analysis.box_integral.partition.subbox_induction ⟷ Mathlib.Analysis.BoxIntegral.Partition.SubboxInduction

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

@@ -143,7 +143,7 @@ theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
       intro J' hJ'
       rcases(split_center J).mem_biUnionTagged.1 hJ' with ⟨J₁, h₁, h₂⟩
       refine' ⟨n J₁ J' + 1, fun i => _⟩
-      simp only [hn J₁ h₁ J' h₂, upper_sub_lower_of_mem_split_center h₁, pow_succ, div_div]
+      simp only [hn J₁ h₁ J' h₂, upper_sub_lower_of_mem_split_center h₁, pow_succ', div_div]
     refine' ⟨_, hP, is_Henstock_bUnion_tagged.2 hHen, is_subordinate_bUnion_tagged.2 hr, hsub, _⟩
     refine' tagged_prepartition.distortion_of_const _ hP.nonempty_boxes fun J' h' => _
     rcases hsub J' h' with ⟨n, hn⟩

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

@@ -152,7 +152,7 @@ theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
       ⟨I.Icc ∩ closed_ball z (r z), inter_mem_nhdsWithin _ (closed_ball_mem_nhds _ (r z).coe_prop),
         _⟩
     intro J Hle n Hmem HIcc Hsub
-    rw [Set.subset_inter_iff] at HIcc 
+    rw [Set.subset_inter_iff] at HIcc
     refine'
       ⟨single _ _ le_rfl _ Hmem, is_partition_single _, is_Henstock_single _,
         (is_subordinate_single _ _).2 HIcc.2, _, distortion_single _ _⟩

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.Analysis.BoxIntegral.Box.SubboxInduction
-import Mathbin.Analysis.BoxIntegral.Partition.Tagged
+import Analysis.BoxIntegral.Box.SubboxInduction
+import Analysis.BoxIntegral.Partition.Tagged
 
 #align_import analysis.box_integral.partition.subbox_induction from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
 

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.subbox_induction
-! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.Analysis.BoxIntegral.Box.SubboxInduction
 import Mathbin.Analysis.BoxIntegral.Partition.Tagged
 
+#align_import analysis.box_integral.partition.subbox_induction from "leanprover-community/mathlib"@"50251fd6309cca5ca2e747882ffecd2729f38c5d"
+
 /-!
 # Induction on subboxes
 

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

@@ -72,11 +72,13 @@ theorem isPartition_splitCenter (I : Box ι) : IsPartition (splitCenter I) := fu
 #align box_integral.prepartition.is_partition_split_center BoxIntegral.Prepartition.isPartition_splitCenter
 -/
 
+#print BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter /-
 theorem upper_sub_lower_of_mem_splitCenter (h : J ∈ splitCenter I) (i : ι) :
     J.upper i - J.lower i = (I.upper i - I.lower i) / 2 :=
   let ⟨s, hs⟩ := mem_splitCenter.1 h
   hs ▸ I.upper_sub_lower_splitCenterBox s i
 #align box_integral.prepartition.upper_sub_lower_of_mem_split_center BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter
+-/
 
 end Prepartition
 
@@ -84,6 +86,7 @@ namespace Box
 
 open Prepartition TaggedPrepartition
 
+#print BoxIntegral.Box.subbox_induction_on /-
 /-- Let `p` be a predicate on `box ι`, let `I` be a box. Suppose that the following two properties
 hold true.
 
@@ -111,7 +114,9 @@ theorem subbox_induction_on {p : Box ι → Prop} (I : Box ι)
   rcases mem_split_center.1 h' with ⟨s, rfl⟩
   exact hs s
 #align box_integral.box.subbox_induction_on BoxIntegral.Box.subbox_induction_on
+-/
 
+#print BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic /-
 /-- Given a box `I` in `ℝⁿ` and a function `r : ℝⁿ → (0, ∞)`, there exists a tagged partition `π` of
 `I` such that
 
@@ -157,6 +162,7 @@ theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
     simp only [tagged_prepartition.mem_single, forall_eq]
     refine' ⟨0, fun i => _⟩; simp
 #align box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic
+-/
 
 end Box
 
@@ -164,6 +170,7 @@ namespace Prepartition
 
 open TaggedPrepartition Finset Function
 
+#print BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq /-
 /-- Given a box `I` in `ℝⁿ`, a function `r : ℝⁿ → (0, ∞)`, and a prepartition `π` of `I`, there
 exists a tagged prepartition `π'` of `I` such that
 
@@ -187,7 +194,9 @@ theorem exists_tagged_le_isHenstock_isSubordinate_iUnion_eq {I : Box ι} (r : (
   rw [distortion_bUnion_tagged]
   exact sup_congr rfl fun J _ => πid J
 #align box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq
+-/
 
+#print BoxIntegral.Prepartition.toSubordinate /-
 /-- Given a prepartition `π` of a box `I` and a function `r : ℝⁿ → (0, ∞)`, `π.to_subordinate r`
 is a tagged partition `π'` such that
 
@@ -200,38 +209,50 @@ is a tagged partition `π'` such that
 def toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) : TaggedPrepartition I :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).some
 #align box_integral.prepartition.to_subordinate BoxIntegral.Prepartition.toSubordinate
+-/
 
+#print BoxIntegral.Prepartition.toSubordinate_toPrepartition_le /-
 theorem toSubordinate_toPrepartition_le (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).toPrepartition ≤ π :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.1
 #align box_integral.prepartition.to_subordinate_to_prepartition_le BoxIntegral.Prepartition.toSubordinate_toPrepartition_le
+-/
 
+#print BoxIntegral.Prepartition.isHenstock_toSubordinate /-
 theorem isHenstock_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsHenstock :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.1
 #align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstock_toSubordinate
+-/
 
+#print BoxIntegral.Prepartition.isSubordinate_toSubordinate /-
 theorem isSubordinate_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsSubordinate r :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.1
 #align box_integral.prepartition.is_subordinate_to_subordinate BoxIntegral.Prepartition.isSubordinate_toSubordinate
+-/
 
+#print BoxIntegral.Prepartition.distortion_toSubordinate /-
 @[simp]
 theorem distortion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).distortion = π.distortion :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.2.1
 #align box_integral.prepartition.distortion_to_subordinate BoxIntegral.Prepartition.distortion_toSubordinate
+-/
 
+#print BoxIntegral.Prepartition.iUnion_toSubordinate /-
 @[simp]
 theorem iUnion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).iUnion = π.iUnion :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.2.2
 #align box_integral.prepartition.Union_to_subordinate BoxIntegral.Prepartition.iUnion_toSubordinate
+-/
 
 end Prepartition
 
 namespace TaggedPrepartition
 
+#print BoxIntegral.TaggedPrepartition.unionComplToSubordinate /-
 /-- Given a tagged prepartition `π₁`, a prepartition `π₂` that covers exactly `I \ π₁.Union`, and
 a function `r : ℝⁿ → (0, ∞)`, returns the union of `π₁` and `π₂.to_subordinate r`. This partition
 `π` has the following properties:
@@ -248,33 +269,42 @@ def unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition
   π₁.disjUnion (π₂.toSubordinate r)
     (((π₂.iUnion_toSubordinate r).trans hU).symm ▸ disjoint_sdiff_self_right)
 #align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinate
+-/
 
+#print BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate /-
 theorem isPartition_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     IsPartition (π₁.unionComplToSubordinate π₂ hU r) :=
   Prepartition.isPartitionDisjUnionOfEqDiff ((π₂.iUnion_toSubordinate r).trans hU)
 #align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate
+-/
 
+#print BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes /-
 @[simp]
 theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π₁.unionComplToSubordinate π₂ hU r).boxes = π₁.boxes ∪ (π₂.toSubordinate r).boxes :=
   rfl
 #align box_integral.tagged_prepartition.union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes
+-/
 
+#print BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes /-
 @[simp]
 theorem iUnion_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π₁.unionComplToSubordinate π₂ hU r).iUnion = I :=
   (isPartition_unionComplToSubordinate _ _ _ _).iUnion_eq
 #align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes
+-/
 
+#print BoxIntegral.TaggedPrepartition.distortion_unionComplToSubordinate /-
 @[simp]
 theorem distortion_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π₁.unionComplToSubordinate π₂ hU r).distortion = max π₁.distortion π₂.distortion := by
   simp [union_compl_to_subordinate]
 #align box_integral.tagged_prepartition.distortion_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.distortion_unionComplToSubordinate
+-/
 
 end TaggedPrepartition
 

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

@@ -150,7 +150,7 @@ theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
       ⟨I.Icc ∩ closed_ball z (r z), inter_mem_nhdsWithin _ (closed_ball_mem_nhds _ (r z).coe_prop),
         _⟩
     intro J Hle n Hmem HIcc Hsub
-    rw [Set.subset_inter_iff] at HIcc
+    rw [Set.subset_inter_iff] at HIcc 
     refine'
       ⟨single _ _ le_rfl _ Hmem, is_partition_single _, is_Henstock_single _,
         (is_subordinate_single _ _).2 HIcc.2, _, distortion_single _ _⟩

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

@@ -39,7 +39,7 @@ namespace BoxIntegral
 
 open Set Metric
 
-open Classical Topology
+open scoped Classical Topology
 
 noncomputable section
 

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

@@ -72,12 +72,6 @@ theorem isPartition_splitCenter (I : Box ι) : IsPartition (splitCenter I) := fu
 #align box_integral.prepartition.is_partition_split_center BoxIntegral.Prepartition.isPartition_splitCenter
 -/
 
-/- warning: box_integral.prepartition.upper_sub_lower_of_mem_split_center -> BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter is a dubious translation:
-lean 3 declaration is
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} {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 (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 I)) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
-but is expected to have type
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} {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 (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 I)) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.upper_sub_lower_of_mem_split_center BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenterₓ'. -/
 theorem upper_sub_lower_of_mem_splitCenter (h : J ∈ splitCenter I) (i : ι) :
     J.upper i - J.lower i = (I.upper i - I.lower i) / 2 :=
   let ⟨s, hs⟩ := mem_splitCenter.1 h
@@ -90,9 +84,6 @@ namespace Box
 
 open Prepartition TaggedPrepartition
 
-/- warning: box_integral.box.subbox_induction_on -> BoxIntegral.Box.subbox_induction_on is a dubious translation:
-<too large>
-Case conversion may be inaccurate. Consider using '#align box_integral.box.subbox_induction_on BoxIntegral.Box.subbox_induction_onₓ'. -/
 /-- Let `p` be a predicate on `box ι`, let `I` be a box. Suppose that the following two properties
 hold true.
 
@@ -121,12 +112,6 @@ theorem subbox_induction_on {p : Box ι → Prop} (I : Box ι)
   exact hs s
 #align box_integral.box.subbox_induction_on BoxIntegral.Box.subbox_induction_on
 
-/- warning: box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic -> BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic is a dubious translation:
-lean 3 declaration is
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-but is expected to have type
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] (I : BoxIntegral.Box.{u1} ι) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), Exists.{succ u1} (BoxIntegral.TaggedPrepartition.{u1} ι I) (fun (π : BoxIntegral.TaggedPrepartition.{u1} ι I) => And (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I π) (And (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π) (And (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) (And (forall (J : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π) -> (Exists.{1} Nat (fun (m : Nat) => forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) m))))) (Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 I))))))
-Case conversion may be inaccurate. Consider using '#align box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homotheticₓ'. -/
 /-- Given a box `I` in `ℝⁿ` and a function `r : ℝⁿ → (0, ∞)`, there exists a tagged partition `π` of
 `I` such that
 
@@ -179,12 +164,6 @@ namespace Prepartition
 
 open TaggedPrepartition Finset Function
 
-/- warning: box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq -> BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq is a dubious translation:
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eqₓ'. -/
 /-- Given a box `I` in `ℝⁿ`, a function `r : ℝⁿ → (0, ∞)`, and a prepartition `π` of `I`, there
 exists a tagged prepartition `π'` of `I` such that
 
@@ -209,12 +188,6 @@ theorem exists_tagged_le_isHenstock_isSubordinate_iUnion_eq {I : Box ι} (r : (
   exact sup_congr rfl fun J _ => πid J
 #align box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.to_subordinate BoxIntegral.Prepartition.toSubordinateₓ'. -/
 /-- Given a prepartition `π` of a box `I` and a function `r : ℝⁿ → (0, ∞)`, `π.to_subordinate r`
 is a tagged partition `π'` such that
 
@@ -228,57 +201,27 @@ def toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) : T
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).some
 #align box_integral.prepartition.to_subordinate BoxIntegral.Prepartition.toSubordinate
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.to_subordinate_to_prepartition_le BoxIntegral.Prepartition.toSubordinate_toPrepartition_leₓ'. -/
 theorem toSubordinate_toPrepartition_le (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).toPrepartition ≤ π :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.1
 #align box_integral.prepartition.to_subordinate_to_prepartition_le BoxIntegral.Prepartition.toSubordinate_toPrepartition_le
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstock_toSubordinateₓ'. -/
 theorem isHenstock_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsHenstock :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.1
 #align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstock_toSubordinate
 
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 theorem isSubordinate_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsSubordinate r :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.1
 #align box_integral.prepartition.is_subordinate_to_subordinate BoxIntegral.Prepartition.isSubordinate_toSubordinate
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_to_subordinate BoxIntegral.Prepartition.distortion_toSubordinateₓ'. -/
 @[simp]
 theorem distortion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).distortion = π.distortion :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.2.1
 #align box_integral.prepartition.distortion_to_subordinate BoxIntegral.Prepartition.distortion_toSubordinate
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_to_subordinate BoxIntegral.Prepartition.iUnion_toSubordinateₓ'. -/
 @[simp]
 theorem iUnion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).iUnion = π.iUnion :=
@@ -289,12 +232,6 @@ end Prepartition
 
 namespace TaggedPrepartition
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinateₓ'. -/
 /-- Given a tagged prepartition `π₁`, a prepartition `π₂` that covers exactly `I \ π₁.Union`, and
 a function `r : ℝⁿ → (0, ∞)`, returns the union of `π₁` and `π₂.to_subordinate r`. This partition
 `π` has the following properties:
@@ -312,24 +249,12 @@ def unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition
     (((π₂.iUnion_toSubordinate r).trans hU).symm ▸ disjoint_sdiff_self_right)
 #align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinate
 
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 theorem isPartition_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     IsPartition (π₁.unionComplToSubordinate π₂ hU r) :=
   Prepartition.isPartitionDisjUnionOfEqDiff ((π₂.iUnion_toSubordinate r).trans hU)
 #align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate
 
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-Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxesₓ'. -/
 @[simp]
 theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
@@ -337,12 +262,6 @@ theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Pr
   rfl
 #align box_integral.tagged_prepartition.union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes
 
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 @[simp]
 theorem iUnion_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
@@ -350,12 +269,6 @@ theorem iUnion_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π
   (isPartition_unionComplToSubordinate _ _ _ _).iUnion_eq
 #align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes
 
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 @[simp]
 theorem distortion_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :

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

@@ -146,8 +146,7 @@ theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
               π.distortion = I.distortion :=
   by
   refine' subbox_induction_on I (fun J hle hJ => _) fun z hz => _
-  · choose! πi hP hHen hr Hn Hd using hJ
-    choose! n hn using Hn
+  · choose! πi hP hHen hr Hn Hd using hJ; choose! n hn using Hn
     have hP : ((split_center J).biUnionTagged πi).IsPartition :=
       (is_partition_split_center _).biUnionTagged hP
     have hsub :
@@ -171,8 +170,7 @@ theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
       ⟨single _ _ le_rfl _ Hmem, is_partition_single _, is_Henstock_single _,
         (is_subordinate_single _ _).2 HIcc.2, _, distortion_single _ _⟩
     simp only [tagged_prepartition.mem_single, forall_eq]
-    refine' ⟨0, fun i => _⟩
-    simp
+    refine' ⟨0, fun i => _⟩; simp
 #align box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic
 
 end Box

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

@@ -91,10 +91,7 @@ namespace Box
 open Prepartition TaggedPrepartition
 
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-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {p : (BoxIntegral.Box.{u1} ι) -> Prop} (I : BoxIntegral.Box.{u1} ι), (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J) J' (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 J)) -> (p J')) -> (p J)) -> (forall (z : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (Exists.{succ u1} (Set.{u1} (ι -> Real)) (fun (U : Set.{u1} (ι -> Real)) => And (Membership.mem.{u1, u1} (Set.{u1} (ι -> Real)) (Filter.{u1} (ι -> Real)) (instMembershipSetFilter.{u1} (ι -> Real)) U (nhdsWithin.{u1} (ι -> Real) (Pi.topologicalSpace.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (a : ι) => UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I))) (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (m : Nat), (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)) z (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 (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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)) -> (HasSubset.Subset.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instHasSubsetSet.{u1} (ι -> Real)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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) U) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) m))) -> (p J)))))) -> (p I)
+<too large>
 Case conversion may be inaccurate. Consider using '#align box_integral.box.subbox_induction_on BoxIntegral.Box.subbox_induction_onₓ'. -/
 /-- Let `p` be a predicate on `box ι`, let `I` be a box. Suppose that the following two properties
 hold true.

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

@@ -94,7 +94,7 @@ open Prepartition TaggedPrepartition
 lean 3 declaration is
   forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {p : (BoxIntegral.Box.{u1} ι) -> Prop} (I : BoxIntegral.Box.{u1} ι), (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) -> (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.hasMem.{u1} ι J) J' (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 J)) -> (p J')) -> (p J)) -> (forall (z : ι -> Real), (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) z (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (Exists.{succ u1} (Set.{u1} (ι -> Real)) (fun (U : Set.{u1} (ι -> Real)) => Exists.{0} (Membership.Mem.{u1, u1} (Set.{u1} (ι -> Real)) (Filter.{u1} (ι -> Real)) (Filter.hasMem.{u1} (ι -> Real)) U (nhdsWithin.{u1} (ι -> Real) (Pi.topologicalSpace.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (a : ι) => UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) z (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) 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(BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) I))) => forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι) J I) -> (forall (m : Nat), (Membership.Mem.{u1, u1} (ι -> Real) (Set.{u1} (ι -> Real)) (Set.hasMem.{u1} (ι -> Real)) z (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)) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J) U) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) m))) -> (p J)))))) -> (p I)
 but is expected to have type
-  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {p : (BoxIntegral.Box.{u1} ι) -> Prop} (I : BoxIntegral.Box.{u1} ι), (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J) J' (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 J)) -> (p J')) -> (p J)) -> (forall (z : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (Exists.{succ u1} (Set.{u1} (ι -> Real)) (fun (U : Set.{u1} (ι -> Real)) => And (Membership.mem.{u1, u1} (Set.{u1} (ι -> Real)) (Filter.{u1} (ι -> Real)) (instMembershipSetFilter.{u1} (ι -> Real)) U (nhdsWithin.{u1} (ι -> Real) (Pi.topologicalSpace.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (a : ι) => UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I))) (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (m : Nat), (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)) z (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 (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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)) -> (HasSubset.Subset.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instHasSubsetSet.{u1} (ι -> Real)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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) U) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) m))) -> (p J)))))) -> (p I)
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {p : (BoxIntegral.Box.{u1} ι) -> Prop} (I : BoxIntegral.Box.{u1} ι), (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J) J' (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 J)) -> (p J')) -> (p J)) -> (forall (z : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (Exists.{succ u1} (Set.{u1} (ι -> Real)) (fun (U : Set.{u1} (ι -> Real)) => And (Membership.mem.{u1, u1} (Set.{u1} (ι -> Real)) (Filter.{u1} (ι -> Real)) (instMembershipSetFilter.{u1} (ι -> Real)) U (nhdsWithin.{u1} (ι -> Real) (Pi.topologicalSpace.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (a : ι) => UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.684 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.682 x._@.Mathlib.Order.Hom.Basic._hyg.684) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.699 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.697 x._@.Mathlib.Order.Hom.Basic._hyg.699))) (BoxIntegral.Box.Icc.{u1} ι) I))) (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (m : Nat), (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)) z (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 (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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)) -> (HasSubset.Subset.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instHasSubsetSet.{u1} (ι -> Real)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.869 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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) U) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) m))) -> (p J)))))) -> (p I)
 Case conversion may be inaccurate. Consider using '#align box_integral.box.subbox_induction_on BoxIntegral.Box.subbox_induction_onₓ'. -/
 /-- Let `p` be a predicate on `box ι`, let `I` be a box. Suppose that the following two properties
 hold true.

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

@@ -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.subbox_induction
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
+! leanprover-community/mathlib commit 50251fd6309cca5ca2e747882ffecd2729f38c5d
 ! 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.Partition.Tagged
 /-!
 # Induction on subboxes
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we prove (see
 `box_integral.tagged_partition.exists_is_Henstock_is_subordinate_homothetic`) that for every box `I`
 in `ℝⁿ` and a function `r : ℝⁿ → ℝ` positive on `I` there exists a tagged partition `π` of `I` such

mathlib commit https://github.com/leanprover-community/mathlib/commit/f8c79b0a623404854a2902b836eac32156fd7712

@@ -44,6 +44,7 @@ variable {ι : Type _} [Fintype ι] {I J : Box ι}
 
 namespace Prepartition
 
+#print BoxIntegral.Prepartition.splitCenter /-
 /-- Split a box in `ℝⁿ` into `2 ^ n` boxes by hyperplanes passing through its center. -/
 def splitCenter (I : Box ι) : Prepartition I
     where
@@ -54,15 +55,26 @@ def splitCenter (I : Box ι) : Prepartition I
     rintro _ ⟨s, rfl⟩ _ ⟨t, rfl⟩ Hne
     exact I.disjoint_split_center_box (mt (congr_arg _) Hne)
 #align box_integral.prepartition.split_center BoxIntegral.Prepartition.splitCenter
+-/
 
+#print BoxIntegral.Prepartition.mem_splitCenter /-
 @[simp]
 theorem mem_splitCenter : J ∈ splitCenter I ↔ ∃ s, I.splitCenterBox s = J := by simp [split_center]
 #align box_integral.prepartition.mem_split_center BoxIntegral.Prepartition.mem_splitCenter
+-/
 
+#print BoxIntegral.Prepartition.isPartition_splitCenter /-
 theorem isPartition_splitCenter (I : Box ι) : IsPartition (splitCenter I) := fun x hx => by
   simp [hx]
 #align box_integral.prepartition.is_partition_split_center BoxIntegral.Prepartition.isPartition_splitCenter
+-/
 
+/- warning: box_integral.prepartition.upper_sub_lower_of_mem_split_center -> BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenter is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} {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 (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 I)) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne))))))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} {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 (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 I)) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0)))))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.upper_sub_lower_of_mem_split_center BoxIntegral.Prepartition.upper_sub_lower_of_mem_splitCenterₓ'. -/
 theorem upper_sub_lower_of_mem_splitCenter (h : J ∈ splitCenter I) (i : ι) :
     J.upper i - J.lower i = (I.upper i - I.lower i) / 2 :=
   let ⟨s, hs⟩ := mem_splitCenter.1 h
@@ -75,6 +87,12 @@ namespace Box
 
 open Prepartition TaggedPrepartition
 
+/- warning: box_integral.box.subbox_induction_on -> BoxIntegral.Box.subbox_induction_on is a dubious translation:
+lean 3 declaration is
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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)) -> (HasSubset.Subset.{u1} (Set.{u1} (ι -> Real)) (Set.hasSubset.{u1} (ι -> Real)) (coeFn.{succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.hasLe.{u1} ι) (Set.hasLe.{u1} (ι -> Real))) (fun (_x : RelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) => (BoxIntegral.Box.{u1} ι) -> (Set.{u1} (ι -> Real))) (RelEmbedding.hasCoeToFun.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.hasLe.{u1} ι)) (LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.hasLe.{u1} (ι -> Real)))) (BoxIntegral.Box.Icc.{u1} ι) J) U) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) m))) -> (p J)))))) -> (p I)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {p : (BoxIntegral.Box.{u1} ι) -> Prop} (I : BoxIntegral.Box.{u1} ι), (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (J' : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Prepartition.{u1} ι J) (BoxIntegral.Prepartition.instMembershipBoxPrepartition.{u1} ι J) J' (BoxIntegral.Prepartition.splitCenter.{u1} ι _inst_1 J)) -> (p J')) -> (p J)) -> (forall (z : ι -> Real), (Membership.mem.{u1, u1} (ι -> Real) ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) I) (Set.instMembershipSet.{u1} (ι -> Real)) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I)) -> (Exists.{succ u1} (Set.{u1} (ι -> Real)) (fun (U : Set.{u1} (ι -> Real)) => And (Membership.mem.{u1, u1} (Set.{u1} (ι -> Real)) (Filter.{u1} (ι -> Real)) (instMembershipSetFilter.{u1} (ι -> Real)) U (nhdsWithin.{u1} (ι -> Real) (Pi.topologicalSpace.{u1, 0} ι (fun (ᾰ : ι) => Real) (fun (a : ι) => UniformSpace.toTopologicalSpace.{0} Real (PseudoMetricSpace.toUniformSpace.{0} Real Real.pseudoMetricSpace))) z (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (_x : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) _x) (RelHomClass.toFunLike.{u1, u1, u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697) (RelEmbedding.instRelHomClassRelEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.680 : BoxIntegral.Box.{u1} ι) (x._@.Mathlib.Order.Hom.Basic._hyg.682 : BoxIntegral.Box.{u1} ι) => LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) x._@.Mathlib.Order.Hom.Basic._hyg.680 x._@.Mathlib.Order.Hom.Basic._hyg.682) (fun (x._@.Mathlib.Order.Hom.Basic._hyg.695 : Set.{u1} (ι -> Real)) (x._@.Mathlib.Order.Hom.Basic._hyg.697 : Set.{u1} (ι -> Real)) => LE.le.{u1} (Set.{u1} (ι -> Real)) (Set.instLESet.{u1} (ι -> Real)) x._@.Mathlib.Order.Hom.Basic._hyg.695 x._@.Mathlib.Order.Hom.Basic._hyg.697))) (BoxIntegral.Box.Icc.{u1} ι) I))) (forall (J : BoxIntegral.Box.{u1} ι), (LE.le.{u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.Box.instLEBox.{u1} ι) J I) -> (forall (m : Nat), (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)) z (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 (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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)) -> (HasSubset.Subset.{u1} ((fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) J) (Set.instHasSubsetSet.{u1} (ι -> Real)) (FunLike.coe.{succ u1, succ u1, succ u1} (OrderEmbedding.{u1, u1} (BoxIntegral.Box.{u1} ι) (Set.{u1} (ι -> Real)) (BoxIntegral.Box.instLEBox.{u1} ι) (Set.instLESet.{u1} (ι -> Real))) (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) => (fun (x._@.Mathlib.Order.RelIso.Basic._hyg.867 : BoxIntegral.Box.{u1} ι) => Set.{u1} (ι -> Real)) a) (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) U) -> (forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) m))) -> (p J)))))) -> (p I)
+Case conversion may be inaccurate. Consider using '#align box_integral.box.subbox_induction_on BoxIntegral.Box.subbox_induction_onₓ'. -/
 /-- Let `p` be a predicate on `box ι`, let `I` be a box. Suppose that the following two properties
 hold true.
 
@@ -103,6 +121,12 @@ theorem subbox_induction_on {p : Box ι → Prop} (I : Box ι)
   exact hs s
 #align box_integral.box.subbox_induction_on BoxIntegral.Box.subbox_induction_on
 
+/- warning: box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic -> BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] (I : BoxIntegral.Box.{u1} ι) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), Exists.{succ u1} (BoxIntegral.TaggedPrepartition.{u1} ι I) (fun (π : BoxIntegral.TaggedPrepartition.{u1} ι I) => And (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I π) (And (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π) (And (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) (And (forall (J : BoxIntegral.Box.{u1} ι), (Membership.Mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.hasMem.{u1} ι I) J π) -> (Exists.{1} Nat (fun (m : Nat) => forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (DivInvMonoid.toHasDiv.{0} Real (DivisionRing.toDivInvMonoid.{0} Real Real.divisionRing))) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.hasSub) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.monoid)) (OfNat.ofNat.{0} Real 2 (OfNat.mk.{0} Real 2 (bit0.{0} Real Real.hasAdd (One.one.{0} Real Real.hasOne)))) m))))) (Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _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) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), Exists.{succ u1} (BoxIntegral.TaggedPrepartition.{u1} ι I) (fun (π : BoxIntegral.TaggedPrepartition.{u1} ι I) => And (BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I π) (And (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π) (And (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π r) (And (forall (J : BoxIntegral.Box.{u1} ι), (Membership.mem.{u1, u1} (BoxIntegral.Box.{u1} ι) (BoxIntegral.TaggedPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.instMembershipBoxTaggedPrepartition.{u1} ι I) J π) -> (Exists.{1} Nat (fun (m : Nat) => forall (i : ι), Eq.{1} Real (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι J i) (BoxIntegral.Box.lower.{u1} ι J i)) (HDiv.hDiv.{0, 0, 0} Real Real Real (instHDiv.{0} Real (LinearOrderedField.toDiv.{0} Real Real.instLinearOrderedFieldReal)) (HSub.hSub.{0, 0, 0} Real Real Real (instHSub.{0} Real Real.instSubReal) (BoxIntegral.Box.upper.{u1} ι I i) (BoxIntegral.Box.lower.{u1} ι I i)) (HPow.hPow.{0, 0, 0} Real Nat Real (instHPow.{0, 0} Real Nat (Monoid.Pow.{0} Real Real.instMonoidReal)) (OfNat.ofNat.{0} Real 2 (instOfNat.{0} Real 2 Real.natCast (instAtLeastTwoHAddNatInstHAddInstAddNatOfNat (OfNat.ofNat.{0} Nat 0 (instOfNatNat 0))))) m))))) (Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π _inst_1) (BoxIntegral.Box.distortion.{u1} ι _inst_1 I))))))
+Case conversion may be inaccurate. Consider using '#align box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homotheticₓ'. -/
 /-- Given a box `I` in `ℝⁿ` and a function `r : ℝⁿ → (0, ∞)`, there exists a tagged partition `π` of
 `I` such that
 
@@ -112,7 +136,7 @@ theorem subbox_induction_on {p : Box ι → Prop} (I : Box ι)
 
 This lemma implies that the Henstock filter is nontrivial, hence the Henstock integral is
 well-defined. -/
-theorem exists_tagged_partition_isHenstock_isSubordinate_homothetic (I : Box ι)
+theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
     (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     ∃ π : TaggedPrepartition I,
       π.IsPartition ∧
@@ -149,7 +173,7 @@ theorem exists_tagged_partition_isHenstock_isSubordinate_homothetic (I : Box ι)
     simp only [tagged_prepartition.mem_single, forall_eq]
     refine' ⟨0, fun i => _⟩
     simp
-#align box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic BoxIntegral.Box.exists_tagged_partition_isHenstock_isSubordinate_homothetic
+#align box_integral.box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic BoxIntegral.Box.exists_taggedPartition_isHenstock_isSubordinate_homothetic
 
 end Box
 
@@ -157,6 +181,12 @@ namespace Prepartition
 
 open TaggedPrepartition Finset Function
 
+/- warning: box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq -> BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) (π : BoxIntegral.Prepartition.{u1} ι I), Exists.{succ u1} (BoxIntegral.TaggedPrepartition.{u1} ι I) (fun (π' : BoxIntegral.TaggedPrepartition.{u1} ι I) => And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π') π) (And (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π') (And (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π' r) (And (Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π' _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π _inst_1)) (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π') (BoxIntegral.Prepartition.iUnion.{u1} ι I π))))))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) (π : BoxIntegral.Prepartition.{u1} ι I), Exists.{succ u1} (BoxIntegral.TaggedPrepartition.{u1} ι I) (fun (π' : BoxIntegral.TaggedPrepartition.{u1} ι I) => And (LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π') π) (And (BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I π') (And (BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 π' r) (And (Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π' _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π _inst_1)) (Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I π') (BoxIntegral.Prepartition.iUnion.{u1} ι I π))))))
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eqₓ'. -/
 /-- Given a box `I` in `ℝⁿ`, a function `r : ℝⁿ → (0, ∞)`, and a prepartition `π` of `I`, there
 exists a tagged prepartition `π'` of `I` such that
 
@@ -181,6 +211,12 @@ theorem exists_tagged_le_isHenstock_isSubordinate_iUnion_eq {I : Box ι} (r : (
   exact sup_congr rfl fun J _ => πid J
 #align box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq
 
+/- warning: box_integral.prepartition.to_subordinate -> BoxIntegral.Prepartition.toSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι}, (BoxIntegral.Prepartition.{u1} ι I) -> ((ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> (BoxIntegral.TaggedPrepartition.{u1} ι I)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι}, (BoxIntegral.Prepartition.{u1} ι I) -> ((ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) -> (BoxIntegral.TaggedPrepartition.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.to_subordinate BoxIntegral.Prepartition.toSubordinateₓ'. -/
 /-- Given a prepartition `π` of a box `I` and a function `r : ℝⁿ → (0, ∞)`, `π.to_subordinate r`
 is a tagged partition `π'` such that
 
@@ -194,27 +230,57 @@ def toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) : T
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).some
 #align box_integral.prepartition.to_subordinate BoxIntegral.Prepartition.toSubordinate
 
+/- warning: box_integral.prepartition.to_subordinate_to_prepartition_le -> BoxIntegral.Prepartition.toSubordinate_toPrepartition_le is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.hasLe.{u1} ι I) (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r)) π
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), LE.le.{u1} (BoxIntegral.Prepartition.{u1} ι I) (BoxIntegral.Prepartition.instLEPrepartition.{u1} ι I) (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r)) π
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.to_subordinate_to_prepartition_le BoxIntegral.Prepartition.toSubordinate_toPrepartition_leₓ'. -/
 theorem toSubordinate_toPrepartition_le (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).toPrepartition ≤ π :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.1
 #align box_integral.prepartition.to_subordinate_to_prepartition_le BoxIntegral.Prepartition.toSubordinate_toPrepartition_le
 
+/- warning: box_integral.prepartition.is_Henstock_to_subordinate -> BoxIntegral.Prepartition.isHenstock_toSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), BoxIntegral.TaggedPrepartition.IsHenstock.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstock_toSubordinateₓ'. -/
 theorem isHenstock_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsHenstock :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.1
 #align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstock_toSubordinate
 
+/- warning: box_integral.prepartition.is_subordinate_to_subordinate -> BoxIntegral.Prepartition.isSubordinate_toSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r) r
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), BoxIntegral.TaggedPrepartition.IsSubordinate.{u1} ι I _inst_1 (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r) r
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.is_subordinate_to_subordinate BoxIntegral.Prepartition.isSubordinate_toSubordinateₓ'. -/
 theorem isSubordinate_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsSubordinate r :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.1
 #align box_integral.prepartition.is_subordinate_to_subordinate BoxIntegral.Prepartition.isSubordinate_toSubordinate
 
+/- warning: box_integral.prepartition.distortion_to_subordinate -> BoxIntegral.Prepartition.distortion_toSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r) _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π _inst_1)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r) _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π _inst_1)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.distortion_to_subordinate BoxIntegral.Prepartition.distortion_toSubordinateₓ'. -/
 @[simp]
 theorem distortion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).distortion = π.distortion :=
   (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.2.1
 #align box_integral.prepartition.distortion_to_subordinate BoxIntegral.Prepartition.distortion_toSubordinate
 
+/- warning: box_integral.prepartition.Union_to_subordinate -> BoxIntegral.Prepartition.iUnion_toSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π : BoxIntegral.Prepartition.{u1} ι I) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π r)) (BoxIntegral.Prepartition.iUnion.{u1} ι I π)
+Case conversion may be inaccurate. Consider using '#align box_integral.prepartition.Union_to_subordinate BoxIntegral.Prepartition.iUnion_toSubordinateₓ'. -/
 @[simp]
 theorem iUnion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).iUnion = π.iUnion :=
@@ -225,6 +291,12 @@ end Prepartition
 
 namespace TaggedPrepartition
 
+/- warning: box_integral.tagged_prepartition.union_compl_to_subordinate -> BoxIntegral.TaggedPrepartition.unionComplToSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), (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.TaggedPrepartition.iUnion.{u1} ι I π₁))) -> ((ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))) -> (BoxIntegral.TaggedPrepartition.{u1} ι I)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I), (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.TaggedPrepartition.iUnion.{u1} ι I π₁))) -> ((ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))) -> (BoxIntegral.TaggedPrepartition.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinateₓ'. -/
 /-- Given a tagged prepartition `π₁`, a prepartition `π₂` that covers exactly `I \ π₁.Union`, and
 a function `r : ℝⁿ → (0, ∞)`, returns the union of `π₁` and `π₂.to_subordinate r`. This partition
 `π` has the following properties:
@@ -242,12 +314,24 @@ def unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition
     (((π₂.iUnion_toSubordinate r).trans hU).symm ▸ disjoint_sdiff_self_right)
 #align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinate
 
+/- warning: box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate -> BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r)
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), BoxIntegral.TaggedPrepartition.IsPartition.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinateₓ'. -/
 theorem isPartition_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     IsPartition (π₁.unionComplToSubordinate π₂ hU r) :=
   Prepartition.isPartitionDisjUnionOfEqDiff ((π₂.iUnion_toSubordinate r).trans hU)
 #align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate
 
+/- warning: box_integral.tagged_prepartition.union_compl_to_subordinate_boxes -> BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r))) (Union.union.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.hasUnion.{u1} (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) a b))) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π₁)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π₂ r))))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), Eq.{succ u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r))) (Union.union.{u1} (Finset.{u1} (BoxIntegral.Box.{u1} ι)) (Finset.instUnionFinset.{u1} (BoxIntegral.Box.{u1} ι) (fun (a : BoxIntegral.Box.{u1} ι) (b : BoxIntegral.Box.{u1} ι) => Classical.propDecidable (Eq.{succ u1} (BoxIntegral.Box.{u1} ι) a b))) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I π₁)) (BoxIntegral.Prepartition.boxes.{u1} ι I (BoxIntegral.TaggedPrepartition.toPrepartition.{u1} ι I (BoxIntegral.Prepartition.toSubordinate.{u1} ι _inst_1 I π₂ r))))
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxesₓ'. -/
 @[simp]
 theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
@@ -255,6 +339,12 @@ theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Pr
   rfl
 #align box_integral.tagged_prepartition.union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes
 
+/- warning: box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes -> BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r)) ((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}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), Eq.{succ u1} (Set.{u1} (ι -> Real)) (BoxIntegral.TaggedPrepartition.iUnion.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r)) (BoxIntegral.Box.toSet.{u1} ι I)
+Case conversion may be inaccurate. Consider using '#align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxesₓ'. -/
 @[simp]
 theorem iUnion_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
@@ -262,6 +352,12 @@ theorem iUnion_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π
   (isPartition_unionComplToSubordinate _ _ _ _).iUnion_eq
 #align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes
 
+/- warning: box_integral.tagged_prepartition.distortion_union_compl_to_subordinate -> BoxIntegral.TaggedPrepartition.distortion_unionComplToSubordinate is a dubious translation:
+lean 3 declaration is
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (coeSort.{1, 2} (Set.{0} Real) Type (Set.hasCoeToSort.{0} Real) (Set.Ioi.{0} Real Real.preorder (OfNat.ofNat.{0} Real 0 (OfNat.mk.{0} Real 0 (Zero.zero.{0} Real Real.hasZero)))))), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r) _inst_1) (LinearOrder.max.{0} NNReal (ConditionallyCompleteLinearOrder.toLinearOrder.{0} NNReal (ConditionallyCompleteLinearOrderBot.toConditionallyCompleteLinearOrder.{0} NNReal NNReal.conditionallyCompleteLinearOrderBot)) (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I π₁ _inst_1) (BoxIntegral.Prepartition.distortion.{u1} ι I π₂ _inst_1))
+but is expected to have type
+  forall {ι : Type.{u1}} [_inst_1 : Fintype.{u1} ι] {I : BoxIntegral.Box.{u1} ι} (π₁ : BoxIntegral.TaggedPrepartition.{u1} ι I) (π₂ : BoxIntegral.Prepartition.{u1} ι I) (hU : 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.TaggedPrepartition.iUnion.{u1} ι I π₁))) (r : (ι -> Real) -> (Set.Elem.{0} Real (Set.Ioi.{0} Real Real.instPreorderReal (OfNat.ofNat.{0} Real 0 (Zero.toOfNat0.{0} Real Real.instZeroReal))))), Eq.{1} NNReal (BoxIntegral.TaggedPrepartition.distortion.{u1} ι I (BoxIntegral.TaggedPrepartition.unionComplToSubordinate.{u1} ι _inst_1 I π₁ π₂ hU r) _inst_1) (Max.max.{0} NNReal (CanonicallyLinearOrderedSemifield.toMax.{0} NNReal NNReal.instCanonicallyLinearOrderedSemifieldNNReal) (BoxIntegral.TaggedPrepartition.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.tagged_prepartition.distortion_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.distortion_unionComplToSubordinateₓ'. -/
 @[simp]
 theorem distortion_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :

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

@@ -124,14 +124,14 @@ theorem exists_tagged_partition_isHenstock_isSubordinate_homothetic (I : Box ι)
   refine' subbox_induction_on I (fun J hle hJ => _) fun z hz => _
   · choose! πi hP hHen hr Hn Hd using hJ
     choose! n hn using Hn
-    have hP : ((split_center J).bUnionTagged πi).IsPartition :=
-      (is_partition_split_center _).bUnionTagged hP
+    have hP : ((split_center J).biUnionTagged πi).IsPartition :=
+      (is_partition_split_center _).biUnionTagged hP
     have hsub :
-      ∀ J' ∈ (split_center J).bUnionTagged πi,
+      ∀ J' ∈ (split_center J).biUnionTagged πi,
         ∃ n : ℕ, ∀ i, (J' : _).upper i - J'.lower i = (J.upper i - J.lower i) / 2 ^ n :=
       by
       intro J' hJ'
-      rcases(split_center J).mem_bUnionTagged.1 hJ' with ⟨J₁, h₁, h₂⟩
+      rcases(split_center J).mem_biUnionTagged.1 hJ' with ⟨J₁, h₁, h₂⟩
       refine' ⟨n J₁ J' + 1, fun i => _⟩
       simp only [hn J₁ h₁ J' h₂, upper_sub_lower_of_mem_split_center h₁, pow_succ, div_div]
     refine' ⟨_, hP, is_Henstock_bUnion_tagged.2 hHen, is_subordinate_bUnion_tagged.2 hr, hsub, _⟩
@@ -166,7 +166,7 @@ exists a tagged prepartition `π'` of `I` such that
 * `π'` covers exactly the same part of `I` as `π`;
 * the distortion of `π'` is equal to the distortion of `π`.
 -/
-theorem exists_tagged_le_isHenstock_isSubordinate_union_eq {I : Box ι} (r : (ι → ℝ) → Ioi (0 : ℝ))
+theorem exists_tagged_le_isHenstock_isSubordinate_iUnion_eq {I : Box ι} (r : (ι → ℝ) → Ioi (0 : ℝ))
     (π : Prepartition I) :
     ∃ π' : TaggedPrepartition I,
       π'.toPrepartition ≤ π ∧
@@ -179,7 +179,7 @@ theorem exists_tagged_le_isHenstock_isSubordinate_union_eq {I : Box ι} (r : (ι
       is_subordinate_bUnion_tagged.2 fun J _ => πir J, _, π.Union_bUnion_partition fun J _ => πip J⟩
   rw [distortion_bUnion_tagged]
   exact sup_congr rfl fun J _ => πid J
-#align box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_union_eq
+#align box_integral.prepartition.exists_tagged_le_is_Henstock_is_subordinate_Union_eq BoxIntegral.Prepartition.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq
 
 /-- Given a prepartition `π` of a box `I` and a function `r : ℝⁿ → (0, ∞)`, `π.to_subordinate r`
 is a tagged partition `π'` such that
@@ -191,35 +191,35 @@ is a tagged partition `π'` such that
 * the distortion of `π'` is equal to the distortion of `π`.
 -/
 def toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) : TaggedPrepartition I :=
-  (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).some
+  (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).some
 #align box_integral.prepartition.to_subordinate BoxIntegral.Prepartition.toSubordinate
 
 theorem toSubordinate_toPrepartition_le (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).toPrepartition ≤ π :=
-  (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.1
+  (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.1
 #align box_integral.prepartition.to_subordinate_to_prepartition_le BoxIntegral.Prepartition.toSubordinate_toPrepartition_le
 
 theorem isHenstock_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsHenstock :=
-  (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.2.1
+  (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.1
 #align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstock_toSubordinate
 
 theorem isSubordinate_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsSubordinate r :=
-  (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.2.2.1
+  (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.1
 #align box_integral.prepartition.is_subordinate_to_subordinate BoxIntegral.Prepartition.isSubordinate_toSubordinate
 
 @[simp]
 theorem distortion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).distortion = π.distortion :=
-  (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.2.2.2.1
+  (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.2.1
 #align box_integral.prepartition.distortion_to_subordinate BoxIntegral.Prepartition.distortion_toSubordinate
 
 @[simp]
-theorem union_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
+theorem iUnion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).iUnion = π.iUnion :=
-  (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.2.2.2.2
-#align box_integral.prepartition.Union_to_subordinate BoxIntegral.Prepartition.union_toSubordinate
+  (π.exists_tagged_le_isHenstock_isSubordinate_iUnion_eq r).choose_spec.2.2.2.2
+#align box_integral.prepartition.Union_to_subordinate BoxIntegral.Prepartition.iUnion_toSubordinate
 
 end Prepartition
 
@@ -239,13 +239,13 @@ a function `r : ℝⁿ → (0, ∞)`, returns the union of `π₁` and `π₂.to
 def unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) : TaggedPrepartition I :=
   π₁.disjUnion (π₂.toSubordinate r)
-    (((π₂.union_toSubordinate r).trans hU).symm ▸ disjoint_sdiff_self_right)
+    (((π₂.iUnion_toSubordinate r).trans hU).symm ▸ disjoint_sdiff_self_right)
 #align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinate
 
 theorem isPartition_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     IsPartition (π₁.unionComplToSubordinate π₂ hU r) :=
-  Prepartition.isPartitionDisjUnionOfEqDiff ((π₂.union_toSubordinate r).trans hU)
+  Prepartition.isPartitionDisjUnionOfEqDiff ((π₂.iUnion_toSubordinate r).trans hU)
 #align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate
 
 @[simp]

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

@@ -170,7 +170,7 @@ theorem exists_tagged_le_isHenstock_isSubordinate_union_eq {I : Box ι} (r : (ι
     (π : Prepartition I) :
     ∃ π' : TaggedPrepartition I,
       π'.toPrepartition ≤ π ∧
-        π'.IsHenstock ∧ π'.IsSubordinate r ∧ π'.distortion = π.distortion ∧ π'.unionᵢ = π.unionᵢ :=
+        π'.IsHenstock ∧ π'.IsSubordinate r ∧ π'.distortion = π.distortion ∧ π'.iUnion = π.iUnion :=
   by
   have := fun J => box.exists_tagged_partition_is_Henstock_is_subordinate_homothetic J r
   choose! πi πip πiH πir hsub πid; clear hsub
@@ -217,7 +217,7 @@ theorem distortion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi
 
 @[simp]
 theorem union_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
-    (π.toSubordinate r).unionᵢ = π.unionᵢ :=
+    (π.toSubordinate r).iUnion = π.iUnion :=
   (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.2.2.2.2
 #align box_integral.prepartition.Union_to_subordinate BoxIntegral.Prepartition.union_toSubordinate
 
@@ -237,34 +237,34 @@ a function `r : ℝⁿ → (0, ∞)`, returns the union of `π₁` and `π₂.to
 * the distortion of `π` is equal to the maximum of the distortions of `π₁` and `π₂`.
 -/
 def unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
-    (hU : π₂.unionᵢ = I \ π₁.unionᵢ) (r : (ι → ℝ) → Ioi (0 : ℝ)) : TaggedPrepartition I :=
+    (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) : TaggedPrepartition I :=
   π₁.disjUnion (π₂.toSubordinate r)
     (((π₂.union_toSubordinate r).trans hU).symm ▸ disjoint_sdiff_self_right)
 #align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinate
 
 theorem isPartition_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
-    (hU : π₂.unionᵢ = I \ π₁.unionᵢ) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
+    (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     IsPartition (π₁.unionComplToSubordinate π₂ hU r) :=
   Prepartition.isPartitionDisjUnionOfEqDiff ((π₂.union_toSubordinate r).trans hU)
 #align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate
 
 @[simp]
 theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
-    (hU : π₂.unionᵢ = I \ π₁.unionᵢ) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
+    (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π₁.unionComplToSubordinate π₂ hU r).boxes = π₁.boxes ∪ (π₂.toSubordinate r).boxes :=
   rfl
 #align box_integral.tagged_prepartition.union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes
 
 @[simp]
-theorem unionᵢ_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
-    (hU : π₂.unionᵢ = I \ π₁.unionᵢ) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
-    (π₁.unionComplToSubordinate π₂ hU r).unionᵢ = I :=
-  (isPartition_unionComplToSubordinate _ _ _ _).unionᵢ_eq
-#align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionᵢ_unionComplToSubordinate_boxes
+theorem iUnion_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
+    (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
+    (π₁.unionComplToSubordinate π₂ hU r).iUnion = I :=
+  (isPartition_unionComplToSubordinate _ _ _ _).iUnion_eq
+#align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.iUnion_unionComplToSubordinate_boxes
 
 @[simp]
 theorem distortion_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
-    (hU : π₂.unionᵢ = I \ π₁.unionᵢ) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
+    (hU : π₂.iUnion = I \ π₁.iUnion) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π₁.unionComplToSubordinate π₂ hU r).distortion = max π₁.distortion π₂.distortion := by
   simp [union_compl_to_subordinate]
 #align box_integral.tagged_prepartition.distortion_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.distortion_unionComplToSubordinate

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

@@ -59,8 +59,9 @@ def splitCenter (I : Box ι) : Prepartition I
 theorem mem_splitCenter : J ∈ splitCenter I ↔ ∃ s, I.splitCenterBox s = J := by simp [split_center]
 #align box_integral.prepartition.mem_split_center BoxIntegral.Prepartition.mem_splitCenter
 
-theorem isPartitionSplitCenter (I : Box ι) : IsPartition (splitCenter I) := fun x hx => by simp [hx]
-#align box_integral.prepartition.is_partition_split_center BoxIntegral.Prepartition.isPartitionSplitCenter
+theorem isPartition_splitCenter (I : Box ι) : IsPartition (splitCenter I) := fun x hx => by
+  simp [hx]
+#align box_integral.prepartition.is_partition_split_center BoxIntegral.Prepartition.isPartition_splitCenter
 
 theorem upper_sub_lower_of_mem_splitCenter (h : J ∈ splitCenter I) (i : ι) :
     J.upper i - J.lower i = (I.upper i - I.lower i) / 2 :=
@@ -198,15 +199,15 @@ theorem toSubordinate_toPrepartition_le (π : Prepartition I) (r : (ι → ℝ)
   (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.1
 #align box_integral.prepartition.to_subordinate_to_prepartition_le BoxIntegral.Prepartition.toSubordinate_toPrepartition_le
 
-theorem isHenstockToSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
+theorem isHenstock_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsHenstock :=
   (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.2.1
-#align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstockToSubordinate
+#align box_integral.prepartition.is_Henstock_to_subordinate BoxIntegral.Prepartition.isHenstock_toSubordinate
 
-theorem isSubordinateToSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
+theorem isSubordinate_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π.toSubordinate r).IsSubordinate r :=
   (π.exists_tagged_le_isHenstock_isSubordinate_union_eq r).choose_spec.2.2.1
-#align box_integral.prepartition.is_subordinate_to_subordinate BoxIntegral.Prepartition.isSubordinateToSubordinate
+#align box_integral.prepartition.is_subordinate_to_subordinate BoxIntegral.Prepartition.isSubordinate_toSubordinate
 
 @[simp]
 theorem distortion_toSubordinate (π : Prepartition I) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
@@ -241,11 +242,11 @@ def unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition
     (((π₂.union_toSubordinate r).trans hU).symm ▸ disjoint_sdiff_self_right)
 #align box_integral.tagged_prepartition.union_compl_to_subordinate BoxIntegral.TaggedPrepartition.unionComplToSubordinate
 
-theorem isPartitionUnionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
+theorem isPartition_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.unionᵢ = I \ π₁.unionᵢ) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     IsPartition (π₁.unionComplToSubordinate π₂ hU r) :=
   Prepartition.isPartitionDisjUnionOfEqDiff ((π₂.union_toSubordinate r).trans hU)
-#align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartitionUnionComplToSubordinate
+#align box_integral.tagged_prepartition.is_partition_union_compl_to_subordinate BoxIntegral.TaggedPrepartition.isPartition_unionComplToSubordinate
 
 @[simp]
 theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
@@ -255,11 +256,11 @@ theorem unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Pr
 #align box_integral.tagged_prepartition.union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionComplToSubordinate_boxes
 
 @[simp]
-theorem union_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
+theorem unionᵢ_unionComplToSubordinate_boxes (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)
     (hU : π₂.unionᵢ = I \ π₁.unionᵢ) (r : (ι → ℝ) → Ioi (0 : ℝ)) :
     (π₁.unionComplToSubordinate π₂ hU r).unionᵢ = I :=
-  (isPartitionUnionComplToSubordinate _ _ _ _).unionᵢ_eq
-#align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.union_unionComplToSubordinate_boxes
+  (isPartition_unionComplToSubordinate _ _ _ _).unionᵢ_eq
+#align box_integral.tagged_prepartition.Union_union_compl_to_subordinate_boxes BoxIntegral.TaggedPrepartition.unionᵢ_unionComplToSubordinate_boxes
 
 @[simp]
 theorem distortion_unionComplToSubordinate (π₁ : TaggedPrepartition I) (π₂ : Prepartition I)

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

We change the following field in the definition of an additive commutative monoid:

 nsmul_succ : ∀ (n : ℕ) (x : G),
-  AddMonoid.nsmul (n + 1) x = x + AddMonoid.nsmul n x
+  AddMonoid.nsmul (n + 1) x = AddMonoid.nsmul n x + x

where the latter is more natural

We adjust the definitions of ^ in monoids, groups, etc. Originally there was a warning comment about why this natural order was preferred

use x * npowRec n x and not npowRec n x * x in the definition to make sure that definitional unfolding of npowRec is blocked, to avoid deep recursion issues.

but it seems to no longer apply.

Remarks on the PR :

• pow_succ and pow_succ' have switched their meanings.
• Most of the time, the proofs were adjusted by priming/unpriming one lemma, or exchanging left and right; a few proofs were more complicated to adjust.
• In particular, [Mathlib/NumberTheory/RamificationInertia.lean] used Ideal.IsPrime.mul_mem_pow which is defined in [Mathlib/RingTheory/DedekindDomain/Ideal.lean]. Changing the order of operation forced me to add the symmetric lemma Ideal.IsPrime.mem_pow_mul.
• the docstring for Cauchy condensation test in [Mathlib/Analysis/PSeries.lean] was mathematically incorrect, I added the mention that the function is antitone.

@@ -119,7 +119,7 @@ theorem exists_taggedPartition_isHenstock_isSubordinate_homothetic (I : Box ι)
       intro J' hJ'
       rcases (splitCenter J).mem_biUnionTagged.1 hJ' with ⟨J₁, h₁, h₂⟩
       refine' ⟨n J₁ J' + 1, fun i => _⟩
-      simp only [hn J₁ h₁ J' h₂, upper_sub_lower_of_mem_splitCenter h₁, pow_succ, div_div]
+      simp only [hn J₁ h₁ J' h₂, upper_sub_lower_of_mem_splitCenter h₁, pow_succ', div_div]
     refine' ⟨_, hP, isHenstock_biUnionTagged.2 hHen, isSubordinate_biUnionTagged.2 hr, hsub, _⟩
     refine' TaggedPrepartition.distortion_of_const _ hP.nonempty_boxes fun J' h' => _
     rcases hsub J' h' with ⟨n, hn⟩

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.

@@ -33,7 +33,8 @@ namespace BoxIntegral
 
 open Set Metric
 
-open Classical Topology
+open scoped Classical
+open Topology
 
 noncomputable section
 

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

This has nice performance benefits.

@@ -37,7 +37,7 @@ open Classical Topology
 
 noncomputable section
 
-variable {ι : Type _} [Fintype ι] {I J : Box ι}
+variable {ι : Type*} [Fintype ι] {I J : Box ι}
 
 namespace Prepartition
 

• 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.subbox_induction
-! leanprover-community/mathlib commit f2ce6086713c78a7f880485f7917ea547a215982
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.Analysis.BoxIntegral.Box.SubboxInduction
 import Mathlib.Analysis.BoxIntegral.Partition.Tagged
 
+#align_import analysis.box_integral.partition.subbox_induction from "leanprover-community/mathlib"@"f2ce6086713c78a7f880485f7917ea547a215982"
+
 /-!
 # Induction on subboxes
 

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

@@ -48,7 +48,7 @@ namespace Prepartition
 def splitCenter (I : Box ι) : Prepartition I where
   boxes := Finset.univ.map (Box.splitCenterBoxEmb I)
   le_of_mem' := by simp [I.splitCenterBox_le]
-  PairwiseDisjoint := by
+  pairwiseDisjoint := by
     rw [Finset.coe_map, Finset.coe_univ, image_univ]
     rintro _ ⟨s, rfl⟩ _ ⟨t, rfl⟩ Hne
     exact I.disjoint_splitCenterBox (mt (congr_arg _) Hne)