analysis.box_integral.partition.basic ⟷ Mathlib.Analysis.BoxIntegral.Partition.Basic

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

@@ -944,7 +944,7 @@ theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUni
 #align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (J «expr ∈ » π) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:642:2: warning: expanding binder collection (J «expr ∈ » π) -/
 #print BoxIntegral.Prepartition.IsPartition.existsUnique /-
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _) (_ : J ∈ π), x ∈ J :=
   by

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

@@ -234,7 +234,7 @@ theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
     choose y hy₁ hy₂
     exact π.eq_of_mem_of_mem h₁ h₂ hy₁ hy₂
   intro i
-  simp only [Set.ext_iff, mem_set_of_eq] at H 
+  simp only [Set.ext_iff, mem_set_of_eq] at H
   cases' (hx₁.1 i).eq_or_lt with hi₁ hi₁
   · have hi₂ : J₂.lower i = x i := (H _).1 hi₁
     have H₁ : x i < J₁.upper i := by simpa only [hi₁] using J₁.lower_lt_upper i
@@ -351,7 +351,7 @@ theorem le_iff_nonempty_imp_le_and_iUnion_subset :
   · refine' fun H => ⟨fun J hJ J' hJ' Hne => _, Union_mono H⟩
     rcases H hJ with ⟨J'', hJ'', Hle⟩; rcases Hne with ⟨x, hx, hx'⟩
     rwa [π₂.eq_of_mem_of_mem hJ' hJ'' hx' (Hle hx)]
-  · rintro ⟨H, HU⟩ J hJ; simp only [Set.subset_def, mem_Union] at HU 
+  · rintro ⟨H, HU⟩ J hJ; simp only [Set.subset_def, mem_Union] at HU
     rcases HU J.upper ⟨J, hJ, J.upper_mem⟩ with ⟨J₂, hJ₂, hx⟩
     exact ⟨J₂, hJ₂, H _ hJ _ hJ₂ ⟨_, J.upper_mem, hx⟩⟩
 #align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset
@@ -379,7 +379,7 @@ def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
   boxes := π.boxes.biUnion fun J => (πi J).boxes
   le_of_mem' J hJ :=
     by
-    simp only [Finset.mem_biUnion, exists_prop, mem_boxes] at hJ 
+    simp only [Finset.mem_biUnion, exists_prop, mem_boxes] at hJ
     rcases hJ with ⟨J', hJ', hJ⟩
     exact ((πi J').le_of_mem hJ).trans (π.le_of_mem hJ')
   PairwiseDisjoint :=
@@ -505,7 +505,7 @@ theorem biUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : B
     rwa [π.bUnion_index_of_mem hJ₁ hJ₂]
   · rintro ⟨J₁, ⟨J₂, hJ₂, hJ₁⟩, hJ⟩
     refine' ⟨J₂, hJ₂, J₁, hJ₁, _⟩
-    rwa [π.bUnion_index_of_mem hJ₂ hJ₁] at hJ 
+    rwa [π.bUnion_index_of_mem hJ₂ hJ₁] at hJ
 #align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.biUnion_assoc
 -/
 
@@ -518,11 +518,11 @@ def ofWithBot (boxes : Finset (WithBot (Box ι)))
     where
   boxes := boxes.eraseNone
   le_of_mem' J hJ := by
-    rw [mem_erase_none] at hJ 
+    rw [mem_erase_none] at hJ
     simpa only [WithBot.some_eq_coe, WithBot.coe_le_coe] using le_of_mem _ hJ
   PairwiseDisjoint J₁ h₁ J₂ h₂ hne :=
     by
-    simp only [mem_coe, mem_erase_none] at h₁ h₂ 
+    simp only [mem_coe, mem_erase_none] at h₁ h₂
     exact box.disjoint_coe.1 (pairwise_disjoint h₁ h₂ (mt Option.some_inj.1 hne))
 #align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBot
 -/
@@ -629,7 +629,7 @@ theorem mem_restrict' : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : Set (
 theorem restrict_mono {π₁ π₂ : Prepartition I} (Hle : π₁ ≤ π₂) : π₁.restrict J ≤ π₂.restrict J :=
   by
   refine' of_with_bot_mono fun J₁ hJ₁ hne => _
-  rw [Finset.mem_image] at hJ₁ ; rcases hJ₁ with ⟨J₁, hJ₁, rfl⟩
+  rw [Finset.mem_image] at hJ₁; rcases hJ₁ with ⟨J₁, hJ₁, rfl⟩
   rcases Hle hJ₁ with ⟨J₂, hJ₂, hle⟩
   exact ⟨_, Finset.mem_image_of_mem _ hJ₂, inf_le_inf_left _ <| WithBot.coe_le_coe.2 hle⟩
 #align box_integral.prepartition.restrict_mono BoxIntegral.Prepartition.restrict_mono
@@ -690,7 +690,7 @@ theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
   by
   fconstructor <;> intro H J hJ
   · rw [← π.restrict_bUnion πi hJ]; exact restrict_mono H
-  · rw [mem_bUnion] at hJ ; rcases hJ with ⟨J₁, h₁, hJ⟩
+  · rw [mem_bUnion] at hJ; rcases hJ with ⟨J₁, h₁, hJ⟩
     rcases H J₁ h₁ hJ with ⟨J₂, h₂, Hle⟩
     rcases π'.mem_restrict.mp h₂ with ⟨J₃, h₃, H⟩
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩

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

@@ -3,8 +3,8 @@ 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.Algebra.BigOperators.Option
-import Mathbin.Analysis.BoxIntegral.Box.Basic
+import Algebra.BigOperators.Option
+import Analysis.BoxIntegral.Box.Basic
 
 #align_import analysis.box_integral.partition.basic from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
 
@@ -944,7 +944,7 @@ theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUni
 #align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (J «expr ∈ » π) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:641:2: warning: expanding binder collection (J «expr ∈ » π) -/
 #print BoxIntegral.Prepartition.IsPartition.existsUnique /-
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _) (_ : J ∈ π), x ∈ J :=
   by

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

@@ -2,15 +2,12 @@
 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.basic
-! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Algebra.BigOperators.Option
 import Mathbin.Analysis.BoxIntegral.Box.Basic
 
+#align_import analysis.box_integral.partition.basic from "leanprover-community/mathlib"@"9d2f0748e6c50d7a2657c564b1ff2c695b39148d"
+
 /-!
 # Partitions of rectangular boxes in `ℝⁿ`
 
@@ -947,7 +944,7 @@ theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUni
 #align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (J «expr ∈ » π) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (J «expr ∈ » π) -/
 #print BoxIntegral.Prepartition.IsPartition.existsUnique /-
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _) (_ : J ∈ π), x ∈ J :=
   by

mathlib commit https://github.com/leanprover-community/mathlib/commit/2a0ce625dbb0ffbc7d1316597de0b25c1ec75303

@@ -791,7 +791,7 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
   by
   simp only [prepartition.Union]
   convert (@Set.biUnion_diff_biUnion_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
-  · ext (J x); simp (config := { contextual := true })
+  · ext J x; simp (config := { contextual := true })
   · convert π.pairwise_disjoint; simp
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
 -/

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

@@ -78,15 +78,19 @@ theorem mem_boxes : J ∈ π.boxes ↔ J ∈ π :=
 #align box_integral.prepartition.mem_boxes BoxIntegral.Prepartition.mem_boxes
 -/
 
+#print BoxIntegral.Prepartition.mem_mk /-
 @[simp]
 theorem mem_mk {s h₁ h₂} : J ∈ (mk s h₁ h₂ : Prepartition I) ↔ J ∈ s :=
   Iff.rfl
 #align box_integral.prepartition.mem_mk BoxIntegral.Prepartition.mem_mk
+-/
 
+#print BoxIntegral.Prepartition.disjoint_coe_of_mem /-
 theorem disjoint_coe_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (h : J₁ ≠ J₂) :
     Disjoint (J₁ : Set (ι → ℝ)) J₂ :=
   π.PairwiseDisjoint h₁ h₂ h
 #align box_integral.prepartition.disjoint_coe_of_mem BoxIntegral.Prepartition.disjoint_coe_of_mem
+-/
 
 #print BoxIntegral.Prepartition.eq_of_mem_of_mem /-
 theorem eq_of_mem_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (hx₁ : x ∈ J₁) (hx₂ : x ∈ J₂) : J₁ = J₂ :=
@@ -112,13 +116,17 @@ theorem le_of_mem (hJ : J ∈ π) : J ≤ I :=
 #align box_integral.prepartition.le_of_mem BoxIntegral.Prepartition.le_of_mem
 -/
 
+#print BoxIntegral.Prepartition.lower_le_lower /-
 theorem lower_le_lower (hJ : J ∈ π) : I.lower ≤ J.lower :=
   Box.antitone_lower (π.le_of_mem hJ)
 #align box_integral.prepartition.lower_le_lower BoxIntegral.Prepartition.lower_le_lower
+-/
 
+#print BoxIntegral.Prepartition.upper_le_upper /-
 theorem upper_le_upper (hJ : J ∈ π) : J.upper ≤ I.upper :=
   Box.monotone_upper (π.le_of_mem hJ)
 #align box_integral.prepartition.upper_le_upper BoxIntegral.Prepartition.upper_le_upper
+-/
 
 #print BoxIntegral.Prepartition.injective_boxes /-
 theorem injective_boxes : Function.Injective (boxes : Prepartition I → Finset (Box ι)) := by
@@ -183,30 +191,41 @@ instance : OrderBot (Prepartition I)
 instance : Inhabited (Prepartition I) :=
   ⟨⊤⟩
 
+#print BoxIntegral.Prepartition.le_def /-
 theorem le_def : π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∃ J' ∈ π₂, J ≤ J' :=
   Iff.rfl
 #align box_integral.prepartition.le_def BoxIntegral.Prepartition.le_def
+-/
 
+#print BoxIntegral.Prepartition.mem_top /-
 @[simp]
 theorem mem_top : J ∈ (⊤ : Prepartition I) ↔ J = I :=
   mem_singleton
 #align box_integral.prepartition.mem_top BoxIntegral.Prepartition.mem_top
+-/
 
+#print BoxIntegral.Prepartition.top_boxes /-
 @[simp]
 theorem top_boxes : (⊤ : Prepartition I).boxes = {I} :=
   rfl
 #align box_integral.prepartition.top_boxes BoxIntegral.Prepartition.top_boxes
+-/
 
+#print BoxIntegral.Prepartition.not_mem_bot /-
 @[simp]
 theorem not_mem_bot : J ∉ (⊥ : Prepartition I) :=
   id
 #align box_integral.prepartition.not_mem_bot BoxIntegral.Prepartition.not_mem_bot
+-/
 
+#print BoxIntegral.Prepartition.bot_boxes /-
 @[simp]
 theorem bot_boxes : (⊥ : Prepartition I).boxes = ∅ :=
   rfl
 #align box_integral.prepartition.bot_boxes BoxIntegral.Prepartition.bot_boxes
+-/
 
+#print BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq /-
 /-- An auxiliary lemma used to prove that the same point can't belong to more than
 `2 ^ fintype.card ι` closed boxes of a prepartition. -/
 theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
@@ -228,7 +247,9 @@ theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
   · have hi₂ : J₂.lower i < x i := (hx₂.1 i).lt_of_ne (mt (H _).2 hi₁.ne)
     exact ⟨x i, ⟨hi₁, hx₁.2 i⟩, ⟨hi₂, hx₂.2 i⟩⟩
 #align box_integral.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq
+-/
 
+#print BoxIntegral.Prepartition.card_filter_mem_Icc_le /-
 /-- The set of boxes of a prepartition that contain `x` in their closures has cardinality
 at most `2 ^ fintype.card ι`. -/
 theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
@@ -240,6 +261,7 @@ theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
       (fun _ _ => Finset.mem_univ _) _
   simpa only [Finset.mem_filter] using π.inj_on_set_of_mem_Icc_set_of_lower_eq x
 #align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_le
+-/
 
 #print BoxIntegral.Prepartition.iUnion /-
 /-- Given a prepartition `π : box_integral.prepartition I`, `π.Union` is the part of `I` covered by
@@ -261,10 +283,12 @@ theorem iUnion_def' : π.iUnion = ⋃ J ∈ π.boxes, ↑J :=
 #align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.iUnion_def'
 -/
 
+#print BoxIntegral.Prepartition.mem_iUnion /-
 @[simp]
 theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
   Set.mem_iUnion₂
 #align box_integral.prepartition.mem_Union BoxIntegral.Prepartition.mem_iUnion
+-/
 
 #print BoxIntegral.Prepartition.iUnion_single /-
 @[simp]
@@ -272,19 +296,25 @@ theorem iUnion_single (h : J ≤ I) : (single I J h).iUnion = J := by simp [Unio
 #align box_integral.prepartition.Union_single BoxIntegral.Prepartition.iUnion_single
 -/
 
+#print BoxIntegral.Prepartition.iUnion_top /-
 @[simp]
 theorem iUnion_top : (⊤ : Prepartition I).iUnion = I := by simp [prepartition.Union]
 #align box_integral.prepartition.Union_top BoxIntegral.Prepartition.iUnion_top
+-/
 
+#print BoxIntegral.Prepartition.iUnion_eq_empty /-
 @[simp]
 theorem iUnion_eq_empty : π₁.iUnion = ∅ ↔ π₁ = ⊥ := by
   simp [← injective_boxes.eq_iff, Finset.ext_iff, prepartition.Union, imp_false]
 #align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.iUnion_eq_empty
+-/
 
+#print BoxIntegral.Prepartition.iUnion_bot /-
 @[simp]
 theorem iUnion_bot : (⊥ : Prepartition I).iUnion = ∅ :=
   iUnion_eq_empty.2 rfl
 #align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.iUnion_bot
+-/
 
 #print BoxIntegral.Prepartition.subset_iUnion /-
 theorem subset_iUnion (h : J ∈ π) : ↑J ⊆ π.iUnion :=
@@ -298,19 +328,24 @@ theorem iUnion_subset : π.iUnion ⊆ I :=
 #align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.iUnion_subset
 -/
 
+#print BoxIntegral.Prepartition.iUnion_mono /-
 @[mono]
 theorem iUnion_mono (h : π₁ ≤ π₂) : π₁.iUnion ⊆ π₂.iUnion := fun x hx =>
   let ⟨J₁, hJ₁, hx⟩ := π₁.mem_iUnion.1 hx
   let ⟨J₂, hJ₂, hle⟩ := h hJ₁
   π₂.mem_iUnion.2 ⟨J₂, hJ₂, hle hx⟩
 #align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.iUnion_mono
+-/
 
+#print BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion /-
 theorem disjoint_boxes_of_disjoint_iUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     Disjoint π₁.boxes π₂.boxes :=
   Finset.disjoint_left.2 fun J h₁ h₂ =>
     Disjoint.le_bot (h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)) ⟨J.upper_mem, J.upper_mem⟩
 #align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion
+-/
 
+#print BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset /-
 theorem le_iff_nonempty_imp_le_and_iUnion_subset :
     π₁ ≤ π₂ ↔
       (∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J') ∧ π₁.iUnion ⊆ π₂.iUnion :=
@@ -323,6 +358,7 @@ theorem le_iff_nonempty_imp_le_and_iUnion_subset :
     rcases HU J.upper ⟨J, hJ, J.upper_mem⟩ with ⟨J₂, hJ₂, hx⟩
     exact ⟨J₂, hJ₂, H _ hJ _ hJ₂ ⟨_, J.upper_mem, hx⟩⟩
 #align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset
+-/
 
 #print BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_superset /-
 theorem eq_of_boxes_subset_iUnion_superset (h₁ : π₁.boxes ⊆ π₂.boxes) (h₂ : π₂.iUnion ⊆ π₁.iUnion) :
@@ -363,18 +399,24 @@ def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
 
 variable {πi πi₁ πi₂ : ∀ J : Box ι, Prepartition J}
 
+#print BoxIntegral.Prepartition.mem_biUnion /-
 @[simp]
 theorem mem_biUnion : J ∈ π.biUnion πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [bUnion]
 #align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_biUnion
+-/
 
+#print BoxIntegral.Prepartition.biUnion_le /-
 theorem biUnion_le (πi : ∀ J, Prepartition J) : π.biUnion πi ≤ π := fun J hJ =>
   let ⟨J', hJ', hJ⟩ := π.mem_biUnion.1 hJ
   ⟨J', hJ', (πi J').le_of_mem hJ⟩
 #align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.biUnion_le
+-/
 
+#print BoxIntegral.Prepartition.biUnion_top /-
 @[simp]
 theorem biUnion_top : (π.biUnion fun _ => ⊤) = π := by ext; simp
 #align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.biUnion_top
+-/
 
 #print BoxIntegral.Prepartition.biUnion_congr /-
 @[congr]
@@ -470,6 +512,7 @@ theorem biUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : B
 #align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.biUnion_assoc
 -/
 
+#print BoxIntegral.Prepartition.ofWithBot /-
 /-- Create a `box_integral.prepartition` from a collection of possibly empty boxes by filtering out
 the empty one if it exists. -/
 def ofWithBot (boxes : Finset (WithBot (Box ι)))
@@ -485,13 +528,17 @@ def ofWithBot (boxes : Finset (WithBot (Box ι)))
     simp only [mem_coe, mem_erase_none] at h₁ h₂ 
     exact box.disjoint_coe.1 (pairwise_disjoint h₁ h₂ (mt Option.some_inj.1 hne))
 #align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBot
+-/
 
+#print BoxIntegral.Prepartition.mem_ofWithBot /-
 @[simp]
 theorem mem_ofWithBot {boxes : Finset (WithBot (Box ι))} {h₁ h₂} :
     J ∈ (ofWithBot boxes h₁ h₂ : Prepartition I) ↔ (J : WithBot (Box ι)) ∈ boxes :=
   mem_eraseNone
 #align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBot
+-/
 
+#print BoxIntegral.Prepartition.iUnion_ofWithBot /-
 @[simp]
 theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
@@ -503,7 +550,9 @@ theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
   simp only [← box.bUnion_coe_eq_coe, @Union_comm _ _ (box ι), @Union_comm _ _ (@Eq _ _ _),
     Union_Union_eq_right]
 #align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.iUnion_ofWithBot
+-/
 
+#print BoxIntegral.Prepartition.ofWithBot_le /-
 theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
     {le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint}
@@ -514,7 +563,9 @@ theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
     simpa only [WithBot.coe_le_coe] using H J hJ WithBot.coe_ne_bot
   simpa [of_with_bot, le_def]
 #align box_integral.prepartition.of_with_bot_le BoxIntegral.Prepartition.ofWithBot_le
+-/
 
+#print BoxIntegral.Prepartition.le_ofWithBot /-
 theorem le_ofWithBot {boxes : Finset (WithBot (Box ι))}
     {le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint}
@@ -525,7 +576,9 @@ theorem le_ofWithBot {boxes : Finset (WithBot (Box ι))}
   lift J' to box ι using ne_bot_of_le_ne_bot WithBot.coe_ne_bot hle
   exact ⟨J', mem_of_with_bot.2 J'mem, WithBot.coe_le_coe.1 hle⟩
 #align box_integral.prepartition.le_of_with_bot BoxIntegral.Prepartition.le_ofWithBot
+-/
 
+#print BoxIntegral.Prepartition.ofWithBot_mono /-
 theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
     {le_of_mem₁ : ∀ J ∈ boxes₁, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint₁ : Set.Pairwise (boxes₁ : Set (WithBot (Box ι))) Disjoint}
@@ -536,7 +589,9 @@ theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
       ofWithBot boxes₂ le_of_mem₂ pairwise_disjoint₂ :=
   le_ofWithBot _ fun J hJ => H J (mem_ofWithBot.1 hJ) WithBot.coe_ne_bot
 #align box_integral.prepartition.of_with_bot_mono BoxIntegral.Prepartition.ofWithBot_mono
+-/
 
+#print BoxIntegral.Prepartition.sum_ofWithBot /-
 theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) (f : Box ι → M) :
@@ -544,6 +599,7 @@ theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (B
       ∑ J in boxes, Option.elim' 0 f J :=
   Finset.sum_eraseNone _ _
 #align box_integral.prepartition.sum_of_with_bot BoxIntegral.Prepartition.sum_ofWithBot
+-/
 
 #print BoxIntegral.Prepartition.restrict /-
 /-- Restrict a prepartition to a box. -/
@@ -558,15 +614,20 @@ def restrict (π : Prepartition I) (J : Box ι) : Prepartition J :=
 #align box_integral.prepartition.restrict BoxIntegral.Prepartition.restrict
 -/
 
+#print BoxIntegral.Prepartition.mem_restrict /-
 @[simp]
 theorem mem_restrict : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : WithBot (Box ι)) = J ⊓ J' := by
   simp [restrict, eq_comm]
 #align box_integral.prepartition.mem_restrict BoxIntegral.Prepartition.mem_restrict
+-/
 
+#print BoxIntegral.Prepartition.mem_restrict' /-
 theorem mem_restrict' : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : Set (ι → ℝ)) = J ∩ J' := by
   simp only [mem_restrict, ← box.with_bot_coe_inj, box.coe_inf, box.coe_coe]
 #align box_integral.prepartition.mem_restrict' BoxIntegral.Prepartition.mem_restrict'
+-/
 
+#print BoxIntegral.Prepartition.restrict_mono /-
 @[mono]
 theorem restrict_mono {π₁ π₂ : Prepartition I} (Hle : π₁ ≤ π₂) : π₁.restrict J ≤ π₂.restrict J :=
   by
@@ -575,6 +636,7 @@ theorem restrict_mono {π₁ π₂ : Prepartition I} (Hle : π₁ ≤ π₂) : 
   rcases Hle hJ₁ with ⟨J₂, hJ₂, hle⟩
   exact ⟨_, Finset.mem_image_of_mem _ hJ₂, inf_le_inf_left _ <| WithBot.coe_le_coe.2 hle⟩
 #align box_integral.prepartition.restrict_mono BoxIntegral.Prepartition.restrict_mono
+-/
 
 #print BoxIntegral.Prepartition.monotone_restrict /-
 theorem monotone_restrict : Monotone fun π : Prepartition I => restrict π J := fun π₁ π₂ =>
@@ -603,10 +665,12 @@ theorem restrict_self : π.restrict I = π :=
 #align box_integral.prepartition.restrict_self BoxIntegral.Prepartition.restrict_self
 -/
 
+#print BoxIntegral.Prepartition.iUnion_restrict /-
 @[simp]
 theorem iUnion_restrict : (π.restrict J).iUnion = J ∩ π.iUnion := by
   simp [restrict, ← inter_Union, ← Union_def]
 #align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.iUnion_restrict
+-/
 
 #print BoxIntegral.Prepartition.restrict_biUnion /-
 @[simp]
@@ -623,6 +687,7 @@ theorem restrict_biUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
 #align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_biUnion
 -/
 
+#print BoxIntegral.Prepartition.biUnion_le_iff /-
 theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π.biUnion πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J :=
   by
@@ -633,7 +698,9 @@ theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     rcases π'.mem_restrict.mp h₂ with ⟨J₃, h₃, H⟩
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩
 #align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.biUnion_le_iff
+-/
 
+#print BoxIntegral.Prepartition.le_biUnion_iff /-
 theorem le_biUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π' ≤ π.biUnion πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J :=
   by
@@ -646,6 +713,7 @@ theorem le_biUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     rcases Hi J hJ this with ⟨Ji, hJi, hlei⟩
     exact ⟨Ji, π.mem_bUnion.2 ⟨J, hJ, hJi⟩, hlei⟩
 #align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_biUnion_iff
+-/
 
 instance : Inf (Prepartition I) :=
   ⟨fun π₁ π₂ => π₁.biUnion fun J => π₂.restrict J⟩
@@ -656,16 +724,20 @@ theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.biUnion
 #align box_integral.prepartition.inf_def BoxIntegral.Prepartition.inf_def
 -/
 
+#print BoxIntegral.Prepartition.mem_inf /-
 @[simp]
 theorem mem_inf {π₁ π₂ : Prepartition I} :
     J ∈ π₁ ⊓ π₂ ↔ ∃ J₁ ∈ π₁, ∃ J₂ ∈ π₂, (J : WithBot (Box ι)) = J₁ ⊓ J₂ := by
   simp only [inf_def, mem_bUnion, mem_restrict]
 #align box_integral.prepartition.mem_inf BoxIntegral.Prepartition.mem_inf
+-/
 
+#print BoxIntegral.Prepartition.iUnion_inf /-
 @[simp]
 theorem iUnion_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).iUnion = π₁.iUnion ∩ π₂.iUnion := by
   simp only [inf_def, Union_bUnion, Union_restrict, ← Union_inter, ← Union_def]
 #align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.iUnion_inf
+-/
 
 instance : SemilatticeInf (Prepartition I) :=
   { Prepartition.hasInf,
@@ -692,10 +764,12 @@ theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧
 #align box_integral.prepartition.mem_filter BoxIntegral.Prepartition.mem_filter
 -/
 
+#print BoxIntegral.Prepartition.filter_le /-
 theorem filter_le (π : Prepartition I) (p : Box ι → Prop) : π.filterₓ p ≤ π := fun J hJ =>
   let ⟨hπ, hp⟩ := π.mem_filter.1 hJ
   ⟨J, hπ, le_rfl⟩
 #align box_integral.prepartition.filter_le BoxIntegral.Prepartition.filter_le
+-/
 
 #print BoxIntegral.Prepartition.filter_of_true /-
 theorem filter_of_true {p : Box ι → Prop} (hp : ∀ J ∈ π, p J) : π.filterₓ p = π := by ext J;
@@ -710,6 +784,7 @@ theorem filter_true : (π.filterₓ fun _ => True) = π :=
 #align box_integral.prepartition.filter_true BoxIntegral.Prepartition.filter_true
 -/
 
+#print BoxIntegral.Prepartition.iUnion_filter_not /-
 @[simp]
 theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
@@ -719,12 +794,16 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
   · ext (J x); simp (config := { contextual := true })
   · convert π.pairwise_disjoint; simp
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
+-/
 
+#print BoxIntegral.Prepartition.sum_fiberwise /-
 theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι → α) (g : Box ι → M) :
     ∑ y in π.boxes.image f, ∑ J in (π.filterₓ fun J => f J = y).boxes, g J = ∑ J in π.boxes, g J :=
   by convert sum_fiberwise_of_maps_to (fun _ => Finset.mem_image_of_mem f) g
 #align box_integral.prepartition.sum_fiberwise BoxIntegral.Prepartition.sum_fiberwise
+-/
 
+#print BoxIntegral.Prepartition.disjUnion /-
 /-- Union of two disjoint prepartitions. -/
 @[simps]
 def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) : Prepartition I
@@ -736,25 +815,32 @@ def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.iUnion π₂.iU
       simpa [pairwise_union_of_symmetric (symmetric_disjoint.comap _), pairwise_disjoint]
     fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)
 #align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnion
+-/
 
+#print BoxIntegral.Prepartition.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.prepartition.mem_disj_union BoxIntegral.Prepartition.mem_disjUnion
+-/
 
+#print BoxIntegral.Prepartition.iUnion_disjUnion /-
 @[simp]
 theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion := by
   simp [disj_union, prepartition.Union, Union_or, Union_union_distrib]
 #align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.iUnion_disjUnion
+-/
 
+#print BoxIntegral.Prepartition.sum_disj_union_boxes /-
 @[simp]
 theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
     (f : Box ι → M) :
     ∑ J in π₁.boxes ∪ π₂.boxes, f J = ∑ J in π₁.boxes, f J + ∑ J in π₂.boxes, f J :=
   sum_union <| disjoint_boxes_of_disjoint_iUnion h
 #align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxes
+-/
 
 section Distortion
 
@@ -780,16 +866,20 @@ theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π,
 #align box_integral.prepartition.distortion_le_iff BoxIntegral.Prepartition.distortion_le_iff
 -/
 
+#print BoxIntegral.Prepartition.distortion_biUnion /-
 theorem distortion_biUnion (π : Prepartition I) (πi : ∀ J, Prepartition J) :
     (π.biUnion πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_biUnion _ _
 #align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_biUnion
+-/
 
+#print BoxIntegral.Prepartition.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.prepartition.distortion_disj_union BoxIntegral.Prepartition.distortion_disjUnion
+-/
 
 #print BoxIntegral.Prepartition.distortion_of_const /-
 theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π, Box.distortion J = c) :
@@ -798,15 +888,19 @@ theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π,
 #align box_integral.prepartition.distortion_of_const BoxIntegral.Prepartition.distortion_of_const
 -/
 
+#print BoxIntegral.Prepartition.distortion_top /-
 @[simp]
 theorem distortion_top (I : Box ι) : distortion (⊤ : Prepartition I) = I.distortion :=
   sup_singleton
 #align box_integral.prepartition.distortion_top BoxIntegral.Prepartition.distortion_top
+-/
 
+#print BoxIntegral.Prepartition.distortion_bot /-
 @[simp]
 theorem distortion_bot (I : Box ι) : distortion (⊥ : Prepartition I) = 0 :=
   sup_empty
 #align box_integral.prepartition.distortion_bot BoxIntegral.Prepartition.distortion_bot
+-/
 
 end Distortion
 
@@ -831,9 +925,11 @@ theorem isPartition_single_iff (h : J ≤ I) : IsPartition (single I J h) ↔ J
 #align box_integral.prepartition.is_partition_single_iff BoxIntegral.Prepartition.isPartition_single_iff
 -/
 
+#print BoxIntegral.Prepartition.isPartitionTop /-
 theorem isPartitionTop (I : Box ι) : IsPartition (⊤ : Prepartition I) := fun x hx =>
   ⟨I, mem_top.2 rfl, hx⟩
 #align box_integral.prepartition.is_partition_top BoxIntegral.Prepartition.isPartitionTop
+-/
 
 namespace IsPartition
 
@@ -873,10 +969,12 @@ theorem eq_of_boxes_subset (h₁ : π₁.IsPartition) (h₂ : π₁.boxes ⊆ π
 #align box_integral.prepartition.is_partition.eq_of_boxes_subset BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset
 -/
 
+#print BoxIntegral.Prepartition.IsPartition.le_iff /-
 theorem le_iff (h : π₂.IsPartition) :
     π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J' :=
   le_iff_nonempty_imp_le_and_iUnion_subset.trans <| and_iff_left <| h.iUnion_subset _
 #align box_integral.prepartition.is_partition.le_iff BoxIntegral.Prepartition.IsPartition.le_iff
+-/
 
 #print BoxIntegral.Prepartition.IsPartition.biUnion /-
 protected theorem biUnion (h : IsPartition π) (hi : ∀ J ∈ π, IsPartition (πi J)) :
@@ -910,10 +1008,12 @@ theorem iUnion_biUnion_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
 #align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.iUnion_biUnion_partition
 -/
 
+#print BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff /-
 theorem isPartitionDisjUnionOfEqDiff (h : π₂.iUnion = I \ π₁.iUnion) :
     IsPartition (π₁.disjUnion π₂ <| h.symm ▸ disjoint_sdiff_self_right) :=
   isPartition_iff_iUnion_eq.2 <| (iUnion_disjUnion _).trans <| by simp [h, π₁.Union_subset]
 #align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff
+-/
 
 end Prepartition
 

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

@@ -402,7 +402,7 @@ theorem iUnion_biUnion (πi : ∀ J : Box ι, Prepartition J) :
 @[simp]
 theorem sum_biUnion_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
     (πi : ∀ J, Prepartition J) (f : Box ι → M) :
-    (∑ J in π.boxes.biUnion fun J => (πi J).boxes, f J) =
+    ∑ J in π.boxes.biUnion fun J => (πi J).boxes, f J =
       ∑ J in π.boxes, ∑ J' in (πi J).boxes, f J' :=
   by
   refine' Finset.sum_biUnion fun J₁ h₁ J₂ h₂ hne => Finset.disjoint_left.2 fun J' h₁' h₂' => _
@@ -540,7 +540,7 @@ theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
 theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) (f : Box ι → M) :
-    (∑ J in (ofWithBot boxes le_of_mem pairwise_disjoint).boxes, f J) =
+    ∑ J in (ofWithBot boxes le_of_mem pairwise_disjoint).boxes, f J =
       ∑ J in boxes, Option.elim' 0 f J :=
   Finset.sum_eraseNone _ _
 #align box_integral.prepartition.sum_of_with_bot BoxIntegral.Prepartition.sum_ofWithBot
@@ -721,8 +721,7 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
 
 theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι → α) (g : Box ι → M) :
-    (∑ y in π.boxes.image f, ∑ J in (π.filterₓ fun J => f J = y).boxes, g J) =
-      ∑ J in π.boxes, g J :=
+    ∑ y in π.boxes.image f, ∑ J in (π.filterₓ fun J => f J = y).boxes, g J = ∑ J in π.boxes, g J :=
   by convert sum_fiberwise_of_maps_to (fun _ => Finset.mem_image_of_mem f) g
 #align box_integral.prepartition.sum_fiberwise BoxIntegral.Prepartition.sum_fiberwise
 
@@ -753,7 +752,7 @@ theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
 @[simp]
 theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
     (f : Box ι → M) :
-    (∑ J in π₁.boxes ∪ π₂.boxes, f J) = (∑ J in π₁.boxes, f J) + ∑ J in π₂.boxes, f J :=
+    ∑ J in π₁.boxes ∪ π₂.boxes, f J = ∑ J in π₁.boxes, f J + ∑ J in π₂.boxes, f J :=
   sum_union <| disjoint_boxes_of_disjoint_iUnion h
 #align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxes
 

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

@@ -852,7 +852,7 @@ theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUni
 #align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 -/
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (J «expr ∈ » π) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:638:2: warning: expanding binder collection (J «expr ∈ » π) -/
 #print BoxIntegral.Prepartition.IsPartition.existsUnique /-
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _) (_ : J ∈ π), x ∈ J :=
   by

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

@@ -210,9 +210,9 @@ theorem bot_boxes : (⊥ : Prepartition I).boxes = ∅ :=
 /-- An auxiliary lemma used to prove that the same point can't belong to more than
 `2 ^ fintype.card ι` closed boxes of a prepartition. -/
 theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
-    InjOn (fun J : Box ι => { i | J.lower i = x i }) { J | J ∈ π ∧ x ∈ J.Icc } :=
+    InjOn (fun J : Box ι => {i | J.lower i = x i}) {J | J ∈ π ∧ x ∈ J.Icc} :=
   by
-  rintro J₁ ⟨h₁, hx₁⟩ J₂ ⟨h₂, hx₂⟩ (H : { i | J₁.lower i = x i } = { i | J₂.lower i = x i })
+  rintro J₁ ⟨h₁, hx₁⟩ J₂ ⟨h₂, hx₂⟩ (H : {i | J₁.lower i = x i} = {i | J₂.lower i = x i})
   suffices ∀ i, (Ioc (J₁.lower i) (J₁.upper i) ∩ Ioc (J₂.lower i) (J₂.upper i)).Nonempty
     by
     choose y hy₁ hy₂
@@ -236,7 +236,7 @@ theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
   by
   rw [← Fintype.card_set]
   refine'
-    Finset.card_le_card_of_inj_on (fun J : box ι => { i | J.lower i = x i })
+    Finset.card_le_card_of_inj_on (fun J : box ι => {i | J.lower i = x i})
       (fun _ _ => Finset.mem_univ _) _
   simpa only [Finset.mem_filter] using π.inj_on_set_of_mem_Icc_set_of_lower_eq x
 #align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_le
@@ -435,7 +435,7 @@ theorem biUnionIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.biUnionI
 
 #print BoxIntegral.Prepartition.mem_biUnionIndex /-
 theorem mem_biUnionIndex (hJ : J ∈ π.biUnion πi) : J ∈ πi (π.biUnionIndex πi J) := by
-  convert(π.mem_bUnion.1 hJ).choose_spec.snd <;> exact dif_pos hJ
+  convert (π.mem_bUnion.1 hJ).choose_spec.snd <;> exact dif_pos hJ
 #align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_biUnionIndex
 -/
 
@@ -715,7 +715,7 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
   by
   simp only [prepartition.Union]
-  convert(@Set.biUnion_diff_biUnion_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
+  convert (@Set.biUnion_diff_biUnion_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
   · ext (J x); simp (config := { contextual := true })
   · convert π.pairwise_disjoint; simp
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not

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

@@ -218,7 +218,7 @@ theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
     choose y hy₁ hy₂
     exact π.eq_of_mem_of_mem h₁ h₂ hy₁ hy₂
   intro i
-  simp only [Set.ext_iff, mem_set_of_eq] at H
+  simp only [Set.ext_iff, mem_set_of_eq] at H 
   cases' (hx₁.1 i).eq_or_lt with hi₁ hi₁
   · have hi₂ : J₂.lower i = x i := (H _).1 hi₁
     have H₁ : x i < J₁.upper i := by simpa only [hi₁] using J₁.lower_lt_upper i
@@ -319,7 +319,7 @@ theorem le_iff_nonempty_imp_le_and_iUnion_subset :
   · refine' fun H => ⟨fun J hJ J' hJ' Hne => _, Union_mono H⟩
     rcases H hJ with ⟨J'', hJ'', Hle⟩; rcases Hne with ⟨x, hx, hx'⟩
     rwa [π₂.eq_of_mem_of_mem hJ' hJ'' hx' (Hle hx)]
-  · rintro ⟨H, HU⟩ J hJ; simp only [Set.subset_def, mem_Union] at HU
+  · rintro ⟨H, HU⟩ J hJ; simp only [Set.subset_def, mem_Union] at HU 
     rcases HU J.upper ⟨J, hJ, J.upper_mem⟩ with ⟨J₂, hJ₂, hx⟩
     exact ⟨J₂, hJ₂, H _ hJ _ hJ₂ ⟨_, J.upper_mem, hx⟩⟩
 #align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset
@@ -346,7 +346,7 @@ def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
   boxes := π.boxes.biUnion fun J => (πi J).boxes
   le_of_mem' J hJ :=
     by
-    simp only [Finset.mem_biUnion, exists_prop, mem_boxes] at hJ
+    simp only [Finset.mem_biUnion, exists_prop, mem_boxes] at hJ 
     rcases hJ with ⟨J', hJ', hJ⟩
     exact ((πi J').le_of_mem hJ).trans (π.le_of_mem hJ')
   PairwiseDisjoint :=
@@ -466,7 +466,7 @@ theorem biUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : B
     rwa [π.bUnion_index_of_mem hJ₁ hJ₂]
   · rintro ⟨J₁, ⟨J₂, hJ₂, hJ₁⟩, hJ⟩
     refine' ⟨J₂, hJ₂, J₁, hJ₁, _⟩
-    rwa [π.bUnion_index_of_mem hJ₂ hJ₁] at hJ
+    rwa [π.bUnion_index_of_mem hJ₂ hJ₁] at hJ 
 #align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.biUnion_assoc
 -/
 
@@ -478,11 +478,11 @@ def ofWithBot (boxes : Finset (WithBot (Box ι)))
     where
   boxes := boxes.eraseNone
   le_of_mem' J hJ := by
-    rw [mem_erase_none] at hJ
+    rw [mem_erase_none] at hJ 
     simpa only [WithBot.some_eq_coe, WithBot.coe_le_coe] using le_of_mem _ hJ
   PairwiseDisjoint J₁ h₁ J₂ h₂ hne :=
     by
-    simp only [mem_coe, mem_erase_none] at h₁ h₂
+    simp only [mem_coe, mem_erase_none] at h₁ h₂ 
     exact box.disjoint_coe.1 (pairwise_disjoint h₁ h₂ (mt Option.some_inj.1 hne))
 #align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBot
 
@@ -571,7 +571,7 @@ theorem mem_restrict' : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : Set (
 theorem restrict_mono {π₁ π₂ : Prepartition I} (Hle : π₁ ≤ π₂) : π₁.restrict J ≤ π₂.restrict J :=
   by
   refine' of_with_bot_mono fun J₁ hJ₁ hne => _
-  rw [Finset.mem_image] at hJ₁; rcases hJ₁ with ⟨J₁, hJ₁, rfl⟩
+  rw [Finset.mem_image] at hJ₁ ; rcases hJ₁ with ⟨J₁, hJ₁, rfl⟩
   rcases Hle hJ₁ with ⟨J₂, hJ₂, hle⟩
   exact ⟨_, Finset.mem_image_of_mem _ hJ₂, inf_le_inf_left _ <| WithBot.coe_le_coe.2 hle⟩
 #align box_integral.prepartition.restrict_mono BoxIntegral.Prepartition.restrict_mono
@@ -628,7 +628,7 @@ theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
   by
   fconstructor <;> intro H J hJ
   · rw [← π.restrict_bUnion πi hJ]; exact restrict_mono H
-  · rw [mem_bUnion] at hJ; rcases hJ with ⟨J₁, h₁, hJ⟩
+  · rw [mem_bUnion] at hJ ; rcases hJ with ⟨J₁, h₁, hJ⟩
     rcases H J₁ h₁ hJ with ⟨J₂, h₂, Hle⟩
     rcases π'.mem_restrict.mp h₂ with ⟨J₃, h₃, H⟩
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩
@@ -854,7 +854,7 @@ theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUni
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (J «expr ∈ » π) -/
 #print BoxIntegral.Prepartition.IsPartition.existsUnique /-
-protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _)(_ : J ∈ π), x ∈ J :=
+protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _) (_ : J ∈ π), x ∈ J :=
   by
   rcases h x hx with ⟨J, h, hx⟩
   exact ExistsUnique.intro₂ J h hx fun J' h' hx' => π.eq_of_mem_of_mem h' h hx' hx

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

@@ -46,7 +46,7 @@ rectangular box, partition
 
 open Set Finset Function
 
-open Classical NNReal BigOperators
+open scoped Classical NNReal BigOperators
 
 noncomputable section
 
@@ -769,13 +769,17 @@ def distortion : ℝ≥0 :=
 #align box_integral.prepartition.distortion BoxIntegral.Prepartition.distortion
 -/
 
+#print BoxIntegral.Prepartition.distortion_le_of_mem /-
 theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
   le_sup h
 #align box_integral.prepartition.distortion_le_of_mem BoxIntegral.Prepartition.distortion_le_of_mem
+-/
 
+#print BoxIntegral.Prepartition.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.prepartition.distortion_le_iff BoxIntegral.Prepartition.distortion_le_iff
+-/
 
 theorem distortion_biUnion (π : Prepartition I) (πi : ∀ J, Prepartition J) :
     (π.biUnion πi).distortion = π.boxes.sup fun J => (πi J).distortion :=

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

@@ -78,23 +78,11 @@ theorem mem_boxes : J ∈ π.boxes ↔ J ∈ π :=
 #align box_integral.prepartition.mem_boxes BoxIntegral.Prepartition.mem_boxes
 -/
 
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 @[simp]
 theorem mem_mk {s h₁ h₂} : J ∈ (mk s h₁ h₂ : Prepartition I) ↔ J ∈ s :=
   Iff.rfl
 #align box_integral.prepartition.mem_mk BoxIntegral.Prepartition.mem_mk
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disjoint_coe_of_mem BoxIntegral.Prepartition.disjoint_coe_of_memₓ'. -/
 theorem disjoint_coe_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (h : J₁ ≠ J₂) :
     Disjoint (J₁ : Set (ι → ℝ)) J₂ :=
   π.PairwiseDisjoint h₁ h₂ h
@@ -124,22 +112,10 @@ theorem le_of_mem (hJ : J ∈ π) : J ≤ I :=
 #align box_integral.prepartition.le_of_mem BoxIntegral.Prepartition.le_of_mem
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.lower_le_lower BoxIntegral.Prepartition.lower_le_lowerₓ'. -/
 theorem lower_le_lower (hJ : J ∈ π) : I.lower ≤ J.lower :=
   Box.antitone_lower (π.le_of_mem hJ)
 #align box_integral.prepartition.lower_le_lower BoxIntegral.Prepartition.lower_le_lower
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.upper_le_upper BoxIntegral.Prepartition.upper_le_upperₓ'. -/
 theorem upper_le_upper (hJ : J ∈ π) : J.upper ≤ I.upper :=
   Box.monotone_upper (π.le_of_mem hJ)
 #align box_integral.prepartition.upper_le_upper BoxIntegral.Prepartition.upper_le_upper
@@ -207,66 +183,30 @@ instance : OrderBot (Prepartition I)
 instance : Inhabited (Prepartition I) :=
   ⟨⊤⟩
 
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 theorem le_def : π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∃ J' ∈ π₂, J ≤ J' :=
   Iff.rfl
 #align box_integral.prepartition.le_def BoxIntegral.Prepartition.le_def
 
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 @[simp]
 theorem mem_top : J ∈ (⊤ : Prepartition I) ↔ J = I :=
   mem_singleton
 #align box_integral.prepartition.mem_top BoxIntegral.Prepartition.mem_top
 
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 @[simp]
 theorem top_boxes : (⊤ : Prepartition I).boxes = {I} :=
   rfl
 #align box_integral.prepartition.top_boxes BoxIntegral.Prepartition.top_boxes
 
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 @[simp]
 theorem not_mem_bot : J ∉ (⊥ : Prepartition I) :=
   id
 #align box_integral.prepartition.not_mem_bot BoxIntegral.Prepartition.not_mem_bot
 
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 @[simp]
 theorem bot_boxes : (⊥ : Prepartition I).boxes = ∅ :=
   rfl
 #align box_integral.prepartition.bot_boxes BoxIntegral.Prepartition.bot_boxes
 
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 /-- An auxiliary lemma used to prove that the same point can't belong to more than
 `2 ^ fintype.card ι` closed boxes of a prepartition. -/
 theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
@@ -289,12 +229,6 @@ theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
     exact ⟨x i, ⟨hi₁, hx₁.2 i⟩, ⟨hi₂, hx₂.2 i⟩⟩
 #align box_integral.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_leₓ'. -/
 /-- The set of boxes of a prepartition that contain `x` in their closures has cardinality
 at most `2 ^ fintype.card ι`. -/
 theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
@@ -327,12 +261,6 @@ theorem iUnion_def' : π.iUnion = ⋃ J ∈ π.boxes, ↑J :=
 #align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.iUnion_def'
 -/
 
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 @[simp]
 theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
   Set.mem_iUnion₂
@@ -344,33 +272,15 @@ theorem iUnion_single (h : J ≤ I) : (single I J h).iUnion = J := by simp [Unio
 #align box_integral.prepartition.Union_single BoxIntegral.Prepartition.iUnion_single
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.iUnion_topₓ'. -/
 @[simp]
 theorem iUnion_top : (⊤ : Prepartition I).iUnion = I := by simp [prepartition.Union]
 #align box_integral.prepartition.Union_top BoxIntegral.Prepartition.iUnion_top
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.iUnion_eq_emptyₓ'. -/
 @[simp]
 theorem iUnion_eq_empty : π₁.iUnion = ∅ ↔ π₁ = ⊥ := by
   simp [← injective_boxes.eq_iff, Finset.ext_iff, prepartition.Union, imp_false]
 #align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.iUnion_eq_empty
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.iUnion_botₓ'. -/
 @[simp]
 theorem iUnion_bot : (⊥ : Prepartition I).iUnion = ∅ :=
   iUnion_eq_empty.2 rfl
@@ -388,12 +298,6 @@ theorem iUnion_subset : π.iUnion ⊆ I :=
 #align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.iUnion_subset
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.iUnion_monoₓ'. -/
 @[mono]
 theorem iUnion_mono (h : π₁ ≤ π₂) : π₁.iUnion ⊆ π₂.iUnion := fun x hx =>
   let ⟨J₁, hJ₁, hx⟩ := π₁.mem_iUnion.1 hx
@@ -401,24 +305,12 @@ theorem iUnion_mono (h : π₁ ≤ π₂) : π₁.iUnion ⊆ π₂.iUnion := fun
   π₂.mem_iUnion.2 ⟨J₂, hJ₂, hle hx⟩
 #align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.iUnion_mono
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnionₓ'. -/
 theorem disjoint_boxes_of_disjoint_iUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     Disjoint π₁.boxes π₂.boxes :=
   Finset.disjoint_left.2 fun J h₁ h₂ =>
     Disjoint.le_bot (h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)) ⟨J.upper_mem, J.upper_mem⟩
 #align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subsetₓ'. -/
 theorem le_iff_nonempty_imp_le_and_iUnion_subset :
     π₁ ≤ π₂ ↔
       (∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J') ∧ π₁.iUnion ⊆ π₂.iUnion :=
@@ -471,33 +363,15 @@ def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
 
 variable {πi πi₁ πi₂ : ∀ J : Box ι, Prepartition J}
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_biUnionₓ'. -/
 @[simp]
 theorem mem_biUnion : J ∈ π.biUnion πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [bUnion]
 #align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_biUnion
 
-/- warning: box_integral.prepartition.bUnion_le -> BoxIntegral.Prepartition.biUnion_le is a dubious translation:
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 theorem biUnion_le (πi : ∀ J, Prepartition J) : π.biUnion πi ≤ π := fun J hJ =>
   let ⟨J', hJ', hJ⟩ := π.mem_biUnion.1 hJ
   ⟨J', hJ', (πi J').le_of_mem hJ⟩
 #align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.biUnion_le
 
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 @[simp]
 theorem biUnion_top : (π.biUnion fun _ => ⊤) = π := by ext; simp
 #align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.biUnion_top
@@ -596,12 +470,6 @@ theorem biUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : B
 #align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.biUnion_assoc
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBotₓ'. -/
 /-- Create a `box_integral.prepartition` from a collection of possibly empty boxes by filtering out
 the empty one if it exists. -/
 def ofWithBot (boxes : Finset (WithBot (Box ι)))
@@ -618,24 +486,12 @@ def ofWithBot (boxes : Finset (WithBot (Box ι)))
     exact box.disjoint_coe.1 (pairwise_disjoint h₁ h₂ (mt Option.some_inj.1 hne))
 #align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBot
 
-/- warning: box_integral.prepartition.mem_of_with_bot -> BoxIntegral.Prepartition.mem_ofWithBot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBotₓ'. -/
 @[simp]
 theorem mem_ofWithBot {boxes : Finset (WithBot (Box ι))} {h₁ h₂} :
     J ∈ (ofWithBot boxes h₁ h₂ : Prepartition I) ↔ (J : WithBot (Box ι)) ∈ boxes :=
   mem_eraseNone
 #align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBot
 
-/- warning: box_integral.prepartition.Union_of_with_bot -> BoxIntegral.Prepartition.iUnion_ofWithBot is a dubious translation:
-lean 3 declaration is
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.iUnion_ofWithBotₓ'. -/
 @[simp]
 theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
@@ -648,12 +504,6 @@ theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
     Union_Union_eq_right]
 #align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.iUnion_ofWithBot
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot_le BoxIntegral.Prepartition.ofWithBot_leₓ'. -/
 theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
     {le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint}
@@ -665,12 +515,6 @@ theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
   simpa [of_with_bot, le_def]
 #align box_integral.prepartition.of_with_bot_le BoxIntegral.Prepartition.ofWithBot_le
 
-/- warning: box_integral.prepartition.le_of_with_bot -> BoxIntegral.Prepartition.le_ofWithBot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_of_with_bot BoxIntegral.Prepartition.le_ofWithBotₓ'. -/
 theorem le_ofWithBot {boxes : Finset (WithBot (Box ι))}
     {le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint}
@@ -682,12 +526,6 @@ theorem le_ofWithBot {boxes : Finset (WithBot (Box ι))}
   exact ⟨J', mem_of_with_bot.2 J'mem, WithBot.coe_le_coe.1 hle⟩
 #align box_integral.prepartition.le_of_with_bot BoxIntegral.Prepartition.le_ofWithBot
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot_mono BoxIntegral.Prepartition.ofWithBot_monoₓ'. -/
 theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
     {le_of_mem₁ : ∀ J ∈ boxes₁, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint₁ : Set.Pairwise (boxes₁ : Set (WithBot (Box ι))) Disjoint}
@@ -699,12 +537,6 @@ theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
   le_ofWithBot _ fun J hJ => H J (mem_ofWithBot.1 hJ) WithBot.coe_ne_bot
 #align box_integral.prepartition.of_with_bot_mono BoxIntegral.Prepartition.ofWithBot_mono
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_of_with_bot BoxIntegral.Prepartition.sum_ofWithBotₓ'. -/
 theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) (f : Box ι → M) :
@@ -726,33 +558,15 @@ def restrict (π : Prepartition I) (J : Box ι) : Prepartition J :=
 #align box_integral.prepartition.restrict BoxIntegral.Prepartition.restrict
 -/
 
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 @[simp]
 theorem mem_restrict : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : WithBot (Box ι)) = J ⊓ J' := by
   simp [restrict, eq_comm]
 #align box_integral.prepartition.mem_restrict BoxIntegral.Prepartition.mem_restrict
 
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 theorem mem_restrict' : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : Set (ι → ℝ)) = J ∩ J' := by
   simp only [mem_restrict, ← box.with_bot_coe_inj, box.coe_inf, box.coe_coe]
 #align box_integral.prepartition.mem_restrict' BoxIntegral.Prepartition.mem_restrict'
 
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 @[mono]
 theorem restrict_mono {π₁ π₂ : Prepartition I} (Hle : π₁ ≤ π₂) : π₁.restrict J ≤ π₂.restrict J :=
   by
@@ -789,12 +603,6 @@ theorem restrict_self : π.restrict I = π :=
 #align box_integral.prepartition.restrict_self BoxIntegral.Prepartition.restrict_self
 -/
 
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 @[simp]
 theorem iUnion_restrict : (π.restrict J).iUnion = J ∩ π.iUnion := by
   simp [restrict, ← inter_Union, ← Union_def]
@@ -815,12 +623,6 @@ theorem restrict_biUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
 #align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_biUnion
 -/
 
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 theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π.biUnion πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J :=
   by
@@ -832,12 +634,6 @@ theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩
 #align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.biUnion_le_iff
 
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 theorem le_biUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π' ≤ π.biUnion πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J :=
   by
@@ -860,24 +656,12 @@ theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.biUnion
 #align box_integral.prepartition.inf_def BoxIntegral.Prepartition.inf_def
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_inf BoxIntegral.Prepartition.mem_infₓ'. -/
 @[simp]
 theorem mem_inf {π₁ π₂ : Prepartition I} :
     J ∈ π₁ ⊓ π₂ ↔ ∃ J₁ ∈ π₁, ∃ J₂ ∈ π₂, (J : WithBot (Box ι)) = J₁ ⊓ J₂ := by
   simp only [inf_def, mem_bUnion, mem_restrict]
 #align box_integral.prepartition.mem_inf BoxIntegral.Prepartition.mem_inf
 
-/- warning: box_integral.prepartition.Union_inf -> BoxIntegral.Prepartition.iUnion_inf is a dubious translation:
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 @[simp]
 theorem iUnion_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).iUnion = π₁.iUnion ∩ π₂.iUnion := by
   simp only [inf_def, Union_bUnion, Union_restrict, ← Union_inter, ← Union_def]
@@ -908,12 +692,6 @@ theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧
 #align box_integral.prepartition.mem_filter BoxIntegral.Prepartition.mem_filter
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.filter_le BoxIntegral.Prepartition.filter_leₓ'. -/
 theorem filter_le (π : Prepartition I) (p : Box ι → Prop) : π.filterₓ p ≤ π := fun J hJ =>
   let ⟨hπ, hp⟩ := π.mem_filter.1 hJ
   ⟨J, hπ, le_rfl⟩
@@ -932,12 +710,6 @@ theorem filter_true : (π.filterₓ fun _ => True) = π :=
 #align box_integral.prepartition.filter_true BoxIntegral.Prepartition.filter_true
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_notₓ'. -/
 @[simp]
 theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
@@ -948,24 +720,12 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
   · convert π.pairwise_disjoint; simp
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_fiberwise BoxIntegral.Prepartition.sum_fiberwiseₓ'. -/
 theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι → α) (g : Box ι → M) :
     (∑ y in π.boxes.image f, ∑ J in (π.filterₓ fun J => f J = y).boxes, g J) =
       ∑ J in π.boxes, g J :=
   by convert sum_fiberwise_of_maps_to (fun _ => Finset.mem_image_of_mem f) g
 #align box_integral.prepartition.sum_fiberwise BoxIntegral.Prepartition.sum_fiberwise
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnionₓ'. -/
 /-- Union of two disjoint prepartitions. -/
 @[simps]
 def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) : Prepartition I
@@ -978,36 +738,18 @@ def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.iUnion π₂.iU
     fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)
 #align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnion
 
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 @[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.prepartition.mem_disj_union BoxIntegral.Prepartition.mem_disjUnion
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.iUnion_disjUnionₓ'. -/
 @[simp]
 theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion := by
   simp [disj_union, prepartition.Union, Union_or, Union_union_distrib]
 #align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.iUnion_disjUnion
 
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 @[simp]
 theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
     (f : Box ι → M) :
@@ -1027,43 +769,19 @@ def distortion : ℝ≥0 :=
 #align box_integral.prepartition.distortion BoxIntegral.Prepartition.distortion
 -/
 
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 theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
   le_sup h
 #align box_integral.prepartition.distortion_le_of_mem BoxIntegral.Prepartition.distortion_le_of_mem
 
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 theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π, Box.distortion J ≤ c :=
   Finset.sup_le_iff
 #align box_integral.prepartition.distortion_le_iff BoxIntegral.Prepartition.distortion_le_iff
 
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 theorem distortion_biUnion (π : Prepartition I) (πi : ∀ J, Prepartition J) :
     (π.biUnion πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_biUnion _ _
 #align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_biUnion
 
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 @[simp]
 theorem distortion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     (π₁.disjUnion π₂ h).distortion = max π₁.distortion π₂.distortion :=
@@ -1077,23 +795,11 @@ theorem distortion_of_const {c} (h₁ : π.boxes.Nonempty) (h₂ : ∀ J ∈ π,
 #align box_integral.prepartition.distortion_of_const BoxIntegral.Prepartition.distortion_of_const
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_top BoxIntegral.Prepartition.distortion_topₓ'. -/
 @[simp]
 theorem distortion_top (I : Box ι) : distortion (⊤ : Prepartition I) = I.distortion :=
   sup_singleton
 #align box_integral.prepartition.distortion_top BoxIntegral.Prepartition.distortion_top
 
-/- warning: box_integral.prepartition.distortion_bot -> BoxIntegral.Prepartition.distortion_bot is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_bot BoxIntegral.Prepartition.distortion_botₓ'. -/
 @[simp]
 theorem distortion_bot (I : Box ι) : distortion (⊥ : Prepartition I) = 0 :=
   sup_empty
@@ -1122,12 +828,6 @@ theorem isPartition_single_iff (h : J ≤ I) : IsPartition (single I J h) ↔ J
 #align box_integral.prepartition.is_partition_single_iff BoxIntegral.Prepartition.isPartition_single_iff
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition_top BoxIntegral.Prepartition.isPartitionTopₓ'. -/
 theorem isPartitionTop (I : Box ι) : IsPartition (⊤ : Prepartition I) := fun x hx =>
   ⟨I, mem_top.2 rfl, hx⟩
 #align box_integral.prepartition.is_partition_top BoxIntegral.Prepartition.isPartitionTop
@@ -1170,12 +870,6 @@ theorem eq_of_boxes_subset (h₁ : π₁.IsPartition) (h₂ : π₁.boxes ⊆ π
 #align box_integral.prepartition.is_partition.eq_of_boxes_subset BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition.le_iff BoxIntegral.Prepartition.IsPartition.le_iffₓ'. -/
 theorem le_iff (h : π₂.IsPartition) :
     π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J' :=
   le_iff_nonempty_imp_le_and_iUnion_subset.trans <| and_iff_left <| h.iUnion_subset _
@@ -1213,12 +907,6 @@ theorem iUnion_biUnion_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
 #align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.iUnion_biUnion_partition
 -/
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiffₓ'. -/
 theorem isPartitionDisjUnionOfEqDiff (h : π₂.iUnion = I \ π₁.iUnion) :
     IsPartition (π₁.disjUnion π₂ <| h.symm ▸ disjoint_sdiff_self_right) :=
   isPartition_iff_iUnion_eq.2 <| (iUnion_disjUnion _).trans <| by simp [h, π₁.Union_subset]

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

@@ -145,10 +145,8 @@ theorem upper_le_upper (hJ : J ∈ π) : J.upper ≤ I.upper :=
 #align box_integral.prepartition.upper_le_upper BoxIntegral.Prepartition.upper_le_upper
 
 #print BoxIntegral.Prepartition.injective_boxes /-
-theorem injective_boxes : Function.Injective (boxes : Prepartition I → Finset (Box ι)) :=
-  by
-  rintro ⟨s₁, h₁, h₁'⟩ ⟨s₂, h₂, h₂'⟩ (rfl : s₁ = s₂)
-  rfl
+theorem injective_boxes : Function.Injective (boxes : Prepartition I → Finset (Box ι)) := by
+  rintro ⟨s₁, h₁, h₁'⟩ ⟨s₂, h₂, h₂'⟩ (rfl : s₁ = s₂); rfl
 #align box_integral.prepartition.injective_boxes BoxIntegral.Prepartition.injective_boxes
 -/
 
@@ -427,11 +425,9 @@ theorem le_iff_nonempty_imp_le_and_iUnion_subset :
   by
   fconstructor
   · refine' fun H => ⟨fun J hJ J' hJ' Hne => _, Union_mono H⟩
-    rcases H hJ with ⟨J'', hJ'', Hle⟩
-    rcases Hne with ⟨x, hx, hx'⟩
+    rcases H hJ with ⟨J'', hJ'', Hle⟩; rcases Hne with ⟨x, hx, hx'⟩
     rwa [π₂.eq_of_mem_of_mem hJ' hJ'' hx' (Hle hx)]
-  · rintro ⟨H, HU⟩ J hJ
-    simp only [Set.subset_def, mem_Union] at HU
+  · rintro ⟨H, HU⟩ J hJ; simp only [Set.subset_def, mem_Union] at HU
     rcases HU J.upper ⟨J, hJ, J.upper_mem⟩ with ⟨J₂, hJ₂, hx⟩
     exact ⟨J₂, hJ₂, H _ hJ _ hJ₂ ⟨_, J.upper_mem, hx⟩⟩
 #align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset
@@ -503,18 +499,13 @@ but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.biUnion.{u1} ι I π (fun (_x : BoxIntegral.Box.{u1} ι) => Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι _x) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι _x)))) π
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.biUnion_topₓ'. -/
 @[simp]
-theorem biUnion_top : (π.biUnion fun _ => ⊤) = π :=
-  by
-  ext
-  simp
+theorem biUnion_top : (π.biUnion fun _ => ⊤) = π := by ext; simp
 #align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.biUnion_top
 
 #print BoxIntegral.Prepartition.biUnion_congr /-
 @[congr]
 theorem biUnion_congr (h : π₁ = π₂) (hi : ∀ J ∈ π₁, πi₁ J = πi₂ J) :
-    π₁.biUnion πi₁ = π₂.biUnion πi₂ := by
-  subst π₂
-  ext J
+    π₁.biUnion πi₁ = π₂.biUnion πi₂ := by subst π₂; ext J;
   simp (config := { contextual := true }) [hi]
 #align box_integral.prepartition.bUnion_congr BoxIntegral.Prepartition.biUnion_congr
 -/
@@ -554,10 +545,8 @@ def biUnionIndex (πi : ∀ J, Prepartition J) (J : Box ι) : Box ι :=
 -/
 
 #print BoxIntegral.Prepartition.biUnionIndex_mem /-
-theorem biUnionIndex_mem (hJ : J ∈ π.biUnion πi) : π.biUnionIndex πi J ∈ π :=
-  by
-  rw [bUnion_index, dif_pos hJ]
-  exact (π.mem_bUnion.1 hJ).choose_spec.fst
+theorem biUnionIndex_mem (hJ : J ∈ π.biUnion πi) : π.biUnionIndex πi J ∈ π := by
+  rw [bUnion_index, dif_pos hJ]; exact (π.mem_bUnion.1 hJ).choose_spec.fst
 #align box_integral.prepartition.bUnion_index_mem BoxIntegral.Prepartition.biUnionIndex_mem
 -/
 
@@ -566,8 +555,7 @@ theorem biUnionIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.biUnionI
   by
   by_cases hJ : J ∈ π.bUnion πi
   · exact π.le_of_mem (π.bUnion_index_mem hJ)
-  · rw [bUnion_index, dif_neg hJ]
-    exact le_rfl
+  · rw [bUnion_index, dif_neg hJ]; exact le_rfl
 #align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.biUnionIndex_le
 -/
 
@@ -729,15 +717,11 @@ theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (B
 /-- Restrict a prepartition to a box. -/
 def restrict (π : Prepartition I) (J : Box ι) : Prepartition J :=
   ofWithBot (π.boxes.image fun J' => J ⊓ J')
-    (fun J' hJ' => by
-      rcases Finset.mem_image.1 hJ' with ⟨J', -, rfl⟩
-      exact inf_le_left)
+    (fun J' hJ' => by rcases Finset.mem_image.1 hJ' with ⟨J', -, rfl⟩; exact inf_le_left)
     (by
       simp only [Set.Pairwise, on_fun, Finset.mem_coe, Finset.mem_image]
       rintro _ ⟨J₁, h₁, rfl⟩ _ ⟨J₂, h₂, rfl⟩ Hne
-      have : J₁ ≠ J₂ := by
-        rintro rfl
-        exact Hne rfl
+      have : J₁ ≠ J₂ := by rintro rfl; exact Hne rfl
       exact ((box.disjoint_coe.2 <| π.disjoint_coe_of_mem h₁ h₂ this).inf_left' _).inf_right' _)
 #align box_integral.prepartition.restrict BoxIntegral.Prepartition.restrict
 -/
@@ -826,8 +810,7 @@ theorem restrict_biUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
     exact WithBot.coe_le_coe.2 (le_of_mem _ h₁)
   · simp only [Union_restrict, Union_bUnion, Set.subset_def, Set.mem_inter_iff, Set.mem_iUnion]
     rintro x ⟨hxJ, J₁, h₁, hx⟩
-    obtain rfl : J = J₁
-    exact π.eq_of_mem_of_mem hJ h₁ hxJ (Union_subset _ hx)
+    obtain rfl : J = J₁; exact π.eq_of_mem_of_mem hJ h₁ hxJ (Union_subset _ hx)
     exact hx
 #align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_biUnion
 -/
@@ -842,10 +825,8 @@ theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π.biUnion πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J :=
   by
   fconstructor <;> intro H J hJ
-  · rw [← π.restrict_bUnion πi hJ]
-    exact restrict_mono H
-  · rw [mem_bUnion] at hJ
-    rcases hJ with ⟨J₁, h₁, hJ⟩
+  · rw [← π.restrict_bUnion πi hJ]; exact restrict_mono H
+  · rw [mem_bUnion] at hJ; rcases hJ with ⟨J₁, h₁, hJ⟩
     rcases H J₁ h₁ hJ with ⟨J₂, h₂, Hle⟩
     rcases π'.mem_restrict.mp h₂ with ⟨J₃, h₃, H⟩
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩
@@ -861,8 +842,7 @@ theorem le_biUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π' ≤ π.biUnion πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J :=
   by
   refine' ⟨fun H => ⟨H.trans (π.bUnion_le πi), fun J hJ => _⟩, _⟩
-  · rw [← π.restrict_bUnion πi hJ]
-    exact restrict_mono H
+  · rw [← π.restrict_bUnion πi hJ]; exact restrict_mono H
   · rintro ⟨H, Hi⟩ J' hJ'
     rcases H hJ' with ⟨J, hJ, hle⟩
     have : J' ∈ π'.restrict J :=
@@ -940,9 +920,7 @@ theorem filter_le (π : Prepartition I) (p : Box ι → Prop) : π.filterₓ p 
 #align box_integral.prepartition.filter_le BoxIntegral.Prepartition.filter_le
 
 #print BoxIntegral.Prepartition.filter_of_true /-
-theorem filter_of_true {p : Box ι → Prop} (hp : ∀ J ∈ π, p J) : π.filterₓ p = π :=
-  by
-  ext J
+theorem filter_of_true {p : Box ι → Prop} (hp : ∀ J ∈ π, p J) : π.filterₓ p = π := by ext J;
   simpa using hp J
 #align box_integral.prepartition.filter_of_true BoxIntegral.Prepartition.filter_of_true
 -/
@@ -966,10 +944,8 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
   by
   simp only [prepartition.Union]
   convert(@Set.biUnion_diff_biUnion_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
-  · ext (J x)
-    simp (config := { contextual := true })
-  · convert π.pairwise_disjoint
-    simp
+  · ext (J x); simp (config := { contextual := true })
+  · convert π.pairwise_disjoint; simp
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
 
 /- warning: box_integral.prepartition.sum_fiberwise -> BoxIntegral.Prepartition.sum_fiberwise is a dubious translation:

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

@@ -267,7 +267,7 @@ theorem bot_boxes : (⊥ : Prepartition I).boxes = ∅ :=
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (x : ι -> Real), Set.InjOn.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => setOf.{u1} ι (fun (i : ι) => Eq.{1} Real (BoxIntegral.Box.lower.{u1} ι J i) (x i))) (setOf.{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.hasMem.{u1} ι I) J π) (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} (π : BoxIntegral.Prepartition.{u1} ι I) (x : ι -> Real), Set.InjOn.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => setOf.{u1} ι (fun (i : ι) => Eq.{1} Real (BoxIntegral.Box.lower.{u1} ι J i) (x i))) (setOf.{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} (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} (π : BoxIntegral.Prepartition.{u1} ι I) (x : ι -> Real), Set.InjOn.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => setOf.{u1} ι (fun (i : ι) => Eq.{1} Real (BoxIntegral.Box.lower.{u1} ι J i) (x i))) (setOf.{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} (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.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eqₓ'. -/
 /-- An auxiliary lemma used to prove that the same point can't belong to more than
 `2 ^ fintype.card ι` closed boxes of a prepartition. -/
@@ -295,7 +295,7 @@ theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (x : ι -> Real), LE.le.{0} Nat Nat.hasLe (Finset.card.{u1} (BoxIntegral.Box.{u1} ι) (Finset.filter.{u1} (BoxIntegral.Box.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => 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)) (fun (a : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (J : BoxIntegral.Box.{u1} ι) => 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)) a)) (BoxIntegral.Prepartition.boxes.{u1} ι I π))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fintype.card.{u1} ι _inst_1))
 but is expected to have type
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+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (x : ι -> Real), LE.le.{0} Nat instLENat (Finset.card.{u1} (BoxIntegral.Box.{u1} ι) (Finset.filter.{u1} (BoxIntegral.Box.{u1} ι) (fun (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)) 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)) (fun (a : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (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)) 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)) a)) (BoxIntegral.Prepartition.boxes.{u1} ι I π))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Fintype.card.{u1} ι _inst_1))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_leₓ'. -/
 /-- The set of boxes of a prepartition that contain `x` in their closures has cardinality
 at most `2 ^ fintype.card ι`. -/

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

@@ -533,12 +533,7 @@ theorem iUnion_biUnion (πi : ∀ J : Box ι, Prepartition J) :
 #align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.iUnion_biUnion
 -/
 
-/- warning: box_integral.prepartition.sum_bUnion_boxes -> BoxIntegral.Prepartition.sum_biUnion_boxes is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.biUnion.{u1, u1} (BoxIntegral.Box.{u1} ι) (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 π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
-but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.biUnion.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => decidableEqOfDecidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b) (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_biUnion_boxesₓ'. -/
+#print BoxIntegral.Prepartition.sum_biUnion_boxes /-
 @[simp]
 theorem sum_biUnion_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
     (πi : ∀ J, Prepartition J) (f : Box ι → M) :
@@ -548,6 +543,7 @@ theorem sum_biUnion_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
   refine' Finset.sum_biUnion fun J₁ h₁ J₂ h₂ hne => Finset.disjoint_left.2 fun J' h₁' h₂' => _
   exact hne (π.eq_of_le_of_le h₁ h₂ ((πi J₁).le_of_mem h₁') ((πi J₂).le_of_mem h₂'))
 #align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_biUnion_boxes
+-/
 
 #print BoxIntegral.Prepartition.biUnionIndex /-
 /-- Given a box `J ∈ π.bUnion πi`, returns the box `J' ∈ π` such that `J ∈ πi J'`.
@@ -614,7 +610,7 @@ theorem biUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : B
 
 /- warning: box_integral.prepartition.of_with_bot -> BoxIntegral.Prepartition.ofWithBot is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))), (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) -> (Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))) -> (BoxIntegral.Prepartition.{u1} ι I)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))), (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) -> (Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))) -> (BoxIntegral.Prepartition.{u1} ι I)
 but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))), (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) -> (Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))) -> (BoxIntegral.Prepartition.{u1} ι I)
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBotₓ'. -/
@@ -636,7 +632,7 @@ def ofWithBot (boxes : Finset (WithBot (Box ι)))
 
 /- warning: box_integral.prepartition.mem_of_with_bot -> BoxIntegral.Prepartition.mem_ofWithBot is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {h₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {h₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes h₁ h₂)) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) boxes)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {h₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {h₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes h₁ h₂)) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) boxes)
 but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {h₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {h₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes h₁ h₂)) (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J) boxes)
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBotₓ'. -/
@@ -648,7 +644,7 @@ theorem mem_ofWithBot {boxes : Finset (WithBot (Box ι))} {h₁ h₂} :
 
 /- warning: box_integral.prepartition.Union_of_with_bot -> BoxIntegral.Prepartition.iUnion_ofWithBot is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.iUnion.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.iUnion.{u1, 0} (ι -> Real) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (HasLiftT.mk.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (CoeTCₓ.coe.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.withBotCoe.{u1} ι))) J)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.iUnion.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.iUnion.{u1, 0} (ι -> Real) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (HasLiftT.mk.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (CoeTCₓ.coe.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.withBotCoe.{u1} ι))) J)))
 but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.iUnion.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.iUnion.{u1, 0} (ι -> Real) (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => BoxIntegral.Box.withBotToSet.{u1} ι J)))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.iUnion_ofWithBotₓ'. -/
@@ -666,7 +662,7 @@ theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
 
 /- warning: box_integral.prepartition.of_with_bot_le -> BoxIntegral.Prepartition.ofWithBot_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasBot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (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) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J'))))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint) π)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasBot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (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) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J'))))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint) π)
 but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.bot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (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) (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J'))))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint) π)
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot_le BoxIntegral.Prepartition.ofWithBot_leₓ'. -/
@@ -683,7 +679,7 @@ theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
 
 /- warning: box_integral.prepartition.le_of_with_bot -> BoxIntegral.Prepartition.le_ofWithBot is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (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) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Exists.{0} (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (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) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Exists.{0} (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint))
 but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, (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) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => And (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J) J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_of_with_bot BoxIntegral.Prepartition.le_ofWithBotₓ'. -/
@@ -700,7 +696,7 @@ theorem le_ofWithBot {boxes : Finset (WithBot (Box ι))}
 
 /- warning: box_integral.prepartition.of_with_bot_mono -> BoxIntegral.Prepartition.ofWithBot_mono is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {boxes₁ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint₁ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes₁) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))} {boxes₂ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₂ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₂) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes₂) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasBot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Exists.{0} (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₁ le_of_mem₁ pairwise_disjoint₁) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₂ le_of_mem₂ pairwise_disjoint₂))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {boxes₁ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint₁ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes₁) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))} {boxes₂ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₂ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₂) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes₂) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasBot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Exists.{0} (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₁ le_of_mem₁ pairwise_disjoint₁) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₂ le_of_mem₂ pairwise_disjoint₂))
 but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {boxes₁ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint₁ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes₁) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))} {boxes₂ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₂ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₂) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes₂) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.bot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => And (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₁ le_of_mem₁ pairwise_disjoint₁) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₂ le_of_mem₂ pairwise_disjoint₂))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot_mono BoxIntegral.Prepartition.ofWithBot_monoₓ'. -/
@@ -717,7 +713,7 @@ theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
 
 /- warning: box_integral.prepartition.sum_of_with_bot -> BoxIntegral.Prepartition.sum_ofWithBot is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) _inst_1 boxes (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Option.elim'.{u1, u2} (BoxIntegral.Box.{u1} ι) M (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))))) f J))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toHasLe.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) _inst_1 boxes (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Option.elim'.{u1, u2} (BoxIntegral.Box.{u1} ι) M (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))))) f J))
 but is expected to have type
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) _inst_1 boxes (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Option.elim'.{u1, u2} (BoxIntegral.Box.{u1} ι) M (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) f J))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_of_with_bot BoxIntegral.Prepartition.sum_ofWithBotₓ'. -/
@@ -1034,7 +1030,7 @@ theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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 π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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) => decidableEqOfDecidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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 π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxesₓ'. -/
 @[simp]
 theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
@@ -1055,17 +1051,25 @@ def distortion : ℝ≥0 :=
 #align box_integral.prepartition.distortion BoxIntegral.Prepartition.distortion
 -/
 
-#print BoxIntegral.Prepartition.distortion_le_of_mem /-
+/- warning: box_integral.prepartition.distortion_le_of_mem -> BoxIntegral.Prepartition.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.Prepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι], (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.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.Prepartition.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.Prepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι], (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{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.Prepartition.distortion.{u1} ι I π _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_le_of_mem BoxIntegral.Prepartition.distortion_le_of_memₓ'. -/
 theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
   le_sup h
 #align box_integral.prepartition.distortion_le_of_mem BoxIntegral.Prepartition.distortion_le_of_mem
--/
 
-#print BoxIntegral.Prepartition.distortion_le_iff /-
+/- warning: box_integral.prepartition.distortion_le_iff -> BoxIntegral.Prepartition.distortion_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{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.Prepartition.distortion.{u1} ι I π _inst_1) c) (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) -> (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.Prepartition.{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.Prepartition.distortion.{u1} ι I π _inst_1) c) (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) -> (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.prepartition.distortion_le_iff BoxIntegral.Prepartition.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.prepartition.distortion_le_iff BoxIntegral.Prepartition.distortion_le_iff
--/
 
 /- warning: box_integral.prepartition.distortion_bUnion -> BoxIntegral.Prepartition.distortion_biUnion is a dubious translation:
 lean 3 declaration is
@@ -1237,7 +1241,7 @@ theorem iUnion_biUnion_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.subst.{succ u1} (Set.{u1} (ι -> Real)) (fun (_x : Set.{u1} (ι -> Real)) => 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.Prepartition.iUnion.{u1} ι I π₁) _x) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) h) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) ((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))) I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.rec.{0, succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) (fun (x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575 : Set.{u1} (ι -> Real)) (h._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11576 : Eq.{succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) => 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.Prepartition.iUnion.{u1} ι I π₁) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Box.toSet.{u1} ι I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.instBooleanAlgebraSet.{u1} (ι -> Real)))) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) h)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.rec.{0, succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) (fun (x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11562 : Set.{u1} (ι -> Real)) (h._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11563 : Eq.{succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11562) => 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.Prepartition.iUnion.{u1} ι I π₁) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11562) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Box.toSet.{u1} ι I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.instBooleanAlgebraSet.{u1} (ι -> Real)))) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) h)))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiffₓ'. -/
 theorem isPartitionDisjUnionOfEqDiff (h : π₂.iUnion = I \ π₁.iUnion) :
     IsPartition (π₁.disjUnion π₂ <| h.symm ▸ disjoint_sdiff_self_right) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/7ad820c4997738e2f542f8a20f32911f52020e26

@@ -537,7 +537,7 @@ theorem iUnion_biUnion (πi : ∀ J : Box ι, Prepartition J) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.biUnion.{u1, u1} (BoxIntegral.Box.{u1} ι) (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 π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.biUnion.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b) (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.biUnion.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => decidableEqOfDecidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b) (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_biUnion_boxesₓ'. -/
 @[simp]
 theorem sum_biUnion_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
@@ -1034,7 +1034,7 @@ theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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 π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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) => decidableEqOfDecidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxesₓ'. -/
 @[simp]
 theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)

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

@@ -309,121 +309,121 @@ theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
   simpa only [Finset.mem_filter] using π.inj_on_set_of_mem_Icc_set_of_lower_eq x
 #align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_le
 
-#print BoxIntegral.Prepartition.unionᵢ /-
+#print BoxIntegral.Prepartition.iUnion /-
 /-- Given a prepartition `π : box_integral.prepartition I`, `π.Union` is the part of `I` covered by
 the boxes of `π`. -/
-protected def unionᵢ : Set (ι → ℝ) :=
+protected def iUnion : Set (ι → ℝ) :=
   ⋃ J ∈ π, ↑J
-#align box_integral.prepartition.Union BoxIntegral.Prepartition.unionᵢ
+#align box_integral.prepartition.Union BoxIntegral.Prepartition.iUnion
 -/
 
-#print BoxIntegral.Prepartition.unionᵢ_def /-
-theorem unionᵢ_def : π.unionᵢ = ⋃ J ∈ π, ↑J :=
+#print BoxIntegral.Prepartition.iUnion_def /-
+theorem iUnion_def : π.iUnion = ⋃ J ∈ π, ↑J :=
   rfl
-#align box_integral.prepartition.Union_def BoxIntegral.Prepartition.unionᵢ_def
+#align box_integral.prepartition.Union_def BoxIntegral.Prepartition.iUnion_def
 -/
 
-#print BoxIntegral.Prepartition.unionᵢ_def' /-
-theorem unionᵢ_def' : π.unionᵢ = ⋃ J ∈ π.boxes, ↑J :=
+#print BoxIntegral.Prepartition.iUnion_def' /-
+theorem iUnion_def' : π.iUnion = ⋃ J ∈ π.boxes, ↑J :=
   rfl
-#align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.unionᵢ_def'
+#align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.iUnion_def'
 -/
 
-/- warning: box_integral.prepartition.mem_Union -> BoxIntegral.Prepartition.mem_unionᵢ is a dubious translation:
+/- warning: box_integral.prepartition.mem_Union -> BoxIntegral.Prepartition.mem_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (BoxIntegral.Prepartition.unionᵢ.{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.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} (ι -> Real) (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasMem.{u1} ι) x J)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (BoxIntegral.Prepartition.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.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} (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.Prepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.instMembershipSet.{u1} (ι -> Real)) x (BoxIntegral.Prepartition.unionᵢ.{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.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{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.prepartition.mem_Union BoxIntegral.Prepartition.mem_unionᵢₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.instMembershipSet.{u1} (ι -> Real)) x (BoxIntegral.Prepartition.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.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{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.prepartition.mem_Union BoxIntegral.Prepartition.mem_iUnionₓ'. -/
 @[simp]
-theorem mem_unionᵢ : x ∈ π.unionᵢ ↔ ∃ J ∈ π, x ∈ J :=
-  Set.mem_unionᵢ₂
-#align box_integral.prepartition.mem_Union BoxIntegral.Prepartition.mem_unionᵢ
+theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J :=
+  Set.mem_iUnion₂
+#align box_integral.prepartition.mem_Union BoxIntegral.Prepartition.mem_iUnion
 
-#print BoxIntegral.Prepartition.unionᵢ_single /-
+#print BoxIntegral.Prepartition.iUnion_single /-
 @[simp]
-theorem unionᵢ_single (h : J ≤ I) : (single I J h).unionᵢ = J := by simp [Union_def]
-#align box_integral.prepartition.Union_single BoxIntegral.Prepartition.unionᵢ_single
+theorem iUnion_single (h : J ≤ I) : (single I J h).iUnion = J := by simp [Union_def]
+#align box_integral.prepartition.Union_single BoxIntegral.Prepartition.iUnion_single
 -/
 
-/- warning: box_integral.prepartition.Union_top -> BoxIntegral.Prepartition.unionᵢ_top is a dubious translation:
+/- warning: box_integral.prepartition.Union_top -> BoxIntegral.Prepartition.iUnion_top is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderTop.{u1} ι I)))) ((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))) I)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderTop.{u1} ι I)))) ((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))) I)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι I)))) (BoxIntegral.Box.toSet.{u1} ι I)
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.unionᵢ_topₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι I)))) (BoxIntegral.Box.toSet.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.iUnion_topₓ'. -/
 @[simp]
-theorem unionᵢ_top : (⊤ : Prepartition I).unionᵢ = I := by simp [prepartition.Union]
-#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.unionᵢ_top
+theorem iUnion_top : (⊤ : Prepartition I).iUnion = I := by simp [prepartition.Union]
+#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.iUnion_top
 
-/- warning: box_integral.prepartition.Union_eq_empty -> BoxIntegral.Prepartition.unionᵢ_eq_empty is a dubious translation:
+/- warning: box_integral.prepartition.Union_eq_empty -> BoxIntegral.Prepartition.iUnion_eq_empty is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.hasEmptyc.{u1} (ι -> Real)))) (Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) π₁ (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.hasEmptyc.{u1} (ι -> Real)))) (Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) π₁ (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.instEmptyCollectionSet.{u1} (ι -> Real)))) (Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) π₁ (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I))))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.unionᵢ_eq_emptyₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.instEmptyCollectionSet.{u1} (ι -> Real)))) (Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) π₁ (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.iUnion_eq_emptyₓ'. -/
 @[simp]
-theorem unionᵢ_eq_empty : π₁.unionᵢ = ∅ ↔ π₁ = ⊥ := by
+theorem iUnion_eq_empty : π₁.iUnion = ∅ ↔ π₁ = ⊥ := by
   simp [← injective_boxes.eq_iff, Finset.ext_iff, prepartition.Union, imp_false]
-#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.unionᵢ_eq_empty
+#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.iUnion_eq_empty
 
-/- warning: box_integral.prepartition.Union_bot -> BoxIntegral.Prepartition.unionᵢ_bot is a dubious translation:
+/- warning: box_integral.prepartition.Union_bot -> BoxIntegral.Prepartition.iUnion_bot is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.hasEmptyc.{u1} (ι -> Real)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.hasEmptyc.{u1} (ι -> Real)))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.instEmptyCollectionSet.{u1} (ι -> Real)))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.unionᵢ_botₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.instEmptyCollectionSet.{u1} (ι -> Real)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.iUnion_botₓ'. -/
 @[simp]
-theorem unionᵢ_bot : (⊥ : Prepartition I).unionᵢ = ∅ :=
-  unionᵢ_eq_empty.2 rfl
-#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.unionᵢ_bot
-
-#print BoxIntegral.Prepartition.subset_unionᵢ /-
-theorem subset_unionᵢ (h : J ∈ π) : ↑J ⊆ π.unionᵢ :=
-  subset_bunionᵢ_of_mem h
-#align box_integral.prepartition.subset_Union BoxIntegral.Prepartition.subset_unionᵢ
+theorem iUnion_bot : (⊥ : Prepartition I).iUnion = ∅ :=
+  iUnion_eq_empty.2 rfl
+#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.iUnion_bot
+
+#print BoxIntegral.Prepartition.subset_iUnion /-
+theorem subset_iUnion (h : J ∈ π) : ↑J ⊆ π.iUnion :=
+  subset_biUnion_of_mem h
+#align box_integral.prepartition.subset_Union BoxIntegral.Prepartition.subset_iUnion
 -/
 
-#print BoxIntegral.Prepartition.unionᵢ_subset /-
-theorem unionᵢ_subset : π.unionᵢ ⊆ I :=
-  unionᵢ₂_subset π.le_of_mem'
-#align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.unionᵢ_subset
+#print BoxIntegral.Prepartition.iUnion_subset /-
+theorem iUnion_subset : π.iUnion ⊆ I :=
+  iUnion₂_subset π.le_of_mem'
+#align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.iUnion_subset
 -/
 
-/- warning: box_integral.prepartition.Union_mono -> BoxIntegral.Prepartition.unionᵢ_mono is a dubious translation:
+/- warning: box_integral.prepartition.Union_mono -> BoxIntegral.Prepartition.iUnion_mono is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.instHasSubsetSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.unionᵢ_monoₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.instHasSubsetSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.iUnion_monoₓ'. -/
 @[mono]
-theorem unionᵢ_mono (h : π₁ ≤ π₂) : π₁.unionᵢ ⊆ π₂.unionᵢ := fun x hx =>
-  let ⟨J₁, hJ₁, hx⟩ := π₁.mem_unionᵢ.1 hx
+theorem iUnion_mono (h : π₁ ≤ π₂) : π₁.iUnion ⊆ π₂.iUnion := fun x hx =>
+  let ⟨J₁, hJ₁, hx⟩ := π₁.mem_iUnion.1 hx
   let ⟨J₂, hJ₂, hle⟩ := h hJ₁
-  π₂.mem_unionᵢ.2 ⟨J₂, hJ₂, hle hx⟩
-#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.unionᵢ_mono
+  π₂.mem_iUnion.2 ⟨J₂, hJ₂, hle hx⟩
+#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.iUnion_mono
 
-/- warning: box_integral.prepartition.disjoint_boxes_of_disjoint_Union -> BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_unionᵢ is a dubious translation:
+/- warning: box_integral.prepartition.disjoint_boxes_of_disjoint_Union -> BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (Disjoint.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.partialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.orderBot.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (Disjoint.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.partialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.orderBot.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (Disjoint.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.partialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_unionᵢₓ'. -/
-theorem disjoint_boxes_of_disjoint_unionᵢ (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (Disjoint.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.partialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnionₓ'. -/
+theorem disjoint_boxes_of_disjoint_iUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     Disjoint π₁.boxes π₂.boxes :=
   Finset.disjoint_left.2 fun J h₁ h₂ =>
-    Disjoint.le_bot (h.mono (π₁.subset_unionᵢ h₁) (π₂.subset_unionᵢ h₂)) ⟨J.upper_mem, J.upper_mem⟩
-#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_unionᵢ
+    Disjoint.le_bot (h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)) ⟨J.upper_mem, J.upper_mem⟩
+#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion
 
-/- warning: box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset -> BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_unionᵢ_subset is a dubious translation:
+/- warning: box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset -> BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) (And (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) ((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'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J J'))) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) (And (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) ((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'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J J'))) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) (And (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Box.toSet.{u1} ι J'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J J'))) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.instHasSubsetSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_unionᵢ_subsetₓ'. -/
-theorem le_iff_nonempty_imp_le_and_unionᵢ_subset :
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) (And (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Box.toSet.{u1} ι J'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J J'))) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.instHasSubsetSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subsetₓ'. -/
+theorem le_iff_nonempty_imp_le_and_iUnion_subset :
     π₁ ≤ π₂ ↔
-      (∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J') ∧ π₁.unionᵢ ⊆ π₂.unionᵢ :=
+      (∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J') ∧ π₁.iUnion ⊆ π₂.iUnion :=
   by
   fconstructor
   · refine' fun H => ⟨fun J hJ J' hJ' Hne => _, Union_mono H⟩
@@ -434,171 +434,171 @@ theorem le_iff_nonempty_imp_le_and_unionᵢ_subset :
     simp only [Set.subset_def, mem_Union] at HU
     rcases HU J.upper ⟨J, hJ, J.upper_mem⟩ with ⟨J₂, hJ₂, hx⟩
     exact ⟨J₂, hJ₂, H _ hJ _ hJ₂ ⟨_, J.upper_mem, hx⟩⟩
-#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_unionᵢ_subset
+#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset
 
-#print BoxIntegral.Prepartition.eq_of_boxes_subset_unionᵢ_superset /-
-theorem eq_of_boxes_subset_unionᵢ_superset (h₁ : π₁.boxes ⊆ π₂.boxes) (h₂ : π₂.unionᵢ ⊆ π₁.unionᵢ) :
+#print BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_superset /-
+theorem eq_of_boxes_subset_iUnion_superset (h₁ : π₁.boxes ⊆ π₂.boxes) (h₂ : π₂.iUnion ⊆ π₁.iUnion) :
     π₁ = π₂ :=
   (le_antisymm fun J hJ => ⟨J, h₁ hJ, le_rfl⟩) <|
-    le_iff_nonempty_imp_le_and_unionᵢ_subset.2
+    le_iff_nonempty_imp_le_and_iUnion_subset.2
       ⟨fun J₁ hJ₁ J₂ hJ₂ Hne =>
         (π₂.eq_of_mem_of_mem hJ₁ (h₁ hJ₂) Hne.choose_spec.1 Hne.choose_spec.2).le, h₂⟩
-#align box_integral.prepartition.eq_of_boxes_subset_Union_superset BoxIntegral.Prepartition.eq_of_boxes_subset_unionᵢ_superset
+#align box_integral.prepartition.eq_of_boxes_subset_Union_superset BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_superset
 -/
 
-#print BoxIntegral.Prepartition.bunionᵢ /-
+#print BoxIntegral.Prepartition.biUnion /-
 /-- Given a prepartition `π` of a box `I` and a collection of prepartitions `πi J` of all boxes
 `J ∈ π`, returns the prepartition of `I` into the union of the boxes of all `πi J`.
 
 Though we only use the values of `πi` on the boxes of `π`, we require `πi` to be a globally defined
 function. -/
 @[simps]
-def bunionᵢ (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
+def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
     where
-  boxes := π.boxes.bunionᵢ fun J => (πi J).boxes
+  boxes := π.boxes.biUnion fun J => (πi J).boxes
   le_of_mem' J hJ :=
     by
-    simp only [Finset.mem_bunionᵢ, exists_prop, mem_boxes] at hJ
+    simp only [Finset.mem_biUnion, exists_prop, mem_boxes] at hJ
     rcases hJ with ⟨J', hJ', hJ⟩
     exact ((πi J').le_of_mem hJ).trans (π.le_of_mem hJ')
   PairwiseDisjoint :=
     by
-    simp only [Set.Pairwise, Finset.mem_coe, Finset.mem_bunionᵢ]
+    simp only [Set.Pairwise, Finset.mem_coe, Finset.mem_biUnion]
     rintro J₁' ⟨J₁, hJ₁, hJ₁'⟩ J₂' ⟨J₂, hJ₂, hJ₂'⟩ Hne
     rw [Function.onFun, Set.disjoint_left]
     rintro x hx₁ hx₂; apply Hne
     obtain rfl : J₁ = J₂
     exact π.eq_of_mem_of_mem hJ₁ hJ₂ ((πi J₁).le_of_mem hJ₁' hx₁) ((πi J₂).le_of_mem hJ₂' hx₂)
     exact (πi J₁).eq_of_mem_of_mem hJ₁' hJ₂' hx₁ hx₂
-#align box_integral.prepartition.bUnion BoxIntegral.Prepartition.bunionᵢ
+#align box_integral.prepartition.bUnion BoxIntegral.Prepartition.biUnion
 -/
 
 variable {πi πi₁ πi₂ : ∀ J : Box ι, Prepartition J}
 
-/- warning: box_integral.prepartition.mem_bUnion -> BoxIntegral.Prepartition.mem_bunionᵢ is a dubious translation:
+/- warning: box_integral.prepartition.mem_bUnion -> BoxIntegral.Prepartition.mem_biUnion 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.Prepartition.{u1} ι J}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.bunionᵢ.{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.Prepartition.{u1} ι J') (BoxIntegral.Prepartition.hasMem.{u1} ι J') J (πi J'))))
+  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.Prepartition.{u1} ι J}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.biUnion.{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.Prepartition.{u1} ι J') (BoxIntegral.Prepartition.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.Prepartition.{u1} ι J}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.bunionᵢ.{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.Prepartition.{u1} ι J') (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J') J (πi J'))))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_bunionᵢₓ'. -/
+  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.Prepartition.{u1} ι J}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.biUnion.{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.Prepartition.{u1} ι J') (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J') J (πi J'))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_biUnionₓ'. -/
 @[simp]
-theorem mem_bunionᵢ : J ∈ π.bunionᵢ πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [bUnion]
-#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_bunionᵢ
+theorem mem_biUnion : J ∈ π.biUnion πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [bUnion]
+#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_biUnion
 
-/- warning: box_integral.prepartition.bUnion_le -> BoxIntegral.Prepartition.bunionᵢ_le is a dubious translation:
+/- warning: box_integral.prepartition.bUnion_le -> BoxIntegral.Prepartition.biUnion_le is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.biUnion.{u1} ι I π πi) π
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.bunionᵢ_leₓ'. -/
-theorem bunionᵢ_le (πi : ∀ J, Prepartition J) : π.bunionᵢ πi ≤ π := fun J hJ =>
-  let ⟨J', hJ', hJ⟩ := π.mem_bunionᵢ.1 hJ
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.biUnion.{u1} ι I π πi) π
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.biUnion_leₓ'. -/
+theorem biUnion_le (πi : ∀ J, Prepartition J) : π.biUnion πi ≤ π := fun J hJ =>
+  let ⟨J', hJ', hJ⟩ := π.mem_biUnion.1 hJ
   ⟨J', hJ', (πi J').le_of_mem hJ⟩
-#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.bunionᵢ_le
+#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.biUnion_le
 
-/- warning: box_integral.prepartition.bUnion_top -> BoxIntegral.Prepartition.bunionᵢ_top is a dubious translation:
+/- warning: box_integral.prepartition.bUnion_top -> BoxIntegral.Prepartition.biUnion_top is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π (fun (_x : BoxIntegral.Box.{u1} ι) => Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (BoxIntegral.Prepartition.hasLe.{u1} ι _x) (BoxIntegral.Prepartition.orderTop.{u1} ι _x)))) π
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.biUnion.{u1} ι I π (fun (_x : BoxIntegral.Box.{u1} ι) => Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (BoxIntegral.Prepartition.hasLe.{u1} ι _x) (BoxIntegral.Prepartition.orderTop.{u1} ι _x)))) π
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π (fun (_x : BoxIntegral.Box.{u1} ι) => Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι _x) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι _x)))) π
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.bunionᵢ_topₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.biUnion.{u1} ι I π (fun (_x : BoxIntegral.Box.{u1} ι) => Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι _x) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι _x)))) π
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.biUnion_topₓ'. -/
 @[simp]
-theorem bunionᵢ_top : (π.bunionᵢ fun _ => ⊤) = π :=
+theorem biUnion_top : (π.biUnion fun _ => ⊤) = π :=
   by
   ext
   simp
-#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.bunionᵢ_top
+#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.biUnion_top
 
-#print BoxIntegral.Prepartition.bunionᵢ_congr /-
+#print BoxIntegral.Prepartition.biUnion_congr /-
 @[congr]
-theorem bunionᵢ_congr (h : π₁ = π₂) (hi : ∀ J ∈ π₁, πi₁ J = πi₂ J) :
-    π₁.bunionᵢ πi₁ = π₂.bunionᵢ πi₂ := by
+theorem biUnion_congr (h : π₁ = π₂) (hi : ∀ J ∈ π₁, πi₁ J = πi₂ J) :
+    π₁.biUnion πi₁ = π₂.biUnion πi₂ := by
   subst π₂
   ext J
   simp (config := { contextual := true }) [hi]
-#align box_integral.prepartition.bUnion_congr BoxIntegral.Prepartition.bunionᵢ_congr
+#align box_integral.prepartition.bUnion_congr BoxIntegral.Prepartition.biUnion_congr
 -/
 
-#print BoxIntegral.Prepartition.bunionᵢ_congr_of_le /-
-theorem bunionᵢ_congr_of_le (h : π₁ = π₂) (hi : ∀ J ≤ I, πi₁ J = πi₂ J) :
-    π₁.bunionᵢ πi₁ = π₂.bunionᵢ πi₂ :=
-  bunionᵢ_congr h fun J hJ => hi J (π₁.le_of_mem hJ)
-#align box_integral.prepartition.bUnion_congr_of_le BoxIntegral.Prepartition.bunionᵢ_congr_of_le
+#print BoxIntegral.Prepartition.biUnion_congr_of_le /-
+theorem biUnion_congr_of_le (h : π₁ = π₂) (hi : ∀ J ≤ I, πi₁ J = πi₂ J) :
+    π₁.biUnion πi₁ = π₂.biUnion πi₂ :=
+  biUnion_congr h fun J hJ => hi J (π₁.le_of_mem hJ)
+#align box_integral.prepartition.bUnion_congr_of_le BoxIntegral.Prepartition.biUnion_congr_of_le
 -/
 
-#print BoxIntegral.Prepartition.unionᵢ_bunionᵢ /-
+#print BoxIntegral.Prepartition.iUnion_biUnion /-
 @[simp]
-theorem unionᵢ_bunionᵢ (πi : ∀ J : Box ι, Prepartition J) :
-    (π.bunionᵢ πi).unionᵢ = ⋃ J ∈ π, (πi J).unionᵢ := by simp [prepartition.Union]
-#align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.unionᵢ_bunionᵢ
+theorem iUnion_biUnion (πi : ∀ J : Box ι, Prepartition J) :
+    (π.biUnion πi).iUnion = ⋃ J ∈ π, (πi J).iUnion := by simp [prepartition.Union]
+#align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.iUnion_biUnion
 -/
 
-/- warning: box_integral.prepartition.sum_bUnion_boxes -> BoxIntegral.Prepartition.sum_bunionᵢ_boxes is a dubious translation:
+/- warning: box_integral.prepartition.sum_bUnion_boxes -> BoxIntegral.Prepartition.sum_biUnion_boxes is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.bunionᵢ.{u1, u1} (BoxIntegral.Box.{u1} ι) (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 π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.biUnion.{u1, u1} (BoxIntegral.Box.{u1} ι) (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 π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.bunionᵢ.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b) (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_bunionᵢ_boxesₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.biUnion.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b) (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_biUnion_boxesₓ'. -/
 @[simp]
-theorem sum_bunionᵢ_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
+theorem sum_biUnion_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
     (πi : ∀ J, Prepartition J) (f : Box ι → M) :
-    (∑ J in π.boxes.bunionᵢ fun J => (πi J).boxes, f J) =
+    (∑ J in π.boxes.biUnion fun J => (πi J).boxes, f J) =
       ∑ J in π.boxes, ∑ J' in (πi J).boxes, f J' :=
   by
-  refine' Finset.sum_bunionᵢ fun J₁ h₁ J₂ h₂ hne => Finset.disjoint_left.2 fun J' h₁' h₂' => _
+  refine' Finset.sum_biUnion fun J₁ h₁ J₂ h₂ hne => Finset.disjoint_left.2 fun J' h₁' h₂' => _
   exact hne (π.eq_of_le_of_le h₁ h₂ ((πi J₁).le_of_mem h₁') ((πi J₂).le_of_mem h₂'))
-#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_bunionᵢ_boxes
+#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_biUnion_boxes
 
-#print BoxIntegral.Prepartition.bunionᵢIndex /-
+#print BoxIntegral.Prepartition.biUnionIndex /-
 /-- Given a box `J ∈ π.bUnion πi`, returns the box `J' ∈ π` such that `J ∈ πi J'`.
 For `J ∉ π.bUnion πi`, returns `I`. -/
-def bunionᵢIndex (πi : ∀ J, Prepartition J) (J : Box ι) : Box ι :=
-  if hJ : J ∈ π.bunionᵢ πi then (π.mem_bunionᵢ.1 hJ).some else I
-#align box_integral.prepartition.bUnion_index BoxIntegral.Prepartition.bunionᵢIndex
+def biUnionIndex (πi : ∀ J, Prepartition J) (J : Box ι) : Box ι :=
+  if hJ : J ∈ π.biUnion πi then (π.mem_biUnion.1 hJ).some else I
+#align box_integral.prepartition.bUnion_index BoxIntegral.Prepartition.biUnionIndex
 -/
 
-#print BoxIntegral.Prepartition.bunionᵢIndex_mem /-
-theorem bunionᵢIndex_mem (hJ : J ∈ π.bunionᵢ πi) : π.bunionᵢIndex πi J ∈ π :=
+#print BoxIntegral.Prepartition.biUnionIndex_mem /-
+theorem biUnionIndex_mem (hJ : J ∈ π.biUnion πi) : π.biUnionIndex πi J ∈ π :=
   by
   rw [bUnion_index, dif_pos hJ]
   exact (π.mem_bUnion.1 hJ).choose_spec.fst
-#align box_integral.prepartition.bUnion_index_mem BoxIntegral.Prepartition.bunionᵢIndex_mem
+#align box_integral.prepartition.bUnion_index_mem BoxIntegral.Prepartition.biUnionIndex_mem
 -/
 
-#print BoxIntegral.Prepartition.bunionᵢIndex_le /-
-theorem bunionᵢIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.bunionᵢIndex πi J ≤ I :=
+#print BoxIntegral.Prepartition.biUnionIndex_le /-
+theorem biUnionIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.biUnionIndex πi J ≤ I :=
   by
   by_cases hJ : J ∈ π.bUnion πi
   · exact π.le_of_mem (π.bUnion_index_mem hJ)
   · rw [bUnion_index, dif_neg hJ]
     exact le_rfl
-#align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.bunionᵢIndex_le
+#align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.biUnionIndex_le
 -/
 
-#print BoxIntegral.Prepartition.mem_bunionᵢIndex /-
-theorem mem_bunionᵢIndex (hJ : J ∈ π.bunionᵢ πi) : J ∈ πi (π.bunionᵢIndex πi J) := by
+#print BoxIntegral.Prepartition.mem_biUnionIndex /-
+theorem mem_biUnionIndex (hJ : J ∈ π.biUnion πi) : J ∈ πi (π.biUnionIndex πi J) := by
   convert(π.mem_bUnion.1 hJ).choose_spec.snd <;> exact dif_pos hJ
-#align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_bunionᵢIndex
+#align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_biUnionIndex
 -/
 
-#print BoxIntegral.Prepartition.le_bunionᵢIndex /-
-theorem le_bunionᵢIndex (hJ : J ∈ π.bunionᵢ πi) : J ≤ π.bunionᵢIndex πi J :=
-  le_of_mem _ (π.mem_bunionᵢIndex hJ)
-#align box_integral.prepartition.le_bUnion_index BoxIntegral.Prepartition.le_bunionᵢIndex
+#print BoxIntegral.Prepartition.le_biUnionIndex /-
+theorem le_biUnionIndex (hJ : J ∈ π.biUnion πi) : J ≤ π.biUnionIndex πi J :=
+  le_of_mem _ (π.mem_biUnionIndex hJ)
+#align box_integral.prepartition.le_bUnion_index BoxIntegral.Prepartition.le_biUnionIndex
 -/
 
-#print BoxIntegral.Prepartition.bunionᵢIndex_of_mem /-
+#print BoxIntegral.Prepartition.biUnionIndex_of_mem /-
 /-- Uniqueness property of `box_integral.partition.bUnion_index`. -/
-theorem bunionᵢIndex_of_mem (hJ : J ∈ π) {J'} (hJ' : J' ∈ πi J) : π.bunionᵢIndex πi J' = J :=
-  have : J' ∈ π.bunionᵢ πi := π.mem_bunionᵢ.2 ⟨J, hJ, hJ'⟩
-  π.eq_of_le_of_le (π.bunionᵢIndex_mem this) hJ (π.le_bunionᵢIndex this) (le_of_mem _ hJ')
-#align box_integral.prepartition.bUnion_index_of_mem BoxIntegral.Prepartition.bunionᵢIndex_of_mem
+theorem biUnionIndex_of_mem (hJ : J ∈ π) {J'} (hJ' : J' ∈ πi J) : π.biUnionIndex πi J' = J :=
+  have : J' ∈ π.biUnion πi := π.mem_biUnion.2 ⟨J, hJ, hJ'⟩
+  π.eq_of_le_of_le (π.biUnionIndex_mem this) hJ (π.le_biUnionIndex this) (le_of_mem _ hJ')
+#align box_integral.prepartition.bUnion_index_of_mem BoxIntegral.Prepartition.biUnionIndex_of_mem
 -/
 
-#print BoxIntegral.Prepartition.bunionᵢ_assoc /-
-theorem bunionᵢ_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : Box ι, Prepartition J) :
-    (π.bunionᵢ fun J => (πi J).bunionᵢ (πi' J)) =
-      (π.bunionᵢ πi).bunionᵢ fun J => πi' (π.bunionᵢIndex πi J) J :=
+#print BoxIntegral.Prepartition.biUnion_assoc /-
+theorem biUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : Box ι, Prepartition J) :
+    (π.biUnion fun J => (πi J).biUnion (πi' J)) =
+      (π.biUnion πi).biUnion fun J => πi' (π.biUnionIndex πi J) J :=
   by
   ext J
   simp only [mem_bUnion, exists_prop]
@@ -609,7 +609,7 @@ theorem bunionᵢ_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J :
   · rintro ⟨J₁, ⟨J₂, hJ₂, hJ₁⟩, hJ⟩
     refine' ⟨J₂, hJ₂, J₁, hJ₁, _⟩
     rwa [π.bUnion_index_of_mem hJ₂ hJ₁] at hJ
-#align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.bunionᵢ_assoc
+#align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.biUnion_assoc
 -/
 
 /- warning: box_integral.prepartition.of_with_bot -> BoxIntegral.Prepartition.ofWithBot is a dubious translation:
@@ -646,23 +646,23 @@ theorem mem_ofWithBot {boxes : Finset (WithBot (Box ι))} {h₁ h₂} :
   mem_eraseNone
 #align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBot
 
-/- warning: box_integral.prepartition.Union_of_with_bot -> BoxIntegral.Prepartition.unionᵢ_ofWithBot is a dubious translation:
+/- warning: box_integral.prepartition.Union_of_with_bot -> BoxIntegral.Prepartition.iUnion_ofWithBot is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.unionᵢ.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.unionᵢ.{u1, 0} (ι -> Real) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (HasLiftT.mk.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (CoeTCₓ.coe.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.withBotCoe.{u1} ι))) J)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.iUnion.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.iUnion.{u1, 0} (ι -> Real) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (HasLiftT.mk.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (CoeTCₓ.coe.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.withBotCoe.{u1} ι))) J)))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.unionᵢ.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.unionᵢ.{u1, 0} (ι -> Real) (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => BoxIntegral.Box.withBotToSet.{u1} ι J)))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.unionᵢ_ofWithBotₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.iUnion.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.iUnion.{u1, 0} (ι -> Real) (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => BoxIntegral.Box.withBotToSet.{u1} ι J)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.iUnion_ofWithBotₓ'. -/
 @[simp]
-theorem unionᵢ_ofWithBot (boxes : Finset (WithBot (Box ι)))
+theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) :
-    (ofWithBot boxes le_of_mem pairwise_disjoint).unionᵢ = ⋃ J ∈ boxes, ↑J :=
+    (ofWithBot boxes le_of_mem pairwise_disjoint).iUnion = ⋃ J ∈ boxes, ↑J :=
   by
   suffices (⋃ (J : box ι) (hJ : ↑J ∈ boxes), ↑J) = ⋃ J ∈ boxes, ↑J by
     simpa [of_with_bot, prepartition.Union]
   simp only [← box.bUnion_coe_eq_coe, @Union_comm _ _ (box ι), @Union_comm _ _ (@Eq _ _ _),
     Union_Union_eq_right]
-#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.unionᵢ_ofWithBot
+#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.iUnion_ofWithBot
 
 /- warning: box_integral.prepartition.of_with_bot_le -> BoxIntegral.Prepartition.ofWithBot_le is a dubious translation:
 lean 3 declaration is
@@ -795,7 +795,7 @@ theorem restrict_boxes_of_le (π : Prepartition I) (h : I ≤ J) : (π.restrict
   by
   simp only [restrict, of_with_bot, erase_none_eq_bUnion]
   refine' finset.image_bUnion.trans _
-  refine' (Finset.bunionᵢ_congr rfl _).trans Finset.bunionᵢ_singleton_eq_self
+  refine' (Finset.biUnion_congr rfl _).trans Finset.biUnion_singleton_eq_self
   intro J' hJ'
   rw [inf_of_le_right, ← WithBot.some_eq_coe, Option.toFinset_some]
   exact WithBot.coe_le_coe.2 ((π.le_of_mem hJ').trans h)
@@ -809,41 +809,41 @@ theorem restrict_self : π.restrict I = π :=
 #align box_integral.prepartition.restrict_self BoxIntegral.Prepartition.restrict_self
 -/
 
-/- warning: box_integral.prepartition.Union_restrict -> BoxIntegral.Prepartition.unionᵢ_restrict is a dubious translation:
+/- warning: box_integral.prepartition.Union_restrict -> BoxIntegral.Prepartition.iUnion_restrict 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), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι J (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι J (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) (BoxIntegral.Prepartition.iUnion.{u1} ι I 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), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι J (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.unionᵢ_restrictₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι J (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Prepartition.iUnion.{u1} ι I π))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.iUnion_restrictₓ'. -/
 @[simp]
-theorem unionᵢ_restrict : (π.restrict J).unionᵢ = J ∩ π.unionᵢ := by
+theorem iUnion_restrict : (π.restrict J).iUnion = J ∩ π.iUnion := by
   simp [restrict, ← inter_Union, ← Union_def]
-#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.unionᵢ_restrict
+#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.iUnion_restrict
 
-#print BoxIntegral.Prepartition.restrict_bunionᵢ /-
+#print BoxIntegral.Prepartition.restrict_biUnion /-
 @[simp]
-theorem restrict_bunionᵢ (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
-    (π.bunionᵢ πi).restrict J = πi J :=
+theorem restrict_biUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
+    (π.biUnion πi).restrict J = πi J :=
   by
   refine' (eq_of_boxes_subset_Union_superset (fun J₁ h₁ => _) _).symm
   · refine' (mem_restrict _).2 ⟨J₁, π.mem_bUnion.2 ⟨J, hJ, h₁⟩, (inf_of_le_right _).symm⟩
     exact WithBot.coe_le_coe.2 (le_of_mem _ h₁)
-  · simp only [Union_restrict, Union_bUnion, Set.subset_def, Set.mem_inter_iff, Set.mem_unionᵢ]
+  · simp only [Union_restrict, Union_bUnion, Set.subset_def, Set.mem_inter_iff, Set.mem_iUnion]
     rintro x ⟨hxJ, J₁, h₁, hx⟩
     obtain rfl : J = J₁
     exact π.eq_of_mem_of_mem hJ h₁ hxJ (Union_subset _ hx)
     exact hx
-#align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_bunionᵢ
+#align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_biUnion
 -/
 
-/- warning: box_integral.prepartition.bUnion_le_iff -> BoxIntegral.Prepartition.bunionᵢ_le_iff is a dubious translation:
+/- warning: box_integral.prepartition.bUnion_le_iff -> BoxIntegral.Prepartition.biUnion_le_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π') (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasLe.{u1} ι J) (πi J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.biUnion.{u1} ι I π πi) π') (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasLe.{u1} ι J) (πi J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J)))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π') (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι J) (πi J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J)))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.bunionᵢ_le_iffₓ'. -/
-theorem bunionᵢ_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
-    π.bunionᵢ πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J :=
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.biUnion.{u1} ι I π πi) π') (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι J) (πi J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.biUnion_le_iffₓ'. -/
+theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
+    π.biUnion πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J :=
   by
   fconstructor <;> intro H J hJ
   · rw [← π.restrict_bUnion πi hJ]
@@ -853,16 +853,16 @@ theorem bunionᵢ_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     rcases H J₁ h₁ hJ with ⟨J₂, h₂, Hle⟩
     rcases π'.mem_restrict.mp h₂ with ⟨J₃, h₃, H⟩
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩
-#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.bunionᵢ_le_iff
+#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.biUnion_le_iff
 
-/- warning: box_integral.prepartition.le_bUnion_iff -> BoxIntegral.Prepartition.le_bunionᵢ_iff is a dubious translation:
+/- warning: box_integral.prepartition.le_bUnion_iff -> BoxIntegral.Prepartition.le_biUnion_iff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π' (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi)) (And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π' π) (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasLe.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J) (πi J))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π' (BoxIntegral.Prepartition.biUnion.{u1} ι I π πi)) (And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π' π) (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasLe.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J) (πi J))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π' (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi)) (And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π' π) (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J) (πi J))))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_bunionᵢ_iffₓ'. -/
-theorem le_bunionᵢ_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
-    π' ≤ π.bunionᵢ πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J :=
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π' (BoxIntegral.Prepartition.biUnion.{u1} ι I π πi)) (And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π' π) (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J) (πi J))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_biUnion_iffₓ'. -/
+theorem le_biUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
+    π' ≤ π.biUnion πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J :=
   by
   refine' ⟨fun H => ⟨H.trans (π.bUnion_le πi), fun J hJ => _⟩, _⟩
   · rw [← π.restrict_bUnion πi hJ]
@@ -873,13 +873,13 @@ theorem le_bunionᵢ_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
       π'.mem_restrict.2 ⟨J', hJ', (inf_of_le_right <| WithBot.coe_le_coe.2 hle).symm⟩
     rcases Hi J hJ this with ⟨Ji, hJi, hlei⟩
     exact ⟨Ji, π.mem_bUnion.2 ⟨J, hJ, hJi⟩, hlei⟩
-#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_bunionᵢ_iff
+#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_biUnion_iff
 
 instance : Inf (Prepartition I) :=
-  ⟨fun π₁ π₂ => π₁.bunionᵢ fun J => π₂.restrict J⟩
+  ⟨fun π₁ π₂ => π₁.biUnion fun J => π₂.restrict J⟩
 
 #print BoxIntegral.Prepartition.inf_def /-
-theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.bunionᵢ fun J => π₂.restrict J :=
+theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.biUnion fun J => π₂.restrict J :=
   rfl
 #align box_integral.prepartition.inf_def BoxIntegral.Prepartition.inf_def
 -/
@@ -896,23 +896,23 @@ theorem mem_inf {π₁ π₂ : Prepartition I} :
   simp only [inf_def, mem_bUnion, mem_restrict]
 #align box_integral.prepartition.mem_inf BoxIntegral.Prepartition.mem_inf
 
-/- warning: box_integral.prepartition.Union_inf -> BoxIntegral.Prepartition.unionᵢ_inf is a dubious translation:
+/- warning: box_integral.prepartition.Union_inf -> BoxIntegral.Prepartition.iUnion_inf is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasInf.{u1} ι I) π₁ π₂)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasInf.{u1} ι I) π₁ π₂)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.inf.{u1} ι I) π₁ π₂)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.unionᵢ_infₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.inf.{u1} ι I) π₁ π₂)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.iUnion_infₓ'. -/
 @[simp]
-theorem unionᵢ_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).unionᵢ = π₁.unionᵢ ∩ π₂.unionᵢ := by
+theorem iUnion_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).iUnion = π₁.iUnion ∩ π₂.iUnion := by
   simp only [inf_def, Union_bUnion, Union_restrict, ← Union_inter, ← Union_def]
-#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.unionᵢ_inf
+#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.iUnion_inf
 
 instance : SemilatticeInf (Prepartition I) :=
   { Prepartition.hasInf,
     Prepartition.partialOrder with
-    inf_le_left := fun π₁ π₂ => π₁.bunionᵢ_le _
-    inf_le_right := fun π₁ π₂ => (bunionᵢ_le_iff _).2 fun J hJ => le_rfl
-    le_inf := fun π π₁ π₂ h₁ h₂ => π₁.le_bunionᵢ_iff.2 ⟨h₁, fun J hJ => restrict_mono h₂⟩ }
+    inf_le_left := fun π₁ π₂ => π₁.biUnion_le _
+    inf_le_right := fun π₁ π₂ => (biUnion_le_iff _).2 fun J hJ => le_rfl
+    le_inf := fun π π₁ π₂ h₁ h₂ => π₁.le_biUnion_iff.2 ⟨h₁, fun J hJ => restrict_mono h₂⟩ }
 
 #print BoxIntegral.Prepartition.filter /-
 /-- The prepartition with boxes `{J ∈ π | p J}`. -/
@@ -958,23 +958,23 @@ theorem filter_true : (π.filterₓ fun _ => True) = π :=
 #align box_integral.prepartition.filter_true BoxIntegral.Prepartition.filter_true
 -/
 
-/- warning: box_integral.prepartition.Union_filter_not -> BoxIntegral.Prepartition.unionᵢ_filter_not is a dubious translation:
+/- warning: box_integral.prepartition.Union_filter_not -> BoxIntegral.Prepartition.iUnion_filter_not is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.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.Prepartition.unionᵢ.{u1} ι I π) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π p)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.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.Prepartition.iUnion.{u1} ι I π) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π p)))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.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.Prepartition.unionᵢ.{u1} ι I π) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π p)))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.unionᵢ_filter_notₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.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.Prepartition.iUnion.{u1} ι I π) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π p)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_notₓ'. -/
 @[simp]
-theorem unionᵢ_filter_not (π : Prepartition I) (p : Box ι → Prop) :
-    (π.filterₓ fun J => ¬p J).unionᵢ = π.unionᵢ \ (π.filterₓ p).unionᵢ :=
+theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
+    (π.filterₓ fun J => ¬p J).iUnion = π.iUnion \ (π.filterₓ p).iUnion :=
   by
   simp only [prepartition.Union]
-  convert(@Set.bunionᵢ_diff_bunionᵢ_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
+  convert(@Set.biUnion_diff_biUnion_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
   · ext (J x)
     simp (config := { contextual := true })
   · convert π.pairwise_disjoint
     simp
-#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.unionᵢ_filter_not
+#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
 
 /- warning: box_integral.prepartition.sum_fiberwise -> BoxIntegral.Prepartition.sum_fiberwise is a dubious translation:
 lean 3 declaration is
@@ -990,57 +990,57 @@ theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι
 
 /- warning: box_integral.prepartition.disj_union -> BoxIntegral.Prepartition.disjUnion is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (BoxIntegral.Prepartition.{u1} ι I)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (BoxIntegral.Prepartition.{u1} ι I)
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (BoxIntegral.Prepartition.{u1} ι I)
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (BoxIntegral.Prepartition.{u1} ι I)
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnionₓ'. -/
 /-- Union of two disjoint prepartitions. -/
 @[simps]
-def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.unionᵢ π₂.unionᵢ) : Prepartition I
+def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) : Prepartition I
     where
   boxes := π₁.boxes ∪ π₂.boxes
   le_of_mem' J hJ := (Finset.mem_union.1 hJ).elim π₁.le_of_mem π₂.le_of_mem
   PairwiseDisjoint :=
     suffices ∀ J₁ ∈ π₁, ∀ J₂ ∈ π₂, J₁ ≠ J₂ → Disjoint (J₁ : Set (ι → ℝ)) J₂ by
       simpa [pairwise_union_of_symmetric (symmetric_disjoint.comap _), pairwise_disjoint]
-    fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_unionᵢ h₁) (π₂.subset_unionᵢ h₂)
+    fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)
 #align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnion
 
 /- warning: box_integral.prepartition.mem_disj_union -> BoxIntegral.Prepartition.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.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ H)) (Or (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π₁) (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π₂))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ H)) (Or (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π₁) (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.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.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ H)) (Or (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π₁) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π₂))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ H)) (Or (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π₁) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π₂))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_disj_union BoxIntegral.Prepartition.mem_disjUnionₓ'. -/
 @[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.prepartition.mem_disj_union BoxIntegral.Prepartition.mem_disjUnion
 
-/- warning: box_integral.prepartition.Union_disj_union -> BoxIntegral.Prepartition.unionᵢ_disjUnion is a dubious translation:
+/- warning: box_integral.prepartition.Union_disj_union -> BoxIntegral.Prepartition.iUnion_disjUnion is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.hasUnion.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.hasUnion.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.instUnionSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.unionᵢ_disjUnionₓ'. -/
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.instUnionSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.iUnion_disjUnionₓ'. -/
 @[simp]
-theorem unionᵢ_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
-    (π₁.disjUnion π₂ h).unionᵢ = π₁.unionᵢ ∪ π₂.unionᵢ := by
+theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
+    (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion := by
   simp [disj_union, prepartition.Union, Union_or, Union_union_distrib]
-#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.unionᵢ_disjUnion
+#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.iUnion_disjUnion
 
 /- warning: box_integral.prepartition.sum_disj_union_boxes -> BoxIntegral.Prepartition.sum_disj_union_boxes is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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 π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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 π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxesₓ'. -/
 @[simp]
-theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.unionᵢ π₂.unionᵢ)
+theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
     (f : Box ι → M) :
     (∑ J in π₁.boxes ∪ π₂.boxes, f J) = (∑ J in π₁.boxes, f J) + ∑ J in π₂.boxes, f J :=
-  sum_union <| disjoint_boxes_of_disjoint_unionᵢ h
+  sum_union <| disjoint_boxes_of_disjoint_iUnion h
 #align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxes
 
 section Distortion
@@ -1067,25 +1067,25 @@ theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π,
 #align box_integral.prepartition.distortion_le_iff BoxIntegral.Prepartition.distortion_le_iff
 -/
 
-/- warning: box_integral.prepartition.distortion_bUnion -> BoxIntegral.Prepartition.distortion_bunionᵢ is a dubious translation:
+/- warning: box_integral.prepartition.distortion_bUnion -> BoxIntegral.Prepartition.distortion_biUnion 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.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.bunionᵢ.{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.Prepartition.distortion.{u1} ι J (πi J) _inst_1))
+  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.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.biUnion.{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.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.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.bunionᵢ.{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.Prepartition.distortion.{u1} ι J (πi J) _inst_1))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_bunionᵢₓ'. -/
-theorem distortion_bunionᵢ (π : Prepartition I) (πi : ∀ J, Prepartition J) :
-    (π.bunionᵢ πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
-  sup_bunionᵢ _ _
-#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_bunionᵢ
+  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.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.biUnion.{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.Prepartition.distortion.{u1} ι J (πi J) _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_biUnionₓ'. -/
+theorem distortion_biUnion (π : Prepartition I) (πi : ∀ J, Prepartition J) :
+    (π.biUnion πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
+  sup_biUnion _ _
+#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_biUnion
 
 /- warning: box_integral.prepartition.distortion_disj_union -> BoxIntegral.Prepartition.distortion_disjUnion is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (BoxIntegral.Prepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π₂ _inst_1))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (BoxIntegral.Prepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π₂ _inst_1))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (BoxIntegral.Prepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π₂ _inst_1))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (BoxIntegral.Prepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π₂ _inst_1))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_disj_union BoxIntegral.Prepartition.distortion_disjUnionₓ'. -/
 @[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.prepartition.distortion_disj_union BoxIntegral.Prepartition.distortion_disjUnion
@@ -1128,11 +1128,11 @@ def IsPartition (π : Prepartition I) :=
 #align box_integral.prepartition.is_partition BoxIntegral.Prepartition.IsPartition
 -/
 
-#print BoxIntegral.Prepartition.isPartition_iff_unionᵢ_eq /-
-theorem isPartition_iff_unionᵢ_eq {π : Prepartition I} : π.IsPartition ↔ π.unionᵢ = I := by
+#print BoxIntegral.Prepartition.isPartition_iff_iUnion_eq /-
+theorem isPartition_iff_iUnion_eq {π : Prepartition I} : π.IsPartition ↔ π.iUnion = I := by
   simp_rw [is_partition, Set.Subset.antisymm_iff, π.Union_subset, true_and_iff, Set.subset_def,
     mem_Union, box.mem_coe]
-#align box_integral.prepartition.is_partition_iff_Union_eq BoxIntegral.Prepartition.isPartition_iff_unionᵢ_eq
+#align box_integral.prepartition.is_partition_iff_Union_eq BoxIntegral.Prepartition.isPartition_iff_iUnion_eq
 -/
 
 #print BoxIntegral.Prepartition.isPartition_single_iff /-
@@ -1156,16 +1156,16 @@ namespace IsPartition
 
 variable {π}
 
-#print BoxIntegral.Prepartition.IsPartition.unionᵢ_eq /-
-theorem unionᵢ_eq (h : π.IsPartition) : π.unionᵢ = I :=
-  isPartition_iff_unionᵢ_eq.1 h
-#align box_integral.prepartition.is_partition.Union_eq BoxIntegral.Prepartition.IsPartition.unionᵢ_eq
+#print BoxIntegral.Prepartition.IsPartition.iUnion_eq /-
+theorem iUnion_eq (h : π.IsPartition) : π.iUnion = I :=
+  isPartition_iff_iUnion_eq.1 h
+#align box_integral.prepartition.is_partition.Union_eq BoxIntegral.Prepartition.IsPartition.iUnion_eq
 -/
 
-#print BoxIntegral.Prepartition.IsPartition.unionᵢ_subset /-
-theorem unionᵢ_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.unionᵢ ⊆ π.unionᵢ :=
-  h.unionᵢ_eq.symm ▸ π₁.unionᵢ_subset
-#align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.unionᵢ_subset
+#print BoxIntegral.Prepartition.IsPartition.iUnion_subset /-
+theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUnion ⊆ π.iUnion :=
+  h.iUnion_eq.symm ▸ π₁.iUnion_subset
+#align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 -/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (J «expr ∈ » π) -/
@@ -1186,7 +1186,7 @@ theorem nonempty_boxes (h : π.IsPartition) : π.boxes.Nonempty :=
 
 #print BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset /-
 theorem eq_of_boxes_subset (h₁ : π₁.IsPartition) (h₂ : π₁.boxes ⊆ π₂.boxes) : π₁ = π₂ :=
-  eq_of_boxes_subset_unionᵢ_superset h₂ <| h₁.unionᵢ_subset _
+  eq_of_boxes_subset_iUnion_superset h₂ <| h₁.iUnion_subset _
 #align box_integral.prepartition.is_partition.eq_of_boxes_subset BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset
 -/
 
@@ -1198,50 +1198,50 @@ but is expected to have type
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition.le_iff BoxIntegral.Prepartition.IsPartition.le_iffₓ'. -/
 theorem le_iff (h : π₂.IsPartition) :
     π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J' :=
-  le_iff_nonempty_imp_le_and_unionᵢ_subset.trans <| and_iff_left <| h.unionᵢ_subset _
+  le_iff_nonempty_imp_le_and_iUnion_subset.trans <| and_iff_left <| h.iUnion_subset _
 #align box_integral.prepartition.is_partition.le_iff BoxIntegral.Prepartition.IsPartition.le_iff
 
-#print BoxIntegral.Prepartition.IsPartition.bunionᵢ /-
-protected theorem bunionᵢ (h : IsPartition π) (hi : ∀ J ∈ π, IsPartition (πi J)) :
-    IsPartition (π.bunionᵢ πi) := fun x hx =>
+#print BoxIntegral.Prepartition.IsPartition.biUnion /-
+protected theorem biUnion (h : IsPartition π) (hi : ∀ J ∈ π, IsPartition (πi J)) :
+    IsPartition (π.biUnion πi) := fun x hx =>
   let ⟨J, hJ, hxi⟩ := h x hx
   let ⟨Ji, hJi, hx⟩ := hi J hJ x hxi
-  ⟨Ji, π.mem_bunionᵢ.2 ⟨J, hJ, hJi⟩, hx⟩
-#align box_integral.prepartition.is_partition.bUnion BoxIntegral.Prepartition.IsPartition.bunionᵢ
+  ⟨Ji, π.mem_biUnion.2 ⟨J, hJ, hJi⟩, hx⟩
+#align box_integral.prepartition.is_partition.bUnion BoxIntegral.Prepartition.IsPartition.biUnion
 -/
 
 #print BoxIntegral.Prepartition.IsPartition.restrict /-
 protected theorem restrict (h : IsPartition π) (hJ : J ≤ I) : IsPartition (π.restrict J) :=
-  isPartition_iff_unionᵢ_eq.2 <| by simp [h.Union_eq, hJ]
+  isPartition_iff_iUnion_eq.2 <| by simp [h.Union_eq, hJ]
 #align box_integral.prepartition.is_partition.restrict BoxIntegral.Prepartition.IsPartition.restrict
 -/
 
 #print BoxIntegral.Prepartition.IsPartition.inf /-
 protected theorem inf (h₁ : IsPartition π₁) (h₂ : IsPartition π₂) : IsPartition (π₁ ⊓ π₂) :=
-  isPartition_iff_unionᵢ_eq.2 <| by simp [h₁.Union_eq, h₂.Union_eq]
+  isPartition_iff_iUnion_eq.2 <| by simp [h₁.Union_eq, h₂.Union_eq]
 #align box_integral.prepartition.is_partition.inf BoxIntegral.Prepartition.IsPartition.inf
 -/
 
 end IsPartition
 
-#print BoxIntegral.Prepartition.unionᵢ_bunionᵢ_partition /-
-theorem unionᵢ_bunionᵢ_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
-    (π.bunionᵢ πi).unionᵢ = π.unionᵢ :=
-  (unionᵢ_bunionᵢ _ _).trans <|
-    unionᵢ_congr_of_surjective id surjective_id fun J =>
-      unionᵢ_congr_of_surjective id surjective_id fun hJ => (h J hJ).unionᵢ_eq
-#align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.unionᵢ_bunionᵢ_partition
+#print BoxIntegral.Prepartition.iUnion_biUnion_partition /-
+theorem iUnion_biUnion_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
+    (π.biUnion πi).iUnion = π.iUnion :=
+  (iUnion_biUnion _ _).trans <|
+    iUnion_congr_of_surjective id surjective_id fun J =>
+      iUnion_congr_of_surjective id surjective_id fun hJ => (h J hJ).iUnion_eq
+#align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.iUnion_biUnion_partition
 -/
 
 /- warning: box_integral.prepartition.is_partition_disj_union_of_eq_diff -> BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff is a dubious translation:
 lean 3 declaration is
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.subst.{succ u1} (Set.{u1} (ι -> Real)) (fun (_x : Set.{u1} (ι -> Real)) => 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.Prepartition.unionᵢ.{u1} ι I π₁) _x) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) h) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) ((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))) I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))))))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.subst.{succ u1} (Set.{u1} (ι -> Real)) (fun (_x : Set.{u1} (ι -> Real)) => 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.Prepartition.iUnion.{u1} ι I π₁) _x) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) h) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) ((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))) I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.rec.{0, succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) (fun (x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575 : Set.{u1} (ι -> Real)) (h._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11576 : Eq.{succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) => 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.Prepartition.unionᵢ.{u1} ι I π₁) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Box.toSet.{u1} ι I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.instBooleanAlgebraSet.{u1} (ι -> Real)))) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) h)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.rec.{0, succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) (fun (x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575 : Set.{u1} (ι -> Real)) (h._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11576 : Eq.{succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) => 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.Prepartition.iUnion.{u1} ι I π₁) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁) (BoxIntegral.Box.toSet.{u1} ι I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.instBooleanAlgebraSet.{u1} (ι -> Real)))) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.iUnion.{u1} ι I π₁)) h)))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiffₓ'. -/
-theorem isPartitionDisjUnionOfEqDiff (h : π₂.unionᵢ = I \ π₁.unionᵢ) :
+theorem isPartitionDisjUnionOfEqDiff (h : π₂.iUnion = I \ π₁.iUnion) :
     IsPartition (π₁.disjUnion π₂ <| h.symm ▸ disjoint_sdiff_self_right) :=
-  isPartition_iff_unionᵢ_eq.2 <| (unionᵢ_disjUnion _).trans <| by simp [h, π₁.Union_subset]
+  isPartition_iff_iUnion_eq.2 <| (iUnion_disjUnion _).trans <| by simp [h, π₁.Union_subset]
 #align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff
 
 end Prepartition

mathlib commit https://github.com/leanprover-community/mathlib/commit/36b8aa61ea7c05727161f96a0532897bd72aedab

@@ -1237,7 +1237,7 @@ theorem unionᵢ_bunionᵢ_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
 lean 3 declaration is
   forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.subst.{succ u1} (Set.{u1} (ι -> Real)) (fun (_x : Set.{u1} (ι -> Real)) => 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.Prepartition.unionᵢ.{u1} ι I π₁) _x) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) h) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) ((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))) I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))))))
 but is expected to have type
-  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.rec.{0, succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) (fun (x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11577 : Set.{u1} (ι -> Real)) (h._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11578 : Eq.{succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11577) => 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.Prepartition.unionᵢ.{u1} ι I π₁) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11577) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Box.toSet.{u1} ι I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.instBooleanAlgebraSet.{u1} (ι -> Real)))) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) h)))
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.rec.{0, succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) (fun (x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575 : Set.{u1} (ι -> Real)) (h._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11576 : Eq.{succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) => 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.Prepartition.unionᵢ.{u1} ι I π₁) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11575) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Box.toSet.{u1} ι I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.instBooleanAlgebraSet.{u1} (ι -> Real)))) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) h)))
 Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiffₓ'. -/
 theorem isPartitionDisjUnionOfEqDiff (h : π₂.unionᵢ = I \ π₁.unionᵢ) :
     IsPartition (π₁.disjUnion π₂ <| h.symm ▸ disjoint_sdiff_self_right) :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/fa78268d4d77cb2b2fbc89f0527e2e7807763780

@@ -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.basic
-! leanprover-community/mathlib commit 84dc0bd6619acaea625086d6f53cb35cdd554219
+! leanprover-community/mathlib commit 9d2f0748e6c50d7a2657c564b1ff2c695b39148d
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.Analysis.BoxIntegral.Box.Basic
 /-!
 # Partitions of rectangular boxes in `ℝⁿ`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define (pre)partitions of rectangular boxes in `ℝⁿ`.  A partition of a box `I` in
 `ℝⁿ` (see `box_integral.prepartition` and `box_integral.prepartition.is_partition`) is a finite set
 of pairwise disjoint boxes such that their union is exactly `I`. We use `boxes : finset (box ι)` to

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

@@ -51,6 +51,7 @@ namespace BoxIntegral
 
 variable {ι : Type _}
 
+#print BoxIntegral.Prepartition /-
 /-- A prepartition of `I : box_integral.box ι` is a finite set of pairwise disjoint subboxes of
 `I`. -/
 structure Prepartition (I : Box ι) where
@@ -58,6 +59,7 @@ structure Prepartition (I : Box ι) where
   le_of_mem' : ∀ J ∈ boxes, J ≤ I
   PairwiseDisjoint : Set.Pairwise (↑boxes) (Disjoint on (coe : Box ι → Set (ι → ℝ)))
 #align box_integral.prepartition BoxIntegral.Prepartition
+-/
 
 namespace Prepartition
 
@@ -66,66 +68,108 @@ variable {I J J₁ J₂ : Box ι} (π : Prepartition I) {π₁ π₂ : Prepartit
 instance : Membership (Box ι) (Prepartition I) :=
   ⟨fun J π => J ∈ π.boxes⟩
 
+#print BoxIntegral.Prepartition.mem_boxes /-
 @[simp]
 theorem mem_boxes : J ∈ π.boxes ↔ J ∈ π :=
   Iff.rfl
 #align box_integral.prepartition.mem_boxes BoxIntegral.Prepartition.mem_boxes
+-/
 
+/- warning: box_integral.prepartition.mem_mk -> BoxIntegral.Prepartition.mem_mk is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {s : Finset.{u1} (BoxIntegral.Box.{u1} ι)} {h₁ : forall (J : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasMem.{u1} (BoxIntegral.Box.{u1} ι)) J s) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I)} {h₂ : Set.Pairwise.{u1} (BoxIntegral.Box.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.Set.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) s) (Function.onFun.{succ u1, succ u1, 1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) Prop (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))))) ((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)))))}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.mk.{u1} ι I s h₁ h₂)) (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasMem.{u1} (BoxIntegral.Box.{u1} ι)) J s)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {s : Finset.{u1} (BoxIntegral.Box.{u1} ι)} {h₁ : forall (J : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instMembershipFinset.{u1} (BoxIntegral.Box.{u1} ι)) J s) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I)} {h₂ : Set.Pairwise.{u1} (BoxIntegral.Box.{u1} ι) (Finset.toSet.{u1} (BoxIntegral.Box.{u1} ι) s) (Function.onFun.{succ u1, succ u1, 1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) Prop (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.Box.toSet.{u1} ι))}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.mk.{u1} ι I s h₁ h₂)) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instMembershipFinset.{u1} (BoxIntegral.Box.{u1} ι)) J s)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_mk BoxIntegral.Prepartition.mem_mkₓ'. -/
 @[simp]
 theorem mem_mk {s h₁ h₂} : J ∈ (mk s h₁ h₂ : Prepartition I) ↔ J ∈ s :=
   Iff.rfl
 #align box_integral.prepartition.mem_mk BoxIntegral.Prepartition.mem_mk
 
+/- warning: box_integral.prepartition.disjoint_coe_of_mem -> BoxIntegral.Prepartition.disjoint_coe_of_mem is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J₁ : BoxIntegral.Box.{u1} ι} {J₂ : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J₁ π) -> (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J₂ π) -> (Ne.{succ u1} (BoxIntegral.Box.{u1} ι) J₁ J₂) -> (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)))) ((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))) J₁) ((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))) J₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J₁ : BoxIntegral.Box.{u1} ι} {J₂ : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J₁ π) -> (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J₂ π) -> (Ne.{succ u1} (BoxIntegral.Box.{u1} ι) J₁ J₂) -> (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.Box.toSet.{u1} ι J₁) (BoxIntegral.Box.toSet.{u1} ι J₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disjoint_coe_of_mem BoxIntegral.Prepartition.disjoint_coe_of_memₓ'. -/
 theorem disjoint_coe_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (h : J₁ ≠ J₂) :
     Disjoint (J₁ : Set (ι → ℝ)) J₂ :=
   π.PairwiseDisjoint h₁ h₂ h
 #align box_integral.prepartition.disjoint_coe_of_mem BoxIntegral.Prepartition.disjoint_coe_of_mem
 
+#print BoxIntegral.Prepartition.eq_of_mem_of_mem /-
 theorem eq_of_mem_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (hx₁ : x ∈ J₁) (hx₂ : x ∈ J₂) : J₁ = J₂ :=
   by_contra fun H => (π.disjoint_coe_of_mem h₁ h₂ H).le_bot ⟨hx₁, hx₂⟩
 #align box_integral.prepartition.eq_of_mem_of_mem BoxIntegral.Prepartition.eq_of_mem_of_mem
+-/
 
+#print BoxIntegral.Prepartition.eq_of_le_of_le /-
 theorem eq_of_le_of_le (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (hle₁ : J ≤ J₁) (hle₂ : J ≤ J₂) : J₁ = J₂ :=
   π.eq_of_mem_of_mem h₁ h₂ (hle₁ J.upper_mem) (hle₂ J.upper_mem)
 #align box_integral.prepartition.eq_of_le_of_le BoxIntegral.Prepartition.eq_of_le_of_le
+-/
 
+#print BoxIntegral.Prepartition.eq_of_le /-
 theorem eq_of_le (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (hle : J₁ ≤ J₂) : J₁ = J₂ :=
   π.eq_of_le_of_le h₁ h₂ le_rfl hle
 #align box_integral.prepartition.eq_of_le BoxIntegral.Prepartition.eq_of_le
+-/
 
+#print BoxIntegral.Prepartition.le_of_mem /-
 theorem le_of_mem (hJ : J ∈ π) : J ≤ I :=
   π.le_of_mem' J hJ
 #align box_integral.prepartition.le_of_mem BoxIntegral.Prepartition.le_of_mem
+-/
 
+/- warning: box_integral.prepartition.lower_le_lower -> BoxIntegral.Prepartition.lower_le_lower 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), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π) -> (LE.le.{u1} (ι -> Real) (Pi.hasLe.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (i : ι) => Real.hasLe)) (BoxIntegral.Box.lower.{u1} ι I) (BoxIntegral.Box.lower.{u1} ι 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), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π) -> (LE.le.{u1} (ι -> Real) (Pi.hasLe.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (i : ι) => Real.instLEReal)) (BoxIntegral.Box.lower.{u1} ι I) (BoxIntegral.Box.lower.{u1} ι J))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.lower_le_lower BoxIntegral.Prepartition.lower_le_lowerₓ'. -/
 theorem lower_le_lower (hJ : J ∈ π) : I.lower ≤ J.lower :=
   Box.antitone_lower (π.le_of_mem hJ)
 #align box_integral.prepartition.lower_le_lower BoxIntegral.Prepartition.lower_le_lower
 
+/- warning: box_integral.prepartition.upper_le_upper -> BoxIntegral.Prepartition.upper_le_upper 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), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π) -> (LE.le.{u1} (ι -> Real) (Pi.hasLe.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (i : ι) => Real.hasLe)) (BoxIntegral.Box.upper.{u1} ι J) (BoxIntegral.Box.upper.{u1} ι I))
+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), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π) -> (LE.le.{u1} (ι -> Real) (Pi.hasLe.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (i : ι) => Real.instLEReal)) (BoxIntegral.Box.upper.{u1} ι J) (BoxIntegral.Box.upper.{u1} ι I))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.upper_le_upper BoxIntegral.Prepartition.upper_le_upperₓ'. -/
 theorem upper_le_upper (hJ : J ∈ π) : J.upper ≤ I.upper :=
   Box.monotone_upper (π.le_of_mem hJ)
 #align box_integral.prepartition.upper_le_upper BoxIntegral.Prepartition.upper_le_upper
 
+#print BoxIntegral.Prepartition.injective_boxes /-
 theorem injective_boxes : Function.Injective (boxes : Prepartition I → Finset (Box ι)) :=
   by
   rintro ⟨s₁, h₁, h₁'⟩ ⟨s₂, h₂, h₂'⟩ (rfl : s₁ = s₂)
   rfl
 #align box_integral.prepartition.injective_boxes BoxIntegral.Prepartition.injective_boxes
+-/
 
+#print BoxIntegral.Prepartition.ext /-
 @[ext]
 theorem ext (h : ∀ J, J ∈ π₁ ↔ J ∈ π₂) : π₁ = π₂ :=
   injective_boxes <| Finset.ext h
 #align box_integral.prepartition.ext BoxIntegral.Prepartition.ext
+-/
 
+#print BoxIntegral.Prepartition.single /-
 /-- The singleton prepartition `{J}`, `J ≤ I`. -/
 @[simps]
 def single (I J : Box ι) (h : J ≤ I) : Prepartition I :=
   ⟨{J}, by simpa, by simp⟩
 #align box_integral.prepartition.single BoxIntegral.Prepartition.single
+-/
 
+#print BoxIntegral.Prepartition.mem_single /-
 @[simp]
 theorem mem_single {J'} (h : J ≤ I) : J' ∈ single I J h ↔ J' = J :=
   mem_singleton
 #align box_integral.prepartition.mem_single BoxIntegral.Prepartition.mem_single
+-/
 
 /-- We say that `π ≤ π'` if each box of `π` is a subbox of some box of `π'`. -/
 instance : LE (Prepartition I) :=
@@ -162,30 +206,66 @@ instance : OrderBot (Prepartition I)
 instance : Inhabited (Prepartition I) :=
   ⟨⊤⟩
 
+/- warning: box_integral.prepartition.le_def -> BoxIntegral.Prepartition.le_def is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) (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 π₁) -> (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' π₂) (fun (H : Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J' π₂) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J J'))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) (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 π₁) -> (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' π₂) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J J'))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_def BoxIntegral.Prepartition.le_defₓ'. -/
 theorem le_def : π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∃ J' ∈ π₂, J ≤ J' :=
   Iff.rfl
 #align box_integral.prepartition.le_def BoxIntegral.Prepartition.le_def
 
+/- warning: box_integral.prepartition.mem_top -> BoxIntegral.Prepartition.mem_top is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderTop.{u1} ι I)))) (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}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι I)))) (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) J I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_top BoxIntegral.Prepartition.mem_topₓ'. -/
 @[simp]
 theorem mem_top : J ∈ (⊤ : Prepartition I) ↔ J = I :=
   mem_singleton
 #align box_integral.prepartition.mem_top BoxIntegral.Prepartition.mem_top
 
+/- warning: box_integral.prepartition.top_boxes -> BoxIntegral.Prepartition.top_boxes is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderTop.{u1} ι I)))) (Singleton.singleton.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasSingleton.{u1} (BoxIntegral.Box.{u1} ι)) I)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι I)))) (Singleton.singleton.{u1, u1} (BoxIntegral.Box.{u1} ι) (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instSingletonFinset.{u1} (BoxIntegral.Box.{u1} ι)) I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.top_boxes BoxIntegral.Prepartition.top_boxesₓ'. -/
 @[simp]
 theorem top_boxes : (⊤ : Prepartition I).boxes = {I} :=
   rfl
 #align box_integral.prepartition.top_boxes BoxIntegral.Prepartition.top_boxes
 
+/- warning: box_integral.prepartition.not_mem_bot -> BoxIntegral.Prepartition.not_mem_bot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι}, Not (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι}, Not (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.not_mem_bot BoxIntegral.Prepartition.not_mem_botₓ'. -/
 @[simp]
 theorem not_mem_bot : J ∉ (⊥ : Prepartition I) :=
   id
 #align box_integral.prepartition.not_mem_bot BoxIntegral.Prepartition.not_mem_bot
 
+/- warning: box_integral.prepartition.bot_boxes -> BoxIntegral.Prepartition.bot_boxes is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasEmptyc.{u1} (BoxIntegral.Box.{u1} ι)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instEmptyCollectionFinset.{u1} (BoxIntegral.Box.{u1} ι)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bot_boxes BoxIntegral.Prepartition.bot_boxesₓ'. -/
 @[simp]
 theorem bot_boxes : (⊥ : Prepartition I).boxes = ∅ :=
   rfl
 #align box_integral.prepartition.bot_boxes BoxIntegral.Prepartition.bot_boxes
 
+/- warning: box_integral.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq -> BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (x : ι -> Real), Set.InjOn.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => setOf.{u1} ι (fun (i : ι) => Eq.{1} Real (BoxIntegral.Box.lower.{u1} ι J i) (x i))) (setOf.{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.hasMem.{u1} ι I) J π) (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} (π : BoxIntegral.Prepartition.{u1} ι I) (x : ι -> Real), Set.InjOn.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => setOf.{u1} ι (fun (i : ι) => Eq.{1} Real (BoxIntegral.Box.lower.{u1} ι J i) (x i))) (setOf.{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} (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))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eqₓ'. -/
 /-- An auxiliary lemma used to prove that the same point can't belong to more than
 `2 ^ fintype.card ι` closed boxes of a prepartition. -/
 theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
@@ -208,6 +288,12 @@ theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
     exact ⟨x i, ⟨hi₁, hx₁.2 i⟩, ⟨hi₂, hx₂.2 i⟩⟩
 #align box_integral.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq
 
+/- warning: box_integral.prepartition.card_filter_mem_Icc_le -> BoxIntegral.Prepartition.card_filter_mem_Icc_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (x : ι -> Real), LE.le.{0} Nat Nat.hasLe (Finset.card.{u1} (BoxIntegral.Box.{u1} ι) (Finset.filter.{u1} (BoxIntegral.Box.{u1} ι) (fun (J : BoxIntegral.Box.{u1} ι) => 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)) (fun (a : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (J : BoxIntegral.Box.{u1} ι) => 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)) a)) (BoxIntegral.Prepartition.boxes.{u1} ι I π))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat (Monoid.Pow.{0} Nat Nat.monoid)) (OfNat.ofNat.{0} Nat 2 (OfNat.mk.{0} Nat 2 (bit0.{0} Nat Nat.hasAdd (One.one.{0} Nat Nat.hasOne)))) (Fintype.card.{u1} ι _inst_1))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) [_inst_1 : Fintype.{u1} ι] (x : ι -> Real), LE.le.{0} Nat instLENat (Finset.card.{u1} (BoxIntegral.Box.{u1} ι) (Finset.filter.{u1} (BoxIntegral.Box.{u1} ι) (fun (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)) 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)) (fun (a : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (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)) 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)) a)) (BoxIntegral.Prepartition.boxes.{u1} ι I π))) (HPow.hPow.{0, 0, 0} Nat Nat Nat (instHPow.{0, 0} Nat Nat instPowNat) (OfNat.ofNat.{0} Nat 2 (instOfNatNat 2)) (Fintype.card.{u1} ι _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_leₓ'. -/
 /-- The set of boxes of a prepartition that contain `x` in their closures has cardinality
 at most `2 ^ fintype.card ι`. -/
 theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
@@ -220,65 +306,119 @@ theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
   simpa only [Finset.mem_filter] using π.inj_on_set_of_mem_Icc_set_of_lower_eq x
 #align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_le
 
+#print BoxIntegral.Prepartition.unionᵢ /-
 /-- Given a prepartition `π : box_integral.prepartition I`, `π.Union` is the part of `I` covered by
 the boxes of `π`. -/
-protected def union : Set (ι → ℝ) :=
+protected def unionᵢ : Set (ι → ℝ) :=
   ⋃ J ∈ π, ↑J
-#align box_integral.prepartition.Union BoxIntegral.Prepartition.union
+#align box_integral.prepartition.Union BoxIntegral.Prepartition.unionᵢ
+-/
 
-theorem union_def : π.unionᵢ = ⋃ J ∈ π, ↑J :=
+#print BoxIntegral.Prepartition.unionᵢ_def /-
+theorem unionᵢ_def : π.unionᵢ = ⋃ J ∈ π, ↑J :=
   rfl
-#align box_integral.prepartition.Union_def BoxIntegral.Prepartition.union_def
+#align box_integral.prepartition.Union_def BoxIntegral.Prepartition.unionᵢ_def
+-/
 
-theorem union_def' : π.unionᵢ = ⋃ J ∈ π.boxes, ↑J :=
+#print BoxIntegral.Prepartition.unionᵢ_def' /-
+theorem unionᵢ_def' : π.unionᵢ = ⋃ J ∈ π.boxes, ↑J :=
   rfl
-#align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.union_def'
+#align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.unionᵢ_def'
+-/
 
+/- warning: box_integral.prepartition.mem_Union -> BoxIntegral.Prepartition.mem_unionᵢ is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) x (BoxIntegral.Prepartition.unionᵢ.{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.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} (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.Prepartition.{u1} ι I) {x : ι -> Real}, Iff (Membership.mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.instMembershipSet.{u1} (ι -> Real)) x (BoxIntegral.Prepartition.unionᵢ.{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.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{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.prepartition.mem_Union BoxIntegral.Prepartition.mem_unionᵢₓ'. -/
 @[simp]
-theorem mem_union : x ∈ π.unionᵢ ↔ ∃ J ∈ π, x ∈ J :=
+theorem mem_unionᵢ : x ∈ π.unionᵢ ↔ ∃ J ∈ π, x ∈ J :=
   Set.mem_unionᵢ₂
-#align box_integral.prepartition.mem_Union BoxIntegral.Prepartition.mem_union
+#align box_integral.prepartition.mem_Union BoxIntegral.Prepartition.mem_unionᵢ
 
+#print BoxIntegral.Prepartition.unionᵢ_single /-
 @[simp]
-theorem union_single (h : J ≤ I) : (single I J h).unionᵢ = J := by simp [Union_def]
-#align box_integral.prepartition.Union_single BoxIntegral.Prepartition.union_single
+theorem unionᵢ_single (h : J ≤ I) : (single I J h).unionᵢ = J := by simp [Union_def]
+#align box_integral.prepartition.Union_single BoxIntegral.Prepartition.unionᵢ_single
+-/
 
+/- warning: box_integral.prepartition.Union_top -> BoxIntegral.Prepartition.unionᵢ_top is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderTop.{u1} ι I)))) ((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))) I)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι I)))) (BoxIntegral.Box.toSet.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.unionᵢ_topₓ'. -/
 @[simp]
-theorem union_top : (⊤ : Prepartition I).unionᵢ = I := by simp [prepartition.Union]
-#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.union_top
-
+theorem unionᵢ_top : (⊤ : Prepartition I).unionᵢ = I := by simp [prepartition.Union]
+#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.unionᵢ_top
+
+/- warning: box_integral.prepartition.Union_eq_empty -> BoxIntegral.Prepartition.unionᵢ_eq_empty is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.hasEmptyc.{u1} (ι -> Real)))) (Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) π₁ (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.instEmptyCollectionSet.{u1} (ι -> Real)))) (Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) π₁ (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.unionᵢ_eq_emptyₓ'. -/
 @[simp]
-theorem union_eq_empty : π₁.unionᵢ = ∅ ↔ π₁ = ⊥ := by
+theorem unionᵢ_eq_empty : π₁.unionᵢ = ∅ ↔ π₁ = ⊥ := by
   simp [← injective_boxes.eq_iff, Finset.ext_iff, prepartition.Union, imp_false]
-#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.union_eq_empty
-
+#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.unionᵢ_eq_empty
+
+/- warning: box_integral.prepartition.Union_bot -> BoxIntegral.Prepartition.unionᵢ_bot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.hasEmptyc.{u1} (ι -> Real)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι}, Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I)))) (EmptyCollection.emptyCollection.{u1} (Set.{u1} (ι -> Real)) (Set.instEmptyCollectionSet.{u1} (ι -> Real)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.unionᵢ_botₓ'. -/
 @[simp]
-theorem union_bot : (⊥ : Prepartition I).unionᵢ = ∅ :=
-  union_eq_empty.2 rfl
-#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.union_bot
+theorem unionᵢ_bot : (⊥ : Prepartition I).unionᵢ = ∅ :=
+  unionᵢ_eq_empty.2 rfl
+#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.unionᵢ_bot
 
-theorem subset_union (h : J ∈ π) : ↑J ⊆ π.unionᵢ :=
+#print BoxIntegral.Prepartition.subset_unionᵢ /-
+theorem subset_unionᵢ (h : J ∈ π) : ↑J ⊆ π.unionᵢ :=
   subset_bunionᵢ_of_mem h
-#align box_integral.prepartition.subset_Union BoxIntegral.Prepartition.subset_union
+#align box_integral.prepartition.subset_Union BoxIntegral.Prepartition.subset_unionᵢ
+-/
 
-theorem union_subset : π.unionᵢ ⊆ I :=
+#print BoxIntegral.Prepartition.unionᵢ_subset /-
+theorem unionᵢ_subset : π.unionᵢ ⊆ I :=
   unionᵢ₂_subset π.le_of_mem'
-#align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.union_subset
+#align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.unionᵢ_subset
+-/
 
+/- warning: box_integral.prepartition.Union_mono -> BoxIntegral.Prepartition.unionᵢ_mono is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.instHasSubsetSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.unionᵢ_monoₓ'. -/
 @[mono]
-theorem union_mono (h : π₁ ≤ π₂) : π₁.unionᵢ ⊆ π₂.unionᵢ := fun x hx =>
+theorem unionᵢ_mono (h : π₁ ≤ π₂) : π₁.unionᵢ ⊆ π₂.unionᵢ := fun x hx =>
   let ⟨J₁, hJ₁, hx⟩ := π₁.mem_unionᵢ.1 hx
   let ⟨J₂, hJ₂, hle⟩ := h hJ₁
   π₂.mem_unionᵢ.2 ⟨J₂, hJ₂, hle hx⟩
-#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.union_mono
-
-theorem disjoint_boxes_of_disjoint_union (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.unionᵢ_mono
+
+/- warning: box_integral.prepartition.disjoint_boxes_of_disjoint_Union -> BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_unionᵢ is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (Disjoint.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.partialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.orderBot.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (Disjoint.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.partialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instOrderBotFinsetToLEToPreorderPartialOrder.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_unionᵢₓ'. -/
+theorem disjoint_boxes_of_disjoint_unionᵢ (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
     Disjoint π₁.boxes π₂.boxes :=
   Finset.disjoint_left.2 fun J h₁ h₂ =>
     Disjoint.le_bot (h.mono (π₁.subset_unionᵢ h₁) (π₂.subset_unionᵢ h₂)) ⟨J.upper_mem, J.upper_mem⟩
-#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_union
-
-theorem le_iff_nonempty_imp_le_and_union_subset :
+#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_unionᵢ
+
+/- warning: box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset -> BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_unionᵢ_subset is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) (And (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) ((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'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J J'))) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) (And (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Box.toSet.{u1} ι J'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J J'))) (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.instHasSubsetSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_unionᵢ_subsetₓ'. -/
+theorem le_iff_nonempty_imp_le_and_unionᵢ_subset :
     π₁ ≤ π₂ ↔
       (∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J') ∧ π₁.unionᵢ ⊆ π₂.unionᵢ :=
   by
@@ -291,23 +431,26 @@ theorem le_iff_nonempty_imp_le_and_union_subset :
     simp only [Set.subset_def, mem_Union] at HU
     rcases HU J.upper ⟨J, hJ, J.upper_mem⟩ with ⟨J₂, hJ₂, hx⟩
     exact ⟨J₂, hJ₂, H _ hJ _ hJ₂ ⟨_, J.upper_mem, hx⟩⟩
-#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_union_subset
+#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_unionᵢ_subset
 
-theorem eq_of_boxes_subset_union_superset (h₁ : π₁.boxes ⊆ π₂.boxes) (h₂ : π₂.unionᵢ ⊆ π₁.unionᵢ) :
+#print BoxIntegral.Prepartition.eq_of_boxes_subset_unionᵢ_superset /-
+theorem eq_of_boxes_subset_unionᵢ_superset (h₁ : π₁.boxes ⊆ π₂.boxes) (h₂ : π₂.unionᵢ ⊆ π₁.unionᵢ) :
     π₁ = π₂ :=
   (le_antisymm fun J hJ => ⟨J, h₁ hJ, le_rfl⟩) <|
-    le_iff_nonempty_imp_le_and_union_subset.2
+    le_iff_nonempty_imp_le_and_unionᵢ_subset.2
       ⟨fun J₁ hJ₁ J₂ hJ₂ Hne =>
         (π₂.eq_of_mem_of_mem hJ₁ (h₁ hJ₂) Hne.choose_spec.1 Hne.choose_spec.2).le, h₂⟩
-#align box_integral.prepartition.eq_of_boxes_subset_Union_superset BoxIntegral.Prepartition.eq_of_boxes_subset_union_superset
+#align box_integral.prepartition.eq_of_boxes_subset_Union_superset BoxIntegral.Prepartition.eq_of_boxes_subset_unionᵢ_superset
+-/
 
+#print BoxIntegral.Prepartition.bunionᵢ /-
 /-- Given a prepartition `π` of a box `I` and a collection of prepartitions `πi J` of all boxes
 `J ∈ π`, returns the prepartition of `I` into the union of the boxes of all `πi J`.
 
 Though we only use the values of `πi` on the boxes of `π`, we require `πi` to be a globally defined
 function. -/
 @[simps]
-def bUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
+def bunionᵢ (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
     where
   boxes := π.boxes.bunionᵢ fun J => (πi J).boxes
   le_of_mem' J hJ :=
@@ -324,44 +467,75 @@ def bUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I
     obtain rfl : J₁ = J₂
     exact π.eq_of_mem_of_mem hJ₁ hJ₂ ((πi J₁).le_of_mem hJ₁' hx₁) ((πi J₂).le_of_mem hJ₂' hx₂)
     exact (πi J₁).eq_of_mem_of_mem hJ₁' hJ₂' hx₁ hx₂
-#align box_integral.prepartition.bUnion BoxIntegral.Prepartition.bUnion
+#align box_integral.prepartition.bUnion BoxIntegral.Prepartition.bunionᵢ
+-/
 
 variable {πi πi₁ πi₂ : ∀ J : Box ι, Prepartition J}
 
+/- warning: box_integral.prepartition.mem_bUnion -> BoxIntegral.Prepartition.mem_bunionᵢ 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.Prepartition.{u1} ι J}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.bunionᵢ.{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.Prepartition.{u1} ι J') (BoxIntegral.Prepartition.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.Prepartition.{u1} ι J}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.bunionᵢ.{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.Prepartition.{u1} ι J') (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J') J (πi J'))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_bunionᵢₓ'. -/
 @[simp]
-theorem mem_bUnion : J ∈ π.bunionᵢ πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [bUnion]
-#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_bUnion
-
-theorem bUnion_le (πi : ∀ J, Prepartition J) : π.bunionᵢ πi ≤ π := fun J hJ =>
+theorem mem_bunionᵢ : J ∈ π.bunionᵢ πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [bUnion]
+#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_bunionᵢ
+
+/- warning: box_integral.prepartition.bUnion_le -> BoxIntegral.Prepartition.bunionᵢ_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.bunionᵢ_leₓ'. -/
+theorem bunionᵢ_le (πi : ∀ J, Prepartition J) : π.bunionᵢ πi ≤ π := fun J hJ =>
   let ⟨J', hJ', hJ⟩ := π.mem_bunionᵢ.1 hJ
   ⟨J', hJ', (πi J').le_of_mem hJ⟩
-#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.bUnion_le
-
+#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.bunionᵢ_le
+
+/- warning: box_integral.prepartition.bUnion_top -> BoxIntegral.Prepartition.bunionᵢ_top is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π (fun (_x : BoxIntegral.Box.{u1} ι) => Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (BoxIntegral.Prepartition.hasLe.{u1} ι _x) (BoxIntegral.Prepartition.orderTop.{u1} ι _x)))) π
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π (fun (_x : BoxIntegral.Box.{u1} ι) => Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι _x) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι _x) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι _x)))) π
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.bunionᵢ_topₓ'. -/
 @[simp]
-theorem bUnion_top : (π.bunionᵢ fun _ => ⊤) = π :=
+theorem bunionᵢ_top : (π.bunionᵢ fun _ => ⊤) = π :=
   by
   ext
   simp
-#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.bUnion_top
+#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.bunionᵢ_top
 
+#print BoxIntegral.Prepartition.bunionᵢ_congr /-
 @[congr]
-theorem bUnion_congr (h : π₁ = π₂) (hi : ∀ J ∈ π₁, πi₁ J = πi₂ J) :
+theorem bunionᵢ_congr (h : π₁ = π₂) (hi : ∀ J ∈ π₁, πi₁ J = πi₂ J) :
     π₁.bunionᵢ πi₁ = π₂.bunionᵢ πi₂ := by
   subst π₂
   ext J
   simp (config := { contextual := true }) [hi]
-#align box_integral.prepartition.bUnion_congr BoxIntegral.Prepartition.bUnion_congr
+#align box_integral.prepartition.bUnion_congr BoxIntegral.Prepartition.bunionᵢ_congr
+-/
 
-theorem bUnion_congr_of_le (h : π₁ = π₂) (hi : ∀ J ≤ I, πi₁ J = πi₂ J) :
+#print BoxIntegral.Prepartition.bunionᵢ_congr_of_le /-
+theorem bunionᵢ_congr_of_le (h : π₁ = π₂) (hi : ∀ J ≤ I, πi₁ J = πi₂ J) :
     π₁.bunionᵢ πi₁ = π₂.bunionᵢ πi₂ :=
-  bUnion_congr h fun J hJ => hi J (π₁.le_of_mem hJ)
-#align box_integral.prepartition.bUnion_congr_of_le BoxIntegral.Prepartition.bUnion_congr_of_le
+  bunionᵢ_congr h fun J hJ => hi J (π₁.le_of_mem hJ)
+#align box_integral.prepartition.bUnion_congr_of_le BoxIntegral.Prepartition.bunionᵢ_congr_of_le
+-/
 
+#print BoxIntegral.Prepartition.unionᵢ_bunionᵢ /-
 @[simp]
-theorem union_bUnion (πi : ∀ J : Box ι, Prepartition J) :
+theorem unionᵢ_bunionᵢ (πi : ∀ J : Box ι, Prepartition J) :
     (π.bunionᵢ πi).unionᵢ = ⋃ J ∈ π, (πi J).unionᵢ := by simp [prepartition.Union]
-#align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.union_bUnion
+#align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.unionᵢ_bunionᵢ
+-/
 
+/- warning: box_integral.prepartition.sum_bUnion_boxes -> BoxIntegral.Prepartition.sum_bunionᵢ_boxes is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.bunionᵢ.{u1, u1} (BoxIntegral.Box.{u1} ι) (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 π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (Finset.bunionᵢ.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b) (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => BoxIntegral.Prepartition.boxes.{u1} ι J (πi J))) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι J (πi J)) (fun (J' : BoxIntegral.Box.{u1} ι) => f J')))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_bunionᵢ_boxesₓ'. -/
 @[simp]
 theorem sum_bunionᵢ_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
     (πi : ∀ J, Prepartition J) (f : Box ι → M) :
@@ -372,43 +546,56 @@ theorem sum_bunionᵢ_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
   exact hne (π.eq_of_le_of_le h₁ h₂ ((πi J₁).le_of_mem h₁') ((πi J₂).le_of_mem h₂'))
 #align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_bunionᵢ_boxes
 
+#print BoxIntegral.Prepartition.bunionᵢIndex /-
 /-- Given a box `J ∈ π.bUnion πi`, returns the box `J' ∈ π` such that `J ∈ πi J'`.
 For `J ∉ π.bUnion πi`, returns `I`. -/
-def bUnionIndex (πi : ∀ J, Prepartition J) (J : Box ι) : Box ι :=
+def bunionᵢIndex (πi : ∀ J, Prepartition J) (J : Box ι) : Box ι :=
   if hJ : J ∈ π.bunionᵢ πi then (π.mem_bunionᵢ.1 hJ).some else I
-#align box_integral.prepartition.bUnion_index BoxIntegral.Prepartition.bUnionIndex
+#align box_integral.prepartition.bUnion_index BoxIntegral.Prepartition.bunionᵢIndex
+-/
 
-theorem bUnionIndex_mem (hJ : J ∈ π.bunionᵢ πi) : π.bUnionIndex πi J ∈ π :=
+#print BoxIntegral.Prepartition.bunionᵢIndex_mem /-
+theorem bunionᵢIndex_mem (hJ : J ∈ π.bunionᵢ πi) : π.bunionᵢIndex πi J ∈ π :=
   by
   rw [bUnion_index, dif_pos hJ]
   exact (π.mem_bUnion.1 hJ).choose_spec.fst
-#align box_integral.prepartition.bUnion_index_mem BoxIntegral.Prepartition.bUnionIndex_mem
+#align box_integral.prepartition.bUnion_index_mem BoxIntegral.Prepartition.bunionᵢIndex_mem
+-/
 
-theorem bUnionIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.bUnionIndex πi J ≤ I :=
+#print BoxIntegral.Prepartition.bunionᵢIndex_le /-
+theorem bunionᵢIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.bunionᵢIndex πi J ≤ I :=
   by
   by_cases hJ : J ∈ π.bUnion πi
   · exact π.le_of_mem (π.bUnion_index_mem hJ)
   · rw [bUnion_index, dif_neg hJ]
     exact le_rfl
-#align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.bUnionIndex_le
+#align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.bunionᵢIndex_le
+-/
 
-theorem mem_bUnionIndex (hJ : J ∈ π.bunionᵢ πi) : J ∈ πi (π.bUnionIndex πi J) := by
+#print BoxIntegral.Prepartition.mem_bunionᵢIndex /-
+theorem mem_bunionᵢIndex (hJ : J ∈ π.bunionᵢ πi) : J ∈ πi (π.bunionᵢIndex πi J) := by
   convert(π.mem_bUnion.1 hJ).choose_spec.snd <;> exact dif_pos hJ
-#align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_bUnionIndex
+#align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_bunionᵢIndex
+-/
 
-theorem le_bUnionIndex (hJ : J ∈ π.bunionᵢ πi) : J ≤ π.bUnionIndex πi J :=
-  le_of_mem _ (π.mem_bUnionIndex hJ)
-#align box_integral.prepartition.le_bUnion_index BoxIntegral.Prepartition.le_bUnionIndex
+#print BoxIntegral.Prepartition.le_bunionᵢIndex /-
+theorem le_bunionᵢIndex (hJ : J ∈ π.bunionᵢ πi) : J ≤ π.bunionᵢIndex πi J :=
+  le_of_mem _ (π.mem_bunionᵢIndex hJ)
+#align box_integral.prepartition.le_bUnion_index BoxIntegral.Prepartition.le_bunionᵢIndex
+-/
 
+#print BoxIntegral.Prepartition.bunionᵢIndex_of_mem /-
 /-- Uniqueness property of `box_integral.partition.bUnion_index`. -/
-theorem bUnionIndex_of_mem (hJ : J ∈ π) {J'} (hJ' : J' ∈ πi J) : π.bUnionIndex πi J' = J :=
+theorem bunionᵢIndex_of_mem (hJ : J ∈ π) {J'} (hJ' : J' ∈ πi J) : π.bunionᵢIndex πi J' = J :=
   have : J' ∈ π.bunionᵢ πi := π.mem_bunionᵢ.2 ⟨J, hJ, hJ'⟩
-  π.eq_of_le_of_le (π.bUnionIndex_mem this) hJ (π.le_bUnionIndex this) (le_of_mem _ hJ')
-#align box_integral.prepartition.bUnion_index_of_mem BoxIntegral.Prepartition.bUnionIndex_of_mem
+  π.eq_of_le_of_le (π.bunionᵢIndex_mem this) hJ (π.le_bunionᵢIndex this) (le_of_mem _ hJ')
+#align box_integral.prepartition.bUnion_index_of_mem BoxIntegral.Prepartition.bunionᵢIndex_of_mem
+-/
 
-theorem bUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : Box ι, Prepartition J) :
+#print BoxIntegral.Prepartition.bunionᵢ_assoc /-
+theorem bunionᵢ_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : Box ι, Prepartition J) :
     (π.bunionᵢ fun J => (πi J).bunionᵢ (πi' J)) =
-      (π.bunionᵢ πi).bunionᵢ fun J => πi' (π.bUnionIndex πi J) J :=
+      (π.bunionᵢ πi).bunionᵢ fun J => πi' (π.bunionᵢIndex πi J) J :=
   by
   ext J
   simp only [mem_bUnion, exists_prop]
@@ -419,8 +606,15 @@ theorem bUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : Bo
   · rintro ⟨J₁, ⟨J₂, hJ₂, hJ₁⟩, hJ⟩
     refine' ⟨J₂, hJ₂, J₁, hJ₁, _⟩
     rwa [π.bUnion_index_of_mem hJ₂ hJ₁] at hJ
-#align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.bUnion_assoc
+#align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.bunionᵢ_assoc
+-/
 
+/- warning: box_integral.prepartition.of_with_bot -> BoxIntegral.Prepartition.ofWithBot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))), (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) -> (Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))) -> (BoxIntegral.Prepartition.{u1} ι I)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))), (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) -> (Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))) -> (BoxIntegral.Prepartition.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBotₓ'. -/
 /-- Create a `box_integral.prepartition` from a collection of possibly empty boxes by filtering out
 the empty one if it exists. -/
 def ofWithBot (boxes : Finset (WithBot (Box ι)))
@@ -437,14 +631,26 @@ def ofWithBot (boxes : Finset (WithBot (Box ι)))
     exact box.disjoint_coe.1 (pairwise_disjoint h₁ h₂ (mt Option.some_inj.1 hne))
 #align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBot
 
+/- warning: box_integral.prepartition.mem_of_with_bot -> BoxIntegral.Prepartition.mem_ofWithBot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {h₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {h₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes h₁ h₂)) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) boxes)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {h₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {h₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes h₁ h₂)) (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J) boxes)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBotₓ'. -/
 @[simp]
 theorem mem_ofWithBot {boxes : Finset (WithBot (Box ι))} {h₁ h₂} :
     J ∈ (ofWithBot boxes h₁ h₂ : Prepartition I) ↔ (J : WithBot (Box ι)) ∈ boxes :=
   mem_eraseNone
 #align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBot
 
+/- warning: box_integral.prepartition.Union_of_with_bot -> BoxIntegral.Prepartition.unionᵢ_ofWithBot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.unionᵢ.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.unionᵢ.{u1, 0} (ι -> Real) (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => (fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (HasLiftT.mk.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (CoeTCₓ.coe.{succ u1, succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.withBotCoe.{u1} ι))) J)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (Set.unionᵢ.{u1, succ u1} (ι -> Real) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Set.unionᵢ.{u1, 0} (ι -> Real) (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) (fun (H : Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) => BoxIntegral.Box.withBotToSet.{u1} ι J)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.unionᵢ_ofWithBotₓ'. -/
 @[simp]
-theorem union_ofWithBot (boxes : Finset (WithBot (Box ι)))
+theorem unionᵢ_ofWithBot (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) :
     (ofWithBot boxes le_of_mem pairwise_disjoint).unionᵢ = ⋃ J ∈ boxes, ↑J :=
@@ -453,8 +659,14 @@ theorem union_ofWithBot (boxes : Finset (WithBot (Box ι)))
     simpa [of_with_bot, prepartition.Union]
   simp only [← box.bUnion_coe_eq_coe, @Union_comm _ _ (box ι), @Union_comm _ _ (@Eq _ _ _),
     Union_Union_eq_right]
-#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.union_ofWithBot
-
+#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.unionᵢ_ofWithBot
+
+/- warning: box_integral.prepartition.of_with_bot_le -> BoxIntegral.Prepartition.ofWithBot_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasBot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (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) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J'))))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint) π)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.bot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (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) (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J'))))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint) π)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot_le BoxIntegral.Prepartition.ofWithBot_leₓ'. -/
 theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
     {le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint}
@@ -466,6 +678,12 @@ theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
   simpa [of_with_bot, le_def]
 #align box_integral.prepartition.of_with_bot_le BoxIntegral.Prepartition.ofWithBot_le
 
+/- warning: box_integral.prepartition.le_of_with_bot -> BoxIntegral.Prepartition.le_ofWithBot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (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) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Exists.{0} (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, (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) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => And (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes) (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J) J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_of_with_bot BoxIntegral.Prepartition.le_ofWithBotₓ'. -/
 theorem le_ofWithBot {boxes : Finset (WithBot (Box ι))}
     {le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint}
@@ -477,6 +695,12 @@ theorem le_ofWithBot {boxes : Finset (WithBot (Box ι))}
   exact ⟨J', mem_of_with_bot.2 J'mem, WithBot.coe_le_coe.1 hle⟩
 #align box_integral.prepartition.le_of_with_bot BoxIntegral.Prepartition.le_ofWithBot
 
+/- warning: box_integral.prepartition.of_with_bot_mono -> BoxIntegral.Prepartition.ofWithBot_mono is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {boxes₁ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint₁ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes₁) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))} {boxes₂ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₂ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₂) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))} {pairwise_disjoint₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes₂) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasBot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Exists.{0} (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) (fun (H : Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) => LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₁ le_of_mem₁ pairwise_disjoint₁) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₂ le_of_mem₂ pairwise_disjoint₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {boxes₁ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₁ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint₁ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes₁) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))} {boxes₂ : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))} {le_of_mem₂ : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₂) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))} {pairwise_disjoint₂ : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes₂) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))}, (forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes₁) -> (Ne.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) J (Bot.bot.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.bot.{u1} (BoxIntegral.Box.{u1} ι)))) -> (Exists.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (fun (J' : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => And (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J' boxes₂) (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J J')))) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₁ le_of_mem₁ pairwise_disjoint₁) (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes₂ le_of_mem₂ pairwise_disjoint₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.of_with_bot_mono BoxIntegral.Prepartition.ofWithBot_monoₓ'. -/
 theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
     {le_of_mem₁ : ∀ J ∈ boxes₁, (J : WithBot (Box ι)) ≤ I}
     {pairwise_disjoint₁ : Set.Pairwise (boxes₁ : Set (WithBot (Box ι))) Disjoint}
@@ -488,6 +712,12 @@ theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
   le_ofWithBot _ fun J hJ => H J (mem_ofWithBot.1 hJ) WithBot.coe_ne_bot
 #align box_integral.prepartition.of_with_bot_mono BoxIntegral.Prepartition.ofWithBot_mono
 
+/- warning: box_integral.prepartition.sum_of_with_bot -> BoxIntegral.Prepartition.sum_ofWithBot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.Mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.hasMem.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)))) J ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (HasLiftT.mk.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (CoeTCₓ.coe.{succ u1, succ u1} (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Set.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.Set.hasCoeT.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))))) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.partialOrder.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)))) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) _inst_1 boxes (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Option.elim'.{u1, u2} (BoxIntegral.Box.{u1} ι) M (OfNat.ofNat.{u2} M 0 (OfNat.mk.{u2} M 0 (Zero.zero.{u2} M (AddZeroClass.toHasZero.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))))) f J))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (boxes : Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (le_of_mem : forall (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)), (Membership.mem.{u1, u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) (Finset.instMembershipFinset.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι))) J boxes) -> (LE.le.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Preorder.toLE.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.preorder.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))) J (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) I))) (pairwise_disjoint : Set.Pairwise.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.toSet.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) boxes) (Disjoint.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.partialOrder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)) (WithBot.orderBot.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι)))))) (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.Prepartition.ofWithBot.{u1} ι I boxes le_of_mem pairwise_disjoint)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) _inst_1 boxes (fun (J : WithBot.{u1} (BoxIntegral.Box.{u1} ι)) => Option.elim'.{u1, u2} (BoxIntegral.Box.{u1} ι) M (OfNat.ofNat.{u2} M 0 (Zero.toOfNat0.{u2} M (AddMonoid.toZero.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) f J))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_of_with_bot BoxIntegral.Prepartition.sum_ofWithBotₓ'. -/
 theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) (f : Box ι → M) :
@@ -496,6 +726,7 @@ theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (B
   Finset.sum_eraseNone _ _
 #align box_integral.prepartition.sum_of_with_bot BoxIntegral.Prepartition.sum_ofWithBot
 
+#print BoxIntegral.Prepartition.restrict /-
 /-- Restrict a prepartition to a box. -/
 def restrict (π : Prepartition I) (J : Box ι) : Prepartition J :=
   ofWithBot (π.boxes.image fun J' => J ⊓ J')
@@ -510,16 +741,35 @@ def restrict (π : Prepartition I) (J : Box ι) : Prepartition J :=
         exact Hne rfl
       exact ((box.disjoint_coe.2 <| π.disjoint_coe_of_mem h₁ h₂ this).inf_left' _).inf_right' _)
 #align box_integral.prepartition.restrict BoxIntegral.Prepartition.restrict
+-/
 
+/- warning: box_integral.prepartition.mem_restrict -> BoxIntegral.Prepartition.mem_restrict is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {J₁ : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasMem.{u1} ι J) J₁ (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (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) => Eq.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J₁) (Inf.inf.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Box.WithBot.hasInf.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J')))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {J₁ : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J) J₁ (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (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) (Eq.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J₁) (Inf.inf.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Box.WithBot.inf.{u1} ι) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J')))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_restrict BoxIntegral.Prepartition.mem_restrictₓ'. -/
 @[simp]
 theorem mem_restrict : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : WithBot (Box ι)) = J ⊓ J' := by
   simp [restrict, eq_comm]
 #align box_integral.prepartition.mem_restrict BoxIntegral.Prepartition.mem_restrict
 
+/- warning: box_integral.prepartition.mem_restrict' -> BoxIntegral.Prepartition.mem_restrict' is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {J₁ : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasMem.{u1} ι J) J₁ (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (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) => Eq.{succ u1} (Set.{u1} (ι -> Real)) ((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))) J₁) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) ((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} {J₁ : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J) J₁ (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (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) (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J₁) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Box.toSet.{u1} ι J')))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_restrict' BoxIntegral.Prepartition.mem_restrict'ₓ'. -/
 theorem mem_restrict' : J₁ ∈ π.restrict J ↔ ∃ J' ∈ π, (J₁ : Set (ι → ℝ)) = J ∩ J' := by
   simp only [mem_restrict, ← box.with_bot_coe_inj, box.coe_inf, box.coe_coe]
 #align box_integral.prepartition.mem_restrict' BoxIntegral.Prepartition.mem_restrict'
 
+/- warning: box_integral.prepartition.restrict_mono -> BoxIntegral.Prepartition.restrict_mono is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasLe.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π₁ J) (BoxIntegral.Prepartition.restrict.{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.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π₁ J) (BoxIntegral.Prepartition.restrict.{u1} ι I π₂ J))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.restrict_mono BoxIntegral.Prepartition.restrict_monoₓ'. -/
 @[mono]
 theorem restrict_mono {π₁ π₂ : Prepartition I} (Hle : π₁ ≤ π₂) : π₁.restrict J ≤ π₂.restrict J :=
   by
@@ -529,10 +779,13 @@ theorem restrict_mono {π₁ π₂ : Prepartition I} (Hle : π₁ ≤ π₂) : 
   exact ⟨_, Finset.mem_image_of_mem _ hJ₂, inf_le_inf_left _ <| WithBot.coe_le_coe.2 hle⟩
 #align box_integral.prepartition.restrict_mono BoxIntegral.Prepartition.restrict_mono
 
+#print BoxIntegral.Prepartition.monotone_restrict /-
 theorem monotone_restrict : Monotone fun π : Prepartition I => restrict π J := fun π₁ π₂ =>
   restrict_mono
 #align box_integral.prepartition.monotone_restrict BoxIntegral.Prepartition.monotone_restrict
+-/
 
+#print BoxIntegral.Prepartition.restrict_boxes_of_le /-
 /-- Restricting to a larger box does not change the set of boxes. We cannot claim equality
 of prepartitions because they have different types. -/
 theorem restrict_boxes_of_le (π : Prepartition I) (h : I ≤ J) : (π.restrict J).boxes = π.boxes :=
@@ -544,19 +797,29 @@ theorem restrict_boxes_of_le (π : Prepartition I) (h : I ≤ J) : (π.restrict
   rw [inf_of_le_right, ← WithBot.some_eq_coe, Option.toFinset_some]
   exact WithBot.coe_le_coe.2 ((π.le_of_mem hJ').trans h)
 #align box_integral.prepartition.restrict_boxes_of_le BoxIntegral.Prepartition.restrict_boxes_of_le
+-/
 
+#print BoxIntegral.Prepartition.restrict_self /-
 @[simp]
 theorem restrict_self : π.restrict I = π :=
   injective_boxes <| restrict_boxes_of_le π le_rfl
 #align box_integral.prepartition.restrict_self BoxIntegral.Prepartition.restrict_self
+-/
 
+/- warning: box_integral.prepartition.Union_restrict -> BoxIntegral.Prepartition.unionᵢ_restrict 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), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι J (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I 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), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι J (BoxIntegral.Prepartition.restrict.{u1} ι I π J)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.unionᵢ_restrictₓ'. -/
 @[simp]
-theorem union_restrict : (π.restrict J).unionᵢ = J ∩ π.unionᵢ := by
+theorem unionᵢ_restrict : (π.restrict J).unionᵢ = J ∩ π.unionᵢ := by
   simp [restrict, ← inter_Union, ← Union_def]
-#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.union_restrict
+#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.unionᵢ_restrict
 
+#print BoxIntegral.Prepartition.restrict_bunionᵢ /-
 @[simp]
-theorem restrict_bUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
+theorem restrict_bunionᵢ (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
     (π.bunionᵢ πi).restrict J = πi J :=
   by
   refine' (eq_of_boxes_subset_Union_superset (fun J₁ h₁ => _) _).symm
@@ -567,9 +830,16 @@ theorem restrict_bUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
     obtain rfl : J = J₁
     exact π.eq_of_mem_of_mem hJ h₁ hxJ (Union_subset _ hx)
     exact hx
-#align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_bUnion
+#align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_bunionᵢ
+-/
 
-theorem bUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
+/- warning: box_integral.prepartition.bUnion_le_iff -> BoxIntegral.Prepartition.bunionᵢ_le_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π') (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasLe.{u1} ι J) (πi J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi) π') (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι J) (πi J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.bunionᵢ_le_iffₓ'. -/
+theorem bunionᵢ_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π.bunionᵢ πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J :=
   by
   fconstructor <;> intro H J hJ
@@ -580,9 +850,15 @@ theorem bUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     rcases H J₁ h₁ hJ with ⟨J₂, h₂, Hle⟩
     rcases π'.mem_restrict.mp h₂ with ⟨J₃, h₃, H⟩
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩
-#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.bUnion_le_iff
-
-theorem le_bUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
+#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.bunionᵢ_le_iff
+
+/- warning: box_integral.prepartition.le_bUnion_iff -> BoxIntegral.Prepartition.le_bunionᵢ_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π' (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi)) (And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π' π) (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasLe.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J) (πi J))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) {πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J} {π' : BoxIntegral.Prepartition.{u1} ι I}, Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π' (BoxIntegral.Prepartition.bunionᵢ.{u1} ι I π πi)) (And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π' π) (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) -> (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι J) (BoxIntegral.Prepartition.restrict.{u1} ι I π' J) (πi J))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_bunionᵢ_iffₓ'. -/
+theorem le_bunionᵢ_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     π' ≤ π.bunionᵢ πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J :=
   by
   refine' ⟨fun H => ⟨H.trans (π.bUnion_le πi), fun J hJ => _⟩, _⟩
@@ -594,33 +870,48 @@ theorem le_bUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
       π'.mem_restrict.2 ⟨J', hJ', (inf_of_le_right <| WithBot.coe_le_coe.2 hle).symm⟩
     rcases Hi J hJ this with ⟨Ji, hJi, hlei⟩
     exact ⟨Ji, π.mem_bUnion.2 ⟨J, hJ, hJi⟩, hlei⟩
-#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_bUnion_iff
+#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_bunionᵢ_iff
 
 instance : Inf (Prepartition I) :=
   ⟨fun π₁ π₂ => π₁.bunionᵢ fun J => π₂.restrict J⟩
 
+#print BoxIntegral.Prepartition.inf_def /-
 theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.bunionᵢ fun J => π₂.restrict J :=
   rfl
 #align box_integral.prepartition.inf_def BoxIntegral.Prepartition.inf_def
+-/
 
+/- warning: box_integral.prepartition.mem_inf -> BoxIntegral.Prepartition.mem_inf is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasInf.{u1} ι I) π₁ π₂)) (Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J₁ : 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) J₁ π₁) (fun (H : Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J₁ π₁) => Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J₂ : 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) J₂ π₂) (fun (H : Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J₂ π₂) => Eq.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J) (Inf.inf.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Box.WithBot.hasInf.{u1} ι) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J₁) ((fun (a : Type.{u1}) (b : Type.{u1}) [self : HasLiftT.{succ u1, succ u1} a b] => self.0) (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (HasLiftT.mk.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (CoeTCₓ.coe.{succ u1, succ u1} (BoxIntegral.Box.{u1} ι) (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.hasCoeT.{u1} (BoxIntegral.Box.{u1} ι)))) J₂)))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {J : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.inf.{u1} ι I) π₁ π₂)) (Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J₁ : BoxIntegral.Box.{u1} ι) => And (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J₁ π₁) (Exists.{succ u1} (BoxIntegral.Box.{u1} ι) (fun (J₂ : BoxIntegral.Box.{u1} ι) => And (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J₂ π₂) (Eq.{succ u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J) (Inf.inf.{u1} (WithBot.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Box.WithBot.inf.{u1} ι) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J₁) (WithBot.some.{u1} (BoxIntegral.Box.{u1} ι) J₂)))))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_inf BoxIntegral.Prepartition.mem_infₓ'. -/
 @[simp]
 theorem mem_inf {π₁ π₂ : Prepartition I} :
     J ∈ π₁ ⊓ π₂ ↔ ∃ J₁ ∈ π₁, ∃ J₂ ∈ π₂, (J : WithBot (Box ι)) = J₁ ⊓ J₂ := by
   simp only [inf_def, mem_bUnion, mem_restrict]
 #align box_integral.prepartition.mem_inf BoxIntegral.Prepartition.mem_inf
 
+/- warning: box_integral.prepartition.Union_inf -> BoxIntegral.Prepartition.unionᵢ_inf is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasInf.{u1} ι I) π₁ π₂)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (Inf.inf.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.inf.{u1} ι I) π₁ π₂)) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.unionᵢ_infₓ'. -/
 @[simp]
-theorem union_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).unionᵢ = π₁.unionᵢ ∩ π₂.unionᵢ := by
+theorem unionᵢ_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).unionᵢ = π₁.unionᵢ ∩ π₂.unionᵢ := by
   simp only [inf_def, Union_bUnion, Union_restrict, ← Union_inter, ← Union_def]
-#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.union_inf
+#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.unionᵢ_inf
 
 instance : SemilatticeInf (Prepartition I) :=
   { Prepartition.hasInf,
     Prepartition.partialOrder with
-    inf_le_left := fun π₁ π₂ => π₁.bUnion_le _
-    inf_le_right := fun π₁ π₂ => (bUnion_le_iff _).2 fun J hJ => le_rfl
-    le_inf := fun π π₁ π₂ h₁ h₂ => π₁.le_bUnion_iff.2 ⟨h₁, fun J hJ => restrict_mono h₂⟩ }
+    inf_le_left := fun π₁ π₂ => π₁.bunionᵢ_le _
+    inf_le_right := fun π₁ π₂ => (bunionᵢ_le_iff _).2 fun J hJ => le_rfl
+    le_inf := fun π π₁ π₂ h₁ h₂ => π₁.le_bunionᵢ_iff.2 ⟨h₁, fun J hJ => restrict_mono h₂⟩ }
 
+#print BoxIntegral.Prepartition.filter /-
 /-- The prepartition with boxes `{J ∈ π | p J}`. -/
 @[simps]
 def filter (π : Prepartition I) (p : Box ι → Prop) : Prepartition I
@@ -629,30 +920,49 @@ def filter (π : Prepartition I) (p : Box ι → Prop) : Prepartition I
   le_of_mem' J hJ := π.le_of_mem (mem_filter.1 hJ).1
   PairwiseDisjoint J₁ h₁ J₂ h₂ := π.disjoint_coe_of_mem (mem_filter.1 h₁).1 (mem_filter.1 h₂).1
 #align box_integral.prepartition.filter BoxIntegral.Prepartition.filter
+-/
 
+#print BoxIntegral.Prepartition.mem_filter /-
 @[simp]
 theorem mem_filter {p : Box ι → Prop} : J ∈ π.filterₓ p ↔ J ∈ π ∧ p J :=
   Finset.mem_filter
 #align box_integral.prepartition.mem_filter BoxIntegral.Prepartition.mem_filter
+-/
 
+/- warning: box_integral.prepartition.filter_le -> BoxIntegral.Prepartition.filter_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.filter.{u1} ι I π p) π
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.filter.{u1} ι I π p) π
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.filter_le BoxIntegral.Prepartition.filter_leₓ'. -/
 theorem filter_le (π : Prepartition I) (p : Box ι → Prop) : π.filterₓ p ≤ π := fun J hJ =>
   let ⟨hπ, hp⟩ := π.mem_filter.1 hJ
   ⟨J, hπ, le_rfl⟩
 #align box_integral.prepartition.filter_le BoxIntegral.Prepartition.filter_le
 
+#print BoxIntegral.Prepartition.filter_of_true /-
 theorem filter_of_true {p : Box ι → Prop} (hp : ∀ J ∈ π, p J) : π.filterₓ p = π :=
   by
   ext J
   simpa using hp J
 #align box_integral.prepartition.filter_of_true BoxIntegral.Prepartition.filter_of_true
+-/
 
+#print BoxIntegral.Prepartition.filter_true /-
 @[simp]
 theorem filter_true : (π.filterₓ fun _ => True) = π :=
   π.filter_of_true fun _ _ => trivial
 #align box_integral.prepartition.filter_true BoxIntegral.Prepartition.filter_true
+-/
 
+/- warning: box_integral.prepartition.Union_filter_not -> BoxIntegral.Prepartition.unionᵢ_filter_not is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.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.Prepartition.unionᵢ.{u1} ι I π) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π p)))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (p : (BoxIntegral.Box.{u1} ι) -> Prop), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.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.Prepartition.unionᵢ.{u1} ι I π) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π p)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.unionᵢ_filter_notₓ'. -/
 @[simp]
-theorem union_filter_not (π : Prepartition I) (p : Box ι → Prop) :
+theorem unionᵢ_filter_not (π : Prepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).unionᵢ = π.unionᵢ \ (π.filterₓ p).unionᵢ :=
   by
   simp only [prepartition.Union]
@@ -661,14 +971,26 @@ theorem union_filter_not (π : Prepartition I) (p : Box ι → Prop) :
     simp (config := { contextual := true })
   · convert π.pairwise_disjoint
     simp
-#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.union_filter_not
-
+#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.unionᵢ_filter_not
+
+/- warning: box_integral.prepartition.sum_fiberwise -> BoxIntegral.Prepartition.sum_fiberwise is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {α : Type.{u2}} {M : Type.{u3}} [_inst_1 : AddCommMonoid.{u3} M] (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> α) (g : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u3} M (Finset.sum.{u3, u2} M α _inst_1 (Finset.image.{u1, u2} (BoxIntegral.Box.{u1} ι) α (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u2} α a b)) f (BoxIntegral.Prepartition.boxes.{u1} ι I π)) (fun (y : α) => Finset.sum.{u3, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π (fun (J : BoxIntegral.Box.{u1} ι) => Eq.{succ u2} α (f J) y))) (fun (J : BoxIntegral.Box.{u1} ι) => g J))) (Finset.sum.{u3, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => g J))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {α : Type.{u3}} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M] (π : BoxIntegral.Prepartition.{u1} ι I) (f : (BoxIntegral.Box.{u1} ι) -> α) (g : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u3} M α _inst_1 (Finset.image.{u1, u3} (BoxIntegral.Box.{u1} ι) α (fun (a : α) (b : α) => Classical.propDecidable (Eq.{succ u3} α a b)) f (BoxIntegral.Prepartition.boxes.{u1} ι I π)) (fun (y : α) => Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.Prepartition.filter.{u1} ι I π (fun (J : BoxIntegral.Box.{u1} ι) => Eq.{succ u3} α (f J) y))) (fun (J : BoxIntegral.Box.{u1} ι) => g J))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π) (fun (J : BoxIntegral.Box.{u1} ι) => g J))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_fiberwise BoxIntegral.Prepartition.sum_fiberwiseₓ'. -/
 theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι → α) (g : Box ι → M) :
     (∑ y in π.boxes.image f, ∑ J in (π.filterₓ fun J => f J = y).boxes, g J) =
       ∑ J in π.boxes, g J :=
   by convert sum_fiberwise_of_maps_to (fun _ => Finset.mem_image_of_mem f) g
 #align box_integral.prepartition.sum_fiberwise BoxIntegral.Prepartition.sum_fiberwise
 
+/- warning: box_integral.prepartition.disj_union -> BoxIntegral.Prepartition.disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (BoxIntegral.Prepartition.{u1} ι I)
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.Prepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (BoxIntegral.Prepartition.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnionₓ'. -/
 /-- Union of two disjoint prepartitions. -/
 @[simps]
 def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.unionᵢ π₂.unionᵢ) : Prepartition I
@@ -681,64 +1003,114 @@ def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.unionᵢ π₂.
     fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_unionᵢ h₁) (π₂.subset_unionᵢ h₂)
 #align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnion
 
+/- warning: box_integral.prepartition.mem_disj_union -> BoxIntegral.Prepartition.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.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Iff (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ H)) (Or (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasMem.{u1} ι I) J π₁) (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.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.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Iff (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ H)) (Or (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π₁) (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι I) J π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.mem_disj_union BoxIntegral.Prepartition.mem_disjUnionₓ'. -/
 @[simp]
 theorem mem_disjUnion (H : Disjoint π₁.unionᵢ π₂.unionᵢ) :
     J ∈ π₁.disjUnion π₂ H ↔ J ∈ π₁ ∨ J ∈ π₂ :=
   Finset.mem_union
 #align box_integral.prepartition.mem_disj_union BoxIntegral.Prepartition.mem_disjUnion
 
+/- warning: box_integral.prepartition.Union_disj_union -> BoxIntegral.Prepartition.unionᵢ_disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.hasUnion.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h)) (Union.union.{u1} (Set.{u1} (ι -> Real)) (Set.instUnionSet.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.unionᵢ_disjUnionₓ'. -/
 @[simp]
-theorem union_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+theorem unionᵢ_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
     (π₁.disjUnion π₂ h).unionᵢ = π₁.unionᵢ ∪ π₂.unionᵢ := by
   simp [disj_union, prepartition.Union, Union_or, Union_union_distrib]
-#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.union_disjUnion
-
+#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.unionᵢ_disjUnion
+
+/- warning: box_integral.prepartition.sum_disj_union_boxes -> BoxIntegral.Prepartition.sum_disj_union_boxes is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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 π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toHasAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} {M : Type.{u2}} [_inst_1 : AddCommMonoid.{u2} M], (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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)) -> (forall (f : (BoxIntegral.Box.{u1} ι) -> M), Eq.{succ u2} M (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (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) => decidableEq_of_decidableLE.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable ((fun (x._@.Mathlib.Init.Algebra.Order._hyg.1911 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Init.Algebra.Order._hyg.1913 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (Preorder.toLE.{u1} (BoxIntegral.Box.{u1} ι) (PartialOrder.toPreorder.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instPartialOrderBox.{u1} ι))) x._@.Mathlib.Init.Algebra.Order._hyg.1911 x._@.Mathlib.Init.Algebra.Order._hyg.1913) a b)) a b)) (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (BoxIntegral.Prepartition.boxes.{u1} ι I π₂)) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (HAdd.hAdd.{u2, u2, u2} M M M (instHAdd.{u2} M (AddZeroClass.toAdd.{u2} M (AddMonoid.toAddZeroClass.{u2} M (AddCommMonoid.toAddMonoid.{u2} M _inst_1)))) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₁) (fun (J : BoxIntegral.Box.{u1} ι) => f J)) (Finset.sum.{u2, u1} M (BoxIntegral.Box.{u1} ι) _inst_1 (BoxIntegral.Prepartition.boxes.{u1} ι I π₂) (fun (J : BoxIntegral.Box.{u1} ι) => f J))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxesₓ'. -/
 @[simp]
 theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.unionᵢ π₂.unionᵢ)
     (f : Box ι → M) :
     (∑ J in π₁.boxes ∪ π₂.boxes, f J) = (∑ J in π₁.boxes, f J) + ∑ J in π₂.boxes, f J :=
-  sum_union <| disjoint_boxes_of_disjoint_union h
+  sum_union <| disjoint_boxes_of_disjoint_unionᵢ h
 #align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxes
 
 section Distortion
 
 variable [Fintype ι]
 
+#print BoxIntegral.Prepartition.distortion /-
 /-- The distortion of a prepartition is the maximum of the distortions of the boxes of this
 prepartition. -/
 def distortion : ℝ≥0 :=
   π.boxes.sup Box.distortion
 #align box_integral.prepartition.distortion BoxIntegral.Prepartition.distortion
+-/
 
+#print BoxIntegral.Prepartition.distortion_le_of_mem /-
 theorem distortion_le_of_mem (h : J ∈ π) : J.distortion ≤ π.distortion :=
   le_sup h
 #align box_integral.prepartition.distortion_le_of_mem BoxIntegral.Prepartition.distortion_le_of_mem
+-/
 
+#print BoxIntegral.Prepartition.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.prepartition.distortion_le_iff BoxIntegral.Prepartition.distortion_le_iff
+-/
 
-theorem distortion_bUnion (π : Prepartition I) (πi : ∀ J, Prepartition J) :
+/- warning: box_integral.prepartition.distortion_bUnion -> BoxIntegral.Prepartition.distortion_bunionᵢ 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.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.bunionᵢ.{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.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.Prepartition.{u1} ι I) (πi : forall (J : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.{u1} ι J), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.bunionᵢ.{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.Prepartition.distortion.{u1} ι J (πi J) _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_bunionᵢₓ'. -/
+theorem distortion_bunionᵢ (π : Prepartition I) (πi : ∀ J, Prepartition J) :
     (π.bunionᵢ πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
   sup_bunionᵢ _ _
-#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_bUnion
-
+#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_bunionᵢ
+
+/- warning: box_integral.prepartition.distortion_disj_union -> BoxIntegral.Prepartition.distortion_disjUnion is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (BoxIntegral.Prepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π₂ _inst_1))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{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.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂)), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ h) _inst_1) (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (BoxIntegral.Prepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π₂ _inst_1))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_disj_union BoxIntegral.Prepartition.distortion_disjUnionₓ'. -/
 @[simp]
 theorem distortion_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
     (π₁.disjUnion π₂ h).distortion = max π₁.distortion π₂.distortion :=
   sup_union
 #align box_integral.prepartition.distortion_disj_union BoxIntegral.Prepartition.distortion_disjUnion
 
+#print BoxIntegral.Prepartition.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.prepartition.distortion_of_const BoxIntegral.Prepartition.distortion_of_const
+-/
 
+/- warning: box_integral.prepartition.distortion_top -> BoxIntegral.Prepartition.distortion_top is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] (I : BoxIntegral.Box.{u1} ι), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderTop.{u1} ι I))) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 I)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] (I : BoxIntegral.Box.{u1} ι), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι I))) _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_top BoxIntegral.Prepartition.distortion_topₓ'. -/
 @[simp]
 theorem distortion_top (I : Box ι) : distortion (⊤ : Prepartition I) = I.distortion :=
   sup_singleton
 #align box_integral.prepartition.distortion_top BoxIntegral.Prepartition.distortion_top
 
+/- warning: box_integral.prepartition.distortion_bot -> BoxIntegral.Prepartition.distortion_bot is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] (I : BoxIntegral.Box.{u1} ι), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toHasBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderBot.{u1} ι I))) _inst_1) (OfNat.ofNat.{0} NNReal 0 (OfNat.mk.{0} NNReal 0 (Zero.zero.{0} NNReal (MulZeroClass.toHasZero.{0} NNReal (NonUnitalNonAssocSemiring.toMulZeroClass.{0} NNReal (NonAssocSemiring.toNonUnitalNonAssocSemiring.{0} NNReal (Semiring.toNonAssocSemiring.{0} NNReal NNReal.semiring)))))))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] (I : BoxIntegral.Box.{u1} ι), Eq.{1} NNReal (BoxIntegral.Prepartition.distortion.{u1} ι I (Bot.bot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderBot.toBot.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderBotPrepartitionInstLEPrepartition.{u1} ι I))) _inst_1) (OfNat.ofNat.{0} NNReal 0 (Zero.toOfNat0.{0} NNReal instNNRealZero))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_bot BoxIntegral.Prepartition.distortion_botₓ'. -/
 @[simp]
 theorem distortion_bot (I : Box ι) : distortion (⊥ : Prepartition I) = 0 :=
   sup_empty
@@ -746,21 +1118,33 @@ theorem distortion_bot (I : Box ι) : distortion (⊥ : Prepartition I) = 0 :=
 
 end Distortion
 
+#print BoxIntegral.Prepartition.IsPartition /-
 /-- A prepartition `π` of `I` is a partition if the boxes of `π` cover the whole `I`. -/
 def IsPartition (π : Prepartition I) :=
   ∀ x ∈ I, ∃ J ∈ π, x ∈ J
 #align box_integral.prepartition.is_partition BoxIntegral.Prepartition.IsPartition
+-/
 
-theorem isPartition_iff_union_eq {π : Prepartition I} : π.IsPartition ↔ π.unionᵢ = I := by
+#print BoxIntegral.Prepartition.isPartition_iff_unionᵢ_eq /-
+theorem isPartition_iff_unionᵢ_eq {π : Prepartition I} : π.IsPartition ↔ π.unionᵢ = I := by
   simp_rw [is_partition, Set.Subset.antisymm_iff, π.Union_subset, true_and_iff, Set.subset_def,
     mem_Union, box.mem_coe]
-#align box_integral.prepartition.is_partition_iff_Union_eq BoxIntegral.Prepartition.isPartition_iff_union_eq
+#align box_integral.prepartition.is_partition_iff_Union_eq BoxIntegral.Prepartition.isPartition_iff_unionᵢ_eq
+-/
 
+#print BoxIntegral.Prepartition.isPartition_single_iff /-
 @[simp]
 theorem isPartition_single_iff (h : J ≤ I) : IsPartition (single I J h) ↔ J = I := by
   simp [is_partition_iff_Union_eq]
 #align box_integral.prepartition.is_partition_single_iff BoxIntegral.Prepartition.isPartition_single_iff
+-/
 
+/- warning: box_integral.prepartition.is_partition_top -> BoxIntegral.Prepartition.isPartitionTop is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} (I : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.IsPartition.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toHasTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.Prepartition.orderTop.{u1} ι I)))
+but is expected to have type
+  forall {ι : Type.{u1}} (I : BoxIntegral.Box.{u1} ι), BoxIntegral.Prepartition.IsPartition.{u1} ι I (Top.top.{u1} (BoxIntegral.Prepartition.{u1} ι I) (OrderTop.toTop.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.Prepartition.instOrderTopPrepartitionInstLEPrepartition.{u1} ι I)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition_top BoxIntegral.Prepartition.isPartitionTopₓ'. -/
 theorem isPartitionTop (I : Box ι) : IsPartition (⊤ : Prepartition I) := fun x hx =>
   ⟨I, mem_top.2 rfl, hx⟩
 #align box_integral.prepartition.is_partition_top BoxIntegral.Prepartition.isPartitionTop
@@ -769,62 +1153,92 @@ namespace IsPartition
 
 variable {π}
 
-theorem union_eq (h : π.IsPartition) : π.unionᵢ = I :=
-  isPartition_iff_union_eq.1 h
-#align box_integral.prepartition.is_partition.Union_eq BoxIntegral.Prepartition.IsPartition.union_eq
+#print BoxIntegral.Prepartition.IsPartition.unionᵢ_eq /-
+theorem unionᵢ_eq (h : π.IsPartition) : π.unionᵢ = I :=
+  isPartition_iff_unionᵢ_eq.1 h
+#align box_integral.prepartition.is_partition.Union_eq BoxIntegral.Prepartition.IsPartition.unionᵢ_eq
+-/
 
-theorem union_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.unionᵢ ⊆ π.unionᵢ :=
+#print BoxIntegral.Prepartition.IsPartition.unionᵢ_subset /-
+theorem unionᵢ_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.unionᵢ ⊆ π.unionᵢ :=
   h.unionᵢ_eq.symm ▸ π₁.unionᵢ_subset
-#align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.union_subset
+#align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.unionᵢ_subset
+-/
 
 /- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (J «expr ∈ » π) -/
+#print BoxIntegral.Prepartition.IsPartition.existsUnique /-
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _)(_ : J ∈ π), x ∈ J :=
   by
   rcases h x hx with ⟨J, h, hx⟩
   exact ExistsUnique.intro₂ J h hx fun J' h' hx' => π.eq_of_mem_of_mem h' h hx' hx
 #align box_integral.prepartition.is_partition.exists_unique BoxIntegral.Prepartition.IsPartition.existsUnique
+-/
 
+#print BoxIntegral.Prepartition.IsPartition.nonempty_boxes /-
 theorem nonempty_boxes (h : π.IsPartition) : π.boxes.Nonempty :=
   let ⟨J, hJ, _⟩ := h _ I.upper_mem
   ⟨J, hJ⟩
 #align box_integral.prepartition.is_partition.nonempty_boxes BoxIntegral.Prepartition.IsPartition.nonempty_boxes
+-/
 
+#print BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset /-
 theorem eq_of_boxes_subset (h₁ : π₁.IsPartition) (h₂ : π₁.boxes ⊆ π₂.boxes) : π₁ = π₂ :=
-  eq_of_boxes_subset_union_superset h₂ <| h₁.unionᵢ_subset _
+  eq_of_boxes_subset_unionᵢ_superset h₂ <| h₁.unionᵢ_subset _
 #align box_integral.prepartition.is_partition.eq_of_boxes_subset BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset
+-/
 
+/- warning: box_integral.prepartition.is_partition.le_iff -> BoxIntegral.Prepartition.IsPartition.le_iff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (BoxIntegral.Prepartition.IsPartition.{u1} ι I π₂) -> (Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) π₁ π₂) (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.hasInter.{u1} (ι -> Real)) ((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) ((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'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J J'))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I}, (BoxIntegral.Prepartition.IsPartition.{u1} ι I π₂) -> (Iff (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) π₁ π₂) (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 π₁) -> (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' π₂) -> (Set.Nonempty.{u1} (ι -> Real) (Inter.inter.{u1} (Set.{u1} (ι -> Real)) (Set.instInterSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι J) (BoxIntegral.Box.toSet.{u1} ι J'))) -> (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J J'))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition.le_iff BoxIntegral.Prepartition.IsPartition.le_iffₓ'. -/
 theorem le_iff (h : π₂.IsPartition) :
     π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J' :=
-  le_iff_nonempty_imp_le_and_union_subset.trans <| and_iff_left <| h.unionᵢ_subset _
+  le_iff_nonempty_imp_le_and_unionᵢ_subset.trans <| and_iff_left <| h.unionᵢ_subset _
 #align box_integral.prepartition.is_partition.le_iff BoxIntegral.Prepartition.IsPartition.le_iff
 
-protected theorem bUnion (h : IsPartition π) (hi : ∀ J ∈ π, IsPartition (πi J)) :
+#print BoxIntegral.Prepartition.IsPartition.bunionᵢ /-
+protected theorem bunionᵢ (h : IsPartition π) (hi : ∀ J ∈ π, IsPartition (πi J)) :
     IsPartition (π.bunionᵢ πi) := fun x hx =>
   let ⟨J, hJ, hxi⟩ := h x hx
   let ⟨Ji, hJi, hx⟩ := hi J hJ x hxi
   ⟨Ji, π.mem_bunionᵢ.2 ⟨J, hJ, hJi⟩, hx⟩
-#align box_integral.prepartition.is_partition.bUnion BoxIntegral.Prepartition.IsPartition.bUnion
+#align box_integral.prepartition.is_partition.bUnion BoxIntegral.Prepartition.IsPartition.bunionᵢ
+-/
 
+#print BoxIntegral.Prepartition.IsPartition.restrict /-
 protected theorem restrict (h : IsPartition π) (hJ : J ≤ I) : IsPartition (π.restrict J) :=
-  isPartition_iff_union_eq.2 <| by simp [h.Union_eq, hJ]
+  isPartition_iff_unionᵢ_eq.2 <| by simp [h.Union_eq, hJ]
 #align box_integral.prepartition.is_partition.restrict BoxIntegral.Prepartition.IsPartition.restrict
+-/
 
+#print BoxIntegral.Prepartition.IsPartition.inf /-
 protected theorem inf (h₁ : IsPartition π₁) (h₂ : IsPartition π₂) : IsPartition (π₁ ⊓ π₂) :=
-  isPartition_iff_union_eq.2 <| by simp [h₁.Union_eq, h₂.Union_eq]
+  isPartition_iff_unionᵢ_eq.2 <| by simp [h₁.Union_eq, h₂.Union_eq]
 #align box_integral.prepartition.is_partition.inf BoxIntegral.Prepartition.IsPartition.inf
+-/
 
 end IsPartition
 
-theorem union_bUnion_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
+#print BoxIntegral.Prepartition.unionᵢ_bunionᵢ_partition /-
+theorem unionᵢ_bunionᵢ_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
     (π.bunionᵢ πi).unionᵢ = π.unionᵢ :=
-  (union_bUnion _ _).trans <|
+  (unionᵢ_bunionᵢ _ _).trans <|
     unionᵢ_congr_of_surjective id surjective_id fun J =>
       unionᵢ_congr_of_surjective id surjective_id fun hJ => (h J hJ).unionᵢ_eq
-#align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.union_bUnion_partition
+#align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.unionᵢ_bunionᵢ_partition
+-/
 
+/- warning: box_integral.prepartition.is_partition_disj_union_of_eq_diff -> BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.subst.{succ u1} (Set.{u1} (ι -> Real)) (fun (_x : Set.{u1} (ι -> Real)) => 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.Prepartition.unionᵢ.{u1} ι I π₁) _x) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (BooleanAlgebra.toHasSdiff.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))) ((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))) I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) h) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) ((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))) I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.booleanAlgebra.{u1} (ι -> Real))))))
+but is expected to have type
+  forall {ι : Type.{u1}} {I : BoxIntegral.Box.{u1} ι} {π₁ : BoxIntegral.Prepartition.{u1} ι I} {π₂ : BoxIntegral.Prepartition.{u1} ι I} (h : Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁))), BoxIntegral.Prepartition.IsPartition.{u1} ι I (BoxIntegral.Prepartition.disjUnion.{u1} ι I π₁ π₂ (Eq.rec.{0, succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) (fun (x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11577 : Set.{u1} (ι -> Real)) (h._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11578 : Eq.{succ u1} (Set.{u1} (ι -> Real)) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11577) => 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.Prepartition.unionᵢ.{u1} ι I π₁) x._@.Mathlib.Analysis.BoxIntegral.Partition.Basic._hyg.11577) (disjoint_sdiff_self_right.{u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁) (BoxIntegral.Box.toSet.{u1} ι I) (BooleanAlgebra.toGeneralizedBooleanAlgebra.{u1} (Set.{u1} (ι -> Real)) (Set.instBooleanAlgebraSet.{u1} (ι -> Real)))) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (Eq.symm.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₂) (SDiff.sdiff.{u1} (Set.{u1} (ι -> Real)) (Set.instSDiffSet.{u1} (ι -> Real)) (BoxIntegral.Box.toSet.{u1} ι I) (BoxIntegral.Prepartition.unionᵢ.{u1} ι I π₁)) h)))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiffₓ'. -/
 theorem isPartitionDisjUnionOfEqDiff (h : π₂.unionᵢ = I \ π₁.unionᵢ) :
     IsPartition (π₁.disjUnion π₂ <| h.symm ▸ disjoint_sdiff_self_right) :=
-  isPartition_iff_union_eq.2 <| (union_disjUnion _).trans <| by simp [h, π₁.Union_subset]
+  isPartition_iff_unionᵢ_eq.2 <| (unionᵢ_disjUnion _).trans <| by simp [h, π₁.Union_subset]
 #align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff
 
 end Prepartition

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

@@ -188,7 +188,7 @@ theorem bot_boxes : (⊥ : Prepartition I).boxes = ∅ :=
 
 /-- An auxiliary lemma used to prove that the same point can't belong to more than
 `2 ^ fintype.card ι` closed boxes of a prepartition. -/
-theorem injOn_setOf_mem_icc_setOf_lower_eq (x : ι → ℝ) :
+theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
     InjOn (fun J : Box ι => { i | J.lower i = x i }) { J | J ∈ π ∧ x ∈ J.Icc } :=
   by
   rintro J₁ ⟨h₁, hx₁⟩ J₂ ⟨h₂, hx₂⟩ (H : { i | J₁.lower i = x i } = { i | J₂.lower i = x i })
@@ -206,11 +206,11 @@ theorem injOn_setOf_mem_icc_setOf_lower_eq (x : ι → ℝ) :
     exact lt_min H₁ H₂
   · have hi₂ : J₂.lower i < x i := (hx₂.1 i).lt_of_ne (mt (H _).2 hi₁.ne)
     exact ⟨x i, ⟨hi₁, hx₁.2 i⟩, ⟨hi₂, hx₂.2 i⟩⟩
-#align box_integral.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq BoxIntegral.Prepartition.injOn_setOf_mem_icc_setOf_lower_eq
+#align box_integral.prepartition.inj_on_set_of_mem_Icc_set_of_lower_eq BoxIntegral.Prepartition.injOn_setOf_mem_Icc_setOf_lower_eq
 
 /-- The set of boxes of a prepartition that contain `x` in their closures has cardinality
 at most `2 ^ fintype.card ι`. -/
-theorem card_filter_mem_icc_le [Fintype ι] (x : ι → ℝ) :
+theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
     (π.boxes.filterₓ fun J : Box ι => x ∈ J.Icc).card ≤ 2 ^ Fintype.card ι :=
   by
   rw [← Fintype.card_set]
@@ -218,7 +218,7 @@ theorem card_filter_mem_icc_le [Fintype ι] (x : ι → ℝ) :
     Finset.card_le_card_of_inj_on (fun J : box ι => { i | J.lower i = x i })
       (fun _ _ => Finset.mem_univ _) _
   simpa only [Finset.mem_filter] using π.inj_on_set_of_mem_Icc_set_of_lower_eq x
-#align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_icc_le
+#align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_le
 
 /-- Given a prepartition `π : box_integral.prepartition I`, `π.Union` is the part of `I` covered by
 the boxes of `π`. -/

mathlib commit https://github.com/leanprover-community/mathlib/commit/ce7e9d53d4bbc38065db3b595cd5bd73c323bc1d

@@ -393,7 +393,7 @@ theorem bUnionIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.bUnionInd
 #align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.bUnionIndex_le
 
 theorem mem_bUnionIndex (hJ : J ∈ π.bunionᵢ πi) : J ∈ πi (π.bUnionIndex πi J) := by
-  convert (π.mem_bUnion.1 hJ).choose_spec.snd <;> exact dif_pos hJ
+  convert(π.mem_bUnion.1 hJ).choose_spec.snd <;> exact dif_pos hJ
 #align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_bUnionIndex
 
 theorem le_bUnionIndex (hJ : J ∈ π.bunionᵢ πi) : J ≤ π.bUnionIndex πi J :=
@@ -656,7 +656,7 @@ theorem union_filter_not (π : Prepartition I) (p : Box ι → Prop) :
     (π.filterₓ fun J => ¬p J).unionᵢ = π.unionᵢ \ (π.filterₓ p).unionᵢ :=
   by
   simp only [prepartition.Union]
-  convert (@Set.bunionᵢ_diff_bunionᵢ_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
+  convert(@Set.bunionᵢ_diff_bunionᵢ_eq _ (box ι) π.boxes (π.filter p).boxes coe _).symm
   · ext (J x)
     simp (config := { contextual := true })
   · convert π.pairwise_disjoint

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

@@ -777,7 +777,7 @@ theorem union_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.union
   h.unionᵢ_eq.symm ▸ π₁.unionᵢ_subset
 #align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.union_subset
 
-/- ./././Mathport/Syntax/Translate/Basic.lean:628:2: warning: expanding binder collection (J «expr ∈ » π) -/
+/- ./././Mathport/Syntax/Translate/Basic.lean:635:2: warning: expanding binder collection (J «expr ∈ » π) -/
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) : ∃! (J : _)(_ : J ∈ π), x ∈ J :=
   by
   rcases h x hx with ⟨J, h, hx⟩

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

@@ -596,7 +596,7 @@ theorem le_bUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
     exact ⟨Ji, π.mem_bUnion.2 ⟨J, hJ, hJi⟩, hlei⟩
 #align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_bUnion_iff
 
-instance : HasInf (Prepartition I) :=
+instance : Inf (Prepartition I) :=
   ⟨fun π₁ π₂ => π₁.bunionᵢ fun J => π₂.restrict J⟩
 
 theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.bunionᵢ fun J => π₂.restrict J :=

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

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

@@ -139,8 +139,10 @@ instance partialOrder : PartialOrder (Prepartition I) where
       fun π₁ π₂ h₁ h₂ => injective_boxes (Subset.antisymm (this h₁ h₂) (this h₂ h₁))
     intro π₁ π₂ h₁ h₂ J hJ
     rcases h₁ hJ with ⟨J', hJ', hle⟩; rcases h₂ hJ' with ⟨J'', hJ'', hle'⟩
-    obtain rfl : J = J''; exact π₁.eq_of_le hJ hJ'' (hle.trans hle')
-    obtain rfl : J' = J; exact le_antisymm ‹_› ‹_›
+    obtain rfl : J = J''
+    · exact π₁.eq_of_le hJ hJ'' (hle.trans hle')
+    obtain rfl : J' = J
+    · exact le_antisymm ‹_› ‹_›
     assumption
 
 instance : OrderTop (Prepartition I) where
@@ -304,8 +306,8 @@ def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I where
     rw [Function.onFun, Set.disjoint_left]
     rintro x hx₁ hx₂; apply Hne
     obtain rfl : J₁ = J₂
-    exact π.eq_of_mem_of_mem hJ₁ hJ₂ ((πi J₁).le_of_mem hJ₁' hx₁) ((πi J₂).le_of_mem hJ₂' hx₂)
-    exact (πi J₁).eq_of_mem_of_mem hJ₁' hJ₂' hx₁ hx₂
+    · exact π.eq_of_mem_of_mem hJ₁ hJ₂ ((πi J₁).le_of_mem hJ₁' hx₁) ((πi J₂).le_of_mem hJ₂' hx₂)
+    · exact (πi J₁).eq_of_mem_of_mem hJ₁' hJ₂' hx₁ hx₂
 #align box_integral.prepartition.bUnion BoxIntegral.Prepartition.biUnion
 
 variable {πi πi₁ πi₂ : ∀ J : Box ι, Prepartition J}
@@ -535,8 +537,8 @@ theorem restrict_biUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
   · simp only [iUnion_restrict, iUnion_biUnion, Set.subset_def, Set.mem_inter_iff, Set.mem_iUnion]
     rintro x ⟨hxJ, J₁, h₁, hx⟩
     obtain rfl : J = J₁
-    exact π.eq_of_mem_of_mem hJ h₁ hxJ (iUnion_subset _ hx)
-    exact hx
+    · exact π.eq_of_mem_of_mem hJ h₁ hxJ (iUnion_subset _ hx)
+    · exact hx
 #align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_biUnion
 
 theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :

More generally, adds a binderPred variant for ExistsUnique.

Uses this syntax to clean up Mathlib.Data.Setoid.Partition and remove Mathport warnings.

@@ -742,9 +742,9 @@ theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUni
 #align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) :
-    ∃! J, ∃! _ : J ∈ π, x ∈ J := by
+    ∃! J ∈ π, x ∈ J := by
   rcases h x hx with ⟨J, h, hx⟩
-  exact ExistsUnique.intro₂ J h hx fun J' h' hx' => π.eq_of_mem_of_mem h' h hx' hx
+  exact ExistsUnique.intro J ⟨h, hx⟩ fun J' ⟨h', hx'⟩ => π.eq_of_mem_of_mem h' h hx' hx
 #align box_integral.prepartition.is_partition.exists_unique BoxIntegral.Prepartition.IsPartition.existsUnique
 
 theorem nonempty_boxes (h : π.IsPartition) : π.boxes.Nonempty :=

Zulip discussion

@@ -742,7 +742,7 @@ theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUni
 #align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) :
-    ∃! (J : _) (_ : J ∈ π), x ∈ J := by
+    ∃! J, ∃! _ : J ∈ π, x ∈ J := by
   rcases h x hx with ⟨J, h, hx⟩
   exact ExistsUnique.intro₂ J h hx fun J' h' hx' => π.eq_of_mem_of_mem h' h hx' hx
 #align box_integral.prepartition.is_partition.exists_unique BoxIntegral.Prepartition.IsPartition.existsUnique

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.

@@ -41,7 +41,8 @@ rectangular box, partition
 
 open Set Finset Function
 
-open Classical NNReal BigOperators
+open scoped Classical
+open NNReal BigOperators
 
 noncomputable section
 

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

This follows on from #6964.

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

@@ -134,8 +134,8 @@ instance partialOrder : PartialOrder (Prepartition I) where
     let ⟨I₃, hI₃, hI₂₃⟩ := h₂₃ hI₂
     ⟨I₃, hI₃, hI₁₂.trans hI₂₃⟩
   le_antisymm := by
-    suffices : ∀ {π₁ π₂ : Prepartition I}, π₁ ≤ π₂ → π₂ ≤ π₁ → π₁.boxes ⊆ π₂.boxes
-    exact fun π₁ π₂ h₁ h₂ => injective_boxes (Subset.antisymm (this h₁ h₂) (this h₂ h₁))
+    suffices ∀ {π₁ π₂ : Prepartition I}, π₁ ≤ π₂ → π₂ ≤ π₁ → π₁.boxes ⊆ π₂.boxes from
+      fun π₁ π₂ h₁ h₂ => injective_boxes (Subset.antisymm (this h₁ h₂) (this h₂ h₁))
     intro π₁ π₂ h₁ h₂ J hJ
     rcases h₁ hJ with ⟨J', hJ', hle⟩; rcases h₂ hJ' with ⟨J'', hJ'', hle'⟩
     obtain rfl : J = J''; exact π₁.eq_of_le hJ hJ'' (hle.trans hle')

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

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

@@ -5,6 +5,7 @@ Authors: Yury Kudryashov
 -/
 import Mathlib.Algebra.BigOperators.Option
 import Mathlib.Analysis.BoxIntegral.Box.Basic
+import Mathlib.Data.Set.Pairwise.Lattice
 
 #align_import analysis.box_integral.partition.basic from "leanprover-community/mathlib"@"84dc0bd6619acaea625086d6f53cb35cdd554219"
 

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

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

@@ -184,7 +184,7 @@ theorem injOn_setOf_mem_Icc_setOf_lower_eq (x : ι → ℝ) :
     exact π.eq_of_mem_of_mem h₁ h₂ hy₁ hy₂
   intro i
   simp only [Set.ext_iff, mem_setOf] at H
-  cases' (hx₁.1 i).eq_or_lt with hi₁ hi₁
+  rcases (hx₁.1 i).eq_or_lt with hi₁ | hi₁
   · have hi₂ : J₂.lower i = x i := (H _).1 hi₁
     have H₁ : x i < J₁.upper i := by simpa only [hi₁] using J₁.lower_lt_upper i
     have H₂ : x i < J₂.upper i := by simpa only [hi₂] using J₂.lower_lt_upper i

Rename union_eq_left_iff_subset to union_eq_left to match sup_eq_left. Similarly for the right and inter versions.

@@ -622,7 +622,7 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
   · simp (config := { contextual := true })
   · rw [Set.PairwiseDisjoint]
     convert π.pairwiseDisjoint
-    rw [Set.union_eq_left_iff_subset, filter_boxes, coe_filter]
+    rw [Set.union_eq_left, filter_boxes, coe_filter]
     exact fun _ ⟨h, _⟩ => h
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
 

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

This has nice performance benefits.

@@ -46,7 +46,7 @@ noncomputable section
 
 namespace BoxIntegral
 
-variable {ι : Type _}
+variable {ι : Type*}
 
 /-- A prepartition of `I : BoxIntegral.Box ι` is a finite set of pairwise disjoint subboxes of
 `I`. -/
@@ -343,7 +343,7 @@ theorem iUnion_biUnion (πi : ∀ J : Box ι, Prepartition J) :
 #align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.iUnion_biUnion
 
 @[simp]
-theorem sum_biUnion_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
+theorem sum_biUnion_boxes {M : Type*} [AddCommMonoid M] (π : Prepartition I)
     (πi : ∀ J, Prepartition J) (f : Box ι → M) :
     (∑ J in π.boxes.biUnion fun J => (πi J).boxes, f J) =
       ∑ J in π.boxes, ∑ J' in (πi J).boxes, f J' := by
@@ -459,7 +459,7 @@ theorem ofWithBot_mono {boxes₁ : Finset (WithBot (Box ι))}
   le_ofWithBot _ fun J hJ => H J (mem_ofWithBot.1 hJ) WithBot.coe_ne_bot
 #align box_integral.prepartition.of_with_bot_mono BoxIntegral.Prepartition.ofWithBot_mono
 
-theorem sum_ofWithBot {M : Type _} [AddCommMonoid M] (boxes : Finset (WithBot (Box ι)))
+theorem sum_ofWithBot {M : Type*} [AddCommMonoid M] (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) (f : Box ι → M) :
     (∑ J in (ofWithBot boxes le_of_mem pairwise_disjoint).boxes, f J) =
@@ -656,7 +656,7 @@ theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
 #align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.iUnion_disjUnion
 
 @[simp]
-theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
+theorem sum_disj_union_boxes {M : Type*} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
     (f : Box ι → M) :
     ∑ J in π₁.boxes ∪ π₂.boxes, f J = (∑ J in π₁.boxes, f J) + ∑ J in π₂.boxes, f J :=
   sum_union <| disjoint_boxes_of_disjoint_iUnion h

• depends on: #5966

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

@@ -2,15 +2,12 @@
 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.basic
-! leanprover-community/mathlib commit 84dc0bd6619acaea625086d6f53cb35cdd554219
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Algebra.BigOperators.Option
 import Mathlib.Analysis.BoxIntegral.Box.Basic
 
+#align_import analysis.box_integral.partition.basic from "leanprover-community/mathlib"@"84dc0bd6619acaea625086d6f53cb35cdd554219"
+
 /-!
 # Partitions of rectangular boxes in `ℝⁿ`
 

• Also remove most superfluous parentheses around big operators (∑, ∏ and variants).
• roughly the used regex: ([^a-zA-Zα-ωΑ-Ω'𝓝ℳ₀𝕂ₛ)]) \(([∑∏][^()∑∏]*,[^()∑∏:]*)\) ([⊂⊆=<≤]) replaced by $1 $2 $3

@@ -661,7 +661,7 @@ theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
 @[simp]
 theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
     (f : Box ι → M) :
-    (∑ J in π₁.boxes ∪ π₂.boxes, f J) = (∑ J in π₁.boxes, f J) + ∑ J in π₂.boxes, f J :=
+    ∑ J in π₁.boxes ∪ π₂.boxes, f J = (∑ J in π₁.boxes, f J) + ∑ J in π₂.boxes, f J :=
   sum_union <| disjoint_boxes_of_disjoint_iUnion h
 #align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxes
 

@@ -425,7 +425,7 @@ theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) :
     (ofWithBot boxes le_of_mem pairwise_disjoint).iUnion = ⋃ J ∈ boxes, ↑J := by
-  suffices (⋃ (J : Box ι) (_ : ↑J ∈ boxes), ↑J) = ⋃ J ∈ boxes, (J : Set (ι → ℝ)) by
+  suffices ⋃ (J : Box ι) (_ : ↑J ∈ boxes), ↑J = ⋃ J ∈ boxes, (J : Set (ι → ℝ)) by
     simpa [ofWithBot, Prepartition.iUnion]
   simp only [← Box.biUnion_coe_eq_coe, @iUnion_comm _ _ (Box ι), @iUnion_comm _ _ (@Eq _ _ _),
     iUnion_iUnion_eq_right]

Co-authored-by: Alex J Best <alex.j.best@gmail.com> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -56,7 +56,7 @@ variable {ι : Type _}
 structure Prepartition (I : Box ι) where
   boxes : Finset (Box ι)
   le_of_mem' : ∀ J ∈ boxes, J ≤ I
-  PairwiseDisjoint : Set.Pairwise (↑boxes) (Disjoint on ((↑) : Box ι → Set (ι → ℝ)))
+  pairwiseDisjoint : Set.Pairwise (↑boxes) (Disjoint on ((↑) : Box ι → Set (ι → ℝ)))
 #align box_integral.prepartition BoxIntegral.Prepartition
 
 namespace Prepartition
@@ -76,7 +76,7 @@ theorem mem_mk {s h₁ h₂} : J ∈ (mk s h₁ h₂ : Prepartition I) ↔ J ∈
 
 theorem disjoint_coe_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (h : J₁ ≠ J₂) :
     Disjoint (J₁ : Set (ι → ℝ)) J₂ :=
-  π.PairwiseDisjoint h₁ h₂ h
+  π.pairwiseDisjoint h₁ h₂ h
 #align box_integral.prepartition.disjoint_coe_of_mem BoxIntegral.Prepartition.disjoint_coe_of_mem
 
 theorem eq_of_mem_of_mem (h₁ : J₁ ∈ π) (h₂ : J₂ ∈ π) (hx₁ : x ∈ J₁) (hx₂ : x ∈ J₂) : J₁ = J₂ :=
@@ -299,7 +299,7 @@ def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I where
     simp only [Finset.mem_biUnion, exists_prop, mem_boxes] at hJ
     rcases hJ with ⟨J', hJ', hJ⟩
     exact ((πi J').le_of_mem hJ).trans (π.le_of_mem hJ')
-  PairwiseDisjoint := by
+  pairwiseDisjoint := by
     simp only [Set.Pairwise, Finset.mem_coe, Finset.mem_biUnion]
     rintro J₁' ⟨J₁, hJ₁, hJ₁'⟩ J₂' ⟨J₂, hJ₂, hJ₂'⟩ Hne
     rw [Function.onFun, Set.disjoint_left]
@@ -409,7 +409,7 @@ def ofWithBot (boxes : Finset (WithBot (Box ι)))
   le_of_mem' J hJ := by
     rw [mem_eraseNone] at hJ
     simpa only [WithBot.some_eq_coe, WithBot.coe_le_coe] using le_of_mem _ hJ
-  PairwiseDisjoint J₁ h₁ J₂ h₂ hne := by
+  pairwiseDisjoint J₁ h₁ J₂ h₂ hne := by
     simp only [mem_coe, mem_eraseNone] at h₁ h₂
     exact Box.disjoint_coe.1 (pairwise_disjoint h₁ h₂ (mt Option.some_inj.1 hne))
 #align box_integral.prepartition.of_with_bot BoxIntegral.Prepartition.ofWithBot
@@ -594,7 +594,7 @@ instance : SemilatticeInf (Prepartition I) :=
 def filter (π : Prepartition I) (p : Box ι → Prop) : Prepartition I where
   boxes := π.boxes.filter p
   le_of_mem' _ hJ := π.le_of_mem (mem_filter.1 hJ).1
-  PairwiseDisjoint _ h₁ _ h₂ := π.disjoint_coe_of_mem (mem_filter.1 h₁).1 (mem_filter.1 h₂).1
+  pairwiseDisjoint _ h₁ _ h₂ := π.disjoint_coe_of_mem (mem_filter.1 h₁).1 (mem_filter.1 h₂).1
 #align box_integral.prepartition.filter BoxIntegral.Prepartition.filter
 
 @[simp]
@@ -624,7 +624,7 @@ theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
   convert (@Set.biUnion_diff_biUnion_eq _ (Box ι) π.boxes (π.filter p).boxes (↑) _).symm
   · simp (config := { contextual := true })
   · rw [Set.PairwiseDisjoint]
-    convert π.PairwiseDisjoint
+    convert π.pairwiseDisjoint
     rw [Set.union_eq_left_iff_subset, filter_boxes, coe_filter]
     exact fun _ ⟨h, _⟩ => h
 #align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
@@ -640,9 +640,9 @@ theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι
 def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) : Prepartition I where
   boxes := π₁.boxes ∪ π₂.boxes
   le_of_mem' J hJ := (Finset.mem_union.1 hJ).elim π₁.le_of_mem π₂.le_of_mem
-  PairwiseDisjoint :=
+  pairwiseDisjoint :=
     suffices ∀ J₁ ∈ π₁, ∀ J₂ ∈ π₂, J₁ ≠ J₂ → Disjoint (J₁ : Set (ι → ℝ)) J₂ by
-      simpa [pairwise_union_of_symmetric (symmetric_disjoint.comap _), PairwiseDisjoint]
+      simpa [pairwise_union_of_symmetric (symmetric_disjoint.comap _), pairwiseDisjoint]
     fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)
 #align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnion
 

@@ -425,7 +425,7 @@ theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) :
     (ofWithBot boxes le_of_mem pairwise_disjoint).iUnion = ⋃ J ∈ boxes, ↑J := by
-  suffices (⋃ (J : Box ι) (_hJ : ↑J ∈ boxes), ↑J) = ⋃ J ∈ boxes, (J : Set (ι → ℝ)) by
+  suffices (⋃ (J : Box ι) (_ : ↑J ∈ boxes), ↑J) = ⋃ J ∈ boxes, (J : Set (ι → ℝ)) by
     simpa [ofWithBot, Prepartition.iUnion]
   simp only [← Box.biUnion_coe_eq_coe, @iUnion_comm _ _ (Box ι), @iUnion_comm _ _ (@Eq _ _ _),
     iUnion_iUnion_eq_right]

As discussed on Zulip

Renames

• supₛ → sSup
• infₛ → sInf
• supᵢ → iSup
• infᵢ → iInf
• bsupₛ → bsSup
• binfₛ → bsInf
• bsupᵢ → biSup
• binfᵢ → biInf
• csupₛ → csSup
• cinfₛ → csInf
• csupᵢ → ciSup
• cinfᵢ → ciInf
• unionₛ → sUnion
• interₛ → sInter
• unionᵢ → iUnion
• interᵢ → iInter
• bunionₛ → bsUnion
• binterₛ → bsInter
• bunionᵢ → biUnion
• binterᵢ → biInter

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -29,7 +29,7 @@ such that
 Then we define a predicate `BoxIntegral.Prepartition.IsPartition`; `π.IsPartition` means that the
 boxes of `π` actually cover the whole `I`. We also define some operations on prepartitions:
 
-* `BoxIntegral.Prepartition.bunionᵢ`: split each box of a partition into smaller boxes;
+* `BoxIntegral.Prepartition.biUnion`: split each box of a partition into smaller boxes;
 * `BoxIntegral.Prepartition.restrict`: restrict a partition to a smaller box.
 
 We also define a `SemilatticeInf` structure on `BoxIntegral.Prepartition I` for all
@@ -207,85 +207,85 @@ theorem card_filter_mem_Icc_le [Fintype ι] (x : ι → ℝ) :
   simpa only [Finset.mem_filter] using π.injOn_setOf_mem_Icc_setOf_lower_eq x
 #align box_integral.prepartition.card_filter_mem_Icc_le BoxIntegral.Prepartition.card_filter_mem_Icc_le
 
-/-- Given a prepartition `π : BoxIntegral.Prepartition I`, `π.unionᵢ` is the part of `I` covered by
+/-- Given a prepartition `π : BoxIntegral.Prepartition I`, `π.iUnion` is the part of `I` covered by
 the boxes of `π`. -/
-protected def unionᵢ : Set (ι → ℝ) :=
+protected def iUnion : Set (ι → ℝ) :=
   ⋃ J ∈ π, ↑J
-#align box_integral.prepartition.Union BoxIntegral.Prepartition.unionᵢ
+#align box_integral.prepartition.Union BoxIntegral.Prepartition.iUnion
 
-theorem unionᵢ_def : π.unionᵢ = ⋃ J ∈ π, ↑J := rfl
-#align box_integral.prepartition.Union_def BoxIntegral.Prepartition.unionᵢ_def
+theorem iUnion_def : π.iUnion = ⋃ J ∈ π, ↑J := rfl
+#align box_integral.prepartition.Union_def BoxIntegral.Prepartition.iUnion_def
 
-theorem unionᵢ_def' : π.unionᵢ = ⋃ J ∈ π.boxes, ↑J := rfl
-#align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.unionᵢ_def'
+theorem iUnion_def' : π.iUnion = ⋃ J ∈ π.boxes, ↑J := rfl
+#align box_integral.prepartition.Union_def' BoxIntegral.Prepartition.iUnion_def'
 
--- Porting note: Previous proof was `:= Set.mem_unionᵢ₂`
+-- Porting note: Previous proof was `:= Set.mem_iUnion₂`
 @[simp]
-theorem mem_unionᵢ : x ∈ π.unionᵢ ↔ ∃ J ∈ π, x ∈ J := by
-  convert Set.mem_unionᵢ₂
+theorem mem_iUnion : x ∈ π.iUnion ↔ ∃ J ∈ π, x ∈ J := by
+  convert Set.mem_iUnion₂
   rw [Box.mem_coe, exists_prop]
-#align box_integral.prepartition.mem_Union BoxIntegral.Prepartition.mem_unionᵢ
+#align box_integral.prepartition.mem_Union BoxIntegral.Prepartition.mem_iUnion
 
 @[simp]
-theorem unionᵢ_single (h : J ≤ I) : (single I J h).unionᵢ = J := by simp [unionᵢ_def]
-#align box_integral.prepartition.Union_single BoxIntegral.Prepartition.unionᵢ_single
+theorem iUnion_single (h : J ≤ I) : (single I J h).iUnion = J := by simp [iUnion_def]
+#align box_integral.prepartition.Union_single BoxIntegral.Prepartition.iUnion_single
 
 @[simp]
-theorem unionᵢ_top : (⊤ : Prepartition I).unionᵢ = I := by simp [Prepartition.unionᵢ]
-#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.unionᵢ_top
+theorem iUnion_top : (⊤ : Prepartition I).iUnion = I := by simp [Prepartition.iUnion]
+#align box_integral.prepartition.Union_top BoxIntegral.Prepartition.iUnion_top
 
 @[simp]
-theorem unionᵢ_eq_empty : π₁.unionᵢ = ∅ ↔ π₁ = ⊥ := by
-  simp [← injective_boxes.eq_iff, Finset.ext_iff, Prepartition.unionᵢ, imp_false]
-#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.unionᵢ_eq_empty
+theorem iUnion_eq_empty : π₁.iUnion = ∅ ↔ π₁ = ⊥ := by
+  simp [← injective_boxes.eq_iff, Finset.ext_iff, Prepartition.iUnion, imp_false]
+#align box_integral.prepartition.Union_eq_empty BoxIntegral.Prepartition.iUnion_eq_empty
 
 @[simp]
-theorem unionᵢ_bot : (⊥ : Prepartition I).unionᵢ = ∅ :=
-  unionᵢ_eq_empty.2 rfl
-#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.unionᵢ_bot
+theorem iUnion_bot : (⊥ : Prepartition I).iUnion = ∅ :=
+  iUnion_eq_empty.2 rfl
+#align box_integral.prepartition.Union_bot BoxIntegral.Prepartition.iUnion_bot
 
-theorem subset_unionᵢ (h : J ∈ π) : ↑J ⊆ π.unionᵢ :=
-  subset_bunionᵢ_of_mem h
-#align box_integral.prepartition.subset_Union BoxIntegral.Prepartition.subset_unionᵢ
+theorem subset_iUnion (h : J ∈ π) : ↑J ⊆ π.iUnion :=
+  subset_biUnion_of_mem h
+#align box_integral.prepartition.subset_Union BoxIntegral.Prepartition.subset_iUnion
 
-theorem unionᵢ_subset : π.unionᵢ ⊆ I :=
-  unionᵢ₂_subset π.le_of_mem'
-#align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.unionᵢ_subset
+theorem iUnion_subset : π.iUnion ⊆ I :=
+  iUnion₂_subset π.le_of_mem'
+#align box_integral.prepartition.Union_subset BoxIntegral.Prepartition.iUnion_subset
 
 @[mono]
-theorem unionᵢ_mono (h : π₁ ≤ π₂) : π₁.unionᵢ ⊆ π₂.unionᵢ := fun _ hx =>
-  let ⟨_, hJ₁, hx⟩ := π₁.mem_unionᵢ.1 hx
+theorem iUnion_mono (h : π₁ ≤ π₂) : π₁.iUnion ⊆ π₂.iUnion := fun _ hx =>
+  let ⟨_, hJ₁, hx⟩ := π₁.mem_iUnion.1 hx
   let ⟨J₂, hJ₂, hle⟩ := h hJ₁
-  π₂.mem_unionᵢ.2 ⟨J₂, hJ₂, hle hx⟩
-#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.unionᵢ_mono
+  π₂.mem_iUnion.2 ⟨J₂, hJ₂, hle hx⟩
+#align box_integral.prepartition.Union_mono BoxIntegral.Prepartition.iUnion_mono
 
-theorem disjoint_boxes_of_disjoint_unionᵢ (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
+theorem disjoint_boxes_of_disjoint_iUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
     Disjoint π₁.boxes π₂.boxes :=
   Finset.disjoint_left.2 fun J h₁ h₂ =>
-    Disjoint.le_bot (h.mono (π₁.subset_unionᵢ h₁) (π₂.subset_unionᵢ h₂)) ⟨J.upper_mem, J.upper_mem⟩
-#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_unionᵢ
+    Disjoint.le_bot (h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)) ⟨J.upper_mem, J.upper_mem⟩
+#align box_integral.prepartition.disjoint_boxes_of_disjoint_Union BoxIntegral.Prepartition.disjoint_boxes_of_disjoint_iUnion
 
-theorem le_iff_nonempty_imp_le_and_unionᵢ_subset :
+theorem le_iff_nonempty_imp_le_and_iUnion_subset :
     π₁ ≤ π₂ ↔
-      (∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J') ∧ π₁.unionᵢ ⊆ π₂.unionᵢ := by
+      (∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J') ∧ π₁.iUnion ⊆ π₂.iUnion := by
   constructor
-  · refine' fun H => ⟨fun J hJ J' hJ' Hne => _, unionᵢ_mono H⟩
+  · refine' fun H => ⟨fun J hJ J' hJ' Hne => _, iUnion_mono H⟩
     rcases H hJ with ⟨J'', hJ'', Hle⟩
     rcases Hne with ⟨x, hx, hx'⟩
     rwa [π₂.eq_of_mem_of_mem hJ' hJ'' hx' (Hle hx)]
   · rintro ⟨H, HU⟩ J hJ
-    simp only [Set.subset_def, mem_unionᵢ] at HU
+    simp only [Set.subset_def, mem_iUnion] at HU
     rcases HU J.upper ⟨J, hJ, J.upper_mem⟩ with ⟨J₂, hJ₂, hx⟩
     exact ⟨J₂, hJ₂, H _ hJ _ hJ₂ ⟨_, J.upper_mem, hx⟩⟩
-#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_unionᵢ_subset
+#align box_integral.prepartition.le_iff_nonempty_imp_le_and_Union_subset BoxIntegral.Prepartition.le_iff_nonempty_imp_le_and_iUnion_subset
 
-theorem eq_of_boxes_subset_unionᵢ_superset (h₁ : π₁.boxes ⊆ π₂.boxes) (h₂ : π₂.unionᵢ ⊆ π₁.unionᵢ) :
+theorem eq_of_boxes_subset_iUnion_superset (h₁ : π₁.boxes ⊆ π₂.boxes) (h₂ : π₂.iUnion ⊆ π₁.iUnion) :
     π₁ = π₂ :=
   le_antisymm (fun J hJ => ⟨J, h₁ hJ, le_rfl⟩) <|
-    le_iff_nonempty_imp_le_and_unionᵢ_subset.2
+    le_iff_nonempty_imp_le_and_iUnion_subset.2
       ⟨fun _ hJ₁ _ hJ₂ Hne =>
         (π₂.eq_of_mem_of_mem hJ₁ (h₁ hJ₂) Hne.choose_spec.1 Hne.choose_spec.2).le, h₂⟩
-#align box_integral.prepartition.eq_of_boxes_subset_Union_superset BoxIntegral.Prepartition.eq_of_boxes_subset_unionᵢ_superset
+#align box_integral.prepartition.eq_of_boxes_subset_Union_superset BoxIntegral.Prepartition.eq_of_boxes_subset_iUnion_superset
 
 /-- Given a prepartition `π` of a box `I` and a collection of prepartitions `πi J` of all boxes
 `J ∈ π`, returns the prepartition of `I` into the union of the boxes of all `πi J`.
@@ -293,111 +293,111 @@ theorem eq_of_boxes_subset_unionᵢ_superset (h₁ : π₁.boxes ⊆ π₂.boxes
 Though we only use the values of `πi` on the boxes of `π`, we require `πi` to be a globally defined
 function. -/
 @[simps]
-def bunionᵢ (πi : ∀ J : Box ι, Prepartition J) : Prepartition I where
-  boxes := π.boxes.bunionᵢ fun J => (πi J).boxes
+def biUnion (πi : ∀ J : Box ι, Prepartition J) : Prepartition I where
+  boxes := π.boxes.biUnion fun J => (πi J).boxes
   le_of_mem' J hJ := by
-    simp only [Finset.mem_bunionᵢ, exists_prop, mem_boxes] at hJ
+    simp only [Finset.mem_biUnion, exists_prop, mem_boxes] at hJ
     rcases hJ with ⟨J', hJ', hJ⟩
     exact ((πi J').le_of_mem hJ).trans (π.le_of_mem hJ')
   PairwiseDisjoint := by
-    simp only [Set.Pairwise, Finset.mem_coe, Finset.mem_bunionᵢ]
+    simp only [Set.Pairwise, Finset.mem_coe, Finset.mem_biUnion]
     rintro J₁' ⟨J₁, hJ₁, hJ₁'⟩ J₂' ⟨J₂, hJ₂, hJ₂'⟩ Hne
     rw [Function.onFun, Set.disjoint_left]
     rintro x hx₁ hx₂; apply Hne
     obtain rfl : J₁ = J₂
     exact π.eq_of_mem_of_mem hJ₁ hJ₂ ((πi J₁).le_of_mem hJ₁' hx₁) ((πi J₂).le_of_mem hJ₂' hx₂)
     exact (πi J₁).eq_of_mem_of_mem hJ₁' hJ₂' hx₁ hx₂
-#align box_integral.prepartition.bUnion BoxIntegral.Prepartition.bunionᵢ
+#align box_integral.prepartition.bUnion BoxIntegral.Prepartition.biUnion
 
 variable {πi πi₁ πi₂ : ∀ J : Box ι, Prepartition J}
 
 @[simp]
-theorem mem_bunionᵢ : J ∈ π.bunionᵢ πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [bunionᵢ]
-#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_bunionᵢ
+theorem mem_biUnion : J ∈ π.biUnion πi ↔ ∃ J' ∈ π, J ∈ πi J' := by simp [biUnion]
+#align box_integral.prepartition.mem_bUnion BoxIntegral.Prepartition.mem_biUnion
 
-theorem bunionᵢ_le (πi : ∀ J, Prepartition J) : π.bunionᵢ πi ≤ π := fun _ hJ =>
-  let ⟨J', hJ', hJ⟩ := π.mem_bunionᵢ.1 hJ
+theorem biUnion_le (πi : ∀ J, Prepartition J) : π.biUnion πi ≤ π := fun _ hJ =>
+  let ⟨J', hJ', hJ⟩ := π.mem_biUnion.1 hJ
   ⟨J', hJ', (πi J').le_of_mem hJ⟩
-#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.bunionᵢ_le
+#align box_integral.prepartition.bUnion_le BoxIntegral.Prepartition.biUnion_le
 
 @[simp]
-theorem bunionᵢ_top : (π.bunionᵢ fun _ => ⊤) = π := by
+theorem biUnion_top : (π.biUnion fun _ => ⊤) = π := by
   ext
   simp
-#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.bunionᵢ_top
+#align box_integral.prepartition.bUnion_top BoxIntegral.Prepartition.biUnion_top
 
 @[congr]
-theorem bunionᵢ_congr (h : π₁ = π₂) (hi : ∀ J ∈ π₁, πi₁ J = πi₂ J) :
-    π₁.bunionᵢ πi₁ = π₂.bunionᵢ πi₂ := by
+theorem biUnion_congr (h : π₁ = π₂) (hi : ∀ J ∈ π₁, πi₁ J = πi₂ J) :
+    π₁.biUnion πi₁ = π₂.biUnion πi₂ := by
   subst π₂
   ext J
-  simp only [mem_bunionᵢ]
+  simp only [mem_biUnion]
   constructor <;> exact fun ⟨J', h₁, h₂⟩ => ⟨J', h₁, hi J' h₁ ▸ h₂⟩
-#align box_integral.prepartition.bUnion_congr BoxIntegral.Prepartition.bunionᵢ_congr
+#align box_integral.prepartition.bUnion_congr BoxIntegral.Prepartition.biUnion_congr
 
-theorem bunionᵢ_congr_of_le (h : π₁ = π₂) (hi : ∀ J ≤ I, πi₁ J = πi₂ J) :
-    π₁.bunionᵢ πi₁ = π₂.bunionᵢ πi₂ :=
-  bunionᵢ_congr h fun J hJ => hi J (π₁.le_of_mem hJ)
-#align box_integral.prepartition.bUnion_congr_of_le BoxIntegral.Prepartition.bunionᵢ_congr_of_le
+theorem biUnion_congr_of_le (h : π₁ = π₂) (hi : ∀ J ≤ I, πi₁ J = πi₂ J) :
+    π₁.biUnion πi₁ = π₂.biUnion πi₂ :=
+  biUnion_congr h fun J hJ => hi J (π₁.le_of_mem hJ)
+#align box_integral.prepartition.bUnion_congr_of_le BoxIntegral.Prepartition.biUnion_congr_of_le
 
 @[simp]
-theorem unionᵢ_bunionᵢ (πi : ∀ J : Box ι, Prepartition J) :
-    (π.bunionᵢ πi).unionᵢ = ⋃ J ∈ π, (πi J).unionᵢ := by simp [Prepartition.unionᵢ]
-#align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.unionᵢ_bunionᵢ
+theorem iUnion_biUnion (πi : ∀ J : Box ι, Prepartition J) :
+    (π.biUnion πi).iUnion = ⋃ J ∈ π, (πi J).iUnion := by simp [Prepartition.iUnion]
+#align box_integral.prepartition.Union_bUnion BoxIntegral.Prepartition.iUnion_biUnion
 
 @[simp]
-theorem sum_bunionᵢ_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
+theorem sum_biUnion_boxes {M : Type _} [AddCommMonoid M] (π : Prepartition I)
     (πi : ∀ J, Prepartition J) (f : Box ι → M) :
-    (∑ J in π.boxes.bunionᵢ fun J => (πi J).boxes, f J) =
+    (∑ J in π.boxes.biUnion fun J => (πi J).boxes, f J) =
       ∑ J in π.boxes, ∑ J' in (πi J).boxes, f J' := by
-  refine' Finset.sum_bunionᵢ fun J₁ h₁ J₂ h₂ hne => Finset.disjoint_left.2 fun J' h₁' h₂' => _
+  refine' Finset.sum_biUnion fun J₁ h₁ J₂ h₂ hne => Finset.disjoint_left.2 fun J' h₁' h₂' => _
   exact hne (π.eq_of_le_of_le h₁ h₂ ((πi J₁).le_of_mem h₁') ((πi J₂).le_of_mem h₂'))
-#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_bunionᵢ_boxes
-
-/-- Given a box `J ∈ π.bunionᵢ πi`, returns the box `J' ∈ π` such that `J ∈ πi J'`.
-For `J ∉ π.bunionᵢ πi`, returns `I`. -/
-def bunionᵢIndex (πi : ∀ (J : Box ι), Prepartition J) (J : Box ι) : Box ι :=
-  if hJ : J ∈ π.bunionᵢ πi then (π.mem_bunionᵢ.1 hJ).choose else I
-#align box_integral.prepartition.bUnion_index BoxIntegral.Prepartition.bunionᵢIndex
-
-theorem bunionᵢIndex_mem (hJ : J ∈ π.bunionᵢ πi) : π.bunionᵢIndex πi J ∈ π := by
-  rw [bunionᵢIndex, dif_pos hJ]
-  exact (π.mem_bunionᵢ.1 hJ).choose_spec.1
-#align box_integral.prepartition.bUnion_index_mem BoxIntegral.Prepartition.bunionᵢIndex_mem
-
-theorem bunionᵢIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.bunionᵢIndex πi J ≤ I := by
-  by_cases hJ : J ∈ π.bunionᵢ πi
-  · exact π.le_of_mem (π.bunionᵢIndex_mem hJ)
-  · rw [bunionᵢIndex, dif_neg hJ]
-#align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.bunionᵢIndex_le
-
-theorem mem_bunionᵢIndex (hJ : J ∈ π.bunionᵢ πi) : J ∈ πi (π.bunionᵢIndex πi J) := by
-  convert (π.mem_bunionᵢ.1 hJ).choose_spec.2 <;> exact dif_pos hJ
-#align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_bunionᵢIndex
-
-theorem le_bunionᵢIndex (hJ : J ∈ π.bunionᵢ πi) : J ≤ π.bunionᵢIndex πi J :=
-  le_of_mem _ (π.mem_bunionᵢIndex hJ)
-#align box_integral.prepartition.le_bUnion_index BoxIntegral.Prepartition.le_bunionᵢIndex
-
-/-- Uniqueness property of `BoxIntegral.Prepartition.bunionᵢIndex`. -/
-theorem bunionᵢIndex_of_mem (hJ : J ∈ π) {J'} (hJ' : J' ∈ πi J) : π.bunionᵢIndex πi J' = J :=
-  have : J' ∈ π.bunionᵢ πi := π.mem_bunionᵢ.2 ⟨J, hJ, hJ'⟩
-  π.eq_of_le_of_le (π.bunionᵢIndex_mem this) hJ (π.le_bunionᵢIndex this) (le_of_mem _ hJ')
-#align box_integral.prepartition.bUnion_index_of_mem BoxIntegral.Prepartition.bunionᵢIndex_of_mem
-
-theorem bunionᵢ_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : Box ι, Prepartition J) :
-    (π.bunionᵢ fun J => (πi J).bunionᵢ (πi' J)) =
-      (π.bunionᵢ πi).bunionᵢ fun J => πi' (π.bunionᵢIndex πi J) J := by
+#align box_integral.prepartition.sum_bUnion_boxes BoxIntegral.Prepartition.sum_biUnion_boxes
+
+/-- Given a box `J ∈ π.biUnion πi`, returns the box `J' ∈ π` such that `J ∈ πi J'`.
+For `J ∉ π.biUnion πi`, returns `I`. -/
+def biUnionIndex (πi : ∀ (J : Box ι), Prepartition J) (J : Box ι) : Box ι :=
+  if hJ : J ∈ π.biUnion πi then (π.mem_biUnion.1 hJ).choose else I
+#align box_integral.prepartition.bUnion_index BoxIntegral.Prepartition.biUnionIndex
+
+theorem biUnionIndex_mem (hJ : J ∈ π.biUnion πi) : π.biUnionIndex πi J ∈ π := by
+  rw [biUnionIndex, dif_pos hJ]
+  exact (π.mem_biUnion.1 hJ).choose_spec.1
+#align box_integral.prepartition.bUnion_index_mem BoxIntegral.Prepartition.biUnionIndex_mem
+
+theorem biUnionIndex_le (πi : ∀ J, Prepartition J) (J : Box ι) : π.biUnionIndex πi J ≤ I := by
+  by_cases hJ : J ∈ π.biUnion πi
+  · exact π.le_of_mem (π.biUnionIndex_mem hJ)
+  · rw [biUnionIndex, dif_neg hJ]
+#align box_integral.prepartition.bUnion_index_le BoxIntegral.Prepartition.biUnionIndex_le
+
+theorem mem_biUnionIndex (hJ : J ∈ π.biUnion πi) : J ∈ πi (π.biUnionIndex πi J) := by
+  convert (π.mem_biUnion.1 hJ).choose_spec.2 <;> exact dif_pos hJ
+#align box_integral.prepartition.mem_bUnion_index BoxIntegral.Prepartition.mem_biUnionIndex
+
+theorem le_biUnionIndex (hJ : J ∈ π.biUnion πi) : J ≤ π.biUnionIndex πi J :=
+  le_of_mem _ (π.mem_biUnionIndex hJ)
+#align box_integral.prepartition.le_bUnion_index BoxIntegral.Prepartition.le_biUnionIndex
+
+/-- Uniqueness property of `BoxIntegral.Prepartition.biUnionIndex`. -/
+theorem biUnionIndex_of_mem (hJ : J ∈ π) {J'} (hJ' : J' ∈ πi J) : π.biUnionIndex πi J' = J :=
+  have : J' ∈ π.biUnion πi := π.mem_biUnion.2 ⟨J, hJ, hJ'⟩
+  π.eq_of_le_of_le (π.biUnionIndex_mem this) hJ (π.le_biUnionIndex this) (le_of_mem _ hJ')
+#align box_integral.prepartition.bUnion_index_of_mem BoxIntegral.Prepartition.biUnionIndex_of_mem
+
+theorem biUnion_assoc (πi : ∀ J, Prepartition J) (πi' : Box ι → ∀ J : Box ι, Prepartition J) :
+    (π.biUnion fun J => (πi J).biUnion (πi' J)) =
+      (π.biUnion πi).biUnion fun J => πi' (π.biUnionIndex πi J) J := by
   ext J
-  simp only [mem_bunionᵢ, exists_prop]
+  simp only [mem_biUnion, exists_prop]
   constructor
   · rintro ⟨J₁, hJ₁, J₂, hJ₂, hJ⟩
     refine' ⟨J₂, ⟨J₁, hJ₁, hJ₂⟩, _⟩
-    rwa [π.bunionᵢIndex_of_mem hJ₁ hJ₂]
+    rwa [π.biUnionIndex_of_mem hJ₁ hJ₂]
   · rintro ⟨J₁, ⟨J₂, hJ₂, hJ₁⟩, hJ⟩
     refine' ⟨J₂, hJ₂, J₁, hJ₁, _⟩
-    rwa [π.bunionᵢIndex_of_mem hJ₂ hJ₁] at hJ
-#align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.bunionᵢ_assoc
+    rwa [π.biUnionIndex_of_mem hJ₂ hJ₁] at hJ
+#align box_integral.prepartition.bUnion_assoc BoxIntegral.Prepartition.biUnion_assoc
 
 /-- Create a `BoxIntegral.Prepartition` from a collection of possibly empty boxes by filtering out
 the empty one if it exists. -/
@@ -421,15 +421,15 @@ theorem mem_ofWithBot {boxes : Finset (WithBot (Box ι))} {h₁ h₂} :
 #align box_integral.prepartition.mem_of_with_bot BoxIntegral.Prepartition.mem_ofWithBot
 
 @[simp]
-theorem unionᵢ_ofWithBot (boxes : Finset (WithBot (Box ι)))
+theorem iUnion_ofWithBot (boxes : Finset (WithBot (Box ι)))
     (le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I)
     (pairwise_disjoint : Set.Pairwise (boxes : Set (WithBot (Box ι))) Disjoint) :
-    (ofWithBot boxes le_of_mem pairwise_disjoint).unionᵢ = ⋃ J ∈ boxes, ↑J := by
+    (ofWithBot boxes le_of_mem pairwise_disjoint).iUnion = ⋃ J ∈ boxes, ↑J := by
   suffices (⋃ (J : Box ι) (_hJ : ↑J ∈ boxes), ↑J) = ⋃ J ∈ boxes, (J : Set (ι → ℝ)) by
-    simpa [ofWithBot, Prepartition.unionᵢ]
-  simp only [← Box.bunionᵢ_coe_eq_coe, @unionᵢ_comm _ _ (Box ι), @unionᵢ_comm _ _ (@Eq _ _ _),
-    unionᵢ_unionᵢ_eq_right]
-#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.unionᵢ_ofWithBot
+    simpa [ofWithBot, Prepartition.iUnion]
+  simp only [← Box.biUnion_coe_eq_coe, @iUnion_comm _ _ (Box ι), @iUnion_comm _ _ (@Eq _ _ _),
+    iUnion_iUnion_eq_right]
+#align box_integral.prepartition.Union_of_with_bot BoxIntegral.Prepartition.iUnion_ofWithBot
 
 theorem ofWithBot_le {boxes : Finset (WithBot (Box ι))}
     {le_of_mem : ∀ J ∈ boxes, (J : WithBot (Box ι)) ≤ I}
@@ -509,9 +509,9 @@ theorem monotone_restrict : Monotone fun π : Prepartition I => restrict π J :=
 /-- Restricting to a larger box does not change the set of boxes. We cannot claim equality
 of prepartitions because they have different types. -/
 theorem restrict_boxes_of_le (π : Prepartition I) (h : I ≤ J) : (π.restrict J).boxes = π.boxes := by
-  simp only [restrict, ofWithBot, eraseNone_eq_bunionᵢ]
-  refine' Finset.image_bunionᵢ.trans _
-  refine' (Finset.bunionᵢ_congr rfl _).trans Finset.bunionᵢ_singleton_eq_self
+  simp only [restrict, ofWithBot, eraseNone_eq_biUnion]
+  refine' Finset.image_biUnion.trans _
+  refine' (Finset.biUnion_congr rfl _).trans Finset.biUnion_singleton_eq_self
   intro J' hJ'
   rw [inf_of_le_right, ← WithBot.some_eq_coe, Option.toFinset_some]
   exact WithBot.coe_le_coe.2 ((π.le_of_mem hJ').trans h)
@@ -523,71 +523,71 @@ theorem restrict_self : π.restrict I = π :=
 #align box_integral.prepartition.restrict_self BoxIntegral.Prepartition.restrict_self
 
 @[simp]
-theorem unionᵢ_restrict : (π.restrict J).unionᵢ = (J : Set (ι → ℝ)) ∩ (π.unionᵢ) := by
-  simp [restrict, ← inter_unionᵢ, ← unionᵢ_def]
-#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.unionᵢ_restrict
+theorem iUnion_restrict : (π.restrict J).iUnion = (J : Set (ι → ℝ)) ∩ (π.iUnion) := by
+  simp [restrict, ← inter_iUnion, ← iUnion_def]
+#align box_integral.prepartition.Union_restrict BoxIntegral.Prepartition.iUnion_restrict
 
 @[simp]
-theorem restrict_bunionᵢ (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
-    (π.bunionᵢ πi).restrict J = πi J := by
-  refine' (eq_of_boxes_subset_unionᵢ_superset (fun J₁ h₁ => _) _).symm
-  · refine' (mem_restrict _).2 ⟨J₁, π.mem_bunionᵢ.2 ⟨J, hJ, h₁⟩, (inf_of_le_right _).symm⟩
+theorem restrict_biUnion (πi : ∀ J, Prepartition J) (hJ : J ∈ π) :
+    (π.biUnion πi).restrict J = πi J := by
+  refine' (eq_of_boxes_subset_iUnion_superset (fun J₁ h₁ => _) _).symm
+  · refine' (mem_restrict _).2 ⟨J₁, π.mem_biUnion.2 ⟨J, hJ, h₁⟩, (inf_of_le_right _).symm⟩
     exact WithBot.coe_le_coe.2 (le_of_mem _ h₁)
-  · simp only [unionᵢ_restrict, unionᵢ_bunionᵢ, Set.subset_def, Set.mem_inter_iff, Set.mem_unionᵢ]
+  · simp only [iUnion_restrict, iUnion_biUnion, Set.subset_def, Set.mem_inter_iff, Set.mem_iUnion]
     rintro x ⟨hxJ, J₁, h₁, hx⟩
     obtain rfl : J = J₁
-    exact π.eq_of_mem_of_mem hJ h₁ hxJ (unionᵢ_subset _ hx)
+    exact π.eq_of_mem_of_mem hJ h₁ hxJ (iUnion_subset _ hx)
     exact hx
-#align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_bunionᵢ
+#align box_integral.prepartition.restrict_bUnion BoxIntegral.Prepartition.restrict_biUnion
 
-theorem bunionᵢ_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
-    π.bunionᵢ πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J := by
+theorem biUnion_le_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
+    π.biUnion πi ≤ π' ↔ ∀ J ∈ π, πi J ≤ π'.restrict J := by
   constructor <;> intro H J hJ
-  · rw [← π.restrict_bunionᵢ πi hJ]
+  · rw [← π.restrict_biUnion πi hJ]
     exact restrict_mono H
-  · rw [mem_bunionᵢ] at hJ
+  · rw [mem_biUnion] at hJ
     rcases hJ with ⟨J₁, h₁, hJ⟩
     rcases H J₁ h₁ hJ with ⟨J₂, h₂, Hle⟩
     rcases π'.mem_restrict.mp h₂ with ⟨J₃, h₃, H⟩
     exact ⟨J₃, h₃, Hle.trans <| WithBot.coe_le_coe.1 <| H.trans_le inf_le_right⟩
-#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.bunionᵢ_le_iff
+#align box_integral.prepartition.bUnion_le_iff BoxIntegral.Prepartition.biUnion_le_iff
 
-theorem le_bunionᵢ_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
-    π' ≤ π.bunionᵢ πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J := by
-  refine' ⟨fun H => ⟨H.trans (π.bunionᵢ_le πi), fun J hJ => _⟩, _⟩
-  · rw [← π.restrict_bunionᵢ πi hJ]
+theorem le_biUnion_iff {πi : ∀ J, Prepartition J} {π' : Prepartition I} :
+    π' ≤ π.biUnion πi ↔ π' ≤ π ∧ ∀ J ∈ π, π'.restrict J ≤ πi J := by
+  refine' ⟨fun H => ⟨H.trans (π.biUnion_le πi), fun J hJ => _⟩, _⟩
+  · rw [← π.restrict_biUnion πi hJ]
     exact restrict_mono H
   · rintro ⟨H, Hi⟩ J' hJ'
     rcases H hJ' with ⟨J, hJ, hle⟩
     have : J' ∈ π'.restrict J :=
       π'.mem_restrict.2 ⟨J', hJ', (inf_of_le_right <| WithBot.coe_le_coe.2 hle).symm⟩
     rcases Hi J hJ this with ⟨Ji, hJi, hlei⟩
-    exact ⟨Ji, π.mem_bunionᵢ.2 ⟨J, hJ, hJi⟩, hlei⟩
-#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_bunionᵢ_iff
+    exact ⟨Ji, π.mem_biUnion.2 ⟨J, hJ, hJi⟩, hlei⟩
+#align box_integral.prepartition.le_bUnion_iff BoxIntegral.Prepartition.le_biUnion_iff
 
 instance inf : Inf (Prepartition I) :=
-  ⟨fun π₁ π₂ => π₁.bunionᵢ fun J => π₂.restrict J⟩
+  ⟨fun π₁ π₂ => π₁.biUnion fun J => π₂.restrict J⟩
 
-theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.bunionᵢ fun J => π₂.restrict J := rfl
+theorem inf_def (π₁ π₂ : Prepartition I) : π₁ ⊓ π₂ = π₁.biUnion fun J => π₂.restrict J := rfl
 #align box_integral.prepartition.inf_def BoxIntegral.Prepartition.inf_def
 
 @[simp]
 theorem mem_inf {π₁ π₂ : Prepartition I} :
     J ∈ π₁ ⊓ π₂ ↔ ∃ J₁ ∈ π₁, ∃ J₂ ∈ π₂, (J : WithBot (Box ι)) = ↑J₁ ⊓ ↑J₂ := by
-  simp only [inf_def, mem_bunionᵢ, mem_restrict]
+  simp only [inf_def, mem_biUnion, mem_restrict]
 #align box_integral.prepartition.mem_inf BoxIntegral.Prepartition.mem_inf
 
 @[simp]
-theorem unionᵢ_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).unionᵢ = π₁.unionᵢ ∩ π₂.unionᵢ := by
-  simp only [inf_def, unionᵢ_bunionᵢ, unionᵢ_restrict, ← unionᵢ_inter, ← unionᵢ_def]
-#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.unionᵢ_inf
+theorem iUnion_inf (π₁ π₂ : Prepartition I) : (π₁ ⊓ π₂).iUnion = π₁.iUnion ∩ π₂.iUnion := by
+  simp only [inf_def, iUnion_biUnion, iUnion_restrict, ← iUnion_inter, ← iUnion_def]
+#align box_integral.prepartition.Union_inf BoxIntegral.Prepartition.iUnion_inf
 
 instance : SemilatticeInf (Prepartition I) :=
   { Prepartition.inf,
     Prepartition.partialOrder with
-    inf_le_left := fun π₁ _ => π₁.bunionᵢ_le _
-    inf_le_right := fun _ _ => (bunionᵢ_le_iff _).2 fun _ _ => le_rfl
-    le_inf := fun _ π₁ _ h₁ h₂ => π₁.le_bunionᵢ_iff.2 ⟨h₁, fun _ _ => restrict_mono h₂⟩ }
+    inf_le_left := fun π₁ _ => π₁.biUnion_le _
+    inf_le_right := fun _ _ => (biUnion_le_iff _).2 fun _ _ => le_rfl
+    le_inf := fun _ π₁ _ h₁ h₂ => π₁.le_biUnion_iff.2 ⟨h₁, fun _ _ => restrict_mono h₂⟩ }
 
 /-- The prepartition with boxes `{J ∈ π | p J}`. -/
 @[simps]
@@ -618,16 +618,16 @@ theorem filter_true : (π.filter fun _ => True) = π :=
 #align box_integral.prepartition.filter_true BoxIntegral.Prepartition.filter_true
 
 @[simp]
-theorem unionᵢ_filter_not (π : Prepartition I) (p : Box ι → Prop) :
-    (π.filter fun J => ¬p J).unionᵢ = π.unionᵢ \ (π.filter p).unionᵢ := by
-  simp only [Prepartition.unionᵢ]
-  convert (@Set.bunionᵢ_diff_bunionᵢ_eq _ (Box ι) π.boxes (π.filter p).boxes (↑) _).symm
+theorem iUnion_filter_not (π : Prepartition I) (p : Box ι → Prop) :
+    (π.filter fun J => ¬p J).iUnion = π.iUnion \ (π.filter p).iUnion := by
+  simp only [Prepartition.iUnion]
+  convert (@Set.biUnion_diff_biUnion_eq _ (Box ι) π.boxes (π.filter p).boxes (↑) _).symm
   · simp (config := { contextual := true })
   · rw [Set.PairwiseDisjoint]
     convert π.PairwiseDisjoint
     rw [Set.union_eq_left_iff_subset, filter_boxes, coe_filter]
     exact fun _ ⟨h, _⟩ => h
-#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.unionᵢ_filter_not
+#align box_integral.prepartition.Union_filter_not BoxIntegral.Prepartition.iUnion_filter_not
 
 theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι → α) (g : Box ι → M) :
     (∑ y in π.boxes.image f, ∑ J in (π.filter fun J => f J = y).boxes, g J) =
@@ -637,32 +637,32 @@ theorem sum_fiberwise {α M} [AddCommMonoid M] (π : Prepartition I) (f : Box ι
 
 /-- Union of two disjoint prepartitions. -/
 @[simps]
-def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.unionᵢ π₂.unionᵢ) : Prepartition I where
+def disjUnion (π₁ π₂ : Prepartition I) (h : Disjoint π₁.iUnion π₂.iUnion) : Prepartition I where
   boxes := π₁.boxes ∪ π₂.boxes
   le_of_mem' J hJ := (Finset.mem_union.1 hJ).elim π₁.le_of_mem π₂.le_of_mem
   PairwiseDisjoint :=
     suffices ∀ J₁ ∈ π₁, ∀ J₂ ∈ π₂, J₁ ≠ J₂ → Disjoint (J₁ : Set (ι → ℝ)) J₂ by
       simpa [pairwise_union_of_symmetric (symmetric_disjoint.comap _), PairwiseDisjoint]
-    fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_unionᵢ h₁) (π₂.subset_unionᵢ h₂)
+    fun J₁ h₁ J₂ h₂ _ => h.mono (π₁.subset_iUnion h₁) (π₂.subset_iUnion h₂)
 #align box_integral.prepartition.disj_union BoxIntegral.Prepartition.disjUnion
 
 @[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.prepartition.mem_disj_union BoxIntegral.Prepartition.mem_disjUnion
 
 @[simp]
-theorem unionᵢ_disjUnion (h : Disjoint π₁.unionᵢ π₂.unionᵢ) :
-    (π₁.disjUnion π₂ h).unionᵢ = π₁.unionᵢ ∪ π₂.unionᵢ := by
-  simp [disjUnion, Prepartition.unionᵢ, unionᵢ_or, unionᵢ_union_distrib]
-#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.unionᵢ_disjUnion
+theorem iUnion_disjUnion (h : Disjoint π₁.iUnion π₂.iUnion) :
+    (π₁.disjUnion π₂ h).iUnion = π₁.iUnion ∪ π₂.iUnion := by
+  simp [disjUnion, Prepartition.iUnion, iUnion_or, iUnion_union_distrib]
+#align box_integral.prepartition.Union_disj_union BoxIntegral.Prepartition.iUnion_disjUnion
 
 @[simp]
-theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.unionᵢ π₂.unionᵢ)
+theorem sum_disj_union_boxes {M : Type _} [AddCommMonoid M] (h : Disjoint π₁.iUnion π₂.iUnion)
     (f : Box ι → M) :
     (∑ J in π₁.boxes ∪ π₂.boxes, f J) = (∑ J in π₁.boxes, f J) + ∑ J in π₂.boxes, f J :=
-  sum_union <| disjoint_boxes_of_disjoint_unionᵢ h
+  sum_union <| disjoint_boxes_of_disjoint_iUnion h
 #align box_integral.prepartition.sum_disj_union_boxes BoxIntegral.Prepartition.sum_disj_union_boxes
 
 section Distortion
@@ -683,13 +683,13 @@ theorem distortion_le_iff {c : ℝ≥0} : π.distortion ≤ c ↔ ∀ J ∈ π,
   Finset.sup_le_iff
 #align box_integral.prepartition.distortion_le_iff BoxIntegral.Prepartition.distortion_le_iff
 
-theorem distortion_bunionᵢ (π : Prepartition I) (πi : ∀ J, Prepartition J) :
-    (π.bunionᵢ πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
-  sup_bunionᵢ _ _
-#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_bunionᵢ
+theorem distortion_biUnion (π : Prepartition I) (πi : ∀ J, Prepartition J) :
+    (π.biUnion πi).distortion = π.boxes.sup fun J => (πi J).distortion :=
+  sup_biUnion _ _
+#align box_integral.prepartition.distortion_bUnion BoxIntegral.Prepartition.distortion_biUnion
 
 @[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.prepartition.distortion_disj_union BoxIntegral.Prepartition.distortion_disjUnion
@@ -716,14 +716,14 @@ def IsPartition (π : Prepartition I) :=
   ∀ x ∈ I, ∃ J ∈ π, x ∈ J
 #align box_integral.prepartition.is_partition BoxIntegral.Prepartition.IsPartition
 
-theorem isPartition_iff_unionᵢ_eq {π : Prepartition I} : π.IsPartition ↔ π.unionᵢ = I := by
-  simp_rw [IsPartition, Set.Subset.antisymm_iff, π.unionᵢ_subset, true_and_iff, Set.subset_def,
-    mem_unionᵢ, Box.mem_coe]
-#align box_integral.prepartition.is_partition_iff_Union_eq BoxIntegral.Prepartition.isPartition_iff_unionᵢ_eq
+theorem isPartition_iff_iUnion_eq {π : Prepartition I} : π.IsPartition ↔ π.iUnion = I := by
+  simp_rw [IsPartition, Set.Subset.antisymm_iff, π.iUnion_subset, true_and_iff, Set.subset_def,
+    mem_iUnion, Box.mem_coe]
+#align box_integral.prepartition.is_partition_iff_Union_eq BoxIntegral.Prepartition.isPartition_iff_iUnion_eq
 
 @[simp]
 theorem isPartition_single_iff (h : J ≤ I) : IsPartition (single I J h) ↔ J = I := by
-  simp [isPartition_iff_unionᵢ_eq]
+  simp [isPartition_iff_iUnion_eq]
 #align box_integral.prepartition.is_partition_single_iff BoxIntegral.Prepartition.isPartition_single_iff
 
 theorem isPartitionTop (I : Box ι) : IsPartition (⊤ : Prepartition I) :=
@@ -734,13 +734,13 @@ namespace IsPartition
 
 variable {π}
 
-theorem unionᵢ_eq (h : π.IsPartition) : π.unionᵢ = I :=
-  isPartition_iff_unionᵢ_eq.1 h
-#align box_integral.prepartition.is_partition.Union_eq BoxIntegral.Prepartition.IsPartition.unionᵢ_eq
+theorem iUnion_eq (h : π.IsPartition) : π.iUnion = I :=
+  isPartition_iff_iUnion_eq.1 h
+#align box_integral.prepartition.is_partition.Union_eq BoxIntegral.Prepartition.IsPartition.iUnion_eq
 
-theorem unionᵢ_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.unionᵢ ⊆ π.unionᵢ :=
-  h.unionᵢ_eq.symm ▸ π₁.unionᵢ_subset
-#align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.unionᵢ_subset
+theorem iUnion_subset (h : π.IsPartition) (π₁ : Prepartition I) : π₁.iUnion ⊆ π.iUnion :=
+  h.iUnion_eq.symm ▸ π₁.iUnion_subset
+#align box_integral.prepartition.is_partition.Union_subset BoxIntegral.Prepartition.IsPartition.iUnion_subset
 
 protected theorem existsUnique (h : π.IsPartition) (hx : x ∈ I) :
     ∃! (J : _) (_ : J ∈ π), x ∈ J := by
@@ -754,41 +754,41 @@ theorem nonempty_boxes (h : π.IsPartition) : π.boxes.Nonempty :=
 #align box_integral.prepartition.is_partition.nonempty_boxes BoxIntegral.Prepartition.IsPartition.nonempty_boxes
 
 theorem eq_of_boxes_subset (h₁ : π₁.IsPartition) (h₂ : π₁.boxes ⊆ π₂.boxes) : π₁ = π₂ :=
-  eq_of_boxes_subset_unionᵢ_superset h₂ <| h₁.unionᵢ_subset _
+  eq_of_boxes_subset_iUnion_superset h₂ <| h₁.iUnion_subset _
 #align box_integral.prepartition.is_partition.eq_of_boxes_subset BoxIntegral.Prepartition.IsPartition.eq_of_boxes_subset
 
 theorem le_iff (h : π₂.IsPartition) :
     π₁ ≤ π₂ ↔ ∀ J ∈ π₁, ∀ J' ∈ π₂, (J ∩ J' : Set (ι → ℝ)).Nonempty → J ≤ J' :=
-  le_iff_nonempty_imp_le_and_unionᵢ_subset.trans <| and_iff_left <| h.unionᵢ_subset _
+  le_iff_nonempty_imp_le_and_iUnion_subset.trans <| and_iff_left <| h.iUnion_subset _
 #align box_integral.prepartition.is_partition.le_iff BoxIntegral.Prepartition.IsPartition.le_iff
 
-protected theorem bunionᵢ (h : IsPartition π) (hi : ∀ J ∈ π, IsPartition (πi J)) :
-    IsPartition (π.bunionᵢ πi) := fun x hx =>
+protected theorem biUnion (h : IsPartition π) (hi : ∀ J ∈ π, IsPartition (πi J)) :
+    IsPartition (π.biUnion πi) := fun x hx =>
   let ⟨J, hJ, hxi⟩ := h x hx
   let ⟨Ji, hJi, hx⟩ := hi J hJ x hxi
-  ⟨Ji, π.mem_bunionᵢ.2 ⟨J, hJ, hJi⟩, hx⟩
-#align box_integral.prepartition.is_partition.bUnion BoxIntegral.Prepartition.IsPartition.bunionᵢ
+  ⟨Ji, π.mem_biUnion.2 ⟨J, hJ, hJi⟩, hx⟩
+#align box_integral.prepartition.is_partition.bUnion BoxIntegral.Prepartition.IsPartition.biUnion
 
 protected theorem restrict (h : IsPartition π) (hJ : J ≤ I) : IsPartition (π.restrict J) :=
-  isPartition_iff_unionᵢ_eq.2 <| by simp [h.unionᵢ_eq, hJ]
+  isPartition_iff_iUnion_eq.2 <| by simp [h.iUnion_eq, hJ]
 #align box_integral.prepartition.is_partition.restrict BoxIntegral.Prepartition.IsPartition.restrict
 
 protected theorem inf (h₁ : IsPartition π₁) (h₂ : IsPartition π₂) : IsPartition (π₁ ⊓ π₂) :=
-  isPartition_iff_unionᵢ_eq.2 <| by simp [h₁.unionᵢ_eq, h₂.unionᵢ_eq]
+  isPartition_iff_iUnion_eq.2 <| by simp [h₁.iUnion_eq, h₂.iUnion_eq]
 #align box_integral.prepartition.is_partition.inf BoxIntegral.Prepartition.IsPartition.inf
 
 end IsPartition
 
-theorem unionᵢ_bunionᵢ_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
-    (π.bunionᵢ πi).unionᵢ = π.unionᵢ :=
-  (unionᵢ_bunionᵢ _ _).trans <|
-    unionᵢ_congr_of_surjective id surjective_id fun J =>
-      unionᵢ_congr_of_surjective id surjective_id fun hJ => (h J hJ).unionᵢ_eq
-#align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.unionᵢ_bunionᵢ_partition
+theorem iUnion_biUnion_partition (h : ∀ J ∈ π, (πi J).IsPartition) :
+    (π.biUnion πi).iUnion = π.iUnion :=
+  (iUnion_biUnion _ _).trans <|
+    iUnion_congr_of_surjective id surjective_id fun J =>
+      iUnion_congr_of_surjective id surjective_id fun hJ => (h J hJ).iUnion_eq
+#align box_integral.prepartition.Union_bUnion_partition BoxIntegral.Prepartition.iUnion_biUnion_partition
 
-theorem isPartitionDisjUnionOfEqDiff (h : π₂.unionᵢ = ↑I \ π₁.unionᵢ) :
+theorem isPartitionDisjUnionOfEqDiff (h : π₂.iUnion = ↑I \ π₁.iUnion) :
     IsPartition (π₁.disjUnion π₂ <| h.symm ▸ disjoint_sdiff_self_right) :=
-  isPartition_iff_unionᵢ_eq.2 <| (unionᵢ_disjUnion _).trans <| by simp [h, π₁.unionᵢ_subset]
+  isPartition_iff_iUnion_eq.2 <| (iUnion_disjUnion _).trans <| by simp [h, π₁.iUnion_subset]
 #align box_integral.prepartition.is_partition_disj_union_of_eq_diff BoxIntegral.Prepartition.isPartitionDisjUnionOfEqDiff
 
 end Prepartition

Co-authored-by: Jeremy Tan Jie Rui <reddeloostw@gmail.com> Co-authored-by: int-y1 <jason_yuen2007@hotmail.com>