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

@@ -252,7 +252,7 @@ theorem norm_torusIntegral_le_of_norm_le_const {C : ℝ} (hf : ∀ θ, ‖f (tor
     ‖∯ x in T(c, R), f x‖ ≤ ((2 * π) ^ (n : ℕ) * ∏ i, |R i|) * C :=
   calc
     ‖∯ x in T(c, R), f x‖ ≤ (∏ i, |R i|) * C * (volume (Icc (0 : ℝⁿ) fun _ => 2 * π)).toReal :=
-      norm_set_integral_le_of_norm_le_const' measure_Icc_lt_top measurableSet_Icc fun θ hθ =>
+      norm_setIntegral_le_of_norm_le_const' measure_Icc_lt_top measurableSet_Icc fun θ hθ =>
         calc
           ‖(∏ i : Fin n, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ)‖ =
               (∏ i : Fin n, |R i|) * ‖f (torusMap c R θ)‖ :=
@@ -285,7 +285,7 @@ theorem torusIntegral_dim1 (f : ℂ¹ → E) (c : ℂ¹) (R : ℝ¹) :
     (OrderIso.funUnique (Fin 1) ℝ).symm.preimage_Icc _ _
   simp only [torusIntegral, circleIntegral, intervalIntegral.integral_of_le real.two_pi_pos.le,
     measure.restrict_congr_set Ioc_ae_eq_Icc, deriv_circleMap, Fin.prod_univ_one, ←
-    ((volume_preserving_fun_unique (Fin 1) ℝ).symm _).set_integral_preimage_emb
+    ((volume_preserving_fun_unique (Fin 1) ℝ).symm _).setIntegral_preimage_emb
       (MeasurableEquiv.measurableEmbedding _),
     this, MeasurableEquiv.funUnique_symm_apply]
   simp only [torusMap, circleMap, zero_add]

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

@@ -232,7 +232,7 @@ theorem torusIntegral_sub (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c
 -/
 
 #print torusIntegral_smul /-
-theorem torusIntegral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
+theorem torusIntegral_smul {𝕜 : Type _} [RCLike 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : ∯ x in T(c, R), a • f x = a • ∯ x in T(c, R), f x := by
   simp only [torusIntegral, integral_smul, ← smul_comm a]
 #align torus_integral_smul torusIntegral_smul

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

@@ -318,7 +318,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     simp only [funext_iff, i.forall_iff_succ_above, circleMap, Fin.insertNth_apply_same,
       eq_self_iff_true, Fin.insertNth_apply_succAbove, imp_true_iff, and_self_iff]
   · have := hf.function_integrable
-    rwa [← hem.integrable_on_comp_preimage e.measurable_embedding, heπ] at this 
+    rwa [← hem.integrable_on_comp_preimage e.measurable_embedding, heπ] at this
 #align torus_integral_succ_above torusIntegral_succAbove
 -/
 

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

@@ -206,7 +206,7 @@ notation3"∯ "(...)" in ""T("c", "R")"", "r:60:(scoped f => torusIntegral f c R
 #print torusIntegral_radius_zero /-
 theorem torusIntegral_radius_zero (hn : n ≠ 0) (f : ℂⁿ → E) (c : ℂⁿ) : ∯ x in T(c, 0), f x = 0 := by
   simp only [torusIntegral, Pi.zero_apply, of_real_zero, MulZeroClass.mul_zero,
-    MulZeroClass.zero_mul, Fin.prod_const, zero_pow' n hn, zero_smul, integral_zero]
+    MulZeroClass.zero_mul, Fin.prod_const, zero_pow n hn, zero_smul, integral_zero]
 #align torus_integral_radius_zero torusIntegral_radius_zero
 -/
 

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

@@ -301,7 +301,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     ∯ x in T(c, R), f x =
       ∮ x in C(c i, R i), ∯ y in T(c ∘ i.succAboveEmb, R ∘ i.succAboveEmb), f (i.insertNth x y) :=
   by
-  set e : ℝ × ℝⁿ ≃ᵐ ℝⁿ⁺¹ := (MeasurableEquiv.piFinSuccAboveEquiv (fun _ => ℝ) i).symm
+  set e : ℝ × ℝⁿ ≃ᵐ ℝⁿ⁺¹ := (MeasurableEquiv.piFinSuccAbove (fun _ => ℝ) i).symm
   have hem : measure_preserving e :=
     (volume_preserving_pi_fin_succ_above_equiv (fun j : Fin (n + 1) => ℝ) i).symm _
   have heπ : (e ⁻¹' Icc 0 fun _ => 2 * π) = Icc 0 (2 * π) ×ˢ Icc (0 : ℝⁿ) fun _ => 2 * π :=
@@ -312,7 +312,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     simp only [torusIntegral, ← integral_smul, deriv_circleMap, i.prod_univ_succ_above _, smul_smul,
       torusMap, circleMap_zero]
     refine' set_integral_congr measurableSet_Icc fun Θ hΘ => _
-    simp only [MeasurableEquiv.piFinSuccAboveEquiv_symm_apply, i.insert_nth_apply_same,
+    simp only [MeasurableEquiv.piFinSuccAbove_symm_apply, i.insert_nth_apply_same,
       i.insert_nth_apply_succ_above, (· ∘ ·)]
     congr 2
     simp only [funext_iff, i.forall_iff_succ_above, circleMap, Fin.insertNth_apply_same,

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

@@ -3,8 +3,8 @@ Copyright (c) 2022 Cuma Kökmen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Cuma Kökmen, Yury Kudryashov
 -/
-import Mathbin.MeasureTheory.Constructions.Prod.Integral
-import Mathbin.MeasureTheory.Integral.CircleIntegral
+import MeasureTheory.Constructions.Prod.Integral
+import MeasureTheory.Integral.CircleIntegral
 
 #align_import measure_theory.integral.torus_integral from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
 

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

@@ -2,15 +2,12 @@
 Copyright (c) 2022 Cuma Kökmen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Cuma Kökmen, Yury Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.integral.torus_integral
-! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Constructions.Prod.Integral
 import Mathbin.MeasureTheory.Integral.CircleIntegral
 
+#align_import measure_theory.integral.torus_integral from "leanprover-community/mathlib"@"44e2ae8cffc713925494e4975ee31ec1d06929b3"
+
 /-!
 # Integral over a torus in `ℂⁿ`
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2fe465deb81bcd7ccafa065bb686888a82f15372

@@ -302,7 +302,7 @@ theorem torusIntegral_dim1 (f : ℂ¹ → E) (c : ℂ¹) (R : ℝ¹) :
 theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : ℝⁿ⁺¹} (hf : TorusIntegrable f c R)
     (i : Fin (n + 1)) :
     ∯ x in T(c, R), f x =
-      ∮ x in C(c i, R i), ∯ y in T(c ∘ i.succAbove, R ∘ i.succAbove), f (i.insertNth x y) :=
+      ∮ x in C(c i, R i), ∯ y in T(c ∘ i.succAboveEmb, R ∘ i.succAboveEmb), f (i.insertNth x y) :=
   by
   set e : ℝ × ℝⁿ ≃ᵐ ℝⁿ⁺¹ := (MeasurableEquiv.piFinSuccAboveEquiv (fun _ => ℝ) i).symm
   have hem : measure_preserving e :=

mathlib commit https://github.com/leanprover-community/mathlib/commit/8efcf8022aac8e01df8d302dcebdbc25d6a886c8

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Cuma Kökmen, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.torus_integral
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
+! leanprover-community/mathlib commit 44e2ae8cffc713925494e4975ee31ec1d06929b3
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -14,6 +14,9 @@ import Mathbin.MeasureTheory.Integral.CircleIntegral
 /-!
 # Integral over a torus in `ℂⁿ`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define the integral of a function `f : ℂⁿ → E` over a torus
 `{z : ℂⁿ | ∀ i, z i ∈ metric.sphere (c i) (R i)}`. In order to do this, we define
 `torus_map (c : ℂⁿ) (R θ : ℝⁿ)` to be the point in `ℂⁿ` given by $z_k=c_k+R_ke^{θ_ki}$,

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

@@ -69,28 +69,20 @@ open Complex Set MeasureTheory Function Filter TopologicalSpace
 
 open scoped Real BigOperators
 
--- mathport name: «exprℝ⁰»
 local notation "ℝ⁰" => Fin 0 → ℝ
 
--- mathport name: «exprℂ⁰»
 local notation "ℂ⁰" => Fin 0 → ℂ
 
--- mathport name: «exprℝ¹»
 local notation "ℝ¹" => Fin 1 → ℝ
 
--- mathport name: «exprℂ¹»
 local notation "ℂ¹" => Fin 1 → ℂ
 
--- mathport name: «exprℝⁿ»
 local notation "ℝⁿ" => Fin n → ℝ
 
--- mathport name: «exprℂⁿ»
 local notation "ℂⁿ" => Fin n → ℂ
 
--- mathport name: «exprℝⁿ⁺¹»
 local notation "ℝⁿ⁺¹" => Fin (n + 1) → ℝ
 
--- mathport name: «exprℂⁿ⁺¹»
 local notation "ℂⁿ⁺¹" => Fin (n + 1) → ℂ
 
 /-!
@@ -106,18 +98,24 @@ def torusMap (c : ℂⁿ) (R : ℝⁿ) : ℝⁿ → ℂⁿ := fun θ i => c i +
 #align torus_map torusMap
 -/
 
+#print torusMap_sub_center /-
 theorem torusMap_sub_center (c : ℂⁿ) (R : ℝⁿ) (θ : ℝⁿ) : torusMap c R θ - c = torusMap 0 R θ := by
   ext1 i; simp [torusMap]
 #align torus_map_sub_center torusMap_sub_center
+-/
 
+#print torusMap_eq_center_iff /-
 theorem torusMap_eq_center_iff {c : ℂⁿ} {R : ℝⁿ} {θ : ℝⁿ} : torusMap c R θ = c ↔ R = 0 := by
   simp [funext_iff, torusMap, exp_ne_zero]
 #align torus_map_eq_center_iff torusMap_eq_center_iff
+-/
 
+#print torusMap_zero_radius /-
 @[simp]
 theorem torusMap_zero_radius (c : ℂⁿ) : torusMap c 0 = const ℝⁿ c := by ext1;
   rw [torusMap_eq_center_iff.2 rfl]
 #align torus_map_zero_radius torusMap_zero_radius
+-/
 
 /-!
 ### Integrability of a function on a generalized torus
@@ -174,6 +172,7 @@ theorem torusIntegrable_zero_radius {f : ℂⁿ → E} {c : ℂⁿ} : TorusInteg
 #align torus_integrable.torus_integrable_zero_radius TorusIntegrable.torusIntegrable_zero_radius
 -/
 
+#print TorusIntegrable.function_integrable /-
 /-- The function given in the definition of `torus_integral` is integrable. -/
 theorem function_integrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :
     IntegrableOn (fun θ : ℝⁿ => (∏ i, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ))
@@ -188,50 +187,65 @@ theorem function_integrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :
           continuous_const
   simp [norm_smul, map_prod]
 #align torus_integrable.function_integrable TorusIntegrable.function_integrable
+-/
 
 end TorusIntegrable
 
 variable [NormedSpace ℂ E] [CompleteSpace E] {f g : ℂⁿ → E} {c : ℂⁿ} {R : ℝⁿ}
 
+#print torusIntegral /-
 /-- The definition of the integral over a generalized torus with center `c ∈ ℂⁿ` and radius `R ∈ ℝⁿ`
 as the `•`-product of the derivative of `torus_map` and `f (torus_map c R θ)`-/
 def torusIntegral (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :=
   ∫ θ : ℝⁿ in Icc (0 : ℝⁿ) fun _ => 2 * π, (∏ i, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ)
 #align torus_integral torusIntegral
+-/
 
--- mathport name: «expr∯ inT( , ), »
 notation3"∯ "(...)" in ""T("c", "R")"", "r:60:(scoped f => torusIntegral f c R) => r
 
+#print torusIntegral_radius_zero /-
 theorem torusIntegral_radius_zero (hn : n ≠ 0) (f : ℂⁿ → E) (c : ℂⁿ) : ∯ x in T(c, 0), f x = 0 := by
   simp only [torusIntegral, Pi.zero_apply, of_real_zero, MulZeroClass.mul_zero,
     MulZeroClass.zero_mul, Fin.prod_const, zero_pow' n hn, zero_smul, integral_zero]
 #align torus_integral_radius_zero torusIntegral_radius_zero
+-/
 
+#print torusIntegral_neg /-
 theorem torusIntegral_neg (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :
     ∯ x in T(c, R), -f x = -∯ x in T(c, R), f x := by simp [torusIntegral, integral_neg]
 #align torus_integral_neg torusIntegral_neg
+-/
 
+#print torusIntegral_add /-
 theorem torusIntegral_add (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c R) :
     ∯ x in T(c, R), f x + g x = (∯ x in T(c, R), f x) + ∯ x in T(c, R), g x := by
   simpa only [torusIntegral, smul_add, Pi.add_apply] using
     integral_add hf.function_integrable hg.function_integrable
 #align torus_integral_add torusIntegral_add
+-/
 
+#print torusIntegral_sub /-
 theorem torusIntegral_sub (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c R) :
     ∯ x in T(c, R), f x - g x = (∯ x in T(c, R), f x) - ∯ x in T(c, R), g x := by
   simpa only [sub_eq_add_neg, ← torusIntegral_neg] using torusIntegral_add hf hg.neg
 #align torus_integral_sub torusIntegral_sub
+-/
 
+#print torusIntegral_smul /-
 theorem torusIntegral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : ∯ x in T(c, R), a • f x = a • ∯ x in T(c, R), f x := by
   simp only [torusIntegral, integral_smul, ← smul_comm a]
 #align torus_integral_smul torusIntegral_smul
+-/
 
+#print torusIntegral_const_mul /-
 theorem torusIntegral_const_mul (a : ℂ) (f : ℂⁿ → ℂ) (c : ℂⁿ) (R : ℝⁿ) :
     ∯ x in T(c, R), a * f x = a * ∯ x in T(c, R), f x :=
   torusIntegral_smul a f c R
 #align torus_integral_const_mul torusIntegral_const_mul
+-/
 
+#print norm_torusIntegral_le_of_norm_le_const /-
 /-- If for all `θ : ℝⁿ`, `‖f (torus_map c R θ)‖` is less than or equal to a constant `C : ℝ`, then
 `‖∯ x in T(c, R), f x‖` is less than or equal to `(2 * π)^n * (∏ i, |R i|) * C`-/
 theorem norm_torusIntegral_le_of_norm_le_const {C : ℝ} (hf : ∀ θ, ‖f (torusMap c R θ)‖ ≤ C) :
@@ -249,7 +263,9 @@ theorem norm_torusIntegral_le_of_norm_le_const {C : ℝ} (hf : ∀ θ, ‖f (tor
       simp only [Pi.zero_def, Real.volume_Icc_pi_toReal fun _ => real.two_pi_pos.le, sub_zero,
         Fin.prod_const, mul_assoc, mul_comm ((2 * π) ^ (n : ℕ))]
 #align norm_torus_integral_le_of_norm_le_const norm_torusIntegral_le_of_norm_le_const
+-/
 
+#print torusIntegral_dim0 /-
 @[simp]
 theorem torusIntegral_dim0 (f : ℂ⁰ → E) (c : ℂ⁰) (R : ℝ⁰) : ∯ x in T(c, R), f x = f c := by
   simp only [torusIntegral, Fin.prod_univ_zero, one_smul,
@@ -257,7 +273,9 @@ theorem torusIntegral_dim0 (f : ℂ⁰ → E) (c : ℂ⁰) (R : ℝ⁰) : ∯ x
     integral_smul_measure, integral_dirac, measure.pi_of_empty _ 0,
     measure.dirac_apply_of_mem (mem_singleton _), Subsingleton.elim (torusMap c R 0) c]
 #align torus_integral_dim0 torusIntegral_dim0
+-/
 
+#print torusIntegral_dim1 /-
 /-- In dimension one, `torus_integral` is the same as `circle_integral`
 (up to the natural equivalence between `ℂ` and `fin 1 → ℂ`). -/
 theorem torusIntegral_dim1 (f : ℂ¹ → E) (c : ℂ¹) (R : ℝ¹) :
@@ -273,8 +291,10 @@ theorem torusIntegral_dim1 (f : ℂ¹ → E) (c : ℂ¹) (R : ℝ¹) :
   simp only [torusMap, circleMap, zero_add]
   rcongr
 #align torus_integral_dim1 torusIntegral_dim1
+-/
 
 /- ./././Mathport/Syntax/Translate/Expr.lean:177:8: unsupported: ambiguous notation -/
+#print torusIntegral_succAbove /-
 /-- Recurrent formula for `torus_integral`, see also `torus_integral_succ`. -/
 theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : ℝⁿ⁺¹} (hf : TorusIntegrable f c R)
     (i : Fin (n + 1)) :
@@ -300,11 +320,14 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
   · have := hf.function_integrable
     rwa [← hem.integrable_on_comp_preimage e.measurable_embedding, heπ] at this 
 #align torus_integral_succ_above torusIntegral_succAbove
+-/
 
+#print torusIntegral_succ /-
 /-- Recurrent formula for `torus_integral`, see also `torus_integral_succ_above`. -/
 theorem torusIntegral_succ {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : ℝⁿ⁺¹} (hf : TorusIntegrable f c R) :
     ∯ x in T(c, R), f x =
       ∮ x in C(c 0, R 0), ∯ y in T(c ∘ Fin.succ, R ∘ Fin.succ), f (Fin.cons x y) :=
   by simpa using torusIntegral_succAbove hf 0
 #align torus_integral_succ torusIntegral_succ
+-/
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/ccdbfb6e5614667af5aa3ab2d50885e0ef44a46f

@@ -98,11 +98,13 @@ local notation "ℂⁿ⁺¹" => Fin (n + 1) → ℂ
 -/
 
 
+#print torusMap /-
 /-- The n dimensional exponential map $θ_i ↦ c + R e^{θ_i*I}, θ ∈ ℝⁿ$ representing
 a torus in `ℂⁿ` with center `c ∈ ℂⁿ` and generalized radius `R ∈ ℝⁿ`, so we can adjust
 it to every n axis. -/
 def torusMap (c : ℂⁿ) (R : ℝⁿ) : ℝⁿ → ℂⁿ := fun θ i => c i + R i * exp (θ i * I)
 #align torus_map torusMap
+-/
 
 theorem torusMap_sub_center (c : ℂⁿ) (R : ℝⁿ) (θ : ℝⁿ) : torusMap c R θ - c = torusMap 0 R θ := by
   ext1 i; simp [torusMap]
@@ -122,43 +124,55 @@ theorem torusMap_zero_radius (c : ℂⁿ) : torusMap c 0 = const ℝⁿ c := by
 -/
 
 
+#print TorusIntegrable /-
 /-- A function `f : ℂⁿ → E` is integrable on the generalized torus if the function
 `f ∘ torus_map c R θ` is integrable on `Icc (0 : ℝⁿ) (λ _, 2 * π)`-/
 def TorusIntegrable (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : Prop :=
   IntegrableOn (fun θ : ℝⁿ => f (torusMap c R θ)) (Icc (0 : ℝⁿ) fun _ => 2 * π) volume
 #align torus_integrable TorusIntegrable
+-/
 
 namespace TorusIntegrable
 
 variable {f g : ℂⁿ → E} {c : ℂⁿ} {R : ℝⁿ}
 
+#print TorusIntegrable.torusIntegrable_const /-
 /-- Constant functions are torus integrable -/
 theorem torusIntegrable_const (a : E) (c : ℂⁿ) (R : ℝⁿ) : TorusIntegrable (fun _ => a) c R := by
   simp [TorusIntegrable, measure_Icc_lt_top]
 #align torus_integrable.torus_integrable_const TorusIntegrable.torusIntegrable_const
+-/
 
+#print TorusIntegrable.neg /-
 /-- If `f` is torus integrable then `-f` is torus integrable. -/
 protected theorem neg (hf : TorusIntegrable f c R) : TorusIntegrable (-f) c R :=
   hf.neg
 #align torus_integrable.neg TorusIntegrable.neg
+-/
 
+#print TorusIntegrable.add /-
 /-- If `f` and `g` are two torus integrable functions, then so is `f + g`. -/
 protected theorem add (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c R) :
     TorusIntegrable (f + g) c R :=
   hf.add hg
 #align torus_integrable.add TorusIntegrable.add
+-/
 
+#print TorusIntegrable.sub /-
 /-- If `f` and `g` are two torus integrable functions, then so is `f - g`. -/
 protected theorem sub (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c R) :
     TorusIntegrable (f - g) c R :=
   hf.sub hg
 #align torus_integrable.sub TorusIntegrable.sub
+-/
 
+#print TorusIntegrable.torusIntegrable_zero_radius /-
 theorem torusIntegrable_zero_radius {f : ℂⁿ → E} {c : ℂⁿ} : TorusIntegrable f c 0 :=
   by
   rw [TorusIntegrable, torusMap_zero_radius]
   apply torus_integrable_const (f c) c 0
 #align torus_integrable.torus_integrable_zero_radius TorusIntegrable.torusIntegrable_zero_radius
+-/
 
 /-- The function given in the definition of `torus_integral` is integrable. -/
 theorem function_integrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :

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

@@ -186,36 +186,35 @@ def torusIntegral (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :=
 #align torus_integral torusIntegral
 
 -- mathport name: «expr∯ inT( , ), »
-notation3"∯ "(...)" in ""T("c", "R")"", "r:(scoped f => torusIntegral f c R) => r
+notation3"∯ "(...)" in ""T("c", "R")"", "r:60:(scoped f => torusIntegral f c R) => r
 
-theorem torusIntegral_radius_zero (hn : n ≠ 0) (f : ℂⁿ → E) (c : ℂⁿ) : (∯ x in T(c, 0), f x) = 0 :=
-  by
+theorem torusIntegral_radius_zero (hn : n ≠ 0) (f : ℂⁿ → E) (c : ℂⁿ) : ∯ x in T(c, 0), f x = 0 := by
   simp only [torusIntegral, Pi.zero_apply, of_real_zero, MulZeroClass.mul_zero,
     MulZeroClass.zero_mul, Fin.prod_const, zero_pow' n hn, zero_smul, integral_zero]
 #align torus_integral_radius_zero torusIntegral_radius_zero
 
 theorem torusIntegral_neg (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :
-    (∯ x in T(c, R), -f x) = -∯ x in T(c, R), f x := by simp [torusIntegral, integral_neg]
+    ∯ x in T(c, R), -f x = -∯ x in T(c, R), f x := by simp [torusIntegral, integral_neg]
 #align torus_integral_neg torusIntegral_neg
 
 theorem torusIntegral_add (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c R) :
-    (∯ x in T(c, R), f x + g x) = (∯ x in T(c, R), f x) + ∯ x in T(c, R), g x := by
+    ∯ x in T(c, R), f x + g x = (∯ x in T(c, R), f x) + ∯ x in T(c, R), g x := by
   simpa only [torusIntegral, smul_add, Pi.add_apply] using
     integral_add hf.function_integrable hg.function_integrable
 #align torus_integral_add torusIntegral_add
 
 theorem torusIntegral_sub (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c R) :
-    (∯ x in T(c, R), f x - g x) = (∯ x in T(c, R), f x) - ∯ x in T(c, R), g x := by
+    ∯ x in T(c, R), f x - g x = (∯ x in T(c, R), f x) - ∯ x in T(c, R), g x := by
   simpa only [sub_eq_add_neg, ← torusIntegral_neg] using torusIntegral_add hf hg.neg
 #align torus_integral_sub torusIntegral_sub
 
 theorem torusIntegral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
-    (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : (∯ x in T(c, R), a • f x) = a • ∯ x in T(c, R), f x := by
+    (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : ∯ x in T(c, R), a • f x = a • ∯ x in T(c, R), f x := by
   simp only [torusIntegral, integral_smul, ← smul_comm a]
 #align torus_integral_smul torusIntegral_smul
 
 theorem torusIntegral_const_mul (a : ℂ) (f : ℂⁿ → ℂ) (c : ℂⁿ) (R : ℝⁿ) :
-    (∯ x in T(c, R), a * f x) = a * ∯ x in T(c, R), f x :=
+    ∯ x in T(c, R), a * f x = a * ∯ x in T(c, R), f x :=
   torusIntegral_smul a f c R
 #align torus_integral_const_mul torusIntegral_const_mul
 
@@ -238,7 +237,7 @@ theorem norm_torusIntegral_le_of_norm_le_const {C : ℝ} (hf : ∀ θ, ‖f (tor
 #align norm_torus_integral_le_of_norm_le_const norm_torusIntegral_le_of_norm_le_const
 
 @[simp]
-theorem torusIntegral_dim0 (f : ℂ⁰ → E) (c : ℂ⁰) (R : ℝ⁰) : (∯ x in T(c, R), f x) = f c := by
+theorem torusIntegral_dim0 (f : ℂ⁰ → E) (c : ℂ⁰) (R : ℝ⁰) : ∯ x in T(c, R), f x = f c := by
   simp only [torusIntegral, Fin.prod_univ_zero, one_smul,
     Subsingleton.elim (fun i : Fin 0 => 2 * π) 0, Icc_self, measure.restrict_singleton, volume_pi,
     integral_smul_measure, integral_dirac, measure.pi_of_empty _ 0,
@@ -248,7 +247,7 @@ theorem torusIntegral_dim0 (f : ℂ⁰ → E) (c : ℂ⁰) (R : ℝ⁰) : (∯ x
 /-- In dimension one, `torus_integral` is the same as `circle_integral`
 (up to the natural equivalence between `ℂ` and `fin 1 → ℂ`). -/
 theorem torusIntegral_dim1 (f : ℂ¹ → E) (c : ℂ¹) (R : ℝ¹) :
-    (∯ x in T(c, R), f x) = ∮ z in C(c 0, R 0), f fun _ => z :=
+    ∯ x in T(c, R), f x = ∮ z in C(c 0, R 0), f fun _ => z :=
   by
   have : ((fun (x : ℝ) (b : Fin 1) => x) ⁻¹' Icc 0 fun _ => 2 * π) = Icc 0 (2 * π) :=
     (OrderIso.funUnique (Fin 1) ℝ).symm.preimage_Icc _ _
@@ -265,7 +264,7 @@ theorem torusIntegral_dim1 (f : ℂ¹ → E) (c : ℂ¹) (R : ℝ¹) :
 /-- Recurrent formula for `torus_integral`, see also `torus_integral_succ`. -/
 theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : ℝⁿ⁺¹} (hf : TorusIntegrable f c R)
     (i : Fin (n + 1)) :
-    (∯ x in T(c, R), f x) =
+    ∯ x in T(c, R), f x =
       ∮ x in C(c i, R i), ∯ y in T(c ∘ i.succAbove, R ∘ i.succAbove), f (i.insertNth x y) :=
   by
   set e : ℝ × ℝⁿ ≃ᵐ ℝⁿ⁺¹ := (MeasurableEquiv.piFinSuccAboveEquiv (fun _ => ℝ) i).symm
@@ -290,7 +289,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
 
 /-- Recurrent formula for `torus_integral`, see also `torus_integral_succ_above`. -/
 theorem torusIntegral_succ {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : ℝⁿ⁺¹} (hf : TorusIntegrable f c R) :
-    (∯ x in T(c, R), f x) =
+    ∯ x in T(c, R), f x =
       ∮ x in C(c 0, R 0), ∯ y in T(c ∘ Fin.succ, R ∘ Fin.succ), f (Fin.cons x y) :=
   by simpa using torusIntegral_succAbove hf 0
 #align torus_integral_succ torusIntegral_succ

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

@@ -232,11 +232,9 @@ theorem norm_torusIntegral_le_of_norm_le_const {C : ℝ} (hf : ∀ θ, ‖f (tor
             by simp [norm_smul]
           _ ≤ (∏ i : Fin n, |R i|) * C :=
             mul_le_mul_of_nonneg_left (hf _) (Finset.prod_nonneg fun _ _ => abs_nonneg _)
-          
     _ = ((2 * π) ^ (n : ℕ) * ∏ i, |R i|) * C := by
       simp only [Pi.zero_def, Real.volume_Icc_pi_toReal fun _ => real.two_pi_pos.le, sub_zero,
         Fin.prod_const, mul_assoc, mul_comm ((2 * π) ^ (n : ℕ))]
-    
 #align norm_torus_integral_le_of_norm_le_const norm_torusIntegral_le_of_norm_le_const
 
 @[simp]

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

@@ -287,7 +287,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     simp only [funext_iff, i.forall_iff_succ_above, circleMap, Fin.insertNth_apply_same,
       eq_self_iff_true, Fin.insertNth_apply_succAbove, imp_true_iff, and_self_iff]
   · have := hf.function_integrable
-    rwa [← hem.integrable_on_comp_preimage e.measurable_embedding, heπ] at this
+    rwa [← hem.integrable_on_comp_preimage e.measurable_embedding, heπ] at this 
 #align torus_integral_succ_above torusIntegral_succAbove
 
 /-- Recurrent formula for `torus_integral`, see also `torus_integral_succ_above`. -/

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

@@ -67,7 +67,7 @@ noncomputable section
 
 open Complex Set MeasureTheory Function Filter TopologicalSpace
 
-open Real BigOperators
+open scoped Real BigOperators
 
 -- mathport name: «exprℝ⁰»
 local notation "ℝ⁰" => Fin 0 → ℝ

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

@@ -104,10 +104,8 @@ it to every n axis. -/
 def torusMap (c : ℂⁿ) (R : ℝⁿ) : ℝⁿ → ℂⁿ := fun θ i => c i + R i * exp (θ i * I)
 #align torus_map torusMap
 
-theorem torusMap_sub_center (c : ℂⁿ) (R : ℝⁿ) (θ : ℝⁿ) : torusMap c R θ - c = torusMap 0 R θ :=
-  by
-  ext1 i
-  simp [torusMap]
+theorem torusMap_sub_center (c : ℂⁿ) (R : ℝⁿ) (θ : ℝⁿ) : torusMap c R θ - c = torusMap 0 R θ := by
+  ext1 i; simp [torusMap]
 #align torus_map_sub_center torusMap_sub_center
 
 theorem torusMap_eq_center_iff {c : ℂⁿ} {R : ℝⁿ} {θ : ℝⁿ} : torusMap c R θ = c ↔ R = 0 := by
@@ -115,9 +113,7 @@ theorem torusMap_eq_center_iff {c : ℂⁿ} {R : ℝⁿ} {θ : ℝⁿ} : torusMa
 #align torus_map_eq_center_iff torusMap_eq_center_iff
 
 @[simp]
-theorem torusMap_zero_radius (c : ℂⁿ) : torusMap c 0 = const ℝⁿ c :=
-  by
-  ext1
+theorem torusMap_zero_radius (c : ℂⁿ) : torusMap c 0 = const ℝⁿ c := by ext1;
   rw [torusMap_eq_center_iff.2 rfl]
 #align torus_map_zero_radius torusMap_zero_radius
 

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

@@ -170,7 +170,7 @@ theorem function_integrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :
       (Icc (0 : ℝⁿ) fun _ => 2 * π) volume :=
   by
   refine' (hf.norm.const_mul (∏ i, |R i|)).mono' _ _
-  · refine' (Continuous.aeStronglyMeasurable _).smul hf.1
+  · refine' (Continuous.aestronglyMeasurable _).smul hf.1
     exact
       continuous_finset_prod Finset.univ fun i hi =>
         (continuous_const.mul

mathlib commit https://github.com/leanprover-community/mathlib/commit/f51de8769c34652d82d1c8e5f8f18f8374782bed

@@ -4,10 +4,11 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Cuma Kökmen, Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.torus_integral
-! leanprover-community/mathlib commit 17ef379e997badd73e5eabb4d38f11919ab3c4b3
+! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
+import Mathbin.MeasureTheory.Constructions.Prod.Integral
 import Mathbin.MeasureTheory.Integral.CircleIntegral
 
 /-!

mathlib commit https://github.com/leanprover-community/mathlib/commit/92c69b77c5a7dc0f7eeddb552508633305157caa

@@ -164,7 +164,7 @@ theorem torusIntegrable_zero_radius {f : ℂⁿ → E} {c : ℂⁿ} : TorusInteg
 #align torus_integrable.torus_integrable_zero_radius TorusIntegrable.torusIntegrable_zero_radius
 
 /-- The function given in the definition of `torus_integral` is integrable. -/
-theorem functionIntegrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :
+theorem function_integrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :
     IntegrableOn (fun θ : ℝⁿ => (∏ i, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ))
       (Icc (0 : ℝⁿ) fun _ => 2 * π) volume :=
   by
@@ -176,7 +176,7 @@ theorem functionIntegrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :
               ((continuous_of_real.comp (continuous_apply i)).mul continuous_const).cexp).mul
           continuous_const
   simp [norm_smul, map_prod]
-#align torus_integrable.function_integrable TorusIntegrable.functionIntegrable
+#align torus_integrable.function_integrable TorusIntegrable.function_integrable
 
 end TorusIntegrable
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/3180fab693e2cee3bff62675571264cb8778b212

@@ -193,8 +193,8 @@ notation3"∯ "(...)" in ""T("c", "R")"", "r:(scoped f => torusIntegral f c R) =
 
 theorem torusIntegral_radius_zero (hn : n ≠ 0) (f : ℂⁿ → E) (c : ℂⁿ) : (∯ x in T(c, 0), f x) = 0 :=
   by
-  simp only [torusIntegral, Pi.zero_apply, of_real_zero, mul_zero, zero_mul, Fin.prod_const,
-    zero_pow' n hn, zero_smul, integral_zero]
+  simp only [torusIntegral, Pi.zero_apply, of_real_zero, MulZeroClass.mul_zero,
+    MulZeroClass.zero_mul, Fin.prod_const, zero_pow' n hn, zero_smul, integral_zero]
 #align torus_integral_radius_zero torusIntegral_radius_zero
 
 theorem torusIntegral_neg (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :

mathlib commit https://github.com/leanprover-community/mathlib/commit/ddec54a71a0dd025c05445d467f1a2b7d586a3ba

@@ -100,7 +100,7 @@ local notation "ℂⁿ⁺¹" => Fin (n + 1) → ℂ
 /-- The n dimensional exponential map $θ_i ↦ c + R e^{θ_i*I}, θ ∈ ℝⁿ$ representing
 a torus in `ℂⁿ` with center `c ∈ ℂⁿ` and generalized radius `R ∈ ℝⁿ`, so we can adjust
 it to every n axis. -/
-def torusMap (c : ℂⁿ) (R : ℝⁿ) : ℝⁿ → ℂⁿ := fun θ i => c i + R i * exp (θ i * i)
+def torusMap (c : ℂⁿ) (R : ℝⁿ) : ℝⁿ → ℂⁿ := fun θ i => c i + R i * exp (θ i * I)
 #align torus_map torusMap
 
 theorem torusMap_sub_center (c : ℂⁿ) (R : ℝⁿ) (θ : ℝⁿ) : torusMap c R θ - c = torusMap 0 R θ :=
@@ -165,7 +165,7 @@ theorem torusIntegrable_zero_radius {f : ℂⁿ → E} {c : ℂⁿ} : TorusInteg
 
 /-- The function given in the definition of `torus_integral` is integrable. -/
 theorem functionIntegrable [NormedSpace ℂ E] (hf : TorusIntegrable f c R) :
-    IntegrableOn (fun θ : ℝⁿ => (∏ i, R i * exp (θ i * i) * i : ℂ) • f (torusMap c R θ))
+    IntegrableOn (fun θ : ℝⁿ => (∏ i, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ))
       (Icc (0 : ℝⁿ) fun _ => 2 * π) volume :=
   by
   refine' (hf.norm.const_mul (∏ i, |R i|)).mono' _ _
@@ -185,7 +185,7 @@ variable [NormedSpace ℂ E] [CompleteSpace E] {f g : ℂⁿ → E} {c : ℂⁿ}
 /-- The definition of the integral over a generalized torus with center `c ∈ ℂⁿ` and radius `R ∈ ℝⁿ`
 as the `•`-product of the derivative of `torus_map` and `f (torus_map c R θ)`-/
 def torusIntegral (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :=
-  ∫ θ : ℝⁿ in Icc (0 : ℝⁿ) fun _ => 2 * π, (∏ i, R i * exp (θ i * i) * i : ℂ) • f (torusMap c R θ)
+  ∫ θ : ℝⁿ in Icc (0 : ℝⁿ) fun _ => 2 * π, (∏ i, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ)
 #align torus_integral torusIntegral
 
 -- mathport name: «expr∯ inT( , ), »
@@ -230,7 +230,7 @@ theorem norm_torusIntegral_le_of_norm_le_const {C : ℝ} (hf : ∀ θ, ‖f (tor
     ‖∯ x in T(c, R), f x‖ ≤ (∏ i, |R i|) * C * (volume (Icc (0 : ℝⁿ) fun _ => 2 * π)).toReal :=
       norm_set_integral_le_of_norm_le_const' measure_Icc_lt_top measurableSet_Icc fun θ hθ =>
         calc
-          ‖(∏ i : Fin n, R i * exp (θ i * i) * i : ℂ) • f (torusMap c R θ)‖ =
+          ‖(∏ i : Fin n, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ)‖ =
               (∏ i : Fin n, |R i|) * ‖f (torusMap c R θ)‖ :=
             by simp [norm_smul]
           _ ≤ (∏ i : Fin n, |R i|) * C :=

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

Done with a global search and replace, and then (to fix the #align lines), replace (#align \S*)setIntegral with $1set_integral.

@@ -194,7 +194,7 @@ theorem norm_torusIntegral_le_of_norm_le_const {C : ℝ} (hf : ∀ θ, ‖f (tor
     ‖∯ x in T(c, R), f x‖ ≤ ((2 * π) ^ (n : ℕ) * ∏ i, |R i|) * C :=
   calc
     ‖∯ x in T(c, R), f x‖ ≤ (∏ i, |R i|) * C * (volume (Icc (0 : ℝⁿ) fun _ => 2 * π)).toReal :=
-      norm_set_integral_le_of_norm_le_const' measure_Icc_lt_top measurableSet_Icc fun θ _ =>
+      norm_setIntegral_le_of_norm_le_const' measure_Icc_lt_top measurableSet_Icc fun θ _ =>
         calc
           ‖(∏ i : Fin n, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ)‖ =
               (∏ i : Fin n, |R i|) * ‖f (torusMap c R θ)‖ :=
@@ -225,7 +225,7 @@ theorem torusIntegral_dim1 (f : ℂ¹ → E) (c : ℂ¹) (R : ℝ¹) :
     rw [Subsingleton.elim i 0]; rfl
   rw [torusIntegral, circleIntegral, intervalIntegral.integral_of_le Real.two_pi_pos.le,
     Measure.restrict_congr_set Ioc_ae_eq_Icc,
-    ← ((volume_preserving_funUnique (Fin 1) ℝ).symm _).set_integral_preimage_emb
+    ← ((volume_preserving_funUnique (Fin 1) ℝ).symm _).setIntegral_preimage_emb
       (MeasurableEquiv.measurableEmbedding _), H₁, H₂]
   simp [circleMap_zero]
 #align torus_integral_dim1 torusIntegral_dim1
@@ -240,12 +240,12 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     (volume_preserving_piFinSuccAbove (fun _ : Fin (n + 1) => ℝ) i).symm _
   have heπ : (e ⁻¹' Icc 0 fun _ => 2 * π) = Icc 0 (2 * π) ×ˢ Icc (0 : ℝⁿ) fun _ => 2 * π :=
     ((OrderIso.piFinSuccAboveIso (fun _ => ℝ) i).symm.preimage_Icc _ _).trans (Icc_prod_eq _ _)
-  rw [torusIntegral, ← hem.map_eq, set_integral_map_equiv, heπ, Measure.volume_eq_prod,
-    set_integral_prod, circleIntegral_def_Icc]
-  · refine' set_integral_congr measurableSet_Icc fun θ _ => _
+  rw [torusIntegral, ← hem.map_eq, setIntegral_map_equiv, heπ, Measure.volume_eq_prod,
+    setIntegral_prod, circleIntegral_def_Icc]
+  · refine' setIntegral_congr measurableSet_Icc fun θ _ => _
     simp (config := { unfoldPartialApp := true }) only [e, torusIntegral, ← integral_smul,
       deriv_circleMap, i.prod_univ_succAbove _, smul_smul, torusMap, circleMap_zero]
-    refine' set_integral_congr measurableSet_Icc fun Θ _ => _
+    refine' setIntegral_congr measurableSet_Icc fun Θ _ => _
     simp only [MeasurableEquiv.piFinSuccAbove_symm_apply, i.insertNth_apply_same,
       i.insertNth_apply_succAbove, (· ∘ ·)]
     congr 2

IsROrC contains data, which goes against the expectation that classes prefixed with Is are prop-valued. People have been complaining about this on and off, so this PR renames IsROrC to RCLike.

@@ -178,7 +178,7 @@ theorem torusIntegral_sub (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c
   simpa only [sub_eq_add_neg, ← torusIntegral_neg] using torusIntegral_add hf hg.neg
 #align torus_integral_sub torusIntegral_sub
 
-theorem torusIntegral_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
+theorem torusIntegral_smul {𝕜 : Type*} [RCLike 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : (∯ x in T(c, R), a • f x) = a • ∯ x in T(c, R), f x := by
   simp only [torusIntegral, integral_smul, ← smul_comm a (_ : ℂ) (_ : E)]
 #align torus_integral_smul torusIntegral_smul

Empty lines were removed by executing the following Python script twice

import os
import re


# Loop through each file in the repository
for dir_path, dirs, files in os.walk('.'):
  for filename in files:
    if filename.endswith('.lean'):
      file_path = os.path.join(dir_path, filename)

      # Open the file and read its contents
      with open(file_path, 'r') as file:
        content = file.read()

      # Use a regular expression to replace sequences of "variable" lines separated by empty lines
      # with sequences without empty lines
      modified_content = re.sub(r'(variable.*\n)\n(variable(?! .* in))', r'\1\2', content)

      # Write the modified content back to the file
      with open(file_path, 'w') as file:
        file.write(modified_content)

@@ -57,7 +57,6 @@ integral, torus
 
 
 variable {n : ℕ}
-
 variable {E : Type*} [NormedAddCommGroup E]
 
 noncomputable section

Classifies by adding issue number #11215 to porting notes claiming "TODO".

@@ -107,7 +107,7 @@ def TorusIntegrable (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : Prop :=
 
 namespace TorusIntegrable
 
--- Porting note: todo: restore notation; `neg`, `add` etc fail if I use notation here
+-- Porting note (#11215): TODO: restore notation; `neg`, `add` etc fail if I use notation here
 variable {f g : (Fin n → ℂ) → E} {c : Fin n → ℂ} {R : Fin n → ℝ}
 
 /-- Constant functions are torus integrable -/

Homogenises porting notes via capitalisation and addition of whitespace.

It makes the following changes:

• converts "--porting note" into "-- Porting note";
• converts "porting note" into "Porting note".

@@ -66,7 +66,7 @@ open Complex Set MeasureTheory Function Filter TopologicalSpace
 
 open scoped Real BigOperators
 
--- porting note: notation copied from `./DivergenceTheorem`
+-- Porting note: notation copied from `./DivergenceTheorem`
 local macro:arg t:term:max noWs "ⁿ⁺¹" : term => `(Fin (n + 1) → $t)
 local macro:arg t:term:max noWs "ⁿ" : term => `(Fin n → $t)
 local macro:arg t:term:max noWs "⁰" : term => `(Fin 0 → $t)
@@ -107,7 +107,7 @@ def TorusIntegrable (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : Prop :=
 
 namespace TorusIntegrable
 
--- porting note: todo: restore notation; `neg`, `add` etc fail if I use notation here
+-- Porting note: todo: restore notation; `neg`, `add` etc fail if I use notation here
 variable {f g : (Fin n → ℂ) → E} {c : Fin n → ℂ} {R : Fin n → ℝ}
 
 /-- Constant functions are torus integrable -/

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

@@ -244,7 +244,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
   rw [torusIntegral, ← hem.map_eq, set_integral_map_equiv, heπ, Measure.volume_eq_prod,
     set_integral_prod, circleIntegral_def_Icc]
   · refine' set_integral_congr measurableSet_Icc fun θ _ => _
-    simp (config := { unfoldPartialApp := true }) only [torusIntegral, ← integral_smul,
+    simp (config := { unfoldPartialApp := true }) only [e, torusIntegral, ← integral_smul,
       deriv_circleMap, i.prod_univ_succAbove _, smul_smul, torusMap, circleMap_zero]
     refine' set_integral_congr measurableSet_Icc fun Θ _ => _
     simp only [MeasurableEquiv.piFinSuccAbove_symm_apply, i.insertNth_apply_same,

This involves moving lemmas from Algebra.GroupPower.Ring to Algebra.GroupWithZero.Basic and changing some 0 < n assumptions to n ≠ 0.

From LeanAPAP

@@ -161,7 +161,7 @@ notation3"∯ "(...)" in ""T("c", "R")"", "r:(scoped f => torusIntegral f c R) =
 theorem torusIntegral_radius_zero (hn : n ≠ 0) (f : ℂⁿ → E) (c : ℂⁿ) :
     (∯ x in T(c, 0), f x) = 0 := by
   simp only [torusIntegral, Pi.zero_apply, ofReal_zero, mul_zero, zero_mul, Fin.prod_const,
-    zero_pow' n hn, zero_smul, integral_zero]
+    zero_pow hn, zero_smul, integral_zero]
 #align torus_integral_radius_zero torusIntegral_radius_zero
 
 theorem torusIntegral_neg (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :

Make all the notations that unambiguously should inherit the docstring of their definition actually inherit it.

Also write a few docstrings by hand. I only wrote the ones I was competent to write and which I was sure of. Some docstrings come from mathlib3 as they were lost during the early port.

This PR is only intended as a first pass There are many more docstrings to add.

@@ -149,12 +149,13 @@ end TorusIntegrable
 
 variable [NormedSpace ℂ E] [CompleteSpace E] {f g : (Fin n → ℂ) → E} {c : Fin n → ℂ} {R : Fin n → ℝ}
 
-/-- The definition of the integral over a generalized torus with center `c ∈ ℂⁿ` and radius `R ∈ ℝⁿ`
+/-- The integral over a generalized torus with center `c ∈ ℂⁿ` and radius `R ∈ ℝⁿ`, defined
 as the `•`-product of the derivative of `torusMap` and `f (torusMap c R θ)`-/
 def torusIntegral (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) :=
   ∫ θ : ℝⁿ in Icc (0 : ℝⁿ) fun _ => 2 * π, (∏ i, R i * exp (θ i * I) * I : ℂ) • f (torusMap c R θ)
 #align torus_integral torusIntegral
 
+@[inherit_doc torusIntegral]
 notation3"∯ "(...)" in ""T("c", "R")"", "r:(scoped f => torusIntegral f c R) => r
 
 theorem torusIntegral_radius_zero (hn : n ≠ 0) (f : ℂⁿ → E) (c : ℂⁿ) :

Replaces Equiv.piFinSuccAboveEquiv with .piFinSuccAbove, and same for MeasurableEquiv.piFinSuccAboveEquiv

@@ -235,9 +235,9 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     (i : Fin (n + 1)) :
     (∯ x in T(c, R), f x) =
       ∮ x in C(c i, R i), ∯ y in T(c ∘ i.succAbove, R ∘ i.succAbove), f (i.insertNth x y) := by
-  set e : ℝ × ℝⁿ ≃ᵐ ℝⁿ⁺¹ := (MeasurableEquiv.piFinSuccAboveEquiv (fun _ => ℝ) i).symm
+  set e : ℝ × ℝⁿ ≃ᵐ ℝⁿ⁺¹ := (MeasurableEquiv.piFinSuccAbove (fun _ => ℝ) i).symm
   have hem : MeasurePreserving e :=
-    (volume_preserving_piFinSuccAboveEquiv (fun _ : Fin (n + 1) => ℝ) i).symm _
+    (volume_preserving_piFinSuccAbove (fun _ : Fin (n + 1) => ℝ) i).symm _
   have heπ : (e ⁻¹' Icc 0 fun _ => 2 * π) = Icc 0 (2 * π) ×ˢ Icc (0 : ℝⁿ) fun _ => 2 * π :=
     ((OrderIso.piFinSuccAboveIso (fun _ => ℝ) i).symm.preimage_Icc _ _).trans (Icc_prod_eq _ _)
   rw [torusIntegral, ← hem.map_eq, set_integral_map_equiv, heπ, Measure.volume_eq_prod,
@@ -246,7 +246,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     simp (config := { unfoldPartialApp := true }) only [torusIntegral, ← integral_smul,
       deriv_circleMap, i.prod_univ_succAbove _, smul_smul, torusMap, circleMap_zero]
     refine' set_integral_congr measurableSet_Icc fun Θ _ => _
-    simp only [MeasurableEquiv.piFinSuccAboveEquiv_symm_apply, i.insertNth_apply_same,
+    simp only [MeasurableEquiv.piFinSuccAbove_symm_apply, i.insertNth_apply_same,
       i.insertNth_apply_succAbove, (· ∘ ·)]
     congr 2
     simp only [funext_iff, i.forall_iff_succAbove, circleMap, Fin.insertNth_apply_same,

PR contents

This is the supremum of

• #8284
• #8056
• #8023
• #8332
• #8226 (already approved)
• #7834 (already approved)

along with some minor fixes from failures on nightly-testing as Mathlib master is merged into it.

Note that some PRs for changes that are already compatible with the current toolchain and will be necessary have already been split out: #8380.

I am hopeful that in future we will be able to progressively merge adaptation PRs into a bump/v4.X.0 branch, so we never end up with a "big merge" like this. However one of these adaptation PRs (#8056) predates my new scheme for combined CI, and it wasn't possible to keep that PR viable in the meantime.

Lean PRs involved in this bump

In particular this includes adjustments for the Lean PRs

• leanprover/lean4#2778
• leanprover/lean4#2790
• leanprover/lean4#2783
• leanprover/lean4#2825
• leanprover/lean4#2722

leanprover/lean4#2778

We can get rid of all the

local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue [lean4#2220](https://github.com/leanprover/lean4/pull/2220)

macros across Mathlib (and in any projects that want to write natural number powers of reals).

leanprover/lean4#2722

Changes the default behaviour of simp to (config := {decide := false}). This makes simp (and consequentially norm_num) less powerful, but also more consistent, and less likely to blow up in long failures. This requires a variety of changes: changing some previously by simp or norm_num to decide or rfl, or adding (config := {decide := true}).

leanprover/lean4#2783

This changed the behaviour of simp so that simp [f] will only unfold "fully applied" occurrences of f. The old behaviour can be recovered with simp (config := { unfoldPartialApp := true }). We may in future add a syntax for this, e.g. simp [!f]; please provide feedback! In the meantime, we have made the following changes:

• switching to using explicit lemmas that have the intended level of application
• (config := { unfoldPartialApp := true }) in some places, to recover the old behaviour
• Using @[eqns] to manually adjust the equation lemmas for a particular definition, recovering the old behaviour just for that definition. See #8371, where we do this for Function.comp and Function.flip.

This change in Lean may require further changes down the line (e.g. adding the !f syntax, and/or upstreaming the special treatment for Function.comp and Function.flip, and/or removing this special treatment). Please keep an open and skeptical mind about these changes!

Co-authored-by: leanprover-community-mathlib4-bot <leanprover-community-mathlib4-bot@users.noreply.github.com> Co-authored-by: Scott Morrison <scott.morrison@gmail.com> Co-authored-by: Eric Wieser <wieser.eric@gmail.com> Co-authored-by: Mauricio Collares <mauricio@collares.org>

@@ -71,7 +71,6 @@ local macro:arg t:term:max noWs "ⁿ⁺¹" : term => `(Fin (n + 1) → $t)
 local macro:arg t:term:max noWs "ⁿ" : term => `(Fin n → $t)
 local macro:arg t:term:max noWs "⁰" : term => `(Fin 0 → $t)
 local macro:arg t:term:max noWs "¹" : term => `(Fin 1 → $t)
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 /-!
 ### `torusMap`, a parametrization of a torus
@@ -244,8 +243,8 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
   rw [torusIntegral, ← hem.map_eq, set_integral_map_equiv, heπ, Measure.volume_eq_prod,
     set_integral_prod, circleIntegral_def_Icc]
   · refine' set_integral_congr measurableSet_Icc fun θ _ => _
-    simp only [torusIntegral, ← integral_smul, deriv_circleMap, i.prod_univ_succAbove _, smul_smul,
-      torusMap, circleMap_zero]
+    simp (config := { unfoldPartialApp := true }) only [torusIntegral, ← integral_smul,
+      deriv_circleMap, i.prod_univ_succAbove _, smul_smul, torusMap, circleMap_zero]
     refine' set_integral_congr measurableSet_Icc fun Θ _ => _
     simp only [MeasurableEquiv.piFinSuccAboveEquiv_symm_apply, i.insertNth_apply_same,
       i.insertNth_apply_succAbove, (· ∘ ·)]

@@ -253,7 +253,7 @@ theorem torusIntegral_succAbove {f : ℂⁿ⁺¹ → E} {c : ℂⁿ⁺¹} {R : 
     simp only [funext_iff, i.forall_iff_succAbove, circleMap, Fin.insertNth_apply_same,
       eq_self_iff_true, Fin.insertNth_apply_succAbove, imp_true_iff, and_self_iff]
   · have := hf.function_integrable
-    rwa [← hem.integrableOn_comp_preimage e.measurableEmbedding, heπ] at this 
+    rwa [← hem.integrableOn_comp_preimage e.measurableEmbedding, heπ] at this
 #align torus_integral_succ_above torusIntegral_succAbove
 
 /-- Recurrent formula for `torusIntegral`, see also `torusIntegral_succAbove`. -/

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

This has nice performance benefits.

@@ -58,7 +58,7 @@ integral, torus
 
 variable {n : ℕ}
 
-variable {E : Type _} [NormedAddCommGroup E]
+variable {E : Type*} [NormedAddCommGroup E]
 
 noncomputable section
 
@@ -179,7 +179,7 @@ theorem torusIntegral_sub (hf : TorusIntegrable f c R) (hg : TorusIntegrable g c
   simpa only [sub_eq_add_neg, ← torusIntegral_neg] using torusIntegral_add hf hg.neg
 #align torus_integral_sub torusIntegral_sub
 
-theorem torusIntegral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
+theorem torusIntegral_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : (∯ x in T(c, R), a • f x) = a • ∯ x in T(c, R), f x := by
   simp only [torusIntegral, integral_smul, ← smul_comm a (_ : ℂ) (_ : E)]
 #align torus_integral_smul torusIntegral_smul

@@ -71,7 +71,7 @@ local macro:arg t:term:max noWs "ⁿ⁺¹" : term => `(Fin (n + 1) → $t)
 local macro:arg t:term:max noWs "ⁿ" : term => `(Fin n → $t)
 local macro:arg t:term:max noWs "⁰" : term => `(Fin 0 → $t)
 local macro:arg t:term:max noWs "¹" : term => `(Fin 1 → $t)
-local macro_rules | `($x ^ $y)   => `(HPow.hPow $x $y) -- Porting note: See Lean 4 issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 /-!
 ### `torusMap`, a parametrization of a torus

• 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) 2022 Cuma Kökmen. All rights reserved.
 Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Cuma Kökmen, Yury Kudryashov
-
-! This file was ported from Lean 3 source module measure_theory.integral.torus_integral
-! leanprover-community/mathlib commit fd5edc43dc4f10b85abfe544b88f82cf13c5f844
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Constructions.Prod.Integral
 import Mathlib.MeasureTheory.Integral.CircleIntegral
 
+#align_import measure_theory.integral.torus_integral from "leanprover-community/mathlib"@"fd5edc43dc4f10b85abfe544b88f82cf13c5f844"
+
 /-!
 # Integral over a torus in `ℂⁿ`
 

Found with git grep -n "λ [a-zA-Z_ ]*,"

@@ -18,11 +18,11 @@ In this file we define the integral of a function `f : ℂⁿ → E` over a toru
 `{z : ℂⁿ | ∀ i, z i ∈ Metric.sphere (c i) (R i)}`. In order to do this, we define
 `torusMap (c : ℂⁿ) (R θ : ℝⁿ)` to be the point in `ℂⁿ` given by $z_k=c_k+R_ke^{θ_ki}$,
 where $i$ is the imaginary unit, then define `torusIntegral f c R` as the integral over
-the cube $[0, (λ _, 2π)] = \{θ\|∀ k, 0 ≤ θ_k ≤ 2π\}$ of the Jacobian of the
+the cube $[0, (fun _ ↦ 2π)] = \{θ\|∀ k, 0 ≤ θ_k ≤ 2π\}$ of the Jacobian of the
 `torusMap` multiplied by `f (torusMap c R θ)`.
 
 We also define a predicate saying that `f ∘ torusMap c R` is integrable on the cube
-`[0, (λ _, 2\pi)]`.
+`[0, (fun _ ↦ 2π)]`.
 
 ## Main definitions
 
@@ -31,7 +31,7 @@ We also define a predicate saying that `f ∘ torusMap c R` is integrable on the
 
 * `TorusIntegrable f c R`: a function `f : ℂⁿ → E` is integrable over the generalized torus
   with center `c : ℂⁿ` and radius `R : ℝⁿ` if `f ∘ torusMap c R` is integrable on the
-  closed cube `Icc (0 : ℝⁿ) (λ _, 2 * π)`;
+  closed cube `Icc (0 : ℝⁿ) (fun _ ↦ 2 * π)`;
 
 * `torusIntegral f c R`: the integral of a function `f : ℂⁿ → E` over a torus with
   center `c ∈ ℂⁿ` and radius `R ∈ ℝⁿ` defined as
@@ -104,7 +104,7 @@ theorem torusMap_zero_radius (c : ℂⁿ) : torusMap c 0 = const ℝⁿ c :=
 -/
 
 /-- A function `f : ℂⁿ → E` is integrable on the generalized torus if the function
-`f ∘ torusMap c R θ` is integrable on `Icc (0 : ℝⁿ) (λ _, 2 * π)`-/
+`f ∘ torusMap c R θ` is integrable on `Icc (0 : ℝⁿ) (fun _ ↦ 2 * π)`. -/
 def TorusIntegrable (f : ℂⁿ → E) (c : ℂⁿ) (R : ℝⁿ) : Prop :=
   IntegrableOn (fun θ : ℝⁿ => f (torusMap c R θ)) (Icc (0 : ℝⁿ) fun _ => 2 * π) volume
 #align torus_integrable TorusIntegrable