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

@@ -4,7 +4,7 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 -/
 import MeasureTheory.Integral.IntervalIntegral
-import Analysis.Calculus.Deriv.Zpow
+import Analysis.Calculus.Deriv.ZPow
 import Analysis.NormedSpace.Pointwise
 import Analysis.SpecialFunctions.NonIntegrable
 import Analysis.Analytic.Basic
@@ -551,7 +551,7 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
 
 #print circleIntegral.integral_smul /-
 @[simp]
-theorem integral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
+theorem integral_smul {𝕜 : Type _} [RCLike 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂ → E) (c : ℂ) (R : ℝ) : ∮ z in C(c, R), a • f z = a • ∮ z in C(c, R), f z := by
   simp only [circleIntegral, ← smul_comm a, intervalIntegral.integral_smul]
 #align circle_integral.integral_smul circleIntegral.integral_smul
@@ -577,7 +577,7 @@ theorem integral_const_mul (a : ℂ) (f : ℂ → ℂ) (c : ℂ) (R : ℝ) :
 @[simp]
 theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
     ∮ z in C(c, R), (z - c)⁻¹ = 2 * π * I := by
-  simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left _ (circleMap_ne_center hR)]
+  simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left₀ _ (circleMap_ne_center hR)]
 #align circle_integral.integral_sub_center_inv circleIntegral.integral_sub_center_inv
 -/
 
@@ -638,7 +638,7 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
       1
     · have hn' : (n + 1 : ℂ) ≠ 0 := by
         rwa [Ne, ← eq_neg_iff_add_eq_zero, ← Int.cast_one, ← Int.cast_neg, Int.cast_inj]
-      simp [mul_assoc, mul_div_cancel_left _ hn']
+      simp [mul_assoc, mul_div_cancel_left₀ _ hn']
     exacts [sub_ne_zero.2, neg_le_iff_add_nonneg.1]
   refine' integral_eq_zero_of_has_deriv_within_at' fun z hz => (hd z _).HasDerivWithinAt
   exact (ne_or_eq z w).imp_right fun h => H <| h ▸ hz
@@ -745,7 +745,7 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     refine' HasSum.smul_const _ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
     convert (hasSum_geometric_of_norm_lt_one this).hMul_right _
-    simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
+    simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel₀ _ (circleMap_ne_center hR.ne')]
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchyPowerSeries_integral
 -/
 
@@ -802,7 +802,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   suffices H : HasSum (fun n : ℕ => ∮ z in C(c, R), ((w - c) / (z - c)) ^ n * (z - c)⁻¹) (2 * π * I)
   · have A : CircleIntegrable (fun _ => (1 : ℂ)) c R := continuous_on_const.circle_integrable'
     refine' (H.unique _).symm
-    simpa only [smul_eq_mul, mul_one, add_sub_cancel'_right] using
+    simpa only [smul_eq_mul, mul_one, add_sub_cancel] using
       hasSum_two_pi_I_cauchyPowerSeries_integral A hw
   have H : ∀ n : ℕ, n ≠ 0 → ∮ z in C(c, R), (z - c) ^ (-n - 1 : ℤ) = 0 := by
     refine' fun n hn => integral_sub_zpow_of_ne _ _ _ _; simpa
@@ -810,7 +810,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   refine' this ▸ hasSum_single _ fun n hn => _
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]
   rw [(integral_congr hR.le fun z hz => _).trans (H n hn), MulZeroClass.mul_zero]
-  rw [← pow_succ', ← zpow_coe_nat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
+  rw [← pow_succ, ← zpow_natCast, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
     sub_eq_add_neg _ (1 : ℤ)]
 #align circle_integral.integral_sub_inv_of_mem_ball circleIntegral.integral_sub_inv_of_mem_ball
 -/

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

@@ -377,7 +377,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
   constructor
   · intro h; contrapose! h; rcases h with ⟨hR, hn, hw⟩
     simp only [circleIntegrable_iff R, deriv_circleMap]
-    rw [← image_circleMap_Ioc] at hw ; rcases hw with ⟨θ, hθ, rfl⟩
+    rw [← image_circleMap_Ioc] at hw; rcases hw with ⟨θ, hθ, rfl⟩
     replace hθ : θ ∈ [0, 2 * π]; exact Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
     refine' not_intervalIntegrable_of_sub_inv_isBigO_punctured _ real.two_pi_pos.ne hθ
     set f : ℝ → ℂ := fun θ' => circleMap c R θ' - circleMap c R θ
@@ -462,7 +462,7 @@ theorem integral_sub_inv_smul_sub_smul (f : ℂ → E) (c w : ℂ) (R : ℝ) :
   rcases eq_or_ne R 0 with (rfl | hR); · simp only [integral_radius_zero]
   have : (circleMap c R ⁻¹' {w}).Countable := (countable_singleton _).preimage_circleMap c hR
   refine' intervalIntegral.integral_congr_ae ((this.ae_not_mem _).mono fun θ hθ hθ' => _)
-  change circleMap c R θ ≠ w at hθ 
+  change circleMap c R θ ≠ w at hθ
   simp only [inv_smul_smul₀ (sub_ne_zero.2 <| hθ)]
 #align circle_integral.integral_sub_inv_smul_sub_smul circleIntegral.integral_sub_inv_smul_sub_smul
 -/
@@ -526,7 +526,7 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
     (hc : ContinuousOn f (sphere c R)) (hf : ∀ z ∈ sphere c R, ‖f z‖ ≤ C)
     (hlt : ∃ z ∈ sphere c R, ‖f z‖ < C) : ‖∮ z in C(c, R), f z‖ < 2 * π * R * C :=
   by
-  rw [← _root_.abs_of_pos hR, ← image_circleMap_Ioc] at hlt 
+  rw [← _root_.abs_of_pos hR, ← image_circleMap_Ioc] at hlt
   rcases hlt with ⟨_, ⟨θ₀, hmem, rfl⟩, hlt⟩
   calc
     ‖∮ z in C(c, R), f z‖ ≤ ∫ θ in 0 ..2 * π, ‖deriv (circleMap c R) θ • f (circleMap c R θ)‖ :=
@@ -627,7 +627,7 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
   by
   rcases em (w ∈ sphere c |R| ∧ n < -1) with (⟨hw, hn⟩ | H)
   · exact integral_sub_zpow_of_undef (hn.trans (by decide)) hw
-  push_neg at H 
+  push_neg at H
   have hd :
     ∀ z, z ≠ w ∨ -1 ≤ n → HasDerivAt (fun z => (z - w) ^ (n + 1) / (n + 1)) ((z - w) ^ n) z :=
     by

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

@@ -810,7 +810,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   refine' this ▸ hasSum_single _ fun n hn => _
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]
   rw [(integral_congr hR.le fun z hz => _).trans (H n hn), MulZeroClass.mul_zero]
-  rw [← pow_succ', ← zpow_ofNat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
+  rw [← pow_succ', ← zpow_coe_nat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
     sub_eq_add_neg _ (1 : ℤ)]
 #align circle_integral.integral_sub_inv_of_mem_ball circleIntegral.integral_sub_inv_of_mem_ball
 -/

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

@@ -655,7 +655,7 @@ series converges to `f w` if `f` is differentiable on the closed ball `metric.cl
 `w` belongs to the corresponding open ball. For any circle integrable function `f`, this power
 series converges to the Cauchy integral for `f`. -/
 def cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ) : FormalMultilinearSeries ℂ ℂ E := fun n =>
-  ContinuousMultilinearMap.mkPiField ℂ _ <|
+  ContinuousMultilinearMap.mkPiRing ℂ _ <|
     (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z
 #align cauchy_power_series cauchyPowerSeries
 -/
@@ -665,7 +665,7 @@ theorem cauchyPowerSeries_apply (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) (w
     (cauchyPowerSeries f c R n fun _ => w) =
       (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z :=
   by
-  simp only [cauchyPowerSeries, ContinuousMultilinearMap.mkPiField_apply, Fin.prod_const,
+  simp only [cauchyPowerSeries, ContinuousMultilinearMap.mkPiRing_apply, Fin.prod_const,
     div_eq_mul_inv, mul_pow, mul_smul, circleIntegral.integral_smul, ← smul_comm (w ^ n)]
 #align cauchy_power_series_apply cauchyPowerSeries_apply
 -/

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

@@ -736,15 +736,15 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     apply_rules [ae_strongly_measurable.smul, hf.def.1] <;>
       · apply Measurable.aestronglyMeasurable; measurability
   · simp [norm_smul, abs_of_pos hR, mul_left_comm R, mul_inv_cancel_left₀ hR.ne', mul_comm ‖_‖]
-  · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_1 hwR.1 hwR.2).hMul_left _
+  · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_one hwR.1 hwR.2).hMul_left _
   ·
-    simpa only [tsum_mul_left, tsum_geometric_of_lt_1 hwR.1 hwR.2] using
+    simpa only [tsum_mul_left, tsum_geometric_of_lt_one hwR.1 hwR.2] using
       hf.norm.mul_continuous_on continuousOn_const
   · refine' eventually_of_forall fun θ hθ => HasSum.const_smul _ _
     simp only [smul_smul]
     refine' HasSum.smul_const _ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
-    convert (hasSum_geometric_of_norm_lt_1 this).hMul_right _
+    convert (hasSum_geometric_of_norm_lt_one this).hMul_right _
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchyPowerSeries_integral
 -/

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

@@ -3,11 +3,11 @@ 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.MeasureTheory.Integral.IntervalIntegral
-import Mathbin.Analysis.Calculus.Deriv.Zpow
-import Mathbin.Analysis.NormedSpace.Pointwise
-import Mathbin.Analysis.SpecialFunctions.NonIntegrable
-import Mathbin.Analysis.Analytic.Basic
+import MeasureTheory.Integral.IntervalIntegral
+import Analysis.Calculus.Deriv.Zpow
+import Analysis.NormedSpace.Pointwise
+import Analysis.SpecialFunctions.NonIntegrable
+import Analysis.Analytic.Basic
 
 #align_import measure_theory.integral.circle_integral from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/32a7e535287f9c73f2e4d2aef306a39190f0b504

@@ -736,7 +736,7 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     apply_rules [ae_strongly_measurable.smul, hf.def.1] <;>
       · apply Measurable.aestronglyMeasurable; measurability
   · simp [norm_smul, abs_of_pos hR, mul_left_comm R, mul_inv_cancel_left₀ hR.ne', mul_comm ‖_‖]
-  · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_1 hwR.1 hwR.2).mul_left _
+  · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_1 hwR.1 hwR.2).hMul_left _
   ·
     simpa only [tsum_mul_left, tsum_geometric_of_lt_1 hwR.1 hwR.2] using
       hf.norm.mul_continuous_on continuousOn_const
@@ -744,7 +744,7 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     simp only [smul_smul]
     refine' HasSum.smul_const _ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
-    convert (hasSum_geometric_of_norm_lt_1 this).mul_right _
+    convert (hasSum_geometric_of_norm_lt_1 this).hMul_right _
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchyPowerSeries_integral
 -/

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

@@ -2,11 +2,6 @@
 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 measure_theory.integral.circle_integral
-! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.IntervalIntegral
 import Mathbin.Analysis.Calculus.Deriv.Zpow
@@ -14,6 +9,8 @@ import Mathbin.Analysis.NormedSpace.Pointwise
 import Mathbin.Analysis.SpecialFunctions.NonIntegrable
 import Mathbin.Analysis.Analytic.Basic
 
+#align_import measure_theory.integral.circle_integral from "leanprover-community/mathlib"@"fd4551cfe4b7484b81c2c9ba3405edae27659676"
+
 /-!
 # Integral over a circle in `ℂ`
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/9240e8be927a0955b9a82c6c85ef499ee3a626b8

@@ -133,7 +133,7 @@ theorem abs_circleMap_zero (R : ℝ) (θ : ℝ) : abs (circleMap 0 R θ) = |R| :
 -/
 
 #print circleMap_mem_sphere' /-
-theorem circleMap_mem_sphere' (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∈ sphere c (|R|) := by simp
+theorem circleMap_mem_sphere' (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∈ sphere c |R| := by simp
 #align circle_map_mem_sphere' circleMap_mem_sphere'
 -/
 
@@ -166,19 +166,19 @@ theorem circleMap_ne_mem_ball {c : ℂ} {R : ℝ} {w : ℂ} (hw : w ∈ ball c R
 #print range_circleMap /-
 /-- The range of `circle_map c R` is the circle with center `c` and radius `|R|`. -/
 @[simp]
-theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c (|R|) :=
+theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c |R| :=
   calc
     range (circleMap c R) = c +ᵥ R • range fun θ : ℝ => exp (θ * I) := by
       simp only [← image_vadd, ← image_smul, ← range_comp, vadd_eq_add, circleMap, (· ∘ ·),
         real_smul]
-    _ = sphere c (|R|) := by simp [smul_sphere R (0 : ℂ) zero_le_one]
+    _ = sphere c |R| := by simp [smul_sphere R (0 : ℂ) zero_le_one]
 #align range_circle_map range_circleMap
 -/
 
 #print image_circleMap_Ioc /-
 /-- The image of `(0, 2π]` under `circle_map c R` is the circle with center `c` and radius `|R|`. -/
 @[simp]
-theorem image_circleMap_Ioc (c : ℂ) (R : ℝ) : circleMap c R '' Ioc 0 (2 * π) = sphere c (|R|) := by
+theorem image_circleMap_Ioc (c : ℂ) (R : ℝ) : circleMap c R '' Ioc 0 (2 * π) = sphere c |R| := by
   rw [← range_circleMap, ← (periodic_circleMap c R).image_Ioc Real.two_pi_pos 0, zero_add]
 #align image_circle_map_Ioc image_circleMap_Ioc
 -/
@@ -319,7 +319,7 @@ theorem out [NormedSpace ℂ E] (hf : CircleIntegrable f c R) :
       (2 * π) :=
   by
   simp only [CircleIntegrable, deriv_circleMap, intervalIntegrable_iff] at *
-  refine' (hf.norm.const_mul (|R|)).mono' _ _
+  refine' (hf.norm.const_mul |R|).mono' _ _
   ·
     exact
       ((continuous_circleMap _ _).AEStronglyMeasurable.mul_const I).smul hf.ae_strongly_measurable
@@ -346,7 +346,7 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
   · simp [h₀]
   refine' ⟨fun h => h.out, fun h => _⟩
   simp only [CircleIntegrable, intervalIntegrable_iff, deriv_circleMap] at h ⊢
-  refine' (h.norm.const_mul (|R|)⁻¹).mono' _ _
+  refine' (h.norm.const_mul |R|⁻¹).mono' _ _
   · have H : ∀ {θ}, circleMap 0 R θ * I ≠ 0 := fun θ => by simp [h₀, I_ne_zero]
     simpa only [inv_smul_smul₀ H] using
       ((continuous_circleMap 0 R).AEStronglyMeasurable.mul_const
@@ -358,7 +358,7 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
 
 #print ContinuousOn.circleIntegrable' /-
 theorem ContinuousOn.circleIntegrable' {f : ℂ → E} {c : ℂ} {R : ℝ}
-    (hf : ContinuousOn f (sphere c (|R|))) : CircleIntegrable f c R :=
+    (hf : ContinuousOn f (sphere c |R|)) : CircleIntegrable f c R :=
   (hf.comp_continuous (continuous_circleMap _ _) (circleMap_mem_sphere' _ _)).IntervalIntegrable _ _
 #align continuous_on.circle_integrable' ContinuousOn.circleIntegrable'
 -/
@@ -375,7 +375,7 @@ theorem ContinuousOn.circleIntegrable {f : ℂ → E} {c : ℂ} {R : ℝ} (hR :
 radius `|R|` if and only if `R = 0` or `0 ≤ n`, or `w` does not belong to this circle. -/
 @[simp]
 theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
-    CircleIntegrable (fun z => (z - w) ^ n) c R ↔ R = 0 ∨ 0 ≤ n ∨ w ∉ sphere c (|R|) :=
+    CircleIntegrable (fun z => (z - w) ^ n) c R ↔ R = 0 ∨ 0 ≤ n ∨ w ∉ sphere c |R| :=
   by
   constructor
   · intro h; contrapose! h; rcases h with ⟨hR, hn, hw⟩
@@ -399,7 +399,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
       (((hasDerivAt_circleMap c R θ).isBigO_sub.mono inf_le_left).inv_rev
             (this.mono fun θ' h₁ h₂ => absurd h₂ h₁.2)).trans
         _
-    refine' is_O.of_bound (|R|)⁻¹ (this.mono fun θ' hθ' => _)
+    refine' is_O.of_bound |R|⁻¹ (this.mono fun θ' hθ' => _)
     set x := abs (f θ')
     suffices x⁻¹ ≤ x ^ n by
       simpa only [inv_mul_cancel_left₀, abs_eq_zero.not.2 hR, norm_eq_abs, map_inv₀,
@@ -418,7 +418,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
 #print circleIntegrable_sub_inv_iff /-
 @[simp]
 theorem circleIntegrable_sub_inv_iff {c w : ℂ} {R : ℝ} :
-    CircleIntegrable (fun z => (z - w)⁻¹) c R ↔ R = 0 ∨ w ∉ sphere c (|R|) := by
+    CircleIntegrable (fun z => (z - w)⁻¹) c R ↔ R = 0 ∨ w ∉ sphere c |R| := by
   simp only [← zpow_neg_one, circleIntegrable_sub_zpow_iff]; norm_num
 #align circle_integrable_sub_inv_iff circleIntegrable_sub_inv_iff
 -/
@@ -487,7 +487,7 @@ theorem integral_sub {f g : ℂ → E} {c : ℂ} {R : ℝ} (hf : CircleIntegrabl
 
 #print circleIntegral.norm_integral_le_of_norm_le_const' /-
 theorem norm_integral_le_of_norm_le_const' {f : ℂ → E} {c : ℂ} {R C : ℝ}
-    (hf : ∀ z ∈ sphere c (|R|), ‖f z‖ ≤ C) : ‖∮ z in C(c, R), f z‖ ≤ 2 * π * |R| * C :=
+    (hf : ∀ z ∈ sphere c |R|, ‖f z‖ ≤ C) : ‖∮ z in C(c, R), f z‖ ≤ 2 * π * |R| * C :=
   calc
     ‖∮ z in C(c, R), f z‖ ≤ |R| * C * |2 * π - 0| :=
       intervalIntegral.norm_integral_le_of_norm_le_const fun θ _ =>
@@ -588,7 +588,7 @@ theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
 /-- If `f' : ℂ → E` is a derivative of a complex differentiable function on the circle
 `metric.sphere c |R|`, then `∮ z in C(c, R), f' z = 0`. -/
 theorem integral_eq_zero_of_hasDerivWithinAt' {f f' : ℂ → E} {c : ℂ} {R : ℝ}
-    (h : ∀ z ∈ sphere c (|R|), HasDerivWithinAt f (f' z) (sphere c (|R|)) z) :
+    (h : ∀ z ∈ sphere c |R|, HasDerivWithinAt f (f' z) (sphere c |R|) z) :
     ∮ z in C(c, R), f' z = 0 :=
   by
   by_cases hi : CircleIntegrable f' c R
@@ -613,8 +613,8 @@ theorem integral_eq_zero_of_hasDerivWithinAt {f f' : ℂ → E} {c : ℂ} {R : 
 #print circleIntegral.integral_sub_zpow_of_undef /-
 /-- If `n < 0` and `|w - c| = |R|`, then `(z - w) ^ n` is not circle integrable on the circle with
 center `c` and radius `(|R|)`, so the integral `∮ z in C(c, R), (z - w) ^ n` is equal to zero. -/
-theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0)
-    (hw : w ∈ sphere c (|R|)) : ∮ z in C(c, R), (z - w) ^ n = 0 :=
+theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0) (hw : w ∈ sphere c |R|) :
+    ∮ z in C(c, R), (z - w) ^ n = 0 :=
   by
   rcases eq_or_ne R 0 with (rfl | h0); · apply integral_radius_zero
   apply integral_undef
@@ -628,7 +628,7 @@ zero. -/
 theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ) :
     ∮ z in C(c, R), (z - w) ^ n = 0 :=
   by
-  rcases em (w ∈ sphere c (|R|) ∧ n < -1) with (⟨hw, hn⟩ | H)
+  rcases em (w ∈ sphere c |R| ∧ n < -1) with (⟨hw, hn⟩ | H)
   · exact integral_sub_zpow_of_undef (hn.trans (by decide)) hw
   push_neg at H 
   have hd :
@@ -676,7 +676,7 @@ theorem cauchyPowerSeries_apply (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) (w
 #print norm_cauchyPowerSeries_le /-
 theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) :
     ‖cauchyPowerSeries f c R n‖ ≤
-      ((2 * π)⁻¹ * ∫ θ : ℝ in 0 ..2 * π, ‖f (circleMap c R θ)‖) * (|R|)⁻¹ ^ n :=
+      ((2 * π)⁻¹ * ∫ θ : ℝ in 0 ..2 * π, ‖f (circleMap c R θ)‖) * |R|⁻¹ ^ n :=
   calc
     ‖cauchyPowerSeries f c R n‖ = (2 * π)⁻¹ * ‖∮ z in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z‖ :=
       by simp [cauchyPowerSeries, norm_smul, real.pi_pos.le]
@@ -688,15 +688,13 @@ theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ)
       (mul_le_mul_of_nonneg_left
         (intervalIntegral.norm_integral_le_integral_norm Real.two_pi_pos.le)
         (by simp [real.pi_pos.le]))
-    _ =
-        (2 * π)⁻¹ *
-          ((|R|)⁻¹ ^ n * (|R| * ((|R|)⁻¹ * ∫ x : ℝ in 0 ..2 * π, ‖f (circleMap c R x)‖))) :=
-      by simp [norm_smul, mul_left_comm (|R|)]
-    _ ≤ ((2 * π)⁻¹ * ∫ θ : ℝ in 0 ..2 * π, ‖f (circleMap c R θ)‖) * (|R|)⁻¹ ^ n :=
+    _ = (2 * π)⁻¹ * (|R|⁻¹ ^ n * (|R| * (|R|⁻¹ * ∫ x : ℝ in 0 ..2 * π, ‖f (circleMap c R x)‖))) :=
+      by simp [norm_smul, mul_left_comm |R|]
+    _ ≤ ((2 * π)⁻¹ * ∫ θ : ℝ in 0 ..2 * π, ‖f (circleMap c R θ)‖) * |R|⁻¹ ^ n :=
       by
       rcases eq_or_ne R 0 with (rfl | hR)
       · cases n <;> simp [-mul_inv_rev, Real.two_pi_pos]
-      · rw [mul_inv_cancel_left₀, mul_assoc, mul_comm ((|R|)⁻¹ ^ n)]
+      · rw [mul_inv_cancel_left₀, mul_assoc, mul_comm (|R|⁻¹ ^ n)]
         rwa [Ne.def, _root_.abs_eq_zero]
 #align norm_cauchy_power_series_le norm_cauchyPowerSeries_le
 -/

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

@@ -102,6 +102,7 @@ theorem periodic_circleMap (c : ℂ) (R : ℝ) : Periodic (circleMap c R) (2 * 
 #align periodic_circle_map periodic_circleMap
 -/
 
+#print Set.Countable.preimage_circleMap /-
 theorem Set.Countable.preimage_circleMap {s : Set ℂ} (hs : s.Countable) (c : ℂ) {R : ℝ}
     (hR : R ≠ 0) : (circleMap c R ⁻¹' s).Countable :=
   show (coe ⁻¹' ((· * I) ⁻¹' (exp ⁻¹' ((· * ·) R ⁻¹' ((· + ·) c ⁻¹' s))))).Countable from
@@ -110,41 +111,59 @@ theorem Set.Countable.preimage_circleMap {s : Set ℂ} (hs : s.Countable) (c : 
           mul_left_injective₀ I_ne_zero).Preimage
       ofReal_injective
 #align set.countable.preimage_circle_map Set.Countable.preimage_circleMap
+-/
 
+#print circleMap_sub_center /-
 @[simp]
 theorem circleMap_sub_center (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ - c = circleMap 0 R θ := by
   simp [circleMap]
 #align circle_map_sub_center circleMap_sub_center
+-/
 
+#print circleMap_zero /-
 theorem circleMap_zero (R θ : ℝ) : circleMap 0 R θ = R * exp (θ * I) :=
   zero_add _
 #align circle_map_zero circleMap_zero
+-/
 
+#print abs_circleMap_zero /-
 @[simp]
 theorem abs_circleMap_zero (R : ℝ) (θ : ℝ) : abs (circleMap 0 R θ) = |R| := by simp [circleMap]
 #align abs_circle_map_zero abs_circleMap_zero
+-/
 
+#print circleMap_mem_sphere' /-
 theorem circleMap_mem_sphere' (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∈ sphere c (|R|) := by simp
 #align circle_map_mem_sphere' circleMap_mem_sphere'
+-/
 
+#print circleMap_mem_sphere /-
 theorem circleMap_mem_sphere (c : ℂ) {R : ℝ} (hR : 0 ≤ R) (θ : ℝ) : circleMap c R θ ∈ sphere c R :=
   by simpa only [_root_.abs_of_nonneg hR] using circleMap_mem_sphere' c R θ
 #align circle_map_mem_sphere circleMap_mem_sphere
+-/
 
+#print circleMap_mem_closedBall /-
 theorem circleMap_mem_closedBall (c : ℂ) {R : ℝ} (hR : 0 ≤ R) (θ : ℝ) :
     circleMap c R θ ∈ closedBall c R :=
   sphere_subset_closedBall (circleMap_mem_sphere c hR θ)
 #align circle_map_mem_closed_ball circleMap_mem_closedBall
+-/
 
+#print circleMap_not_mem_ball /-
 theorem circleMap_not_mem_ball (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∉ ball c R := by
   simp [dist_eq, le_abs_self]
 #align circle_map_not_mem_ball circleMap_not_mem_ball
+-/
 
+#print circleMap_ne_mem_ball /-
 theorem circleMap_ne_mem_ball {c : ℂ} {R : ℝ} {w : ℂ} (hw : w ∈ ball c R) (θ : ℝ) :
     circleMap c R θ ≠ w :=
   (ne_of_mem_of_not_mem hw (circleMap_not_mem_ball _ _ _)).symm
 #align circle_map_ne_mem_ball circleMap_ne_mem_ball
+-/
 
+#print range_circleMap /-
 /-- The range of `circle_map c R` is the circle with center `c` and radius `|R|`. -/
 @[simp]
 theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c (|R|) :=
@@ -154,43 +173,58 @@ theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c (
         real_smul]
     _ = sphere c (|R|) := by simp [smul_sphere R (0 : ℂ) zero_le_one]
 #align range_circle_map range_circleMap
+-/
 
+#print image_circleMap_Ioc /-
 /-- The image of `(0, 2π]` under `circle_map c R` is the circle with center `c` and radius `|R|`. -/
 @[simp]
 theorem image_circleMap_Ioc (c : ℂ) (R : ℝ) : circleMap c R '' Ioc 0 (2 * π) = sphere c (|R|) := by
   rw [← range_circleMap, ← (periodic_circleMap c R).image_Ioc Real.two_pi_pos 0, zero_add]
 #align image_circle_map_Ioc image_circleMap_Ioc
+-/
 
+#print circleMap_eq_center_iff /-
 @[simp]
 theorem circleMap_eq_center_iff {c : ℂ} {R : ℝ} {θ : ℝ} : circleMap c R θ = c ↔ R = 0 := by
   simp [circleMap, exp_ne_zero]
 #align circle_map_eq_center_iff circleMap_eq_center_iff
+-/
 
+#print circleMap_zero_radius /-
 @[simp]
 theorem circleMap_zero_radius (c : ℂ) : circleMap c 0 = const ℝ c :=
   funext fun θ => circleMap_eq_center_iff.2 rfl
 #align circle_map_zero_radius circleMap_zero_radius
+-/
 
+#print circleMap_ne_center /-
 theorem circleMap_ne_center {c : ℂ} {R : ℝ} (hR : R ≠ 0) {θ : ℝ} : circleMap c R θ ≠ c :=
   mt circleMap_eq_center_iff.1 hR
 #align circle_map_ne_center circleMap_ne_center
+-/
 
+#print hasDerivAt_circleMap /-
 theorem hasDerivAt_circleMap (c : ℂ) (R : ℝ) (θ : ℝ) :
     HasDerivAt (circleMap c R) (circleMap 0 R θ * I) θ := by
   simpa only [mul_assoc, one_mul, of_real_clm_apply, circleMap, of_real_one, zero_add] using
     ((of_real_clm.has_deriv_at.mul_const I).cexp.const_mul (R : ℂ)).const_add c
 #align has_deriv_at_circle_map hasDerivAt_circleMap
+-/
 
+#print differentiable_circleMap /-
 /- TODO: prove `cont_diff ℝ (circle_map c R)`. This needs a version of `cont_diff.mul`
 for multiplication in a normed algebra over the base field. -/
 theorem differentiable_circleMap (c : ℂ) (R : ℝ) : Differentiable ℝ (circleMap c R) := fun θ =>
   (hasDerivAt_circleMap c R θ).DifferentiableAt
 #align differentiable_circle_map differentiable_circleMap
+-/
 
+#print continuous_circleMap /-
 @[continuity]
 theorem continuous_circleMap (c : ℂ) (R : ℝ) : Continuous (circleMap c R) :=
   (differentiable_circleMap c R).Continuous
 #align continuous_circle_map continuous_circleMap
+-/
 
 #print measurable_circleMap /-
 @[measurability]
@@ -199,25 +233,34 @@ theorem measurable_circleMap (c : ℂ) (R : ℝ) : Measurable (circleMap c R) :=
 #align measurable_circle_map measurable_circleMap
 -/
 
+#print deriv_circleMap /-
 @[simp]
 theorem deriv_circleMap (c : ℂ) (R : ℝ) (θ : ℝ) : deriv (circleMap c R) θ = circleMap 0 R θ * I :=
   (hasDerivAt_circleMap _ _ _).deriv
 #align deriv_circle_map deriv_circleMap
+-/
 
+#print deriv_circleMap_eq_zero_iff /-
 theorem deriv_circleMap_eq_zero_iff {c : ℂ} {R : ℝ} {θ : ℝ} : deriv (circleMap c R) θ = 0 ↔ R = 0 :=
   by simp [I_ne_zero]
 #align deriv_circle_map_eq_zero_iff deriv_circleMap_eq_zero_iff
+-/
 
+#print deriv_circleMap_ne_zero /-
 theorem deriv_circleMap_ne_zero {c : ℂ} {R : ℝ} {θ : ℝ} (hR : R ≠ 0) :
     deriv (circleMap c R) θ ≠ 0 :=
   mt deriv_circleMap_eq_zero_iff.1 hR
 #align deriv_circle_map_ne_zero deriv_circleMap_ne_zero
+-/
 
+#print lipschitzWith_circleMap /-
 theorem lipschitzWith_circleMap (c : ℂ) (R : ℝ) : LipschitzWith R.nnabs (circleMap c R) :=
   lipschitzWith_of_nnnorm_deriv_le (differentiable_circleMap _ _) fun θ =>
     NNReal.coe_le_coe.1 <| by simp
 #align lipschitz_with_circle_map lipschitzWith_circleMap
+-/
 
+#print continuous_circleMap_inv /-
 theorem continuous_circleMap_inv {R : ℝ} {z w : ℂ} (hw : w ∈ ball z R) :
     Continuous fun θ => (circleMap z R θ - w)⁻¹ :=
   by
@@ -225,6 +268,7 @@ theorem continuous_circleMap_inv {R : ℝ} {z w : ℂ} (hw : w ∈ ball z R) :
     exact fun θ => circleMap_ne_mem_ball hw θ
   continuity
 #align continuous_circle_map_inv continuous_circleMap_inv
+-/
 
 /-!
 ### Integrability of a function on a circle
@@ -267,6 +311,7 @@ theorem neg (hf : CircleIntegrable f c R) : CircleIntegrable (-f) c R :=
 #align circle_integrable.neg CircleIntegrable.neg
 -/
 
+#print CircleIntegrable.out /-
 /-- The function we actually integrate over `[0, 2π]` in the definition of `circle_integral` is
 integrable. -/
 theorem out [NormedSpace ℂ E] (hf : CircleIntegrable f c R) :
@@ -280,6 +325,7 @@ theorem out [NormedSpace ℂ E] (hf : CircleIntegrable f c R) :
       ((continuous_circleMap _ _).AEStronglyMeasurable.mul_const I).smul hf.ae_strongly_measurable
   · simp [norm_smul]
 #align circle_integrable.out CircleIntegrable.out
+-/
 
 end CircleIntegrable
 
@@ -290,6 +336,7 @@ theorem circleIntegrable_zero_radius {f : ℂ → E} {c : ℂ} : CircleIntegrabl
 #align circle_integrable_zero_radius circleIntegrable_zero_radius
 -/
 
+#print circleIntegrable_iff /-
 theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R : ℝ) :
     CircleIntegrable f c R ↔
       IntervalIntegrable (fun θ : ℝ => deriv (circleMap c R) θ • f (circleMap c R θ)) volume 0
@@ -307,17 +354,23 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
         h.ae_strongly_measurable
   · simp [norm_smul, h₀]
 #align circle_integrable_iff circleIntegrable_iff
+-/
 
+#print ContinuousOn.circleIntegrable' /-
 theorem ContinuousOn.circleIntegrable' {f : ℂ → E} {c : ℂ} {R : ℝ}
     (hf : ContinuousOn f (sphere c (|R|))) : CircleIntegrable f c R :=
   (hf.comp_continuous (continuous_circleMap _ _) (circleMap_mem_sphere' _ _)).IntervalIntegrable _ _
 #align continuous_on.circle_integrable' ContinuousOn.circleIntegrable'
+-/
 
+#print ContinuousOn.circleIntegrable /-
 theorem ContinuousOn.circleIntegrable {f : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R)
     (hf : ContinuousOn f (sphere c R)) : CircleIntegrable f c R :=
   ContinuousOn.circleIntegrable' <| (abs_of_nonneg hR).symm ▸ hf
 #align continuous_on.circle_integrable ContinuousOn.circleIntegrable
+-/
 
+#print circleIntegrable_sub_zpow_iff /-
 /-- The function `λ z, (z - w) ^ n`, `n : ℤ`, is circle integrable on the circle with center `c` and
 radius `|R|` if and only if `R = 0` or `0 ≤ n`, or `w` does not belong to this circle. -/
 @[simp]
@@ -360,41 +413,52 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
       ((continuous_on_id.sub continuousOn_const).zpow₀ _ fun z hz =>
           H.symm.imp_left fun hw => sub_ne_zero.2 <| ne_of_mem_of_not_mem hz hw).circleIntegrable']
 #align circle_integrable_sub_zpow_iff circleIntegrable_sub_zpow_iff
+-/
 
+#print circleIntegrable_sub_inv_iff /-
 @[simp]
 theorem circleIntegrable_sub_inv_iff {c w : ℂ} {R : ℝ} :
     CircleIntegrable (fun z => (z - w)⁻¹) c R ↔ R = 0 ∨ w ∉ sphere c (|R|) := by
   simp only [← zpow_neg_one, circleIntegrable_sub_zpow_iff]; norm_num
 #align circle_integrable_sub_inv_iff circleIntegrable_sub_inv_iff
+-/
 
 variable [NormedSpace ℂ E] [CompleteSpace E]
 
+#print circleIntegral /-
 /-- Definition for $\oint_{|z-c|=R} f(z)\,dz$. -/
 def circleIntegral (f : ℂ → E) (c : ℂ) (R : ℝ) : E :=
   ∫ θ : ℝ in 0 ..2 * π, deriv (circleMap c R) θ • f (circleMap c R θ)
 #align circle_integral circleIntegral
+-/
 
--- mathport name: «expr∮ inC( , ), »
 notation3"∮ "(...)" in ""C("c", "R")"", "r:60:(scoped f => circleIntegral f c R) => r
 
+#print circleIntegral_def_Icc /-
 theorem circleIntegral_def_Icc (f : ℂ → E) (c : ℂ) (R : ℝ) :
     ∮ z in C(c, R), f z = ∫ θ in Icc 0 (2 * π), deriv (circleMap c R) θ • f (circleMap c R θ) := by
   simp only [circleIntegral, intervalIntegral.integral_of_le real.two_pi_pos.le,
     measure.restrict_congr_set Ioc_ae_eq_Icc]
 #align circle_integral_def_Icc circleIntegral_def_Icc
+-/
 
 namespace circleIntegral
 
+#print circleIntegral.integral_radius_zero /-
 @[simp]
 theorem integral_radius_zero (f : ℂ → E) (c : ℂ) : ∮ z in C(c, 0), f z = 0 := by
   simp [circleIntegral]
 #align circle_integral.integral_radius_zero circleIntegral.integral_radius_zero
+-/
 
+#print circleIntegral.integral_congr /-
 theorem integral_congr {f g : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R) (h : EqOn f g (sphere c R)) :
     ∮ z in C(c, R), f z = ∮ z in C(c, R), g z :=
   intervalIntegral.integral_congr fun θ hθ => by simp only [h (circleMap_mem_sphere _ hR _)]
 #align circle_integral.integral_congr circleIntegral.integral_congr
+-/
 
+#print circleIntegral.integral_sub_inv_smul_sub_smul /-
 theorem integral_sub_inv_smul_sub_smul (f : ℂ → E) (c w : ℂ) (R : ℝ) :
     ∮ z in C(c, R), (z - w)⁻¹ • (z - w) • f z = ∮ z in C(c, R), f z :=
   by
@@ -404,18 +468,24 @@ theorem integral_sub_inv_smul_sub_smul (f : ℂ → E) (c w : ℂ) (R : ℝ) :
   change circleMap c R θ ≠ w at hθ 
   simp only [inv_smul_smul₀ (sub_ne_zero.2 <| hθ)]
 #align circle_integral.integral_sub_inv_smul_sub_smul circleIntegral.integral_sub_inv_smul_sub_smul
+-/
 
+#print circleIntegral.integral_undef /-
 theorem integral_undef {f : ℂ → E} {c : ℂ} {R : ℝ} (hf : ¬CircleIntegrable f c R) :
     ∮ z in C(c, R), f z = 0 :=
   intervalIntegral.integral_undef (mt (circleIntegrable_iff R).mpr hf)
 #align circle_integral.integral_undef circleIntegral.integral_undef
+-/
 
+#print circleIntegral.integral_sub /-
 theorem integral_sub {f g : ℂ → E} {c : ℂ} {R : ℝ} (hf : CircleIntegrable f c R)
     (hg : CircleIntegrable g c R) :
     ∮ z in C(c, R), f z - g z = (∮ z in C(c, R), f z) - ∮ z in C(c, R), g z := by
   simp only [circleIntegral, smul_sub, intervalIntegral.integral_sub hf.out hg.out]
 #align circle_integral.integral_sub circleIntegral.integral_sub
+-/
 
+#print circleIntegral.norm_integral_le_of_norm_le_const' /-
 theorem norm_integral_le_of_norm_le_const' {f : ℂ → E} {c : ℂ} {R C : ℝ}
     (hf : ∀ z ∈ sphere c (|R|), ‖f z‖ ≤ C) : ‖∮ z in C(c, R), f z‖ ≤ 2 * π * |R| * C :=
   calc
@@ -428,7 +498,9 @@ theorem norm_integral_le_of_norm_le_const' {f : ℂ → E} {c : ℂ} {R C : ℝ}
             mul_le_mul_of_nonneg_left (hf _ <| circleMap_mem_sphere' _ _ _) (abs_nonneg _)
     _ = 2 * π * |R| * C := by rw [sub_zero, _root_.abs_of_pos Real.two_pi_pos]; ac_rfl
 #align circle_integral.norm_integral_le_of_norm_le_const' circleIntegral.norm_integral_le_of_norm_le_const'
+-/
 
+#print circleIntegral.norm_integral_le_of_norm_le_const /-
 theorem norm_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ} (hR : 0 ≤ R)
     (hf : ∀ z ∈ sphere c R, ‖f z‖ ≤ C) : ‖∮ z in C(c, R), f z‖ ≤ 2 * π * R * C :=
   have : |R| = R := abs_of_nonneg hR
@@ -436,7 +508,9 @@ theorem norm_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ}
     ‖∮ z in C(c, R), f z‖ ≤ 2 * π * |R| * C := norm_integral_le_of_norm_le_const' <| by rwa [this]
     _ = 2 * π * R * C := by rw [this]
 #align circle_integral.norm_integral_le_of_norm_le_const circleIntegral.norm_integral_le_of_norm_le_const
+-/
 
+#print circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const /-
 theorem norm_two_pi_i_inv_smul_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ}
     (hR : 0 ≤ R) (hf : ∀ z ∈ sphere c R, ‖f z‖ ≤ C) :
     ‖(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), f z‖ ≤ R * C :=
@@ -445,7 +519,9 @@ theorem norm_two_pi_i_inv_smul_integral_le_of_norm_le_const {f : ℂ → E} {c :
   rw [norm_smul, this, ← div_eq_inv_mul, div_le_iff Real.two_pi_pos, mul_comm (R * C), ← mul_assoc]
   exact norm_integral_le_of_norm_le_const hR hf
 #align circle_integral.norm_two_pi_I_inv_smul_integral_le_of_norm_le_const circleIntegral.norm_two_pi_i_inv_smul_integral_le_of_norm_le_const
+-/
 
+#print circleIntegral.norm_integral_lt_of_norm_le_const_of_lt /-
 /-- If `f` is continuous on the circle `|z - c| = R`, `R > 0`, the `‖f z‖` is less than or equal to
 `C : ℝ` on this circle, and this norm is strictly less than `C` at some point `z` of the circle,
 then `‖∮ z in C(c, R), f z‖ < 2 * π * R * C`. -/
@@ -474,31 +550,41 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
       · exact (mul_lt_mul_left hR).2 hlt
     _ = 2 * π * R * C := by simp [mul_assoc]
 #align circle_integral.norm_integral_lt_of_norm_le_const_of_lt circleIntegral.norm_integral_lt_of_norm_le_const_of_lt
+-/
 
+#print circleIntegral.integral_smul /-
 @[simp]
 theorem integral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂ → E) (c : ℂ) (R : ℝ) : ∮ z in C(c, R), a • f z = a • ∮ z in C(c, R), f z := by
   simp only [circleIntegral, ← smul_comm a, intervalIntegral.integral_smul]
 #align circle_integral.integral_smul circleIntegral.integral_smul
+-/
 
+#print circleIntegral.integral_smul_const /-
 @[simp]
 theorem integral_smul_const (f : ℂ → ℂ) (a : E) (c : ℂ) (R : ℝ) :
     ∮ z in C(c, R), f z • a = (∮ z in C(c, R), f z) • a := by
   simp only [circleIntegral, intervalIntegral.integral_smul_const, ← smul_assoc]
 #align circle_integral.integral_smul_const circleIntegral.integral_smul_const
+-/
 
+#print circleIntegral.integral_const_mul /-
 @[simp]
 theorem integral_const_mul (a : ℂ) (f : ℂ → ℂ) (c : ℂ) (R : ℝ) :
     ∮ z in C(c, R), a * f z = a * ∮ z in C(c, R), f z :=
   integral_smul a f c R
 #align circle_integral.integral_const_mul circleIntegral.integral_const_mul
+-/
 
+#print circleIntegral.integral_sub_center_inv /-
 @[simp]
 theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
     ∮ z in C(c, R), (z - c)⁻¹ = 2 * π * I := by
   simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left _ (circleMap_ne_center hR)]
 #align circle_integral.integral_sub_center_inv circleIntegral.integral_sub_center_inv
+-/
 
+#print circleIntegral.integral_eq_zero_of_hasDerivWithinAt' /-
 /-- If `f' : ℂ → E` is a derivative of a complex differentiable function on the circle
 `metric.sphere c |R|`, then `∮ z in C(c, R), f' z = 0`. -/
 theorem integral_eq_zero_of_hasDerivWithinAt' {f f' : ℂ → E} {c : ℂ} {R : ℝ}
@@ -513,14 +599,18 @@ theorem integral_eq_zero_of_hasDerivWithinAt' {f f' : ℂ → E} {c : ℂ} {R :
         (differentiable_circleMap _ _ _).HasDerivAt (circleMap_mem_sphere' _ _)
   · exact integral_undef hi
 #align circle_integral.integral_eq_zero_of_has_deriv_within_at' circleIntegral.integral_eq_zero_of_hasDerivWithinAt'
+-/
 
+#print circleIntegral.integral_eq_zero_of_hasDerivWithinAt /-
 /-- If `f' : ℂ → E` is a derivative of a complex differentiable function on the circle
 `metric.sphere c R`, then `∮ z in C(c, R), f' z = 0`. -/
 theorem integral_eq_zero_of_hasDerivWithinAt {f f' : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R)
     (h : ∀ z ∈ sphere c R, HasDerivWithinAt f (f' z) (sphere c R) z) : ∮ z in C(c, R), f' z = 0 :=
   integral_eq_zero_of_hasDerivWithinAt' <| (abs_of_nonneg hR).symm.subst h
 #align circle_integral.integral_eq_zero_of_has_deriv_within_at circleIntegral.integral_eq_zero_of_hasDerivWithinAt
+-/
 
+#print circleIntegral.integral_sub_zpow_of_undef /-
 /-- If `n < 0` and `|w - c| = |R|`, then `(z - w) ^ n` is not circle integrable on the circle with
 center `c` and radius `(|R|)`, so the integral `∮ z in C(c, R), (z - w) ^ n` is equal to zero. -/
 theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0)
@@ -530,7 +620,9 @@ theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0)
   apply integral_undef
   simp [circleIntegrable_sub_zpow_iff, *]
 #align circle_integral.integral_sub_zpow_of_undef circleIntegral.integral_sub_zpow_of_undef
+-/
 
+#print circleIntegral.integral_sub_zpow_of_ne /-
 /-- If `n ≠ -1` is an integer number, then the integral of `(z - w) ^ n` over the circle equals
 zero. -/
 theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ) :
@@ -554,9 +646,11 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
   refine' integral_eq_zero_of_has_deriv_within_at' fun z hz => (hd z _).HasDerivWithinAt
   exact (ne_or_eq z w).imp_right fun h => H <| h ▸ hz
 #align circle_integral.integral_sub_zpow_of_ne circleIntegral.integral_sub_zpow_of_ne
+-/
 
 end circleIntegral
 
+#print cauchyPowerSeries /-
 /-- The power series that is equal to
 $\sum_{n=0}^{\infty} \oint_{|z-c|=R} \left(\frac{w-c}{z - c}\right)^n \frac{1}{z-c}f(z)\,dz$ at
 `w - c`. The coefficients of this power series depend only on `f ∘ circle_map c R`, and the power
@@ -567,7 +661,9 @@ def cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ) : FormalMultilinearSer
   ContinuousMultilinearMap.mkPiField ℂ _ <|
     (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z
 #align cauchy_power_series cauchyPowerSeries
+-/
 
+#print cauchyPowerSeries_apply /-
 theorem cauchyPowerSeries_apply (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) (w : ℂ) :
     (cauchyPowerSeries f c R n fun _ => w) =
       (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z :=
@@ -575,7 +671,9 @@ theorem cauchyPowerSeries_apply (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) (w
   simp only [cauchyPowerSeries, ContinuousMultilinearMap.mkPiField_apply, Fin.prod_const,
     div_eq_mul_inv, mul_pow, mul_smul, circleIntegral.integral_smul, ← smul_comm (w ^ n)]
 #align cauchy_power_series_apply cauchyPowerSeries_apply
+-/
 
+#print norm_cauchyPowerSeries_le /-
 theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) :
     ‖cauchyPowerSeries f c R n‖ ≤
       ((2 * π)⁻¹ * ∫ θ : ℝ in 0 ..2 * π, ‖f (circleMap c R θ)‖) * (|R|)⁻¹ ^ n :=
@@ -601,7 +699,9 @@ theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ)
       · rw [mul_inv_cancel_left₀, mul_assoc, mul_comm ((|R|)⁻¹ ^ n)]
         rwa [Ne.def, _root_.abs_eq_zero]
 #align norm_cauchy_power_series_le norm_cauchyPowerSeries_le
+-/
 
+#print le_radius_cauchyPowerSeries /-
 theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
     ↑R ≤ (cauchyPowerSeries f c R).radius :=
   by
@@ -620,7 +720,9 @@ theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
         (intervalIntegral.integral_nonneg real.two_pi_pos.le fun _ _ => norm_nonneg _)
   · rw [inv_pow, inv_mul_cancel_right₀ hR]
 #align le_radius_cauchy_power_series le_radius_cauchyPowerSeries
+-/
 
+#print hasSum_two_pi_I_cauchyPowerSeries_integral /-
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R` multiplied
 by `2πI` converges to the integral `∮ z in C(c, R), (z - w)⁻¹ • f z` on the open disc
 `metric.ball c R`. -/
@@ -650,7 +752,9 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     convert (hasSum_geometric_of_norm_lt_1 this).mul_right _
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchyPowerSeries_integral
+-/
 
+#print hasSum_cauchyPowerSeries_integral /-
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R`, `R > 0`,
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
@@ -662,7 +766,9 @@ theorem hasSum_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w
   simp only [cauchyPowerSeries_apply]
   exact (hasSum_two_pi_I_cauchyPowerSeries_integral hf hw).const_smul _
 #align has_sum_cauchy_power_series_integral hasSum_cauchyPowerSeries_integral
+-/
 
+#print sum_cauchyPowerSeries_eq_integral /-
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R`, `R > 0`,
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
@@ -671,7 +777,9 @@ theorem sum_cauchyPowerSeries_eq_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w
     (cauchyPowerSeries f c R).Sum w = (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z :=
   (hasSum_cauchyPowerSeries_integral hf hw).tsum_eq
 #align sum_cauchy_power_series_eq_integral sum_cauchyPowerSeries_eq_integral
+-/
 
+#print hasFPowerSeriesOn_cauchy_integral /-
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R`, `R > 0`,
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
@@ -686,9 +794,11 @@ theorem hasFPowerSeriesOn_cauchy_integral {f : ℂ → E} {c : ℂ} {R : ℝ≥0
       rw [← norm_eq_abs, ← coe_nnnorm, NNReal.coe_lt_coe, ← ENNReal.coe_lt_coe]
       exact mem_emetric_ball_zero_iff.1 hy }
 #align has_fpower_series_on_cauchy_integral hasFPowerSeriesOn_cauchy_integral
+-/
 
 namespace circleIntegral
 
+#print circleIntegral.integral_sub_inv_of_mem_ball /-
 /-- Integral $\oint_{|z-c|=R} \frac{dz}{z-w}=2πi$ whenever $|w-c|<R$. -/
 theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R) :
     ∮ z in C(c, R), (z - w)⁻¹ = 2 * π * I :=
@@ -708,6 +818,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   rw [← pow_succ', ← zpow_ofNat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
     sub_eq_add_neg _ (1 : ℤ)]
 #align circle_integral.integral_sub_inv_of_mem_ball circleIntegral.integral_sub_inv_of_mem_ball
+-/
 
 end circleIntegral
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/c471da714c044131b90c133701e51b877c246677

@@ -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 measure_theory.integral.circle_integral
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
+! leanprover-community/mathlib commit fd4551cfe4b7484b81c2c9ba3405edae27659676
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
@@ -17,6 +17,9 @@ import Mathbin.Analysis.Analytic.Basic
 /-!
 # Integral over a circle in `ℂ`
 
+> THIS FILE IS SYNCHRONIZED WITH MATHLIB4.
+> Any changes to this file require a corresponding PR to mathlib4.
+
 In this file we define `∮ z in C(c, R), f z` to be the integral $\oint_{|z-c|=|R|} f(z)\,dz$ and
 prove some properties of this integral. We give definition and prove most lemmas for a function
 `f : ℂ → E`, where `E` is a complex Banach space. For this reason,

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

@@ -372,11 +372,10 @@ def circleIntegral (f : ℂ → E) (c : ℂ) (R : ℝ) : E :=
 #align circle_integral circleIntegral
 
 -- mathport name: «expr∮ inC( , ), »
-notation3"∮ "(...)" in ""C("c", "R")"", "r:(scoped f => circleIntegral f c R) => r
+notation3"∮ "(...)" in ""C("c", "R")"", "r:60:(scoped f => circleIntegral f c R) => r
 
 theorem circleIntegral_def_Icc (f : ℂ → E) (c : ℂ) (R : ℝ) :
-    (∮ z in C(c, R), f z) = ∫ θ in Icc 0 (2 * π), deriv (circleMap c R) θ • f (circleMap c R θ) :=
-  by
+    ∮ z in C(c, R), f z = ∫ θ in Icc 0 (2 * π), deriv (circleMap c R) θ • f (circleMap c R θ) := by
   simp only [circleIntegral, intervalIntegral.integral_of_le real.two_pi_pos.le,
     measure.restrict_congr_set Ioc_ae_eq_Icc]
 #align circle_integral_def_Icc circleIntegral_def_Icc
@@ -384,17 +383,17 @@ theorem circleIntegral_def_Icc (f : ℂ → E) (c : ℂ) (R : ℝ) :
 namespace circleIntegral
 
 @[simp]
-theorem integral_radius_zero (f : ℂ → E) (c : ℂ) : (∮ z in C(c, 0), f z) = 0 := by
+theorem integral_radius_zero (f : ℂ → E) (c : ℂ) : ∮ z in C(c, 0), f z = 0 := by
   simp [circleIntegral]
 #align circle_integral.integral_radius_zero circleIntegral.integral_radius_zero
 
 theorem integral_congr {f g : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R) (h : EqOn f g (sphere c R)) :
-    (∮ z in C(c, R), f z) = ∮ z in C(c, R), g z :=
+    ∮ z in C(c, R), f z = ∮ z in C(c, R), g z :=
   intervalIntegral.integral_congr fun θ hθ => by simp only [h (circleMap_mem_sphere _ hR _)]
 #align circle_integral.integral_congr circleIntegral.integral_congr
 
 theorem integral_sub_inv_smul_sub_smul (f : ℂ → E) (c w : ℂ) (R : ℝ) :
-    (∮ z in C(c, R), (z - w)⁻¹ • (z - w) • f z) = ∮ z in C(c, R), f z :=
+    ∮ z in C(c, R), (z - w)⁻¹ • (z - w) • f z = ∮ z in C(c, R), f z :=
   by
   rcases eq_or_ne R 0 with (rfl | hR); · simp only [integral_radius_zero]
   have : (circleMap c R ⁻¹' {w}).Countable := (countable_singleton _).preimage_circleMap c hR
@@ -404,13 +403,13 @@ theorem integral_sub_inv_smul_sub_smul (f : ℂ → E) (c w : ℂ) (R : ℝ) :
 #align circle_integral.integral_sub_inv_smul_sub_smul circleIntegral.integral_sub_inv_smul_sub_smul
 
 theorem integral_undef {f : ℂ → E} {c : ℂ} {R : ℝ} (hf : ¬CircleIntegrable f c R) :
-    (∮ z in C(c, R), f z) = 0 :=
+    ∮ z in C(c, R), f z = 0 :=
   intervalIntegral.integral_undef (mt (circleIntegrable_iff R).mpr hf)
 #align circle_integral.integral_undef circleIntegral.integral_undef
 
 theorem integral_sub {f g : ℂ → E} {c : ℂ} {R : ℝ} (hf : CircleIntegrable f c R)
     (hg : CircleIntegrable g c R) :
-    (∮ z in C(c, R), f z - g z) = (∮ z in C(c, R), f z) - ∮ z in C(c, R), g z := by
+    ∮ z in C(c, R), f z - g z = (∮ z in C(c, R), f z) - ∮ z in C(c, R), g z := by
   simp only [circleIntegral, smul_sub, intervalIntegral.integral_sub hf.out hg.out]
 #align circle_integral.integral_sub circleIntegral.integral_sub
 
@@ -475,25 +474,25 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
 
 @[simp]
 theorem integral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
-    (f : ℂ → E) (c : ℂ) (R : ℝ) : (∮ z in C(c, R), a • f z) = a • ∮ z in C(c, R), f z := by
+    (f : ℂ → E) (c : ℂ) (R : ℝ) : ∮ z in C(c, R), a • f z = a • ∮ z in C(c, R), f z := by
   simp only [circleIntegral, ← smul_comm a, intervalIntegral.integral_smul]
 #align circle_integral.integral_smul circleIntegral.integral_smul
 
 @[simp]
 theorem integral_smul_const (f : ℂ → ℂ) (a : E) (c : ℂ) (R : ℝ) :
-    (∮ z in C(c, R), f z • a) = (∮ z in C(c, R), f z) • a := by
+    ∮ z in C(c, R), f z • a = (∮ z in C(c, R), f z) • a := by
   simp only [circleIntegral, intervalIntegral.integral_smul_const, ← smul_assoc]
 #align circle_integral.integral_smul_const circleIntegral.integral_smul_const
 
 @[simp]
 theorem integral_const_mul (a : ℂ) (f : ℂ → ℂ) (c : ℂ) (R : ℝ) :
-    (∮ z in C(c, R), a * f z) = a * ∮ z in C(c, R), f z :=
+    ∮ z in C(c, R), a * f z = a * ∮ z in C(c, R), f z :=
   integral_smul a f c R
 #align circle_integral.integral_const_mul circleIntegral.integral_const_mul
 
 @[simp]
 theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
-    (∮ z in C(c, R), (z - c)⁻¹) = 2 * π * I := by
+    ∮ z in C(c, R), (z - c)⁻¹ = 2 * π * I := by
   simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left _ (circleMap_ne_center hR)]
 #align circle_integral.integral_sub_center_inv circleIntegral.integral_sub_center_inv
 
@@ -501,7 +500,7 @@ theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
 `metric.sphere c |R|`, then `∮ z in C(c, R), f' z = 0`. -/
 theorem integral_eq_zero_of_hasDerivWithinAt' {f f' : ℂ → E} {c : ℂ} {R : ℝ}
     (h : ∀ z ∈ sphere c (|R|), HasDerivWithinAt f (f' z) (sphere c (|R|)) z) :
-    (∮ z in C(c, R), f' z) = 0 :=
+    ∮ z in C(c, R), f' z = 0 :=
   by
   by_cases hi : CircleIntegrable f' c R
   · rw [← sub_eq_zero.2 ((periodic_circleMap c R).comp f).Eq]
@@ -515,14 +514,14 @@ theorem integral_eq_zero_of_hasDerivWithinAt' {f f' : ℂ → E} {c : ℂ} {R :
 /-- If `f' : ℂ → E` is a derivative of a complex differentiable function on the circle
 `metric.sphere c R`, then `∮ z in C(c, R), f' z = 0`. -/
 theorem integral_eq_zero_of_hasDerivWithinAt {f f' : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R)
-    (h : ∀ z ∈ sphere c R, HasDerivWithinAt f (f' z) (sphere c R) z) : (∮ z in C(c, R), f' z) = 0 :=
+    (h : ∀ z ∈ sphere c R, HasDerivWithinAt f (f' z) (sphere c R) z) : ∮ z in C(c, R), f' z = 0 :=
   integral_eq_zero_of_hasDerivWithinAt' <| (abs_of_nonneg hR).symm.subst h
 #align circle_integral.integral_eq_zero_of_has_deriv_within_at circleIntegral.integral_eq_zero_of_hasDerivWithinAt
 
 /-- If `n < 0` and `|w - c| = |R|`, then `(z - w) ^ n` is not circle integrable on the circle with
 center `c` and radius `(|R|)`, so the integral `∮ z in C(c, R), (z - w) ^ n` is equal to zero. -/
 theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0)
-    (hw : w ∈ sphere c (|R|)) : (∮ z in C(c, R), (z - w) ^ n) = 0 :=
+    (hw : w ∈ sphere c (|R|)) : ∮ z in C(c, R), (z - w) ^ n = 0 :=
   by
   rcases eq_or_ne R 0 with (rfl | h0); · apply integral_radius_zero
   apply integral_undef
@@ -532,7 +531,7 @@ theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0)
 /-- If `n ≠ -1` is an integer number, then the integral of `(z - w) ^ n` over the circle equals
 zero. -/
 theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ) :
-    (∮ z in C(c, R), (z - w) ^ n) = 0 :=
+    ∮ z in C(c, R), (z - w) ^ n = 0 :=
   by
   rcases em (w ∈ sphere c (|R|) ∧ n < -1) with (⟨hw, hn⟩ | H)
   · exact integral_sub_zpow_of_undef (hn.trans (by decide)) hw
@@ -689,7 +688,7 @@ namespace circleIntegral
 
 /-- Integral $\oint_{|z-c|=R} \frac{dz}{z-w}=2πi$ whenever $|w-c|<R$. -/
 theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R) :
-    (∮ z in C(c, R), (z - w)⁻¹) = 2 * π * I :=
+    ∮ z in C(c, R), (z - w)⁻¹ = 2 * π * I :=
   by
   have hR : 0 < R := dist_nonneg.trans_lt hw
   suffices H : HasSum (fun n : ℕ => ∮ z in C(c, R), ((w - c) / (z - c)) ^ n * (z - c)⁻¹) (2 * π * I)
@@ -697,9 +696,9 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
     refine' (H.unique _).symm
     simpa only [smul_eq_mul, mul_one, add_sub_cancel'_right] using
       hasSum_two_pi_I_cauchyPowerSeries_integral A hw
-  have H : ∀ n : ℕ, n ≠ 0 → (∮ z in C(c, R), (z - c) ^ (-n - 1 : ℤ)) = 0 := by
+  have H : ∀ n : ℕ, n ≠ 0 → ∮ z in C(c, R), (z - c) ^ (-n - 1 : ℤ) = 0 := by
     refine' fun n hn => integral_sub_zpow_of_ne _ _ _ _; simpa
-  have : (∮ z in C(c, R), ((w - c) / (z - c)) ^ 0 * (z - c)⁻¹) = 2 * π * I := by simp [hR.ne']
+  have : ∮ z in C(c, R), ((w - c) / (z - c)) ^ 0 * (z - c)⁻¹ = 2 * π * I := by simp [hR.ne']
   refine' this ▸ hasSum_single _ fun n hn => _
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]
   rw [(integral_congr hR.le fun z hz => _).trans (H n hn), MulZeroClass.mul_zero]

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

@@ -85,15 +85,19 @@ open Complex MeasureTheory TopologicalSpace Metric Function Set Filter Asymptoti
 -/
 
 
+#print circleMap /-
 /-- The exponential map $θ ↦ c + R e^{θi}$. The range of this map is the circle in `ℂ` with center
 `c` and radius `|R|`. -/
 def circleMap (c : ℂ) (R : ℝ) : ℝ → ℂ := fun θ => c + R * exp (θ * I)
 #align circle_map circleMap
+-/
 
+#print periodic_circleMap /-
 /-- `circle_map` is `2π`-periodic. -/
 theorem periodic_circleMap (c : ℂ) (R : ℝ) : Periodic (circleMap c R) (2 * π) := fun θ => by
   simp [circleMap, add_mul, exp_periodic _]
 #align periodic_circle_map periodic_circleMap
+-/
 
 theorem Set.Countable.preimage_circleMap {s : Set ℂ} (hs : s.Countable) (c : ℂ) {R : ℝ}
     (hR : R ≠ 0) : (circleMap c R ⁻¹' s).Countable :=
@@ -146,7 +150,6 @@ theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c (
       simp only [← image_vadd, ← image_smul, ← range_comp, vadd_eq_add, circleMap, (· ∘ ·),
         real_smul]
     _ = sphere c (|R|) := by simp [smul_sphere R (0 : ℂ) zero_le_one]
-    
 #align range_circle_map range_circleMap
 
 /-- The image of `(0, 2π]` under `circle_map c R` is the circle with center `c` and radius `|R|`. -/
@@ -186,10 +189,12 @@ theorem continuous_circleMap (c : ℂ) (R : ℝ) : Continuous (circleMap c R) :=
   (differentiable_circleMap c R).Continuous
 #align continuous_circle_map continuous_circleMap
 
+#print measurable_circleMap /-
 @[measurability]
 theorem measurable_circleMap (c : ℂ) (R : ℝ) : Measurable (circleMap c R) :=
   (continuous_circleMap c R).Measurable
 #align measurable_circle_map measurable_circleMap
+-/
 
 @[simp]
 theorem deriv_circleMap (c : ℂ) (R : ℝ) (θ : ℝ) : deriv (circleMap c R) θ = circleMap 0 R θ * I :=
@@ -223,6 +228,7 @@ theorem continuous_circleMap_inv {R : ℝ} {z w : ℂ} (hw : w ∈ ball z R) :
 -/
 
 
+#print CircleIntegrable /-
 /-- We say that a function `f : ℂ → E` is integrable on the circle with center `c` and radius `R` if
 the function `f ∘ circle_map c R` is integrable on `[0, 2π]`.
 
@@ -232,24 +238,31 @@ to integrability of `f ∘ circle_map c R` whenever `R ≠ 0`. -/
 def CircleIntegrable (f : ℂ → E) (c : ℂ) (R : ℝ) : Prop :=
   IntervalIntegrable (fun θ : ℝ => f (circleMap c R θ)) volume 0 (2 * π)
 #align circle_integrable CircleIntegrable
+-/
 
+#print circleIntegrable_const /-
 @[simp]
 theorem circleIntegrable_const (a : E) (c : ℂ) (R : ℝ) : CircleIntegrable (fun _ => a) c R :=
   intervalIntegrable_const
 #align circle_integrable_const circleIntegrable_const
+-/
 
 namespace CircleIntegrable
 
 variable {f g : ℂ → E} {c : ℂ} {R : ℝ}
 
+#print CircleIntegrable.add /-
 theorem add (hf : CircleIntegrable f c R) (hg : CircleIntegrable g c R) :
     CircleIntegrable (f + g) c R :=
   hf.add hg
 #align circle_integrable.add CircleIntegrable.add
+-/
 
+#print CircleIntegrable.neg /-
 theorem neg (hf : CircleIntegrable f c R) : CircleIntegrable (-f) c R :=
   hf.neg
 #align circle_integrable.neg CircleIntegrable.neg
+-/
 
 /-- The function we actually integrate over `[0, 2π]` in the definition of `circle_integral` is
 integrable. -/
@@ -267,10 +280,12 @@ theorem out [NormedSpace ℂ E] (hf : CircleIntegrable f c R) :
 
 end CircleIntegrable
 
+#print circleIntegrable_zero_radius /-
 @[simp]
 theorem circleIntegrable_zero_radius {f : ℂ → E} {c : ℂ} : CircleIntegrable f c 0 := by
   simp [CircleIntegrable]
 #align circle_integrable_zero_radius circleIntegrable_zero_radius
+-/
 
 theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R : ℝ) :
     CircleIntegrable f c R ↔
@@ -290,14 +305,14 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
   · simp [norm_smul, h₀]
 #align circle_integrable_iff circleIntegrable_iff
 
-theorem ContinuousOn.circle_integrable' {f : ℂ → E} {c : ℂ} {R : ℝ}
+theorem ContinuousOn.circleIntegrable' {f : ℂ → E} {c : ℂ} {R : ℝ}
     (hf : ContinuousOn f (sphere c (|R|))) : CircleIntegrable f c R :=
   (hf.comp_continuous (continuous_circleMap _ _) (circleMap_mem_sphere' _ _)).IntervalIntegrable _ _
-#align continuous_on.circle_integrable' ContinuousOn.circle_integrable'
+#align continuous_on.circle_integrable' ContinuousOn.circleIntegrable'
 
 theorem ContinuousOn.circleIntegrable {f : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R)
     (hf : ContinuousOn f (sphere c R)) : CircleIntegrable f c R :=
-  ContinuousOn.circle_integrable' <| (abs_of_nonneg hR).symm ▸ hf
+  ContinuousOn.circleIntegrable' <| (abs_of_nonneg hR).symm ▸ hf
 #align continuous_on.circle_integrable ContinuousOn.circleIntegrable
 
 /-- The function `λ z, (z - w) ^ n`, `n : ℤ`, is circle integrable on the circle with center `c` and
@@ -340,7 +355,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
   · rintro (rfl | H)
     exacts [circleIntegrable_zero_radius,
       ((continuous_on_id.sub continuousOn_const).zpow₀ _ fun z hz =>
-          H.symm.imp_left fun hw => sub_ne_zero.2 <| ne_of_mem_of_not_mem hz hw).circle_integrable']
+          H.symm.imp_left fun hw => sub_ne_zero.2 <| ne_of_mem_of_not_mem hz hw).circleIntegrable']
 #align circle_integrable_sub_zpow_iff circleIntegrable_sub_zpow_iff
 
 @[simp]
@@ -409,9 +424,7 @@ theorem norm_integral_le_of_norm_le_const' {f : ℂ → E} {c : ℂ} {R C : ℝ}
             simp [norm_smul]
           _ ≤ |R| * C :=
             mul_le_mul_of_nonneg_left (hf _ <| circleMap_mem_sphere' _ _ _) (abs_nonneg _)
-          
     _ = 2 * π * |R| * C := by rw [sub_zero, _root_.abs_of_pos Real.two_pi_pos]; ac_rfl
-    
 #align circle_integral.norm_integral_le_of_norm_le_const' circleIntegral.norm_integral_le_of_norm_le_const'
 
 theorem norm_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ} (hR : 0 ≤ R)
@@ -420,7 +433,6 @@ theorem norm_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ}
   calc
     ‖∮ z in C(c, R), f z‖ ≤ 2 * π * |R| * C := norm_integral_le_of_norm_le_const' <| by rwa [this]
     _ = 2 * π * R * C := by rw [this]
-    
 #align circle_integral.norm_integral_le_of_norm_le_const circleIntegral.norm_integral_le_of_norm_le_const
 
 theorem norm_two_pi_i_inv_smul_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ}
@@ -459,7 +471,6 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
       · exact mul_le_mul_of_nonneg_left (hf _ <| circleMap_mem_sphere _ hR.le _) hR.le
       · exact (mul_lt_mul_left hR).2 hlt
     _ = 2 * π * R * C := by simp [mul_assoc]
-    
 #align circle_integral.norm_integral_lt_of_norm_le_const_of_lt circleIntegral.norm_integral_lt_of_norm_le_const_of_lt
 
 @[simp]
@@ -488,7 +499,7 @@ theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
 
 /-- If `f' : ℂ → E` is a derivative of a complex differentiable function on the circle
 `metric.sphere c |R|`, then `∮ z in C(c, R), f' z = 0`. -/
-theorem integral_eq_zero_of_has_deriv_within_at' {f f' : ℂ → E} {c : ℂ} {R : ℝ}
+theorem integral_eq_zero_of_hasDerivWithinAt' {f f' : ℂ → E} {c : ℂ} {R : ℝ}
     (h : ∀ z ∈ sphere c (|R|), HasDerivWithinAt f (f' z) (sphere c (|R|)) z) :
     (∮ z in C(c, R), f' z) = 0 :=
   by
@@ -499,13 +510,13 @@ theorem integral_eq_zero_of_has_deriv_within_at' {f f' : ℂ → E} {c : ℂ} {R
       (h _ (circleMap_mem_sphere' _ _ _)).scomp_hasDerivAt θ
         (differentiable_circleMap _ _ _).HasDerivAt (circleMap_mem_sphere' _ _)
   · exact integral_undef hi
-#align circle_integral.integral_eq_zero_of_has_deriv_within_at' circleIntegral.integral_eq_zero_of_has_deriv_within_at'
+#align circle_integral.integral_eq_zero_of_has_deriv_within_at' circleIntegral.integral_eq_zero_of_hasDerivWithinAt'
 
 /-- If `f' : ℂ → E` is a derivative of a complex differentiable function on the circle
 `metric.sphere c R`, then `∮ z in C(c, R), f' z = 0`. -/
 theorem integral_eq_zero_of_hasDerivWithinAt {f f' : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R)
     (h : ∀ z ∈ sphere c R, HasDerivWithinAt f (f' z) (sphere c R) z) : (∮ z in C(c, R), f' z) = 0 :=
-  integral_eq_zero_of_has_deriv_within_at' <| (abs_of_nonneg hR).symm.subst h
+  integral_eq_zero_of_hasDerivWithinAt' <| (abs_of_nonneg hR).symm.subst h
 #align circle_integral.integral_eq_zero_of_has_deriv_within_at circleIntegral.integral_eq_zero_of_hasDerivWithinAt
 
 /-- If `n < 0` and `|w - c| = |R|`, then `(z - w) ^ n` is not circle integrable on the circle with
@@ -587,7 +598,6 @@ theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ)
       · cases n <;> simp [-mul_inv_rev, Real.two_pi_pos]
       · rw [mul_inv_cancel_left₀, mul_assoc, mul_comm ((|R|)⁻¹ ^ n)]
         rwa [Ne.def, _root_.abs_eq_zero]
-    
 #align norm_cauchy_power_series_le norm_cauchyPowerSeries_le
 
 theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
@@ -612,7 +622,7 @@ theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R` multiplied
 by `2πI` converges to the integral `∮ z in C(c, R), (z - w)⁻¹ • f z` on the open disc
 `metric.ball c R`. -/
-theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
+theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
     (hf : CircleIntegrable f c R) (hw : abs w < R) :
     HasSum (fun n : ℕ => ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z)
       (∮ z in C(c, R), (z - (c + w))⁻¹ • f z) :=
@@ -637,7 +647,7 @@ theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
     convert (hasSum_geometric_of_norm_lt_1 this).mul_right _
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
-#align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchy_power_series_integral
+#align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchyPowerSeries_integral
 
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R`, `R > 0`,
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
@@ -648,7 +658,7 @@ theorem hasSum_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w
       ((2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z) :=
   by
   simp only [cauchyPowerSeries_apply]
-  exact (hasSum_two_pi_I_cauchy_power_series_integral hf hw).const_smul _
+  exact (hasSum_two_pi_I_cauchyPowerSeries_integral hf hw).const_smul _
 #align has_sum_cauchy_power_series_integral hasSum_cauchyPowerSeries_integral
 
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R`, `R > 0`,
@@ -663,7 +673,7 @@ theorem sum_cauchyPowerSeries_eq_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R`, `R > 0`,
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
-theorem has_fpower_series_on_cauchy_integral {f : ℂ → E} {c : ℂ} {R : ℝ≥0}
+theorem hasFPowerSeriesOn_cauchy_integral {f : ℂ → E} {c : ℂ} {R : ℝ≥0}
     (hf : CircleIntegrable f c R) (hR : 0 < R) :
     HasFPowerSeriesOnBall (fun w => (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z)
       (cauchyPowerSeries f c R) c R :=
@@ -673,7 +683,7 @@ theorem has_fpower_series_on_cauchy_integral {f : ℂ → E} {c : ℂ} {R : ℝ
       refine' hasSum_cauchyPowerSeries_integral hf _
       rw [← norm_eq_abs, ← coe_nnnorm, NNReal.coe_lt_coe, ← ENNReal.coe_lt_coe]
       exact mem_emetric_ball_zero_iff.1 hy }
-#align has_fpower_series_on_cauchy_integral has_fpower_series_on_cauchy_integral
+#align has_fpower_series_on_cauchy_integral hasFPowerSeriesOn_cauchy_integral
 
 namespace circleIntegral
 
@@ -686,7 +696,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   · have A : CircleIntegrable (fun _ => (1 : ℂ)) c R := continuous_on_const.circle_integrable'
     refine' (H.unique _).symm
     simpa only [smul_eq_mul, mul_one, add_sub_cancel'_right] using
-      hasSum_two_pi_I_cauchy_power_series_integral A hw
+      hasSum_two_pi_I_cauchyPowerSeries_integral A hw
   have H : ∀ n : ℕ, n ≠ 0 → (∮ z in C(c, R), (z - c) ^ (-n - 1 : ℤ)) = 0 := by
     refine' fun n hn => integral_sub_zpow_of_ne _ _ _ _; simpa
   have : (∮ z in C(c, R), ((w - c) / (z - c)) ^ 0 * (z - c)⁻¹) = 2 * π * I := by simp [hR.ne']

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

@@ -525,13 +525,13 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
   by
   rcases em (w ∈ sphere c (|R|) ∧ n < -1) with (⟨hw, hn⟩ | H)
   · exact integral_sub_zpow_of_undef (hn.trans (by decide)) hw
-  push_neg  at H 
+  push_neg at H 
   have hd :
     ∀ z, z ≠ w ∨ -1 ≤ n → HasDerivAt (fun z => (z - w) ^ (n + 1) / (n + 1)) ((z - w) ^ n) z :=
     by
     intro z hne
-    convert((hasDerivAt_zpow (n + 1) _ (hne.imp _ _)).comp z
-            ((hasDerivAt_id z).sub_const w)).div_const
+    convert
+      ((hasDerivAt_zpow (n + 1) _ (hne.imp _ _)).comp z ((hasDerivAt_id z).sub_const w)).div_const
         _ using
       1
     · have hn' : (n + 1 : ℂ) ≠ 0 := by
@@ -635,7 +635,7 @@ theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {
     simp only [smul_smul]
     refine' HasSum.smul_const _ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
-    convert(hasSum_geometric_of_norm_lt_1 this).mul_right _
+    convert (hasSum_geometric_of_norm_lt_1 this).mul_right _
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchy_power_series_integral
 

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

@@ -663,9 +663,9 @@ theorem sum_cauchyPowerSeries_eq_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w
 /-- For any circle integrable function `f`, the power series `cauchy_power_series f c R`, `R > 0`,
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
-theorem hasFpowerSeriesOnCauchyIntegral {f : ℂ → E} {c : ℂ} {R : ℝ≥0} (hf : CircleIntegrable f c R)
-    (hR : 0 < R) :
-    HasFpowerSeriesOnBall (fun w => (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z)
+theorem has_fpower_series_on_cauchy_integral {f : ℂ → E} {c : ℂ} {R : ℝ≥0}
+    (hf : CircleIntegrable f c R) (hR : 0 < R) :
+    HasFPowerSeriesOnBall (fun w => (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z)
       (cauchyPowerSeries f c R) c R :=
   { r_le := le_radius_cauchyPowerSeries _ _ _
     r_pos := ENNReal.coe_pos.2 hR
@@ -673,7 +673,7 @@ theorem hasFpowerSeriesOnCauchyIntegral {f : ℂ → E} {c : ℂ} {R : ℝ≥0}
       refine' hasSum_cauchyPowerSeries_integral hf _
       rw [← norm_eq_abs, ← coe_nnnorm, NNReal.coe_lt_coe, ← ENNReal.coe_lt_coe]
       exact mem_emetric_ball_zero_iff.1 hy }
-#align has_fpower_series_on_cauchy_integral hasFpowerSeriesOnCauchyIntegral
+#align has_fpower_series_on_cauchy_integral has_fpower_series_on_cauchy_integral
 
 namespace circleIntegral
 

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

@@ -280,7 +280,7 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
   by_cases h₀ : R = 0
   · simp [h₀]
   refine' ⟨fun h => h.out, fun h => _⟩
-  simp only [CircleIntegrable, intervalIntegrable_iff, deriv_circleMap] at h⊢
+  simp only [CircleIntegrable, intervalIntegrable_iff, deriv_circleMap] at h ⊢
   refine' (h.norm.const_mul (|R|)⁻¹).mono' _ _
   · have H : ∀ {θ}, circleMap 0 R θ * I ≠ 0 := fun θ => by simp [h₀, I_ne_zero]
     simpa only [inv_smul_smul₀ H] using
@@ -309,7 +309,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
   constructor
   · intro h; contrapose! h; rcases h with ⟨hR, hn, hw⟩
     simp only [circleIntegrable_iff R, deriv_circleMap]
-    rw [← image_circleMap_Ioc] at hw; rcases hw with ⟨θ, hθ, rfl⟩
+    rw [← image_circleMap_Ioc] at hw ; rcases hw with ⟨θ, hθ, rfl⟩
     replace hθ : θ ∈ [0, 2 * π]; exact Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
     refine' not_intervalIntegrable_of_sub_inv_isBigO_punctured _ real.two_pi_pos.ne hθ
     set f : ℝ → ℂ := fun θ' => circleMap c R θ' - circleMap c R θ
@@ -338,7 +338,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
     rw [← zpow_neg_one]
     refine' (zpow_strictAnti this.1 this.2).le_iff_le.2 (Int.lt_add_one_iff.1 _); exact hn
   · rintro (rfl | H)
-    exacts[circleIntegrable_zero_radius,
+    exacts [circleIntegrable_zero_radius,
       ((continuous_on_id.sub continuousOn_const).zpow₀ _ fun z hz =>
           H.symm.imp_left fun hw => sub_ne_zero.2 <| ne_of_mem_of_not_mem hz hw).circle_integrable']
 #align circle_integrable_sub_zpow_iff circleIntegrable_sub_zpow_iff
@@ -384,7 +384,7 @@ theorem integral_sub_inv_smul_sub_smul (f : ℂ → E) (c w : ℂ) (R : ℝ) :
   rcases eq_or_ne R 0 with (rfl | hR); · simp only [integral_radius_zero]
   have : (circleMap c R ⁻¹' {w}).Countable := (countable_singleton _).preimage_circleMap c hR
   refine' intervalIntegral.integral_congr_ae ((this.ae_not_mem _).mono fun θ hθ hθ' => _)
-  change circleMap c R θ ≠ w at hθ
+  change circleMap c R θ ≠ w at hθ 
   simp only [inv_smul_smul₀ (sub_ne_zero.2 <| hθ)]
 #align circle_integral.integral_sub_inv_smul_sub_smul circleIntegral.integral_sub_inv_smul_sub_smul
 
@@ -439,7 +439,7 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
     (hc : ContinuousOn f (sphere c R)) (hf : ∀ z ∈ sphere c R, ‖f z‖ ≤ C)
     (hlt : ∃ z ∈ sphere c R, ‖f z‖ < C) : ‖∮ z in C(c, R), f z‖ < 2 * π * R * C :=
   by
-  rw [← _root_.abs_of_pos hR, ← image_circleMap_Ioc] at hlt
+  rw [← _root_.abs_of_pos hR, ← image_circleMap_Ioc] at hlt 
   rcases hlt with ⟨_, ⟨θ₀, hmem, rfl⟩, hlt⟩
   calc
     ‖∮ z in C(c, R), f z‖ ≤ ∫ θ in 0 ..2 * π, ‖deriv (circleMap c R) θ • f (circleMap c R θ)‖ :=
@@ -525,7 +525,7 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
   by
   rcases em (w ∈ sphere c (|R|) ∧ n < -1) with (⟨hw, hn⟩ | H)
   · exact integral_sub_zpow_of_undef (hn.trans (by decide)) hw
-  push_neg  at H
+  push_neg  at H 
   have hd :
     ∀ z, z ≠ w ∨ -1 ≤ n → HasDerivAt (fun z => (z - w) ^ (n + 1) / (n + 1)) ((z - w) ^ n) z :=
     by
@@ -537,7 +537,7 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
     · have hn' : (n + 1 : ℂ) ≠ 0 := by
         rwa [Ne, ← eq_neg_iff_add_eq_zero, ← Int.cast_one, ← Int.cast_neg, Int.cast_inj]
       simp [mul_assoc, mul_div_cancel_left _ hn']
-    exacts[sub_ne_zero.2, neg_le_iff_add_nonneg.1]
+    exacts [sub_ne_zero.2, neg_le_iff_add_nonneg.1]
   refine' integral_eq_zero_of_has_deriv_within_at' fun z hz => (hd z _).HasDerivWithinAt
   exact (ne_or_eq z w).imp_right fun h => H <| h ▸ hz
 #align circle_integral.integral_sub_zpow_of_ne circleIntegral.integral_sub_zpow_of_ne

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

@@ -76,7 +76,7 @@ variable {E : Type _} [NormedAddCommGroup E]
 
 noncomputable section
 
-open Real NNReal Interval Pointwise Topology
+open scoped Real NNReal Interval Pointwise Topology
 
 open Complex MeasureTheory TopologicalSpace Metric Function Set Filter Asymptotics
 

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

@@ -213,9 +213,7 @@ theorem lipschitzWith_circleMap (c : ℂ) (R : ℝ) : LipschitzWith R.nnabs (cir
 theorem continuous_circleMap_inv {R : ℝ} {z w : ℂ} (hw : w ∈ ball z R) :
     Continuous fun θ => (circleMap z R θ - w)⁻¹ :=
   by
-  have : ∀ θ, circleMap z R θ - w ≠ 0 :=
-    by
-    simp_rw [sub_ne_zero]
+  have : ∀ θ, circleMap z R θ - w ≠ 0 := by simp_rw [sub_ne_zero];
     exact fun θ => circleMap_ne_mem_ball hw θ
   continuity
 #align continuous_circle_map_inv continuous_circleMap_inv
@@ -309,14 +307,10 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
     CircleIntegrable (fun z => (z - w) ^ n) c R ↔ R = 0 ∨ 0 ≤ n ∨ w ∉ sphere c (|R|) :=
   by
   constructor
-  · intro h
-    contrapose! h
-    rcases h with ⟨hR, hn, hw⟩
+  · intro h; contrapose! h; rcases h with ⟨hR, hn, hw⟩
     simp only [circleIntegrable_iff R, deriv_circleMap]
-    rw [← image_circleMap_Ioc] at hw
-    rcases hw with ⟨θ, hθ, rfl⟩
-    replace hθ : θ ∈ [0, 2 * π]
-    exact Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
+    rw [← image_circleMap_Ioc] at hw; rcases hw with ⟨θ, hθ, rfl⟩
+    replace hθ : θ ∈ [0, 2 * π]; exact Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
     refine' not_intervalIntegrable_of_sub_inv_isBigO_punctured _ real.two_pi_pos.ne hθ
     set f : ℝ → ℂ := fun θ' => circleMap c R θ' - circleMap c R θ
     have : ∀ᶠ θ' in 𝓝[≠] θ, f θ' ∈ ball (0 : ℂ) 1 \ {0} :=
@@ -342,8 +336,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
         not_false_iff] using this
     have : x ∈ Ioo (0 : ℝ) 1 := by simpa [and_comm, x] using hθ'
     rw [← zpow_neg_one]
-    refine' (zpow_strictAnti this.1 this.2).le_iff_le.2 (Int.lt_add_one_iff.1 _)
-    exact hn
+    refine' (zpow_strictAnti this.1 this.2).le_iff_le.2 (Int.lt_add_one_iff.1 _); exact hn
   · rintro (rfl | H)
     exacts[circleIntegrable_zero_radius,
       ((continuous_on_id.sub continuousOn_const).zpow₀ _ fun z hz =>
@@ -352,10 +345,8 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
 
 @[simp]
 theorem circleIntegrable_sub_inv_iff {c w : ℂ} {R : ℝ} :
-    CircleIntegrable (fun z => (z - w)⁻¹) c R ↔ R = 0 ∨ w ∉ sphere c (|R|) :=
-  by
-  simp only [← zpow_neg_one, circleIntegrable_sub_zpow_iff]
-  norm_num
+    CircleIntegrable (fun z => (z - w)⁻¹) c R ↔ R = 0 ∨ w ∉ sphere c (|R|) := by
+  simp only [← zpow_neg_one, circleIntegrable_sub_zpow_iff]; norm_num
 #align circle_integrable_sub_inv_iff circleIntegrable_sub_inv_iff
 
 variable [NormedSpace ℂ E] [CompleteSpace E]
@@ -390,8 +381,7 @@ theorem integral_congr {f g : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R) (h :
 theorem integral_sub_inv_smul_sub_smul (f : ℂ → E) (c w : ℂ) (R : ℝ) :
     (∮ z in C(c, R), (z - w)⁻¹ • (z - w) • f z) = ∮ z in C(c, R), f z :=
   by
-  rcases eq_or_ne R 0 with (rfl | hR)
-  · simp only [integral_radius_zero]
+  rcases eq_or_ne R 0 with (rfl | hR); · simp only [integral_radius_zero]
   have : (circleMap c R ⁻¹' {w}).Countable := (countable_singleton _).preimage_circleMap c hR
   refine' intervalIntegral.integral_congr_ae ((this.ae_not_mem _).mono fun θ hθ hθ' => _)
   change circleMap c R θ ≠ w at hθ
@@ -420,9 +410,7 @@ theorem norm_integral_le_of_norm_le_const' {f : ℂ → E} {c : ℂ} {R C : ℝ}
           _ ≤ |R| * C :=
             mul_le_mul_of_nonneg_left (hf _ <| circleMap_mem_sphere' _ _ _) (abs_nonneg _)
           
-    _ = 2 * π * |R| * C := by
-      rw [sub_zero, _root_.abs_of_pos Real.two_pi_pos]
-      ac_rfl
+    _ = 2 * π * |R| * C := by rw [sub_zero, _root_.abs_of_pos Real.two_pi_pos]; ac_rfl
     
 #align circle_integral.norm_integral_le_of_norm_le_const' circleIntegral.norm_integral_le_of_norm_le_const'
 
@@ -637,8 +625,7 @@ theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {
       (fun n θ => ‖f (circleMap c R θ)‖ * (abs w / R) ^ n) (fun n => _) (fun n => _) _ _ _
   · simp only [deriv_circleMap]
     apply_rules [ae_strongly_measurable.smul, hf.def.1] <;>
-      · apply Measurable.aestronglyMeasurable
-        measurability
+      · apply Measurable.aestronglyMeasurable; measurability
   · simp [norm_smul, abs_of_pos hR, mul_left_comm R, mul_inv_cancel_left₀ hR.ne', mul_comm ‖_‖]
   · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_1 hwR.1 hwR.2).mul_left _
   ·
@@ -700,10 +687,8 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
     refine' (H.unique _).symm
     simpa only [smul_eq_mul, mul_one, add_sub_cancel'_right] using
       hasSum_two_pi_I_cauchy_power_series_integral A hw
-  have H : ∀ n : ℕ, n ≠ 0 → (∮ z in C(c, R), (z - c) ^ (-n - 1 : ℤ)) = 0 :=
-    by
-    refine' fun n hn => integral_sub_zpow_of_ne _ _ _ _
-    simpa
+  have H : ∀ n : ℕ, n ≠ 0 → (∮ z in C(c, R), (z - c) ^ (-n - 1 : ℤ)) = 0 := by
+    refine' fun n hn => integral_sub_zpow_of_ne _ _ _ _; simpa
   have : (∮ z in C(c, R), ((w - c) / (z - c)) ^ 0 * (z - c)⁻¹) = 2 * π * I := by simp [hR.ne']
   refine' this ▸ hasSum_single _ fun n hn => _
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]

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

@@ -4,11 +4,12 @@ Released under Apache 2.0 license as described in the file LICENSE.
 Authors: Yury Kudryashov
 
 ! This file was ported from Lean 3 source module measure_theory.integral.circle_integral
-! leanprover-community/mathlib commit 639b66d9330da2cd8dd02be1a51b6d10d058e5e4
+! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
 ! Please do not edit these lines, except to modify the commit id
 ! if you have ported upstream changes.
 -/
 import Mathbin.MeasureTheory.Integral.IntervalIntegral
+import Mathbin.Analysis.Calculus.Deriv.Zpow
 import Mathbin.Analysis.NormedSpace.Pointwise
 import Mathbin.Analysis.SpecialFunctions.NonIntegrable
 import Mathbin.Analysis.Analytic.Basic

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

@@ -262,7 +262,7 @@ theorem out [NormedSpace ℂ E] (hf : CircleIntegrable f c R) :
   refine' (hf.norm.const_mul (|R|)).mono' _ _
   ·
     exact
-      ((continuous_circleMap _ _).AeStronglyMeasurable.mul_const I).smul hf.ae_strongly_measurable
+      ((continuous_circleMap _ _).AEStronglyMeasurable.mul_const I).smul hf.ae_strongly_measurable
   · simp [norm_smul]
 #align circle_integrable.out CircleIntegrable.out
 
@@ -285,8 +285,8 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
   refine' (h.norm.const_mul (|R|)⁻¹).mono' _ _
   · have H : ∀ {θ}, circleMap 0 R θ * I ≠ 0 := fun θ => by simp [h₀, I_ne_zero]
     simpa only [inv_smul_smul₀ H] using
-      ((continuous_circleMap 0 R).AeStronglyMeasurable.mul_const
-                  I).AEMeasurable.inv.AeStronglyMeasurable.smul
+      ((continuous_circleMap 0 R).AEStronglyMeasurable.mul_const
+                  I).AEMeasurable.inv.AEStronglyMeasurable.smul
         h.ae_strongly_measurable
   · simp [norm_smul, h₀]
 #align circle_integrable_iff circleIntegrable_iff
@@ -636,7 +636,7 @@ theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {
       (fun n θ => ‖f (circleMap c R θ)‖ * (abs w / R) ^ n) (fun n => _) (fun n => _) _ _ _
   · simp only [deriv_circleMap]
     apply_rules [ae_strongly_measurable.smul, hf.def.1] <;>
-      · apply Measurable.aeStronglyMeasurable
+      · apply Measurable.aestronglyMeasurable
         measurability
   · simp [norm_smul, abs_of_pos hR, mul_left_comm R, mul_inv_cancel_left₀ hR.ne', mul_comm ‖_‖]
   · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_1 hwR.1 hwR.2).mul_left _

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

@@ -236,7 +236,7 @@ def CircleIntegrable (f : ℂ → E) (c : ℂ) (R : ℝ) : Prop :=
 
 @[simp]
 theorem circleIntegrable_const (a : E) (c : ℂ) (R : ℝ) : CircleIntegrable (fun _ => a) c R :=
-  intervalIntegrableConst
+  intervalIntegrable_const
 #align circle_integrable_const circleIntegrable_const
 
 namespace CircleIntegrable
@@ -286,7 +286,7 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
   · have H : ∀ {θ}, circleMap 0 R θ * I ≠ 0 := fun θ => by simp [h₀, I_ne_zero]
     simpa only [inv_smul_smul₀ H] using
       ((continuous_circleMap 0 R).AeStronglyMeasurable.mul_const
-                  I).AeMeasurable.inv.AeStronglyMeasurable.smul
+                  I).AEMeasurable.inv.AeStronglyMeasurable.smul
         h.ae_strongly_measurable
   · simp [norm_smul, h₀]
 #align circle_integrable_iff circleIntegrable_iff

mathlib commit https://github.com/leanprover-community/mathlib/commit/039ef89bef6e58b32b62898dd48e9d1a4312bb65

@@ -316,7 +316,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
     rcases hw with ⟨θ, hθ, rfl⟩
     replace hθ : θ ∈ [0, 2 * π]
     exact Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
-    refine' not_intervalIntegrable_of_sub_inv_isO_punctured _ real.two_pi_pos.ne hθ
+    refine' not_intervalIntegrable_of_sub_inv_isBigO_punctured _ real.two_pi_pos.ne hθ
     set f : ℝ → ℂ := fun θ' => circleMap c R θ' - circleMap c R θ
     have : ∀ᶠ θ' in 𝓝[≠] θ, f θ' ∈ ball (0 : ℂ) 1 \ {0} :=
       by
@@ -330,7 +330,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
         mem_singleton_iff, mem_ball, mem_diff, mem_ball_zero_iff, norm_eq_abs, not_false_iff,
         and_self_iff, imp_true_iff]
     refine'
-      (((hasDerivAt_circleMap c R θ).isO_sub.mono inf_le_left).inv_rev
+      (((hasDerivAt_circleMap c R θ).isBigO_sub.mono inf_le_left).inv_rev
             (this.mono fun θ' h₁ h₂ => absurd h₂ h₁.2)).trans
         _
     refine' is_O.of_bound (|R|)⁻¹ (this.mono fun θ' hθ' => _)

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

@@ -541,8 +541,8 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
     ∀ z, z ≠ w ∨ -1 ≤ n → HasDerivAt (fun z => (z - w) ^ (n + 1) / (n + 1)) ((z - w) ^ n) z :=
     by
     intro z hne
-    convert
-      ((hasDerivAt_zpow (n + 1) _ (hne.imp _ _)).comp z ((hasDerivAt_id z).sub_const w)).div_const
+    convert((hasDerivAt_zpow (n + 1) _ (hne.imp _ _)).comp z
+            ((hasDerivAt_id z).sub_const w)).div_const
         _ using
       1
     · have hn' : (n + 1 : ℂ) ≠ 0 := by
@@ -647,7 +647,7 @@ theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {
     simp only [smul_smul]
     refine' HasSum.smul_const _ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
-    convert (hasSum_geometric_of_norm_lt_1 this).mul_right _
+    convert(hasSum_geometric_of_norm_lt_1 this).mul_right _
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchy_power_series_integral
 

mathlib commit https://github.com/leanprover-community/mathlib/commit/2af0836443b4cfb5feda0df0051acdb398304931

@@ -99,7 +99,7 @@ theorem Set.Countable.preimage_circleMap {s : Set ℂ} (hs : s.Countable) (c : 
   show (coe ⁻¹' ((· * I) ⁻¹' (exp ⁻¹' ((· * ·) R ⁻¹' ((· + ·) c ⁻¹' s))))).Countable from
     (((hs.Preimage (add_right_injective _)).Preimage <|
                 mul_right_injective₀ <| ofReal_ne_zero.2 hR).preimage_cexp.Preimage <|
-          mul_left_injective₀ i_ne_zero).Preimage
+          mul_left_injective₀ I_ne_zero).Preimage
       ofReal_injective
 #align set.countable.preimage_circle_map Set.Countable.preimage_circleMap
 
@@ -113,8 +113,7 @@ theorem circleMap_zero (R θ : ℝ) : circleMap 0 R θ = R * exp (θ * I) :=
 #align circle_map_zero circleMap_zero
 
 @[simp]
-theorem abs_circleMap_zero (R : ℝ) (θ : ℝ) :
-    Complex.AbsTheory.Complex.abs (circleMap 0 R θ) = |R| := by simp [circleMap]
+theorem abs_circleMap_zero (R : ℝ) (θ : ℝ) : abs (circleMap 0 R θ) = |R| := by simp [circleMap]
 #align abs_circle_map_zero abs_circleMap_zero
 
 theorem circleMap_mem_sphere' (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∈ sphere c (|R|) := by simp
@@ -625,7 +624,7 @@ theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
 by `2πI` converges to the integral `∮ z in C(c, R), (z - w)⁻¹ • f z` on the open disc
 `metric.ball c R`. -/
 theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
-    (hf : CircleIntegrable f c R) (hw : Complex.AbsTheory.Complex.abs w < R) :
+    (hf : CircleIntegrable f c R) (hw : abs w < R) :
     HasSum (fun n : ℕ => ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z)
       (∮ z in C(c, R), (z - (c + w))⁻¹ • f z) :=
   by
@@ -656,7 +655,7 @@ theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
 theorem hasSum_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
-    (hf : CircleIntegrable f c R) (hw : Complex.AbsTheory.Complex.abs w < R) :
+    (hf : CircleIntegrable f c R) (hw : abs w < R) :
     HasSum (fun n => cauchyPowerSeries f c R n fun _ => w)
       ((2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z) :=
   by
@@ -668,7 +667,7 @@ theorem hasSum_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
 theorem sum_cauchyPowerSeries_eq_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
-    (hf : CircleIntegrable f c R) (hw : Complex.AbsTheory.Complex.abs w < R) :
+    (hf : CircleIntegrable f c R) (hw : abs w < R) :
     (cauchyPowerSeries f c R).Sum w = (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z :=
   (hasSum_cauchyPowerSeries_integral hf hw).tsum_eq
 #align sum_cauchy_power_series_eq_integral sum_cauchyPowerSeries_eq_integral

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

@@ -614,7 +614,7 @@ theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
       _
   rw [_root_.abs_of_nonneg R.coe_nonneg]
   cases' eq_or_ne (R ^ n : ℝ) 0 with hR hR
-  · rw [hR, mul_zero]
+  · rw [hR, MulZeroClass.mul_zero]
     exact
       mul_nonneg (inv_nonneg.2 real.two_pi_pos.le)
         (intervalIntegral.integral_nonneg real.two_pi_pos.le fun _ _ => norm_nonneg _)
@@ -707,7 +707,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   have : (∮ z in C(c, R), ((w - c) / (z - c)) ^ 0 * (z - c)⁻¹) = 2 * π * I := by simp [hR.ne']
   refine' this ▸ hasSum_single _ fun n hn => _
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]
-  rw [(integral_congr hR.le fun z hz => _).trans (H n hn), mul_zero]
+  rw [(integral_congr hR.le fun z hz => _).trans (H n hn), MulZeroClass.mul_zero]
   rw [← pow_succ', ← zpow_ofNat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
     sub_eq_add_neg _ (1 : ℤ)]
 #align circle_integral.integral_sub_inv_of_mem_ball circleIntegral.integral_sub_inv_of_mem_ball

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

@@ -86,7 +86,7 @@ open Complex MeasureTheory TopologicalSpace Metric Function Set Filter Asymptoti
 
 /-- The exponential map $θ ↦ c + R e^{θi}$. The range of this map is the circle in `ℂ` with center
 `c` and radius `|R|`. -/
-def circleMap (c : ℂ) (R : ℝ) : ℝ → ℂ := fun θ => c + R * exp (θ * i)
+def circleMap (c : ℂ) (R : ℝ) : ℝ → ℂ := fun θ => c + R * exp (θ * I)
 #align circle_map circleMap
 
 /-- `circle_map` is `2π`-periodic. -/
@@ -96,11 +96,11 @@ theorem periodic_circleMap (c : ℂ) (R : ℝ) : Periodic (circleMap c R) (2 * 
 
 theorem Set.Countable.preimage_circleMap {s : Set ℂ} (hs : s.Countable) (c : ℂ) {R : ℝ}
     (hR : R ≠ 0) : (circleMap c R ⁻¹' s).Countable :=
-  show (coe ⁻¹' ((· * i) ⁻¹' (exp ⁻¹' ((· * ·) R ⁻¹' ((· + ·) c ⁻¹' s))))).Countable from
+  show (coe ⁻¹' ((· * I) ⁻¹' (exp ⁻¹' ((· * ·) R ⁻¹' ((· + ·) c ⁻¹' s))))).Countable from
     (((hs.Preimage (add_right_injective _)).Preimage <|
-                mul_right_injective₀ <| of_real_ne_zero.2 hR).preimage_cexp.Preimage <|
+                mul_right_injective₀ <| ofReal_ne_zero.2 hR).preimage_cexp.Preimage <|
           mul_left_injective₀ i_ne_zero).Preimage
-      of_real_injective
+      ofReal_injective
 #align set.countable.preimage_circle_map Set.Countable.preimage_circleMap
 
 @[simp]
@@ -108,12 +108,13 @@ theorem circleMap_sub_center (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ -
   simp [circleMap]
 #align circle_map_sub_center circleMap_sub_center
 
-theorem circleMap_zero (R θ : ℝ) : circleMap 0 R θ = R * exp (θ * i) :=
+theorem circleMap_zero (R θ : ℝ) : circleMap 0 R θ = R * exp (θ * I) :=
   zero_add _
 #align circle_map_zero circleMap_zero
 
 @[simp]
-theorem abs_circleMap_zero (R : ℝ) (θ : ℝ) : abs (circleMap 0 R θ) = |R| := by simp [circleMap]
+theorem abs_circleMap_zero (R : ℝ) (θ : ℝ) :
+    Complex.AbsTheory.Complex.abs (circleMap 0 R θ) = |R| := by simp [circleMap]
 #align abs_circle_map_zero abs_circleMap_zero
 
 theorem circleMap_mem_sphere' (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∈ sphere c (|R|) := by simp
@@ -141,7 +142,7 @@ theorem circleMap_ne_mem_ball {c : ℂ} {R : ℝ} {w : ℂ} (hw : w ∈ ball c R
 @[simp]
 theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c (|R|) :=
   calc
-    range (circleMap c R) = c +ᵥ R • range fun θ : ℝ => exp (θ * i) := by
+    range (circleMap c R) = c +ᵥ R • range fun θ : ℝ => exp (θ * I) := by
       simp only [← image_vadd, ← image_smul, ← range_comp, vadd_eq_add, circleMap, (· ∘ ·),
         real_smul]
     _ = sphere c (|R|) := by simp [smul_sphere R (0 : ℂ) zero_le_one]
@@ -169,7 +170,7 @@ theorem circleMap_ne_center {c : ℂ} {R : ℝ} (hR : R ≠ 0) {θ : ℝ} : circ
 #align circle_map_ne_center circleMap_ne_center
 
 theorem hasDerivAt_circleMap (c : ℂ) (R : ℝ) (θ : ℝ) :
-    HasDerivAt (circleMap c R) (circleMap 0 R θ * i) θ := by
+    HasDerivAt (circleMap c R) (circleMap 0 R θ * I) θ := by
   simpa only [mul_assoc, one_mul, of_real_clm_apply, circleMap, of_real_one, zero_add] using
     ((of_real_clm.has_deriv_at.mul_const I).cexp.const_mul (R : ℂ)).const_add c
 #align has_deriv_at_circle_map hasDerivAt_circleMap
@@ -191,7 +192,7 @@ theorem measurable_circleMap (c : ℂ) (R : ℝ) : Measurable (circleMap c R) :=
 #align measurable_circle_map measurable_circleMap
 
 @[simp]
-theorem deriv_circleMap (c : ℂ) (R : ℝ) (θ : ℝ) : deriv (circleMap c R) θ = circleMap 0 R θ * i :=
+theorem deriv_circleMap (c : ℂ) (R : ℝ) (θ : ℝ) : deriv (circleMap c R) θ = circleMap 0 R θ * I :=
   (hasDerivAt_circleMap _ _ _).deriv
 #align deriv_circle_map deriv_circleMap
 
@@ -436,7 +437,7 @@ theorem norm_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ}
 
 theorem norm_two_pi_i_inv_smul_integral_le_of_norm_le_const {f : ℂ → E} {c : ℂ} {R C : ℝ}
     (hR : 0 ≤ R) (hf : ∀ z ∈ sphere c R, ‖f z‖ ≤ C) :
-    ‖(2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), f z‖ ≤ R * C :=
+    ‖(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), f z‖ ≤ R * C :=
   by
   have : ‖(2 * π * I : ℂ)⁻¹‖ = (2 * π)⁻¹ := by simp [real.pi_pos.le]
   rw [norm_smul, this, ← div_eq_inv_mul, div_le_iff Real.two_pi_pos, mul_comm (R * C), ← mul_assoc]
@@ -493,7 +494,7 @@ theorem integral_const_mul (a : ℂ) (f : ℂ → ℂ) (c : ℂ) (R : ℝ) :
 
 @[simp]
 theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
-    (∮ z in C(c, R), (z - c)⁻¹) = 2 * π * i := by
+    (∮ z in C(c, R), (z - c)⁻¹) = 2 * π * I := by
   simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left _ (circleMap_ne_center hR)]
 #align circle_integral.integral_sub_center_inv circleIntegral.integral_sub_center_inv
 
@@ -563,12 +564,12 @@ series converges to `f w` if `f` is differentiable on the closed ball `metric.cl
 series converges to the Cauchy integral for `f`. -/
 def cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ) : FormalMultilinearSeries ℂ ℂ E := fun n =>
   ContinuousMultilinearMap.mkPiField ℂ _ <|
-    (2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z
+    (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z
 #align cauchy_power_series cauchyPowerSeries
 
 theorem cauchyPowerSeries_apply (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) (w : ℂ) :
     (cauchyPowerSeries f c R n fun _ => w) =
-      (2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z :=
+      (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z :=
   by
   simp only [cauchyPowerSeries, ContinuousMultilinearMap.mkPiField_apply, Fin.prod_const,
     div_eq_mul_inv, mul_pow, mul_smul, circleIntegral.integral_smul, ← smul_comm (w ^ n)]
@@ -624,7 +625,7 @@ theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
 by `2πI` converges to the integral `∮ z in C(c, R), (z - w)⁻¹ • f z` on the open disc
 `metric.ball c R`. -/
 theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
-    (hf : CircleIntegrable f c R) (hw : abs w < R) :
+    (hf : CircleIntegrable f c R) (hw : Complex.AbsTheory.Complex.abs w < R) :
     HasSum (fun n : ℕ => ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z)
       (∮ z in C(c, R), (z - (c + w))⁻¹ • f z) :=
   by
@@ -655,9 +656,9 @@ theorem hasSum_two_pi_I_cauchy_power_series_integral {f : ℂ → E} {c : ℂ} {
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
 theorem hasSum_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
-    (hf : CircleIntegrable f c R) (hw : abs w < R) :
+    (hf : CircleIntegrable f c R) (hw : Complex.AbsTheory.Complex.abs w < R) :
     HasSum (fun n => cauchyPowerSeries f c R n fun _ => w)
-      ((2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z) :=
+      ((2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z) :=
   by
   simp only [cauchyPowerSeries_apply]
   exact (hasSum_two_pi_I_cauchy_power_series_integral hf hw).const_smul _
@@ -667,8 +668,8 @@ theorem hasSum_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w
 converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z` on the open
 disc `metric.ball c R`. -/
 theorem sum_cauchyPowerSeries_eq_integral {f : ℂ → E} {c : ℂ} {R : ℝ} {w : ℂ}
-    (hf : CircleIntegrable f c R) (hw : abs w < R) :
-    (cauchyPowerSeries f c R).Sum w = (2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z :=
+    (hf : CircleIntegrable f c R) (hw : Complex.AbsTheory.Complex.abs w < R) :
+    (cauchyPowerSeries f c R).Sum w = (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - (c + w))⁻¹ • f z :=
   (hasSum_cauchyPowerSeries_integral hf hw).tsum_eq
 #align sum_cauchy_power_series_eq_integral sum_cauchyPowerSeries_eq_integral
 
@@ -677,7 +678,7 @@ converges to the Cauchy integral `(2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R),
 disc `metric.ball c R`. -/
 theorem hasFpowerSeriesOnCauchyIntegral {f : ℂ → E} {c : ℂ} {R : ℝ≥0} (hf : CircleIntegrable f c R)
     (hR : 0 < R) :
-    HasFpowerSeriesOnBall (fun w => (2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z)
+    HasFpowerSeriesOnBall (fun w => (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z)
       (cauchyPowerSeries f c R) c R :=
   { r_le := le_radius_cauchyPowerSeries _ _ _
     r_pos := ENNReal.coe_pos.2 hR
@@ -691,7 +692,7 @@ namespace circleIntegral
 
 /-- Integral $\oint_{|z-c|=R} \frac{dz}{z-w}=2πi$ whenever $|w-c|<R$. -/
 theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R) :
-    (∮ z in C(c, R), (z - w)⁻¹) = 2 * π * i :=
+    (∮ z in C(c, R), (z - w)⁻¹) = 2 * π * I :=
   by
   have hR : 0 < R := dist_nonneg.trans_lt hw
   suffices H : HasSum (fun n : ℕ => ∮ z in C(c, R), ((w - c) / (z - c)) ^ n * (z - c)⁻¹) (2 * π * I)

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

@@ -585,8 +585,9 @@ theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ)
           ∫ θ in 0 ..2 * π,
             ‖deriv (circleMap c R) θ •
                 (circleMap c R θ - c)⁻¹ ^ n • (circleMap c R θ - c)⁻¹ • f (circleMap c R θ)‖ :=
-      mul_le_mul_of_nonneg_left (intervalIntegral.norm_integral_le_integral_norm Real.two_pi_pos.le)
-        (by simp [real.pi_pos.le])
+      (mul_le_mul_of_nonneg_left
+        (intervalIntegral.norm_integral_le_integral_norm Real.two_pi_pos.le)
+        (by simp [real.pi_pos.le]))
     _ =
         (2 * π)⁻¹ *
           ((|R|)⁻¹ ^ n * (|R| * ((|R|)⁻¹ * ∫ x : ℝ in 0 ..2 * π, ‖f (circleMap c R x)‖))) :=

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

@@ -679,10 +679,10 @@ theorem hasFpowerSeriesOnCauchyIntegral {f : ℂ → E} {c : ℂ} {R : ℝ≥0}
     HasFpowerSeriesOnBall (fun w => (2 * π * i : ℂ)⁻¹ • ∮ z in C(c, R), (z - w)⁻¹ • f z)
       (cauchyPowerSeries f c R) c R :=
   { r_le := le_radius_cauchyPowerSeries _ _ _
-    r_pos := Ennreal.coe_pos.2 hR
+    r_pos := ENNReal.coe_pos.2 hR
     HasSum := fun y hy => by
       refine' hasSum_cauchyPowerSeries_integral hf _
-      rw [← norm_eq_abs, ← coe_nnnorm, NNReal.coe_lt_coe, ← Ennreal.coe_lt_coe]
+      rw [← norm_eq_abs, ← coe_nnnorm, NNReal.coe_lt_coe, ← ENNReal.coe_lt_coe]
       exact mem_emetric_ball_zero_iff.1 hy }
 #align has_fpower_series_on_cauchy_integral hasFpowerSeriesOnCauchyIntegral
 

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

@@ -317,7 +317,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
     set x := abs (f θ')
     suffices x⁻¹ ≤ x ^ n by
       simpa only [inv_mul_cancel_left₀, abs_eq_zero.not.2 hR, norm_eq_abs, map_inv₀,
-        Algebra.id.smul_eq_mul, map_mul, abs_circleMap_zero, abs_I, mul_one, abs_zpow, Ne.def,
+        Algebra.id.smul_eq_mul, map_mul, abs_circleMap_zero, abs_I, mul_one, abs_zpow, Ne,
         not_false_iff] using this
     have : x ∈ Ioo (0 : ℝ) 1 := by simpa [x, and_comm] using hθ'
     rw [← zpow_neg_one]
@@ -554,7 +554,7 @@ theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ)
         rw [← mul_assoc, inv_mul_cancel (Real.two_pi_pos.ne.symm), one_mul]
         apply norm_nonneg
       · rw [mul_inv_cancel_left₀, mul_assoc, mul_comm (|R|⁻¹ ^ n)]
-        rwa [Ne.def, _root_.abs_eq_zero]
+        rwa [Ne, _root_.abs_eq_zero]
 #align norm_cauchy_power_series_le norm_cauchyPowerSeries_le
 
 theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :

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.

@@ -656,7 +656,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]
   rw [(integral_congr hR.le fun z hz => _).trans (H n hn), mul_zero]
   intro z _
-  rw [← pow_succ', ← zpow_natCast, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
+  rw [← pow_succ, ← zpow_natCast, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
     sub_eq_add_neg _ (1 : ℤ)]
 #align circle_integral.integral_sub_inv_of_mem_ball circleIntegral.integral_sub_inv_of_mem_ball
 

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.

@@ -437,7 +437,7 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
 #align circle_integral.norm_integral_lt_of_norm_le_const_of_lt circleIntegral.norm_integral_lt_of_norm_le_const_of_lt
 
 @[simp]
-theorem integral_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
+theorem integral_smul {𝕜 : Type*} [RCLike 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂ → E) (c : ℂ) (R : ℝ) : (∮ z in C(c, R), a • f z) = a • ∮ z in C(c, R), f z := by
   simp only [circleIntegral, ← smul_comm a (_ : ℂ) (_ : E), intervalIntegral.integral_smul]
 #align circle_integral.integral_smul circleIntegral.integral_smul

Lemma names around cancellation of multiplication and division are a mess.

This PR renames a handful of them according to the following table (each big row contains the multiplicative statement, then the three rows contain the GroupWithZero lemma name, the Group lemma, the AddGroup lemma name).

| Statement | New name | Old name | |

@@ -457,7 +457,7 @@ theorem integral_const_mul (a : ℂ) (f : ℂ → ℂ) (c : ℂ) (R : ℝ) :
 @[simp]
 theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
     (∮ z in C(c, R), (z - c)⁻¹) = 2 * π * I := by
-  simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left _ (circleMap_ne_center hR),
+  simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left₀ _ (circleMap_ne_center hR),
     -- Porting note: `simp` didn't need a hint to apply `integral_const` here
     intervalIntegral.integral_const I]
 #align circle_integral.integral_sub_center_inv circleIntegral.integral_sub_center_inv
@@ -506,7 +506,7 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
       ((hasDerivAt_id z).sub_const w)).div_const _ using 1
     · have hn' : (n + 1 : ℂ) ≠ 0 := by
         rwa [Ne, ← eq_neg_iff_add_eq_zero, ← Int.cast_one, ← Int.cast_neg, Int.cast_inj]
-      simp [mul_assoc, mul_div_cancel_left _ hn']
+      simp [mul_assoc, mul_div_cancel_left₀ _ hn']
     exacts [sub_ne_zero.2, neg_le_iff_add_nonneg.1]
   refine' integral_eq_zero_of_hasDerivWithinAt' fun z hz => (hd z _).hasDerivWithinAt
   exact (ne_or_eq z w).imp_right fun (h : z = w) => H <| h ▸ hz
@@ -601,7 +601,7 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     refine' HasSum.smul_const _ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
     convert (hasSum_geometric_of_norm_lt_one this).mul_right _ using 1
-    simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
+    simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel₀ _ (circleMap_ne_center hR.ne')]
 set_option linter.uppercaseLean3 false in
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchyPowerSeries_integral
 
@@ -647,7 +647,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
       (2 * π * I) by
     have A : CircleIntegrable (fun _ => (1 : ℂ)) c R := continuousOn_const.circleIntegrable'
     refine' (H.unique _).symm
-    simpa only [smul_eq_mul, mul_one, add_sub_cancel'_right] using
+    simpa only [smul_eq_mul, mul_one, add_sub_cancel] using
       hasSum_two_pi_I_cauchyPowerSeries_integral A hw
   have H : ∀ n : ℕ, n ≠ 0 → (∮ z in C(c, R), (z - c) ^ (-n - 1 : ℤ)) = 0 := by
     refine' fun n hn => integral_sub_zpow_of_ne _ _ _ _; simpa

This will become an error in 2024-03-16 nightly, possibly not permanently.

Co-authored-by: Scott Morrison <scott@tqft.net>

@@ -587,7 +587,7 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
   refine' intervalIntegral.hasSum_integral_of_dominated_convergence
       (fun n θ => ‖f (circleMap c R θ)‖ * (abs w / R) ^ n) (fun n => _) (fun n => _) _ _ _
   · simp only [deriv_circleMap]
-    apply_rules [AEStronglyMeasurable.smul, hf.def.1] <;> apply Measurable.aestronglyMeasurable
+    apply_rules [AEStronglyMeasurable.smul, hf.def'.1] <;> apply Measurable.aestronglyMeasurable
     -- Porting note: these were `measurability`
     · exact (measurable_circleMap 0 R).mul_const I
     · exact (((measurable_circleMap c R).sub measurable_const).const_div w).pow measurable_const

... and add a deprecated alias for the old name. This is mostly just me discovering the power of F2

@@ -656,7 +656,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]
   rw [(integral_congr hR.le fun z hz => _).trans (H n hn), mul_zero]
   intro z _
-  rw [← pow_succ', ← zpow_coe_nat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
+  rw [← pow_succ', ← zpow_natCast, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
     sub_eq_add_neg _ (1 : ℤ)]
 #align circle_integral.integral_sub_inv_of_mem_ball circleIntegral.integral_sub_inv_of_mem_ball
 

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".

@@ -458,7 +458,7 @@ theorem integral_const_mul (a : ℂ) (f : ℂ → ℂ) (c : ℂ) (R : ℝ) :
 theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
     (∮ z in C(c, R), (z - c)⁻¹) = 2 * π * I := by
   simp [circleIntegral, ← div_eq_mul_inv, mul_div_cancel_left _ (circleMap_ne_center hR),
-    -- porting note: `simp` didn't need a hint to apply `integral_const` here
+    -- Porting note: `simp` didn't need a hint to apply `integral_const` here
     intervalIntegral.integral_const I]
 #align circle_integral.integral_sub_center_inv circleIntegral.integral_sub_center_inv
 

Previously these were syntactically identical to the corresponding zpow_coe_nat and coe_nat_zsmul lemmas, now they are about OfNat.ofNat.

Unfortunately, almost every call site uses the ofNat name to refer to Nat.cast, so the downstream proofs had to be adjusted too.

@@ -656,7 +656,7 @@ theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R)
   simp only [div_eq_mul_inv, mul_pow, integral_const_mul, mul_assoc]
   rw [(integral_congr hR.le fun z hz => _).trans (H n hn), mul_zero]
   intro z _
-  rw [← pow_succ', ← zpow_ofNat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
+  rw [← pow_succ', ← zpow_coe_nat, inv_zpow, ← zpow_neg, Int.ofNat_succ, neg_add,
     sub_eq_add_neg _ (1 : ℤ)]
 #align circle_integral.integral_sub_inv_of_mem_ball circleIntegral.integral_sub_inv_of_mem_ball
 

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

@@ -319,7 +319,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
       simpa only [inv_mul_cancel_left₀, abs_eq_zero.not.2 hR, norm_eq_abs, map_inv₀,
         Algebra.id.smul_eq_mul, map_mul, abs_circleMap_zero, abs_I, mul_one, abs_zpow, Ne.def,
         not_false_iff] using this
-    have : x ∈ Ioo (0 : ℝ) 1 := by simpa [and_comm] using hθ'
+    have : x ∈ Ioo (0 : ℝ) 1 := by simpa [x, and_comm] using hθ'
     rw [← zpow_neg_one]
     refine' (zpow_strictAnti this.1 this.2).le_iff_le.2 (Int.lt_add_one_iff.1 _); exact hn
   · rintro (rfl | H)

Use Lean 4 syntax fun x ↦ instead, matching the style guide. This is close to exhaustive for doc comments; mathlib has about 460 remaining uses of λ (not all in Lean 3 syntax).

@@ -293,8 +293,8 @@ theorem ContinuousOn.circleIntegrable {f : ℂ → E} {c : ℂ} {R : ℝ} (hR :
   ContinuousOn.circleIntegrable' <| (_root_.abs_of_nonneg hR).symm ▸ hf
 #align continuous_on.circle_integrable ContinuousOn.circleIntegrable
 
-/-- The function `λ z, (z - w) ^ n`, `n : ℤ`, is circle integrable on the circle with center `c` and
-radius `|R|` if and only if `R = 0` or `0 ≤ n`, or `w` does not belong to this circle. -/
+/-- The function `fun z ↦ (z - w) ^ n`, `n : ℤ`, is circle integrable on the circle with center `c`
+and radius `|R|` if and only if `R = 0` or `0 ≤ n`, or `w` does not belong to this circle. -/
 @[simp]
 theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
     CircleIntegrable (fun z => (z - w) ^ n) c R ↔ R = 0 ∨ 0 ≤ n ∨ w ∉ sphere c |R| := by

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

This follows on from #6964.

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

@@ -302,13 +302,13 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
   · intro h; contrapose! h; rcases h with ⟨hR, hn, hw⟩
     simp only [circleIntegrable_iff R, deriv_circleMap]
     rw [← image_circleMap_Ioc] at hw; rcases hw with ⟨θ, hθ, rfl⟩
-    replace hθ : θ ∈ [[0, 2 * π]]; exact Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
+    replace hθ : θ ∈ [[0, 2 * π]] := Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
     refine' not_intervalIntegrable_of_sub_inv_isBigO_punctured _ Real.two_pi_pos.ne hθ
     set f : ℝ → ℂ := fun θ' => circleMap c R θ' - circleMap c R θ
     have : ∀ᶠ θ' in 𝓝[≠] θ, f θ' ∈ ball (0 : ℂ) 1 \ {0} := by
-      suffices : ∀ᶠ z in 𝓝[≠] circleMap c R θ, z - circleMap c R θ ∈ ball (0 : ℂ) 1 \ {0}
-      exact ((differentiable_circleMap c R θ).hasDerivAt.tendsto_punctured_nhds
-        (deriv_circleMap_ne_zero hR)).eventually this
+      suffices ∀ᶠ z in 𝓝[≠] circleMap c R θ, z - circleMap c R θ ∈ ball (0 : ℂ) 1 \ {0} from
+        ((differentiable_circleMap c R θ).hasDerivAt.tendsto_punctured_nhds
+          (deriv_circleMap_ne_zero hR)).eventually this
       filter_upwards [self_mem_nhdsWithin, mem_nhdsWithin_of_mem_nhds (ball_mem_nhds _ zero_lt_one)]
       simp_all [dist_eq, sub_eq_zero]
     refine' (((hasDerivAt_circleMap c R θ).isBigO_sub.mono inf_le_left).inv_rev
@@ -643,8 +643,9 @@ namespace circleIntegral
 theorem integral_sub_inv_of_mem_ball {c w : ℂ} {R : ℝ} (hw : w ∈ ball c R) :
     (∮ z in C(c, R), (z - w)⁻¹) = 2 * π * I := by
   have hR : 0 < R := dist_nonneg.trans_lt hw
-  suffices H : HasSum (fun n : ℕ => ∮ z in C(c, R), ((w - c) / (z - c)) ^ n * (z - c)⁻¹) (2 * π * I)
-  · have A : CircleIntegrable (fun _ => (1 : ℂ)) c R := continuousOn_const.circleIntegrable'
+  suffices H : HasSum (fun n : ℕ => ∮ z in C(c, R), ((w - c) / (z - c)) ^ n * (z - c)⁻¹)
+      (2 * π * I) by
+    have A : CircleIntegrable (fun _ => (1 : ℂ)) c R := continuousOn_const.circleIntegrable'
     refine' (H.unique _).symm
     simpa only [smul_eq_mul, mul_one, add_sub_cancel'_right] using
       hasSum_two_pi_I_cauchyPowerSeries_integral A hw

This matches the generality of the non-continuous versions.

The norm_smulRight lemma is the only new result.

@@ -522,14 +522,14 @@ series converges to `f w` if `f` is differentiable on the closed ball `Metric.cl
 `w` belongs to the corresponding open ball. For any circle integrable function `f`, this power
 series converges to the Cauchy integral for `f`. -/
 def cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ) : FormalMultilinearSeries ℂ ℂ E := fun n =>
-  ContinuousMultilinearMap.mkPiField ℂ _ <|
+  ContinuousMultilinearMap.mkPiRing ℂ _ <|
     (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z
 #align cauchy_power_series cauchyPowerSeries
 
 theorem cauchyPowerSeries_apply (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) (w : ℂ) :
     (cauchyPowerSeries f c R n fun _ => w) =
       (2 * π * I : ℂ)⁻¹ • ∮ z in C(c, R), (w / (z - c)) ^ n • (z - c)⁻¹ • f z := by
-  simp only [cauchyPowerSeries, ContinuousMultilinearMap.mkPiField_apply, Fin.prod_const,
+  simp only [cauchyPowerSeries, ContinuousMultilinearMap.mkPiRing_apply, Fin.prod_const,
     div_eq_mul_inv, mul_pow, mul_smul, circleIntegral.integral_smul]
   rw [← smul_comm (w ^ n)]
 #align cauchy_power_series_apply cauchyPowerSeries_apply

See here on Zulip.

This PR changes a bunch of names containing nhds_0 or/and lt_1 to nhds_zero or/and lt_one.

@@ -593,14 +593,14 @@ theorem hasSum_two_pi_I_cauchyPowerSeries_integral {f : ℂ → E} {c : ℂ} {R
     · exact (((measurable_circleMap c R).sub measurable_const).const_div w).pow measurable_const
     · exact ((measurable_circleMap c R).sub measurable_const).inv
   · simp [norm_smul, abs_of_pos hR, mul_left_comm R, inv_mul_cancel_left₀ hR.ne', mul_comm ‖_‖]
-  · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_1 hwR.1 hwR.2).mul_left _
-  · simpa only [tsum_mul_left, tsum_geometric_of_lt_1 hwR.1 hwR.2] using
+  · exact eventually_of_forall fun _ _ => (summable_geometric_of_lt_one hwR.1 hwR.2).mul_left _
+  · simpa only [tsum_mul_left, tsum_geometric_of_lt_one hwR.1 hwR.2] using
       hf.norm.mul_continuousOn continuousOn_const
   · refine' eventually_of_forall fun θ _ => HasSum.const_smul _ _
     simp only [smul_smul]
     refine' HasSum.smul_const _ _
     have : ‖w / (circleMap c R θ - c)‖ < 1 := by simpa [abs_of_pos hR] using hwR.2
-    convert (hasSum_geometric_of_norm_lt_1 this).mul_right _ using 1
+    convert (hasSum_geometric_of_norm_lt_one this).mul_right _ using 1
     simp [← sub_sub, ← mul_inv, sub_mul, div_mul_cancel _ (circleMap_ne_center hR.ne')]
 set_option linter.uppercaseLean3 false in
 #align has_sum_two_pi_I_cauchy_power_series_integral hasSum_two_pi_I_cauchyPowerSeries_integral

Rename

• Complex.equivRealProdClm → Complex.equivRealProdCLM;
  • TODO: should this one use CLE?
• Complex.reClm → Complex.reCLM;
• Complex.imClm → Complex.imCLM;
• Complex.conjLie → Complex.conjLIE;
• Complex.conjCle → Complex.conjCLE;
• Complex.ofRealLi → Complex.ofRealLI;
• Complex.ofRealClm → Complex.ofRealCLM;
• fderivInnerClm → fderivInnerCLM;
• LinearPMap.adjointDomainMkClm → LinearPMap.adjointDomainMkCLM;
• LinearPMap.adjointDomainMkClmExtend → LinearPMap.adjointDomainMkCLMExtend;
• IsROrC.reClm → IsROrC.reCLM;
• IsROrC.imClm → IsROrC.imCLM;
• IsROrC.conjLie → IsROrC.conjLIE;
• IsROrC.conjCle → IsROrC.conjCLE;
• IsROrC.ofRealLi → IsROrC.ofRealLI;
• IsROrC.ofRealClm → IsROrC.ofRealCLM;
• MeasureTheory.condexpL1Clm → MeasureTheory.condexpL1CLM;
• algebraMapClm → algebraMapCLM;
• WeakDual.CharacterSpace.toClm → WeakDual.CharacterSpace.toCLM;
• BoundedContinuousFunction.evalClm → BoundedContinuousFunction.evalCLM;
• ContinuousMap.evalClm → ContinuousMap.evalCLM;
• TrivSqZeroExt.fstClm → TrivSqZeroExt.fstClm;
• TrivSqZeroExt.sndClm → TrivSqZeroExt.sndCLM;
• TrivSqZeroExt.inlClm → TrivSqZeroExt.inlCLM;
• TrivSqZeroExt.inrClm → TrivSqZeroExt.inrCLM

and related theorems.

@@ -169,8 +169,8 @@ theorem circleMap_ne_center {c : ℂ} {R : ℝ} (hR : R ≠ 0) {θ : ℝ} : circ
 
 theorem hasDerivAt_circleMap (c : ℂ) (R : ℝ) (θ : ℝ) :
     HasDerivAt (circleMap c R) (circleMap 0 R θ * I) θ := by
-  simpa only [mul_assoc, one_mul, ofRealClm_apply, circleMap, ofReal_one, zero_add]
-    using (((ofRealClm.hasDerivAt (x := θ)).mul_const I).cexp.const_mul (R : ℂ)).const_add c
+  simpa only [mul_assoc, one_mul, ofRealCLM_apply, circleMap, ofReal_one, zero_add]
+    using (((ofRealCLM.hasDerivAt (x := θ)).mul_const I).cexp.const_mul (R : ℂ)).const_add c
 #align has_deriv_at_circle_map hasDerivAt_circleMap
 
 /- TODO: prove `ContDiff ℝ (circleMap c R)`. This needs a version of `ContDiff.mul`

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

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

@@ -565,7 +565,7 @@ theorem le_radius_cauchyPowerSeries (f : ℂ → E) (c : ℂ) (R : ℝ≥0) :
   refine' (mul_le_mul_of_nonneg_right (norm_cauchyPowerSeries_le _ _ _ _)
     (pow_nonneg R.coe_nonneg _)).trans _
   rw [_root_.abs_of_nonneg R.coe_nonneg]
-  cases' eq_or_ne (R ^ n : ℝ) 0 with hR hR
+  rcases eq_or_ne (R ^ n : ℝ) 0 with hR | hR
   · rw_mod_cast [hR, mul_zero]
     exact mul_nonneg (inv_nonneg.2 Real.two_pi_pos.le)
       (intervalIntegral.integral_nonneg Real.two_pi_pos.le fun _ _ => norm_nonneg _)

I used the regex \(\(· (.) ·\) (.)\), replacing with ($2 $1 ·).

@@ -95,7 +95,7 @@ theorem periodic_circleMap (c : ℂ) (R : ℝ) : Periodic (circleMap c R) (2 * 
 theorem Set.Countable.preimage_circleMap {s : Set ℂ} (hs : s.Countable) (c : ℂ) {R : ℝ}
     (hR : R ≠ 0) : (circleMap c R ⁻¹' s).Countable :=
   show (((↑) : ℝ → ℂ) ⁻¹' ((· * I) ⁻¹'
-      (exp ⁻¹' ((· * ·) (R : ℂ) ⁻¹' ((· + ·) c ⁻¹' s))))).Countable from
+      (exp ⁻¹' ((R * ·) ⁻¹' ((c + ·) ⁻¹' s))))).Countable from
     (((hs.preimage (add_right_injective _)).preimage <|
       mul_right_injective₀ <| ofReal_ne_zero.2 hR).preimage_cexp.preimage <|
         mul_left_injective₀ I_ne_zero).preimage ofReal_injective

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>

@@ -71,8 +71,6 @@ integral, circle, Cauchy integral
 
 variable {E : Type*} [NormedAddCommGroup E]
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
-
 noncomputable section
 
 open scoped Real NNReal Interval Pointwise Topology
@@ -142,8 +140,8 @@ theorem circleMap_ne_mem_ball {c : ℂ} {R : ℝ} {w : ℂ} (hw : w ∈ ball c R
 theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c |R| :=
   calc
     range (circleMap c R) = c +ᵥ R • range fun θ : ℝ => exp (θ * I) := by
-      simp only [← image_vadd, ← image_smul, ← range_comp, vadd_eq_add, circleMap, (· ∘ ·),
-        real_smul]
+      simp (config := { unfoldPartialApp := true }) only [← image_vadd, ← image_smul, ← range_comp,
+        vadd_eq_add, circleMap, Function.comp_def, real_smul]
     _ = sphere c |R| := by
       rw [Complex.range_exp_mul_I, smul_sphere R 0 zero_le_one]
       simp
@@ -274,7 +272,7 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
     CircleIntegrable f c R ↔ IntervalIntegrable (fun θ : ℝ =>
       deriv (circleMap c R) θ • f (circleMap c R θ)) volume 0 (2 * π) := by
   by_cases h₀ : R = 0
-  · simp [h₀, const]
+  · simp (config := { unfoldPartialApp := true }) [h₀, const]
   refine' ⟨fun h => h.out, fun h => _⟩
   simp only [CircleIntegrable, intervalIntegrable_iff, deriv_circleMap] at h ⊢
   refine' (h.norm.const_mul |R|⁻¹).mono' _ _
@@ -357,7 +355,7 @@ namespace circleIntegral
 
 @[simp]
 theorem integral_radius_zero (f : ℂ → E) (c : ℂ) : (∮ z in C(c, 0), f z) = 0 := by
-  simp [circleIntegral, const]
+  simp (config := { unfoldPartialApp := true }) [circleIntegral, const]
 #align circle_integral.integral_radius_zero circleIntegral.integral_radius_zero
 
 theorem integral_congr {f g : ℂ → E} {c : ℂ} {R : ℝ} (hR : 0 ≤ R) (h : EqOn f g (sphere c R)) :

@@ -517,7 +517,8 @@ theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ)
 end circleIntegral
 
 /-- The power series that is equal to
-$\sum_{n=0}^{\infty} \oint_{|z-c|=R} \left(\frac{w-c}{z - c}\right)^n \frac{1}{z-c}f(z)\,dz$ at
+$\frac{1}{2πi}\sum_{n=0}^{\infty}
+  \oint_{|z-c|=R} \left(\frac{w-c}{z - c}\right)^n \frac{1}{z-c}f(z)\,dz$ at
 `w - c`. The coefficients of this power series depend only on `f ∘ circleMap c R`, and the power
 series converges to `f w` if `f` is differentiable on the closed ball `Metric.closedBall c R` and
 `w` belongs to the corresponding open ball. For any circle integrable function `f`, this power
@@ -635,10 +636,7 @@ theorem hasFPowerSeriesOn_cauchy_integral {f : ℂ → E} {c : ℂ} {R : ℝ≥0
       (cauchyPowerSeries f c R) c R :=
   { r_le := le_radius_cauchyPowerSeries _ _ _
     r_pos := ENNReal.coe_pos.2 hR
-    hasSum := fun hy => by
-      refine' hasSum_cauchyPowerSeries_integral hf _
-      rw [← norm_eq_abs, ← coe_nnnorm, NNReal.coe_lt_coe, ← ENNReal.coe_lt_coe]
-      exact mem_emetric_ball_zero_iff.1 hy }
+    hasSum := fun hy ↦ hasSum_cauchyPowerSeries_integral hf <| by simpa using hy }
 #align has_fpower_series_on_cauchy_integral hasFPowerSeriesOn_cauchy_integral
 
 namespace circleIntegral

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

This has nice performance benefits.

@@ -69,7 +69,7 @@ integral, circle, Cauchy integral
 -/
 
 
-variable {E : Type _} [NormedAddCommGroup E]
+variable {E : Type*} [NormedAddCommGroup E]
 
 local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
@@ -439,7 +439,7 @@ theorem norm_integral_lt_of_norm_le_const_of_lt {f : ℂ → E} {c : ℂ} {R C :
 #align circle_integral.norm_integral_lt_of_norm_le_const_of_lt circleIntegral.norm_integral_lt_of_norm_le_const_of_lt
 
 @[simp]
-theorem integral_smul {𝕜 : Type _} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
+theorem integral_smul {𝕜 : Type*} [IsROrC 𝕜] [NormedSpace 𝕜 E] [SMulCommClass 𝕜 ℂ E] (a : 𝕜)
     (f : ℂ → E) (c : ℂ) (R : ℝ) : (∮ z in C(c, R), a • f z) = a • ∮ z in C(c, R), f z := by
   simp only [circleIntegral, ← smul_comm a (_ : ℂ) (_ : E), intervalIntegral.integral_smul]
 #align circle_integral.integral_smul circleIntegral.integral_smul

@@ -71,7 +71,7 @@ integral, circle, Cauchy integral
 
 variable {E : Type _} [NormedAddCommGroup E]
 
-local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue #2220
+local macro_rules | `($x ^ $y) => `(HPow.hPow $x $y) -- Porting note: See issue lean4#2220
 
 noncomputable section
 

• depends on: #5966

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

@@ -2,11 +2,6 @@
 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 measure_theory.integral.circle_integral
-! leanprover-community/mathlib commit 3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe
-! Please do not edit these lines, except to modify the commit id
-! if you have ported upstream changes.
 -/
 import Mathlib.MeasureTheory.Integral.IntervalIntegral
 import Mathlib.Analysis.Calculus.Deriv.ZPow
@@ -14,6 +9,8 @@ import Mathlib.Analysis.NormedSpace.Pointwise
 import Mathlib.Analysis.SpecialFunctions.NonIntegrable
 import Mathlib.Analysis.Analytic.Basic
 
+#align_import measure_theory.integral.circle_integral from "leanprover-community/mathlib"@"3bce8d800a6f2b8f63fe1e588fd76a9ff4adcebe"
+
 /-!
 # Integral over a circle in `ℂ`
 

This is the second half of the changes originally in #5699, removing all occurrences of ; after a space and implementing a linter rule to enforce it.

In most cases this 2-character substring has a space after it, so the following command was run first:

find . -type f -name "*.lean" -exec sed -i -E 's/ ; /; /g' {} \;

The remaining cases were few enough in number that they were done manually.

@@ -306,7 +306,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
   constructor
   · intro h; contrapose! h; rcases h with ⟨hR, hn, hw⟩
     simp only [circleIntegrable_iff R, deriv_circleMap]
-    rw [← image_circleMap_Ioc] at hw ; rcases hw with ⟨θ, hθ, rfl⟩
+    rw [← image_circleMap_Ioc] at hw; rcases hw with ⟨θ, hθ, rfl⟩
     replace hθ : θ ∈ [[0, 2 * π]]; exact Icc_subset_uIcc (Ioc_subset_Icc_self hθ)
     refine' not_intervalIntegrable_of_sub_inv_isBigO_punctured _ Real.two_pi_pos.ne hθ
     set f : ℝ → ℂ := fun θ' => circleMap c R θ' - circleMap c R θ

@@ -119,7 +119,7 @@ theorem circleMap_zero (R θ : ℝ) : circleMap 0 R θ = R * exp (θ * I) :=
 theorem abs_circleMap_zero (R : ℝ) (θ : ℝ) : abs (circleMap 0 R θ) = |R| := by simp [circleMap]
 #align abs_circle_map_zero abs_circleMap_zero
 
-theorem circleMap_mem_sphere' (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∈ sphere c (|R|) := by simp
+theorem circleMap_mem_sphere' (c : ℂ) (R : ℝ) (θ : ℝ) : circleMap c R θ ∈ sphere c |R| := by simp
 #align circle_map_mem_sphere' circleMap_mem_sphere'
 
 theorem circleMap_mem_sphere (c : ℂ) {R : ℝ} (hR : 0 ≤ R) (θ : ℝ) : circleMap c R θ ∈ sphere c R :=
@@ -142,19 +142,19 @@ theorem circleMap_ne_mem_ball {c : ℂ} {R : ℝ} {w : ℂ} (hw : w ∈ ball c R
 
 /-- The range of `circleMap c R` is the circle with center `c` and radius `|R|`. -/
 @[simp]
-theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c (|R|) :=
+theorem range_circleMap (c : ℂ) (R : ℝ) : range (circleMap c R) = sphere c |R| :=
   calc
     range (circleMap c R) = c +ᵥ R • range fun θ : ℝ => exp (θ * I) := by
       simp only [← image_vadd, ← image_smul, ← range_comp, vadd_eq_add, circleMap, (· ∘ ·),
         real_smul]
-    _ = sphere c (|R|) := by
+    _ = sphere c |R| := by
       rw [Complex.range_exp_mul_I, smul_sphere R 0 zero_le_one]
       simp
 #align range_circle_map range_circleMap
 
 /-- The image of `(0, 2π]` under `circleMap c R` is the circle with center `c` and radius `|R|`. -/
 @[simp]
-theorem image_circleMap_Ioc (c : ℂ) (R : ℝ) : circleMap c R '' Ioc 0 (2 * π) = sphere c (|R|) := by
+theorem image_circleMap_Ioc (c : ℂ) (R : ℝ) : circleMap c R '' Ioc 0 (2 * π) = sphere c |R| := by
   rw [← range_circleMap, ← (periodic_circleMap c R).image_Ioc Real.two_pi_pos 0, zero_add]
 #align image_circle_map_Ioc image_circleMap_Ioc
 
@@ -261,7 +261,7 @@ theorem out [NormedSpace ℂ E] (hf : CircleIntegrable f c R) :
     IntervalIntegrable (fun θ : ℝ => deriv (circleMap c R) θ • f (circleMap c R θ)) volume 0
       (2 * π) := by
   simp only [CircleIntegrable, deriv_circleMap, intervalIntegrable_iff] at *
-  refine' (hf.norm.const_mul (|R|)).mono' _ _
+  refine' (hf.norm.const_mul |R|).mono' _ _
   · exact ((continuous_circleMap _ _).aestronglyMeasurable.mul_const I).smul hf.aestronglyMeasurable
   · simp [norm_smul]
 #align circle_integrable.out CircleIntegrable.out
@@ -280,7 +280,7 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
   · simp [h₀, const]
   refine' ⟨fun h => h.out, fun h => _⟩
   simp only [CircleIntegrable, intervalIntegrable_iff, deriv_circleMap] at h ⊢
-  refine' (h.norm.const_mul (|R|)⁻¹).mono' _ _
+  refine' (h.norm.const_mul |R|⁻¹).mono' _ _
   · have H : ∀ {θ}, circleMap 0 R θ * I ≠ 0 := fun {θ} => by simp [h₀, I_ne_zero]
     simpa only [inv_smul_smul₀ H]
       using ((continuous_circleMap 0 R).aestronglyMeasurable.mul_const
@@ -289,7 +289,7 @@ theorem circleIntegrable_iff [NormedSpace ℂ E] {f : ℂ → E} {c : ℂ} (R :
 #align circle_integrable_iff circleIntegrable_iff
 
 theorem ContinuousOn.circleIntegrable' {f : ℂ → E} {c : ℂ} {R : ℝ}
-    (hf : ContinuousOn f (sphere c (|R|))) : CircleIntegrable f c R :=
+    (hf : ContinuousOn f (sphere c |R|)) : CircleIntegrable f c R :=
   (hf.comp_continuous (continuous_circleMap _ _) (circleMap_mem_sphere' _ _)).intervalIntegrable _ _
 #align continuous_on.circle_integrable' ContinuousOn.circleIntegrable'
 
@@ -302,7 +302,7 @@ theorem ContinuousOn.circleIntegrable {f : ℂ → E} {c : ℂ} {R : ℝ} (hR :
 radius `|R|` if and only if `R = 0` or `0 ≤ n`, or `w` does not belong to this circle. -/
 @[simp]
 theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
-    CircleIntegrable (fun z => (z - w) ^ n) c R ↔ R = 0 ∨ 0 ≤ n ∨ w ∉ sphere c (|R|) := by
+    CircleIntegrable (fun z => (z - w) ^ n) c R ↔ R = 0 ∨ 0 ≤ n ∨ w ∉ sphere c |R| := by
   constructor
   · intro h; contrapose! h; rcases h with ⟨hR, hn, hw⟩
     simp only [circleIntegrable_iff R, deriv_circleMap]
@@ -318,7 +318,7 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
       simp_all [dist_eq, sub_eq_zero]
     refine' (((hasDerivAt_circleMap c R θ).isBigO_sub.mono inf_le_left).inv_rev
       (this.mono fun θ' h₁ h₂ => absurd h₂ h₁.2)).trans _
-    refine' IsBigO.of_bound (|R|)⁻¹ (this.mono fun θ' hθ' => _)
+    refine' IsBigO.of_bound |R|⁻¹ (this.mono fun θ' hθ' => _)
     set x := abs (f θ')
     suffices x⁻¹ ≤ x ^ n by
       simpa only [inv_mul_cancel_left₀, abs_eq_zero.not.2 hR, norm_eq_abs, map_inv₀,
@@ -330,13 +330,13 @@ theorem circleIntegrable_sub_zpow_iff {c w : ℂ} {R : ℝ} {n : ℤ} :
   · rintro (rfl | H)
     exacts [circleIntegrable_zero_radius,
       ((continuousOn_id.sub continuousOn_const).zpow₀ _ fun z hz =>
-        H.symm.imp_left fun (hw : w ∉ sphere c (|R|)) =>
+        H.symm.imp_left fun (hw : w ∉ sphere c |R|) =>
           sub_ne_zero.2 <| ne_of_mem_of_not_mem hz hw).circleIntegrable']
 #align circle_integrable_sub_zpow_iff circleIntegrable_sub_zpow_iff
 
 @[simp]
 theorem circleIntegrable_sub_inv_iff {c w : ℂ} {R : ℝ} :
-    CircleIntegrable (fun z => (z - w)⁻¹) c R ↔ R = 0 ∨ w ∉ sphere c (|R|) := by
+    CircleIntegrable (fun z => (z - w)⁻¹) c R ↔ R = 0 ∨ w ∉ sphere c |R| := by
   simp only [← zpow_neg_one, circleIntegrable_sub_zpow_iff]; norm_num
 #align circle_integrable_sub_inv_iff circleIntegrable_sub_inv_iff
 
@@ -389,7 +389,7 @@ theorem integral_sub {f g : ℂ → E} {c : ℂ} {R : ℝ} (hf : CircleIntegrabl
 #align circle_integral.integral_sub circleIntegral.integral_sub
 
 theorem norm_integral_le_of_norm_le_const' {f : ℂ → E} {c : ℂ} {R C : ℝ}
-    (hf : ∀ z ∈ sphere c (|R|), ‖f z‖ ≤ C) : ‖∮ z in C(c, R), f z‖ ≤ 2 * π * |R| * C :=
+    (hf : ∀ z ∈ sphere c |R|, ‖f z‖ ≤ C) : ‖∮ z in C(c, R), f z‖ ≤ 2 * π * |R| * C :=
   calc
     ‖∮ z in C(c, R), f z‖ ≤ |R| * C * |2 * π - 0| :=
       intervalIntegral.norm_integral_le_of_norm_le_const fun θ _ =>
@@ -470,7 +470,7 @@ theorem integral_sub_center_inv (c : ℂ) {R : ℝ} (hR : R ≠ 0) :
 /-- If `f' : ℂ → E` is a derivative of a complex differentiable function on the circle
 `Metric.sphere c |R|`, then `∮ z in C(c, R), f' z = 0`. -/
 theorem integral_eq_zero_of_hasDerivWithinAt' {f f' : ℂ → E} {c : ℂ} {R : ℝ}
-    (h : ∀ z ∈ sphere c (|R|), HasDerivWithinAt f (f' z) (sphere c (|R|)) z) :
+    (h : ∀ z ∈ sphere c |R|, HasDerivWithinAt f (f' z) (sphere c |R|) z) :
     (∮ z in C(c, R), f' z) = 0 := by
   by_cases hi : CircleIntegrable f' c R
   · rw [← sub_eq_zero.2 ((periodic_circleMap c R).comp f).eq]
@@ -488,9 +488,9 @@ theorem integral_eq_zero_of_hasDerivWithinAt {f f' : ℂ → E} {c : ℂ} {R : 
 #align circle_integral.integral_eq_zero_of_has_deriv_within_at circleIntegral.integral_eq_zero_of_hasDerivWithinAt
 
 /-- If `n < 0` and `|w - c| = |R|`, then `(z - w) ^ n` is not circle integrable on the circle with
-center `c` and radius `(|R|)`, so the integral `∮ z in C(c, R), (z - w) ^ n` is equal to zero. -/
+center `c` and radius `|R|`, so the integral `∮ z in C(c, R), (z - w) ^ n` is equal to zero. -/
 theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0)
-    (hw : w ∈ sphere c (|R|)) : (∮ z in C(c, R), (z - w) ^ n) = 0 := by
+    (hw : w ∈ sphere c |R|) : (∮ z in C(c, R), (z - w) ^ n) = 0 := by
   rcases eq_or_ne R 0 with (rfl | h0)
   · apply integral_radius_zero
   · apply integral_undef
@@ -501,7 +501,7 @@ theorem integral_sub_zpow_of_undef {n : ℤ} {c w : ℂ} {R : ℝ} (hn : n < 0)
 zero. -/
 theorem integral_sub_zpow_of_ne {n : ℤ} (hn : n ≠ -1) (c w : ℂ) (R : ℝ) :
     (∮ z in C(c, R), (z - w) ^ n) = 0 := by
-  rcases em (w ∈ sphere c (|R|) ∧ n < -1) with (⟨hw, hn⟩ | H)
+  rcases em (w ∈ sphere c |R| ∧ n < -1) with (⟨hw, hn⟩ | H)
   · exact integral_sub_zpow_of_undef (hn.trans (by decide)) hw
   push_neg at H
   have hd : ∀ z, z ≠ w ∨ -1 ≤ n →
@@ -540,7 +540,7 @@ theorem cauchyPowerSeries_apply (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) (w
 
 theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ) :
     ‖cauchyPowerSeries f c R n‖ ≤
-      ((2 * π)⁻¹ * ∫ θ : ℝ in (0)..2 * π, ‖f (circleMap c R θ)‖) * (|R|)⁻¹ ^ n :=
+      ((2 * π)⁻¹ * ∫ θ : ℝ in (0)..2 * π, ‖f (circleMap c R θ)‖) * |R|⁻¹ ^ n :=
   calc
     ‖cauchyPowerSeries f c R n‖ = (2 * π)⁻¹ * ‖∮ z in C(c, R), (z - c)⁻¹ ^ n • (z - c)⁻¹ • f z‖ :=
       by simp [cauchyPowerSeries, norm_smul, Real.pi_pos.le]
@@ -550,14 +550,14 @@ theorem norm_cauchyPowerSeries_le (f : ℂ → E) (c : ℂ) (R : ℝ) (n : ℕ)
         (intervalIntegral.norm_integral_le_integral_norm Real.two_pi_pos.le)
         (by simp [Real.pi_pos.le]))
     _ = (2 * π)⁻¹ *
-        ((|R|)⁻¹ ^ n * (|R| * ((|R|)⁻¹ * ∫ x : ℝ in (0)..2 * π, ‖f (circleMap c R x)‖))) := by
-      simp [norm_smul, mul_left_comm (|R|)]
-    _ ≤ ((2 * π)⁻¹ * ∫ θ : ℝ in (0)..2 * π, ‖f (circleMap c R θ)‖) * (|R|)⁻¹ ^ n := by
+        (|R|⁻¹ ^ n * (|R| * (|R|⁻¹ * ∫ x : ℝ in (0)..2 * π, ‖f (circleMap c R x)‖))) := by
+      simp [norm_smul, mul_left_comm |R|]
+    _ ≤ ((2 * π)⁻¹ * ∫ θ : ℝ in (0)..2 * π, ‖f (circleMap c R θ)‖) * |R|⁻¹ ^ n := by
       rcases eq_or_ne R 0 with (rfl | hR)
       · cases n <;> simp [-mul_inv_rev]
         rw [← mul_assoc, inv_mul_cancel (Real.two_pi_pos.ne.symm), one_mul]
         apply norm_nonneg
-      · rw [mul_inv_cancel_left₀, mul_assoc, mul_comm ((|R|)⁻¹ ^ n)]
+      · rw [mul_inv_cancel_left₀, mul_assoc, mul_comm (|R|⁻¹ ^ n)]
         rwa [Ne.def, _root_.abs_eq_zero]
 #align norm_cauchy_power_series_le norm_cauchyPowerSeries_le
 

Co-authored-by: Scott Morrison <scott.morrison@anu.edu.au> Co-authored-by: Parcly Taxel <reddeloostw@gmail.com>

@@ -347,7 +347,7 @@ def circleIntegral (f : ℂ → E) (c : ℂ) (R : ℝ) : E :=
   ∫ θ : ℝ in (0)..2 * π, deriv (circleMap c R) θ • f (circleMap c R θ)
 #align circle_integral circleIntegral
 
-notation3"∮ "(...)" in ""C("c", "R")"", "r:(scoped f => circleIntegral f c R) => r
+notation3 "∮ "(...)" in ""C("c", "R")"", "r:(scoped f => circleIntegral f c R) => r
 
 theorem circleIntegral_def_Icc (f : ℂ → E) (c : ℂ) (R : ℝ) :
     (∮ z in C(c, R), f z) = ∫ θ in Icc 0 (2 * π),

Co-authored-by: Parcly Taxel <reddeloostw@gmail.com> Co-authored-by: Yury G. Kudryashov <urkud@urkud.name>