj_union BoxIntegral.TaggedPrepartition.distortion_disjUnion
+-/
 
 #print BoxIntegral.TaggedPrepartition.distortion_of_const /-
 theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π, Box.distortion J = c) :
@@ -513,11 +577,13 @@ theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π,
 #align box_integral.tagged_prepartition.distortion_of_const BoxIntegral.TaggedPrepartition.distortion_of_const
 -/
 
+#print BoxIntegral.TaggedPrepartition.distortion_single /-
 @[simp]
 theorem distortion_single (hJ : J ≤ I) (h : x ∈ I.Icc) :
     distortion (single I J hJ x h) = J.distortion :=
   sup_singleton
 #align box_integral.tagged_prepartition.distortion_single BoxIntegral.TaggedPrepartition.distortion_single
+-/
 
 #print BoxIntegral.TaggedPrepartition.distortion_filter_le /-
 theorem distortion_filter_le (p : Box ι → Prop) : (π.filterₓ p).distortion ≤ π.distortion :=

2ed2c631

bump to nightly-2023-06-09-07

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

16afdc39

Diff

@@ -300,7 +300,6 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
       rw [Finset.mem_filter] at hJ ⊢; rcases hJ with ⟨hJ, rfl⟩
       exact ⟨hJ, h J hJ⟩
     _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_Icc_le x
-    
 #align box_integral.tagged_prepartition.is_Henstock.card_filter_tag_eq_le BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le
 -/
 
@@ -345,7 +344,6 @@ theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.I
   calc
     diam J.Icc ≤ diam (closedBall (π.Tag J) (r <| π.Tag J)) := diam_mono (h J hJ) bounded_closedBall
     _ ≤ 2 * r (π.Tag J) := diam_closedBall (le_of_lt (r _).2)
-    
 #align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le
 
 /-- Tagged prepartition with single box and prescribed tag. -/

2ed2c631

bump to nightly-2023-06-01-16

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

b9c87c70

Diff

@@ -297,7 +297,7 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
         (π.boxes.filterₓ fun J : Box ι => x ∈ J.Icc).card :=
       by
       refine' Finset.card_le_of_subset fun J hJ => _
-      rw [Finset.mem_filter] at hJ⊢; rcases hJ with ⟨hJ, rfl⟩
+      rw [Finset.mem_filter] at hJ ⊢; rcases hJ with ⟨hJ, rfl⟩
       exact ⟨hJ, h J hJ⟩
     _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_Icc_le x
     
@@ -405,7 +405,7 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π
   Tag := π₁.boxes.piecewise π₁.Tag π₂.Tag
   tag_mem_Icc J := by
     dsimp only [Finset.piecewise]; split_ifs
-    exacts[π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
+    exacts [π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
 #align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnion
 
 @[simp]

2ed2c631

bump to nightly-2023-05-28-18

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

8d353152

Diff

@@ -33,7 +33,7 @@ rectangular box, box partition
 
 noncomputable section
 
-open Classical ENNReal NNReal
+open scoped Classical ENNReal NNReal
 
 open Set Function
 
@@ -477,13 +477,17 @@ def distortion : ℝ≥0 :=
 #align box_integral.tagged_prepartition.distortion BoxIntegral.TaggedPrepartition.distortion
 -/
 
+#print BoxIntegral.TaggedPrepartition.distortion_le_of_mem /-
 theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
   le_sup h
 #align box_integral.tagged_prepartition.distortion_le_of_mem BoxIntegral.TaggedPrepartition.distortion_le_of_mem
+-/
 
+#print BoxIntegral.TaggedPrepartition.distortion_le_iff /-
 theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π, Box.distortion J ≤ c :=
   Finset.sup_le_iff
 #align box_integral.tagged_prepartition.distortion_le_iff BoxIntegral.TaggedPrepartition.distortion_le_iff
+-/
 
 @[simp]
 theorem BoxIntegral.Prepartition.distortion_biUnionTagged (π : Prepartition I)
@@ -517,9 +521,11 @@ theorem distortion_single (hJ : J ≤ I) (h : x ∈ I.Icc) :
   sup_singleton
 #align box_integral.tagged_prepartition.distortion_single BoxIntegral.TaggedPrepartition.distortion_single
 
+#print BoxIntegral.TaggedPrepartition.distortion_filter_le /-
 theorem distortion_filter_le (p : Box ι → Prop) : (π.filterₓ p).distortion ≤ π.distortion :=
   sup_mono (filter_subset _ _)
 #align box_integral.tagged_prepartition.distortion_filter_le BoxIntegral.TaggedPrepartition.distortion_filter_le
+-/
 
 end Distortion

2ed2c631

bump to nightly-2023-05-28-06

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

ba5d8b97

Diff

@@ -65,12 +65,6 @@ theorem mem_toPrepartition {π : TaggedPrepartition I} : J ∈ π.toPrepartition
 #align box_integral.tagged_prepartition.mem_to_prepartition BoxIntegral.TaggedPrepartition.mem_toPrepartition
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_mk BoxIntegral.TaggedPrepartition.mem_mkₓ'. -/
 @[simp]
 theorem mem_mk (π : Prepartition I) (f h) : J ∈ mk π f h ↔ J ∈ π :=
   Iff.rfl
@@ -89,12 +83,6 @@ theorem iUnion_def : π.iUnion = ⋃ J ∈ π, ↑J :=
 #align box_integral.tagged_prepartition.Union_def BoxIntegral.TaggedPrepartition.iUnion_def
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.iUnion_mkₓ'. -/
 @[simp]
 theorem iUnion_mk (π : Prepartition I) (f h) : (mk π f h).iUnion = π.iUnion :=
   rfl
@@ -107,12 +95,6 @@ theorem iUnion_toPrepartition : π.toPrepartition.iUnion = π.iUnion :=
 #align box_integral.tagged_prepartition.Union_to_prepartition BoxIntegral.TaggedPrepartition.iUnion_toPrepartition
 -/
 
-/- warning: box_integral.tagged_prepartition.mem_Union -> BoxIntegral.TaggedPrepartition.mem_iUnion is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_Union BoxIntegral.TaggedPrepartition.mem_iUnionₓ'. -/
 @[simp]
 theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
   Set.mem_iUnion₂
@@ -158,12 +140,6 @@ theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧
 #align box_integral.tagged_prepartition.mem_filter BoxIntegral.TaggedPrepartition.mem_filter
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_filter_not BoxIntegral.TaggedPrepartition.iUnion_filter_notₓ'. -/
 @[simp]
 theorem iUnion_filter_not (π : TaggedPrepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
@@ -188,12 +164,6 @@ def biUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : Ta
 #align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.biUnionTagged
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_bUnion_tagged BoxIntegral.Prepartition.mem_biUnionTaggedₓ'. -/
 @[simp]
 theorem mem_biUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} :
     J ∈ π.biUnionTagged πi ↔ ∃ J' ∈ π, J ∈ πi J' :=
@@ -334,12 +304,6 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
 #align box_integral.tagged_prepartition.is_Henstock.card_filter_tag_eq_le BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate BoxIntegral.TaggedPrepartition.IsSubordinateₓ'. -/
 /-- A tagged partition `π` is subordinate to `r : (ι → ℝ) → ℝ` if each box `J ∈ π` is included in
 the closed ball with center `π.tag J` and radius `r (π.tag J)`. -/
 def IsSubordinate [Fintype ι] (π : TaggedPrepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) : Prop :=
@@ -348,12 +312,6 @@ def IsSubordinate [Fintype ι] (π : TaggedPrepartition I) (r : (ι → ℝ) →
 
 variable {r r₁ r₂ : (ι → ℝ) → Ioi (0 : ℝ)}
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate_bUnion_tagged BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTaggedₓ'. -/
 @[simp]
 theorem isSubordinate_biUnionTagged [Fintype ι] {π : Prepartition I}
     {πi : ∀ J, TaggedPrepartition J} :
@@ -361,57 +319,27 @@ theorem isSubordinate_biUnionTagged [Fintype ι] {π : Prepartition I}
   π.forall_biUnionTagged (fun x J => J.Icc ⊆ closedBall x (r x)) πi
 #align box_integral.tagged_prepartition.is_subordinate_bUnion_tagged BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartitionₓ'. -/
 theorem IsSubordinate.biUnionPrepartition [Fintype ι] (h : IsSubordinate π r)
     (πi : ∀ J, Prepartition J) : IsSubordinate (π.biUnionPrepartition πi) r := fun J hJ =>
   Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_biUnionIndex hJ) <|
     h _ <| π.toPrepartition.biUnionIndex_mem hJ
 #align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartition
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.inf_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartitionₓ'. -/
 theorem IsSubordinate.infPrepartition [Fintype ι] (h : IsSubordinate π r) (π' : Prepartition I) :
     IsSubordinate (π.infPrepartition π') r :=
   h.biUnionPrepartition _
 #align box_integral.tagged_prepartition.is_subordinate.inf_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition
 
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 theorem IsSubordinate.mono' [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ J ∈ π, r₁ (π.Tag J) ≤ r₂ (π.Tag J)) : π.IsSubordinate r₂ := fun J hJ x hx =>
   closedBall_subset_closedBall (h _ hJ) (hr₁ _ hJ hx)
 #align box_integral.tagged_prepartition.is_subordinate.mono' BoxIntegral.TaggedPrepartition.IsSubordinate.mono'
 
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 theorem IsSubordinate.mono [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ x ∈ I.Icc, r₁ x ≤ r₂ x) : π.IsSubordinate r₂ :=
   hr₁.mono' fun J _ => h _ <| π.tag_mem_Icc J
 #align box_integral.tagged_prepartition.is_subordinate.mono BoxIntegral.TaggedPrepartition.IsSubordinate.mono
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_leₓ'. -/
 theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.IsSubordinate r)
     (hJ : J ∈ π.boxes) : diam J.Icc ≤ 2 * r (π.Tag J) :=
   calc
@@ -420,24 +348,12 @@ theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.I
     
 #align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.single BoxIntegral.TaggedPrepartition.singleₓ'. -/
 /-- Tagged prepartition with single box and prescribed tag. -/
 @[simps (config := { fullyApplied := false })]
 def single (I J : Box ι) (hJ : J ≤ I) (x : ι → ℝ) (h : x ∈ I.Icc) : TaggedPrepartition I :=
   ⟨Prepartition.single I J hJ, fun J => x, fun J => h⟩
 #align box_integral.tagged_prepartition.single BoxIntegral.TaggedPrepartition.single
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_single BoxIntegral.TaggedPrepartition.mem_singleₓ'. -/
 @[simp]
 theorem mem_single {J'} (hJ : J ≤ I) (h : x ∈ I.Icc) : J' ∈ single I J hJ x h ↔ J' = J :=
   Finset.mem_singleton
@@ -446,89 +362,41 @@ theorem mem_single {J'} (hJ : J ≤ I) (h : x ∈ I.Icc) : J' ∈ single I J hJ
 instance (I : Box ι) : Inhabited (TaggedPrepartition I) :=
   ⟨single I I le_rfl I.upper I.upper_mem_Icc⟩
 
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 theorem isPartition_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (single I J hJ x h).IsPartition ↔ J = I :=
   Prepartition.isPartition_single_iff hJ
 #align box_integral.tagged_prepartition.is_partition_single_iff BoxIntegral.TaggedPrepartition.isPartition_single_iff
 
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 theorem isPartition_single (h : x ∈ I.Icc) : (single I I le_rfl x h).IsPartition :=
   Prepartition.isPartitionTop I
 #align box_integral.tagged_prepartition.is_partition_single BoxIntegral.TaggedPrepartition.isPartition_single
 
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 theorem forall_mem_single (p : (ι → ℝ) → Box ι → Prop) (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (∀ J' ∈ single I J hJ x h, p ((single I J hJ x h).Tag J') J') ↔ p x J := by simp
 #align box_integral.tagged_prepartition.forall_mem_single BoxIntegral.TaggedPrepartition.forall_mem_single
 
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 @[simp]
 theorem isHenstock_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     IsHenstock (single I J hJ x h) ↔ x ∈ J.Icc :=
   forall_mem_single (fun x J => x ∈ J.Icc) hJ h
 #align box_integral.tagged_prepartition.is_Henstock_single_iff BoxIntegral.TaggedPrepartition.isHenstock_single_iff
 
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 @[simp]
 theorem isHenstock_single (h : x ∈ I.Icc) : IsHenstock (single I I le_rfl x h) :=
   (isHenstock_single_iff (le_refl I) h).2 h
 #align box_integral.tagged_prepartition.is_Henstock_single BoxIntegral.TaggedPrepartition.isHenstock_single
 
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 @[simp]
 theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
     IsSubordinate (single I J hJ x h) r ↔ J.Icc ⊆ closedBall x (r x) :=
   forall_mem_single (fun x J => J.Icc ⊆ closedBall x (r x)) hJ h
 #align box_integral.tagged_prepartition.is_subordinate_single BoxIntegral.TaggedPrepartition.isSubordinate_single
 
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 @[simp]
 theorem iUnion_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).iUnion = J :=
   Prepartition.iUnion_single hJ
 #align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.iUnion_single
 
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 /-- Union of two tagged prepartitions with disjoint unions of boxes. -/
 def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) :
     TaggedPrepartition I
@@ -540,70 +408,34 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π
     exacts[π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
 #align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnion
 
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 @[simp]
 theorem disjUnion_boxes (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).boxes = π₁.boxes ∪ π₂.boxes :=
   rfl
 #align box_integral.tagged_prepartition.disj_union_boxes BoxIntegral.TaggedPrepartition.disjUnion_boxes
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_disj_union BoxIntegral.TaggedPrepartition.mem_disjUnionₓ'. -/
 @[simp]
 theorem mem_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     J ∈ π₁.disjUnion π₂ h ↔ J ∈ π₁ ∨ J ∈ π₂ :=
   Finset.mem_union
 #align box_integral.tagged_prepartition.mem_disj_union BoxIntegral.TaggedPrepartition.mem_disjUnion
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.iUnion_disjUnionₓ'. -/
 @[simp]
 theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion :=
   Prepartition.iUnion_disjUnion _
 #align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.iUnion_disjUnion
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.disj_union_tag_of_mem_left BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_leftₓ'. -/
 theorem disjUnion_tag_of_mem_left (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₁) :
     (π₁.disjUnion π₂ h).Tag J = π₁.Tag J :=
   dif_pos hJ
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_left BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.disj_union_tag_of_mem_right BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_rightₓ'. -/
 theorem disjUnion_tag_of_mem_right (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₂) :
     (π₁.disjUnion π₂ h).Tag J = π₂.Tag J :=
   dif_neg fun h₁ => h.le_bot ⟨π₁.subset_iUnion h₁ J.upper_mem, π₂.subset_iUnion hJ J.upper_mem⟩
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_right BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.disj_union BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnionₓ'. -/
 theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h₂ : IsSubordinate π₂ r)
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsSubordinate (π₁.disjUnion π₂ h) r :=
   by
@@ -612,12 +444,6 @@ theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h
   · rw [disj_union_tag_of_mem_right _ hJ]; exact h₂ _ hJ
 #align box_integral.tagged_prepartition.is_subordinate.disj_union BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_Henstock.disj_union BoxIntegral.TaggedPrepartition.IsHenstock.disjUnionₓ'. -/
 theorem IsHenstock.disjUnion (h₁ : IsHenstock π₁) (h₂ : IsHenstock π₂)
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsHenstock (π₁.disjUnion π₂ h) :=
   by
@@ -651,32 +477,14 @@ def distortion : ℝ≥0 :=
 #align box_integral.tagged_prepartition.distortion BoxIntegral.TaggedPrepartition.distortion
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_le_of_mem BoxIntegral.TaggedPrepartition.distortion_le_of_memₓ'. -/
 theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
   le_sup h
 #align box_integral.tagged_prepartition.distortion_le_of_mem BoxIntegral.TaggedPrepartition.distortion_le_of_mem
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_le_iff BoxIntegral.TaggedPrepartition.distortion_le_iffₓ'. -/
 theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π, Box.distortion J ≤ c :=
   Finset.sup_le_iff
 #align box_integral.tagged_prepartition.distortion_le_iff BoxIntegral.TaggedPrepartition.distortion_le_iff
 
-/- warning: box_integral.prepartition.distortion_bUnion_tagged -> BoxIntegral.Prepartition.distortion_biUnionTagged is a dubious translation:
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-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} [_inst_1 : Fintype.{u1} ι] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.TaggedPrepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.biUnionTagged.{u1} ι I π πi) _inst_1) (Finset.sup.{0, u1} NNReal (BoxIntegral.Box.{u1} ι) instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.TaggedPrepartition.distortion.{u1} ι J (πi J) _inst_1))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_bUnion_tagged BoxIntegral.Prepartition.distortion_biUnionTaggedₓ'. -/
 @[simp]
 theorem BoxIntegral.Prepartition.distortion_biUnionTagged (π : Prepartition I)
     (πi : ∀ J, TaggedPrepartition J) :
@@ -684,24 +492,12 @@ theorem BoxIntegral.Prepartition.distortion_biUnionTagged (π : Prepartition I)
   sup_biUnion _ _
 #align box_integral.prepartition.distortion_bUnion_tagged BoxIntegral.Prepartition.distortion_biUnionTagged
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_bUnion_prepartition BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartitionₓ'. -/
 @[simp]
 theorem distortion_biUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) :
     (π.biUnionPrepartition πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_biUnion _ _
 #align box_integral.tagged_prepartition.distortion_bUnion_prepartition BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition
 
-/- warning: box_integral.tagged_prepartition.distortion_disj_union -> BoxIntegral.TaggedPrepartition.distortion_disjUnion is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} [_inst_1 : Fintype.{u1} ι] (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₂ _inst_1))
-but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} [_inst_1 : Fintype.{u1} ι] (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₂ _inst_1))
-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_disj_union BoxIntegral.TaggedPrepartition.distortion_disjUnionₓ'. -/
 @[simp]
 theorem distortion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).distortion = max π₁.distortion π₂.distortion :=
@@ -715,24 +511,12 @@ theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π,
 #align box_integral.tagged_prepartition.distortion_of_const BoxIntegral.TaggedPrepartition.distortion_of_const
 -/
 
-/- warning: box_integral.tagged_prepartition.distortion_single -> BoxIntegral.TaggedPrepartition.distortion_single is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J)
-but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J)
-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_single BoxIntegral.TaggedPrepartition.distortion_singleₓ'. -/
 @[simp]
 theorem distortion_single (hJ : J ≤ I) (h : x ∈ I.Icc) :
     distortion (single I J hJ x h) = J.distortion :=
   sup_singleton
 #align box_integral.tagged_prepartition.distortion_single BoxIntegral.TaggedPrepartition.distortion_single
 
-/- warning: box_integral.tagged_prepartition.distortion_filter_le -> BoxIntegral.TaggedPrepartition.distortion_filter_le is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (p : (BoxIntegral.Box.{u1} ι) -> Prop), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π p) _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1)
-but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (p : (BoxIntegral.Box.{u1} ι) -> Prop), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π p) _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1)
-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_filter_le BoxIntegral.TaggedPrepartition.distortion_filter_leₓ'. -/
 theorem distortion_filter_le (p : Box ι → Prop) : (π.filterₓ p).distortion ≤ π.distortion :=
   sup_mono (filter_subset _ _)
 #align box_integral.tagged_prepartition.distortion_filter_le BoxIntegral.TaggedPrepartition.distortion_filter_le

2ed2c631

bump to nightly-2023-05-28-04

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

6797a637

Diff

@@ -226,10 +226,8 @@ theorem forall_biUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepar
   by
   simp only [bex_imp, mem_bUnion_tagged]
   refine' ⟨fun H J hJ J' hJ' => _, fun H J' J hJ hJ' => _⟩
-  · rw [← π.tag_bUnion_tagged hJ hJ']
-    exact H J' J hJ hJ'
-  · rw [π.tag_bUnion_tagged hJ hJ']
-    exact H J hJ J' hJ'
+  · rw [← π.tag_bUnion_tagged hJ hJ']; exact H J' J hJ hJ'
+  · rw [π.tag_bUnion_tagged hJ hJ']; exact H J hJ J' hJ'
 #align box_integral.prepartition.forall_bUnion_tagged BoxIntegral.Prepartition.forall_biUnionTagged
 -/
 
@@ -538,8 +536,7 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π
   toPrepartition := π₁.toPrepartition.disjUnion π₂.toPrepartition h
   Tag := π₁.boxes.piecewise π₁.Tag π₂.Tag
   tag_mem_Icc J := by
-    dsimp only [Finset.piecewise]
-    split_ifs
+    dsimp only [Finset.piecewise]; split_ifs
     exacts[π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
 #align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnion
 
@@ -611,10 +608,8 @@ theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsSubordinate (π₁.disjUnion π₂ h) r :=
   by
   refine' fun J hJ => (Finset.mem_union.1 hJ).elim (fun hJ => _) fun hJ => _
-  · rw [disj_union_tag_of_mem_left _ hJ]
-    exact h₁ _ hJ
-  · rw [disj_union_tag_of_mem_right _ hJ]
-    exact h₂ _ hJ
+  · rw [disj_union_tag_of_mem_left _ hJ]; exact h₁ _ hJ
+  · rw [disj_union_tag_of_mem_right _ hJ]; exact h₂ _ hJ
 #align box_integral.tagged_prepartition.is_subordinate.disj_union BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion
 
 /- warning: box_integral.tagged_prepartition.is_Henstock.disj_union -> BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion is a dubious translation:
@@ -627,10 +622,8 @@ theorem IsHenstock.disjUnion (h₁ : IsHenstock π₁) (h₂ : IsHenstock π₂)
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsHenstock (π₁.disjUnion π₂ h) :=
   by
   refine' fun J hJ => (Finset.mem_union.1 hJ).elim (fun hJ => _) fun hJ => _
-  · rw [disj_union_tag_of_mem_left _ hJ]
-    exact h₁ _ hJ
-  · rw [disj_union_tag_of_mem_right _ hJ]
-    exact h₂ _ hJ
+  · rw [disj_union_tag_of_mem_left _ hJ]; exact h₁ _ hJ
+  · rw [disj_union_tag_of_mem_right _ hJ]; exact h₂ _ hJ
 #align box_integral.tagged_prepartition.is_Henstock.disj_union BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion
 
 #print BoxIntegral.TaggedPrepartition.embedBox /-
@@ -641,9 +634,7 @@ def embedBox (I J : Box ι) (h : I ≤ J) : TaggedPrepartition I ↪ TaggedPrepa
     { π with
       le_of_mem' := fun J' hJ' => (π.le_of_mem' J' hJ').trans h
       tag_mem_Icc := fun J => Box.le_iff_Icc.1 h (π.tag_mem_Icc J) }
-  inj' := by
-    rintro ⟨⟨b₁, h₁le, h₁d⟩, t₁, ht₁⟩ ⟨⟨b₂, h₂le, h₂d⟩, t₂, ht₂⟩ H
-    simpa using H
+  inj' := by rintro ⟨⟨b₁, h₁le, h₁d⟩, t₁, ht₁⟩ ⟨⟨b₂, h₂le, h₂d⟩, t₂, ht₂⟩ H; simpa using H
 #align box_integral.tagged_prepartition.embed_box BoxIntegral.TaggedPrepartition.embedBox
 -/

2ed2c631

bump to nightly-2023-05-19-16

mathlib commit https://github.com/leanprover-community/mathlib/commit/95a87616d63b3cb49d3fe678d416fbe9c4217bf4

a31df521

Diff

@@ -69,7 +69,7 @@ theorem mem_toPrepartition {π : TaggedPrepartition I} : J ∈ π.toPrepartition
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) (f J) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) (f J) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) (f J) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_mk BoxIntegral.TaggedPrepartition.mem_mkₓ'. -/
 @[simp]
 theorem mem_mk (π : Prepartition I) (f h) : J ∈ mk π f h ↔ J ∈ π :=
@@ -93,7 +93,7 @@ theorem iUnion_def : π.iUnion = ⋃ J ∈ π, ↑J :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) (f J) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) (f J) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) (f J) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.iUnion_mkₓ'. -/
 @[simp]
 theorem iUnion_mk (π : Prepartition I) (f h) : (mk π f h).iUnion = π.iUnion :=
@@ -401,7 +401,7 @@ theorem IsSubordinate.mono' [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r₁ : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} {r₂ : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₁) -> (forall (x : ι -> Real), (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) (r₁ x) (r₂ x))) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₂)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r₁ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} {r₂ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₁) -> (forall (x : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (LE.le.{0} (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (r₁ x) (r₂ x))) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₂)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r₁ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} {r₂ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₁) -> (forall (x : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (LE.le.{0} (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (r₁ x) (r₂ x))) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₂)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.mono BoxIntegral.TaggedPrepartition.IsSubordinate.monoₓ'. -/
 theorem IsSubordinate.mono [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ x ∈ I.Icc, r₁ x ≤ r₂ x) : π.IsSubordinate r₂ :=
@@ -412,7 +412,7 @@ theorem IsSubordinate.mono [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasMem.{u1} (BoxIntegral.Box.{u1} ι)) J (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π))) -> (LE.le.{0} Real Real.hasLe (Metric.diam.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))))) (r (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instMembershipFinset.{u1} (BoxIntegral.Box.{u1} ι)) J (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π))) -> (LE.le.{0} Real Real.instLEReal (Metric.diam.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) J)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (r (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instMembershipFinset.{u1} (BoxIntegral.Box.{u1} ι)) J (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π))) -> (LE.le.{0} Real Real.instLEReal (Metric.diam.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) J)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (r (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)))))
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_leₓ'. -/
 theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.IsSubordinate r)
     (hJ : J ∈ π.boxes) : diam J.Icc ≤ 2 * r (π.Tag J) :=
@@ -426,7 +426,7 @@ theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.I
 lean 3 declaration is
   forall {ι : Type.{u1}} (I : BoxIntegral.Box.{u1} ι) (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) -> (forall (x : ι -> Real), (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (BoxIntegral.TaggedPrepartition.{u1} ι I))
 but is expected to have type
-  forall {ι : Type.{u1}} (I : BoxIntegral.Box.{u1} ι) (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (x : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (BoxIntegral.TaggedPrepartition.{u1} ι I))
+  forall {ι : Type.{u1}} (I : BoxIntegral.Box.{u1} ι) (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (x : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (BoxIntegral.TaggedPrepartition.{u1} ι I))
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.single BoxIntegral.TaggedPrepartition.singleₓ'. -/
 /-- Tagged prepartition with single box and prescribed tag. -/
 @[simps (config := { fullyApplied := false })]
@@ -438,7 +438,7 @@ def single (I J : Box ι) (hJ : J ≤ I) (x : ι → ℝ) (h : x ∈ I.Icc) : Ta
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {J' : BoxIntegral.Box.{u1} ι} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J' J)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {J' : BoxIntegral.Box.{u1} ι} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J' J)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {J' : BoxIntegral.Box.{u1} ι} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J' J)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_single BoxIntegral.TaggedPrepartition.mem_singleₓ'. -/
 @[simp]
 theorem mem_single {J'} (hJ : J ≤ I) (h : x ∈ I.Icc) : J' ∈ single I J hJ x h ↔ J' = J :=
@@ -452,7 +452,7 @@ instance (I : Box ι) : Inhabited (TaggedPrepartition I) :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J I)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J I)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J I)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_partition_single_iff BoxIntegral.TaggedPrepartition.isPartition_single_iffₓ'. -/
 theorem isPartition_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (single I J hJ x h).IsPartition ↔ J = I :=
@@ -463,7 +463,7 @@ theorem isPartition_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) I) x h)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) I) x h)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) I) x h)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_partition_single BoxIntegral.TaggedPrepartition.isPartition_singleₓ'. -/
 theorem isPartition_single (h : x ∈ I.Icc) : (single I I le_rfl x h).IsPartition :=
   Prepartition.isPartitionTop I
@@ -473,7 +473,7 @@ theorem isPartition_single (h : x ∈ I.Icc) : (single I I le_rfl x h).IsPartiti
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (p : (ι -> Real) -> (BoxIntegral.Box.{u1} ι) -> Prop) (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) -> (p (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) J') J')) (p x J)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (p : (ι -> Real) -> (BoxIntegral.Box.{u1} ι) -> Prop) (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) -> (p (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) J') J')) (p x J)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (p : (ι -> Real) -> (BoxIntegral.Box.{u1} ι) -> Prop) (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) -> (p (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) J') J')) (p x J)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.forall_mem_single BoxIntegral.TaggedPrepartition.forall_mem_singleₓ'. -/
 theorem forall_mem_single (p : (ι → ℝ) → Box ι → Prop) (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (∀ J' ∈ single I J hJ x h, p ((single I J hJ x h).Tag J') J') ↔ p x J := by simp
@@ -483,7 +483,7 @@ theorem forall_mem_single (p : (ι → ℝ) → Box ι → Prop) (hJ : J ≤ I)
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) J))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) J))
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_Henstock_single_iff BoxIntegral.TaggedPrepartition.isHenstock_single_iffₓ'. -/
 @[simp]
 theorem isHenstock_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
@@ -495,7 +495,7 @@ theorem isHenstock_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) I) x h)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) I) x h)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) I) x h)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_Henstock_single BoxIntegral.TaggedPrepartition.isHenstock_singleₓ'. -/
 @[simp]
 theorem isHenstock_single (h : x ∈ I.Icc) : IsHenstock (single I I le_rfl x h) :=
@@ -506,7 +506,7 @@ theorem isHenstock_single (h : x ∈ I.Icc) : IsHenstock (single I I le_rfl x h)
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) r) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J) (Metric.closedBall.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))))) (r x))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) r) (HasSubset.Subset.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instHasSubsetSet.{u1} (ι -> Real)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) J) (Metric.closedBall.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) x (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (r x))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) r) (HasSubset.Subset.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instHasSubsetSet.{u1} (ι -> Real)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) J) (Metric.closedBall.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) x (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (r x))))
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate_single BoxIntegral.TaggedPrepartition.isSubordinate_singleₓ'. -/
 @[simp]
 theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
@@ -518,7 +518,7 @@ theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.Set.hasCoeT.{u1} ι))) J)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (BoxIntegral.Box.toSet.{u1} ι J)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (BoxIntegral.Box.toSet.{u1} ι J)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.iUnion_singleₓ'. -/
 @[simp]
 theorem iUnion_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).iUnion = J :=
@@ -728,7 +728,7 @@ theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π,
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J)
 Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_single BoxIntegral.TaggedPrepartition.distortion_singleₓ'. -/
 @[simp]
 theorem distortion_single (hJ : J ≤ I) (h : x ∈ I.Icc) :

2ed2c631

bump to nightly-2023-05-18-03

mathlib commit https://github.com/leanprover-community/mathlib/commit/c89fe2d59ae06402c3f55f978016d1ada444f57e

b46e9d53

Diff

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module analysis.box_integral.partition.tagged
-! leanprover-community/mathlib commit 6ca1a09bc9aa75824bf97388c9e3b441fc4ccf3f
+! leanprover-community/mathlib commit 2ed2c6310e6f1c5562bdf6bfbda55ebbf6891abe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -13,6 +13,9 @@ import Mathbin.Analysis.BoxIntegral.Partition.Basic
 /-!
 # Tagged partitions
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 A tagged (pre)partition is a (pre)partition `π` enriched with a tagged point for each box of
 ‵π`. For simplicity we require that the function `box_integral.tagged_prepartition.tag` is defined
 on all boxes `J : box ι` but use its values only on boxes of the partition. Given `π :

6ca1a09b

bump to nightly-2023-05-16-20

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

b550b1b3

Diff

@@ -38,6 +38,7 @@ namespace BoxIntegral
 
 variable {ι : Type _}
 
+#print BoxIntegral.TaggedPrepartition /-
 /-- A tagged prepartition is a prepartition enriched with a tagged point for each box of the
 prepartition. For simiplicity we require that `tag` is defined for all boxes in `ι → ℝ` but
 we will use onle the values of `tag` on the boxes of the partition. -/
@@ -45,6 +46,7 @@ structure TaggedPrepartition (I : Box ι) extends Prepartition I where
   Tag : Box ι → ι → ℝ
   tag_mem_Icc : ∀ J, tag J ∈ I.Icc
 #align box_integral.tagged_prepartition BoxIntegral.TaggedPrepartition
+-/
 
 namespace TaggedPrepartition
 
@@ -53,73 +55,117 @@ variable {I J J₁ J₂ : Box ι} (π : TaggedPrepartition I) {x : ι → ℝ}
 instance : Membership (Box ι) (TaggedPrepartition I) :=
   ⟨fun J π => J ∈ π.boxes⟩
 
+#print BoxIntegral.TaggedPrepartition.mem_toPrepartition /-
 @[simp]
 theorem mem_toPrepartition {π : TaggedPrepartition I} : J ∈ π.toPrepartition ↔ J ∈ π :=
   Iff.rfl
 #align box_integral.tagged_prepartition.mem_to_prepartition BoxIntegral.TaggedPrepartition.mem_toPrepartition
+-/
 
+/- warning: box_integral.tagged_prepartition.mem_mk -> BoxIntegral.TaggedPrepartition.mem_mk is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) (f J) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) (f J) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_mk BoxIntegral.TaggedPrepartition.mem_mkₓ'. -/
 @[simp]
 theorem mem_mk (π : Prepartition I) (f h) : J ∈ mk π f h ↔ J ∈ π :=
   Iff.rfl
 #align box_integral.tagged_prepartition.mem_mk BoxIntegral.TaggedPrepartition.mem_mk
 
+#print BoxIntegral.TaggedPrepartition.iUnion /-
 /-- Union of all boxes of a tagged prepartition. -/
-def union : Set (ι → ℝ) :=
+def iUnion : Set (ι → ℝ) :=
   π.toPrepartition.iUnion
-#align box_integral.tagged_prepartition.Union BoxIntegral.TaggedPrepartition.union
+#align box_integral.tagged_prepartition.Union BoxIntegral.TaggedPrepartition.iUnion
+-/
 
-theorem union_def : π.iUnion = ⋃ J ∈ π, ↑J :=
+#print BoxIntegral.TaggedPrepartition.iUnion_def /-
+theorem iUnion_def : π.iUnion = ⋃ J ∈ π, ↑J :=
   rfl
-#align box_integral.tagged_prepartition.Union_def BoxIntegral.TaggedPrepartition.union_def
+#align box_integral.tagged_prepartition.Union_def BoxIntegral.TaggedPrepartition.iUnion_def
+-/
 
+/- warning: box_integral.tagged_prepartition.Union_mk -> BoxIntegral.TaggedPrepartition.iUnion_mk is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) (f J) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> ι -> Real) (h : forall (J : BoxIntegral.Box.{u1} ι), Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) (f J) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.mk.{u1} ι I π f h)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.iUnion_mkₓ'. -/
 @[simp]
-theorem union_mk (π : Prepartition I) (f h) : (mk π f h).iUnion = π.iUnion :=
+theorem iUnion_mk (π : Prepartition I) (f h) : (mk π f h).iUnion = π.iUnion :=
   rfl
-#align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.union_mk
+#align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.iUnion_mk
 
+#print BoxIntegral.TaggedPrepartition.iUnion_toPrepartition /-
 @[simp]
 theorem iUnion_toPrepartition : π.toPrepartition.iUnion = π.iUnion :=
   rfl
 #align box_integral.tagged_prepartition.Union_to_prepartition BoxIntegral.TaggedPrepartition.iUnion_toPrepartition
+-/
 
+/- warning: box_integral.tagged_prepartition.mem_Union -> BoxIntegral.TaggedPrepartition.mem_iUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π)) (Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => Exists.{0} (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π) (fun (H : Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π) => Membership.Mem.{u1, u1} (ι -> Real) (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasMem.{u1} ι) x J)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.instMembershipSet.{u1} (ι -> Real)) x (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π)) (Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => And (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π) (Membership.mem.{u1, u1} (ι -> Real) (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instMembershipForAllRealBox.{u1} ι) x J)))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_Union BoxIntegral.TaggedPrepartition.mem_iUnionₓ'. -/
 @[simp]
-theorem mem_union : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
+theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
   Set.mem_iUnion₂
-#align box_integral.tagged_prepartition.mem_Union BoxIntegral.TaggedPrepartition.mem_union
+#align box_integral.tagged_prepartition.mem_Union BoxIntegral.TaggedPrepartition.mem_iUnion
 
-theorem subset_union (h : J ∈ π) : ↑J ⊆ π.iUnion :=
+#print BoxIntegral.TaggedPrepartition.subset_iUnion /-
+theorem subset_iUnion (h : J ∈ π) : ↑J ⊆ π.iUnion :=
   subset_biUnion_of_mem h
-#align box_integral.tagged_prepartition.subset_Union BoxIntegral.TaggedPrepartition.subset_union
+#align box_integral.tagged_prepartition.subset_Union BoxIntegral.TaggedPrepartition.subset_iUnion
+-/
 
-theorem union_subset : π.iUnion ⊆ I :=
+#print BoxIntegral.TaggedPrepartition.iUnion_subset /-
+theorem iUnion_subset : π.iUnion ⊆ I :=
   iUnion₂_subset π.le_of_mem'
-#align box_integral.tagged_prepartition.Union_subset BoxIntegral.TaggedPrepartition.union_subset
+#align box_integral.tagged_prepartition.Union_subset BoxIntegral.TaggedPrepartition.iUnion_subset
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsPartition /-
 /-- A tagged prepartition is a partition if it covers the whole box. -/
 def IsPartition :=
   π.toPrepartition.IsPartition
 #align box_integral.tagged_prepartition.is_partition BoxIntegral.TaggedPrepartition.IsPartition
+-/
 
-theorem isPartition_iff_union_eq : IsPartition π ↔ π.iUnion = I :=
+#print BoxIntegral.TaggedPrepartition.isPartition_iff_iUnion_eq /-
+theorem isPartition_iff_iUnion_eq : IsPartition π ↔ π.iUnion = I :=
   Prepartition.isPartition_iff_iUnion_eq
-#align box_integral.tagged_prepartition.is_partition_iff_Union_eq BoxIntegral.TaggedPrepartition.isPartition_iff_union_eq
+#align box_integral.tagged_prepartition.is_partition_iff_Union_eq BoxIntegral.TaggedPrepartition.isPartition_iff_iUnion_eq
+-/
 
+#print BoxIntegral.TaggedPrepartition.filter /-
 /-- The tagged partition made of boxes of `π` that satisfy predicate `p`. -/
 @[simps (config := { fullyApplied := false })]
 def filter (p : Box ι → Prop) : TaggedPrepartition I :=
   ⟨π.1.filterₓ p, π.2, π.3⟩
 #align box_integral.tagged_prepartition.filter BoxIntegral.TaggedPrepartition.filter
+-/
 
+#print BoxIntegral.TaggedPrepartition.mem_filter /-
 @[simp]
 theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧ p J :=
   Finset.mem_filter
 #align box_integral.tagged_prepartition.mem_filter BoxIntegral.TaggedPrepartition.mem_filter
+-/
 
+/- warning: box_integral.tagged_prepartition.Union_filter_not -> BoxIntegral.TaggedPrepartition.iUnion_filter_not is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π (fun (J : BoxIntegral.Box.{u1} ι) => Not (p J)))) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π p)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π (fun (J : BoxIntegral.Box.{u1} ι) => Not (p J)))) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π p)))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_filter_not BoxIntegral.TaggedPrepartition.iUnion_filter_notₓ'. -/
 @[simp]
-theorem union_filter_not (π : TaggedPrepartition I) (p : Box ι → Prop) :
+theorem iUnion_filter_not (π : TaggedPrepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
   π.toPrepartition.iUnion_filter_not p
-#align box_integral.tagged_prepartition.Union_filter_not BoxIntegral.TaggedPrepartition.union_filter_not
+#align box_integral.tagged_prepartition.Union_filter_not BoxIntegral.TaggedPrepartition.iUnion_filter_not
 
 end TaggedPrepartition
 
@@ -127,39 +173,52 @@ namespace Prepartition
 
 variable {I J : Box ι}
 
+#print BoxIntegral.Prepartition.biUnionTagged /-
 /-- Given a partition `π` of `I : box_integral.box ι` and a collection of tagged partitions
 `πi J` of all boxes `J ∈ π`, returns the tagged partition of `I` into all the boxes of `πi J`
 with tags coming from `(πi J).tag`. -/
-def bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : TaggedPrepartition I
+def biUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : TaggedPrepartition I
     where
   toPrepartition := π.biUnion fun J => (πi J).toPrepartition
   Tag J := (πi (π.biUnionIndex (fun J => (πi J).toPrepartition) J)).Tag J
   tag_mem_Icc J := Box.le_iff_Icc.1 (π.biUnionIndex_le _ _) ((πi _).tag_mem_Icc _)
-#align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.bUnionTagged
+#align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.biUnionTagged
+-/
 
+/- warning: box_integral.prepartition.mem_bUnion_tagged -> BoxIntegral.Prepartition.mem_biUnionTagged is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.TaggedPrepartition.{u1} ι J}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.biUnionTagged.{u1} ι I π πi)) (Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J' : BoxIntegral.Box.{u1} ι) => Exists.{0} (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J' π) (fun (H : Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J' π) => Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι J') (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι J') J (πi J'))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.TaggedPrepartition.{u1} ι J}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.biUnionTagged.{u1} ι I π πi)) (Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J' : BoxIntegral.Box.{u1} ι) => And (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J' π) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι J') (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι J') J (πi J'))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_bUnion_tagged BoxIntegral.Prepartition.mem_biUnionTaggedₓ'. -/
 @[simp]
-theorem mem_bUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} :
-    J ∈ π.bUnionTagged πi ↔ ∃ J' ∈ π, J ∈ πi J' :=
+theorem mem_biUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} :
+    J ∈ π.biUnionTagged πi ↔ ∃ J' ∈ π, J ∈ πi J' :=
   π.mem_biUnion
-#align box_integral.prepartition.mem_bUnion_tagged BoxIntegral.Prepartition.mem_bUnionTagged
+#align box_integral.prepartition.mem_bUnion_tagged BoxIntegral.Prepartition.mem_biUnionTagged
 
-theorem tag_bUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} (hJ : J ∈ π) {J'}
-    (hJ' : J' ∈ πi J) : (π.bUnionTagged πi).Tag J' = (πi J).Tag J' :=
+#print BoxIntegral.Prepartition.tag_biUnionTagged /-
+theorem tag_biUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} (hJ : J ∈ π) {J'}
+    (hJ' : J' ∈ πi J) : (π.biUnionTagged πi).Tag J' = (πi J).Tag J' :=
   by
   have : J' ∈ π.bUnion_tagged πi := π.mem_bUnion.2 ⟨J, hJ, hJ'⟩
   obtain rfl := π.bUnion_index_of_mem hJ hJ'
   rfl
-#align box_integral.prepartition.tag_bUnion_tagged BoxIntegral.Prepartition.tag_bUnionTagged
+#align box_integral.prepartition.tag_bUnion_tagged BoxIntegral.Prepartition.tag_biUnionTagged
+-/
 
+#print BoxIntegral.Prepartition.iUnion_biUnionTagged /-
 @[simp]
-theorem union_bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) :
-    (π.bUnionTagged πi).iUnion = ⋃ J ∈ π, (πi J).iUnion :=
+theorem iUnion_biUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) :
+    (π.biUnionTagged πi).iUnion = ⋃ J ∈ π, (πi J).iUnion :=
   iUnion_biUnion _ _
-#align box_integral.prepartition.Union_bUnion_tagged BoxIntegral.Prepartition.union_bUnionTagged
+#align box_integral.prepartition.Union_bUnion_tagged BoxIntegral.Prepartition.iUnion_biUnionTagged
+-/
 
-theorem forall_bUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepartition I)
+#print BoxIntegral.Prepartition.forall_biUnionTagged /-
+theorem forall_biUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepartition I)
     (πi : ∀ J, TaggedPrepartition J) :
-    (∀ J ∈ π.bUnionTagged πi, p ((π.bUnionTagged πi).Tag J) J) ↔
+    (∀ J ∈ π.biUnionTagged πi, p ((π.biUnionTagged πi).Tag J) J) ↔
       ∀ J ∈ π, ∀ J' ∈ πi J, p ((πi J).Tag J') J' :=
   by
   simp only [bex_imp, mem_bUnion_tagged]
@@ -168,13 +227,16 @@ theorem forall_bUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepart
     exact H J' J hJ hJ'
   · rw [π.tag_bUnion_tagged hJ hJ']
     exact H J hJ J' hJ'
-#align box_integral.prepartition.forall_bUnion_tagged BoxIntegral.Prepartition.forall_bUnionTagged
+#align box_integral.prepartition.forall_bUnion_tagged BoxIntegral.Prepartition.forall_biUnionTagged
+-/
 
-theorem IsPartition.bUnionTagged {π : Prepartition I} (h : IsPartition π)
+#print BoxIntegral.Prepartition.IsPartition.biUnionTagged /-
+theorem IsPartition.biUnionTagged {π : Prepartition I} (h : IsPartition π)
     {πi : ∀ J, TaggedPrepartition J} (hi : ∀ J ∈ π, (πi J).IsPartition) :
-    (π.bUnionTagged πi).IsPartition :=
+    (π.biUnionTagged πi).IsPartition :=
   h.biUnion hi
-#align box_integral.prepartition.is_partition.bUnion_tagged BoxIntegral.Prepartition.IsPartition.bUnionTagged
+#align box_integral.prepartition.is_partition.bUnion_tagged BoxIntegral.Prepartition.IsPartition.biUnionTagged
+-/
 
 end Prepartition
 
@@ -182,63 +244,80 @@ namespace TaggedPrepartition
 
 variable {I J : Box ι} {π π₁ π₂ : TaggedPrepartition I} {x : ι → ℝ}
 
+#print BoxIntegral.TaggedPrepartition.biUnionPrepartition /-
 /-- Given a tagged partition `π` of `I` and a (not tagged) partition `πi J hJ` of each `J ∈ π`,
 returns the tagged partition of `I` into all the boxes of all `πi J hJ`. The tag of a box `J`
 is defined to be the `π.tag` of the box of the partition `π` that includes `J`.
 
 Note that usually the result is not a Henstock partition. -/
 @[simps (config := { fullyApplied := false }) Tag]
-def bUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) : TaggedPrepartition I
+def biUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) : TaggedPrepartition I
     where
   toPrepartition := π.toPrepartition.biUnion πi
   Tag J := π.Tag (π.toPrepartition.biUnionIndex πi J)
   tag_mem_Icc J := π.tag_mem_Icc _
-#align box_integral.tagged_prepartition.bUnion_prepartition BoxIntegral.TaggedPrepartition.bUnionPrepartition
+#align box_integral.tagged_prepartition.bUnion_prepartition BoxIntegral.TaggedPrepartition.biUnionPrepartition
+-/
 
-theorem IsPartition.bUnionPrepartition {π : TaggedPrepartition I} (h : IsPartition π)
+#print BoxIntegral.TaggedPrepartition.IsPartition.biUnionPrepartition /-
+theorem IsPartition.biUnionPrepartition {π : TaggedPrepartition I} (h : IsPartition π)
     {πi : ∀ J, Prepartition J} (hi : ∀ J ∈ π, (πi J).IsPartition) :
-    (π.bUnionPrepartition πi).IsPartition :=
+    (π.biUnionPrepartition πi).IsPartition :=
   h.biUnion hi
-#align box_integral.tagged_prepartition.is_partition.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsPartition.bUnionPrepartition
+#align box_integral.tagged_prepartition.is_partition.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsPartition.biUnionPrepartition
+-/
 
+#print BoxIntegral.TaggedPrepartition.infPrepartition /-
 /-- Given two partitions `π₁` and `π₁`, one of them tagged and the other is not, returns the tagged
 partition with `to_partition = π₁.to_partition ⊓ π₂` and tags coming from `π₁`.
 
 Note that usually the result is not a Henstock partition. -/
 def infPrepartition (π : TaggedPrepartition I) (π' : Prepartition I) : TaggedPrepartition I :=
-  π.bUnionPrepartition fun J => π'.restrict J
+  π.biUnionPrepartition fun J => π'.restrict J
 #align box_integral.tagged_prepartition.inf_prepartition BoxIntegral.TaggedPrepartition.infPrepartition
+-/
 
+#print BoxIntegral.TaggedPrepartition.infPrepartition_toPrepartition /-
 @[simp]
 theorem infPrepartition_toPrepartition (π : TaggedPrepartition I) (π' : Prepartition I) :
     (π.infPrepartition π').toPrepartition = π.toPrepartition ⊓ π' :=
   rfl
 #align box_integral.tagged_prepartition.inf_prepartition_to_prepartition BoxIntegral.TaggedPrepartition.infPrepartition_toPrepartition
+-/
 
+#print BoxIntegral.TaggedPrepartition.mem_infPrepartition_comm /-
 theorem mem_infPrepartition_comm :
     J ∈ π₁.infPrepartition π₂.toPrepartition ↔ J ∈ π₂.infPrepartition π₁.toPrepartition := by
   simp only [← mem_to_prepartition, inf_prepartition_to_prepartition, inf_comm]
 #align box_integral.tagged_prepartition.mem_inf_prepartition_comm BoxIntegral.TaggedPrepartition.mem_infPrepartition_comm
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsPartition.infPrepartition /-
 theorem IsPartition.infPrepartition (h₁ : π₁.IsPartition) {π₂ : Prepartition I}
     (h₂ : π₂.IsPartition) : (π₁.infPrepartition π₂).IsPartition :=
   h₁.inf h₂
 #align box_integral.tagged_prepartition.is_partition.inf_prepartition BoxIntegral.TaggedPrepartition.IsPartition.infPrepartition
+-/
 
 open Metric
 
+#print BoxIntegral.TaggedPrepartition.IsHenstock /-
 /-- A tagged partition is said to be a Henstock partition if for each `J ∈ π`, the tag of `J`
 belongs to `J.Icc`. -/
 def IsHenstock (π : TaggedPrepartition I) : Prop :=
   ∀ J ∈ π, π.Tag J ∈ J.Icc
 #align box_integral.tagged_prepartition.is_Henstock BoxIntegral.TaggedPrepartition.IsHenstock
+-/
 
+#print BoxIntegral.TaggedPrepartition.isHenstock_biUnionTagged /-
 @[simp]
-theorem isHenstock_bUnionTagged {π : Prepartition I} {πi : ∀ J, TaggedPrepartition J} :
-    IsHenstock (π.bUnionTagged πi) ↔ ∀ J ∈ π, (πi J).IsHenstock :=
-  π.forall_bUnionTagged (fun x J => x ∈ J.Icc) πi
-#align box_integral.tagged_prepartition.is_Henstock_bUnion_tagged BoxIntegral.TaggedPrepartition.isHenstock_bUnionTagged
+theorem isHenstock_biUnionTagged {π : Prepartition I} {πi : ∀ J, TaggedPrepartition J} :
+    IsHenstock (π.biUnionTagged πi) ↔ ∀ J ∈ π, (πi J).IsHenstock :=
+  π.forall_biUnionTagged (fun x J => x ∈ J.Icc) πi
+#align box_integral.tagged_prepartition.is_Henstock_bUnion_tagged BoxIntegral.TaggedPrepartition.isHenstock_biUnionTagged
+-/
 
+#print BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le /-
 /-- In a Henstock prepartition, there are at most `2 ^ fintype.card ι` boxes with a given tag. -/
 theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : ι → ℝ) :
     (π.boxes.filterₓ fun J => π.Tag J = x).card ≤ 2 ^ Fintype.card ι :=
@@ -252,7 +331,14 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
     _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_Icc_le x
     
 #align box_integral.tagged_prepartition.is_Henstock.card_filter_tag_eq_le BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le
+-/
 
+/- warning: box_integral.tagged_prepartition.is_subordinate -> BoxIntegral.TaggedPrepartition.IsSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.{u1} ι I) -> ((ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> Prop
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.{u1} ι I) -> ((ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) -> Prop
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate BoxIntegral.TaggedPrepartition.IsSubordinateₓ'. -/
 /-- A tagged partition `π` is subordinate to `r : (ι → ℝ) → ℝ` if each box `J ∈ π` is included in
 the closed ball with center `π.tag J` and radius `r (π.tag J)`. -/
 def IsSubordinate [Fintype ι] (π : TaggedPrepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) : Prop :=
@@ -261,34 +347,70 @@ def IsSubordinate [Fintype ι] (π : TaggedPrepartition I) (r : (ι → ℝ) →
 
 variable {r r₁ r₂ : (ι → ℝ) → Ioi (0 : ℝ)}
 
+/- warning: box_integral.tagged_prepartition.is_subordinate_bUnion_tagged -> BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.Prepartition.{u1} ι I} {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.TaggedPrepartition.{u1} ι J}, Iff (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.Prepartition.biUnionTagged.{u1} ι I π πi) r) (forall (J : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι J _inst_1 (πi J) r))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.Prepartition.{u1} ι I} {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.TaggedPrepartition.{u1} ι J}, Iff (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.Prepartition.biUnionTagged.{u1} ι I π πi) r) (forall (J : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι J _inst_1 (πi J) r))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate_bUnion_tagged BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTaggedₓ'. -/
 @[simp]
-theorem isSubordinate_bUnionTagged [Fintype ι] {π : Prepartition I}
+theorem isSubordinate_biUnionTagged [Fintype ι] {π : Prepartition I}
     {πi : ∀ J, TaggedPrepartition J} :
-    IsSubordinate (π.bUnionTagged πi) r ↔ ∀ J ∈ π, (πi J).IsSubordinate r :=
-  π.forall_bUnionTagged (fun x J => J.Icc ⊆ closedBall x (r x)) πi
-#align box_integral.tagged_prepartition.is_subordinate_bUnion_tagged BoxIntegral.TaggedPrepartition.isSubordinate_bUnionTagged
-
-theorem IsSubordinate.bUnionPrepartition [Fintype ι] (h : IsSubordinate π r)
-    (πi : ∀ J, Prepartition J) : IsSubordinate (π.bUnionPrepartition πi) r := fun J hJ =>
+    IsSubordinate (π.biUnionTagged πi) r ↔ ∀ J ∈ π, (πi J).IsSubordinate r :=
+  π.forall_biUnionTagged (fun x J => J.Icc ⊆ closedBall x (r x)) πi
+#align box_integral.tagged_prepartition.is_subordinate_bUnion_tagged BoxIntegral.TaggedPrepartition.isSubordinate_biUnionTagged
+
+/- warning: box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition -> BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartition is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π : BoxIntegral.TaggedPrepartition.{u1} ι I} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (forall (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.biUnionPrepartition.{u1} ι I π πi) r)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π : BoxIntegral.TaggedPrepartition.{u1} ι I} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (forall (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.biUnionPrepartition.{u1} ι I π πi) r)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartitionₓ'. -/
+theorem IsSubordinate.biUnionPrepartition [Fintype ι] (h : IsSubordinate π r)
+    (πi : ∀ J, Prepartition J) : IsSubordinate (π.biUnionPrepartition πi) r := fun J hJ =>
   Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_biUnionIndex hJ) <|
     h _ <| π.toPrepartition.biUnionIndex_mem hJ
-#align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.bUnionPrepartition
-
+#align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.biUnionPrepartition
+
+/- warning: box_integral.tagged_prepartition.is_subordinate.inf_prepartition -> BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π : BoxIntegral.TaggedPrepartition.{u1} ι I} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (forall (π' : BoxIntegral.Prepartition.{u1} ι I), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.infPrepartition.{u1} ι I π π') r)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π : BoxIntegral.TaggedPrepartition.{u1} ι I} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (forall (π' : BoxIntegral.Prepartition.{u1} ι I), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.infPrepartition.{u1} ι I π π') r)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.inf_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartitionₓ'. -/
 theorem IsSubordinate.infPrepartition [Fintype ι] (h : IsSubordinate π r) (π' : Prepartition I) :
     IsSubordinate (π.infPrepartition π') r :=
-  h.bUnionPrepartition _
+  h.biUnionPrepartition _
 #align box_integral.tagged_prepartition.is_subordinate.inf_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.infPrepartition
 
+/- warning: box_integral.tagged_prepartition.is_subordinate.mono' -> BoxIntegral.TaggedPrepartition.IsSubordinate.mono' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r₁ : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} {r₂ : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₁) -> (forall (J : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π) -> (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) (r₁ (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)) (r₂ (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)))) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₂)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r₁ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} {r₂ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₁) -> (forall (J : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π) -> (LE.le.{0} (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (r₁ (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)) (r₂ (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)))) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₂)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.mono' BoxIntegral.TaggedPrepartition.IsSubordinate.mono'ₓ'. -/
 theorem IsSubordinate.mono' [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ J ∈ π, r₁ (π.Tag J) ≤ r₂ (π.Tag J)) : π.IsSubordinate r₂ := fun J hJ x hx =>
   closedBall_subset_closedBall (h _ hJ) (hr₁ _ hJ hx)
 #align box_integral.tagged_prepartition.is_subordinate.mono' BoxIntegral.TaggedPrepartition.IsSubordinate.mono'
 
+/- warning: box_integral.tagged_prepartition.is_subordinate.mono -> BoxIntegral.TaggedPrepartition.IsSubordinate.mono is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r₁ : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} {r₂ : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₁) -> (forall (x : ι -> Real), (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (LE.le.{0} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) (Subtype.hasLe.{0} Real Real.hasLe (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) (r₁ x) (r₂ x))) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₂)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {r₁ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} {r₂ : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₁) -> (forall (x : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (LE.le.{0} (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (Subtype.le.{0} Real Real.instLEReal (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (r₁ x) (r₂ x))) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r₂)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.mono BoxIntegral.TaggedPrepartition.IsSubordinate.monoₓ'. -/
 theorem IsSubordinate.mono [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ x ∈ I.Icc, r₁ x ≤ r₂ x) : π.IsSubordinate r₂ :=
   hr₁.mono' fun J _ => h _ <| π.tag_mem_Icc J
 #align box_integral.tagged_prepartition.is_subordinate.mono BoxIntegral.TaggedPrepartition.IsSubordinate.mono
 
+/- warning: box_integral.tagged_prepartition.is_subordinate.diam_le -> BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasMem.{u1} (BoxIntegral.Box.{u1} ι)) J (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π))) -> (LE.le.{0} Real Real.hasLe (Metric.diam.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.hasMul) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))))) (r (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] {π : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) -> (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instMembershipFinset.{u1} (BoxIntegral.Box.{u1} ι)) J (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π))) -> (LE.le.{0} Real Real.instLEReal (Metric.diam.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) J)) (HMul.hMul.{0, 0, 0} Real Real Real (instHMul.{0} Real Real.instMulReal) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (r (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π J)))))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_leₓ'. -/
 theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.IsSubordinate r)
     (hJ : J ∈ π.boxes) : diam J.Icc ≤ 2 * r (π.Tag J) :=
   calc
@@ -297,12 +419,24 @@ theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.I
     
 #align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le
 
+/- warning: box_integral.tagged_prepartition.single -> BoxIntegral.TaggedPrepartition.single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (I : BoxIntegral.Box.{u1} ι) (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) -> (forall (x : ι -> Real), (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (BoxIntegral.TaggedPrepartition.{u1} ι I))
+but is expected to have type
+  forall {ι : Type.{u1}} (I : BoxIntegral.Box.{u1} ι) (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (x : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (BoxIntegral.TaggedPrepartition.{u1} ι I))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.single BoxIntegral.TaggedPrepartition.singleₓ'. -/
 /-- Tagged prepartition with single box and prescribed tag. -/
 @[simps (config := { fullyApplied := false })]
 def single (I J : Box ι) (hJ : J ≤ I) (x : ι → ℝ) (h : x ∈ I.Icc) : TaggedPrepartition I :=
   ⟨Prepartition.single I J hJ, fun J => x, fun J => h⟩
 #align box_integral.tagged_prepartition.single BoxIntegral.TaggedPrepartition.single
 
+/- warning: box_integral.tagged_prepartition.mem_single -> BoxIntegral.TaggedPrepartition.mem_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {J' : BoxIntegral.Box.{u1} ι} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J' J)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {J' : BoxIntegral.Box.{u1} ι} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J' J)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_single BoxIntegral.TaggedPrepartition.mem_singleₓ'. -/
 @[simp]
 theorem mem_single {J'} (hJ : J ≤ I) (h : x ∈ I.Icc) : J' ∈ single I J hJ x h ↔ J' = J :=
   Finset.mem_singleton
@@ -311,41 +445,89 @@ theorem mem_single {J'} (hJ : J ≤ I) (h : x ∈ I.Icc) : J' ∈ single I J hJ
 instance (I : Box ι) : Inhabited (TaggedPrepartition I) :=
   ⟨single I I le_rfl I.upper I.upper_mem_Icc⟩
 
+/- warning: box_integral.tagged_prepartition.is_partition_single_iff -> BoxIntegral.TaggedPrepartition.isPartition_single_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J I)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J I)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_partition_single_iff BoxIntegral.TaggedPrepartition.isPartition_single_iffₓ'. -/
 theorem isPartition_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (single I J hJ x h).IsPartition ↔ J = I :=
   Prepartition.isPartition_single_iff hJ
 #align box_integral.tagged_prepartition.is_partition_single_iff BoxIntegral.TaggedPrepartition.isPartition_single_iff
 
+/- warning: box_integral.tagged_prepartition.is_partition_single -> BoxIntegral.TaggedPrepartition.isPartition_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) I) x h)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) I) x h)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_partition_single BoxIntegral.TaggedPrepartition.isPartition_singleₓ'. -/
 theorem isPartition_single (h : x ∈ I.Icc) : (single I I le_rfl x h).IsPartition :=
   Prepartition.isPartitionTop I
 #align box_integral.tagged_prepartition.is_partition_single BoxIntegral.TaggedPrepartition.isPartition_single
 
+/- warning: box_integral.tagged_prepartition.forall_mem_single -> BoxIntegral.TaggedPrepartition.forall_mem_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (p : (ι -> Real) -> (BoxIntegral.Box.{u1} ι) -> Prop) (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) -> (p (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) J') J')) (p x J)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (p : (ι -> Real) -> (BoxIntegral.Box.{u1} ι) -> Prop) (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J' (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) -> (p (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) J') J')) (p x J)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.forall_mem_single BoxIntegral.TaggedPrepartition.forall_mem_singleₓ'. -/
 theorem forall_mem_single (p : (ι → ℝ) → Box ι → Prop) (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (∀ J' ∈ single I J hJ x h, p ((single I J hJ x h).Tag J') J') ↔ p x J := by simp
 #align box_integral.tagged_prepartition.forall_mem_single BoxIntegral.TaggedPrepartition.forall_mem_single
 
+/- warning: box_integral.tagged_prepartition.is_Henstock_single_iff -> BoxIntegral.TaggedPrepartition.isHenstock_single_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J))
+but is expected to have type
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+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_Henstock_single_iff BoxIntegral.TaggedPrepartition.isHenstock_single_iffₓ'. -/
 @[simp]
 theorem isHenstock_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     IsHenstock (single I J hJ x h) ↔ x ∈ J.Icc :=
   forall_mem_single (fun x J => x ∈ J.Icc) hJ h
 #align box_integral.tagged_prepartition.is_Henstock_single_iff BoxIntegral.TaggedPrepartition.isHenstock_single_iff
 
+/- warning: box_integral.tagged_prepartition.is_Henstock_single -> BoxIntegral.TaggedPrepartition.isHenstock_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) I) x h)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I I (le_rfl.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) I) x h)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_Henstock_single BoxIntegral.TaggedPrepartition.isHenstock_singleₓ'. -/
 @[simp]
 theorem isHenstock_single (h : x ∈ I.Icc) : IsHenstock (single I I le_rfl x h) :=
   (isHenstock_single_iff (le_refl I) h).2 h
 #align box_integral.tagged_prepartition.is_Henstock_single BoxIntegral.TaggedPrepartition.isHenstock_single
 
+/- warning: box_integral.tagged_prepartition.is_subordinate_single -> BoxIntegral.TaggedPrepartition.isSubordinate_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) r) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J) (Metric.closedBall.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) x ((fun (a : Type) (b : Type) [self : HasLiftT.{1, 1} a b] => self.0) (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (HasLiftT.mk.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (CoeTCₓ.coe.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeBase.{1, 1} (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))) Real (coeSubtype.{1} Real (fun (x : Real) => Membership.Mem.{0, 0} Real (Set.{0} Real) (Set.hasMem.{0} Real) x (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero))))))))) (r x))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Iff (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) r) (HasSubset.Subset.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instHasSubsetSet.{u1} (ι -> Real)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) J) (Metric.closedBall.{u1} (ι -> Real) (pseudoMetricSpacePi.{u1, 0} ι (fun (ᾰ : ι) => Real) _inst_1 (fun (b : ι) => Real.pseudoMetricSpace)) x (Subtype.val.{1} Real (fun (x : Real) => Membership.mem.{0, 0} Real (Set.{0} Real) (Set.instMembershipSet.{0} Real) x (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal)))) (r x))))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate_single BoxIntegral.TaggedPrepartition.isSubordinate_singleₓ'. -/
 @[simp]
 theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
     IsSubordinate (single I J hJ x h) r ↔ J.Icc ⊆ closedBall x (r x) :=
   forall_mem_single (fun x J => J.Icc ⊆ closedBall x (r x)) hJ h
 #align box_integral.tagged_prepartition.is_subordinate_single BoxIntegral.TaggedPrepartition.isSubordinate_single
 
+/- warning: box_integral.tagged_prepartition.Union_single -> BoxIntegral.TaggedPrepartition.iUnion_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.Set.hasCoeT.{u1} ι))) J)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h)) (BoxIntegral.Box.toSet.{u1} ι J)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.iUnion_singleₓ'. -/
 @[simp]
-theorem union_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).iUnion = J :=
+theorem iUnion_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).iUnion = J :=
   Prepartition.iUnion_single hJ
-#align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.union_single
-
+#align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.iUnion_single
+
+/- warning: box_integral.tagged_prepartition.disj_union -> BoxIntegral.TaggedPrepartition.disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I), (Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)) -> (BoxIntegral.TaggedPrepartition.{u1} ι I)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I), (Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)) -> (BoxIntegral.TaggedPrepartition.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnionₓ'. -/
 /-- Union of two tagged prepartitions with disjoint unions of boxes. -/
 def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) :
     TaggedPrepartition I
@@ -358,34 +540,70 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π
     exacts[π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
 #align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnion
 
+/- warning: box_integral.tagged_prepartition.disj_union_boxes -> BoxIntegral.TaggedPrepartition.disjUnion_boxes is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h))) (Union.union.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasUnion.{u1} (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) a b))) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π₁)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π₂)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h))) (Union.union.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instUnionFinset.{u1} (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) a b))) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π₁)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π₂)))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.disj_union_boxes BoxIntegral.TaggedPrepartition.disjUnion_boxesₓ'. -/
 @[simp]
 theorem disjUnion_boxes (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).boxes = π₁.boxes ∪ π₂.boxes :=
   rfl
 #align box_integral.tagged_prepartition.disj_union_boxes BoxIntegral.TaggedPrepartition.disjUnion_boxes
 
+/- warning: box_integral.tagged_prepartition.mem_disj_union -> BoxIntegral.TaggedPrepartition.mem_disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Or (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π₁) (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Or (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π₁) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.mem_disj_union BoxIntegral.TaggedPrepartition.mem_disjUnionₓ'. -/
 @[simp]
 theorem mem_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     J ∈ π₁.disjUnion π₂ h ↔ J ∈ π₁ ∨ J ∈ π₂ :=
   Finset.mem_union
 #align box_integral.tagged_prepartition.mem_disj_union BoxIntegral.TaggedPrepartition.mem_disjUnion
 
+/- warning: box_integral.tagged_prepartition.Union_disj_union -> BoxIntegral.TaggedPrepartition.iUnion_disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.hasUnion.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.instUnionSet.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.iUnion_disjUnionₓ'. -/
 @[simp]
-theorem union_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
+theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion :=
   Prepartition.iUnion_disjUnion _
-#align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.union_disjUnion
-
+#align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.iUnion_disjUnion
+
+/- warning: box_integral.tagged_prepartition.disj_union_tag_of_mem_left -> BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π₁) -> (Eq.{succ u1} (ι -> Real) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) J) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π₁ J))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π₁) -> (Eq.{succ u1} (ι -> Real) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) J) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π₁ J))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.disj_union_tag_of_mem_left BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_leftₓ'. -/
 theorem disjUnion_tag_of_mem_left (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₁) :
     (π₁.disjUnion π₂ h).Tag J = π₁.Tag J :=
   dif_pos hJ
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_left BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left
 
+/- warning: box_integral.tagged_prepartition.disj_union_tag_of_mem_right -> BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π₂) -> (Eq.{succ u1} (ι -> Real) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) J) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π₂ J))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π₂) -> (Eq.{succ u1} (ι -> Real) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) J) (BoxIntegral.TaggedPrepartition.tag.{u1} ι I π₂ J))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.disj_union_tag_of_mem_right BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_rightₓ'. -/
 theorem disjUnion_tag_of_mem_right (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₂) :
     (π₁.disjUnion π₂ h).Tag J = π₂.Tag J :=
   dif_neg fun h₁ => h.le_bot ⟨π₁.subset_iUnion h₁ J.upper_mem, π₂.subset_iUnion hJ J.upper_mem⟩
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_right BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right
 
+/- warning: box_integral.tagged_prepartition.is_subordinate.disj_union -> BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} {r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π₁ r) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π₂ r) -> (forall (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) r)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} {r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))} [_inst_1 : Fintype.{u1} ι], (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π₁ r) -> (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π₂ r) -> (forall (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) r)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_subordinate.disj_union BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnionₓ'. -/
 theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h₂ : IsSubordinate π₂ r)
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsSubordinate (π₁.disjUnion π₂ h) r :=
   by
@@ -396,6 +614,12 @@ theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h
     exact h₂ _ hJ
 #align box_integral.tagged_prepartition.is_subordinate.disj_union BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion
 
+/- warning: box_integral.tagged_prepartition.is_Henstock.disj_union -> BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π₁) -> (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π₂) -> (forall (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I}, (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π₁) -> (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π₂) -> (forall (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_Henstock.disj_union BoxIntegral.TaggedPrepartition.IsHenstock.disjUnionₓ'. -/
 theorem IsHenstock.disjUnion (h₁ : IsHenstock π₁) (h₂ : IsHenstock π₂)
     (h : Disjoint π₁.iUnion π₂.iUnion) : IsHenstock (π₁.disjUnion π₂ h) :=
   by
@@ -406,6 +630,7 @@ theorem IsHenstock.disjUnion (h₁ : IsHenstock π₁) (h₂ : IsHenstock π₂)
     exact h₂ _ hJ
 #align box_integral.tagged_prepartition.is_Henstock.disj_union BoxIntegral.TaggedPrepartition.IsHenstock.disjUnion
 
+#print BoxIntegral.TaggedPrepartition.embedBox /-
 /-- If `I ≤ J`, then every tagged prepartition of `I` is a tagged prepartition of `J`. -/
 def embedBox (I J : Box ι) (h : I ≤ J) : TaggedPrepartition I ↪ TaggedPrepartition J
     where
@@ -417,6 +642,7 @@ def embedBox (I J : Box ι) (h : I ≤ J) : TaggedPrepartition I ↪ TaggedPrepa
     rintro ⟨⟨b₁, h₁le, h₁d⟩, t₁, ht₁⟩ ⟨⟨b₂, h₂le, h₂d⟩, t₂, ht₂⟩ H
     simpa using H
 #align box_integral.tagged_prepartition.embed_box BoxIntegral.TaggedPrepartition.embedBox
+-/
 
 section Distortion
 
@@ -424,49 +650,95 @@ variable [Fintype ι] (π)
 
 open Finset
 
+#print BoxIntegral.TaggedPrepartition.distortion /-
 /-- The distortion of a tagged prepartition is the maximum of distortions of its boxes. -/
 def distortion : ℝ≥0 :=
   π.toPrepartition.distortion
 #align box_integral.tagged_prepartition.distortion BoxIntegral.TaggedPrepartition.distortion
+-/
 
+/- warning: box_integral.tagged_prepartition.distortion_le_of_mem -> BoxIntegral.TaggedPrepartition.distortion_le_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι], (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι], (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_le_of_mem BoxIntegral.TaggedPrepartition.distortion_le_of_memₓ'. -/
 theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
   le_sup h
 #align box_integral.tagged_prepartition.distortion_le_of_mem BoxIntegral.TaggedPrepartition.distortion_le_of_mem
 
+/- warning: box_integral.tagged_prepartition.distortion_le_iff -> BoxIntegral.TaggedPrepartition.distortion_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] {c : NNReal}, Iff (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1) c) (forall (J : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π) -> (LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J) c))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] {c : NNReal}, Iff (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1) c) (forall (J : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π) -> (LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J) c))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_le_iff BoxIntegral.TaggedPrepartition.distortion_le_iffₓ'. -/
 theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π, Box.distortion J ≤ c :=
   Finset.sup_le_iff
 #align box_integral.tagged_prepartition.distortion_le_iff BoxIntegral.TaggedPrepartition.distortion_le_iff
 
+/- warning: box_integral.prepartition.distortion_bUnion_tagged -> BoxIntegral.Prepartition.distortion_biUnionTagged is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} [_inst_1 : Fintype.{u1} ι] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.TaggedPrepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.biUnionTagged.{u1} ι I π πi) _inst_1) (Finset.sup.{0, u1} NNReal (BoxIntegral.Box.{u1} ι) NNReal.semilatticeSup NNReal.orderBot (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.TaggedPrepartition.distortion.{u1} ι J (πi J) _inst_1))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} [_inst_1 : Fintype.{u1} ι] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.TaggedPrepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.biUnionTagged.{u1} ι I π πi) _inst_1) (Finset.sup.{0, u1} NNReal (BoxIntegral.Box.{u1} ι) instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.TaggedPrepartition.distortion.{u1} ι J (πi J) _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_bUnion_tagged BoxIntegral.Prepartition.distortion_biUnionTaggedₓ'. -/
 @[simp]
-theorem BoxIntegral.Prepartition.distortion_bUnionTagged (π : Prepartition I)
+theorem BoxIntegral.Prepartition.distortion_biUnionTagged (π : Prepartition I)
     (πi : ∀ J, TaggedPrepartition J) :
-    (π.bUnionTagged πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
+    (π.biUnionTagged πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_biUnion _ _
-#align box_integral.prepartition.distortion_bUnion_tagged BoxIntegral.Prepartition.distortion_bUnionTagged
-
+#align box_integral.prepartition.distortion_bUnion_tagged BoxIntegral.Prepartition.distortion_biUnionTagged
+
+/- warning: box_integral.tagged_prepartition.distortion_bUnion_prepartition -> BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} [_inst_1 : Fintype.{u1} ι] (π : BoxIntegral.TaggedPrepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.biUnionPrepartition.{u1} ι I π πi) _inst_1) (Finset.sup.{0, u1} NNReal (BoxIntegral.Box.{u1} ι) NNReal.semilatticeSup NNReal.orderBot (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π)) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.distortion.{u1} ι J (πi J) _inst_1))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} [_inst_1 : Fintype.{u1} ι] (π : BoxIntegral.TaggedPrepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.biUnionPrepartition.{u1} ι I π πi) _inst_1) (Finset.sup.{0, u1} NNReal (BoxIntegral.Box.{u1} ι) instNNRealSemilatticeSup NNReal.instOrderBotNNRealToLEToPreorderToPartialOrderInstNNRealStrictOrderedSemiring (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π)) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.distortion.{u1} ι J (πi J) _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_bUnion_prepartition BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartitionₓ'. -/
 @[simp]
-theorem distortion_bUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) :
-    (π.bUnionPrepartition πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
+theorem distortion_biUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) :
+    (π.biUnionPrepartition πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_biUnion _ _
-#align box_integral.tagged_prepartition.distortion_bUnion_prepartition BoxIntegral.TaggedPrepartition.distortion_bUnionPrepartition
-
+#align box_integral.tagged_prepartition.distortion_bUnion_prepartition BoxIntegral.TaggedPrepartition.distortion_biUnionPrepartition
+
+/- warning: box_integral.tagged_prepartition.distortion_disj_union -> BoxIntegral.TaggedPrepartition.distortion_disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} [_inst_1 : Fintype.{u1} ι] (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.completeBooleanAlgebra.{u1} (ι -> Real))))))) (GeneralizedBooleanAlgebra.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real)))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₂ _inst_1))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I} {π₂ : BoxIntegral.TaggedPrepartition.{u1} ι I} [_inst_1 : Fintype.{u1} ι] (h : Disjoint.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoundedOrder.toOrderBot.{u1} (Set.{u1} (ι -> Real)) (Preorder.toLE.{u1} (Set.{u1} (ι -> Real)) (PartialOrder.toPreorder.{u1} (Set.{u1} (ι -> Real)) (CompleteSemilatticeInf.toPartialOrder.{u1} (Set.{u1} (ι -> Real)) (CompleteLattice.toCompleteSemilatticeInf.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))))) (CompleteLattice.toBoundedOrder.{u1} (Set.{u1} (ι -> Real)) (Order.Coframe.toCompleteLattice.{u1} (Set.{u1} (ι -> Real)) (CompleteDistribLattice.toCoframe.{u1} (Set.{u1} (ι -> Real)) (CompleteBooleanAlgebra.toCompleteDistribLattice.{u1} (Set.{u1} (ι -> Real)) (Set.instCompleteBooleanAlgebraSet.{u1} (ι -> Real))))))) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₁) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₂ _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_disj_union BoxIntegral.TaggedPrepartition.distortion_disjUnionₓ'. -/
 @[simp]
 theorem distortion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).distortion = max π₁.distortion π₂.distortion :=
   sup_union
 #align box_integral.tagged_prepartition.distortion_disj_union BoxIntegral.TaggedPrepartition.distortion_disjUnion
 
+#print BoxIntegral.TaggedPrepartition.distortion_of_const /-
 theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π, Box.distortion J = c) :
     π.distortion = c :=
   (sup_congr rfl h₂).trans (sup_const h₁ _)
 #align box_integral.tagged_prepartition.distortion_of_const BoxIntegral.TaggedPrepartition.distortion_of_const
+-/
 
+/- warning: box_integral.tagged_prepartition.distortion_single -> BoxIntegral.TaggedPrepartition.distortion_single is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) (h : Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {x : ι -> Real} [_inst_1 : Fintype.{u1} ι] (hJ : LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) (h : Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) x (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.single.{u1} ι I J hJ x h) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 J)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_single BoxIntegral.TaggedPrepartition.distortion_singleₓ'. -/
 @[simp]
 theorem distortion_single (hJ : J ≤ I) (h : x ∈ I.Icc) :
     distortion (single I J hJ x h) = J.distortion :=
   sup_singleton
 #align box_integral.tagged_prepartition.distortion_single BoxIntegral.TaggedPrepartition.distortion_single
 
+/- warning: box_integral.tagged_prepartition.distortion_filter_le -> BoxIntegral.TaggedPrepartition.distortion_filter_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (p : (BoxIntegral.Box.{u1} ι) -> Prop), LE.le.{0} NNReal (Preorder.toHasLe.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (OrderedCancelAddCommMonoid.toPartialOrder.{0} NNReal (StrictOrderedSemiring.toOrderedCancelAddCommMonoid.{0} NNReal NNReal.strictOrderedSemiring)))) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π p) _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.TaggedPrepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (p : (BoxIntegral.Box.{u1} ι) -> Prop), LE.le.{0} NNReal (Preorder.toLE.{0} NNReal (PartialOrder.toPreorder.{0} NNReal (StrictOrderedSemiring.toPartialOrder.{0} NNReal instNNRealStrictOrderedSemiring))) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.filter.{u1} ι I π p) _inst_1) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.distortion_filter_le BoxIntegral.TaggedPrepartition.distortion_filter_leₓ'. -/
 theorem distortion_filter_le (p : Box ι → Prop) : (π.filterₓ p).distortion ≤ π.distortion :=
   sup_mono (filter_subset _ _)
 #align box_integral.tagged_prepartition.distortion_filter_le BoxIntegral.TaggedPrepartition.distortion_filter_le

6ca1a09b

bump to nightly-2023-05-14-08

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

d31da313

Diff

@@ -65,34 +65,34 @@ theorem mem_mk (π : Prepartition I) (f h) : J ∈ mk π f h ↔ J ∈ π :=
 
 /-- Union of all boxes of a tagged prepartition. -/
 def union : Set (ι → ℝ) :=
-  π.toPrepartition.unionᵢ
+  π.toPrepartition.iUnion
 #align box_integral.tagged_prepartition.Union BoxIntegral.TaggedPrepartition.union
 
-theorem union_def : π.unionᵢ = ⋃ J ∈ π, ↑J :=
+theorem union_def : π.iUnion = ⋃ J ∈ π, ↑J :=
   rfl
 #align box_integral.tagged_prepartition.Union_def BoxIntegral.TaggedPrepartition.union_def
 
 @[simp]
-theorem union_mk (π : Prepartition I) (f h) : (mk π f h).unionᵢ = π.unionᵢ :=
+theorem union_mk (π : Prepartition I) (f h) : (mk π f h).iUnion = π.iUnion :=
   rfl
 #align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.union_mk
 
 @[simp]
-theorem unionᵢ_toPrepartition : π.toPrepartition.unionᵢ = π.unionᵢ :=
+theorem iUnion_toPrepartition : π.toPrepartition.iUnion = π.iUnion :=
   rfl
-#align box_integral.tagged_prepartition.Union_to_prepartition BoxIntegral.TaggedPrepartition.unionᵢ_toPrepartition
+#align box_integral.tagged_prepartition.Union_to_prepartition BoxIntegral.TaggedPrepartition.iUnion_toPrepartition
 
 @[simp]
-theorem mem_union : x ∈ π.unionᵢ ↔ ∃ J ∈ π, x ∈ J :=
-  Set.mem_unionᵢ₂
+theorem mem_union : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
+  Set.mem_iUnion₂
 #align box_integral.tagged_prepartition.mem_Union BoxIntegral.TaggedPrepartition.mem_union
 
-theorem subset_union (h : J ∈ π) : ↑J ⊆ π.unionᵢ :=
-  subset_bunionᵢ_of_mem h
+theorem subset_union (h : J ∈ π) : ↑J ⊆ π.iUnion :=
+  subset_biUnion_of_mem h
 #align box_integral.tagged_prepartition.subset_Union BoxIntegral.TaggedPrepartition.subset_union
 
-theorem union_subset : π.unionᵢ ⊆ I :=
-  unionᵢ₂_subset π.le_of_mem'
+theorem union_subset : π.iUnion ⊆ I :=
+  iUnion₂_subset π.le_of_mem'
 #align box_integral.tagged_prepartition.Union_subset BoxIntegral.TaggedPrepartition.union_subset
 
 /-- A tagged prepartition is a partition if it covers the whole box. -/
@@ -100,8 +100,8 @@ def IsPartition :=
   π.toPrepartition.IsPartition
 #align box_integral.tagged_prepartition.is_partition BoxIntegral.TaggedPrepartition.IsPartition
 
-theorem isPartition_iff_union_eq : IsPartition π ↔ π.unionᵢ = I :=
-  Prepartition.isPartition_iff_unionᵢ_eq
+theorem isPartition_iff_union_eq : IsPartition π ↔ π.iUnion = I :=
+  Prepartition.isPartition_iff_iUnion_eq
 #align box_integral.tagged_prepartition.is_partition_iff_Union_eq BoxIntegral.TaggedPrepartition.isPartition_iff_union_eq
 
 /-- The tagged partition made of boxes of `π` that satisfy predicate `p`. -/
@@ -117,8 +117,8 @@ theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧
 
 @[simp]
 theorem union_filter_not (π : TaggedPrepartition I) (p : Box ι → Prop) :
-    (π.filterₓ fun J => ¬p J).unionᵢ = π.unionᵢ \ (π.filterₓ p).unionᵢ :=
-  π.toPrepartition.unionᵢ_filter_not p
+    (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
+  π.toPrepartition.iUnion_filter_not p
 #align box_integral.tagged_prepartition.Union_filter_not BoxIntegral.TaggedPrepartition.union_filter_not
 
 end TaggedPrepartition
@@ -132,15 +132,15 @@ variable {I J : Box ι}
 with tags coming from `(πi J).tag`. -/
 def bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : TaggedPrepartition I
     where
-  toPrepartition := π.bunionᵢ fun J => (πi J).toPrepartition
-  Tag J := (πi (π.bunionᵢIndex (fun J => (πi J).toPrepartition) J)).Tag J
-  tag_mem_Icc J := Box.le_iff_Icc.1 (π.bunionᵢIndex_le _ _) ((πi _).tag_mem_Icc _)
+  toPrepartition := π.biUnion fun J => (πi J).toPrepartition
+  Tag J := (πi (π.biUnionIndex (fun J => (πi J).toPrepartition) J)).Tag J
+  tag_mem_Icc J := Box.le_iff_Icc.1 (π.biUnionIndex_le _ _) ((πi _).tag_mem_Icc _)
 #align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.bUnionTagged
 
 @[simp]
 theorem mem_bUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} :
     J ∈ π.bUnionTagged πi ↔ ∃ J' ∈ π, J ∈ πi J' :=
-  π.mem_bunionᵢ
+  π.mem_biUnion
 #align box_integral.prepartition.mem_bUnion_tagged BoxIntegral.Prepartition.mem_bUnionTagged
 
 theorem tag_bUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition J} (hJ : J ∈ π) {J'}
@@ -153,8 +153,8 @@ theorem tag_bUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition
 
 @[simp]
 theorem union_bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) :
-    (π.bUnionTagged πi).unionᵢ = ⋃ J ∈ π, (πi J).unionᵢ :=
-  unionᵢ_bunionᵢ _ _
+    (π.bUnionTagged πi).iUnion = ⋃ J ∈ π, (πi J).iUnion :=
+  iUnion_biUnion _ _
 #align box_integral.prepartition.Union_bUnion_tagged BoxIntegral.Prepartition.union_bUnionTagged
 
 theorem forall_bUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepartition I)
@@ -173,7 +173,7 @@ theorem forall_bUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepart
 theorem IsPartition.bUnionTagged {π : Prepartition I} (h : IsPartition π)
     {πi : ∀ J, TaggedPrepartition J} (hi : ∀ J ∈ π, (πi J).IsPartition) :
     (π.bUnionTagged πi).IsPartition :=
-  h.bunionᵢ hi
+  h.biUnion hi
 #align box_integral.prepartition.is_partition.bUnion_tagged BoxIntegral.Prepartition.IsPartition.bUnionTagged
 
 end Prepartition
@@ -190,15 +190,15 @@ Note that usually the result is not a Henstock partition. -/
 @[simps (config := { fullyApplied := false }) Tag]
 def bUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) : TaggedPrepartition I
     where
-  toPrepartition := π.toPrepartition.bunionᵢ πi
-  Tag J := π.Tag (π.toPrepartition.bunionᵢIndex πi J)
+  toPrepartition := π.toPrepartition.biUnion πi
+  Tag J := π.Tag (π.toPrepartition.biUnionIndex πi J)
   tag_mem_Icc J := π.tag_mem_Icc _
 #align box_integral.tagged_prepartition.bUnion_prepartition BoxIntegral.TaggedPrepartition.bUnionPrepartition
 
 theorem IsPartition.bUnionPrepartition {π : TaggedPrepartition I} (h : IsPartition π)
     {πi : ∀ J, Prepartition J} (hi : ∀ J ∈ π, (πi J).IsPartition) :
     (π.bUnionPrepartition πi).IsPartition :=
-  h.bunionᵢ hi
+  h.biUnion hi
 #align box_integral.tagged_prepartition.is_partition.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsPartition.bUnionPrepartition
 
 /-- Given two partitions `π₁` and `π₁`, one of them tagged and the other is not, returns the tagged
@@ -270,8 +270,8 @@ theorem isSubordinate_bUnionTagged [Fintype ι] {π : Prepartition I}
 
 theorem IsSubordinate.bUnionPrepartition [Fintype ι] (h : IsSubordinate π r)
     (πi : ∀ J, Prepartition J) : IsSubordinate (π.bUnionPrepartition πi) r := fun J hJ =>
-  Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_bunionᵢIndex hJ) <|
-    h _ <| π.toPrepartition.bunionᵢIndex_mem hJ
+  Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_biUnionIndex hJ) <|
+    h _ <| π.toPrepartition.biUnionIndex_mem hJ
 #align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.bUnionPrepartition
 
 theorem IsSubordinate.infPrepartition [Fintype ι] (h : IsSubordinate π r) (π' : Prepartition I) :
@@ -342,12 +342,12 @@ theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
 #align box_integral.tagged_prepartition.is_subordinate_single BoxIntegral.TaggedPrepartition.isSubordinate_single
 
 @[simp]
-theorem union_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).unionᵢ = J :=
-  Prepartition.unionᵢ_single hJ
+theorem union_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).iUnion = J :=
+  Prepartition.iUnion_single hJ
 #align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.union_single
 
 /-- Union of two tagged prepartitions with disjoint unions of boxes. -/
-def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) :
     TaggedPrepartition I
     where
   toPrepartition := π₁.toPrepartition.disjUnion π₂.toPrepartition h
@@ -359,35 +359,35 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.unionᵢ
 #align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnion
 
 @[simp]
-theorem disjUnion_boxes (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+theorem disjUnion_boxes (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).boxes = π₁.boxes ∪ π₂.boxes :=
   rfl
 #align box_integral.tagged_prepartition.disj_union_boxes BoxIntegral.TaggedPrepartition.disjUnion_boxes
 
 @[simp]
-theorem mem_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+theorem mem_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     J ∈ π₁.disjUnion π₂ h ↔ J ∈ π₁ ∨ J ∈ π₂ :=
   Finset.mem_union
 #align box_integral.tagged_prepartition.mem_disj_union BoxIntegral.TaggedPrepartition.mem_disjUnion
 
 @[simp]
-theorem union_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
-    (π₁.disjUnion π₂ h).unionᵢ = π₁.unionᵢ ∪ π₂.unionᵢ :=
-  Prepartition.unionᵢ_disjUnion _
+theorem union_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
+    (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion :=
+  Prepartition.iUnion_disjUnion _
 #align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.union_disjUnion
 
-theorem disjUnion_tag_of_mem_left (h : Disjoint π₁.unionᵢ π₂.unionᵢ) (hJ : J ∈ π₁) :
+theorem disjUnion_tag_of_mem_left (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₁) :
     (π₁.disjUnion π₂ h).Tag J = π₁.Tag J :=
   dif_pos hJ
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_left BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_left
 
-theorem disjUnion_tag_of_mem_right (h : Disjoint π₁.unionᵢ π₂.unionᵢ) (hJ : J ∈ π₂) :
+theorem disjUnion_tag_of_mem_right (h : Disjoint π₁.iUnion π₂.iUnion) (hJ : J ∈ π₂) :
     (π₁.disjUnion π₂ h).Tag J = π₂.Tag J :=
-  dif_neg fun h₁ => h.le_bot ⟨π₁.subset_unionᵢ h₁ J.upper_mem, π₂.subset_unionᵢ hJ J.upper_mem⟩
+  dif_neg fun h₁ => h.le_bot ⟨π₁.subset_iUnion h₁ J.upper_mem, π₂.subset_iUnion hJ J.upper_mem⟩
 #align box_integral.tagged_prepartition.disj_union_tag_of_mem_right BoxIntegral.TaggedPrepartition.disjUnion_tag_of_mem_right
 
 theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h₂ : IsSubordinate π₂ r)
-    (h : Disjoint π₁.unionᵢ π₂.unionᵢ) : IsSubordinate (π₁.disjUnion π₂ h) r :=
+    (h : Disjoint π₁.iUnion π₂.iUnion) : IsSubordinate (π₁.disjUnion π₂ h) r :=
   by
   refine' fun J hJ => (Finset.mem_union.1 hJ).elim (fun hJ => _) fun hJ => _
   · rw [disj_union_tag_of_mem_left _ hJ]
@@ -397,7 +397,7 @@ theorem IsSubordinate.disjUnion [Fintype ι] (h₁ : IsSubordinate π₁ r) (h
 #align box_integral.tagged_prepartition.is_subordinate.disj_union BoxIntegral.TaggedPrepartition.IsSubordinate.disjUnion
 
 theorem IsHenstock.disjUnion (h₁ : IsHenstock π₁) (h₂ : IsHenstock π₂)
-    (h : Disjoint π₁.unionᵢ π₂.unionᵢ) : IsHenstock (π₁.disjUnion π₂ h) :=
+    (h : Disjoint π₁.iUnion π₂.iUnion) : IsHenstock (π₁.disjUnion π₂ h) :=
   by
   refine' fun J hJ => (Finset.mem_union.1 hJ).elim (fun hJ => _) fun hJ => _
   · rw [disj_union_tag_of_mem_left _ hJ]
@@ -441,17 +441,17 @@ theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π,
 theorem BoxIntegral.Prepartition.distortion_bUnionTagged (π : Prepartition I)
     (πi : ∀ J, TaggedPrepartition J) :
     (π.bUnionTagged πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
-  sup_bunionᵢ _ _
+  sup_biUnion _ _
 #align box_integral.prepartition.distortion_bUnion_tagged BoxIntegral.Prepartition.distortion_bUnionTagged
 
 @[simp]
 theorem distortion_bUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) :
     (π.bUnionPrepartition πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
-  sup_bunionᵢ _ _
+  sup_biUnion _ _
 #align box_integral.tagged_prepartition.distortion_bUnion_prepartition BoxIntegral.TaggedPrepartition.distortion_bUnionPrepartition
 
 @[simp]
-theorem distortion_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+theorem distortion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).distortion = max π₁.distortion π₂.distortion :=
   sup_union
 #align box_integral.tagged_prepartition.distortion_disj_union BoxIntegral.TaggedPrepartition.distortion_disjUnion

6ca1a09b

bump to nightly-2023-04-26-06

mathlib commit https://github.com/leanprover-community/mathlib/commit/d2d964c64f8ddcccd6704a731c41f95d13e72f5c

dfb5811a

Diff

@@ -78,9 +78,9 @@ theorem union_mk (π : Prepartition I) (f h) : (mk π f h).unionᵢ = π.union
 #align box_integral.tagged_prepartition.Union_mk BoxIntegral.TaggedPrepartition.union_mk
 
 @[simp]
-theorem union_toPrepartition : π.toPrepartition.unionᵢ = π.unionᵢ :=
+theorem unionᵢ_toPrepartition : π.toPrepartition.unionᵢ = π.unionᵢ :=
   rfl
-#align box_integral.tagged_prepartition.Union_to_prepartition BoxIntegral.TaggedPrepartition.union_toPrepartition
+#align box_integral.tagged_prepartition.Union_to_prepartition BoxIntegral.TaggedPrepartition.unionᵢ_toPrepartition
 
 @[simp]
 theorem mem_union : x ∈ π.unionᵢ ↔ ∃ J ∈ π, x ∈ J :=
@@ -101,7 +101,7 @@ def IsPartition :=
 #align box_integral.tagged_prepartition.is_partition BoxIntegral.TaggedPrepartition.IsPartition
 
 theorem isPartition_iff_union_eq : IsPartition π ↔ π.unionᵢ = I :=
-  Prepartition.isPartition_iff_union_eq
+  Prepartition.isPartition_iff_unionᵢ_eq
 #align box_integral.tagged_prepartition.is_partition_iff_Union_eq BoxIntegral.TaggedPrepartition.isPartition_iff_union_eq
 
 /-- The tagged partition made of boxes of `π` that satisfy predicate `p`. -/
@@ -118,7 +118,7 @@ theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧
 @[simp]
 theorem union_filter_not (π : TaggedPrepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).unionᵢ = π.unionᵢ \ (π.filterₓ p).unionᵢ :=
-  π.toPrepartition.union_filter_not p
+  π.toPrepartition.unionᵢ_filter_not p
 #align box_integral.tagged_prepartition.Union_filter_not BoxIntegral.TaggedPrepartition.union_filter_not
 
 end TaggedPrepartition
@@ -133,8 +133,8 @@ with tags coming from `(πi J).tag`. -/
 def bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : TaggedPrepartition I
     where
   toPrepartition := π.bunionᵢ fun J => (πi J).toPrepartition
-  Tag J := (πi (π.bUnionIndex (fun J => (πi J).toPrepartition) J)).Tag J
-  tag_mem_Icc J := Box.le_iff_Icc.1 (π.bUnionIndex_le _ _) ((πi _).tag_mem_Icc _)
+  Tag J := (πi (π.bunionᵢIndex (fun J => (πi J).toPrepartition) J)).Tag J
+  tag_mem_Icc J := Box.le_iff_Icc.1 (π.bunionᵢIndex_le _ _) ((πi _).tag_mem_Icc _)
 #align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.bUnionTagged
 
 @[simp]
@@ -154,7 +154,7 @@ theorem tag_bUnionTagged (π : Prepartition I) {πi : ∀ J, TaggedPrepartition
 @[simp]
 theorem union_bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) :
     (π.bUnionTagged πi).unionᵢ = ⋃ J ∈ π, (πi J).unionᵢ :=
-  union_bUnion _ _
+  unionᵢ_bunionᵢ _ _
 #align box_integral.prepartition.Union_bUnion_tagged BoxIntegral.Prepartition.union_bUnionTagged
 
 theorem forall_bUnionTagged (p : (ι → ℝ) → Box ι → Prop) (π : Prepartition I)
@@ -191,7 +191,7 @@ Note that usually the result is not a Henstock partition. -/
 def bUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J) : TaggedPrepartition I
     where
   toPrepartition := π.toPrepartition.bunionᵢ πi
-  Tag J := π.Tag (π.toPrepartition.bUnionIndex πi J)
+  Tag J := π.Tag (π.toPrepartition.bunionᵢIndex πi J)
   tag_mem_Icc J := π.tag_mem_Icc _
 #align box_integral.tagged_prepartition.bUnion_prepartition BoxIntegral.TaggedPrepartition.bUnionPrepartition
 
@@ -270,8 +270,8 @@ theorem isSubordinate_bUnionTagged [Fintype ι] {π : Prepartition I}
 
 theorem IsSubordinate.bUnionPrepartition [Fintype ι] (h : IsSubordinate π r)
     (πi : ∀ J, Prepartition J) : IsSubordinate (π.bUnionPrepartition πi) r := fun J hJ =>
-  Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_bUnionIndex hJ) <|
-    h _ <| π.toPrepartition.bUnionIndex_mem hJ
+  Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_bunionᵢIndex hJ) <|
+    h _ <| π.toPrepartition.bunionᵢIndex_mem hJ
 #align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.bUnionPrepartition
 
 theorem IsSubordinate.infPrepartition [Fintype ι] (h : IsSubordinate π r) (π' : Prepartition I) :
@@ -316,9 +316,9 @@ theorem isPartition_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
   Prepartition.isPartition_single_iff hJ
 #align box_integral.tagged_prepartition.is_partition_single_iff BoxIntegral.TaggedPrepartition.isPartition_single_iff
 
-theorem isPartitionSingle (h : x ∈ I.Icc) : (single I I le_rfl x h).IsPartition :=
+theorem isPartition_single (h : x ∈ I.Icc) : (single I I le_rfl x h).IsPartition :=
   Prepartition.isPartitionTop I
-#align box_integral.tagged_prepartition.is_partition_single BoxIntegral.TaggedPrepartition.isPartitionSingle
+#align box_integral.tagged_prepartition.is_partition_single BoxIntegral.TaggedPrepartition.isPartition_single
 
 theorem forall_mem_single (p : (ι → ℝ) → Box ι → Prop) (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (∀ J' ∈ single I J hJ x h, p ((single I J hJ x h).Tag J') J') ↔ p x J := by simp
@@ -331,9 +331,9 @@ theorem isHenstock_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
 #align box_integral.tagged_prepartition.is_Henstock_single_iff BoxIntegral.TaggedPrepartition.isHenstock_single_iff
 
 @[simp]
-theorem isHenstockSingle (h : x ∈ I.Icc) : IsHenstock (single I I le_rfl x h) :=
+theorem isHenstock_single (h : x ∈ I.Icc) : IsHenstock (single I I le_rfl x h) :=
   (isHenstock_single_iff (le_refl I) h).2 h
-#align box_integral.tagged_prepartition.is_Henstock_single BoxIntegral.TaggedPrepartition.isHenstockSingle
+#align box_integral.tagged_prepartition.is_Henstock_single BoxIntegral.TaggedPrepartition.isHenstock_single
 
 @[simp]
 theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
@@ -343,7 +343,7 @@ theorem isSubordinate_single [Fintype ι] (hJ : J ≤ I) (h : x ∈ I.Icc) :
 
 @[simp]
 theorem union_single (hJ : J ≤ I) (h : x ∈ I.Icc) : (single I J hJ x h).unionᵢ = J :=
-  Prepartition.union_single hJ
+  Prepartition.unionᵢ_single hJ
 #align box_integral.tagged_prepartition.Union_single BoxIntegral.TaggedPrepartition.union_single
 
 /-- Union of two tagged prepartitions with disjoint unions of boxes. -/
@@ -373,7 +373,7 @@ theorem mem_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
 @[simp]
 theorem union_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
     (π₁.disjUnion π₂ h).unionᵢ = π₁.unionᵢ ∪ π₂.unionᵢ :=
-  Prepartition.union_disjUnion _
+  Prepartition.unionᵢ_disjUnion _
 #align box_integral.tagged_prepartition.Union_disj_union BoxIntegral.TaggedPrepartition.union_disjUnion
 
 theorem disjUnion_tag_of_mem_left (h : Disjoint π₁.unionᵢ π₂.unionᵢ) (hJ : J ∈ π₁) :

6ca1a09b

bump to nightly-2023-04-20-08

mathlib commit https://github.com/leanprover-community/mathlib/commit/730c6d4cab72b9d84fcfb9e95e8796e9cd8f40ba

8f3c244e

Diff

@@ -134,7 +134,7 @@ def bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : Tag
     where
   toPrepartition := π.bunionᵢ fun J => (πi J).toPrepartition
   Tag J := (πi (π.bUnionIndex (fun J => (πi J).toPrepartition) J)).Tag J
-  tag_mem_Icc J := Box.le_iff_icc.1 (π.bUnionIndex_le _ _) ((πi _).tag_mem_Icc _)
+  tag_mem_Icc J := Box.le_iff_Icc.1 (π.bUnionIndex_le _ _) ((πi _).tag_mem_Icc _)
 #align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.bUnionTagged
 
 @[simp]
@@ -270,7 +270,7 @@ theorem isSubordinate_bUnionTagged [Fintype ι] {π : Prepartition I}
 
 theorem IsSubordinate.bUnionPrepartition [Fintype ι] (h : IsSubordinate π r)
     (πi : ∀ J, Prepartition J) : IsSubordinate (π.bUnionPrepartition πi) r := fun J hJ =>
-  Subset.trans (Box.le_iff_icc.1 <| π.toPrepartition.le_bUnionIndex hJ) <|
+  Subset.trans (Box.le_iff_Icc.1 <| π.toPrepartition.le_bUnionIndex hJ) <|
     h _ <| π.toPrepartition.bUnionIndex_mem hJ
 #align box_integral.tagged_prepartition.is_subordinate.bUnion_prepartition BoxIntegral.TaggedPrepartition.IsSubordinate.bUnionPrepartition
 
@@ -309,7 +309,7 @@ theorem mem_single {J'} (hJ : J ≤ I) (h : x ∈ I.Icc) : J' ∈ single I J hJ
 #align box_integral.tagged_prepartition.mem_single BoxIntegral.TaggedPrepartition.mem_single
 
 instance (I : Box ι) : Inhabited (TaggedPrepartition I) :=
-  ⟨single I I le_rfl I.upper I.upper_mem_icc⟩
+  ⟨single I I le_rfl I.upper I.upper_mem_Icc⟩
 
 theorem isPartition_single_iff (hJ : J ≤ I) (h : x ∈ I.Icc) :
     (single I J hJ x h).IsPartition ↔ J = I :=
@@ -412,7 +412,7 @@ def embedBox (I J : Box ι) (h : I ≤ J) : TaggedPrepartition I ↪ TaggedPrepa
   toFun π :=
     { π with
       le_of_mem' := fun J' hJ' => (π.le_of_mem' J' hJ').trans h
-      tag_mem_Icc := fun J => Box.le_iff_icc.1 h (π.tag_mem_Icc J) }
+      tag_mem_Icc := fun J => Box.le_iff_Icc.1 h (π.tag_mem_Icc J) }
   inj' := by
     rintro ⟨⟨b₁, h₁le, h₁d⟩, t₁, ht₁⟩ ⟨⟨b₂, h₂le, h₂d⟩, t₂, ht₂⟩ H
     simpa using H

6ca1a09b

bump to nightly-2023-04-14-22

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ebf83ed9c262adbf983ef64d5e8c2ae94b625f4

60fdc414

Diff

@@ -43,7 +43,7 @@ prepartition. For simiplicity we require that `tag` is defined for all boxes in
 we will use onle the values of `tag` on the boxes of the partition. -/
 structure TaggedPrepartition (I : Box ι) extends Prepartition I where
   Tag : Box ι → ι → ℝ
-  tag_mem_icc : ∀ J, tag J ∈ I.Icc
+  tag_mem_Icc : ∀ J, tag J ∈ I.Icc
 #align box_integral.tagged_prepartition BoxIntegral.TaggedPrepartition
 
 namespace TaggedPrepartition
@@ -134,7 +134,7 @@ def bUnionTagged (π : Prepartition I) (πi : ∀ J, TaggedPrepartition J) : Tag
     where
   toPrepartition := π.bunionᵢ fun J => (πi J).toPrepartition
   Tag J := (πi (π.bUnionIndex (fun J => (πi J).toPrepartition) J)).Tag J
-  tag_mem_icc J := Box.le_iff_icc.1 (π.bUnionIndex_le _ _) ((πi _).tag_mem_icc _)
+  tag_mem_Icc J := Box.le_iff_icc.1 (π.bUnionIndex_le _ _) ((πi _).tag_mem_Icc _)
 #align box_integral.prepartition.bUnion_tagged BoxIntegral.Prepartition.bUnionTagged
 
 @[simp]
@@ -192,7 +192,7 @@ def bUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J, Prepartition J)
     where
   toPrepartition := π.toPrepartition.bunionᵢ πi
   Tag J := π.Tag (π.toPrepartition.bUnionIndex πi J)
-  tag_mem_icc J := π.tag_mem_icc _
+  tag_mem_Icc J := π.tag_mem_Icc _
 #align box_integral.tagged_prepartition.bUnion_prepartition BoxIntegral.TaggedPrepartition.bUnionPrepartition
 
 theorem IsPartition.bUnionPrepartition {π : TaggedPrepartition I} (h : IsPartition π)
@@ -249,7 +249,7 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
       refine' Finset.card_le_of_subset fun J hJ => _
       rw [Finset.mem_filter] at hJ⊢; rcases hJ with ⟨hJ, rfl⟩
       exact ⟨hJ, h J hJ⟩
-    _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_icc_le x
+    _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_Icc_le x
     
 #align box_integral.tagged_prepartition.is_Henstock.card_filter_tag_eq_le BoxIntegral.TaggedPrepartition.IsHenstock.card_filter_tag_eq_le
 
@@ -286,7 +286,7 @@ theorem IsSubordinate.mono' [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π
 
 theorem IsSubordinate.mono [Fintype ι] {π : TaggedPrepartition I} (hr₁ : π.IsSubordinate r₁)
     (h : ∀ x ∈ I.Icc, r₁ x ≤ r₂ x) : π.IsSubordinate r₂ :=
-  hr₁.mono' fun J _ => h _ <| π.tag_mem_icc J
+  hr₁.mono' fun J _ => h _ <| π.tag_mem_Icc J
 #align box_integral.tagged_prepartition.is_subordinate.mono BoxIntegral.TaggedPrepartition.IsSubordinate.mono
 
 theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.IsSubordinate r)
@@ -352,7 +352,7 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.unionᵢ
     where
   toPrepartition := π₁.toPrepartition.disjUnion π₂.toPrepartition h
   Tag := π₁.boxes.piecewise π₁.Tag π₂.Tag
-  tag_mem_icc J := by
+  tag_mem_Icc J := by
     dsimp only [Finset.piecewise]
     split_ifs
     exacts[π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
@@ -412,7 +412,7 @@ def embedBox (I J : Box ι) (h : I ≤ J) : TaggedPrepartition I ↪ TaggedPrepa
   toFun π :=
     { π with
       le_of_mem' := fun J' hJ' => (π.le_of_mem' J' hJ').trans h
-      tag_mem_icc := fun J => Box.le_iff_icc.1 h (π.tag_mem_icc J) }
+      tag_mem_Icc := fun J => Box.le_iff_icc.1 h (π.tag_mem_Icc J) }
   inj' := by
     rintro ⟨⟨b₁, h₁le, h₁d⟩, t₁, ht₁⟩ ⟨⟨b₂, h₂le, h₂d⟩, t₂, ht₂⟩ H
     simpa using H

6ca1a09b

bump to nightly-2023-02-27-10

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

49ff026a

Diff

@@ -30,7 +30,7 @@ rectangular box, box partition
 
 noncomputable section
 
-open Classical Ennreal NNReal
+open Classical ENNReal NNReal
 
 open Set Function

6ca1a09b

bump to nightly-2023-02-21-16

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

1107b979

Changes in mathlib4

mathlib3

mathlib4

6ca1a09b

chore: scope open Classical (#11199)

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.

c747be0a

Diff

@@ -27,7 +27,8 @@ rectangular box, box partition
 
 noncomputable section
 
-open Classical ENNReal NNReal
+open scoped Classical
+open ENNReal NNReal
 
 open Set Function

6ca1a09b

doc: fix typos in tags header (#11088)

Fix 1 typo, 5 lowercase, 4 header depths

ab90a4e3

Diff

@@ -19,7 +19,7 @@ called a *Henstock* partition. We do not include this assumption into the defini
 (pre)partition because McShane integral is defined as a limit along tagged partitions without this
 requirement.
 
-### Tags
+## Tags
 
 rectangular box, box partition
 -/

6ca1a09b

chore: Improve Finset lemma names (#8894)

Change a few lemma names that have historically bothered me.

Finset.card_le_of_subset → Finset.card_le_card
Multiset.card_le_of_le → Multiset.card_le_card
Multiset.card_lt_of_lt → Multiset.card_lt_card
Set.ncard_le_of_subset → Set.ncard_le_ncard
Finset.image_filter → Finset.filter_image
CompleteLattice.finset_sup_compact_of_compact → CompleteLattice.isCompactElement_finset_sup

7d3d6e43

Diff

@@ -237,7 +237,7 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
   calc
     (π.boxes.filter fun J => π.tag J = x).card ≤
         (π.boxes.filter fun J : Box ι => x ∈ Box.Icc J).card := by
-      refine' Finset.card_le_of_subset fun J hJ => _
+      refine' Finset.card_le_card fun J hJ => _
       rw [Finset.mem_filter] at hJ ⊢; rcases hJ with ⟨hJ, rfl⟩
       exact ⟨hJ, h J hJ⟩
     _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_Icc_le x

6ca1a09b

style: shorten simps configurations (#8296)

Use .asFn and .lemmasOnly as simps configuration options.

For reference, these are defined here:

https://github.com/leanprover-community/mathlib4/blob/4055c8b471380825f07416b12cb0cf266da44d84/Mathlib/Tactic/Simps/Basic.lean#L843-L851

e0637173

Diff

@@ -99,7 +99,7 @@ theorem isPartition_iff_iUnion_eq : IsPartition π ↔ π.iUnion = I :=
 #align box_integral.tagged_prepartition.is_partition_iff_Union_eq BoxIntegral.TaggedPrepartition.isPartition_iff_iUnion_eq
 
 /-- The tagged partition made of boxes of `π` that satisfy predicate `p`. -/
-@[simps! (config := { fullyApplied := false })]
+@[simps! (config := .asFn)]
 def filter (p : Box ι → Prop) : TaggedPrepartition I :=
   ⟨π.1.filter p, π.2, π.3⟩
 #align box_integral.tagged_prepartition.filter BoxIntegral.TaggedPrepartition.filter
@@ -178,7 +178,7 @@ returns the tagged partition of `I` into all the boxes of all `πi J hJ`. The ta
 is defined to be the `π.tag` of the box of the partition `π` that includes `J`.
 
 Note that usually the result is not a Henstock partition. -/
-@[simps (config := { fullyApplied := false }) tag]
+@[simps (config := .asFn) tag]
 def biUnionPrepartition (π : TaggedPrepartition I) (πi : ∀ J : Box ι, Prepartition J) :
     TaggedPrepartition I where
   toPrepartition := π.toPrepartition.biUnion πi
@@ -289,7 +289,7 @@ theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.I
 #align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le
 
 /-- Tagged prepartition with single box and prescribed tag. -/
-@[simps! (config := { fullyApplied := false })]
+@[simps! (config := .asFn)]
 def single (I J : Box ι) (hJ : J ≤ I) (x : ι → ℝ) (h : x ∈ Box.Icc I) : TaggedPrepartition I :=
   ⟨Prepartition.single I J hJ, fun _ => x, fun _ => h⟩
 #align box_integral.tagged_prepartition.single BoxIntegral.TaggedPrepartition.single

6ca1a09b

refactor(Topology/MetricSpace): remove Metric.Bounded (#7240)

Use Bornology.IsBounded instead.

98e78f90

Diff

@@ -284,7 +284,7 @@ theorem IsSubordinate.diam_le [Fintype ι] {π : TaggedPrepartition I} (h : π.I
     (hJ : J ∈ π.boxes) : diam (Box.Icc J) ≤ 2 * r (π.tag J) :=
   calc
     diam (Box.Icc J) ≤ diam (closedBall (π.tag J) (r <| π.tag J)) :=
-      diam_mono (h J hJ) bounded_closedBall
+      diam_mono (h J hJ) isBounded_closedBall
     _ ≤ 2 * r (π.tag J) := diam_closedBall (le_of_lt (r _).2)
 #align box_integral.tagged_prepartition.is_subordinate.diam_le BoxIntegral.TaggedPrepartition.IsSubordinate.diam_le

6ca1a09b

chore: banish Type _ and Sort _ (#6499)

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

This has nice performance benefits.

32de3f67

Diff

@@ -33,7 +33,7 @@ open Set Function
 
 namespace BoxIntegral
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 /-- A tagged prepartition is a prepartition enriched with a tagged point for each box of the
 prepartition. For simplicity we require that `tag` is defined for all boxes in `ι → ℝ` but

6ca1a09b

chore: script to replace headers with #align_import statements (#5979)

depends on: #5966

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

89aa3a3b

Diff

@@ -2,14 +2,11 @@
 Copyright (c) 2021 Yury Kudryashov. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
-
-! This file was ported from Lean 3 source module analysis.box_integral.partition.tagged
-! leanprover-community/mathlib commit 6ca1a09bc9aa75824bf97388c9e3b441fc4ccf3f
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.BoxIntegral.Partition.Basic
 
+#align_import analysis.box_integral.partition.tagged from "leanprover-community/mathlib"@"6ca1a09bc9aa75824bf97388c9e3b441fc4ccf3f"
+
 /-!
 # Tagged partitions

6ca1a09b

chore: clean up spacing around at and goals (#5387)

Changes are of the form

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

2a870323

Diff

@@ -241,7 +241,7 @@ theorem IsHenstock.card_filter_tag_eq_le [Fintype ι] (h : π.IsHenstock) (x : 
     (π.boxes.filter fun J => π.tag J = x).card ≤
         (π.boxes.filter fun J : Box ι => x ∈ Box.Icc J).card := by
       refine' Finset.card_le_of_subset fun J hJ => _
-      rw [Finset.mem_filter] at hJ⊢; rcases hJ with ⟨hJ, rfl⟩
+      rw [Finset.mem_filter] at hJ ⊢; rcases hJ with ⟨hJ, rfl⟩
       exact ⟨hJ, h J hJ⟩
     _ ≤ 2 ^ Fintype.card ι := π.toPrepartition.card_filter_mem_Icc_le x
 set_option linter.uppercaseLean3 false in

6ca1a09b

chore: fix many typos (#4967)

These are all doc fixes

6f9e51c3

Diff

@@ -39,8 +39,8 @@ namespace BoxIntegral
 variable {ι : Type _}
 
 /-- A tagged prepartition is a prepartition enriched with a tagged point for each box of the
-prepartition. For simiplicity we require that `tag` is defined for all boxes in `ι → ℝ` but
-we will use onle the values of `tag` on the boxes of the partition. -/
+prepartition. For simplicity we require that `tag` is defined for all boxes in `ι → ℝ` but
+we will use only the values of `tag` on the boxes of the partition. -/
 structure TaggedPrepartition (I : Box ι) extends Prepartition I where
   tag : Box ι → ι → ℝ
   tag_mem_Icc : ∀ J, tag J ∈ Box.Icc I

6ca1a09b

chore: add space after exacts (#4945)

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

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

bf799bb9

Diff

@@ -350,7 +350,7 @@ def disjUnion (π₁ π₂ : TaggedPrepartition I) (h : Disjoint π₁.iUnion π
   tag_mem_Icc J := by
     dsimp only [Finset.piecewise]
     split_ifs
-    exacts[π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
+    exacts [π₁.tag_mem_Icc J, π₂.tag_mem_Icc J]
 #align box_integral.tagged_prepartition.disj_union BoxIntegral.TaggedPrepartition.disjUnion
 
 @[simp]

6ca1a09b

feat: port Analysis.BoxIntegral.Partition.Tagged (#3669)

73a6416b

`analysis.box_integral.partition.tagged` ⟷ `Mathlib.Analysis.BoxIntegral.Partition.Tagged`

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 448

analysis.box_integral.partition.tagged ⟷ Mathlib.Analysis.BoxIntegral.Partition.Tagged

Changes since the initial port

Changes in mathlib3

Changes in mathlib3port

Changes in mathlib4

Dependencies 10 + 448

`analysis.box_integral.partition.tagged` ⟷ `Mathlib.Analysis.BoxIntegral.Partition.Tagged`